Subgroups — #28292625

Order 13568.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811459	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#11719945	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288391	C₂	1	4	yes	maximal, complemented
4	#20288387	C₂	1	4	yes	maximal, complemented
5	#20288380	C₂	1	4	yes	maximal, complemented
6	#20288376	C₂	1	4	yes	maximal, complemented
7	#20288369	C₂	1	2	yes	maximal, complemented
8	#20288362	C₂	1	2	yes	maximal, complemented
9	#20288357	C₂	1	2	yes	maximal, complemented
10	#20288353	C₂	1	4	yes	maximal, complemented
11	#20288348	C₂	1	2	yes	maximal, complemented
12	#20288344	C₂	1	4	yes	maximal, complemented
13	D₄×#11719945	C₂	1	8	yes	maximal, complemented
14	#20288198	C₂	1	8	yes	maximal, complemented
15	#20288048	C₂	1	1	yes	maximal, characteristic, complemented
16	#20288045	C₂	1	4	yes	maximal, complemented
17	#20288044	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16811134	C₂	1	1	yes	maximal, characteristic, complemented
19	#525×D₅₃	C₂	1	4	yes	maximal, complemented
20	#20287916	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811459	—	2	16	no	—
23	C₂×#13133265	C₂²	1	2	yes	complemented
24	C₂×#13133264	C₂²	1	2	yes	complemented
25	C₂×#13133264	C₂²	1	2	yes	complemented
26	C₂×#13133263	C₂²	1	2	yes	complemented
27	C₂×#13133263	C₂²	1	2	yes	complemented
28	C₂×#13133262	C₂²	1	4	yes	complemented
29	C₂×#13133262	C₂²	1	2	yes	complemented
30	C₂²×#11719945	—	2	16	no	—
31	C₂²×#11719945	C₂²	1	1	yes	characteristic
32	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#11719945	C₂²	1	2	yes	complemented
34	C₂²×#11719945	C₂²	1	2	yes	complemented
35	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
37	C₂²×#11719945	C₂²	1	4	yes	complemented
38	C₂²×#11719945	C₂²	1	4	yes	complemented
39	C₂²×#11719945	C₂²	1	4	yes	complemented
40	C₂²×#11719945	C₂²	1	4	yes	complemented
41	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#11719945	C₂²	1	4	yes	complemented
43	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
44	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
45	C₂³×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
46	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
47	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
48	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
49	#16811294	C₂²	1	8	yes	complemented
50	#16811291	C₂²	1	8	yes	complemented
51	D₄×Dic₁₀₆	C₂²	1	8	yes	complemented
52	#16811286	C₂²	1	8	yes	complemented
53	#16811283	C₂²	1	8	yes	complemented
54	#16811282	C₂²	1	8	yes	complemented
55	#16811282	C₂²	1	8	yes	complemented
56	#16811279	C₂²	1	8	yes	complemented
57	#16811278	C₂²	1	8	yes	complemented
58	#16811275	C₂²	1	8	yes	complemented
59	#16811274	C₂²	1	16	yes	complemented
60	#16811271	C₂²	1	16	yes	complemented
61	#16811270	C₂²	1	8	yes	complemented
62	#16811269	C₂²	1	8	yes	complemented
63	#16811269	C₂²	1	8	yes	complemented
64	#16811265	C₂²	1	16	yes	complemented
65	#16811264	C₂²	1	8	yes	complemented
66	#16811263	C₂²	1	16	yes	complemented
67	#16811263	C₂²	1	16	yes	complemented
68	#16811260	C₂²	1	16	yes	complemented
69	D₄×D₂₁₂	C₂²	1	8	yes	complemented
70	#16811257	C₂²	1	8	yes	complemented
71	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
72	#16811255	C₂²	1	16	yes	complemented
73	#16811204	C₂²	1	4	yes	complemented
74	#16811203	C₂²	1	8	yes	complemented
75	#16811202	C₂²	1	8	yes	complemented
76	#16811201	C₂²	1	4	yes	complemented
77	#16811199	C₂²	1	2	yes	complemented
78	#16811199	C₂²	1	2	yes	complemented
79	#16811197	C₂²	1	2	yes	complemented
80	#16811196	C₂²	1	8	yes	complemented
81	#16811195	C₂²	1	8	yes	complemented
82	#16811194	C₂²	1	2	yes	complemented
83	#16811192	C₂²	1	2	yes	complemented
84	#16811192	C₂²	1	2	yes	complemented
85	#16811190	C₂²	1	2	yes	complemented
86	#16811189	C₂²	1	8	yes	complemented
87	#16811188	C₂²	1	8	yes	complemented
88	#16811187	C₂²	1	2	yes	complemented
89	#16811185	C₂²	1	4	yes	complemented
90	#16811184	C₂²	1	8	yes	complemented
91	#16811183	C₂²	1	8	yes	complemented
92	#16811182	C₂²	1	4	yes	complemented
93	#16811173	C₂²	1	4	yes	complemented
94	#16811170	C₂²	1	16	yes	complemented
95	#16811169	C₂²	1	4	yes	complemented
96	#16811136	C₂²	1	8	yes	complemented
