Subgroups — D₅₃×#3488 #28292395

Order 13568.

12366 conjugacy classes of subgroups.

The subgroup lattice has 1706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288385	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288384	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288383	C₂	1	2	yes	maximal, complemented
6	#20288382	C₂	1	3	yes	maximal, complemented
7	#20288381	C₂	1	2	yes	maximal, complemented
8	#20288380	C₂	1	3	yes	maximal, complemented
9	#20288379	C₂	1	3	yes	maximal, complemented
10	#20288378	C₂	1	6	yes	maximal, complemented
11	#20288377	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288376	C₂	1	3	yes	maximal, complemented
13	#20288375	C₂	1	6	yes	maximal, complemented
14	#550×D₅₃	C₂	1	2	yes	maximal, complemented
15	#548×D₅₃	C₂	1	2	yes	maximal, complemented
16	#546×D₅₃	C₂	1	6	yes	maximal, complemented
17	D₄²×D₅₃	C₂	1	6	yes	maximal, complemented
18	#537×D₅₃	C₂	1	3	yes	maximal, complemented
19	#535×D₅₃	C₂	1	3	yes	maximal, complemented
20	#525×D₅₃	C₂	1	3	yes	maximal, complemented
21	C₂×#121×D₅₃	C₂	1	3	yes	maximal, complemented
22	#520×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3488	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13133263	C₂²	1	3	yes	complemented
26	C₂×#13133263	C₂²	1	2	yes	complemented
27	C₂×#13133262	C₂²	1	6	yes	complemented
28	C₂×#13133262	C₂²	1	3	yes	complemented
29	H(5,𝔽₂)×D₅₃	—	2	16	no	—
30	C₂²×#11719949	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#11719945	C₂²	1	3	yes	complemented
32	C₂²×#11719947	C₂²	1	3	yes	complemented
33	C₂×#41×D₅₃	—	2	16	no	—
34	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
35	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
37	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
38	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
39	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
40	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
42	C₂×#41×D₅₃	C₂²	1	3	yes	complemented
43	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
46	C₂²×D₄×D₅₃	C₂²	1	3	yes	complemented
47	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
48	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
49	C₂³×C₄×D₅₃	C₂²	1	3	yes	complemented
50	#16811295	C₂²	1	2	yes	complemented
51	#16811294	C₂²	1	6	yes	complemented
52	#16811293	C₂²	1	6	yes	complemented
53	#16811292	C₂²	1	2	yes	complemented
54	#16811292	C₂²	1	2	yes	complemented
55	#16811291	C₂²	1	6	yes	complemented
56	#16811291	C₂²	1	6	yes	complemented
57	#16811285	C₂²	1	2	yes	complemented
58	#16811284	C₂²	1	2	yes	complemented
59	#16811283	C₂²	1	6	yes	complemented
60	#16811282	C₂²	1	6	yes	complemented
61	#16811281	C₂²	1	6	yes	complemented
62	#16811280	C₂²	1	2	yes	complemented
63	#16811279	C₂²	1	6	yes	complemented
64	#16811270	C₂²	1	6	yes	complemented
65	#16811269	C₂²	1	6	yes	complemented
66	#16811268	C₂²	1	6	yes	complemented
67	#16811267	C₂²	1	6	yes	complemented
68	#16811266	C₂²	1	6	yes	complemented
69	#16811265	C₂²	1	12	yes	complemented
70	#16811264	C₂²	1	6	yes	complemented
71	#16811263	C₂²	1	12	yes	complemented
72	#16811262	C₂²	1	12	yes	complemented
73	#16811261	C₂²	1	6	yes	complemented
74	#16811260	C₂²	1	12	yes	complemented
75	D₄×D₂₁₂	C₂²	1	6	yes	complemented
76	D₄×D₂₁₂	C₂²	1	6	yes	complemented
77	#16811258	C₂²	1	6	yes	complemented
78	#16811257	C₂²	1	12	yes	complemented
79	#16811257	C₂²	1	6	yes	complemented
80	#16811257	C₂²	1	6	yes	complemented
81	D₄×C₂²⋊D₅₃	C₂²	1	12	yes	complemented
82	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
83	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
84	#16811255	C₂²	1	12	yes	complemented
85	#16811255	C₂²	1	12	yes	complemented
86	#16811204	C₂²	1	3	yes	complemented
87	#16811203	C₂²	1	6	yes	complemented
88	#16811203	C₂²	1	6	yes	complemented
89	#16811202	C₂²	1	6	yes	complemented
90	#16811202	C₂²	1	6	yes	complemented
91	#16811201	C₂²	1	3	yes	complemented
92	#16811201	C₂²	1	3	yes	complemented
93	#16811200	C₂²	1	12	yes	complemented
94	#16811192	C₂²	1	3	yes	complemented
95	#16811191	C₂²	1	6	yes	complemented
96	#16811190	C₂²	1	3	yes	complemented
97	#16811189	C₂²	1	6	yes	complemented
98	#16811189	C₂²	1	6	yes	complemented
99	#16811188	C₂²	1	12	yes	complemented
100	#16811187	C₂²	1	3	yes	complemented
101	#16811186	C₂²	1	6	yes	complemented
102	#127×D₅₃	C₂²	1	6	yes	complemented
103	#124×D₅₃	C₂²	1	6	yes	complemented
104	#16811136	C₂²	1	3	yes	complemented
105	#16811136	C₂²	1	3	yes	complemented
106	#16811135	C₂²	1	3	yes	complemented
107	#16811134	C₂²	1	3	yes	complemented
108	#16811133	C₂²	1	3	yes	complemented
109	#16811133	C₂²	1	3	yes	complemented
110	#16811132	C₂²	1	6	yes	complemented
111	#16811132	C₂²	1	6	yes	complemented
112	#16811131	C₂²	1	6	yes	complemented
113	#16811130	C₂²	1	3	yes	complemented
114	#16811129	C₂²	1	6	yes	complemented
115	#123×D₅₃	C₂²	1	6	yes	complemented
116	C₂²⋊Q₈×D₅₃	C₂²	1	3	yes	complemented
117	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
118	C₂²⋊Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#13133192	C₂²	1	3	yes	complemented
120	C₂×#13133191	C₂²	1	3	yes	complemented
121	C₂×#13133190	C₂²	1	6	yes	complemented
122	C₂×#13133189	C₂²	1	6	yes	complemented
123	C₂×#13133188	C₂²	1	3	yes	complemented
124	#121×D₅₃	C₂²	1	3	yes	complemented
125	#121×D₅₃	C₂²	1	6	yes	complemented
126	#121×D₅₃	C₂²	1	12	yes	complemented
127	#121×D₅₃	C₂²	1	6	yes	complemented
128	#121×D₅₃	C₂²	1	6	yes	complemented
129	#121×D₅₃	C₂²	1	6	yes	complemented
130	#121×D₅₃	C₂²	1	3	yes	complemented
131	#121×D₅₃	C₂²	1	6	yes	complemented
132	#121×D₅₃	C₂²	1	6	yes	complemented
133	#121×D₅₃	C₂²	1	6	yes	complemented
134	#121×D₅₃	C₂²	1	6	yes	complemented
135	#120×D₅₃	C₂²	1	12	yes	complemented
136	#120×D₅₃	C₂²	1	6	yes	complemented
137	#16811106	C₂²	1	1	yes	characteristic, complemented
138	#16811105	C₂²	1	2	yes	complemented
139	#16811104	C₂²	1	3	yes	complemented
140	#16811103	C₂²	1	3	yes	complemented
141	#16811102	C₂²	1	6	yes	complemented
142	C₄×Q₈×D₅₃	C₂²	1	2	yes	complemented
143	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
144	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
145	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
146	#117×D₅₃	C₂²	1	3	yes	complemented
147	C₂×C₄⋊C₄×D₅₃	C₂²	1	3	yes	complemented
148	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	complemented
149	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#550	C₂²	1	2	yes	complemented
152	C₅₃×#548	C₂²	1	2	yes	complemented
153	C₅₃×#546	C₂²	1	6	yes	complemented
154	D₄²×C₅₃	C₂²	1	6	yes	complemented
155	C₅₃×#537	C₂²	1	3	yes	complemented
156	C₅₃×#535	C₂²	1	3	yes	complemented
157	C₅₃×#525	C₂²	1	3	yes	complemented
158	C₂×#121×C₅₃	C₂²	1	3	yes	complemented
159	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
160	C₂⁴×D₅₃	C₂³	1	3	yes	—
161	C₂⁴×D₅₃	C₂³	1	6	yes	—
162	#13133263	—	2	8	no	—
163	#13133263	—	2	16	no	—
164	#13133263	—	2	24	no	—
165	#13133262	—	2	48	no	—
166	#13133262	—	2	24	no	—
167	C₂×#11719949	—	2	8	no	—
168	C₂×#11719949	C₂³	1	1	yes	characteristic
169	C₂×#11719949	C₂³	1	3	yes	complemented
170	C₂×#11719949	C₂³	1	2	yes	complemented
171	C₂×#11719949	C₂³	1	1	yes	characteristic, complemented
172	C₂×#11719949	C₂³	1	3	yes	complemented
173	C₂×#11719949	C₂³	1	3	yes	complemented
174	C₂×#11719945	—	2	24	no	—
175	C₂×#11719945	C₂³	1	3	yes	—
176	C₂×#11719945	C₂³	1	6	yes	complemented
177	C₂×#11719945	C₂³	1	3	yes	complemented
178	C₂×#11719945	C₂³	1	6	yes	complemented
179	C₂×#11719945	C₂³	1	3	yes	complemented
180	C₂×#11719945	C₂³	1	6	yes	complemented
181	C₂×#11719945	C₂³	1	3	yes	complemented
182	C₂×#11719945	C₂³	1	6	yes	complemented
183	C₂×#11719945	C₂³	1	3	yes	complemented
184	C₂×#11719947	—	2	24	no	—
185	C₂×#11719947	C₂³	1	3	yes	—
186	C₂×#11719947	C₂³	1	3	yes	complemented
187	C₂×#11719947	C₂³	1	6	yes	complemented
188	C₂×#11719947	C₂³	1	3	yes	complemented
189	C₂×#11719947	C₂³	1	6	yes	complemented
190	C₂×#11719947	C₂³	1	3	yes	complemented
191	C₂×#11719947	C₂³	1	3	yes	complemented
192	C₂×#11719947	C₂³	1	6	yes	complemented
193	C₂×#11719947	C₂³	1	6	yes	complemented
194	#41×D₅₃	—	2	8	no	—
195	#41×D₅₃	—	2	8	no	—
196	#41×D₅₃	—	2	8	no	—
197	#41×D₅₃	—	2	16	no	—
198	#41×D₅₃	—	2	24	no	—
199	#41×D₅₃	—	2	24	no	—
200	#41×D₅₃	—	2	24	no	—
201	#41×D₅₃	—	2	24	no	—
202	#41×D₅₃	—	2	24	no	—
203	#41×D₅₃	D₄	1	16	yes	complemented
204	C₂²×Dic₁₀₆	C₂³	1	3	yes	complemented
205	C₂×Q₈×D₅₃	—	2	8	no	—
206	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
207	C₂×Q₈×D₅₃	C₂³	1	3	yes	—
208	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
209	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic, complemented
210	C₂×Q₈×D₅₃	C₂³	1	3	yes	complemented
211	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
212	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
213	C₂²×D₂₁₂	C₂³	1	3	yes	complemented
