Subgroups — D₄×#41×D₅₃ #28291045

Order 13568.

12314 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₅₃	C₂	1	2	yes	maximal, complemented
2	D₄×#11719949	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288205	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288204	C₂	1	2	yes	maximal, complemented
6	D₄×#11719945	C₂	1	3	yes	maximal, complemented
7	#20288202	C₂	1	3	yes	maximal, complemented
8	#20288201	C₂	1	3	yes	maximal, complemented
9	#41×C₂²⋊D₅₃	C₂	1	2	yes	maximal, complemented
10	#20288199	C₂	1	6	yes	maximal, complemented
11	#20288198	C₂	1	6	yes	maximal, complemented
12	D₄×#11719947	C₂	1	3	yes	maximal, complemented
13	#550×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#548×D₅₃	C₂	1	2	yes	maximal, complemented
16	#547×D₅₃	C₂	1	3	yes	maximal, complemented
17	#546×D₅₃	C₂	1	6	yes	maximal, complemented
18	D₄²×D₅₃	C₂	1	3	yes	maximal, complemented
19	#532×D₅₃	C₂	1	3	yes	maximal, complemented
20	#525×D₅₃	C₂	1	6	yes	maximal, complemented
21	C₄×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₄×D₅₃	C₂	1	3	yes	maximal, complemented
23	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11719949	C₂²	1	2	yes	complemented
25	C₂²×#11719945	C₂²	1	6	yes	complemented
26	C₂²×#11719947	C₂²	1	6	yes	complemented
27	C₂×#41×D₅₃	—	2	32	no	—
28	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
29	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
30	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
31	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
32	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
33	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
34	C₂×#41×D₅₃	C₂²	1	6	yes	complemented
35	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
36	C₂²×Q₈×D₅₃	C₂²	1	2	yes	complemented
37	C₂²×D₄×D₅₃	C₂²	1	3	yes	—
38	C₂²×D₄×D₅₃	C₂²	1	6	yes	complemented
39	C₂³×C₄×D₅₃	C₂²	1	6	yes	complemented
40	#16811295	C₂²	1	1	yes	characteristic, complemented
41	#16811294	C₂²	1	3	yes	complemented
42	#16811293	C₂²	1	3	yes	complemented
43	#16811292	C₂²	1	2	yes	complemented
44	#16811291	C₂²	1	6	yes	complemented
45	Q₈×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
46	D₄×Dic₁₀₆	C₂²	1	3	yes	complemented
47	#16811288	C₂²	1	3	yes	complemented
48	Q₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
49	#16811286	C₂²	1	6	yes	complemented
50	#16811285	C₂²	1	2	yes	complemented
51	#16811284	C₂²	1	2	yes	complemented
52	#16811283	C₂²	1	6	yes	complemented
53	#16811282	C₂²	1	6	yes	complemented
54	#16811281	C₂²	1	6	yes	complemented
55	#16811280	C₂²	1	2	yes	complemented
56	#16811279	C₂²	1	6	yes	complemented
57	#16811278	C₂²	1	3	yes	complemented
58	#16811277	C₂²	1	3	yes	complemented
59	#16811276	C₂²	1	3	yes	complemented
60	#16811275	C₂²	1	6	yes	complemented
61	#16811274	C₂²	1	6	yes	complemented
62	#16811273	C₂²	1	6	yes	complemented
63	#16811272	C₂²	1	6	yes	complemented
64	#16811271	C₂²	1	12	yes	complemented
65	#16811270	C₂²	1	6	yes	complemented
66	#16811269	C₂²	1	6	yes	complemented
67	#16811268	C₂²	1	6	yes	complemented
68	#16811267	C₂²	1	6	yes	complemented
69	#16811266	C₂²	1	6	yes	complemented
70	#16811265	C₂²	1	12	yes	complemented
71	#16811264	C₂²	1	6	yes	complemented
72	#16811263	C₂²	1	12	yes	complemented
73	#16811262	C₂²	1	12	yes	complemented
74	#16811261	C₂²	1	6	yes	complemented
75	#16811260	C₂²	1	12	yes	complemented
76	D₄×D₂₁₂	C₂²	1	3	yes	complemented
77	D₄×D₂₁₂	C₂²	1	3	yes	complemented
78	#16811258	C₂²	1	3	yes	complemented
79	#16811257	C₂²	1	6	yes	complemented
80	#16811257	C₂²	1	6	yes	complemented
81	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
82	D₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
83	#16811255	C₂²	1	12	yes	complemented
84	#16811174	C₂²	1	3	yes	complemented
85	#16811173	C₂²	1	3	yes	complemented
86	#16811172	C₂²	1	6	yes	complemented
87	#16811171	C₂²	1	3	yes	complemented
88	#16811170	C₂²	1	6	yes	complemented
89	#16811170	C₂²	1	6	yes	complemented
90	#16811169	C₂²	1	6	yes	complemented
91	#16811168	C₂²	1	6	yes	complemented
92	#16811168	C₂²	1	6	yes	complemented
93	C₄⋊Q₈×D₅₃	C₂²	1	3	yes	complemented
94	#127×D₅₃	C₂²	1	3	yes	complemented
95	#124×D₅₃	C₂²	1	6	yes	complemented
96	#16811136	C₂²	1	6	yes	complemented
97	#16811136	C₂²	1	6	yes	complemented
98	#16811135	C₂²	1	6	yes	complemented
99	#16811134	C₂²	1	6	yes	complemented
100	#16811133	C₂²	1	6	yes	complemented
101	#16811133	C₂²	1	6	yes	complemented
102	#16811132	C₂²	1	12	yes	complemented
103	#16811132	C₂²	1	12	yes	complemented
104	#16811131	C₂²	1	12	yes	complemented
105	#16811130	C₂²	1	6	yes	complemented
106	#16811129	C₂²	1	12	yes	complemented
107	#123×D₅₃	C₂²	1	12	yes	complemented
108	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
109	C₂²⋊Q₈×D₅₃	C₂²	1	6	yes	complemented
110	#121×D₅₃	C₂²	1	6	yes	complemented
111	#121×D₅₃	C₂²	1	6	yes	complemented
112	#121×D₅₃	C₂²	1	6	yes	complemented
113	#121×D₅₃	C₂²	1	6	yes	complemented
114	#120×D₅₃	C₂²	1	12	yes	complemented
115	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₄×#11719949	C₂²	1	1	yes	characteristic, complemented
117	C₄×#11719949	C₂²	1	1	yes	characteristic, complemented
118	C₄×#11719945	C₂²	1	3	yes	complemented
119	#16811091	C₂²	1	3	yes	complemented
120	C₄×#11719947	C₂²	1	3	yes	complemented
121	C₄×#11719947	C₂²	1	3	yes	complemented
122	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₄×D₂₁₂	C₂²	1	3	yes	complemented
125	C₂×D₄×Dic₅₃	C₂²	1	3	yes	complemented
126	C₂×#13133179	C₂²	1	3	yes	complemented
127	C₂×C₄×C₂²⋊D₅₃	C₂²	1	6	yes	complemented
128	C₂×#13133177	C₂²	1	6	yes	complemented
129	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
130	C₄×D₄×D₅₃	C₂²	1	3	yes	—
131	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
132	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
133	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
134	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
135	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
136	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
137	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
138	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
139	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
140	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
141	C₄×D₄×D₅₃	C₂²	1	6	yes	complemented
142	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
143	C₄×D₄×D₅₃	C₂²	1	3	yes	complemented
144	#117×D₅₃	C₂²	1	3	yes	complemented
145	C₂×C₄⋊C₄×D₅₃	C₂²	1	3	yes	complemented
146	C₂×C₂²⋊C₄×D₅₃	C₂²	1	6	yes	complemented
147	C₂×C₄²×D₅₃	C₂²	1	3	yes	complemented
148	C₂²×#41×C₅₃	C₂²	1	2	yes	complemented
149	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
150	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#548	C₂²	1	2	yes	complemented
152	C₅₃×#547	C₂²	1	3	yes	complemented
153	C₅₃×#546	C₂²	1	6	yes	complemented
154	D₄²×C₅₃	C₂²	1	3	yes	complemented
155	C₅₃×#532	C₂²	1	3	yes	complemented
156	C₅₃×#525	C₂²	1	6	yes	complemented
157	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
158	C₂×C₄×D₄×C₅₃	C₂²	1	3	yes	complemented
159	C₂⁴×D₅₃	C₂³	1	6	yes	—
160	C₂×#11719949	—	2	16	no	—
161	C₂×#11719949	C₂³	1	1	yes	characteristic
162	C₂×#11719949	C₂³	1	6	yes	complemented
163	C₂×#11719949	C₂³	1	2	yes	complemented
164	C₂×#11719949	C₂³	1	6	yes	complemented
165	C₂×#11719945	—	2	48	no	—
166	C₂×#11719945	C₂³	1	3	yes	—
167	C₂×#11719945	C₂³	1	12	yes	complemented
168	C₂×#11719945	C₂³	1	6	yes	complemented
169	C₂×#11719945	C₂³	1	6	yes	complemented
170	C₂×#11719945	C₂³	1	12	yes	complemented
171	C₂×#11719945	C₂³	1	6	yes	complemented
172	C₂×#11719947	—	2	48	no	—
173	C₂×#11719947	C₂³	1	3	yes	—
174	C₂×#11719947	C₂³	1	6	yes	complemented
175	C₂×#11719947	C₂³	1	12	yes	complemented
176	C₂×#11719947	C₂³	1	6	yes	complemented
177	C₂×#11719947	C₂³	1	12	yes	complemented
178	C₂×#11719947	C₂³	1	6	yes	complemented
179	#41×D₅₃	—	2	16	no	—
180	#41×D₅₃	—	2	16	no	—
181	#41×D₅₃	—	2	16	no	—
182	#41×D₅₃	—	2	48	no	—
183	#41×D₅₃	—	2	48	no	—
184	#41×D₅₃	—	2	48	no	—
185	#41×D₅₃	—	2	48	no	—
186	#41×D₅₃	D₄	1	16	yes	direct product factor
187	C₂²×Dic₁₀₆	C₂³	1	6	yes	complemented
188	C₂×Q₈×D₅₃	—	2	16	no	—
189	C₂×Q₈×D₅₃	C₂³	1	6	yes	—