97	#16811135	C₂²	1	4	yes	complemented
98	#16811135	C₂²	1	4	yes	complemented
99	#16811134	C₂²	1	2	yes	complemented
100	#16811134	C₂²	1	2	yes	complemented
101	#16811134	C₂²	1	2	yes	complemented
102	#16811134	C₂²	1	2	yes	complemented
103	#16811134	C₂²	1	4	yes	complemented
104	#16811134	C₂²	1	4	yes	complemented
105	#16811134	C₂²	1	4	yes	complemented
106	#16811133	C₂²	1	8	yes	complemented
107	#16811132	C₂²	1	16	yes	complemented
108	#16811132	C₂²	1	16	yes	complemented
109	#16811131	C₂²	1	8	yes	complemented
110	#16811130	C₂²	1	4	yes	complemented
111	#16811129	C₂²	1	8	yes	complemented
112	C₂×#13133200	C₂²	1	2	yes	complemented
113	#123×D₅₃	C₂²	1	8	yes	complemented
114	C₂×#13133196	C₂²	1	2	yes	complemented
115	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
116	C₂×#13133191	C₂²	1	2	yes	complemented
117	#121×D₅₃	C₂²	1	8	yes	complemented
118	C₂×#13133186	C₂²	1	2	yes	complemented
119	#120×D₅₃	C₂²	1	8	yes	complemented
120	#16811104	C₂²	1	4	yes	complemented
121	#16811103	C₂²	1	4	yes	complemented
122	#16811100	C₂²	1	2	yes	complemented
123	#16811097	C₂²	1	2	yes	complemented
124	#16811096	C₂²	1	4	yes	complemented
125	C₄×#11719945	C₂²	1	4	yes	complemented
126	#16811091	C₂²	1	4	yes	complemented
127	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
128	C₄×D₄×D₅₃	C₂²	1	16	yes	complemented
129	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
130	#117×D₅₃	C₂²	1	4	yes	complemented
131	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#525	C₂²	1	2	yes	complemented
134	C₅₃×#525	C₂²	1	2	yes	complemented
135	C₅₃×#525	C₂²	1	2	yes	complemented
136	C₅₃×#525	C₂²	1	2	yes	complemented
137	C₅₃×#525	C₂²	1	4	yes	complemented
138	C₅₃×#525	C₂²	1	4	yes	complemented
139	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
140	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
141	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
142	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
143	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
144	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₂⁴×D₅₃	C₂³	1	2	yes	—
146	#13133265	—	2	16	no	—
147	#13133264	—	2	16	no	—
148	#13133264	—	2	16	no	—
149	#13133263	—	2	16	no	—
150	#13133263	—	2	16	no	—
151	#13133262	—	2	32	no	—
152	#13133262	—	2	16	no	—
153	C₂×#11719949	C₂³	1	4	yes	complemented
154	C₂×#11719949	C₂³	1	4	yes	complemented
155	C₂×#11719945	—	2	8	no	—
156	C₂×#11719945	—	2	8	no	—
157	C₂×#11719945	—	2	16	no	—
158	C₂×#11719945	—	2	32	no	—
159	C₂×#11719945	—	2	32	no	—
160	C₂×#11719945	—	2	32	no	—
161	C₂×#11719945	—	2	32	no	—
162	C₂×#11719945	—	2	32	no	—
163	C₂×#11719945	—	2	8	no	—
164	C₂×#11719945	—	2	16	no	—
165	C₂×#11719945	—	2	8	no	—
166	C₂×#11719945	D₄	1	16	yes	complemented
167	C₂×#11719945	C₂³	1	8	yes	—
168	C₂×#11719945	C₂³	1	4	yes	—
169	C₂×#11719945	C₂³	1	4	yes	—
170	C₂×#11719945	C₂³	1	8	yes	—
171	C₂×#11719945	C₂³	1	4	yes	—
172	C₂×#11719945	C₂³	1	4	yes	—
173	C₂×#11719945	C₂³	1	8	yes	—
174	C₂×#11719945	C₂³	1	2	yes	—
175	C₂×#11719945	C₂³	1	2	yes	—
176	C₂×#11719945	C₂³	1	2	yes	—
177	C₂×#11719945	C₂³	1	2	yes	—
178	C₂×#11719945	C₂³	1	8	yes	—
179	C₂×#11719945	C₂³	1	2	yes	—
180	C₂×#11719945	C₂³	1	2	yes	—
181	C₂×#11719945	C₂³	1	2	yes	—
182	C₂×#11719945	C₂³	1	2	yes	—
183	C₂×#11719945	C₂³	1	2	yes	—
184	C₂×#11719945	C₂³	1	2	yes	—
185	C₂×#11719945	C₂³	1	4	yes	complemented
186	C₂×#11719945	C₂³	1	8	yes	complemented
187	C₂×#11719945	C₂³	1	4	yes	complemented
188	C₂×#11719945	C₂³	1	8	yes	complemented
189	C₂×#11719945	C₂³	1	2	yes	complemented
190	C₂×#11719945	C₂³	1	2	yes	complemented
191	C₂×#11719947	C₂³	1	8	yes	—
192	C₂×#11719947	C₂³	1	8	yes	complemented
193	C₂×#11719947	C₂³	1	4	yes	complemented
194	C₂×#11719947	C₂³	1	4	yes	complemented
195	#41×D₅₃	—	2	32	no	—
196	#41×D₅₃	—	2	32	no	—
197	C₂²×Dic₁₀₆	—	2	8	no	—
198	C₂²×Dic₁₀₆	C₂³	1	4	yes	—
199	C₂²×Dic₁₀₆	C₂³	1	4	yes	—
200	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
201	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
202	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
203	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
204	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
205	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