214	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
215	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
216	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
217	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
218	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
219	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
220	C₂×D₄×D₅₃	—	2	24	no	—
221	C₂×D₄×D₅₃	—	2	48	no	—
222	C₂×D₄×D₅₃	—	2	24	no	—
223	C₂×D₄×D₅₃	—	4	24	no	—
224	C₂×D₄×D₅₃	C₂³	1	6	yes	—
225	C₂×D₄×D₅₃	C₂³	1	6	yes	—
226	C₂×D₄×D₅₃	C₂³	1	6	yes	—
227	C₂×D₄×D₅₃	C₂³	1	3	yes	—
228	C₂×D₄×D₅₃	C₂³	1	6	yes	—
229	C₂×D₄×D₅₃	C₂³	1	3	yes	—
230	C₂×D₄×D₅₃	C₂³	1	6	yes	—
231	C₂×D₄×D₅₃	C₂³	1	12	yes	—
232	C₂×D₄×D₅₃	C₂³	1	3	yes	—
233	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
234	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
235	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
236	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
237	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
238	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
239	C₂×D₄×D₅₃	C₂³	1	3	yes	complemented
240	C₂×D₄×D₅₃	C₂³	1	3	yes	complemented
241	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
242	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
243	C₂³×Dic₅₃	C₂³	1	3	yes	complemented
244	C₂²×C₄×D₅₃	—	2	24	no	—
245	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
246	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
247	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
248	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
249	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
251	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
252	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
253	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
254	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
255	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
256	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
257	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
258	C₂²×C₄×D₅₃	C₂³	1	3	yes	complemented
259	#13133214	C₂³	1	6	yes	complemented
260	#13133213	C₂³	1	12	yes	complemented
261	#13133213	C₂³	1	6	yes	complemented
262	#13133213	C₂³	1	6	yes	complemented
263	#13133213	C₂³	1	12	yes	complemented
264	#13133206	C₂³	1	6	yes	complemented
265	#13133205	C₂³	1	6	yes	complemented
266	#13133204	C₂³	1	6	yes	complemented
267	#13133203	C₂³	1	12	yes	complemented
268	#13133203	C₂³	1	12	yes	complemented
269	#13133202	C₂³	1	6	yes	complemented
270	#13133202	C₂³	1	6	yes	complemented
271	#13133201	C₂³	1	6	yes	complemented
272	#13133200	C₂³	1	6	yes	complemented
273	#13133199	C₂³	1	6	yes	complemented
274	#13133199	C₂³	1	6	yes	complemented
275	#13133198	C₂³	1	6	yes	complemented
276	#13133197	C₂³	1	6	yes	complemented
277	#13133197	C₂³	1	1	yes	characteristic, complemented
278	#13133197	C₂³	1	3	yes	complemented
279	#13133196	C₂³	1	6	yes	complemented
280	#13133196	C₂³	1	1	yes	characteristic, complemented
281	#13133196	C₂³	1	3	yes	complemented
282	#13133195	C₂³	1	12	yes	complemented
283	#13133195	C₂³	1	2	yes	complemented
284	#13133195	C₂³	1	6	yes	complemented
285	#13133194	C₂³	1	12	yes	complemented
286	#13133194	C₂³	1	2	yes	complemented
287	#13133194	C₂³	1	6	yes	complemented
288	#13133193	C₂³	1	6	yes	complemented
289	#13133193	C₂³	1	1	yes	characteristic, complemented
290	#13133193	C₂³	1	3	yes	complemented
291	#13133192	C₂³	1	12	yes	complemented
292	#13133192	C₂³	1	6	yes	complemented
293	#13133192	C₂³	1	6	yes	complemented
294	#13133192	C₂³	1	6	yes	complemented
295	#13133192	C₂³	1	3	yes	complemented
296	#13133192	C₂³	1	6	yes	complemented
297	#13133192	C₂³	1	3	yes	complemented
298	#13133191	C₂³	1	12	yes	complemented
299	#13133191	C₂³	1	6	yes	complemented
300	#13133191	C₂³	1	6	yes	complemented
301	#13133191	C₂³	1	6	yes	complemented
302	#13133191	C₂³	1	3	yes	complemented
303	#13133191	C₂³	1	6	yes	complemented
304	#13133191	C₂³	1	3	yes	complemented
305	#13133190	C₂³	1	12	yes	complemented
306	#13133190	C₂³	1	12	yes	complemented
307	#13133190	C₂³	1	12	yes	complemented
308	#13133190	C₂³	1	12	yes	complemented
309	#13133190	C₂³	1	12	yes	complemented
310	#13133190	C₂³	1	6	yes	complemented
311	#13133190	C₂³	1	12	yes	complemented
312	#13133190	C₂³	1	6	yes	complemented
313	#13133189	C₂³	1	12	yes	complemented
314	#13133189	C₂³	1	12	yes	complemented
315	#13133189	C₂³	1	12	yes	complemented
316	#13133189	C₂³	1	12	yes	complemented
317	#13133189	C₂³	1	6	yes	complemented
318	#13133189	C₂³	1	12	yes	complemented
319	#13133189	C₂³	1	6	yes	complemented
320	#13133189	C₂³	1	12	yes	complemented
321	#13133188	C₂³	1	6	yes	complemented
322	#13133188	C₂³	1	12	yes	complemented
323	#13133188	C₂³	1	6	yes	complemented
324	#13133188	C₂³	1	6	yes	complemented
325	#13133188	C₂³	1	3	yes	complemented
326	#13133188	C₂³	1	6	yes	complemented
327	#13133188	C₂³	1	3	yes	complemented
328	#13133187	C₂³	1	12	yes	complemented
329	#13133187	C₂³	1	12	yes	complemented
330	#13133187	C₂³	1	12	yes	complemented
331	#13133187	C₂³	1	6	yes	complemented
332	#13133187	C₂³	1	6	yes	complemented
333	#13133187	C₂³	1	6	yes	complemented
334	#13133186	C₂³	1	12	yes	complemented
335	#13133186	C₂³	1	6	yes	complemented
336	#13133185	C₂³	1	12	yes	complemented
337	#13133185	C₂³	1	12	yes	complemented
338	#13133185	C₂³	1	6	yes	complemented
339	#13133185	C₂³	1	6	yes	complemented
340	#13133185	C₂³	1	6	yes	complemented
341	#13133185	C₂³	1	12	yes	complemented
342	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
343	C₄×Dic₁₀₆	C₂³	1	6	yes	complemented
344	#13133182	C₂³	1	6	yes	complemented
345	C₄×D₂₁₂	C₂³	1	6	yes	complemented
346	C₄×D₂₁₂	C₂³	1	6	yes	complemented
347	C₄×D₂₁₂	C₂³	1	6	yes	complemented
348	D₄×Dic₅₃	C₂³	1	6	yes	complemented
349	D₄×Dic₅₃	C₂³	1	6	yes	complemented
350	D₄×Dic₅₃	C₂³	1	6	yes	complemented
351	#13133179	C₂³	1	6	yes	complemented
352	#13133179	C₂³	1	6	yes	complemented
353	#13133179	C₂³	1	6	yes	complemented
354	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
355	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
356	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
357	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
358	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
359	#13133177	C₂³	1	12	yes	complemented
360	#13133177	C₂³	1	6	yes	complemented
361	#13133177	C₂³	1	6	yes	complemented
362	#13133177	C₂³	1	6	yes	complemented
363	#13133177	C₂³	1	6	yes	complemented
364	#13133176	C₂³	1	3	yes	complemented
365	#13133175	C₂³	1	3	yes	complemented
366	#13133175	C₂³	1	3	yes	complemented
367	#13133174	C₂³	1	6	yes	complemented
368	#13133173	C₂³	1	6	yes	complemented
369	C₂×C₄⋊Dic₅₃	C₂³	1	3	yes	complemented
370	C₂×#11719919	C₂³	1	6	yes	complemented
371	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
372	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
373	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
374	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
375	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
376	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
377	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
378	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	complemented
379	C₂×#11719921	C₂³	1	6	yes	complemented
380	C₂×#11719921	C₂³	1	6	yes	complemented
381	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
382	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
383	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
384	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
385	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
386	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
387	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	complemented
388	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	complemented
389	C₄²×D₅₃	C₂³	1	6	yes	—
390	H(5,𝔽₂)×C₅₃	—	2	8	no	—
391	C₂×#41×C₅₃	—	2	8	no	—
392	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
393	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
394	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic, complemented
395	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
396	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
397	C₂×#41×C₅₃	C₂³	1	3	yes	complemented
398	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
399	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
400	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
401	C₂²×D₄×C₅₃	C₂³	1	3	yes	complemented
402	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
403	C₂³×C₄×C₅₃	C₂³	1	3	yes	complemented
404	#127×C₅₃	C₂³	1	6	yes	complemented
405	#124×C₅₃	C₂³	1	6	yes	complemented
406	#123×C₅₃	C₂³	1	6	yes	complemented
407	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
408	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