190	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
191	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
192	C₂×Q₈×D₅₃	C₂³	1	6	yes	complemented
193	C₂²×D₂₁₂	C₂³	1	3	yes	—
194	C₂²×D₂₁₂	C₂³	1	6	yes	complemented
195	C₂²×C₂²⋊D₅₃	C₂³	1	6	yes	—
196	C₂²×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
197	C₂×D₄×D₅₃	—	2	48	no	—
198	C₂×D₄×D₅₃	—	2	24	no	—
199	C₂×D₄×D₅₃	C₂³	1	6	yes	—
200	C₂×D₄×D₅₃	C₂³	1	3	yes	—
201	C₂×D₄×D₅₃	C₂³	1	6	yes	—
202	C₂×D₄×D₅₃	C₂³	1	3	yes	—
203	C₂×D₄×D₅₃	C₂³	1	3	yes	—
204	C₂×D₄×D₅₃	C₂³	1	12	yes	—
205	C₂×D₄×D₅₃	C₂³	1	6	yes	—
206	C₂×D₄×D₅₃	C₂³	1	6	yes	—
207	C₂×D₄×D₅₃	C₂³	1	3	yes	—
208	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂×D₄×D₅₃	C₂³	1	12	yes	complemented
210	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
211	C₂×D₄×D₅₃	C₂³	1	6	yes	complemented
212	C₂³×Dic₅₃	C₂³	1	6	yes	complemented
213	C₂²×C₄×D₅₃	—	2	48	no	—
214	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
215	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
216	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
217	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
218	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
219	C₂²×C₄×D₅₃	C₂³	1	6	yes	—
220	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
221	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
222	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
223	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
224	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
225	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
226	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
227	C₂²×C₄×D₅₃	C₂³	1	6	yes	complemented
228	#13133217	C₂³	1	3	yes	complemented
229	#13133216	C₂³	1	6	yes	complemented
230	#13133216	C₂³	1	6	yes	complemented
231	#13133215	C₂³	1	6	yes	complemented
232	#13133214	C₂³	1	3	yes	complemented
233	#13133213	C₂³	1	6	yes	complemented
234	#13133213	C₂³	1	6	yes	complemented
235	#13133213	C₂³	1	6	yes	complemented
236	#13133206	C₂³	1	6	yes	complemented
237	#13133205	C₂³	1	6	yes	complemented
238	#13133204	C₂³	1	6	yes	complemented
239	#13133203	C₂³	1	12	yes	complemented
240	#13133203	C₂³	1	12	yes	complemented
241	#13133202	C₂³	1	12	yes	complemented
242	#13133202	C₂³	1	12	yes	complemented
243	#13133201	C₂³	1	12	yes	complemented
244	#13133200	C₂³	1	12	yes	complemented
245	#13133199	C₂³	1	12	yes	complemented
246	#13133199	C₂³	1	12	yes	complemented
247	#13133198	C₂³	1	12	yes	complemented
248	#13133197	C₂³	1	6	yes	complemented
249	#13133197	C₂³	1	6	yes	complemented
250	#13133196	C₂³	1	6	yes	complemented
251	#13133196	C₂³	1	6	yes	complemented
252	#13133195	C₂³	1	12	yes	complemented
253	#13133195	C₂³	1	12	yes	complemented
254	#13133194	C₂³	1	12	yes	complemented
255	#13133194	C₂³	1	12	yes	complemented
256	#13133193	C₂³	1	6	yes	complemented
257	#13133193	C₂³	1	6	yes	complemented
258	#13133192	C₂³	1	6	yes	complemented
259	#13133192	C₂³	1	6	yes	complemented
260	#13133192	C₂³	1	6	yes	complemented
261	#13133192	C₂³	1	6	yes	complemented
262	#13133191	C₂³	1	6	yes	complemented
263	#13133191	C₂³	1	6	yes	complemented
264	#13133191	C₂³	1	6	yes	complemented
265	#13133191	C₂³	1	6	yes	complemented
266	#13133190	C₂³	1	12	yes	complemented
267	#13133190	C₂³	1	12	yes	complemented
268	#13133190	C₂³	1	12	yes	complemented
269	#13133190	C₂³	1	12	yes	complemented
270	#13133189	C₂³	1	12	yes	complemented
271	#13133189	C₂³	1	12	yes	complemented
272	#13133189	C₂³	1	12	yes	complemented
273	#13133189	C₂³	1	12	yes	complemented
274	#13133188	C₂³	1	6	yes	complemented
275	#13133188	C₂³	1	6	yes	complemented
276	#13133188	C₂³	1	6	yes	complemented
277	#13133188	C₂³	1	6	yes	complemented
278	#13133187	C₂³	1	12	yes	complemented
279	#13133187	C₂³	1	12	yes	complemented
280	#13133187	C₂³	1	12	yes	complemented
281	#13133186	C₂³	1	12	yes	complemented
282	#13133185	C₂³	1	12	yes	complemented
283	#13133185	C₂³	1	12	yes	complemented
284	#13133185	C₂³	1	12	yes	complemented
285	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
286	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
287	C₄×Dic₁₀₆	C₂³	1	3	yes	complemented
288	C₄×Dic₁₀₆	C₂³	1	3	yes	complemented
289	#13133182	C₂³	1	3	yes	complemented
290	#13133182	C₂³	1	3	yes	complemented
291	C₄×D₂₁₂	C₂³	1	3	yes	—
292	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
293	C₄×D₂₁₂	C₂³	1	3	yes	complemented
294	C₄×D₂₁₂	C₂³	1	6	yes	complemented
295	C₄×D₂₁₂	C₂³	1	3	yes	complemented
296	C₄×D₂₁₂	C₂³	1	3	yes	complemented
297	C₄×D₂₁₂	C₂³	1	6	yes	complemented
298	C₄×D₂₁₂	C₂³	1	3	yes	complemented
299	C₄×D₂₁₂	C₂³	1	6	yes	complemented
300	D₄×Dic₅₃	C₂³	1	3	yes	—
301	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
302	D₄×Dic₅₃	C₂³	1	3	yes	complemented
303	D₄×Dic₅₃	C₂³	1	3	yes	complemented
304	D₄×Dic₅₃	C₂³	1	3	yes	complemented
305	D₄×Dic₅₃	C₂³	1	6	yes	complemented
306	D₄×Dic₅₃	C₂³	1	6	yes	complemented
307	D₄×Dic₅₃	C₂³	1	3	yes	complemented
308	D₄×Dic₅₃	C₂³	1	6	yes	complemented
309	#13133179	C₂³	1	3	yes	—
310	#13133179	C₂³	1	1	yes	characteristic
311	#13133179	C₂³	1	3	yes	complemented
312	#13133179	C₂³	1	6	yes	complemented
313	#13133179	C₂³	1	3	yes	complemented
314	#13133179	C₂³	1	3	yes	complemented
315	#13133179	C₂³	1	6	yes	complemented
316	#13133179	C₂³	1	3	yes	complemented
317	#13133179	C₂³	1	6	yes	complemented
318	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	—
319	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
320	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
321	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
322	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
323	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
324	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
325	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
326	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
327	C₄×C₂²⋊D₅₃	C₂³	1	6	yes	complemented
328	C₄×C₂²⋊D₅₃	C₂³	1	12	yes	complemented
329	#13133177	C₂³	1	6	yes	—
330	#13133177	C₂³	1	2	yes	—
331	#13133177	C₂³	1	6	yes	complemented
332	#13133177	C₂³	1	6	yes	complemented
333	#13133177	C₂³	1	6	yes	complemented
334	#13133177	C₂³	1	6	yes	complemented
335	#13133177	C₂³	1	6	yes	complemented
336	#13133177	C₂³	1	6	yes	complemented
337	#13133177	C₂³	1	6	yes	complemented
338	#13133177	C₂³	1	6	yes	complemented
339	#13133177	C₂³	1	12	yes	complemented
340	#13133176	C₂³	1	3	yes	complemented
341	#13133175	C₂³	1	3	yes	complemented
342	#13133175	C₂³	1	3	yes	complemented
343	#13133174	C₂³	1	6	yes	complemented
344	#13133173	C₂³	1	6	yes	complemented
345	C₂×C₄⋊Dic₅₃	C₂³	1	3	yes	complemented
346	C₂×#11719919	C₂³	1	6	yes	complemented
347	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
348	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
349	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
350	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
351	C₄⋊C₄×D₅₃	C₂³	1	3	yes	—
352	C₄⋊C₄×D₅₃	C₂³	1	6	yes	—
353	C₄⋊C₄×D₅₃	C₂³	1	6	yes	complemented
354	C₄⋊C₄×D₅₃	C₂³	1	3	yes	complemented
355	C₄⋊C₄×D₅₃	C₂³	1	3	yes	complemented
356	C₂×C₂²⋊Dic₅₃	C₂³	1	6	yes	complemented
357	C₂×#11719921	C₂³	1	6	yes	complemented
358	C₂×#11719921	C₂³	1	6	yes	complemented
359	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
360	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
361	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
362	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
363	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	—
364	C₂²⋊C₄×D₅₃	C₂³	1	12	yes	—
365	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
366	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
367	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
368	C₂²⋊C₄×D₅₃	C₂³	1	6	yes	complemented
369	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
370	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
371	C₂×C₄×Dic₅₃	C₂³	1	3	yes	complemented
372	C₄²×D₅₃	C₂³	1	1	yes	characteristic
373	C₄²×D₅₃	C₂³	1	3	yes	—
374	C₄²×D₅₃	C₂³	1	3	yes	—
375	C₄²×D₅₃	C₂³	1	3	yes	—
376	C₄²×D₅₃	C₂³	1	3	yes	complemented
377	C₄²×D₅₃	C₂³	1	3	yes	complemented