206	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
207	C₂²×D₂₁₂	—	2	8	no	—
208	C₂²×D₂₁₂	C₂³	1	4	yes	—
209	C₂²×D₂₁₂	C₂³	1	4	yes	—
210	C₂²×D₂₁₂	C₂³	1	2	yes	—
211	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
212	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
213	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
214	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
215	C₂²×C₂²⋊D₅₃	—	2	16	no	—
216	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
217	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
218	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
219	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
220	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
221	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
222	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
223	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
224	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
225	C₂×D₄×D₅₃	C₂³	1	8	yes	—
226	C₂×D₄×D₅₃	C₂³	1	16	yes	—
227	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
228	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
229	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
230	C₂³×Dic₅₃	C₂³	1	2	yes	—
231	C₂²×C₄×D₅₃	—	2	16	no	—
232	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
233	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
234	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
235	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
236	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
237	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
238	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
239	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
240	#13133217	C₂³	1	4	yes	complemented
241	#13133216	C₂³	1	16	yes	complemented
242	#13133215	C₂³	1	4	yes	complemented
243	#13133214	C₂³	1	4	yes	complemented
244	#13133213	C₂³	1	4	yes	complemented
245	#13133213	C₂³	1	16	yes	complemented
246	#13133206	C₂³	1	4	yes	complemented
247	#13133205	C₂³	1	4	yes	complemented
248	#13133205	C₂³	1	4	yes	complemented
249	#13133204	C₂³	1	4	yes	complemented
250	#13133203	C₂³	1	16	yes	complemented
251	#13133203	C₂³	1	16	yes	complemented
252	#13133202	C₂³	1	16	yes	complemented
253	#13133202	C₂³	1	16	yes	complemented
254	#13133201	C₂³	1	8	yes	—
255	#13133201	C₂³	1	8	yes	complemented
256	#13133200	C₂³	1	4	yes	—
257	#13133200	C₂³	1	4	yes	—
258	#13133200	C₂³	1	8	yes	complemented
259	#13133200	C₂³	1	8	yes	complemented
260	#13133199	C₂³	1	16	yes	complemented
261	#13133199	C₂³	1	16	yes	complemented
262	#13133198	C₂³	1	8	yes	—
263	#13133197	C₂³	1	8	yes	complemented
264	#13133197	C₂³	1	8	yes	complemented
265	#13133196	C₂³	1	4	yes	—
266	#13133196	C₂³	1	4	yes	—
267	#13133196	C₂³	1	8	yes	complemented
268	#13133196	C₂³	1	4	yes	complemented
269	#13133196	C₂³	1	4	yes	complemented
270	#13133195	C₂³	1	16	yes	complemented
271	#13133195	C₂³	1	16	yes	complemented
272	#13133194	C₂³	1	16	yes	—
273	#13133194	C₂³	1	16	yes	complemented
274	#13133193	C₂³	1	8	yes	complemented
275	#13133192	C₂³	1	16	yes	complemented
276	#13133192	C₂³	1	8	yes	complemented
277	#13133192	C₂³	1	8	yes	complemented
278	#13133191	C₂³	1	4	yes	—
279	#13133191	C₂³	1	4	yes	—
280	#13133191	C₂³	1	4	yes	complemented
281	#13133191	C₂³	1	8	yes	complemented
282	#13133191	C₂³	1	16	yes	complemented
283	#13133191	C₂³	1	4	yes	complemented
284	#13133190	C₂³	1	16	yes	complemented
285	#13133190	C₂³	1	16	yes	complemented
286	#13133190	C₂³	1	16	yes	complemented
287	#13133190	C₂³	1	16	yes	complemented
288	#13133189	C₂³	1	16	yes	—
289	#13133189	C₂³	1	16	yes	complemented
290	#13133189	C₂³	1	16	yes	complemented
291	#13133188	C₂³	1	16	yes	complemented
292	#13133188	C₂³	1	8	yes	complemented
293	#13133187	C₂³	1	16	yes	—
294	#13133187	C₂³	1	8	yes	—
295	#13133187	C₂³	1	8	yes	complemented
296	#13133187	C₂³	1	16	yes	complemented
297	#13133186	C₂³	1	4	yes	—
298	#13133186	C₂³	1	4	yes	—
299	#13133186	C₂³	1	8	yes	—
300	#13133186	C₂³	1	8	yes	complemented
301	#13133185	C₂³	1	16	yes	—
302	#13133185	C₂³	1	8	yes	—
303	#13133185	C₂³	1	16	yes	complemented
304	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