409	C₂²⋊Q₈×C₅₃	C₂³	1	3	yes	complemented
410	#121×C₅₃	C₂³	1	6	yes	complemented
411	#121×C₅₃	C₂³	1	6	yes	complemented
412	#121×C₅₃	C₂³	1	6	yes	complemented
413	#121×C₅₃	C₂³	1	3	yes	complemented
414	#121×C₅₃	C₂³	1	6	yes	complemented
415	#121×C₅₃	C₂³	1	3	yes	complemented
416	#121×C₅₃	C₂³	1	12	yes	complemented
417	#120×C₅₃	C₂³	1	6	yes	complemented
418	#120×C₅₃	C₂³	1	12	yes	complemented
419	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
420	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
421	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
422	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
423	#117×C₅₃	C₂³	1	3	yes	complemented
424	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	complemented
425	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	complemented
426	C₂⁴×C₅₃	C₂⁴	1	3	yes	—
427	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
428	C₂³×D₅₃	—	2	12	no	—
429	C₂³×D₅₃	—	2	12	no	—
430	C₂³×D₅₃	—	2	24	no	—
431	C₂³×D₅₃	—	4	6	no	—
432	C₂³×D₅₃	—	4	12	no	—
433	C₂³×D₅₃	—	4	12	no	—
434	C₂³×D₅₃	C₂⁴	1	6	yes	—
435	C₂³×D₅₃	C₂⁴	1	3	yes	—
436	C₂³×D₅₃	C₂⁴	1	3	yes	—
437	C₂³×D₅₃	C₂⁴	1	3	yes	—
438	C₂³×D₅₃	C₂⁴	1	3	yes	—
439	C₂³×D₅₃	C₂⁴	1	3	yes	—
440	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
441	C₂³×D₅₃	C₂⁴	1	12	yes	—
442	C₂³×D₅₃	C₂⁴	1	6	yes	—
443	#41×C₅₃	—	2	4	no	—
444	#41×C₅₃	—	2	8	no	—
445	#41×C₅₃	—	2	12	no	—
446	#41×C₅₃	—	2	12	no	—
447	#41×C₅₃	—	2	12	no	—
448	#41×C₅₃	C₂×D₄	1	8	yes	complemented
449	C₂×Q₈×C₅₃	—	2	4	no	—
450	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂×Q₈×C₅₃	C₂⁴	1	3	yes	—
452	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂×D₄×C₅₃	—	2	12	no	—
454	C₂×D₄×C₅₃	—	2	24	no	—
455	C₂×D₄×C₅₃	—	2	12	no	—
456	C₂×D₄×C₅₃	—	4	12	no	—
457	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
458	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
459	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
460	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
461	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
462	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
463	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
464	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
465	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
466	C₂²×C₄×C₅₃	—	2	12	no	—
467	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
468	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
469	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
470	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
471	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
473	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
474	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
475	C₂×C₂²⋊D₅₃	—	2	24	no	—
476	C₂×C₂²⋊D₅₃	—	2	48	no	—
477	C₂×C₂²⋊D₅₃	—	2	24	no	—
478	C₂×C₂²⋊D₅₃	—	4	12	no	—
479	C₂×C₂²⋊D₅₃	—	4	12	no	—
480	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
481	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
482	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
483	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
484	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
485	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
486	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
487	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
488	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
489	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
490	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
491	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
492	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
493	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
494	C₂²×Dic₅₃	—	2	12	no	—
495	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
496	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
497	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
498	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
499	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
500	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
501	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
502	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
503	#11719949	—	2	4	no	—
504	#11719949	—	2	8	no	—
505	#11719949	—	2	12	no	—
506	#11719949	—	2	12	no	—
507	#11719949	—	2	12	no	—
508	#11719949	C₂×D₄	1	8	yes	complemented
509	Q₈×D₅₃	—	2	4	no	—
510	Q₈×D₅₃	—	2	12	no	—
511	Q₈×D₅₃	—	2	4	no	—
512	Q₈×D₅₃	—	2	12	no	—
513	Q₈×D₅₃	C₂×D₄	1	8	yes	complemented
514	#11719947	—	2	12	no	—
515	#11719947	—	2	24	no	—
516	#11719947	—	2	24	no	—
517	#11719947	—	2	24	no	—
518	#11719947	—	2	12	no	—
519	#11719947	—	2	12	no	—
520	#11719947	—	2	12	no	—
521	#11719947	—	2	24	no	—
522	#11719947	C₂×D₄	1	24	yes	complemented
523	D₄×D₅₃	—	2	24	no	—
524	D₄×D₅₃	—	2	24	no	—
525	D₄×D₅₃	—	2	24	no	—
526	D₄×D₅₃	—	2	12	no	—
527	D₄×D₅₃	—	2	24	no	—
528	D₄×D₅₃	—	2	24	no	—
529	D₄×D₅₃	—	2	48	no	—
530	D₄×D₅₃	—	2	12	no	—
531	D₄×D₅₃	—	2	24	no	—
532	D₄×D₅₃	—	2	12	no	—
533	D₄×D₅₃	—	2	24	no	—
534	D₄×D₅₃	—	2	12	no	—
535	D₄×D₅₃	—	2	24	no	—
536	D₄×D₅₃	—	2	24	no	—
537	D₄×D₅₃	—	4	24	no	—
538	D₄×D₅₃	—	4	12	no	—
539	D₄×D₅₃	—	4	24	no	—
540	D₄×D₅₃	—	4	24	no	—
541	D₄×D₅₃	C₂×D₄	1	24	yes	complemented
542	#11719945	—	2	12	no	—
543	#11719945	—	2	12	no	—
544	#11719945	—	2	24	no	—
545	#11719945	—	2	12	no	—
546	#11719945	—	2	24	no	—
547	#11719945	—	2	24	no	—
548	#11719945	—	2	12	no	—
549	#11719945	—	2	24	no	—
550	#11719945	C₂×D₄	1	24	yes	complemented
551	C₂×D₂₁₂	—	2	12	no	—
552	C₂×D₂₁₂	—	2	12	no	—
553	C₂×D₂₁₂	—	2	24	no	—
554	C₂×D₂₁₂	—	4	12	no	—
555	C₂×D₂₁₂	C₂⁴	1	6	yes	—
556	C₂×D₂₁₂	C₂⁴	1	6	yes	—
557	C₂×D₂₁₂	C₂⁴	1	6	yes	—
558	C₂×D₂₁₂	C₂⁴	1	3	yes	—
559	C₂×D₂₁₂	C₂⁴	1	6	yes	—
560	C₂×D₂₁₂	C₂⁴	1	3	yes	—
561	C₂×D₂₁₂	C₂⁴	1	6	yes	—
562	C₂×D₂₁₂	C₂⁴	1	12	yes	—
563	C₂×D₂₁₂	C₂⁴	1	3	yes	—
564	C₂×C₄×D₅₃	—	2	12	no	—
565	C₂×C₄×D₅₃	—	2	12	no	—
566	C₂×C₄×D₅₃	—	2	12	no	—
567	C₂×C₄×D₅₃	—	2	4	no	—
568	C₂×C₄×D₅₃	—	2	12	no	—
569	C₂×C₄×D₅₃	—	2	12	no	—
570	C₂×C₄×D₅₃	—	2	12	no	—
571	C₂×C₄×D₅₃	—	2	24	no	—
572	C₂×C₄×D₅₃	—	2	12	no	—
573	C₂×C₄×D₅₃	—	2	12	no	—
574	C₂×C₄×D₅₃	—	2	12	no	—
575	C₂×C₄×D₅₃	—	2	12	no	—
576	C₂×C₄×D₅₃	—	4	12	no	—
577	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	complemented
578	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
579	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
580	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
581	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
582	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
583	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
584	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
585	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
586	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
587	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
588	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
589	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
590	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
591	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
592	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
593	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
594	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
595	C₂×C₄×D₅₃	C₂⁴	1	12	yes	—
596	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
597	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
598	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
599	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
600	C₂×Dic₁₀₆	—	2	12	no	—
601	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
602	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
603	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
604	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
605	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
606	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
607	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
608	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
610	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
611	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
612	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
613	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
614	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
615	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
616	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
617	C₄²×C₅₃	C₂⁴	1	6	yes	—
618	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
619	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
620	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
621	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
622	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