378	C₄²×D₅₃	C₂³	1	3	yes	complemented
379	C₄²×D₅₃	C₂³	1	3	yes	complemented
380	C₂×#41×C₅₃	—	2	16	no	—
381	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
382	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
383	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
384	C₂×#41×C₅₃	C₂³	1	6	yes	complemented
385	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
386	C₂²×D₄×C₅₃	C₂³	1	3	yes	—
387	C₂²×D₄×C₅₃	C₂³	1	6	yes	complemented
388	C₂³×C₄×C₅₃	C₂³	1	6	yes	complemented
389	C₄⋊Q₈×C₅₃	C₂³	1	3	yes	complemented
390	#127×C₅₃	C₂³	1	3	yes	complemented
391	#124×C₅₃	C₂³	1	6	yes	complemented
392	#123×C₅₃	C₂³	1	12	yes	complemented
393	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
394	C₂²⋊Q₈×C₅₃	C₂³	1	6	yes	complemented
395	#121×C₅₃	C₂³	1	6	yes	complemented
396	#121×C₅₃	C₂³	1	6	yes	complemented
397	#121×C₅₃	C₂³	1	6	yes	complemented
398	#121×C₅₃	C₂³	1	6	yes	complemented
399	#120×C₅₃	C₂³	1	12	yes	complemented
400	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
401	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
402	C₄×D₄×C₅₃	C₂³	1	3	yes	—
403	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
404	C₄×D₄×C₅₃	C₂³	1	3	yes	complemented
405	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
406	C₄×D₄×C₅₃	C₂³	1	3	yes	complemented
407	C₄×D₄×C₅₃	C₂³	1	3	yes	complemented
408	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
409	C₄×D₄×C₅₃	C₂³	1	3	yes	complemented
410	C₄×D₄×C₅₃	C₂³	1	6	yes	complemented
411	#117×C₅₃	C₂³	1	3	yes	complemented
412	C₂×C₄⋊C₄×C₅₃	C₂³	1	3	yes	complemented
413	C₂×C₂²⋊C₄×C₅₃	C₂³	1	6	yes	complemented
414	C₂×C₄²×C₅₃	C₂³	1	3	yes	complemented
415	C₂⁴×C₅₃	C₂⁴	1	6	yes	—
416	C₂³×D₅₃	—	2	24	no	—
417	C₂³×D₅₃	—	2	24	no	—
418	C₂³×D₅₃	—	4	12	no	—
419	C₂³×D₅₃	C₂⁴	1	6	yes	—
420	C₂³×D₅₃	C₂⁴	1	6	yes	—
421	C₂³×D₅₃	C₂⁴	1	6	yes	—
422	C₂³×D₅₃	C₂⁴	1	6	yes	—
423	C₂³×D₅₃	C₂⁴	1	3	yes	—
424	C₂³×D₅₃	C₂⁴	1	2	yes	—
425	#41×C₅₃	—	2	8	no	—
426	#41×C₅₃	—	2	24	no	—
427	#41×C₅₃	—	2	24	no	—
428	#41×C₅₃	C₂×D₄	1	8	yes	complemented
429	C₂×Q₈×C₅₃	—	2	8	no	—
430	C₂×Q₈×C₅₃	C₂⁴	1	6	yes	—
431	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂×D₄×C₅₃	—	2	24	no	—
433	C₂×D₄×C₅₃	—	2	12	no	—
434	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
435	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
436	C₂×D₄×C₅₃	C₂⁴	1	12	yes	—
437	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
438	C₂×D₄×C₅₃	C₂⁴	1	6	yes	—
439	C₂×D₄×C₅₃	C₂⁴	1	3	yes	—
440	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	—	2	24	no	—
442	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
443	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
444	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
445	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
446	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
447	C₂²×C₄×C₅₃	C₂⁴	1	6	yes	—
448	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
449	C₂²×C₄×C₅₃	C₂⁴	1	3	yes	—
450	C₂×C₂²⋊D₅₃	—	2	48	no	—
451	C₂×C₂²⋊D₅₃	—	2	24	no	—
452	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
453	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
454	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
455	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
456	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
457	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
458	C₂×C₂²⋊D₅₃	C₂⁴	1	12	yes	—
459	C₂×C₂²⋊D₅₃	C₂⁴	1	6	yes	—
460	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
461	C₂²×Dic₅₃	—	2	24	no	—
462	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
463	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
464	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
465	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
466	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
467	C₂²×Dic₅₃	C₂⁴	1	6	yes	—
468	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
469	C₂²×Dic₅₃	C₂⁴	1	3	yes	—
470	#11719949	—	2	8	no	—
471	#11719949	—	2	24	no	—
472	#11719949	—	2	24	no	—
473	#11719949	C₂×D₄	1	8	yes	complemented
474	Q₈×D₅₃	—	2	8	no	—
475	Q₈×D₅₃	—	2	24	no	—
476	Q₈×D₅₃	—	2	24	no	—
477	Q₈×D₅₃	C₂×D₄	1	8	yes	complemented
478	#11719947	—	2	24	no	—
479	#11719947	—	2	48	no	—
480	#11719947	—	2	48	no	—
481	#11719947	—	2	24	no	—
482	#11719947	—	2	24	no	—
483	#11719947	C₂×D₄	1	24	yes	complemented
484	D₄×D₅₃	—	2	48	no	—
485	D₄×D₅₃	—	2	24	no	—
486	D₄×D₅₃	—	2	24	no	—
487	D₄×D₅₃	—	2	12	no	—
488	D₄×D₅₃	—	2	48	no	—
489	D₄×D₅₃	—	2	24	no	—
490	D₄×D₅₃	—	2	24	no	—
491	D₄×D₅₃	—	2	12	no	—
492	D₄×D₅₃	—	2	24	no	—
493	D₄×D₅₃	—	2	12	no	—
494	D₄×D₅₃	—	4	12	no	—
495	D₄×D₅₃	C₂×D₄	1	24	yes	complemented
496	D₄×D₅₃	#41	1	8	yes	direct product factor
497	#11719945	—	2	24	no	—
498	#11719945	—	2	48	no	—
499	#11719945	—	2	24	no	—
500	#11719945	—	2	48	no	—
501	#11719945	—	2	24	no	—
502	#11719945	C₂×D₄	1	24	yes	complemented
503	C₂×D₂₁₂	—	2	24	no	—
504	C₂×D₂₁₂	—	2	12	no	—
505	C₂×D₂₁₂	C₂⁴	1	6	yes	—
506	C₂×D₂₁₂	C₂⁴	1	3	yes	—
507	C₂×D₂₁₂	C₂⁴	1	12	yes	—
508	C₂×D₂₁₂	C₂⁴	1	6	yes	—
509	C₂×D₂₁₂	C₂⁴	1	6	yes	—
510	C₂×D₂₁₂	C₂⁴	1	3	yes	—
511	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
512	C₂×C₄×D₅₃	—	2	24	no	—
513	C₂×C₄×D₅₃	—	2	24	no	—
514	C₂×C₄×D₅₃	—	2	24	no	—
515	C₂×C₄×D₅₃	—	2	8	no	—
516	C₂×C₄×D₅₃	—	2	24	no	—
517	C₂×C₄×D₅₃	—	2	24	no	—
518	C₂×C₄×D₅₃	—	2	24	no	—
519	C₂×C₄×D₅₃	—	2	24	no	—
520	C₂×C₄×D₅₃	—	2	24	no	—
521	C₂×C₄×D₅₃	—	2	24	no	—
522	C₂×C₄×D₅₃	—	2	24	no	—
523	C₂×C₄×D₅₃	—	2	12	no	—
524	C₂×C₄×D₅₃	—	4	6	no	—
525	C₂×C₄×D₅₃	C₂×D₄	1	24	yes	complemented
526	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
527	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
528	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
529	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
530	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
531	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
532	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
533	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
534	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
535	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
536	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
537	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
538	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
539	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
540	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
541	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
542	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
543	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
544	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
545	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
546	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
547	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
548	C₂×C₄×D₅₃	C₂⁴	1	3	yes	—
549	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
550	C₂×Dic₁₀₆	—	2	24	no	—
551	C₂×Dic₁₀₆	C₂⁴	1	12	yes	—
552	C₂×Dic₁₀₆	C₂⁴	1	6	yes	—
553	C₂×Dic₁₀₆	C₂⁴	1	3	yes	—
554	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
555	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
556	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
557	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
558	C₄⋊C₄×C₅₃	C₂⁴	1	3	yes	—
559	C₄⋊C₄×C₅₃	C₂⁴	1	6	yes	—
560	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
561	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
562	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
563	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
564	C₂²⋊C₄×C₅₃	C₂⁴	1	6	yes	—
565	C₂²⋊C₄×C₅₃	C₂⁴	1	12	yes	—
566	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
567	C₄²×C₅₃	C₂⁴	1	3	yes	—
568	C₄²×C₅₃	C₂⁴	1	3	yes	—
569	C₄²×C₅₃	C₂⁴	1	3	yes	—
570	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
571	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
572	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
573	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
574	C₂²⋊Dic₅₃	C₂⁴	1	6	yes	—
575	C₂²⋊Dic₅₃	C₂⁴	1	12	yes	—
576	#11719921	C₂⁴	1	2	yes	—
577	#11719921	C₂⁴	1	2	yes	—
578	#11719921	C₂⁴	1	6	yes	—
579	#11719921	C₂⁴	1	6	yes	—