305	#13133182	C₂³	1	8	yes	complemented
306	C₄×D₂₁₂	C₂³	1	8	yes	complemented
307	C₄×D₂₁₂	C₂³	1	16	yes	complemented
308	D₄×Dic₅₃	C₂³	1	16	yes	—
309	#13133179	C₂³	1	8	yes	complemented
310	#13133179	C₂³	1	16	yes	complemented
311	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
312	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
313	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
314	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
315	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
316	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
317	#13133177	C₂³	1	16	yes	—
318	#13133177	C₂³	1	16	yes	complemented
319	#13133177	C₂³	1	16	yes	complemented
320	#13133176	C₂³	1	2	yes	—
321	#13133176	C₂³	1	2	yes	—
322	#13133176	C₂³	1	2	yes	complemented
323	#13133176	C₂³	1	2	yes	complemented
324	#13133175	C₂³	1	8	yes	complemented
325	#13133174	C₂³	1	8	yes	complemented
326	#13133173	C₂³	1	8	yes	—
327	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
328	C₂×#11719919	C₂³	1	4	yes	complemented
329	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
330	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
331	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
332	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
333	C₂×#11719921	C₂³	1	4	yes	complemented
334	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
335	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
336	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
337	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
338	C₄²×D₅₃	C₂³	1	8	yes	complemented
339	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×#41×C₅₃	—	2	8	no	—
341	C₂×#41×C₅₃	C₂³	1	2	yes	—
342	C₂×#41×C₅₃	C₂³	1	2	yes	—
343	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
344	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
345	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
346	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
347	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
348	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
349	C₂³×C₄×C₅₃	—	2	8	no	—
350	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
351	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
352	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
354	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
355	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
361	#123×C₅₃	C₂³	1	4	yes	—
362	#123×C₅₃	C₂³	1	4	yes	—
363	#123×C₅₃	C₂³	1	8	yes	complemented
364	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
365	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
366	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
367	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
368	#121×C₅₃	C₂³	1	4	yes	—
369	#121×C₅₃	C₂³	1	4	yes	—
370	#121×C₅₃	C₂³	1	4	yes	complemented
371	#121×C₅₃	C₂³	1	4	yes	complemented
372	#120×C₅₃	C₂³	1	4	yes	—
373	#120×C₅₃	C₂³	1	4	yes	—
374	#120×C₅₃	C₂³	1	8	yes	—
375	C₄×D₄×C₅₃	C₂³	1	8	yes	—
376	C₄×D₄×C₅₃	C₂³	1	8	yes	—
377	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
378	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
379	#117×C₅₃	C₂³	1	2	yes	—
380	#117×C₅₃	C₂³	1	2	yes	—
381	#117×C₅₃	C₂³	1	2	yes	complemented
382	#117×C₅₃	C₂³	1	2	yes	complemented
383	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
384	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
385	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
386	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
387	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
388	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
389	C₂⁴×C₅₃	—	2	4	no	—
390	C₂⁴×C₅₃	—	4	4	no	—
391	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
393	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
394	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
395	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂³×D₅₃	—	2	8	no	—
398	C₂³×D₅₃	—	4	8	no	—
399	C₂³×D₅₃	C₂⁴	1	8	yes	—
400	C₂³×D₅₃	C₂⁴	1	8	yes	—
401	C₂³×D₅₃	C₂⁴	1	2	yes	—
402	C₂³×D₅₃	C₂⁴	1	2	yes	—
403	C₂³×D₅₃	C₂⁴	1	2	yes	—
404	#41×C₅₃	—	2	8	no	—
405	#41×C₅₃	—	2	8	no	—
406	#41×C₅₃	—	2	8	no	—
407	#41×C₅₃	—	2	8	no	—
408	C₂×Q₈×C₅₃	—	2	4	no	—