623	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
624	#11719921	C₂⁴	1	6	yes	—
625	#11719921	C₂⁴	1	6	yes	—
626	#11719921	C₂⁴	1	12	yes	—
627	#11719921	C₂⁴	1	12	yes	—
628	#11719921	C₂⁴	1	6	yes	—
629	#11719921	C₂⁴	1	6	yes	—
630	#11719921	C₂⁴	1	2	yes	—
631	#11719921	C₂⁴	1	6	yes	—
632	#11719921	C₂⁴	1	6	yes	—
633	#11719921	C₂⁴	1	2	yes	—
634	#11719921	C₂⁴	1	6	yes	—
635	#11719921	C₂⁴	1	6	yes	—
636	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
637	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
638	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
639	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
640	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
641	#11719919	C₂⁴	1	6	yes	—
642	#11719919	C₂⁴	1	12	yes	—
643	#11719919	C₂⁴	1	2	yes	—
644	#11719919	C₂⁴	1	2	yes	—
645	#11719919	C₂⁴	1	2	yes	—
646	#11719919	C₂⁴	1	6	yes	—
647	#11719919	C₂⁴	1	6	yes	—
648	C₄×Dic₅₃	C₂⁴	1	6	yes	—
649	C₄×Dic₅₃	C₂⁴	1	6	yes	—
650	C₄×Dic₅₃	C₂⁴	1	6	yes	—
651	C₂³×C₅₃	—	2	6	no	—
652	C₂³×C₅₃	—	2	6	no	—
653	C₂³×C₅₃	—	2	12	no	—
654	C₂³×C₅₃	—	4	3	no	—
655	C₂³×C₅₃	—	4	6	no	—
656	C₂³×C₅₃	—	4	6	no	—
657	C₂³×C₅₃	C₂⁵	1	3	yes	—
658	C₂³×C₅₃	C₂⁵	1	6	yes	—
659	C₂³×C₅₃	C₂⁵	1	3	yes	—
660	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
661	C₂²×D₅₃	—	2	2	no	—
662	C₂²×D₅₃	—	2	6	no	—
663	C₂²×D₅₃	—	2	2	no	—
664	C₂²×D₅₃	—	2	6	no	—
665	C₂²×D₅₃	—	2	6	no	—
666	C₂²×D₅₃	—	2	6	no	—
667	C₂²×D₅₃	—	2	12	no	—
668	C₂²×D₅₃	—	2	6	no	—
669	C₂²×D₅₃	—	2	6	no	—
670	C₂²×D₅₃	—	2	6	no	—
671	C₂²×D₅₃	—	2	12	no	—
672	C₂²×D₅₃	—	2	12	no	—
673	C₂²×D₅₃	—	2	6	no	—
674	C₂²×D₅₃	—	2	6	no	—
675	C₂²×D₅₃	—	2	6	no	—
676	C₂²×D₅₃	—	2	6	no	—
677	C₂²×D₅₃	—	2	12	no	—
678	C₂²×D₅₃	—	2	24	no	—
679	C₂²×D₅₃	—	4	3	no	—
680	C₂²×D₅₃	—	4	3	no	—
681	C₂²×D₅₃	—	4	3	no	—
682	C₂²×D₅₃	—	4	48	no	—
683	C₂²×D₅₃	—	4	6	no	—
684	C₂²×D₅₃	—	4	12	no	—
685	C₂²×D₅₃	—	4	12	no	—
686	C₂²×D₅₃	—	4	6	no	—
687	C₂²×D₅₃	—	8	48	no	—
688	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
689	C₂²×D₅₃	H(5,𝔽₂)	1	4	yes	complemented
690	C₂²×D₅₃	C₂⁵	1	3	yes	—
691	C₂²×D₅₃	C₂⁵	1	6	yes	—
692	C₂²×D₅₃	C₂⁵	1	3	yes	—
693	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
694	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
695	Q₈×C₅₃	—	2	6	no	—
696	Q₈×C₅₃	—	2	2	no	—
697	Q₈×C₅₃	C₂²×D₄	1	4	yes	complemented
698	D₄×C₅₃	—	2	12	no	—
699	D₄×C₅₃	—	2	12	no	—
700	D₄×C₅₃	—	2	12	no	—
701	D₄×C₅₃	—	2	12	no	—
702	D₄×C₅₃	—	2	6	no	—
703	D₄×C₅₃	—	2	6	no	—
704	D₄×C₅₃	—	4	12	no	—
705	D₄×C₅₃	—	4	6	no	—
706	D₄×C₅₃	C₂²×D₄	1	12	yes	complemented
707	C₂×C₄×C₅₃	—	2	6	no	—
708	C₂×C₄×C₅₃	—	2	6	no	—
709	C₂×C₄×C₅₃	—	2	2	no	—
710	C₂×C₄×C₅₃	—	2	6	no	—
711	C₂×C₄×C₅₃	—	2	6	no	—
712	C₂×C₄×C₅₃	—	2	12	no	—
713	C₂×C₄×C₅₃	—	4	6	no	—
714	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	complemented
715	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
716	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
717	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
718	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
719	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
720	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
721	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
722	C₂²⋊D₅₃	—	2	12	no	—
723	C₂²⋊D₅₃	—	2	12	no	—
724	C₂²⋊D₅₃	—	2	12	no	—
725	C₂²⋊D₅₃	—	2	12	no	—
726	C₂²⋊D₅₃	—	2	12	no	—
727	C₂²⋊D₅₃	—	2	12	no	—
728	C₂²⋊D₅₃	—	2	12	no	—
729	C₂²⋊D₅₃	—	2	24	no	—
730	C₂²⋊D₅₃	—	2	12	no	—
731	C₂²⋊D₅₃	—	4	12	no	—
732	C₂²⋊D₅₃	—	4	12	no	—
733	C₂²⋊D₅₃	—	4	6	no	—
734	C₂²⋊D₅₃	—	4	6	no	—
735	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	complemented
736	C₂×Dic₅₃	—	2	6	no	—
737	C₂×Dic₅₃	—	2	6	no	—
738	C₂×Dic₅₃	—	2	2	no	—
739	C₂×Dic₅₃	—	2	6	no	—
740	C₂×Dic₅₃	—	2	6	no	—
741	C₂×Dic₅₃	—	2	12	no	—
742	C₂×Dic₅₃	—	4	6	no	—
743	C₂×Dic₅₃	C₂²×D₄	1	12	yes	complemented
744	C₂×Dic₅₃	C₂⁵	1	3	yes	—
745	C₂×Dic₅₃	C₂⁵	1	2	yes	—
746	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
747	C₂×Dic₅₃	C₂⁵	1	6	yes	—
748	C₂×Dic₅₃	C₂⁵	1	2	yes	—
749	C₂×Dic₅₃	C₂⁵	1	3	yes	—
750	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
751	D₂₁₂	—	2	12	no	—
752	D₂₁₂	—	2	12	no	—
753	D₂₁₂	—	2	12	no	—
754	D₂₁₂	—	2	12	no	—
755	D₂₁₂	—	2	6	no	—
756	D₂₁₂	—	2	6	no	—
757	D₂₁₂	—	4	12	no	—
758	D₂₁₂	—	4	6	no	—
759	D₂₁₂	C₂²×D₄	1	12	yes	complemented
760	C₄×D₅₃	—	2	2	no	—
761	C₄×D₅₃	—	2	6	no	—
762	C₄×D₅₃	—	2	4	no	—
763	C₄×D₅₃	—	2	6	no	—
764	C₄×D₅₃	—	2	6	no	—
765	C₄×D₅₃	—	2	12	no	—
766	C₄×D₅₃	—	2	4	no	—
767	C₄×D₅₃	—	2	2	no	—
768	C₄×D₅₃	—	2	6	no	—
769	C₄×D₅₃	—	2	6	no	—
770	C₄×D₅₃	—	2	6	no	—
771	C₄×D₅₃	—	2	12	no	—
772	C₄×D₅₃	—	2	2	no	—
773	C₄×D₅₃	—	2	6	no	—
774	C₄×D₅₃	—	2	6	no	—
775	C₄×D₅₃	—	2	6	no	—
776	C₄×D₅₃	—	2	12	no	—
777	C₄×D₅₃	—	4	12	no	—
778	C₄×D₅₃	C₂²×D₄	1	4	yes	—
779	C₄×D₅₃	C₂²×D₄	1	12	yes	—
780	C₄×D₅₃	C₂²×D₄	1	12	yes	complemented
781	C₄×D₅₃	C₂²×D₄	1	12	yes	complemented
782	Dic₁₀₆	—	2	6	no	—
783	Dic₁₀₆	—	2	2	no	—
784	Dic₁₀₆	—	2	12	no	—
785	Dic₁₀₆	—	2	4	no	—
786	Dic₁₀₆	C₂²×D₄	1	12	yes	complemented
787	C₂×#3488	—	53	1	no	maximal, Sylow
788	C₂²×C₅₃	—	2	1	no	—
789	C₂²×C₅₃	—	2	3	no	—
790	C₂²×C₅₃	—	2	1	no	—
791	C₂²×C₅₃	—	2	3	no	—
792	C₂²×C₅₃	—	2	3	no	—
793	C₂²×C₅₃	—	2	6	no	—
794	C₂²×C₅₃	—	2	6	no	—
795	C₂²×C₅₃	—	2	3	no	—
796	C₂²×C₅₃	—	2	3	no	—
797	C₂²×C₅₃	—	2	6	no	—
798	C₂²×C₅₃	—	4	12	no	—
799	C₂²×C₅₃	—	8	12	no	—
800	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
801	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	complemented
802	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
803	C₂×D₅₃	—	2	1	no	—
804	C₂×D₅₃	—	2	3	no	—
805	C₂×D₅₃	—	2	1	no	—
806	C₂×D₅₃	—	2	3	no	—
807	C₂×D₅₃	—	2	8	no	—
808	C₂×D₅₃	—	2	24	no	—
809	C₂×D₅₃	—	2	3	no	—
810	C₂×D₅₃	—	2	6	no	—
811	C₂×D₅₃	—	2	6	no	—
812	C₂×D₅₃	—	2	3	no	—
813	C₂×D₅₃	—	2	3	no	—
814	C₂×D₅₃	—	2	6	no	—
815	C₂×D₅₃	—	4	12	no	—
816	C₂×D₅₃	—	4	12	no	—
817	C₂×D₅₃	—	4	12	no	—
818	C₂×D₅₃	—	4	12	no	—
819	C₂×D₅₃	—	4	24	no	—
820	C₂×D₅₃	—	8	24	no	—
821	C₂×D₅₃	—	8	12	no	—
822	C₂×D₅₃	C₂³×D₄	1	6	yes	—
823	C₂×D₅₃	C₂³×D₄	1	2	yes	—
824	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
825	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	complemented
826	C₂×D₅₃	#585	1	2	yes	—
827	C₄×C₅₃	—	2	3	no	—
828	C₄×C₅₃	—	2	2	no	—
829	C₄×C₅₃	—	2	1	no	—
830	C₄×C₅₃	—	2	6	no	—
831	C₄×C₅₃	—	2	2	no	—
832	C₄×C₅₃	C₂³×D₄	1	6	yes	—
833	C₄×C₅₃	C₂³×D₄	1	2	yes	—
834	Dic₅₃	—	2	3	no	—
835	Dic₅₃	—	2	2	no	—
836	Dic₅₃	—	2	1	no	—
837	Dic₅₃	—	2	6	no	—
838	Dic₅₃	—	2	2	no	—
839	Dic₅₃	C₂³×D₄	1	6	yes	—
840	Dic₅₃	C₂³×D₄	1	2	yes	—
841	C₂²×H(5,𝔽₂)	—	53	1	no	—
842	C₂³×#41	—	53	1	no	—
843	#3488	—	53	1	no	—
844	#3488	—	53	1	no	—
845	#3488	—	53	2	no	—
846	#3488	—	53	2	no	—
847	#3488	—	53	6	no	—
848	#3488	—	53	6	no	—
849	#3488	—	53	3	no	—
850	#3488	—	53	3	no	—
851	#3488	—	53	3	no	—
852	#3488	—	53	3	no	—
853	#3488	—	53	1	no	—
854	#3488	D₅₃	1	1	yes	characteristic, direct product factor
855	C₂×#550	—	53	2	no	—
856	C₂×#548	—	53	2	no	—
857	C₂×#546	—	53	6	no	—
858	C₂×D₄²	—	53	6	no	—
859	C₂×#537	—	53	3	no	—
860	C₂×#535	—	53	3	no	—
861	C₂×#525	—	53	3	no	—
862	C₂²×#121	—	53	3	no	—
863	C₂×#520	—	53	1	no	—
864	C₂×C₅₃	—	2	2	no	—
865	C₂×C₅₃	—	2	6	no	—
866	C₂×C₅₃	—	4	3	no	—
867	C₂×C₅₃	—	4	6	no	—
868	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
869	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
870	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
871	D₅₃	—	2	2	no	—
872	D₅₃	—	2	6	no	—
873	D₅₃	—	4	3	no	—
874	D₅₃	—	4	6	no	—
875	D₅₃	#3488	1	4	yes	direct product factor
876	C₂×H(5,𝔽₂)	—	53	1	no	—
877	C₂×H(5,𝔽₂)	—	53	2	no	—
878	C₂×H(5,𝔽₂)	—	53	3	no	—
879	C₂×H(5,𝔽₂)	—	53	6	no	—
880	C₂×H(5,𝔽₂)	—	53	3	no	—
881	C₂×H(5,𝔽₂)	—	106	16	no	—
882	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
883	C₂²×#41	—	53	1	no	—
884	C₂²×#41	—	53	1	no	—
885	C₂²×#41	—	53	3	no	—
886	C₂²×#41	—	53	3	no	—
887	C₂²×#41	—	53	1	no	—
888	C₂²×#41	—	53	1	no	—
889	C₂²×#41	—	53	3	no	—
890	C₂²×#41	—	53	3	no	—
891	C₂²×#41	—	53	3	no	—
892	C₂²×#41	—	53	2	no	—
893	C₂²×#41	—	53	1	no	—
894	C₂²×#41	—	53	3	no	—
895	C₂²×#41	—	53	3	no	—
896	C₂²×#41	—	106	16	no	—
897	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
898	C₂³×Q₈	—	53	1	no	—
899	C₂³×D₄	—	53	3	no	—
900	C₂³×D₄	—	53	3	no	—
901	C₂³×D₄	—	53	6	no	—
902	C₂³×D₄	—	53	6	no	—
903	C₂⁴×C₄	—	53	3	no	—
904	#550	—	53	2	no	—
905	#550	—	53	2	no	—
906	#550	—	53	6	no	—
907	#550	—	53	6	no	—
908	#550	—	53	6	no	—
909	#550	—	53	2	no	—
910	#550	—	53	6	no	—
911	#550	C₂×D₅₃	1	2	yes	complemented
912	#548	—	53	2	no	—
913	#548	—	53	2	no	—
914	#548	—	53	6	no	—
915	#548	—	53	6	no	—
916	#548	—	53	6	no	—
917	#548	—	53	2	no	—
918	#548	—	53	6	no	—
919	#548	C₂×D₅₃	1	2	yes	complemented
920	#546	—	53	6	no	—
921	#546	—	53	6	no	—
922	#546	—	53	6	no	—
923	#546	—	53	12	no	—
924	#546	—	53	6	no	—
925	#546	—	53	6	no	—
926	#546	—	53	12	no	—
927	#546	—	53	12	no	—
928	#546	—	53	6	no	—
929	#546	—	53	6	no	—
930	#546	—	53	12	no	—