580	#11719921	C₂⁴	1	6	yes	—
581	#11719921	C₂⁴	1	6	yes	—
582	#11719921	C₂⁴	1	6	yes	—
583	#11719921	C₂⁴	1	6	yes	—
584	#11719921	C₂⁴	1	6	yes	—
585	#11719921	C₂⁴	1	6	yes	—
586	#11719921	C₂⁴	1	12	yes	—
587	#11719921	C₂⁴	1	12	yes	—
588	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
589	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
590	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
591	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
592	C₄⋊Dic₅₃	C₂⁴	1	3	yes	—
593	C₄⋊Dic₅₃	C₂⁴	1	6	yes	—
594	#11719919	C₂⁴	1	2	yes	—
595	#11719919	C₂⁴	1	6	yes	—
596	#11719919	C₂⁴	1	6	yes	—
597	#11719919	C₂⁴	1	6	yes	—
598	#11719919	C₂⁴	1	6	yes	—
599	#11719919	C₂⁴	1	6	yes	—
600	#11719919	C₂⁴	1	12	yes	—
601	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
602	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
603	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
604	C₄×Dic₅₃	C₂⁴	1	3	yes	—
605	C₄×Dic₅₃	C₂⁴	1	3	yes	—
606	C₄×Dic₅₃	C₂⁴	1	3	yes	—
607	C₄×Dic₅₃	C₂⁴	1	3	yes	—
608	C₄×Dic₅₃	C₂⁴	1	3	yes	—
609	C₄×Dic₅₃	C₂⁴	1	3	yes	—
610	C₄×Dic₅₃	C₂⁴	1	3	yes	—
611	C₄×Dic₅₃	C₂⁴	1	3	yes	—
612	C₄×Dic₅₃	C₂⁴	1	3	yes	—
613	C₂³×C₅₃	—	2	12	no	—
614	C₂³×C₅₃	—	2	12	no	—
615	C₂³×C₅₃	—	4	6	no	—
616	C₂³×C₅₃	C₂⁵	1	6	yes	—
617	C₂³×C₅₃	C₂⁵	1	3	yes	—
618	C₂³×C₅₃	C₂⁵	1	2	yes	—
619	C₂²×D₅₃	—	2	4	no	—
620	C₂²×D₅₃	—	2	6	no	—
621	C₂²×D₅₃	—	2	6	no	—
622	C₂²×D₅₃	—	2	4	no	—
623	C₂²×D₅₃	—	2	12	no	—
624	C₂²×D₅₃	—	2	12	no	—
625	C₂²×D₅₃	—	2	12	no	—
626	C₂²×D₅₃	—	2	12	no	—
627	C₂²×D₅₃	—	2	12	no	—
628	C₂²×D₅₃	—	2	12	no	—
629	C₂²×D₅₃	—	2	12	no	—
630	C₂²×D₅₃	—	2	12	no	—
631	C₂²×D₅₃	—	2	12	no	—
632	C₂²×D₅₃	—	4	6	no	—
633	C₂²×D₅₃	—	4	6	no	—
634	C₂²×D₅₃	—	4	6	no	—
635	C₂²×D₅₃	—	4	96	no	—
636	C₂²×D₅₃	C₂²×D₄	1	12	yes	—
637	C₂²×D₅₃	C₂×#41	1	8	yes	complemented
638	C₂²×D₅₃	C₂⁵	1	6	yes	—
639	C₂²×D₅₃	C₂⁵	1	3	yes	—
640	C₂²×D₅₃	C₂⁵	1	2	yes	—
641	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
642	Q₈×C₅₃	—	2	12	no	—
643	Q₈×C₅₃	C₂²×D₄	1	4	yes	complemented
644	D₄×C₅₃	—	2	24	no	—
645	D₄×C₅₃	—	2	12	no	—
646	D₄×C₅₃	—	2	12	no	—
647	D₄×C₅₃	—	2	6	no	—
648	D₄×C₅₃	—	4	6	no	—
649	D₄×C₅₃	C₂²×D₄	1	12	yes	complemented
650	D₄×C₅₃	C₂×#41	1	4	yes	complemented
651	C₂×C₄×C₅₃	—	2	12	no	—
652	C₂×C₄×C₅₃	—	2	12	no	—
653	C₂×C₄×C₅₃	—	2	4	no	—
654	C₂×C₄×C₅₃	—	2	12	no	—
655	C₂×C₄×C₅₃	—	2	12	no	—
656	C₂×C₄×C₅₃	—	2	6	no	—
657	C₂×C₄×C₅₃	—	4	3	no	—
658	C₂×C₄×C₅₃	C₂²×D₄	1	12	yes	complemented
659	C₂×C₄×C₅₃	C₂⁵	1	6	yes	—
660	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
661	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
662	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
663	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
664	C₂×C₄×C₅₃	C₂⁵	1	3	yes	—
665	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
666	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
667	C₂²⋊D₅₃	—	2	24	no	—
668	C₂²⋊D₅₃	—	2	12	no	—
669	C₂²⋊D₅₃	—	2	24	no	—
670	C₂²⋊D₅₃	—	2	12	no	—
671	C₂²⋊D₅₃	—	2	24	no	—
672	C₂²⋊D₅₃	—	2	12	no	—
673	C₂²⋊D₅₃	—	4	12	no	—
674	C₂²⋊D₅₃	C₂²×D₄	1	24	yes	complemented
675	C₂²⋊D₅₃	C₂×#41	1	8	yes	complemented
676	C₂×Dic₅₃	—	2	12	no	—
677	C₂×Dic₅₃	—	2	12	no	—
678	C₂×Dic₅₃	—	2	4	no	—
679	C₂×Dic₅₃	—	2	12	no	—
680	C₂×Dic₅₃	—	2	12	no	—
681	C₂×Dic₅₃	—	2	6	no	—
682	C₂×Dic₅₃	—	4	3	no	—
683	C₂×Dic₅₃	C₂²×D₄	1	12	yes	complemented
684	C₂×Dic₅₃	C₂⁵	1	6	yes	—
685	C₂×Dic₅₃	C₂⁵	1	2	yes	—
686	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
687	C₂×Dic₅₃	C₂⁵	1	3	yes	—
688	C₂×Dic₅₃	C₂⁵	1	3	yes	—
689	C₂×Dic₅₃	C₂⁵	1	3	yes	—
690	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
691	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
692	D₂₁₂	—	2	24	no	—
693	D₂₁₂	—	2	12	no	—
694	D₂₁₂	—	2	12	no	—
695	D₂₁₂	—	2	6	no	—
696	D₂₁₂	—	4	6	no	—
697	D₂₁₂	C₂²×D₄	1	12	yes	complemented
698	D₂₁₂	C₂×#41	1	4	yes	complemented
699	C₄×D₅₃	—	2	4	no	—
700	C₄×D₅₃	—	2	12	no	—
701	C₄×D₅₃	—	2	12	no	—
702	C₄×D₅₃	—	2	12	no	—
703	C₄×D₅₃	—	2	6	no	—
704	C₄×D₅₃	—	2	2	no	—
705	C₄×D₅₃	—	2	6	no	—
706	C₄×D₅₃	—	2	4	no	—
707	C₄×D₅₃	—	2	12	no	—
708	C₄×D₅₃	—	2	12	no	—
709	C₄×D₅₃	—	2	12	no	—
710	C₄×D₅₃	—	2	6	no	—
711	C₄×D₅₃	—	2	4	no	—
712	C₄×D₅₃	—	2	12	no	—
713	C₄×D₅₃	—	2	12	no	—
714	C₄×D₅₃	—	2	12	no	—
715	C₄×D₅₃	—	2	6	no	—
716	C₄×D₅₃	—	4	3	no	—
717	C₄×D₅₃	—	4	3	no	—
718	C₄×D₅₃	C₂²×D₄	1	4	yes	—
719	C₄×D₅₃	C₂²×D₄	1	12	yes	—
720	C₄×D₅₃	C₂²×D₄	1	12	yes	complemented
721	C₄×D₅₃	C₂²×D₄	1	12	yes	complemented
722	C₄×D₅₃	C₂×#41	1	4	yes	complemented
723	Dic₁₀₆	—	2	12	no	—
724	Dic₁₀₆	—	2	24	no	—
725	Dic₁₀₆	C₂²×D₄	1	12	yes	complemented
726	C₂×D₄×#41	—	53	1	no	maximal, Sylow
727	C₂²×C₅₃	—	2	2	no	—
728	C₂²×C₅₃	—	2	3	no	—
729	C₂²×C₅₃	—	2	3	no	—
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	2	6	no	—
732	C₂²×C₅₃	—	2	6	no	—
733	C₂²×C₅₃	—	2	6	no	—
734	C₂²×C₅₃	—	4	24	no	—
735	C₂²×C₅₃	C₂³×D₄	1	6	yes	—
736	C₂²×C₅₃	C₂²×#41	1	4	yes	complemented
737	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
738	C₂×D₅₃	—	2	2	no	—
739	C₂×D₅₃	—	2	3	no	—
740	C₂×D₅₃	—	2	3	no	—
741	C₂×D₅₃	—	2	2	no	—
742	C₂×D₅₃	—	2	16	no	—
743	C₂×D₅₃	—	2	24	no	—
744	C₂×D₅₃	—	2	6	no	—
745	C₂×D₅₃	—	2	6	no	—
746	C₂×D₅₃	—	2	6	no	—
747	C₂×D₅₃	—	4	24	no	—
748	C₂×D₅₃	—	4	24	no	—
749	C₂×D₅₃	—	4	24	no	—
750	C₂×D₅₃	—	4	24	no	—
751	C₂×D₅₃	C₂³×D₄	1	6	yes	—
752	C₂×D₅₃	C₂³×D₄	1	2	yes	—
753	C₂×D₅₃	C₂²×#41	1	2	yes	—
754	C₂×D₅₃	C₂²×#41	1	4	yes	complemented
755	C₂×D₅₃	#585	1	2	yes	—
756	C₄×C₅₃	—	2	6	no	—
757	C₄×C₅₃	—	2	2	no	—
758	C₄×C₅₃	—	2	3	no	—
759	C₄×C₅₃	—	2	1	no	—
760	C₄×C₅₃	—	2	3	no	—
761	C₄×C₅₃	C₂³×D₄	1	6	yes	—
762	C₄×C₅₃	C₂³×D₄	1	2	yes	—
763	C₄×C₅₃	C₂²×#41	1	2	yes	complemented
764	Dic₅₃	—	2	6	no	—
765	Dic₅₃	—	2	2	no	—
766	Dic₅₃	—	2	3	no	—
767	Dic₅₃	—	2	1	no	—
768	Dic₅₃	—	2	3	no	—
769	Dic₅₃	C₂³×D₄	1	6	yes	—
770	Dic₅₃	C₂³×D₄	1	2	yes	—
771	Dic₅₃	C₂²×#41	1	2	yes	complemented
772	C₂³×#41	—	53	2	no	—
773	D₄×#41	—	53	2	no	—
774	D₄×#41	—	53	1	no	—
775	D₄×#41	—	53	1	no	—
776	D₄×#41	—	53	2	no	—
777	D₄×#41	—	53	3	no	—
778	D₄×#41	—	53	6	no	—
779	D₄×#41	—	53	3	no	—
780	D₄×#41	—	53	3	no	—
781	D₄×#41	—	53	6	no	—
782	D₄×#41	—	53	1	no	—
783	D₄×#41	—	53	3	no	—
784	D₄×#41	D₅₃	1	1	yes	characteristic, direct product factor
785	C₂×#550	—	53	1	no	—
786	C₂×D₄×Q₈	—	53	1	no	—
787	C₂×#548	—	53	2	no	—
788	C₂×#547	—	53	3	no	—
789	C₂×#546	—	53	6	no	—
790	C₂×D₄²	—	53	3	no	—
791	C₂×#532	—	53	3	no	—
792	C₂×#525	—	53	6	no	—
793	C₂×C₄×#41	—	53	1	no	—
794	C₂²×C₄×D₄	—	53	3	no	—
795	C₂×C₅₃	—	2	4	no	—
796	C₂×C₅₃	—	2	6	no	—
797	C₂×C₅₃	—	4	6	no	—
798	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
799	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
800	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
801	D₅₃	—	2	4	no	—
802	D₅₃	—	2	6	no	—
803	D₅₃	—	4	6	no	—
804	D₅₃	D₄×#41	1	4	yes	direct product factor
805	C₂²×#41	—	53	1	no	—
806	C₂²×#41	—	53	2	no	—
807	C₂²×#41	—	53	6	no	—
808	C₂²×#41	—	53	6	no	—
809	C₂²×#41	—	53	2	no	—
810	C₂²×#41	—	53	2	no	—
811	C₂²×#41	—	53	6	no	—
812	C₂²×#41	—	53	6	no	—
813	C₂²×#41	—	53	2	no	—
814	C₂²×#41	—	53	6	no	—
815	C₂²×#41	—	53	6	no	—
816	C₂²×#41	—	106	32	no	—
817	C₂²×#41	C₂×D₅₃	1	2	yes	complemented
818	C₂³×Q₈	—	53	2	no	—
819	C₂³×D₄	—	53	3	no	—
820	C₂³×D₄	—	53	6	no	—
821	C₂⁴×C₄	—	53	6	no	—
822	#550	—	53	2	no	—
823	#550	—	53	3	no	—
824	#550	—	53	6	no	—
825	#550	—	53	1	no	—
826	#550	—	53	3	no	—
827	#550	C₂×D₅₃	1	1	yes	characteristic, complemented
828	D₄×Q₈	—	53	2	no	—
829	D₄×Q₈	—	53	3	no	—
830	D₄×Q₈	—	53	6	no	—
831	D₄×Q₈	—	53	1	no	—
832	D₄×Q₈	—	53	3	no	—
833	D₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
834	#548	—	53	2	no	—
835	#548	—	53	2	no	—
836	#548	—	53	6	no	—
837	#548	—	53	6	no	—
838	#548	—	53	6	no	—
839	#548	—	53	2	no	—
840	#548	—	53	6	no	—
841	#548	C₂×D₅₃	1	2	yes	complemented
842	#547	—	53	6	no	—
843	#547	—	53	3	no	—
844	#547	—	53	12	no	—
845	#547	—	53	6	no	—
846	#547	—	53	6	no	—
847	#547	—	53	3	no	—
848	#547	—	53	3	no	—
849	#547	—	53	6	no	—
850	#547	C₂×D₅₃	1	3	yes	complemented
851	#546	—	53	6	no	—
852	#546	—	53	6	no	—
853	#546	—	53	6	no	—
854	#546	—	53	12	no	—
855	#546	—	53	6	no	—
856	#546	—	53	6	no	—
857	#546	—	53	12	no	—
858	#546	—	53	12	no	—
859	#546	—	53	6	no	—
860	#546	—	53	6	no	—
861	#546	—	53	12	no	—