409	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
410	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
411	C₂×D₄×C₅₃	—	2	8	no	—
412	C₂×D₄×C₅₃	—	2	4	no	—
413	C₂×D₄×C₅₃	—	4	8	no	—
414	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
415	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
416	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
417	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
418	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
419	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
420	C₂²×C₄×C₅₃	—	2	4	no	—
421	C₂²×C₄×C₅₃	—	2	4	no	—
422	C₂²×C₄×C₅₃	—	2	4	no	—
423	C₂²×C₄×C₅₃	—	2	4	no	—
424	C₂²×C₄×C₅₃	—	2	4	no	—
425	C₂²×C₄×C₅₃	—	2	8	no	—
426	C₂²×C₄×C₅₃	—	2	8	no	—
427	C₂²×C₄×C₅₃	—	2	8	no	—
428	C₂²×C₄×C₅₃	—	2	8	no	—
429	C₂²×C₄×C₅₃	—	2	8	no	—
430	C₂²×C₄×C₅₃	C₂×D₄	1	8	yes	complemented
431	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
432	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
433	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
434	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
435	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
436	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
437	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
438	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
439	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
440	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
441	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
442	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
443	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
446	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
447	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂×C₂²⋊D₅₃	—	2	8	no	—
454	C₂×C₂²⋊D₅₃	—	2	8	no	—
455	C₂×C₂²⋊D₅₃	—	2	8	no	—
456	C₂×C₂²⋊D₅₃	—	2	32	no	—
457	C₂×C₂²⋊D₅₃	—	2	32	no	—
458	C₂×C₂²⋊D₅₃	—	2	32	no	—
459	C₂×C₂²⋊D₅₃	—	2	8	no	—
460	C₂×C₂²⋊D₅₃	—	4	8	no	—
461	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
462	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
463	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
464	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
465	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
466	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
467	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
468	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
469	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
470	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
471	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
472	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
473	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
474	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
475	C₂²×Dic₅₃	—	2	8	no	—
476	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
477	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
478	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
479	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
480	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
481	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
482	#11719949	—	2	16	no	—
483	#11719949	—	2	16	no	—
484	Q₈×D₅₃	—	2	16	no	—
485	Q₈×D₅₃	—	2	16	no	—
486	#11719947	—	2	32	no	—
487	#11719947	—	2	32	no	—
488	#11719947	—	2	16	no	—
489	#11719947	—	2	16	no	—
490	D₄×D₅₃	—	2	32	no	—
491	D₄×D₅₃	—	2	32	no	—
492	D₄×D₅₃	—	2	16	no	—
493	D₄×D₅₃	—	2	16	no	—
494	D₄×D₅₃	—	4	32	no	—
495	#11719945	—	2	8	no	—
496	#11719945	—	2	8	no	—
497	#11719945	—	2	8	no	—
498	#11719945	—	2	8	no	—
499	#11719945	—	2	8	no	—
500	#11719945	—	2	8	no	—
501	#11719945	—	2	8	no	—
502	#11719945	—	2	8	no	—
503	#11719945	—	2	32	no	—
504	#11719945	—	2	32	no	—
505	#11719945	—	2	32	no	—
506	#11719945	—	2	16	no	—
507	#11719945	—	2	16	no	—
508	#11719945	—	2	16	no	—
509	#11719945	—	2	32	no	—
510	#11719945	—	2	32	no	—
511	#11719945	—	2	32	no	—
512	#11719945	—	2	16	no	—
513	#11719945	—	2	16	no	—
514	#11719945	—	2	16	no	—
515	#11719945	C₂×D₄	1	16	yes	complemented
516	#11719945	C₂×D₄	1	16	yes	complemented
517	#11719945	C₂×D₄	1	16	yes	complemented
518	#11719945	C₂×D₄	1	16	yes	complemented
519	C₂×D₂₁₂	—	2	8	no	—