931	#546	C₂×D₅₃	1	6	yes	complemented
932	D₄²	—	53	6	no	—
933	D₄²	—	53	6	no	—
934	D₄²	—	53	12	no	—
935	D₄²	—	53	6	no	—
936	D₄²	—	53	12	no	—
937	D₄²	—	53	6	no	—
938	D₄²	—	53	6	no	—
939	D₄²	—	53	12	no	—
940	D₄²	—	53	12	no	—
941	D₄²	—	53	6	no	—
942	D₄²	—	53	6	no	—
943	D₄²	C₂×D₅₃	1	6	yes	complemented
944	#537	—	53	3	no	—
945	#537	—	53	3	no	—
946	#537	—	53	6	no	—
947	#537	—	53	6	no	—
948	#537	—	53	12	no	—
949	#537	—	53	6	no	—
950	#537	—	53	6	no	—
951	#537	—	53	3	no	—
952	#537	C₂×D₅₃	1	3	yes	complemented
953	#535	—	53	3	no	—
954	#535	—	53	3	no	—
955	#535	—	53	6	no	—
956	#535	—	53	6	no	—
957	#535	—	53	6	no	—
958	#535	—	53	6	no	—
959	#535	—	53	12	no	—
960	#535	—	53	3	no	—
961	#535	C₂×D₅₃	1	3	yes	complemented
962	C₂×#127	—	53	6	no	—
963	C₂×#124	—	53	6	no	—
964	#525	—	53	3	no	—
965	#525	—	53	3	no	—
966	#525	—	53	6	no	—
967	#525	—	53	3	no	—
968	#525	—	53	3	no	—
969	#525	—	53	3	no	—
970	#525	—	53	3	no	—
971	#525	—	53	6	no	—
972	#525	—	53	6	no	—
973	#525	—	53	6	no	—
974	#525	—	53	3	no	—
975	#525	C₂×D₅₃	1	3	yes	complemented
976	C₂×#123	—	53	6	no	—
977	C₂×C₂²⋊Q₈	—	53	1	no	—
978	C₂×C₂²⋊Q₈	—	53	3	no	—
979	C₂×C₂²⋊Q₈	—	53	6	no	—
980	C₂×#121	—	53	3	no	—
981	C₂×#121	—	53	6	no	—
982	C₂×#121	—	53	3	no	—
983	C₂×#121	—	53	3	no	—
984	C₂×#121	—	53	6	no	—
985	C₂×#121	—	53	6	no	—
986	C₂×#121	—	53	6	no	—
987	C₂×#121	—	53	6	no	—
988	C₂×#121	—	53	6	no	—
989	C₂×#121	—	53	6	no	—
990	C₂×#121	—	53	6	no	—
991	C₂×#121	—	53	3	no	—
992	C₂×#121	—	53	12	no	—
993	C₂×#121	—	53	6	no	—
994	C₂×#121	—	53	3	no	—
995	C₂×#121	—	53	6	no	—
996	C₂×#121	C₂×D₅₃	1	3	yes	complemented
997	C₂×#120	—	53	6	no	—
998	C₂×#120	—	53	12	no	—
999	#520	—	53	1	no	—
1000	#520	—	53	2	no	—
1001	#520	—	53	6	no	—
1002	#520	—	53	3	no	—
1003	#520	—	53	3	no	—
1004	#520	C₂×D₅₃	1	1	yes	characteristic, complemented
1005	C₂×C₄×Q₈	—	53	2	no	—
1006	C₂×C₄×D₄	—	53	6	no	—
1007	C₂×C₄×D₄	—	53	6	no	—
1008	C₂×C₄×D₄	—	53	6	no	—
1009	C₂×#117	—	53	3	no	—
1010	C₂²×C₄⋊C₄	—	53	3	no	—
1011	C₂²×C₂²⋊C₄	—	53	6	no	—
1012	C₅₃	C₂×#3488	1	1	yes	characteristic, complemented, Sylow
1013	C₂⁵	—	53	3	no	—
1014	C₂⁵	—	53	6	no	—
1015	H(5,𝔽₂)	—	2	8	no	—
1016	H(5,𝔽₂)	—	106	48	no	—
1017	H(5,𝔽₂)	—	106	24	no	—
1018	H(5,𝔽₂)	—	106	16	no	—
1019	H(5,𝔽₂)	—	106	24	no	—
1020	H(5,𝔽₂)	—	106	8	no	—
1021	C₂×#41	—	2	8	no	—
1022	C₂×#41	—	53	16	no	—
1023	C₂×#41	—	53	1	no	—
1024	C₂×#41	—	53	3	no	—
1025	C₂×#41	—	53	3	no	—
1026	C₂×#41	—	53	3	no	—
1027	C₂×#41	—	53	2	no	—
1028	C₂×#41	—	53	1	no	—
1029	C₂×#41	—	53	3	no	—
1030	C₂×#41	—	53	6	no	—
1031	C₂×#41	—	53	3	no	—
1032	C₂×#41	—	53	6	no	—
1033	C₂×#41	—	53	3	no	—
1034	C₂×#41	—	53	3	no	—
1035	C₂×#41	—	53	6	no	—
1036	C₂×#41	—	53	6	no	—
1037	C₂×#41	—	53	3	no	—
1038	C₂×#41	—	53	3	no	—
1039	C₂×#41	—	53	6	no	—
1040	C₂×#41	—	53	3	no	—
1041	C₂×#41	—	53	6	no	—
1042	C₂×#41	—	53	3	no	—
1043	C₂×#41	—	53	3	no	—
1044	C₂×#41	—	53	6	no	—
1045	C₂×#41	—	53	6	no	—
1046	C₂×#41	—	53	3	no	—
1047	C₂×#41	—	106	24	no	—
1048	C₂×#41	—	106	24	no	—
1049	C₂×#41	—	106	24	no	—
1050	C₂×#41	—	106	24	no	—
1051	C₂×#41	—	106	24	no	—
1052	C₂×#41	—	106	8	no	—
1053	C₂×#41	—	106	8	no	—
1054	C₂×#41	—	106	16	no	—
1055	C₂×#41	—	106	8	no	—
1056	C₂×#41	—	106	24	no	—
1057	C₂×#41	—	106	24	no	—
1058	C₂×#41	—	106	8	no	—
1059	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1060	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
1061	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
1062	C₂×#41	C₂²×D₅₃	1	3	yes	complemented
1063	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
1064	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic, complemented
1065	C₂²×Q₈	—	53	1	no	—
1066	C₂²×Q₈	—	53	1	no	—
1067	C₂²×Q₈	—	53	3	no	—
1068	C₂²×Q₈	—	53	3	no	—
1069	C₂²×Q₈	—	53	1	no	—
1070	C₂²×Q₈	—	53	3	no	—
1071	C₂²×Q₈	—	106	8	no	—
1072	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1073	C₂²×D₄	—	53	3	no	—
1074	C₂²×D₄	—	53	6	no	—
1075	C₂²×D₄	—	53	6	no	—
1076	C₂²×D₄	—	53	12	no	—
1077	C₂²×D₄	—	53	6	no	—
1078	C₂²×D₄	—	53	6	no	—
1079	C₂²×D₄	—	53	6	no	—
1080	C₂²×D₄	—	53	6	no	—
1081	C₂²×D₄	—	53	6	no	—
1082	C₂²×D₄	—	53	3	no	—
1083	C₂²×D₄	—	53	6	no	—
1084	C₂²×D₄	—	53	3	no	—
1085	C₂²×D₄	—	53	6	no	—
1086	C₂²×D₄	—	53	6	no	—
1087	C₂²×D₄	—	53	6	no	—
1088	C₂²×D₄	—	53	3	no	—
1089	C₂²×D₄	—	53	3	no	—
1090	C₂²×D₄	—	53	12	no	—
1091	C₂²×D₄	—	53	6	no	—
1092	C₂²×D₄	—	53	6	no	—
1093	C₂²×D₄	—	53	6	no	—
1094	C₂²×D₄	—	53	12	no	—
1095	C₂²×D₄	—	53	12	no	—
1096	C₂²×D₄	—	53	12	no	—
1097	C₂²×D₄	—	53	3	no	—
1098	C₂²×D₄	—	53	3	no	—
1099	C₂²×D₄	—	53	6	no	—
1100	C₂²×D₄	—	53	6	no	—
1101	C₂²×D₄	—	106	24	no	—
1102	C₂²×D₄	—	106	24	no	—
1103	C₂²×D₄	—	106	48	no	—
1104	C₂²×D₄	—	212	24	no	—
1105	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
1106	C₂²×D₄	C₂²×D₅₃	1	3	yes	complemented
1107	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
1108	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
1109	C₂³×C₄	—	53	3	no	—
1110	C₂³×C₄	—	53	3	no	—
1111	C₂³×C₄	—	53	3	no	—
1112	C₂³×C₄	—	53	3	no	—
1113	C₂³×C₄	—	53	3	no	—
1114	C₂³×C₄	—	53	6	no	—
1115	C₂³×C₄	—	53	1	no	—
1116	C₂³×C₄	—	53	3	no	—
1117	C₂³×C₄	—	53	3	no	—
1118	C₂³×C₄	—	53	3	no	—
1119	C₂³×C₄	—	53	3	no	—
1120	C₂³×C₄	—	53	3	no	—
1121	C₂³×C₄	—	53	3	no	—
1122	C₂³×C₄	—	53	3	no	—
1123	C₂³×C₄	—	53	6	no	—
1124	C₂³×C₄	—	106	24	no	—
1125	C₂³×C₄	C₂²×D₅₃	1	3	yes	complemented
1126	#127	—	53	12	no	—
1127	#127	—	53	12	no	—
1128	#127	—	53	6	no	—
1129	#127	—	53	6	no	—
1130	#127	—	53	6	no	—
1131	#127	C₂²×D₅₃	1	6	yes	complemented
1132	#124	—	53	6	no	—
1133	#124	—	53	6	no	—
1134	#124	—	53	12	no	—
1135	#124	—	53	12	no	—
1136	#124	—	53	6	no	—
1137	#124	C₂²×D₅₃	1	6	yes	complemented
1138	#123	—	53	6	no	—
1139	#123	—	53	6	no	—
1140	#123	—	53	6	no	—
1141	#123	—	53	6	no	—
1142	#123	—	53	6	no	—
1143	#123	—	53	6	no	—
1144	#123	—	53	6	no	—
1145	#123	C₂²×D₅₃	1	6	yes	complemented
1146	C₂²⋊Q₈	—	53	1	no	—
1147	C₂²⋊Q₈	—	53	3	no	—
1148	C₂²⋊Q₈	—	53	6	no	—
1149	C₂²⋊Q₈	—	53	1	no	—
1150	C₂²⋊Q₈	—	53	3	no	—
1151	C₂²⋊Q₈	—	53	6	no	—
1152	C₂²⋊Q₈	—	53	2	no	—
1153	C₂²⋊Q₈	—	53	1	no	—
1154	C₂²⋊Q₈	—	53	6	no	—
1155	C₂²⋊Q₈	—	53	3	no	—
1156	C₂²⋊Q₈	—	53	12	no	—
1157	C₂²⋊Q₈	—	53	6	no	—
1158	C₂²⋊Q₈	—	53	2	no	—
1159	C₂²⋊Q₈	—	53	6	no	—
1160	C₂²⋊Q₈	—	53	12	no	—
1161	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1162	C₂²⋊Q₈	C₂²×D₅₃	1	3	yes	complemented
1163	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1164	#121	—	53	3	no	—
1165	#121	—	53	6	no	—
1166	#121	—	53	6	no	—
1167	#121	—	53	12	no	—
1168	#121	—	53	6	no	—
1169	#121	—	53	12	no	—
1170	#121	—	53	6	no	—
1171	#121	—	53	12	no	—
1172	#121	—	53	3	no	—
1173	#121	—	53	6	no	—
1174	#121	—	53	12	no	—
1175	#121	—	53	12	no	—
1176	#121	—	53	12	no	—
1177	#121	—	53	6	no	—
1178	#121	—	53	12	no	—
1179	#121	—	53	3	no	—
1180	#121	—	53	6	no	—
1181	#121	—	53	6	no	—
1182	#121	—	53	6	no	—
1183	#121	—	53	3	no	—
1184	#121	—	53	12	no	—
1185	#121	—	53	6	no	—
1186	#121	—	53	3	no	—
1187	#121	—	53	6	no	—
1188	#121	—	53	6	no	—
1189	#121	—	53	6	no	—
1190	#121	—	53	3	no	—
1191	#121	—	53	12	no	—
1192	#121	—	53	6	no	—
1193	#121	—	53	6	no	—
1194	#121	—	53	12	no	—
1195	#121	—	53	12	no	—
1196	#121	—	53	12	no	—
1197	#121	—	53	6	no	—
1198	#121	—	53	12	no	—
1199	#121	—	53	12	no	—
1200	#121	—	53	12	no	—
1201	#121	C₂²×D₅₃	1	3	yes	complemented
1202	#121	C₂²×D₅₃	1	6	yes	complemented
1203	#121	C₂²×D₅₃	1	6	yes	complemented
1204	#121	C₂²×D₅₃	1	6	yes	complemented
1205	#121	C₂²×D₅₃	1	3	yes	complemented
1206	#121	C₂²×D₅₃	1	12	yes	complemented
1207	#121	C₂²×D₅₃	1	6	yes	complemented
1208	#120	—	53	6	no	—
1209	#120	—	53	12	no	—
1210	#120	—	53	6	no	—
1211	#120	—	53	6	no	—
1212	#120	—	53	6	no	—
1213	#120	—	53	12	no	—
1214	#120	—	53	12	no	—
1215	#120	—	53	12	no	—
1216	#120	—	53	6	no	—
1217	#120	—	53	6	no	—
1218	#120	—	53	6	no	—
1219	#120	—	53	12	no	—
1220	#120	—	53	12	no	—
1221	#120	—	53	12	no	—
1222	#120	C₂²×D₅₃	1	6	yes	complemented
1223	#120	C₂²×D₅₃	1	12	yes	complemented
1224	C₄×Q₈	—	53	2	no	—
1225	C₄×Q₈	—	53	6	no	—
1226	C₄×Q₈	—	53	6	no	—
1227	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1228	C₄×D₄	—	53	6	no	—
1229	C₄×D₄	—	53	6	no	—
1230	C₄×D₄	—	53	6	no	—
1231	C₄×D₄	—	53	12	no	—
1232	C₄×D₄	—	53	6	no	—
1233	C₄×D₄	—	53	6	no	—
1234	C₄×D₄	—	53	6	no	—
1235	C₄×D₄	—	53	6	no	—
1236	C₄×D₄	—	53	6	no	—
1237	C₄×D₄	—	53	6	no	—
1238	C₄×D₄	—	53	6	no	—
1239	C₄×D₄	—	53	12	no	—
1240	C₄×D₄	—	53	6	no	—
1241	C₄×D₄	—	53	6	no	—
1242	C₄×D₄	—	53	6	no	—
1243	C₄×D₄	—	53	6	no	—
1244	C₄×D₄	—	53	6	no	—
1245	C₄×D₄	—	53	6	no	—
1246	C₄×D₄	—	53	6	no	—
1247	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1248	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1249	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1250	#117	—	53	3	no	—
1251	#117	—	53	3	no	—
1252	#117	—	53	3	no	—
1253	#117	—	53	6	no	—
1254	#117	—	53	6	no	—
1255	#117	C₂²×D₅₃	1	3	yes	complemented
1256	C₂×C₄⋊C₄	—	53	6	no	—
1257	C₂×C₄⋊C₄	—	53	3	no	—