862	#546	C₂×D₅₃	1	6	yes	complemented
863	D₄²	—	53	6	no	—
864	D₄²	—	53	6	no	—
865	D₄²	—	53	3	no	—
866	D₄²	—	53	6	no	—
867	D₄²	—	53	6	no	—
868	D₄²	—	53	12	no	—
869	D₄²	—	53	3	no	—
870	D₄²	—	53	3	no	—
871	D₄²	C₂×D₅₃	1	3	yes	complemented
872	#532	—	53	6	no	—
873	#532	—	53	3	no	—
874	#532	—	53	3	no	—
875	#532	—	53	6	no	—
876	#532	—	53	6	no	—
877	#532	—	53	6	no	—
878	#532	—	53	6	no	—
879	#532	—	53	6	no	—
880	#532	—	53	3	no	—
881	#532	C₂×D₅₃	1	3	yes	complemented
882	C₂×C₄⋊Q₈	—	53	3	no	—
883	C₂×#127	—	53	3	no	—
884	C₂×#124	—	53	6	no	—
885	#525	—	53	6	no	—
886	#525	—	53	6	no	—
887	#525	—	53	12	no	—
888	#525	—	53	6	no	—
889	#525	—	53	6	no	—
890	#525	—	53	6	no	—
891	#525	—	53	6	no	—
892	#525	—	53	12	no	—
893	#525	—	53	12	no	—
894	#525	—	53	12	no	—
895	#525	—	53	6	no	—
896	#525	C₂×D₅₃	1	6	yes	complemented
897	C₂×#123	—	53	12	no	—
898	C₂×C₂²⋊Q₈	—	53	6	no	—
899	C₂×C₂²⋊Q₈	—	53	6	no	—
900	C₂×#121	—	53	6	no	—
901	C₂×#121	—	53	6	no	—
902	C₂×#121	—	53	6	no	—
903	C₂×#121	—	53	6	no	—
904	C₂×#120	—	53	12	no	—
905	C₄×#41	—	53	1	no	—
906	C₄×#41	—	53	1	no	—
907	C₄×#41	—	53	1	no	—
908	C₄×#41	—	53	3	no	—
909	C₄×#41	—	53	3	no	—
910	C₄×#41	—	53	3	no	—
911	C₄×#41	—	53	3	no	—
912	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
913	C₂×C₄×Q₈	—	53	1	no	—
914	C₂×C₄×Q₈	—	53	1	no	—
915	C₂×C₄×D₄	—	53	3	no	—
916	C₂×C₄×D₄	—	53	6	no	—
917	C₂×C₄×D₄	—	53	1	no	—
918	C₂×C₄×D₄	—	53	3	no	—
919	C₂×C₄×D₄	—	53	3	no	—
920	C₂×C₄×D₄	—	53	3	no	—
921	C₂×C₄×D₄	—	53	6	no	—
922	C₂×C₄×D₄	—	53	3	no	—
923	C₂×C₄×D₄	—	53	6	no	—
924	C₂×C₄×D₄	—	53	3	no	—
925	C₂×C₄×D₄	—	53	6	no	—
926	C₂×C₄×D₄	—	53	3	no	—
927	C₂×C₄×D₄	—	53	6	no	—
928	C₂×C₄×D₄	—	53	3	no	—
929	C₂×C₄×D₄	—	53	3	no	—
930	C₂×C₄×D₄	—	53	3	no	—
931	C₂×C₄×D₄	—	53	6	no	—
932	C₂×C₄×D₄	—	53	3	no	—
933	C₂×C₄×D₄	—	53	6	no	—
934	C₂×C₄×D₄	—	53	3	no	—
935	C₂×C₄×D₄	C₂×D₅₃	1	3	yes	complemented
936	C₂×#117	—	53	3	no	—
937	C₂²×C₄⋊C₄	—	53	3	no	—
938	C₂²×C₂²⋊C₄	—	53	6	no	—
939	C₂²×C₄²	—	53	3	no	—
940	C₅₃	C₂×D₄×#41	1	1	yes	characteristic, complemented, Sylow
941	C₂⁵	—	53	6	no	—
942	C₂×#41	—	2	16	no	—
943	C₂×#41	—	53	16	no	—
944	C₂×#41	—	53	1	no	—
945	C₂×#41	—	53	6	no	—
946	C₂×#41	—	53	6	no	—
947	C₂×#41	—	53	2	no	—
948	C₂×#41	—	53	3	no	—
949	C₂×#41	—	53	12	no	—
950	C₂×#41	—	53	6	no	—
951	C₂×#41	—	53	6	no	—
952	C₂×#41	—	53	12	no	—
953	C₂×#41	—	53	6	no	—
954	C₂×#41	—	53	3	no	—
955	C₂×#41	—	53	12	no	—
956	C₂×#41	—	53	6	no	—
957	C₂×#41	—	53	6	no	—
958	C₂×#41	—	53	12	no	—
959	C₂×#41	—	53	6	no	—
960	C₂×#41	—	106	48	no	—
961	C₂×#41	—	106	48	no	—
962	C₂×#41	—	106	48	no	—
963	C₂×#41	—	106	48	no	—
964	C₂×#41	—	106	16	no	—
965	C₂×#41	—	106	16	no	—
966	C₂×#41	—	106	16	no	—
967	C₂×#41	—	106	48	no	—
968	C₂×#41	—	106	48	no	—
969	C₂×#41	—	106	16	no	—
970	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
972	C₂×#41	C₂²×D₅₃	1	6	yes	complemented
973	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
974	C₂²×Q₈	—	53	1	no	—
975	C₂²×Q₈	—	53	6	no	—
976	C₂²×Q₈	—	53	6	no	—
977	C₂²×Q₈	—	53	2	no	—
978	C₂²×Q₈	—	53	6	no	—
979	C₂²×Q₈	—	106	16	no	—
980	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
981	C₂²×D₄	—	53	1	no	—
982	C₂²×D₄	—	53	3	no	—
983	C₂²×D₄	—	53	6	no	—
984	C₂²×D₄	—	53	12	no	—
985	C₂²×D₄	—	53	6	no	—
986	C₂²×D₄	—	53	3	no	—
987	C₂²×D₄	—	53	6	no	—
988	C₂²×D₄	—	53	3	no	—
989	C₂²×D₄	—	53	3	no	—
990	C₂²×D₄	—	53	12	no	—
991	C₂²×D₄	—	53	6	no	—
992	C₂²×D₄	—	53	12	no	—
993	C₂²×D₄	—	53	6	no	—
994	C₂²×D₄	—	53	6	no	—
995	C₂²×D₄	—	53	6	no	—
996	C₂²×D₄	—	53	3	no	—
997	C₂²×D₄	—	53	6	no	—
998	C₂²×D₄	—	106	48	no	—
999	C₂²×D₄	—	106	24	no	—
1000	C₂²×D₄	C₂²×D₅₃	1	3	yes	—
1001	C₂²×D₄	C₂²×D₅₃	1	6	yes	complemented
1002	C₂³×C₄	—	53	3	no	—
1003	C₂³×C₄	—	53	6	no	—
1004	C₂³×C₄	—	53	6	no	—
1005	C₂³×C₄	—	53	3	no	—
1006	C₂³×C₄	—	53	2	no	—
1007	C₂³×C₄	—	53	6	no	—
1008	C₂³×C₄	—	53	6	no	—
1009	C₂³×C₄	—	53	6	no	—
1010	C₂³×C₄	—	53	6	no	—
1011	C₂³×C₄	—	53	6	no	—
1012	C₂³×C₄	—	53	6	no	—
1013	C₂³×C₄	—	53	6	no	—
1014	C₂³×C₄	—	53	6	no	—
1015	C₂³×C₄	—	53	6	no	—
1016	C₂³×C₄	—	53	3	no	—
1017	C₂³×C₄	—	106	48	no	—
1018	C₂³×C₄	C₂²×D₅₃	1	6	yes	complemented
1019	C₄⋊Q₈	—	53	6	no	—
1020	C₄⋊Q₈	—	53	6	no	—
1021	C₄⋊Q₈	—	53	6	no	—
1022	C₄⋊Q₈	—	53	3	no	—
1023	C₄⋊Q₈	C₂²×D₅₃	1	3	yes	complemented
1024	#127	—	53	6	no	—
1025	#127	—	53	6	no	—
1026	#127	—	53	6	no	—
1027	#127	—	53	3	no	—
1028	#127	C₂²×D₅₃	1	3	yes	complemented
1029	#124	—	53	6	no	—
1030	#124	—	53	6	no	—
1031	#124	—	53	12	no	—
1032	#124	—	53	12	no	—
1033	#124	—	53	6	no	—
1034	#124	C₂²×D₅₃	1	6	yes	complemented
1035	#123	—	53	12	no	—
1036	#123	—	53	12	no	—
1037	#123	—	53	12	no	—
1038	#123	—	53	12	no	—
1039	#123	—	53	12	no	—
1040	#123	—	53	12	no	—
1041	#123	—	53	12	no	—
1042	#123	C₂²×D₅₃	1	12	yes	complemented
1043	C₂²⋊Q₈	—	53	6	no	—
1044	C₂²⋊Q₈	—	53	6	no	—
1045	C₂²⋊Q₈	—	53	6	no	—
1046	C₂²⋊Q₈	—	53	6	no	—
1047	C₂²⋊Q₈	—	53	12	no	—
1048	C₂²⋊Q₈	—	53	6	no	—
1049	C₂²⋊Q₈	—	53	12	no	—
1050	C₂²⋊Q₈	—	53	6	no	—
1051	C₂²⋊Q₈	—	53	12	no	—
1052	C₂²⋊Q₈	—	53	12	no	—
1053	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1054	C₂²⋊Q₈	C₂²×D₅₃	1	6	yes	complemented
1055	#121	—	53	6	no	—
1056	#121	—	53	12	no	—
1057	#121	—	53	6	no	—
1058	#121	—	53	12	no	—
1059	#121	—	53	6	no	—
1060	#121	—	53	12	no	—
1061	#121	—	53	6	no	—
1062	#121	—	53	12	no	—
1063	#121	—	53	6	no	—
1064	#121	—	53	6	no	—
1065	#121	—	53	6	no	—
1066	#121	—	53	6	no	—
1067	#121	—	53	6	no	—
1068	#121	—	53	6	no	—
1069	#121	—	53	6	no	—
1070	#121	—	53	6	no	—
1071	#121	—	53	12	no	—
1072	#121	—	53	12	no	—
1073	#121	—	53	12	no	—
1074	#121	—	53	12	no	—
1075	#121	C₂²×D₅₃	1	6	yes	complemented
1076	#121	C₂²×D₅₃	1	6	yes	complemented
1077	#121	C₂²×D₅₃	1	6	yes	complemented
1078	#121	C₂²×D₅₃	1	6	yes	complemented
1079	#120	—	53	12	no	—
1080	#120	—	53	12	no	—
1081	#120	—	53	12	no	—
1082	#120	—	53	12	no	—
1083	#120	—	53	12	no	—
1084	#120	—	53	12	no	—
1085	#120	—	53	12	no	—
1086	#120	C₂²×D₅₃	1	12	yes	complemented
1087	C₄×Q₈	—	53	1	no	—
1088	C₄×Q₈	—	53	1	no	—
1089	C₄×Q₈	—	53	3	no	—
1090	C₄×Q₈	—	53	3	no	—
1091	C₄×Q₈	—	53	3	no	—
1092	C₄×Q₈	—	53	3	no	—
1093	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1094	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1095	C₄×D₄	—	53	1	no	—
1096	C₄×D₄	—	53	6	no	—
1097	C₄×D₄	—	53	3	no	—
1098	C₄×D₄	—	53	3	no	—
1099	C₄×D₄	—	53	6	no	—
1100	C₄×D₄	—	53	3	no	—
1101	C₄×D₄	—	53	3	no	—
1102	C₄×D₄	—	53	3	no	—
1103	C₄×D₄	—	53	6	no	—
1104	C₄×D₄	—	53	2	no	—
1105	C₄×D₄	—	53	6	no	—
1106	C₄×D₄	—	53	6	no	—
1107	C₄×D₄	—	53	6	no	—
1108	C₄×D₄	—	53	6	no	—
1109	C₄×D₄	—	53	6	no	—
1110	C₄×D₄	—	53	6	no	—
1111	C₄×D₄	—	53	6	no	—
1112	C₄×D₄	—	53	6	no	—
1113	C₄×D₄	—	53	6	no	—
1114	C₄×D₄	—	53	12	no	—
1115	C₄×D₄	—	53	1	no	—
1116	C₄×D₄	—	53	6	no	—
1117	C₄×D₄	—	53	3	no	—
1118	C₄×D₄	—	53	3	no	—
1119	C₄×D₄	—	53	6	no	—
1120	C₄×D₄	—	53	3	no	—
1121	C₄×D₄	—	53	3	no	—
1122	C₄×D₄	—	53	3	no	—
1123	C₄×D₄	—	53	6	no	—
1124	C₄×D₄	—	53	2	no	—
1125	C₄×D₄	—	53	6	no	—
1126	C₄×D₄	—	53	6	no	—
1127	C₄×D₄	—	53	6	no	—
1128	C₄×D₄	—	53	6	no	—
1129	C₄×D₄	—	53	6	no	—
1130	C₄×D₄	—	53	6	no	—
1131	C₄×D₄	—	53	6	no	—
1132	C₄×D₄	—	53	6	no	—
1133	C₄×D₄	—	53	6	no	—
1134	C₄×D₄	—	53	12	no	—
1135	C₄×D₄	—	53	1	no	—
1136	C₄×D₄	—	53	6	no	—
1137	C₄×D₄	—	53	3	no	—
1138	C₄×D₄	—	53	3	no	—
1139	C₄×D₄	—	53	6	no	—
1140	C₄×D₄	—	53	3	no	—
1141	C₄×D₄	—	53	3	no	—
1142	C₄×D₄	—	53	3	no	—
1143	C₄×D₄	—	53	6	no	—
1144	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1145	C₄×D₄	C₂²×D₅₃	1	3	yes	—
1146	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1147	C₄×D₄	C₂²×D₅₃	1	3	yes	complemented
1148	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1149	C₄×D₄	C₂²×D₅₃	1	3	yes	complemented
1150	C₄×D₄	C₂²×D₅₃	1	3	yes	complemented
1151	C₄×D₄	C₂²×D₅₃	1	3	yes	complemented
1152	C₄×D₄	C₂²×D₅₃	1	6	yes	complemented
1153	#117	—	53	3	no	—
1154	#117	—	53	3	no	—
1155	#117	—	53	3	no	—
1156	#117	—	53	6	no	—
1157	#117	—	53	6	no	—
1158	#117	C₂²×D₅₃	1	3	yes	complemented
1159	C₂×C₄⋊C₄	—	53	6	no	—
1160	C₂×C₄⋊C₄	—	53	3	no	—
1161	C₂×C₄⋊C₄	—	53	1	no	—
1162	C₂×C₄⋊C₄	—	53	3	no	—
1163	C₂×C₄⋊C₄	—	53	6	no	—
1164	C₂×C₄⋊C₄	—	53	6	no	—
1165	C₂×C₄⋊C₄	—	53	3	no	—
1166	C₂×C₄⋊C₄	—	53	3	no	—
1167	C₂×C₄⋊C₄	—	53	3	no	—
1168	C₂×C₄⋊C₄	—	53	3	no	—
1169	C₂×C₄⋊C₄	—	53	6	no	—