520	C₂×D₂₁₂	—	2	4	no	—
521	C₂×D₂₁₂	—	2	4	no	—
522	C₂×D₂₁₂	—	2	16	no	—
523	C₂×D₂₁₂	—	2	16	no	—
524	C₂×D₂₁₂	—	2	16	no	—
525	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
526	C₂×D₂₁₂	C₂⁴	1	8	yes	—
527	C₂×D₂₁₂	C₂⁴	1	8	yes	—
528	C₂×D₂₁₂	C₂⁴	1	2	yes	—
529	C₂×D₂₁₂	C₂⁴	1	2	yes	—
530	C₂×D₂₁₂	C₂⁴	1	2	yes	—
531	C₂×D₂₁₂	C₂⁴	1	2	yes	—
532	C₂×D₂₁₂	C₂⁴	1	16	yes	—
533	C₂×D₂₁₂	C₂⁴	1	2	yes	—
534	C₂×D₂₁₂	C₂⁴	1	2	yes	—
535	C₂×C₄×D₅₃	—	2	8	no	—
536	C₂×C₄×D₅₃	—	2	8	no	—
537	C₂×C₄×D₅₃	—	2	8	no	—
538	C₂×C₄×D₅₃	—	2	8	no	—
539	C₂×C₄×D₅₃	—	2	32	no	—
540	C₂×C₄×D₅₃	—	2	32	no	—
541	C₂×C₄×D₅₃	—	2	32	no	—
542	C₂×C₄×D₅₃	C₂×D₄	1	16	yes	complemented
543	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
544	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
545	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
546	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
547	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
548	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
549	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
550	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
551	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
552	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
553	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
554	C₂×Dic₁₀₆	—	2	4	no	—
555	C₂×Dic₁₀₆	—	2	4	no	—
556	C₂×Dic₁₀₆	—	2	8	no	—
557	C₂×Dic₁₀₆	—	2	16	no	—
558	C₂×Dic₁₀₆	—	2	16	no	—
559	C₂×Dic₁₀₆	—	2	16	no	—
560	C₂×Dic₁₀₆	C₂×D₄	1	8	yes	complemented
561	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
562	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
563	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
564	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
565	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
566	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
567	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
568	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
569	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
570	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
571	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
572	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
573	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
574	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
575	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
576	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
577	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
578	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
579	C₄²×C₅₃	C₂⁴	1	4	yes	—
580	C₄²×C₅₃	C₂⁴	1	4	yes	—
581	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
582	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
583	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
584	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
585	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
586	#11719921	C₂⁴	1	16	yes	—
587	#11719921	C₂⁴	1	16	yes	—
588	#11719921	C₂⁴	1	16	yes	—
589	#11719921	C₂⁴	1	8	yes	—
590	#11719921	C₂⁴	1	16	yes	—
591	#11719921	C₂⁴	1	8	yes	—
592	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
593	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
594	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
595	#11719919	C₂⁴	1	8	yes	—
596	#11719919	C₂⁴	1	16	yes	—
597	#11719919	C₂⁴	1	16	yes	—
598	#11719919	C₂⁴	1	8	yes	—
599	C₄×Dic₅₃	C₂⁴	1	4	yes	—
600	C₄×Dic₅₃	C₂⁴	1	16	yes	—
601	C₄×Dic₅₃	C₂⁴	1	4	yes	—
602	C₂³×C₅₃	—	2	2	no	—
603	C₂³×C₅₃	—	2	4	no	—
604	C₂³×C₅₃	—	2	4	no	—
605	C₂³×C₅₃	—	2	4	no	—
606	C₂³×C₅₃	—	2	2	no	—
607	C₂³×C₅₃	—	2	4	no	—
608	C₂³×C₅₃	—	2	4	no	—
609	C₂³×C₅₃	—	2	4	no	—
610	C₂³×C₅₃	—	4	2	no	—
611	C₂³×C₅₃	—	4	2	no	—
612	C₂³×C₅₃	—	4	2	no	—
613	C₂³×C₅₃	—	4	2	no	—
614	C₂³×C₅₃	—	4	4	no	—
615	C₂³×C₅₃	—	4	16	no	—
616	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
617	C₂³×C₅₃	C₂⁵	1	4	yes	—
618	C₂³×C₅₃	C₂⁵	1	2	yes	—
619	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
620	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
621	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
622	C₂³×C₅₃	C₂⁵	1	2	yes	—
623	C₂²×D₅₃	—	2	4	no	—
624	C₂²×D₅₃	—	2	16	no	—
625	C₂²×D₅₃	—	2	4	no	—