1258	C₂×C₄⋊C₄	—	53	3	no	—
1259	C₂×C₄⋊C₄	—	53	6	no	—
1260	C₂×C₄⋊C₄	—	53	6	no	—
1261	C₂×C₄⋊C₄	—	53	6	no	—
1262	C₂×C₄⋊C₄	—	53	1	no	—
1263	C₂×C₄⋊C₄	—	53	2	no	—
1264	C₂×C₄⋊C₄	—	53	6	no	—
1265	C₂×C₄⋊C₄	C₂²×D₅₃	1	3	yes	complemented
1266	C₂×C₂²⋊C₄	—	53	6	no	—
1267	C₂×C₂²⋊C₄	—	53	6	no	—
1268	C₂×C₂²⋊C₄	—	53	6	no	—
1269	C₂×C₂²⋊C₄	—	53	6	no	—
1270	C₂×C₂²⋊C₄	—	53	12	no	—
1271	C₂×C₂²⋊C₄	—	53	12	no	—
1272	C₂×C₂²⋊C₄	—	53	12	no	—
1273	C₂×C₂²⋊C₄	—	53	6	no	—
1274	C₂×C₂²⋊C₄	—	53	2	no	—
1275	C₂×C₂²⋊C₄	—	53	6	no	—
1276	C₂×C₂²⋊C₄	—	53	6	no	—
1277	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	complemented
1278	C₂×C₄²	—	53	6	no	—
1279	C₂⁴	—	53	3	no	—
1280	C₂⁴	—	53	1	no	—
1281	C₂⁴	—	53	6	no	—
1282	C₂⁴	—	53	3	no	—
1283	C₂⁴	—	53	3	no	—
1284	C₂⁴	—	53	3	no	—
1285	C₂⁴	—	53	3	no	—
1286	C₂⁴	—	53	12	no	—
1287	C₂⁴	—	53	6	no	—
1288	C₂⁴	—	106	24	no	—
1289	C₂⁴	—	106	12	no	—
1290	C₂⁴	—	106	12	no	—
1291	C₂⁴	—	212	12	no	—
1292	C₂⁴	—	212	12	no	—
1293	C₂⁴	—	212	6	no	—
1294	C₂⁴	C₂³×D₅₃	1	3	yes	—
1295	C₂⁴	C₂³×D₅₃	1	6	yes	—
1296	#41	—	2	4	no	—
1297	#41	—	2	8	no	—
1298	#41	—	2	12	no	—
1299	#41	—	2	12	no	—
1300	#41	—	2	12	no	—
1301	#41	—	53	8	no	—
1302	#41	—	53	24	no	—
1303	#41	—	53	24	no	—
1304	#41	—	106	24	no	—
1305	#41	—	106	24	no	—
1306	#41	—	106	24	no	—
1307	#41	—	106	12	no	—
1308	#41	—	106	12	no	—
1309	#41	—	106	24	no	—
1310	#41	—	106	24	no	—
1311	#41	—	106	12	no	—
1312	#41	—	106	24	no	—
1313	#41	—	106	12	no	—
1314	#41	—	106	12	no	—
1315	#41	—	106	12	no	—
1316	#41	—	106	24	no	—
1317	#41	—	106	12	no	—
1318	#41	—	106	24	no	—
1319	#41	—	106	12	no	—
1320	#41	—	106	4	no	—
1321	#41	—	106	8	no	—
1322	#41	—	106	12	no	—
1323	#41	—	106	12	no	—
1324	#41	—	106	12	no	—
1325	#41	D₄×D₅₃	1	8	yes	complemented
1326	C₂×Q₈	—	2	4	no	—
1327	C₂×Q₈	—	53	8	no	—
1328	C₂×Q₈	—	53	3	no	—
1329	C₂×Q₈	—	53	2	no	—
1330	C₂×Q₈	—	53	1	no	—
1331	C₂×Q₈	—	53	6	no	—
1332	C₂×Q₈	—	53	3	no	—
1333	C₂×Q₈	—	106	12	no	—
1334	C₂×Q₈	—	106	12	no	—
1335	C₂×Q₈	—	106	4	no	—
1336	C₂×Q₈	—	106	12	no	—
1337	C₂×Q₈	—	106	4	no	—
1338	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1339	C₂×Q₈	C₂³×D₅₃	1	3	yes	—
1340	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1341	C₂×D₄	—	2	12	no	—
1342	C₂×D₄	—	2	24	no	—
1343	C₂×D₄	—	2	12	no	—
1344	C₂×D₄	—	4	12	no	—
1345	C₂×D₄	—	53	6	no	—
1346	C₂×D₄	—	53	24	no	—
1347	C₂×D₄	—	53	6	no	—
1348	C₂×D₄	—	53	6	no	—
1349	C₂×D₄	—	53	6	no	—
1350	C₂×D₄	—	53	6	no	—
1351	C₂×D₄	—	53	6	no	—
1352	C₂×D₄	—	53	6	no	—
1353	C₂×D₄	—	53	6	no	—
1354	C₂×D₄	—	53	12	no	—
1355	C₂×D₄	—	53	6	no	—
1356	C₂×D₄	—	53	6	no	—
1357	C₂×D₄	—	53	6	no	—
1358	C₂×D₄	—	53	12	no	—
1359	C₂×D₄	—	53	12	no	—
1360	C₂×D₄	—	53	3	no	—
1361	C₂×D₄	—	53	6	no	—
1362	C₂×D₄	—	53	6	no	—
1363	C₂×D₄	—	53	6	no	—
1364	C₂×D₄	—	53	3	no	—
1365	C₂×D₄	—	53	6	no	—
1366	C₂×D₄	—	53	3	no	—
1367	C₂×D₄	—	53	6	no	—
1368	C₂×D₄	—	53	12	no	—
1369	C₂×D₄	—	106	12	no	—
1370	C₂×D₄	—	106	24	no	—
1371	C₂×D₄	—	106	12	no	—
1372	C₂×D₄	—	106	24	no	—
1373	C₂×D₄	—	106	12	no	—
1374	C₂×D₄	—	106	24	no	—
1375	C₂×D₄	—	106	24	no	—
1376	C₂×D₄	—	106	24	no	—
1377	C₂×D₄	—	106	24	no	—
1378	C₂×D₄	—	106	12	no	—
1379	C₂×D₄	—	106	48	no	—
1380	C₂×D₄	—	106	24	no	—
1381	C₂×D₄	—	106	24	no	—
1382	C₂×D₄	—	106	24	no	—
1383	C₂×D₄	—	106	24	no	—
1384	C₂×D₄	—	106	24	no	—
1385	C₂×D₄	—	106	48	no	—
1386	C₂×D₄	—	106	12	no	—
1387	C₂×D₄	—	106	24	no	—
1388	C₂×D₄	—	106	12	no	—
1389	C₂×D₄	—	212	12	no	—
1390	C₂×D₄	—	212	12	no	—
1391	C₂×D₄	—	212	24	no	—
1392	C₂×D₄	—	212	24	no	—
1393	C₂×D₄	—	212	24	no	—
1394	C₂×D₄	—	212	12	no	—
1395	C₂×D₄	—	212	12	no	—
1396	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1397	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1398	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1399	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1400	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1401	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1402	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1403	C₂×D₄	C₂³×D₅₃	1	12	yes	—
1404	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1405	C₂²×C₄	—	2	12	no	—
1406	C₂²×C₄	—	53	3	no	—
1407	C₂²×C₄	—	53	24	no	—
1408	C₂²×C₄	—	53	3	no	—
1409	C₂²×C₄	—	53	1	no	—
1410	C₂²×C₄	—	53	3	no	—
1411	C₂²×C₄	—	53	3	no	—
1412	C₂²×C₄	—	53	3	no	—
1413	C₂²×C₄	—	53	3	no	—
1414	C₂²×C₄	—	53	3	no	—
1415	C₂²×C₄	—	53	6	no	—
1416	C₂²×C₄	—	53	1	no	—
1417	C₂²×C₄	—	53	3	no	—
1418	C₂²×C₄	—	53	6	no	—
1419	C₂²×C₄	—	53	2	no	—
1420	C₂²×C₄	—	53	6	no	—
1421	C₂²×C₄	—	53	1	no	—
1422	C₂²×C₄	—	53	3	no	—
1423	C₂²×C₄	—	53	2	no	—
1424	C₂²×C₄	—	53	3	no	—
1425	C₂²×C₄	—	53	3	no	—
1426	C₂²×C₄	—	53	3	no	—
1427	C₂²×C₄	—	53	3	no	—
1428	C₂²×C₄	—	53	3	no	—
1429	C₂²×C₄	—	53	3	no	—
1430	C₂²×C₄	—	53	6	no	—
1431	C₂²×C₄	—	53	6	no	—
1432	C₂²×C₄	—	53	1	no	—
1433	C₂²×C₄	—	53	1	no	—
1434	C₂²×C₄	—	53	3	no	—
1435	C₂²×C₄	—	53	3	no	—
1436	C₂²×C₄	—	53	12	no	—
1437	C₂²×C₄	—	106	4	no	—
1438	C₂²×C₄	—	106	12	no	—
1439	C₂²×C₄	—	106	12	no	—
1440	C₂²×C₄	—	106	12	no	—
1441	C₂²×C₄	—	106	12	no	—
1442	C₂²×C₄	—	106	12	no	—
1443	C₂²×C₄	—	106	12	no	—
1444	C₂²×C₄	—	106	12	no	—
1445	C₂²×C₄	—	106	12	no	—
1446	C₂²×C₄	—	106	24	no	—
1447	C₂²×C₄	—	106	12	no	—
1448	C₂²×C₄	—	106	12	no	—
1449	C₂²×C₄	—	106	12	no	—
1450	C₂²×C₄	—	212	12	no	—
1451	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1452	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1453	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1454	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1455	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1456	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1457	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1458	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1459	C₄⋊C₄	—	53	6	no	—
1460	C₄⋊C₄	—	53	3	no	—
1461	C₄⋊C₄	—	53	12	no	—
1462	C₄⋊C₄	—	53	6	no	—
1463	C₄⋊C₄	—	53	2	no	—
1464	C₄⋊C₄	—	53	1	no	—
1465	C₄⋊C₄	—	53	2	no	—
1466	C₄⋊C₄	—	53	2	no	—
1467	C₄⋊C₄	—	53	2	no	—
1468	C₄⋊C₄	—	53	6	no	—
1469	C₄⋊C₄	—	53	6	no	—
1470	C₄⋊C₄	—	53	6	no	—
1471	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1472	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1473	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1474	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1475	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1476	C₂²⋊C₄	—	53	6	no	—
1477	C₂²⋊C₄	—	53	12	no	—
1478	C₂²⋊C₄	—	53	6	no	—
1479	C₂²⋊C₄	—	53	2	no	—
1480	C₂²⋊C₄	—	53	6	no	—
1481	C₂²⋊C₄	—	53	6	no	—
1482	C₂²⋊C₄	—	53	6	no	—
1483	C₂²⋊C₄	—	53	6	no	—
1484	C₂²⋊C₄	—	53	12	no	—
1485	C₂²⋊C₄	—	53	12	no	—
1486	C₂²⋊C₄	—	53	6	no	—
1487	C₂²⋊C₄	—	53	6	no	—
1488	C₂²⋊C₄	—	53	2	no	—
1489	C₂²⋊C₄	—	53	2	no	—
1490	C₂²⋊C₄	—	53	6	no	—
1491	C₂²⋊C₄	—	53	6	no	—
1492	C₂²⋊C₄	—	53	6	no	—
1493	C₂²⋊C₄	—	53	6	no	—
1494	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1495	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
1496	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1497	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1498	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1499	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1500	C₄²	—	53	6	no	—
1501	C₄²	—	53	6	no	—
1502	C₄²	—	53	6	no	—
1503	C₄²	C₂³×D₅₃	1	6	yes	—
1504	C₂³	—	2	6	no	—
1505	C₂³	—	2	6	no	—
1506	C₂³	—	2	12	no	—
1507	C₂³	—	4	3	no	—
1508	C₂³	—	4	6	no	—
1509	C₂³	—	4	6	no	—
1510	C₂³	—	53	1	no	—
1511	C₂³	—	53	12	no	—
1512	C₂³	—	53	4	no	—
1513	C₂³	—	53	3	no	—
1514	C₂³	—	53	1	no	—
1515	C₂³	—	53	6	no	—
1516	C₂³	—	53	3	no	—
1517	C₂³	—	106	2	no	—
1518	C₂³	—	106	6	no	—
1519	C₂³	—	106	6	no	—
1520	C₂³	—	106	2	no	—
1521	C₂³	—	106	24	no	—
1522	C₂³	—	106	6	no	—
1523	C₂³	—	106	6	no	—
1524	C₂³	—	106	6	no	—
1525	C₂³	—	106	12	no	—
1526	C₂³	—	106	12	no	—
1527	C₂³	—	106	6	no	—
1528	C₂³	—	106	6	no	—
1529	C₂³	—	106	6	no	—
1530	C₂³	—	106	6	no	—
1531	C₂³	—	106	12	no	—
1532	C₂³	—	106	12	no	—
1533	C₂³	—	106	6	no	—
1534	C₂³	—	106	6	no	—
1535	C₂³	—	424	48	no	—
1536	C₂³	—	212	6	no	—
1537	C₂³	—	212	12	no	—
1538	C₂³	—	212	6	no	—
1539	C₂³	—	212	12	no	—
1540	C₂³	—	212	3	no	—
1541	C₂³	—	212	3	no	—
1542	C₂³	—	212	3	no	—
1543	C₂³	—	212	48	no	—
1544	C₂³	C₂⁴×D₅₃	1	6	yes	—
1545	C₂³	C₂⁴×D₅₃	1	3	yes	—
1546	C₂³	C₂⁴×D₅₃	1	3	yes	—
1547	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1548	Q₈	—	2	6	no	—
1549	Q₈	—	2	2	no	—
1550	Q₈	—	53	12	no	—
1551	Q₈	—	106	12	no	—
1552	Q₈	—	106	4	no	—
1553	Q₈	—	106	6	no	—
1554	Q₈	—	106	2	no	—
1555	Q₈	C₂×D₄×D₅₃	1	4	yes	complemented
1556	D₄	—	2	12	no	—
1557	D₄	—	2	12	no	—
1558	D₄	—	2	12	no	—
1559	D₄	—	2	6	no	—
1560	D₄	—	2	12	no	—
1561	D₄	—	2	6	no	—
1562	D₄	—	4	12	no	—
1563	D₄	—	4	6	no	—
1564	D₄	—	53	24	no	—
1565	D₄	—	53	12	no	—
1566	D₄	—	106	12	no	—
1567	D₄	—	106	12	no	—
1568	D₄	—	106	12	no	—
1569	D₄	—	106	12	no	—
1570	D₄	—	106	24	no	—
1571	D₄	—	106	12	no	—
1572	D₄	—	106	12	no	—
1573	D₄	—	106	12	no	—
1574	D₄	—	106	12	no	—
1575	D₄	—	106	12	no	—
1576	D₄	—	106	12	no	—