1170	C₂×C₄⋊C₄	C₂²×D₅₃	1	3	yes	complemented
1171	C₂×C₂²⋊C₄	—	53	6	no	—
1172	C₂×C₂²⋊C₄	—	53	6	no	—
1173	C₂×C₂²⋊C₄	—	53	6	no	—
1174	C₂×C₂²⋊C₄	—	53	2	no	—
1175	C₂×C₂²⋊C₄	—	53	6	no	—
1176	C₂×C₂²⋊C₄	—	53	6	no	—
1177	C₂×C₂²⋊C₄	—	53	6	no	—
1178	C₂×C₂²⋊C₄	—	53	6	no	—
1179	C₂×C₂²⋊C₄	—	53	6	no	—
1180	C₂×C₂²⋊C₄	—	53	6	no	—
1181	C₂×C₂²⋊C₄	—	53	6	no	—
1182	C₂×C₂²⋊C₄	—	53	6	no	—
1183	C₂×C₂²⋊C₄	—	53	12	no	—
1184	C₂×C₂²⋊C₄	C₂²×D₅₃	1	6	yes	complemented
1185	C₂×C₄²	—	53	3	no	—
1186	C₂×C₄²	—	53	3	no	—
1187	C₂×C₄²	—	53	3	no	—
1188	C₂×C₄²	—	53	3	no	—
1189	C₂×C₄²	—	53	1	no	—
1190	C₂×C₄²	—	53	3	no	—
1191	C₂×C₄²	—	53	3	no	—
1192	C₂×C₄²	—	53	3	no	—
1193	C₂×C₄²	—	53	3	no	—
1194	C₂×C₄²	—	53	3	no	—
1195	C₂×C₄²	—	53	3	no	—
1196	C₂×C₄²	C₂²×D₅₃	1	3	yes	complemented
1197	C₂⁴	—	53	2	no	—
1198	C₂⁴	—	53	3	no	—
1199	C₂⁴	—	53	6	no	—
1200	C₂⁴	—	53	6	no	—
1201	C₂⁴	—	53	6	no	—
1202	C₂⁴	—	53	6	no	—
1203	C₂⁴	—	106	24	no	—
1204	C₂⁴	—	106	24	no	—
1205	C₂⁴	—	212	12	no	—
1206	C₂⁴	C₂³×D₅₃	1	6	yes	—
1207	#41	—	2	8	no	—
1208	#41	—	2	24	no	—
1209	#41	—	2	24	no	—
1210	#41	—	53	8	no	—
1211	#41	—	53	24	no	—
1212	#41	—	53	24	no	—
1213	#41	—	106	48	no	—
1214	#41	—	106	48	no	—
1215	#41	—	106	24	no	—
1216	#41	—	106	24	no	—
1217	#41	—	106	48	no	—
1218	#41	—	106	24	no	—
1219	#41	—	106	24	no	—
1220	#41	—	106	48	no	—
1221	#41	—	106	24	no	—
1222	#41	—	106	24	no	—
1223	#41	—	106	8	no	—
1224	#41	—	106	24	no	—
1225	#41	—	106	24	no	—
1226	#41	D₄×D₅₃	1	8	yes	direct product factor
1227	C₂×Q₈	—	2	8	no	—
1228	C₂×Q₈	—	53	8	no	—
1229	C₂×Q₈	—	53	3	no	—
1230	C₂×Q₈	—	53	12	no	—
1231	C₂×Q₈	—	53	6	no	—
1232	C₂×Q₈	—	106	24	no	—
1233	C₂×Q₈	—	106	24	no	—
1234	C₂×Q₈	—	106	24	no	—
1235	C₂×Q₈	—	106	8	no	—
1236	C₂×Q₈	C₂³×D₅₃	1	6	yes	—
1237	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1238	C₂×D₄	—	2	24	no	—
1239	C₂×D₄	—	2	12	no	—
1240	C₂×D₄	—	53	2	no	—
1241	C₂×D₄	—	53	6	no	—
1242	C₂×D₄	—	53	24	no	—
1243	C₂×D₄	—	53	8	no	—
1244	C₂×D₄	—	53	6	no	—
1245	C₂×D₄	—	53	6	no	—
1246	C₂×D₄	—	53	6	no	—
1247	C₂×D₄	—	53	12	no	—
1248	C₂×D₄	—	53	12	no	—
1249	C₂×D₄	—	53	12	no	—
1250	C₂×D₄	—	53	12	no	—
1251	C₂×D₄	—	53	1	no	—
1252	C₂×D₄	—	53	3	no	—
1253	C₂×D₄	—	53	6	no	—
1254	C₂×D₄	—	53	3	no	—
1255	C₂×D₄	—	53	12	no	—
1256	C₂×D₄	—	53	6	no	—
1257	C₂×D₄	—	53	6	no	—
1258	C₂×D₄	—	106	12	no	—
1259	C₂×D₄	—	106	24	no	—
1260	C₂×D₄	—	106	12	no	—
1261	C₂×D₄	—	106	24	no	—
1262	C₂×D₄	—	106	24	no	—
1263	C₂×D₄	—	106	12	no	—
1264	C₂×D₄	—	106	48	no	—
1265	C₂×D₄	—	106	24	no	—
1266	C₂×D₄	—	106	24	no	—
1267	C₂×D₄	—	106	48	no	—
1268	C₂×D₄	—	106	24	no	—
1269	C₂×D₄	—	106	48	no	—
1270	C₂×D₄	—	106	24	no	—
1271	C₂×D₄	—	106	12	no	—
1272	C₂×D₄	—	212	12	no	—
1273	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1274	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1275	C₂×D₄	C₂³×D₅₃	1	12	yes	—
1276	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1277	C₂×D₄	C₂³×D₅₃	1	6	yes	—
1278	C₂×D₄	C₂³×D₅₃	1	3	yes	—
1279	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1280	C₂²×C₄	—	2	24	no	—
1281	C₂²×C₄	—	53	3	no	—
1282	C₂²×C₄	—	53	24	no	—
1283	C₂²×C₄	—	53	1	no	—
1284	C₂²×C₄	—	53	3	no	—
1285	C₂²×C₄	—	53	3	no	—
1286	C₂²×C₄	—	53	1	no	—
1287	C₂²×C₄	—	53	3	no	—
1288	C₂²×C₄	—	53	3	no	—
1289	C₂²×C₄	—	53	6	no	—
1290	C₂²×C₄	—	53	2	no	—
1291	C₂²×C₄	—	53	6	no	—
1292	C₂²×C₄	—	53	6	no	—
1293	C₂²×C₄	—	53	6	no	—
1294	C₂²×C₄	—	53	3	no	—
1295	C₂²×C₄	—	53	1	no	—
1296	C₂²×C₄	—	53	3	no	—
1297	C₂²×C₄	—	53	3	no	—
1298	C₂²×C₄	—	53	3	no	—
1299	C₂²×C₄	—	53	3	no	—
1300	C₂²×C₄	—	53	2	no	—
1301	C₂²×C₄	—	53	6	no	—
1302	C₂²×C₄	—	53	6	no	—
1303	C₂²×C₄	—	53	6	no	—
1304	C₂²×C₄	—	53	2	no	—
1305	C₂²×C₄	—	53	6	no	—
1306	C₂²×C₄	—	53	6	no	—
1307	C₂²×C₄	—	53	6	no	—
1308	C₂²×C₄	—	53	6	no	—
1309	C₂²×C₄	—	53	6	no	—
1310	C₂²×C₄	—	53	2	no	—
1311	C₂²×C₄	—	53	6	no	—
1312	C₂²×C₄	—	53	3	no	—
1313	C₂²×C₄	—	53	3	no	—
1314	C₂²×C₄	—	106	8	no	—
1315	C₂²×C₄	—	106	24	no	—
1316	C₂²×C₄	—	106	24	no	—
1317	C₂²×C₄	—	106	24	no	—
1318	C₂²×C₄	—	106	24	no	—
1319	C₂²×C₄	—	106	24	no	—
1320	C₂²×C₄	—	106	24	no	—
1321	C₂²×C₄	—	106	24	no	—
1322	C₂²×C₄	—	106	24	no	—
1323	C₂²×C₄	—	106	12	no	—
1324	C₂²×C₄	—	106	24	no	—
1325	C₂²×C₄	—	106	24	no	—
1326	C₂²×C₄	—	106	24	no	—
1327	C₂²×C₄	—	212	6	no	—
1328	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1329	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1330	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1331	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1332	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1333	C₂²×C₄	C₂³×D₅₃	1	6	yes	—
1334	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1335	C₂²×C₄	C₂³×D₅₃	1	3	yes	—
1336	C₄⋊C₄	—	53	2	no	—
1337	C₄⋊C₄	—	53	1	no	—
1338	C₄⋊C₄	—	53	6	no	—
1339	C₄⋊C₄	—	53	3	no	—
1340	C₄⋊C₄	—	53	6	no	—
1341	C₄⋊C₄	—	53	6	no	—
1342	C₄⋊C₄	—	53	6	no	—
1343	C₄⋊C₄	—	53	6	no	—
1344	C₄⋊C₄	—	53	6	no	—
1345	C₄⋊C₄	—	53	3	no	—
1346	C₄⋊C₄	—	53	3	no	—
1347	C₄⋊C₄	—	53	12	no	—
1348	C₄⋊C₄	—	53	6	no	—
1349	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1350	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1351	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1352	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1353	C₄⋊C₄	C₂³×D₅₃	1	3	yes	—
1354	C₄⋊C₄	C₂³×D₅₃	1	6	yes	—
1355	C₂²⋊C₄	—	53	2	no	—
1356	C₂²⋊C₄	—	53	6	no	—
1357	C₂²⋊C₄	—	53	6	no	—
1358	C₂²⋊C₄	—	53	6	no	—
1359	C₂²⋊C₄	—	53	6	no	—
1360	C₂²⋊C₄	—	53	12	no	—
1361	C₂²⋊C₄	—	53	2	no	—
1362	C₂²⋊C₄	—	53	2	no	—
1363	C₂²⋊C₄	—	53	6	no	—
1364	C₂²⋊C₄	—	53	6	no	—
1365	C₂²⋊C₄	—	53	6	no	—
1366	C₂²⋊C₄	—	53	6	no	—
1367	C₂²⋊C₄	—	53	6	no	—
1368	C₂²⋊C₄	—	53	6	no	—
1369	C₂²⋊C₄	—	53	6	no	—
1370	C₂²⋊C₄	—	53	6	no	—
1371	C₂²⋊C₄	—	53	12	no	—
1372	C₂²⋊C₄	—	53	12	no	—
1373	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1374	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1375	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1376	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1377	C₂²⋊C₄	C₂³×D₅₃	1	6	yes	—
1378	C₂²⋊C₄	C₂³×D₅₃	1	12	yes	—
1379	C₄²	—	53	1	no	—
1380	C₄²	—	53	1	no	—
1381	C₄²	—	53	3	no	—
1382	C₄²	—	53	3	no	—
1383	C₄²	—	53	3	no	—
1384	C₄²	—	53	3	no	—
1385	C₄²	—	53	3	no	—
1386	C₄²	—	53	3	no	—
1387	C₄²	—	53	3	no	—
1388	C₄²	—	53	3	no	—
1389	C₄²	—	53	1	no	—
1390	C₄²	—	53	3	no	—
1391	C₄²	C₂³×D₅₃	1	3	yes	—
1392	C₄²	C₂³×D₅₃	1	3	yes	—
1393	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1394	C₄²	C₂³×D₅₃	1	3	yes	—
1395	C₂³	—	2	12	no	—
1396	C₂³	—	2	12	no	—
1397	C₂³	—	4	6	no	—
1398	C₂³	—	53	1	no	—
1399	C₂³	—	53	12	no	—
1400	C₂³	—	53	8	no	—
1401	C₂³	—	53	2	no	—
1402	C₂³	—	53	3	no	—
1403	C₂³	—	53	6	no	—
1404	C₂³	—	106	4	no	—
1405	C₂³	—	106	6	no	—
1406	C₂³	—	106	6	no	—
1407	C₂³	—	106	4	no	—
1408	C₂³	—	106	12	no	—
1409	C₂³	—	106	12	no	—
1410	C₂³	—	106	12	no	—
1411	C₂³	—	106	12	no	—
1412	C₂³	—	106	12	no	—
1413	C₂³	—	106	12	no	—
1414	C₂³	—	106	12	no	—
1415	C₂³	—	106	12	no	—
1416	C₂³	—	106	12	no	—
1417	C₂³	—	212	6	no	—
1418	C₂³	—	212	6	no	—
1419	C₂³	—	212	6	no	—
1420	C₂³	—	212	96	no	—
1421	C₂³	C₂⁴×D₅₃	1	6	yes	—
1422	C₂³	C₂⁴×D₅₃	1	3	yes	—
1423	C₂³	C₂⁴×D₅₃	1	2	yes	—
1424	Q₈	—	2	12	no	—
1425	Q₈	—	53	12	no	—
1426	Q₈	—	106	24	no	—
1427	Q₈	—	106	12	no	—
1428	Q₈	C₂×D₄×D₅₃	1	4	yes	complemented
1429	D₄	—	2	24	no	—
1430	D₄	—	2	12	no	—
1431	D₄	—	2	12	no	—
1432	D₄	—	2	6	no	—
1433	D₄	—	4	6	no	—
1434	D₄	—	53	24	no	—
1435	D₄	—	53	8	no	—
1436	D₄	—	53	12	no	—
1437	D₄	—	53	4	no	—
1438	D₄	—	106	12	no	—
1439	D₄	—	106	24	no	—
1440	D₄	—	106	12	no	—
1441	D₄	—	106	24	no	—
1442	D₄	—	106	12	no	—
1443	D₄	—	106	24	no	—
1444	D₄	—	106	24	no	—
1445	D₄	—	106	12	no	—
1446	D₄	—	106	12	no	—
1447	D₄	—	106	6	no	—
1448	D₄	—	212	6	no	—
1449	D₄	—	212	12	no	—
1450	D₄	C₂×D₄×D₅₃	1	12	yes	complemented
1451	D₄	#41×D₅₃	1	4	yes	direct product factor
1452	C₂×C₄	—	2	12	no	—
1453	C₂×C₄	—	2	4	no	—
1454	C₂×C₄	—	2	12	no	—
1455	C₂×C₄	—	2	12	no	—
1456	C₂×C₄	—	2	12	no	—
1457	C₂×C₄	—	2	6	no	—
1458	C₂×C₄	—	4	3	no	—
1459	C₂×C₄	—	53	12	no	—
1460	C₂×C₄	—	53	1	no	—
1461	C₂×C₄	—	53	1	no	—
1462	C₂×C₄	—	53	3	no	—
1463	C₂×C₄	—	53	4	no	—
1464	C₂×C₄	—	53	12	no	—
1465	C₂×C₄	—	53	12	no	—
1466	C₂×C₄	—	53	12	no	—
1467	C₂×C₄	—	53	4	no	—
1468	C₂×C₄	—	53	1	no	—
1469	C₂×C₄	—	53	3	no	—
1470	C₂×C₄	—	53	3	no	—