626	C₂²×D₅₃	—	2	16	no	—
627	C₂²×D₅₃	—	2	16	no	—
628	C₂²×D₅₃	—	4	4	no	—
629	C₂²×D₅₃	—	4	8	no	—
630	C₂²×D₅₃	—	4	4	no	—
631	C₂²×D₅₃	—	4	16	no	—
632	C₂²×D₅₃	—	4	4	no	—
633	C₂²×D₅₃	—	4	32	no	—
634	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
635	C₂²×D₅₃	C₂⁵	1	4	yes	—
636	C₂²×D₅₃	C₂⁵	1	4	yes	—
637	C₂²×D₅₃	C₂⁵	1	4	yes	—
638	Q₈×C₅₃	—	2	4	no	—
639	Q₈×C₅₃	—	2	4	no	—
640	D₄×C₅₃	—	2	8	no	—
641	D₄×C₅₃	—	2	8	no	—
642	D₄×C₅₃	—	2	16	no	—
643	D₄×C₅₃	—	2	4	no	—
644	D₄×C₅₃	—	2	4	no	—
645	D₄×C₅₃	—	4	8	no	—
646	C₂×C₄×C₅₃	—	2	2	no	—
647	C₂×C₄×C₅₃	—	2	2	no	—
648	C₂×C₄×C₅₃	—	2	4	no	—
649	C₂×C₄×C₅₃	—	2	4	no	—
650	C₂×C₄×C₅₃	—	2	4	no	—
651	C₂×C₄×C₅₃	—	2	4	no	—
652	C₂×C₄×C₅₃	—	2	4	no	—
653	C₂×C₄×C₅₃	—	2	8	no	—
654	C₂×C₄×C₅₃	—	2	4	no	—
655	C₂×C₄×C₅₃	—	2	4	no	—
656	C₂×C₄×C₅₃	—	2	8	no	—
657	C₂×C₄×C₅₃	—	2	4	no	—
658	C₂×C₄×C₅₃	—	2	4	no	—
659	C₂×C₄×C₅₃	—	2	4	no	—
660	C₂×C₄×C₅₃	—	2	4	no	—
661	C₂×C₄×C₅₃	—	4	4	no	—
662	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
663	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
664	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
665	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
666	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
667	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
668	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
669	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
670	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
671	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
672	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
673	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
674	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
675	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
676	C₂²⋊D₅₃	—	2	8	no	—
677	C₂²⋊D₅₃	—	2	8	no	—
678	C₂²⋊D₅₃	—	2	8	no	—
679	C₂²⋊D₅₃	—	2	8	no	—
680	C₂²⋊D₅₃	—	2	16	no	—
681	C₂²⋊D₅₃	—	2	16	no	—
682	C₂²⋊D₅₃	—	2	16	no	—
683	C₂²⋊D₅₃	—	2	16	no	—
684	C₂²⋊D₅₃	—	2	16	no	—
685	C₂²⋊D₅₃	—	4	16	no	—
686	C₂²⋊D₅₃	—	4	8	no	—
687	C₂²⋊D₅₃	C₂²×D₄	1	16	yes	—
688	C₂²⋊D₅₃	C₂²×D₄	1	16	yes	—
689	C₂×Dic₅₃	—	2	4	no	—
690	C₂×Dic₅₃	—	2	4	no	—
691	C₂×Dic₅₃	—	2	16	no	—
692	C₂×Dic₅₃	—	2	16	no	—
693	C₂×Dic₅₃	—	4	4	no	—
694	C₂×Dic₅₃	C₂²×D₄	1	8	yes	—
695	C₂×Dic₅₃	C₂⁵	1	4	yes	—
696	C₂×Dic₅₃	C₂⁵	1	4	yes	—
697	C₂×Dic₅₃	C₂⁵	1	8	yes	—
698	C₂×Dic₅₃	C₂⁵	1	4	yes	—
699	D₂₁₂	—	2	16	no	—
700	D₂₁₂	—	2	16	no	—
701	D₂₁₂	—	2	4	no	—
702	D₂₁₂	—	2	4	no	—
703	D₂₁₂	—	2	4	no	—
704	D₂₁₂	—	2	4	no	—
705	D₂₁₂	—	4	16	no	—
706	D₂₁₂	C₂²×D₄	1	8	yes	—
707	D₂₁₂	C₂²×D₄	1	8	yes	—
708	C₄×D₅₃	—	2	16	no	—
709	C₄×D₅₃	—	2	16	no	—
710	C₄×D₅₃	—	2	8	no	—
711	C₄×D₅₃	—	2	8	no	—
712	C₄×D₅₃	—	2	8	no	—
713	C₄×D₅₃	—	2	8	no	—
714	C₄×D₅₃	—	2	16	no	—
715	C₄×D₅₃	—	2	16	no	—
716	C₄×D₅₃	—	4	16	no	—
717	C₄×D₅₃	C₂²×D₄	1	16	yes	—
718	C₄×D₅₃	C₂²×D₄	1	16	yes	—
719	Dic₁₀₆	—	2	4	no	—
720	Dic₁₀₆	—	2	4	no	—
721	Dic₁₀₆	—	2	4	no	—
722	Dic₁₀₆	—	2	4	no	—
723	Dic₁₀₆	—	2	16	no	—
724	Dic₁₀₆	—	2	16	no	—
725	Dic₁₀₆	C₂²×D₄	1	8	yes	—
726	Dic₁₀₆	C₂²×D₄	1	8	yes	—
727	#62811	—	53	1	no	maximal, Sylow
728	C₂²×C₅₃	—	2	8	no	—
729	C₂²×C₅₃	—	2	2	no	—
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	2	2	no	—
732	C₂²×C₅₃	—	2	2	no	—
733	C₂²×C₅₃	—	2	2	no	—
734	C₂²×C₅₃	—	2	4	no	—
735	C₂²×C₅₃	—	2	2	no	—
736	C₂²×C₅₃	—	2	2	no	—
737	C₂²×C₅₃	—	2	8	no	—
738	C₂²×C₅₃	—	2	2	no	—
739	C₂²×C₅₃	—	4	4	no	—
740	C₂²×C₅₃	—	4	8	no	—
741	C₂²×C₅₃	—	4	8	no	—
742	C₂²×C₅₃	—	4	4	no	—
743	C₂²×C₅₃	—	8	4	no	—
744	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
745	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
746	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
747	C₂²×C₅₃	#585	1	4	yes	complemented
748	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
749	C₂×D₅₃	—	2	8	no	—
750	C₂×D₅₃	—	2	4	no	—
751	C₂×D₅₃	—	2	4	no	—
752	C₂×D₅₃	—	2	8	no	—
753	C₂×D₅₃	—	2	8	no	—
754	C₂×D₅₃	—	4	8	no	—
755	C₂×D₅₃	—	4	32	no	—
756	C₂×D₅₃	—	4	8	no	—
757	C₂×D₅₃	—	8	16	no	—
758	C₂×D₅₃	—	8	4	no	—
759	C₂×D₅₃	C₂³×D₄	1	8	yes	—
760	C₄×C₅₃	—	2	2	no	—
761	C₄×C₅₃	—	2	4	no	—
762	C₄×C₅₃	—	2	2	no	—
763	C₄×C₅₃	—	2	8	no	—
764	C₄×C₅₃	C₂³×D₄	1	2	yes	—
765	C₄×C₅₃	C₂³×D₄	1	2	yes	—
766	C₄×C₅₃	C₂³×D₄	1	2	yes	—
767	C₄×C₅₃	C₂³×D₄	1	2	yes	—
768	Dic₅₃	—	2	4	no	—