1577	D₄	—	106	12	no	—
1578	D₄	—	106	6	no	—
1579	D₄	—	106	12	no	—
1580	D₄	—	106	6	no	—
1581	D₄	—	212	6	no	—
1582	D₄	—	212	12	no	—
1583	D₄	—	212	6	no	—
1584	D₄	—	212	6	no	—
1585	D₄	—	212	12	no	—
1586	D₄	—	212	12	no	—
1587	D₄	C₂×D₄×D₅₃	1	12	yes	complemented
1588	C₂×C₄	—	2	6	no	—
1589	C₂×C₄	—	2	2	no	—
1590	C₂×C₄	—	2	6	no	—
1591	C₂×C₄	—	2	6	no	—
1592	C₂×C₄	—	2	6	no	—
1593	C₂×C₄	—	2	12	no	—
1594	C₂×C₄	—	4	6	no	—
1595	C₂×C₄	—	53	12	no	—
1596	C₂×C₄	—	53	3	no	—
1597	C₂×C₄	—	53	1	no	—
1598	C₂×C₄	—	53	4	no	—
1599	C₂×C₄	—	53	12	no	—
1600	C₂×C₄	—	53	12	no	—
1601	C₂×C₄	—	53	12	no	—
1602	C₂×C₄	—	53	2	no	—
1603	C₂×C₄	—	53	6	no	—
1604	C₂×C₄	—	53	1	no	—
1605	C₂×C₄	—	53	3	no	—
1606	C₂×C₄	—	53	2	no	—
1607	C₂×C₄	—	106	2	no	—
1608	C₂×C₄	—	106	6	no	—
1609	C₂×C₄	—	106	6	no	—
1610	C₂×C₄	—	106	6	no	—
1611	C₂×C₄	—	106	12	no	—
1612	C₂×C₄	—	106	2	no	—
1613	C₂×C₄	—	106	4	no	—
1614	C₂×C₄	—	106	6	no	—
1615	C₂×C₄	—	106	6	no	—
1616	C₂×C₄	—	106	6	no	—
1617	C₂×C₄	—	106	12	no	—
1618	C₂×C₄	—	106	4	no	—
1619	C₂×C₄	—	106	2	no	—
1620	C₂×C₄	—	106	6	no	—
1621	C₂×C₄	—	106	6	no	—
1622	C₂×C₄	—	106	6	no	—
1623	C₂×C₄	—	106	12	no	—
1624	C₂×C₄	—	106	6	no	—
1625	C₂×C₄	—	106	2	no	—
1626	C₂×C₄	—	106	6	no	—
1627	C₂×C₄	—	106	6	no	—
1628	C₂×C₄	—	106	6	no	—
1629	C₂×C₄	—	106	12	no	—
1630	C₂×C₄	—	212	12	no	—
1631	C₂×C₄	—	212	6	no	—
1632	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	complemented
1633	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1634	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1635	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1636	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1637	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1638	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1639	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1640	C₂²	—	2	1	no	—
1641	C₂²	—	2	3	no	—
1642	C₂²	—	2	1	no	—
1643	C₂²	—	2	3	no	—
1644	C₂²	—	2	3	no	—
1645	C₂²	—	2	6	no	—
1646	C₂²	—	2	6	no	—
1647	C₂²	—	2	3	no	—
1648	C₂²	—	2	3	no	—
1649	C₂²	—	2	6	no	—
1650	C₂²	—	4	12	no	—
1651	C₂²	—	8	12	no	—
1652	C₂²	—	53	2	no	—
1653	C₂²	—	53	2	no	—
1654	C₂²	—	53	2	no	—
1655	C₂²	—	53	6	no	—
1656	C₂²	—	53	2	no	—
1657	C₂²	—	106	24	no	—
1658	C₂²	—	106	8	no	—
1659	C₂²	—	106	1	no	—
1660	C₂²	—	106	3	no	—
1661	C₂²	—	106	3	no	—
1662	C₂²	—	106	1	no	—
1663	C₂²	—	106	3	no	—
1664	C₂²	—	106	6	no	—
1665	C₂²	—	106	6	no	—
1666	C₂²	—	106	3	no	—
1667	C₂²	—	106	3	no	—
1668	C₂²	—	106	6	no	—
1669	C₂²	—	424	12	no	—
1670	C₂²	—	424	24	no	—
1671	C₂²	—	212	12	no	—
1672	C₂²	—	212	12	no	—
1673	C₂²	—	212	24	no	—
1674	C₂²	—	212	12	no	—
1675	C₂²	—	212	12	no	—
1676	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1677	C₂²	H(5,𝔽₂)×D₅₃	1	2	yes	complemented
1678	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1679	C₄	—	2	1	no	—
1680	C₄	—	2	2	no	—
1681	C₄	—	2	3	no	—
1682	C₄	—	2	6	no	—
1683	C₄	—	2	2	no	—
1684	C₄	—	53	2	no	—
1685	C₄	—	53	6	no	—
1686	C₄	—	106	1	no	—
1687	C₄	—	106	2	no	—
1688	C₄	—	106	3	no	—
1689	C₄	—	106	6	no	—
1690	C₄	—	106	2	no	—
1691	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1692	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1693	C₂	—	2	2	no	—
1694	C₂	—	2	6	no	—
1695	C₂	—	4	3	no	—
1696	C₂	—	4	6	no	—
1697	C₂	—	53	4	no	—
1698	C₂	—	106	6	no	—
1699	C₂	—	106	2	no	—
1700	C₂	—	212	6	no	—
1701	C₂	—	212	3	no	—
1702	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1703	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1704	C₂	#585×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3488	C₂
hypercenter	#3488	D₅₃
hypocenter	C₅₃	C₂×#3488
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
2. C₂²×#41×D₅₃	C₂	semidirect
3. #20288385	C₂	semidirect
4. #20288384	C₂	semidirect
5. #20288383	C₂	semidirect
6. #20288382	C₂	semidirect
7. #20288381	C₂	semidirect
8. #20288380	C₂	semidirect
9. #20288379	C₂	semidirect
10. #20288378	C₂	semidirect
11. #20288377	C₂	semidirect
12. #20288376	C₂	semidirect
13. #20288375	C₂	semidirect
14. #550×D₅₃	C₂	semidirect
15. #548×D₅₃	C₂	semidirect
16. #546×D₅₃	C₂	semidirect
17. D₄²×D₅₃	C₂	semidirect
18. #537×D₅₃	C₂	semidirect
19. #535×D₅₃	C₂	semidirect
20. #525×D₅₃	C₂	semidirect
21. C₂×#121×D₅₃	C₂	semidirect
22. #520×D₅₃	C₂	semidirect
23. C₅₃×#3488	C₂	semidirect
24. C₂×#13133263	C₂²	semidirect
25. C₂×#13133263	C₂²	semidirect
26. C₂×#13133263	C₂²	semidirect
27. C₂×#13133262	C₂²	semidirect
28. C₂×#13133262	C₂²	semidirect
30. C₂²×#11719949	C₂²	semidirect
31. C₂²×#11719945	C₂²	semidirect
32. C₂²×#11719947	C₂²	semidirect
35. C₂×#41×D₅₃	C₂²	semidirect
36. C₂×#41×D₅₃	C₂²	semidirect
37. C₂×#41×D₅₃	C₂²	semidirect
38. C₂×#41×D₅₃	C₂²	semidirect
39. C₂×#41×D₅₃	C₂²	semidirect
40. C₂×#41×D₅₃	C₂²	semidirect
41. C₂×#41×D₅₃	C₂²	semidirect
42. C₂×#41×D₅₃	C₂²	semidirect
43. C₂×#41×D₅₃	C₂²	semidirect
44. C₂²×Q₈×D₅₃	C₂²	semidirect
45. C₂²×D₄×D₅₃	C₂²	semidirect
46. C₂²×D₄×D₅₃	C₂²	semidirect
47. C₂²×D₄×D₅₃	C₂²	semidirect
48. C₂²×D₄×D₅₃	C₂²	semidirect
49. C₂³×C₄×D₅₃	C₂²	semidirect
50. #16811295	C₂²	semidirect
51. #16811294	C₂²	semidirect
52. #16811293	C₂²	semidirect
53. #16811292	C₂²	semidirect
54. #16811292	C₂²	semidirect
55. #16811291	C₂²	semidirect
56. #16811291	C₂²	semidirect
57. #16811285	C₂²	semidirect
58. #16811284	C₂²	semidirect
59. #16811283	C₂²	semidirect
60. #16811282	C₂²	semidirect
61. #16811281	C₂²	semidirect
62. #16811280	C₂²	semidirect
63. #16811279	C₂²	semidirect
64. #16811270	C₂²	semidirect
65. #16811269	C₂²	semidirect
66. #16811268	C₂²	semidirect
67. #16811267	C₂²	semidirect
68. #16811266	C₂²	semidirect
69. #16811265	C₂²	semidirect
70. #16811264	C₂²	semidirect
71. #16811263	C₂²	semidirect
72. #16811262	C₂²	semidirect
73. #16811261	C₂²	semidirect
74. #16811260	C₂²	semidirect
75. D₄×D₂₁₂	C₂²	semidirect
76. D₄×D₂₁₂	C₂²	semidirect
77. #16811258	C₂²	semidirect
78. #16811257	C₂²	semidirect
79. #16811257	C₂²	semidirect
80. #16811257	C₂²	semidirect
81. D₄×C₂²⋊D₅₃	C₂²	semidirect
82. D₄×C₂²⋊D₅₃	C₂²	semidirect
83. D₄×C₂²⋊D₅₃	C₂²	semidirect
84. #16811255	C₂²	semidirect
85. #16811255	C₂²	semidirect
86. #16811204	C₂²	semidirect
87. #16811203	C₂²	semidirect
88. #16811203	C₂²	semidirect
89. #16811202	C₂²	semidirect
90. #16811202	C₂²	semidirect
91. #16811201	C₂²	semidirect
92. #16811201	C₂²	semidirect
93. #16811200	C₂²	semidirect
94. #16811192	C₂²	semidirect
95. #16811191	C₂²	semidirect
96. #16811190	C₂²	semidirect
97. #16811189	C₂²	semidirect
98. #16811189	C₂²	semidirect
99. #16811188	C₂²	semidirect
100. #16811187	C₂²	semidirect
101. #16811186	C₂²	semidirect
102. #127×D₅₃	C₂²	semidirect
103. #124×D₅₃	C₂²	semidirect
104. #16811136	C₂²	semidirect
105. #16811136	C₂²	semidirect
106. #16811135	C₂²	semidirect
107. #16811134	C₂²	semidirect
108. #16811133	C₂²	semidirect
109. #16811133	C₂²	semidirect
110. #16811132	C₂²	semidirect
111. #16811132	C₂²	semidirect
112. #16811131	C₂²	semidirect
113. #16811130	C₂²	semidirect
114. #16811129	C₂²	semidirect
115. #123×D₅₃	C₂²	semidirect
116. C₂²⋊Q₈×D₅₃	C₂²	semidirect
117. C₂²⋊Q₈×D₅₃	C₂²	semidirect
118. C₂²⋊Q₈×D₅₃	C₂²	semidirect
119. C₂×#13133192	C₂²	semidirect
120. C₂×#13133191	C₂²	semidirect
121. C₂×#13133190	C₂²	semidirect
122. C₂×#13133189	C₂²	semidirect
123. C₂×#13133188	C₂²	semidirect
124. #121×D₅₃	C₂²	semidirect
125. #121×D₅₃	C₂²	semidirect
126. #121×D₅₃	C₂²	semidirect
127. #121×D₅₃	C₂²	semidirect
128. #121×D₅₃	C₂²	semidirect
129. #121×D₅₃	C₂²	semidirect
130. #121×D₅₃	C₂²	semidirect
131. #121×D₅₃	C₂²	semidirect
132. #121×D₅₃	C₂²	semidirect
133. #121×D₅₃	C₂²	semidirect
134. #121×D₅₃	C₂²	semidirect
135. #120×D₅₃	C₂²	semidirect
136. #120×D₅₃	C₂²	semidirect
137. #16811106	C₂²	semidirect
138. #16811105	C₂²	semidirect
139. #16811104	C₂²	semidirect
140. #16811103	C₂²	semidirect
141. #16811102	C₂²	semidirect
142. C₄×Q₈×D₅₃	C₂²	semidirect
143. C₄×D₄×D₅₃	C₂²	semidirect
144. C₄×D₄×D₅₃	C₂²	semidirect
145. C₄×D₄×D₅₃	C₂²	semidirect
146. #117×D₅₃	C₂²	semidirect
147. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
148. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
149. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
150. C₂²×#41×C₅₃	C₂²	semidirect
151. C₅₃×#550	C₂²	semidirect
152. C₅₃×#548	C₂²	semidirect
153. C₅₃×#546	C₂²	semidirect
154. D₄²×C₅₃	C₂²	semidirect
155. C₅₃×#537	C₂²	semidirect
156. C₅₃×#535	C₂²	semidirect
157. C₅₃×#525	C₂²	semidirect
158. C₂×#121×C₅₃	C₂²	semidirect
159. C₅₃×#520	C₂²	semidirect
169. C₂×#11719949	C₂³	semidirect
170. C₂×#11719949	C₂³	semidirect
171. C₂×#11719949	C₂³	semidirect
172. C₂×#11719949	C₂³	semidirect
173. C₂×#11719949	C₂³	semidirect
176. C₂×#11719945	C₂³	semidirect
177. C₂×#11719945	C₂³	semidirect
178. C₂×#11719945	C₂³	semidirect
179. C₂×#11719945	C₂³	semidirect
180. C₂×#11719945	C₂³	semidirect
181. C₂×#11719945	C₂³	semidirect
182. C₂×#11719945	C₂³	semidirect
183. C₂×#11719945	C₂³	semidirect