1471	C₂×C₄	—	53	2	no	—
1472	C₂×C₄	—	53	6	no	—
1473	C₂×C₄	—	106	4	no	—
1474	C₂×C₄	—	106	12	no	—
1475	C₂×C₄	—	106	12	no	—
1476	C₂×C₄	—	106	12	no	—
1477	C₂×C₄	—	106	6	no	—
1478	C₂×C₄	—	106	4	no	—
1479	C₂×C₄	—	106	12	no	—
1480	C₂×C₄	—	106	12	no	—
1481	C₂×C₄	—	106	12	no	—
1482	C₂×C₄	—	106	6	no	—
1483	C₂×C₄	—	106	2	no	—
1484	C₂×C₄	—	106	6	no	—
1485	C₂×C₄	—	106	4	no	—
1486	C₂×C₄	—	106	12	no	—
1487	C₂×C₄	—	106	12	no	—
1488	C₂×C₄	—	106	12	no	—
1489	C₂×C₄	—	106	6	no	—
1490	C₂×C₄	—	106	12	no	—
1491	C₂×C₄	—	106	4	no	—
1492	C₂×C₄	—	106	12	no	—
1493	C₂×C₄	—	106	12	no	—
1494	C₂×C₄	—	106	12	no	—
1495	C₂×C₄	—	106	6	no	—
1496	C₂×C₄	—	212	3	no	—
1497	C₂×C₄	—	212	3	no	—
1498	C₂×C₄	—	212	3	no	—
1499	C₂×C₄	C₂×D₄×D₅₃	1	12	yes	complemented
1500	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1501	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1502	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1503	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1504	C₂×C₄	C₂⁴×D₅₃	1	6	yes	—
1505	C₂×C₄	C₂⁴×D₅₃	1	3	yes	—
1506	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1507	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1508	C₂²	—	2	2	no	—
1509	C₂²	—	2	3	no	—
1510	C₂²	—	2	3	no	—
1511	C₂²	—	2	2	no	—
1512	C₂²	—	2	6	no	—
1513	C₂²	—	2	6	no	—
1514	C₂²	—	2	6	no	—
1515	C₂²	—	4	24	no	—
1516	C₂²	—	53	2	no	—
1517	C₂²	—	53	2	no	—
1518	C₂²	—	53	2	no	—
1519	C₂²	—	53	6	no	—
1520	C₂²	—	53	4	no	—
1521	C₂²	—	106	16	no	—
1522	C₂²	—	106	24	no	—
1523	C₂²	—	106	2	no	—
1524	C₂²	—	106	3	no	—
1525	C₂²	—	106	3	no	—
1526	C₂²	—	106	2	no	—
1527	C₂²	—	106	6	no	—
1528	C₂²	—	106	6	no	—
1529	C₂²	—	106	6	no	—
1530	C₂²	—	212	24	no	—
1531	C₂²	—	212	24	no	—
1532	C₂²	—	212	24	no	—
1533	C₂²	—	212	24	no	—
1534	C₂²	C₂²×D₄×D₅₃	1	6	yes	—
1535	C₂²	C₂×#41×D₅₃	1	4	yes	complemented
1536	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1537	C₄	—	2	2	no	—
1538	C₄	—	2	6	no	—
1539	C₄	—	2	3	no	—
1540	C₄	—	2	1	no	—
1541	C₄	—	2	3	no	—
1542	C₄	—	53	2	no	—
1543	C₄	—	53	6	no	—
1544	C₄	—	53	2	no	—
1545	C₄	—	106	2	no	—
1546	C₄	—	106	6	no	—
1547	C₄	—	106	3	no	—
1548	C₄	—	106	1	no	—
1549	C₄	—	106	3	no	—
1550	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1551	C₄	C₂²×D₄×D₅₃	1	6	yes	—
1552	C₄	C₂×#41×D₅₃	1	2	yes	complemented
1553	C₂	—	2	4	no	—
1554	C₂	—	2	6	no	—
1555	C₂	—	4	6	no	—
1556	C₂	—	53	4	no	—
1557	C₂	—	106	4	no	—
1558	C₂	—	106	6	no	—
1559	C₂	—	212	6	no	—
1560	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1561	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1562	C₂	#585×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	D₄×#41×C₅₃	C₂
hypercenter	D₄×#41	D₅₃
hypocenter	C₅₃	C₂×D₄×#41
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ D₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₅₃	C₂	semidirect
2. D₄×#11719949	C₂	semidirect
3. #41×D₂₁₂	C₂	semidirect
4. #20288205	C₂	semidirect
5. #20288204	C₂	semidirect
6. D₄×#11719945	C₂	semidirect
7. #20288202	C₂	semidirect
8. #20288201	C₂	semidirect
9. #41×C₂²⋊D₅₃	C₂	semidirect
10. #20288199	C₂	semidirect
11. #20288198	C₂	semidirect
12. D₄×#11719947	C₂	semidirect
13. #550×D₅₃	C₂	semidirect
14. D₄×Q₈×D₅₃	C₂	semidirect
15. #548×D₅₃	C₂	semidirect
16. #547×D₅₃	C₂	semidirect
17. #546×D₅₃	C₂	semidirect
18. D₄²×D₅₃	C₂	semidirect
19. #532×D₅₃	C₂	semidirect
20. #525×D₅₃	C₂	semidirect
21. C₄×#41×D₅₃	C₂	semidirect
22. C₂×C₄×D₄×D₅₃	C₂	semidirect
23. D₄×#41×C₅₃	C₂	semidirect
24. C₂²×#11719949	C₂²	semidirect
25. C₂²×#11719945	C₂²	semidirect
26. C₂²×#11719947	C₂²	semidirect
29. C₂×#41×D₅₃	C₂²	semidirect
30. C₂×#41×D₅₃	C₂²	semidirect
31. C₂×#41×D₅₃	C₂²	semidirect
32. C₂×#41×D₅₃	C₂²	semidirect
33. C₂×#41×D₅₃	C₂²	semidirect
34. C₂×#41×D₅₃	C₂²	semidirect
35. C₂×#41×D₅₃	C₂²	semidirect
36. C₂²×Q₈×D₅₃	C₂²	semidirect
38. C₂²×D₄×D₅₃	C₂²	semidirect
39. C₂³×C₄×D₅₃	C₂²	semidirect
40. #16811295	C₂²	semidirect
41. #16811294	C₂²	semidirect
42. #16811293	C₂²	semidirect
43. #16811292	C₂²	semidirect
44. #16811291	C₂²	semidirect
45. Q₈×D₂₁₂	C₂²	semidirect
46. D₄×Dic₁₀₆	C₂²	semidirect
47. #16811288	C₂²	semidirect
48. Q₈×C₂²⋊D₅₃	C₂²	semidirect
49. #16811286	C₂²	semidirect
50. #16811285	C₂²	semidirect
51. #16811284	C₂²	semidirect
52. #16811283	C₂²	semidirect
53. #16811282	C₂²	semidirect
54. #16811281	C₂²	semidirect
55. #16811280	C₂²	semidirect
56. #16811279	C₂²	semidirect
57. #16811278	C₂²	semidirect
58. #16811277	C₂²	semidirect
59. #16811276	C₂²	semidirect
60. #16811275	C₂²	semidirect
61. #16811274	C₂²	semidirect
62. #16811273	C₂²	semidirect
63. #16811272	C₂²	semidirect
64. #16811271	C₂²	semidirect
65. #16811270	C₂²	semidirect
66. #16811269	C₂²	semidirect
67. #16811268	C₂²	semidirect
68. #16811267	C₂²	semidirect
69. #16811266	C₂²	semidirect
70. #16811265	C₂²	semidirect
71. #16811264	C₂²	semidirect
72. #16811263	C₂²	semidirect
73. #16811262	C₂²	semidirect
74. #16811261	C₂²	semidirect
75. #16811260	C₂²	semidirect
76. D₄×D₂₁₂	C₂²	semidirect
77. D₄×D₂₁₂	C₂²	semidirect
78. #16811258	C₂²	semidirect
79. #16811257	C₂²	semidirect
80. #16811257	C₂²	semidirect
81. D₄×C₂²⋊D₅₃	C₂²	semidirect
82. D₄×C₂²⋊D₅₃	C₂²	semidirect
83. #16811255	C₂²	semidirect
84. #16811174	C₂²	semidirect
85. #16811173	C₂²	semidirect
86. #16811172	C₂²	semidirect
87. #16811171	C₂²	semidirect
88. #16811170	C₂²	semidirect
89. #16811170	C₂²	semidirect
90. #16811169	C₂²	semidirect
91. #16811168	C₂²	semidirect
92. #16811168	C₂²	semidirect
93. C₄⋊Q₈×D₅₃	C₂²	semidirect
94. #127×D₅₃	C₂²	semidirect
95. #124×D₅₃	C₂²	semidirect
96. #16811136	C₂²	semidirect
97. #16811136	C₂²	semidirect
98. #16811135	C₂²	semidirect
99. #16811134	C₂²	semidirect
100. #16811133	C₂²	semidirect
101. #16811133	C₂²	semidirect
102. #16811132	C₂²	semidirect
103. #16811132	C₂²	semidirect
104. #16811131	C₂²	semidirect
105. #16811130	C₂²	semidirect
106. #16811129	C₂²	semidirect
107. #123×D₅₃	C₂²	semidirect
108. C₂²⋊Q₈×D₅₃	C₂²	semidirect
109. C₂²⋊Q₈×D₅₃	C₂²	semidirect
110. #121×D₅₃	C₂²	semidirect
111. #121×D₅₃	C₂²	semidirect
112. #121×D₅₃	C₂²	semidirect
113. #121×D₅₃	C₂²	semidirect
114. #120×D₅₃	C₂²	semidirect
115. #41×Dic₅₃	C₂²	semidirect
116. C₄×#11719949	C₂²	semidirect
117. C₄×#11719949	C₂²	semidirect
118. C₄×#11719945	C₂²	semidirect
119. #16811091	C₂²	semidirect
120. C₄×#11719947	C₂²	semidirect
121. C₄×#11719947	C₂²	semidirect
122. C₄×Q₈×D₅₃	C₂²	semidirect
123. C₄×Q₈×D₅₃	C₂²	semidirect
124. C₂×C₄×D₂₁₂	C₂²	semidirect
125. C₂×D₄×Dic₅₃	C₂²	semidirect
126. C₂×#13133179	C₂²	semidirect
127. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
128. C₂×#13133177	C₂²	semidirect
131. C₄×D₄×D₅₃	C₂²	semidirect
132. C₄×D₄×D₅₃	C₂²	semidirect
133. C₄×D₄×D₅₃	C₂²	semidirect
134. C₄×D₄×D₅₃	C₂²	semidirect
135. C₄×D₄×D₅₃	C₂²	semidirect
136. C₄×D₄×D₅₃	C₂²	semidirect
137. C₄×D₄×D₅₃	C₂²	semidirect
138. C₄×D₄×D₅₃	C₂²	semidirect
139. C₄×D₄×D₅₃	C₂²	semidirect
140. C₄×D₄×D₅₃	C₂²	semidirect
141. C₄×D₄×D₅₃	C₂²	semidirect
142. C₄×D₄×D₅₃	C₂²	semidirect
143. C₄×D₄×D₅₃	C₂²	semidirect
144. #117×D₅₃	C₂²	semidirect
145. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
146. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
147. C₂×C₄²×D₅₃	C₂²	semidirect
148. C₂²×#41×C₅₃	C₂²	semidirect
149. C₅₃×#550	C₂²	semidirect
150. D₄×Q₈×C₅₃	C₂²	semidirect
151. C₅₃×#548	C₂²	semidirect
152. C₅₃×#547	C₂²	semidirect
153. C₅₃×#546	C₂²	semidirect
154. D₄²×C₅₃	C₂²	semidirect
155. C₅₃×#532	C₂²	semidirect
156. C₅₃×#525	C₂²	semidirect
157. C₄×#41×C₅₃	C₂²	semidirect
158. C₂×C₄×D₄×C₅₃	C₂²	semidirect
162. C₂×#11719949	C₂³	semidirect
163. C₂×#11719949	C₂³	semidirect
164. C₂×#11719949	C₂³	semidirect
167. C₂×#11719945	C₂³	semidirect
168. C₂×#11719945	C₂³	semidirect
169. C₂×#11719945	C₂³	semidirect
170. C₂×#11719945	C₂³	semidirect
171. C₂×#11719945	C₂³	semidirect
174. C₂×#11719947	C₂³	semidirect
175. C₂×#11719947	C₂³	semidirect
176. C₂×#11719947	C₂³	semidirect
177. C₂×#11719947	C₂³	semidirect
178. C₂×#11719947	C₂³	semidirect
186. #41×D₅₃	D₄	direct (N × H)
187. C₂²×Dic₁₀₆	C₂³	semidirect
191. C₂×Q₈×D₅₃	C₂³	semidirect
192. C₂×Q₈×D₅₃	C₂³	semidirect
194. C₂²×D₂₁₂	C₂³	semidirect
196. C₂²×C₂²⋊D₅₃	C₂³	semidirect
209. C₂×D₄×D₅₃	C₂³	semidirect