186. C₂×#11719947	C₂³	semidirect
187. C₂×#11719947	C₂³	semidirect
188. C₂×#11719947	C₂³	semidirect
189. C₂×#11719947	C₂³	semidirect
190. C₂×#11719947	C₂³	semidirect
191. C₂×#11719947	C₂³	semidirect
192. C₂×#11719947	C₂³	semidirect
193. C₂×#11719947	C₂³	semidirect
203. #41×D₅₃	D₄	semidirect
204. C₂²×Dic₁₀₆	C₂³	semidirect
209. C₂×Q₈×D₅₃	C₂³	semidirect
210. C₂×Q₈×D₅₃	C₂³	semidirect
211. C₂²×D₂₁₂	C₂³	semidirect
212. C₂²×D₂₁₂	C₂³	semidirect
213. C₂²×D₂₁₂	C₂³	semidirect
214. C₂²×D₂₁₂	C₂³	semidirect
215. C₂²×C₂²⋊D₅₃	C₂³	semidirect
216. C₂²×C₂²⋊D₅₃	C₂³	semidirect
217. C₂²×C₂²⋊D₅₃	C₂³	semidirect
218. C₂²×C₂²⋊D₅₃	C₂³	semidirect
219. C₂²×C₂²⋊D₅₃	C₂³	semidirect
233. C₂×D₄×D₅₃	C₂³	semidirect
234. C₂×D₄×D₅₃	C₂³	semidirect
235. C₂×D₄×D₅₃	C₂³	semidirect
236. C₂×D₄×D₅₃	C₂³	semidirect
237. C₂×D₄×D₅₃	C₂³	semidirect
238. C₂×D₄×D₅₃	C₂³	semidirect
239. C₂×D₄×D₅₃	C₂³	semidirect
240. C₂×D₄×D₅₃	C₂³	semidirect
241. C₂×D₄×D₅₃	C₂³	semidirect
242. C₂×D₄×D₅₃	C₂³	semidirect
243. C₂³×Dic₅₃	C₂³	semidirect
253. C₂²×C₄×D₅₃	C₂³	semidirect
254. C₂²×C₄×D₅₃	C₂³	semidirect
255. C₂²×C₄×D₅₃	C₂³	semidirect
256. C₂²×C₄×D₅₃	C₂³	semidirect
257. C₂²×C₄×D₅₃	C₂³	semidirect
258. C₂²×C₄×D₅₃	C₂³	semidirect
259. #13133214	C₂³	semidirect
260. #13133213	C₂³	semidirect
261. #13133213	C₂³	semidirect
262. #13133213	C₂³	semidirect
263. #13133213	C₂³	semidirect
264. #13133206	C₂³	semidirect
265. #13133205	C₂³	semidirect
266. #13133204	C₂³	semidirect
267. #13133203	C₂³	semidirect
268. #13133203	C₂³	semidirect
269. #13133202	C₂³	semidirect
270. #13133202	C₂³	semidirect
271. #13133201	C₂³	semidirect
272. #13133200	C₂³	semidirect
273. #13133199	C₂³	semidirect
274. #13133199	C₂³	semidirect
275. #13133198	C₂³	semidirect
276. #13133197	C₂³	semidirect
277. #13133197	C₂³	semidirect
278. #13133197	C₂³	semidirect
279. #13133196	C₂³	semidirect
280. #13133196	C₂³	semidirect
281. #13133196	C₂³	semidirect
282. #13133195	C₂³	semidirect
283. #13133195	C₂³	semidirect
284. #13133195	C₂³	semidirect
285. #13133194	C₂³	semidirect
286. #13133194	C₂³	semidirect
287. #13133194	C₂³	semidirect
288. #13133193	C₂³	semidirect
289. #13133193	C₂³	semidirect
290. #13133193	C₂³	semidirect
291. #13133192	C₂³	semidirect
292. #13133192	C₂³	semidirect
293. #13133192	C₂³	semidirect
294. #13133192	C₂³	semidirect
295. #13133192	C₂³	semidirect
296. #13133192	C₂³	semidirect
297. #13133192	C₂³	semidirect
298. #13133191	C₂³	semidirect
299. #13133191	C₂³	semidirect
300. #13133191	C₂³	semidirect
301. #13133191	C₂³	semidirect
302. #13133191	C₂³	semidirect
303. #13133191	C₂³	semidirect
304. #13133191	C₂³	semidirect
305. #13133190	C₂³	semidirect
306. #13133190	C₂³	semidirect
307. #13133190	C₂³	semidirect
308. #13133190	C₂³	semidirect
309. #13133190	C₂³	semidirect
310. #13133190	C₂³	semidirect
311. #13133190	C₂³	semidirect
312. #13133190	C₂³	semidirect
313. #13133189	C₂³	semidirect
314. #13133189	C₂³	semidirect
315. #13133189	C₂³	semidirect
316. #13133189	C₂³	semidirect
317. #13133189	C₂³	semidirect
318. #13133189	C₂³	semidirect
319. #13133189	C₂³	semidirect
320. #13133189	C₂³	semidirect
321. #13133188	C₂³	semidirect
322. #13133188	C₂³	semidirect
323. #13133188	C₂³	semidirect
324. #13133188	C₂³	semidirect
325. #13133188	C₂³	semidirect
326. #13133188	C₂³	semidirect
327. #13133188	C₂³	semidirect
328. #13133187	C₂³	semidirect
329. #13133187	C₂³	semidirect
330. #13133187	C₂³	semidirect
331. #13133187	C₂³	semidirect
332. #13133187	C₂³	semidirect
333. #13133187	C₂³	semidirect
334. #13133186	C₂³	semidirect
335. #13133186	C₂³	semidirect
336. #13133185	C₂³	semidirect
337. #13133185	C₂³	semidirect
338. #13133185	C₂³	semidirect
339. #13133185	C₂³	semidirect
340. #13133185	C₂³	semidirect
341. #13133185	C₂³	semidirect
342. Q₈×Dic₅₃	C₂³	semidirect
343. C₄×Dic₁₀₆	C₂³	semidirect
344. #13133182	C₂³	semidirect
345. C₄×D₂₁₂	C₂³	semidirect
346. C₄×D₂₁₂	C₂³	semidirect
347. C₄×D₂₁₂	C₂³	semidirect
348. D₄×Dic₅₃	C₂³	semidirect
349. D₄×Dic₅₃	C₂³	semidirect
350. D₄×Dic₅₃	C₂³	semidirect
351. #13133179	C₂³	semidirect
352. #13133179	C₂³	semidirect
353. #13133179	C₂³	semidirect
354. C₄×C₂²⋊D₅₃	C₂³	semidirect
355. C₄×C₂²⋊D₅₃	C₂³	semidirect
356. C₄×C₂²⋊D₅₃	C₂³	semidirect
357. C₄×C₂²⋊D₅₃	C₂³	semidirect
358. C₄×C₂²⋊D₅₃	C₂³	semidirect
359. #13133177	C₂³	semidirect
360. #13133177	C₂³	semidirect
361. #13133177	C₂³	semidirect
362. #13133177	C₂³	semidirect
363. #13133177	C₂³	semidirect
364. #13133176	C₂³	semidirect
365. #13133175	C₂³	semidirect
366. #13133175	C₂³	semidirect
367. #13133174	C₂³	semidirect
368. #13133173	C₂³	semidirect
369. C₂×C₄⋊Dic₅₃	C₂³	semidirect
370. C₂×#11719919	C₂³	semidirect
376. C₄⋊C₄×D₅₃	C₂³	semidirect
377. C₄⋊C₄×D₅₃	C₂³	semidirect
378. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
379. C₂×#11719921	C₂³	semidirect
380. C₂×#11719921	C₂³	semidirect
387. C₂²⋊C₄×D₅₃	C₂³	semidirect
388. C₂²⋊C₄×D₅₃	C₂³	semidirect
393. C₂×#41×C₅₃	C₂³	semidirect
394. C₂×#41×C₅₃	C₂³	semidirect
395. C₂×#41×C₅₃	C₂³	semidirect
396. C₂×#41×C₅₃	C₂³	semidirect
397. C₂×#41×C₅₃	C₂³	semidirect
398. C₂²×Q₈×C₅₃	C₂³	semidirect
399. C₂²×D₄×C₅₃	C₂³	semidirect
400. C₂²×D₄×C₅₃	C₂³	semidirect
401. C₂²×D₄×C₅₃	C₂³	semidirect
402. C₂²×D₄×C₅₃	C₂³	semidirect
403. C₂³×C₄×C₅₃	C₂³	semidirect
404. #127×C₅₃	C₂³	semidirect
405. #124×C₅₃	C₂³	semidirect
406. #123×C₅₃	C₂³	semidirect
407. C₂²⋊Q₈×C₅₃	C₂³	semidirect
408. C₂²⋊Q₈×C₅₃	C₂³	semidirect
409. C₂²⋊Q₈×C₅₃	C₂³	semidirect
410. #121×C₅₃	C₂³	semidirect
411. #121×C₅₃	C₂³	semidirect
412. #121×C₅₃	C₂³	semidirect
413. #121×C₅₃	C₂³	semidirect
414. #121×C₅₃	C₂³	semidirect
415. #121×C₅₃	C₂³	semidirect
416. #121×C₅₃	C₂³	semidirect
417. #120×C₅₃	C₂³	semidirect
418. #120×C₅₃	C₂³	semidirect
419. C₄×Q₈×C₅₃	C₂³	semidirect
420. C₄×D₄×C₅₃	C₂³	semidirect
421. C₄×D₄×C₅₃	C₂³	semidirect
422. C₄×D₄×C₅₃	C₂³	semidirect
423. #117×C₅₃	C₂³	semidirect
424. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
425. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
448. #41×C₅₃	C₂×D₄	semidirect
508. #11719949	C₂×D₄	semidirect
513. Q₈×D₅₃	C₂×D₄	semidirect
522. #11719947	C₂×D₄	semidirect
541. D₄×D₅₃	C₂×D₄	semidirect
550. #11719945	C₂×D₄	semidirect
577. C₂×C₄×D₅₃	C₂×D₄	semidirect
689. C₂²×D₅₃	H(5,𝔽₂)	semidirect
697. Q₈×C₅₃	C₂²×D₄	semidirect
706. D₄×C₅₃	C₂²×D₄	semidirect
714. C₂×C₄×C₅₃	C₂²×D₄	semidirect
735. C₂²⋊D₅₃	C₂²×D₄	semidirect
743. C₂×Dic₅₃	C₂²×D₄	semidirect
759. D₂₁₂	C₂²×D₄	semidirect
780. C₄×D₅₃	C₂²×D₄	semidirect
781. C₄×D₅₃	C₂²×D₄	semidirect
786. Dic₁₀₆	C₂²×D₄	semidirect
801. C₂²×C₅₃	C₂×H(5,𝔽₂)	semidirect
825. C₂×D₅₃	C₂×H(5,𝔽₂)	semidirect
854. #3488	D₅₃	direct (N × H)
875. D₅₃	#3488	direct (N × H)
882. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
897. C₂²×#41	C₂×D₅₃	semidirect
911. #550	C₂×D₅₃	semidirect
919. #548	C₂×D₅₃	semidirect
931. #546	C₂×D₅₃	semidirect
943. D₄²	C₂×D₅₃	semidirect
952. #537	C₂×D₅₃	semidirect
961. #535	C₂×D₅₃	semidirect
975. #525	C₂×D₅₃	semidirect
996. C₂×#121	C₂×D₅₃	semidirect
1004. #520	C₂×D₅₃	semidirect
1012. C₅₃	C₂×#3488	semidirect
1060. C₂×#41	C₂²×D₅₃	semidirect
1061. C₂×#41	C₂²×D₅₃	semidirect
1062. C₂×#41	C₂²×D₅₃	semidirect
1063. C₂×#41	C₂²×D₅₃	semidirect
1064. C₂×#41	C₂²×D₅₃	semidirect
1072. C₂²×Q₈	C₂²×D₅₃	semidirect
1105. C₂²×D₄	C₂²×D₅₃	semidirect
1106. C₂²×D₄	C₂²×D₅₃	semidirect
1107. C₂²×D₄	C₂²×D₅₃	semidirect
1108. C₂²×D₄	C₂²×D₅₃	semidirect
1125. C₂³×C₄	C₂²×D₅₃	semidirect
1131. #127	C₂²×D₅₃	semidirect
1137. #124	C₂²×D₅₃	semidirect
1145. #123	C₂²×D₅₃	semidirect
1161. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1162. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1163. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1201. #121	C₂²×D₅₃	semidirect
1202. #121	C₂²×D₅₃	semidirect
1203. #121	C₂²×D₅₃	semidirect
1204. #121	C₂²×D₅₃	semidirect
1205. #121	C₂²×D₅₃	semidirect
1206. #121	C₂²×D₅₃	semidirect
1207. #121	C₂²×D₅₃	semidirect
1222. #120	C₂²×D₅₃	semidirect
1223. #120	C₂²×D₅₃	semidirect
1227. C₄×Q₈	C₂²×D₅₃	semidirect
1247. C₄×D₄	C₂²×D₅₃	semidirect
1248. C₄×D₄	C₂²×D₅₃	semidirect
1249. C₄×D₄	C₂²×D₅₃	semidirect
1255. #117	C₂²×D₅₃	semidirect
1265. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1277. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1325. #41	D₄×D₅₃	semidirect
1555. Q₈	C₂×D₄×D₅₃	semidirect
1587. D₄	C₂×D₄×D₅₃	semidirect
1632. C₂×C₄	C₂×D₄×D₅₃	semidirect
1677. C₂²	H(5,𝔽₂)×D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×H(5,𝔽₂)×D₅₃	2
C₂²×#41×D₅₃	2
#20288385	2
#20288384	2
#20288383	2
#20288382	2
#20288381	2
#20288380	2
#20288379	2
#20288378	2
#20288377	2
#20288376	2
#20288375	2
#550×D₅₃	2
#548×D₅₃	2
#546×D₅₃	2
D₄²×D₅₃	2
#537×D₅₃	2
#535×D₅₃	2
#525×D₅₃	2
C₂×#121×D₅₃	2
#520×D₅₃	2
C₅₃×#3488	2
C₂×#3488	53

Subgroups — D53×#3488 #28292395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3488 #28292395