210. C₂×D₄×D₅₃	C₂³	semidirect
211. C₂×D₄×D₅₃	C₂³	semidirect
212. C₂³×Dic₅₃	C₂³	semidirect
222. C₂²×C₄×D₅₃	C₂³	semidirect
223. C₂²×C₄×D₅₃	C₂³	semidirect
224. C₂²×C₄×D₅₃	C₂³	semidirect
225. C₂²×C₄×D₅₃	C₂³	semidirect
226. C₂²×C₄×D₅₃	C₂³	semidirect
227. C₂²×C₄×D₅₃	C₂³	semidirect
228. #13133217	C₂³	semidirect
229. #13133216	C₂³	semidirect
230. #13133216	C₂³	semidirect
231. #13133215	C₂³	semidirect
232. #13133214	C₂³	semidirect
233. #13133213	C₂³	semidirect
234. #13133213	C₂³	semidirect
235. #13133213	C₂³	semidirect
236. #13133206	C₂³	semidirect
237. #13133205	C₂³	semidirect
238. #13133204	C₂³	semidirect
239. #13133203	C₂³	semidirect
240. #13133203	C₂³	semidirect
241. #13133202	C₂³	semidirect
242. #13133202	C₂³	semidirect
243. #13133201	C₂³	semidirect
244. #13133200	C₂³	semidirect
245. #13133199	C₂³	semidirect
246. #13133199	C₂³	semidirect
247. #13133198	C₂³	semidirect
248. #13133197	C₂³	semidirect
249. #13133197	C₂³	semidirect
250. #13133196	C₂³	semidirect
251. #13133196	C₂³	semidirect
252. #13133195	C₂³	semidirect
253. #13133195	C₂³	semidirect
254. #13133194	C₂³	semidirect
255. #13133194	C₂³	semidirect
256. #13133193	C₂³	semidirect
257. #13133193	C₂³	semidirect
258. #13133192	C₂³	semidirect
259. #13133192	C₂³	semidirect
260. #13133192	C₂³	semidirect
261. #13133192	C₂³	semidirect
262. #13133191	C₂³	semidirect
263. #13133191	C₂³	semidirect
264. #13133191	C₂³	semidirect
265. #13133191	C₂³	semidirect
266. #13133190	C₂³	semidirect
267. #13133190	C₂³	semidirect
268. #13133190	C₂³	semidirect
269. #13133190	C₂³	semidirect
270. #13133189	C₂³	semidirect
271. #13133189	C₂³	semidirect
272. #13133189	C₂³	semidirect
273. #13133189	C₂³	semidirect
274. #13133188	C₂³	semidirect
275. #13133188	C₂³	semidirect
276. #13133188	C₂³	semidirect
277. #13133188	C₂³	semidirect
278. #13133187	C₂³	semidirect
279. #13133187	C₂³	semidirect
280. #13133187	C₂³	semidirect
281. #13133186	C₂³	semidirect
282. #13133185	C₂³	semidirect
283. #13133185	C₂³	semidirect
284. #13133185	C₂³	semidirect
285. Q₈×Dic₅₃	C₂³	semidirect
286. Q₈×Dic₅₃	C₂³	semidirect
287. C₄×Dic₁₀₆	C₂³	semidirect
288. C₄×Dic₁₀₆	C₂³	semidirect
289. #13133182	C₂³	semidirect
290. #13133182	C₂³	semidirect
293. C₄×D₂₁₂	C₂³	semidirect
294. C₄×D₂₁₂	C₂³	semidirect
295. C₄×D₂₁₂	C₂³	semidirect
296. C₄×D₂₁₂	C₂³	semidirect
297. C₄×D₂₁₂	C₂³	semidirect
298. C₄×D₂₁₂	C₂³	semidirect
299. C₄×D₂₁₂	C₂³	semidirect
302. D₄×Dic₅₃	C₂³	semidirect
303. D₄×Dic₅₃	C₂³	semidirect
304. D₄×Dic₅₃	C₂³	semidirect
305. D₄×Dic₅₃	C₂³	semidirect
306. D₄×Dic₅₃	C₂³	semidirect
307. D₄×Dic₅₃	C₂³	semidirect
308. D₄×Dic₅₃	C₂³	semidirect
311. #13133179	C₂³	semidirect
312. #13133179	C₂³	semidirect
313. #13133179	C₂³	semidirect
314. #13133179	C₂³	semidirect
315. #13133179	C₂³	semidirect
316. #13133179	C₂³	semidirect
317. #13133179	C₂³	semidirect
320. C₄×C₂²⋊D₅₃	C₂³	semidirect
321. C₄×C₂²⋊D₅₃	C₂³	semidirect
322. C₄×C₂²⋊D₅₃	C₂³	semidirect
323. C₄×C₂²⋊D₅₃	C₂³	semidirect
324. C₄×C₂²⋊D₅₃	C₂³	semidirect
325. C₄×C₂²⋊D₅₃	C₂³	semidirect
326. C₄×C₂²⋊D₅₃	C₂³	semidirect
327. C₄×C₂²⋊D₅₃	C₂³	semidirect
328. C₄×C₂²⋊D₅₃	C₂³	semidirect
331. #13133177	C₂³	semidirect
332. #13133177	C₂³	semidirect
333. #13133177	C₂³	semidirect
334. #13133177	C₂³	semidirect
335. #13133177	C₂³	semidirect
336. #13133177	C₂³	semidirect
337. #13133177	C₂³	semidirect
338. #13133177	C₂³	semidirect
339. #13133177	C₂³	semidirect
340. #13133176	C₂³	semidirect
341. #13133175	C₂³	semidirect
342. #13133175	C₂³	semidirect
343. #13133174	C₂³	semidirect
344. #13133173	C₂³	semidirect
345. C₂×C₄⋊Dic₅₃	C₂³	semidirect
346. C₂×#11719919	C₂³	semidirect
353. C₄⋊C₄×D₅₃	C₂³	semidirect
354. C₄⋊C₄×D₅₃	C₂³	semidirect
355. C₄⋊C₄×D₅₃	C₂³	semidirect
356. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
357. C₂×#11719921	C₂³	semidirect
358. C₂×#11719921	C₂³	semidirect
365. C₂²⋊C₄×D₅₃	C₂³	semidirect
366. C₂²⋊C₄×D₅₃	C₂³	semidirect
367. C₂²⋊C₄×D₅₃	C₂³	semidirect
368. C₂²⋊C₄×D₅₃	C₂³	semidirect
369. C₂×C₄×Dic₅₃	C₂³	semidirect
370. C₂×C₄×Dic₅₃	C₂³	semidirect
371. C₂×C₄×Dic₅₃	C₂³	semidirect
376. C₄²×D₅₃	C₂³	semidirect
377. C₄²×D₅₃	C₂³	semidirect
378. C₄²×D₅₃	C₂³	semidirect
379. C₄²×D₅₃	C₂³	semidirect
382. C₂×#41×C₅₃	C₂³	semidirect
383. C₂×#41×C₅₃	C₂³	semidirect
384. C₂×#41×C₅₃	C₂³	semidirect
385. C₂²×Q₈×C₅₃	C₂³	semidirect
387. C₂²×D₄×C₅₃	C₂³	semidirect
388. C₂³×C₄×C₅₃	C₂³	semidirect
389. C₄⋊Q₈×C₅₃	C₂³	semidirect
390. #127×C₅₃	C₂³	semidirect
391. #124×C₅₃	C₂³	semidirect
392. #123×C₅₃	C₂³	semidirect
393. C₂²⋊Q₈×C₅₃	C₂³	semidirect
394. C₂²⋊Q₈×C₅₃	C₂³	semidirect
395. #121×C₅₃	C₂³	semidirect
396. #121×C₅₃	C₂³	semidirect
397. #121×C₅₃	C₂³	semidirect
398. #121×C₅₃	C₂³	semidirect
399. #120×C₅₃	C₂³	semidirect
400. C₄×Q₈×C₅₃	C₂³	semidirect
401. C₄×Q₈×C₅₃	C₂³	semidirect
404. C₄×D₄×C₅₃	C₂³	semidirect
405. C₄×D₄×C₅₃	C₂³	semidirect
406. C₄×D₄×C₅₃	C₂³	semidirect
407. C₄×D₄×C₅₃	C₂³	semidirect
408. C₄×D₄×C₅₃	C₂³	semidirect
409. C₄×D₄×C₅₃	C₂³	semidirect
410. C₄×D₄×C₅₃	C₂³	semidirect
411. #117×C₅₃	C₂³	semidirect
412. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
413. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
414. C₂×C₄²×C₅₃	C₂³	semidirect
428. #41×C₅₃	C₂×D₄	semidirect
473. #11719949	C₂×D₄	semidirect
477. Q₈×D₅₃	C₂×D₄	semidirect
483. #11719947	C₂×D₄	semidirect
495. D₄×D₅₃	C₂×D₄	semidirect
496. D₄×D₅₃	#41	direct (N × H)
502. #11719945	C₂×D₄	semidirect
525. C₂×C₄×D₅₃	C₂×D₄	semidirect
637. C₂²×D₅₃	C₂×#41	semidirect
643. Q₈×C₅₃	C₂²×D₄	semidirect
649. D₄×C₅₃	C₂²×D₄	semidirect
650. D₄×C₅₃	C₂×#41	semidirect
658. C₂×C₄×C₅₃	C₂²×D₄	semidirect
674. C₂²⋊D₅₃	C₂²×D₄	semidirect
675. C₂²⋊D₅₃	C₂×#41	semidirect
683. C₂×Dic₅₃	C₂²×D₄	semidirect
697. D₂₁₂	C₂²×D₄	semidirect
698. D₂₁₂	C₂×#41	semidirect
720. C₄×D₅₃	C₂²×D₄	semidirect
721. C₄×D₅₃	C₂²×D₄	semidirect
722. C₄×D₅₃	C₂×#41	semidirect
725. Dic₁₀₆	C₂²×D₄	semidirect
736. C₂²×C₅₃	C₂²×#41	semidirect
754. C₂×D₅₃	C₂²×#41	semidirect
763. C₄×C₅₃	C₂²×#41	semidirect
771. Dic₅₃	C₂²×#41	semidirect
784. D₄×#41	D₅₃	direct (N × H)
804. D₅₃	D₄×#41	direct (N × H)
817. C₂²×#41	C₂×D₅₃	semidirect
827. #550	C₂×D₅₃	semidirect
833. D₄×Q₈	C₂×D₅₃	semidirect
841. #548	C₂×D₅₃	semidirect
850. #547	C₂×D₅₃	semidirect
862. #546	C₂×D₅₃	semidirect
871. D₄²	C₂×D₅₃	semidirect
881. #532	C₂×D₅₃	semidirect
896. #525	C₂×D₅₃	semidirect
912. C₄×#41	C₂×D₅₃	semidirect
935. C₂×C₄×D₄	C₂×D₅₃	semidirect
940. C₅₃	C₂×D₄×#41	semidirect
971. C₂×#41	C₂²×D₅₃	semidirect
972. C₂×#41	C₂²×D₅₃	semidirect
973. C₂×#41	C₂²×D₅₃	semidirect
980. C₂²×Q₈	C₂²×D₅₃	semidirect
1001. C₂²×D₄	C₂²×D₅₃	semidirect
1018. C₂³×C₄	C₂²×D₅₃	semidirect
1023. C₄⋊Q₈	C₂²×D₅₃	semidirect
1028. #127	C₂²×D₅₃	semidirect
1034. #124	C₂²×D₅₃	semidirect
1042. #123	C₂²×D₅₃	semidirect
1053. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1054. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1075. #121	C₂²×D₅₃	semidirect
1076. #121	C₂²×D₅₃	semidirect
1077. #121	C₂²×D₅₃	semidirect
1078. #121	C₂²×D₅₃	semidirect
1086. #120	C₂²×D₅₃	semidirect
1093. C₄×Q₈	C₂²×D₅₃	semidirect
1094. C₄×Q₈	C₂²×D₅₃	semidirect
1146. C₄×D₄	C₂²×D₅₃	semidirect
1147. C₄×D₄	C₂²×D₅₃	semidirect
1148. C₄×D₄	C₂²×D₅₃	semidirect
1149. C₄×D₄	C₂²×D₅₃	semidirect
1150. C₄×D₄	C₂²×D₅₃	semidirect
1151. C₄×D₄	C₂²×D₅₃	semidirect
1152. C₄×D₄	C₂²×D₅₃	semidirect
1158. #117	C₂²×D₅₃	semidirect
1170. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1184. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1196. C₂×C₄²	C₂²×D₅₃	semidirect
1226. #41	D₄×D₅₃	direct (N × H)
1428. Q₈	C₂×D₄×D₅₃	semidirect
1450. D₄	C₂×D₄×D₅₃	semidirect
1451. D₄	#41×D₅₃	direct (N × H)
1499. C₂×C₄	C₂×D₄×D₅₃	semidirect
1535. C₂²	C₂×#41×D₅₃	semidirect
1552. C₄	C₂×#41×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#41×D₅₃	2
D₄×#11719949	2
#41×D₂₁₂	2
#20288205	2
#20288204	2
D₄×#11719945	2
#20288202	2
#20288201	2
#41×C₂²⋊D₅₃	2
#20288199	2
#20288198	2
D₄×#11719947	2
#550×D₅₃	2
D₄×Q₈×D₅₃	2
#548×D₅₃	2
#547×D₅₃	2
#546×D₅₃	2
D₄²×D₅₃	2
#532×D₅₃	2
#525×D₅₃	2
C₄×#41×D₅₃	2
C₂×C₄×D₄×D₅₃	2
D₄×#41×C₅₃	2
C₂×D₄×#41	53

Subgroups — D4×#41×D53 #28291045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#41×D₅₃ #28291045