769	Dic₅₃	—	2	4	no	—
770	Dic₅₃	—	2	8	no	—
771	Dic₅₃	C₂³×D₄	1	8	yes	—
772	C₂×#585	—	53	1	no	—
773	C₂³×#41	—	53	1	no	—
774	#3489	—	53	4	no	—
775	#3489	—	53	4	no	—
776	#3488	—	53	4	no	—
777	#3488	—	53	4	no	—
778	#3487	—	53	2	no	—
779	#3486	—	53	2	no	—
780	#3485	—	53	2	no	—
781	#3485	—	53	4	no	—
782	#3484	—	53	2	no	—
783	#3484	—	53	4	no	—
784	D₄×#41	—	53	8	no	—
785	D₄×#41	—	53	8	no	—
786	#3449	—	53	1	no	—
787	#3449	—	53	4	no	—
788	#3449	—	53	1	no	—
789	C₂×#525	—	53	1	no	—
790	C₂×#525	—	53	4	no	—
791	C₂×#525	D₅₃	1	1	yes	characteristic, complemented
792	#3428	—	53	1	no	—
793	C₂×C₅₃	—	2	2	no	—
794	C₂×C₅₃	—	2	4	no	—
795	C₂×C₅₃	—	2	2	no	—
796	C₂×C₅₃	—	2	2	no	—
797	C₂×C₅₃	—	4	4	no	—
798	C₂×C₅₃	—	4	2	no	—
799	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
800	C₂×C₅₃	C₂×#585	1	2	yes	—
801	D₅₃	—	2	8	no	—
802	D₅₃	—	4	4	no	—
803	D₅₃	—	4	4	no	—
804	#585	—	106	16	no	—
805	C₂×2₋¹⁺⁴	—	53	2	no	—
806	C₂×2₋¹⁺⁴	—	53	2	no	—
807	C₂×2₋¹⁺⁴	—	53	2	no	—
808	C₂×H(5,𝔽₂)	—	53	2	no	—
809	C₂×H(5,𝔽₂)	—	53	2	no	—
810	C₂×H(5,𝔽₂)	—	53	4	no	—
811	C₂×H(5,𝔽₂)	—	53	2	no	—
812	C₂²×#41	—	53	4	no	—
813	C₂²×#41	—	53	4	no	—
814	C₂²×#41	—	53	1	no	—
815	C₂²×#41	—	53	2	no	—
816	C₂²×#41	—	53	1	no	—
817	C₂²×#41	—	53	4	no	—
818	C₂²×#41	—	53	4	no	—
819	C₂²×#41	—	53	1	no	—
820	C₂²×#41	—	53	2	no	—
821	C₂²×#41	—	53	1	no	—
822	C₂²×#41	—	53	4	no	—
823	C₂²×#41	—	53	4	no	—
824	C₂²×#41	—	53	1	no	—
825	C₂²×#41	—	53	4	no	—
826	C₂²×#41	—	106	16	no	—
827	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
828	C₂³×Q₈	—	53	1	no	—
829	C₂³×D₄	—	53	2	no	—
830	C₂³×D₄	—	53	1	no	—
831	C₂⁴×C₄	—	53	2	no	—
832	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
833	#550	—	53	8	no	—
834	#550	—	53	8	no	—
835	D₄×Q₈	—	53	8	no	—
836	D₄×Q₈	—	53	8	no	—
837	#548	—	53	8	no	—
838	#548	—	53	8	no	—
839	#548	—	53	8	no	—
840	#548	—	53	8	no	—
841	#547	—	53	16	no	—
842	#547	—	53	8	no	—
843	#547	—	53	8	no	—
844	#547	—	53	16	no	—
845	#546	—	53	16	no	—
846	#546	—	53	8	no	—
847	#546	—	53	8	no	—
848	#546	—	53	16	no	—
849	#546	—	53	8	no	—
850	#546	—	53	8	no	—
851	#546	—	53	16	no	—
852	#546	—	53	16	no	—
853	D₄²	—	53	16	no	—
854	D₄²	—	53	8	no	—
855	D₄²	—	53	16	no	—
856	D₄²	—	53	8	no	—
857	#537	—	53	4	no	—
858	#537	—	53	8	no	—
859	#537	—	53	8	no	—
860	#537	—	53	4	no	—
861	#536	—	53	2	no	—
862	#536	—	53	2	no	—
863	#536	—	53	8	no	—
864	#536	—	53	8	no	—
865	#536	—	53	2	no	—
866	#536	—	53	2	no	—
867	#535	—	53	2	no	—
868	#535	—	53	2	no	—
869	#535	—	53	8	no	—
870	#535	—	53	8	no	—
871	#535	—	53	2	no	—
872	#535	—	53	2	no	—
873	#534	—	53	4	no	—
874	#534	—	53	8	no	—
875	#534	—	53	8	no	—
876	#534	—	53	4	no	—
877	#532	—	53	4	no	—
878	#532	—	53	16	no	—
879	#532	—	53	4	no	—
880	#525	—	53	4	no	—
881	#525	—	53	2	no	—
882	#525	—	53	2	no	—
883	#525	—	53	4	no	—
884	#525	—	53	2	no	—
885	#525	—	53	2	no	—
886	#525	—	53	4	no	—
887	#525	—	53	4	no	—
888	#525	—	53	8	no	—
889	#525	—	53	8	no	—
890	#525	—	53	8	no	—
891	#525	—	53	8	no	—
892	#525	—	53	16	no	—
893	#525	—	53	16	no	—
894	#525	—	53	4	no	—
895	#525	—	53	4	no	—
896	#525	C₂×D₅₃	1	2	yes	complemented
897	#525	C₂×D₅₃	1	2	yes	complemented
898	#525	C₂×D₅₃	1	2	yes	complemented
899	#525	C₂×D₅₃	1	2	yes	complemented
900	#525	C₂×D₅₃	1	4	yes	complemented
901	#525	C₂×D₅₃	1	4	yes	complemented
902	C₂×#123	—	53	2	no	—
903	C₂×#123	—	53	8	no	—
904	C₂×#123	C₂×D₅₃	1	2	yes	complemented
905	C₂×C₂²⋊Q₈	—	53	2	no	—
906	C₂×C₂²⋊Q₈	—	53	8	no	—
907	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
908	C₂×#121	—	53	2	no	—
909	C₂×#121	—	53	8	no	—
910	C₂×#121	C₂×D₅₃	1	2	yes	complemented
911	C₂×#120	—	53	2	no	—
912	C₂×#120	—	53	8	no	—
913	C₂×#120	C₂×D₅₃	1	2	yes	complemented
914	#520	—	53	4	no	—
915	#520	—	53	4	no	—
916	#519	—	53	2	no	—
917	#518	—	53	2	no	—
918	#518	—	53	4	no	—
919	C₄×#41	—	53	4	no	—
920	C₄×#41	—	53	4	no	—
921	C₂×C₄×D₄	—	53	4	no	—
922	C₂×C₄×D₄	—	53	16	no	—
923	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
924	C₂×#117	—	53	1	no	—
925	C₂×#117	—	53	4	no	—
926	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
927	C₅₃	#62811	1	1	yes	characteristic, complemented, Sylow
928	C₂⁵	—	53	2	no	—
929	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
930	2₋¹⁺⁴	—	106	16	no	—
931	2₋¹⁺⁴	—	106	16	no	—
932	2₋¹⁺⁴	—	106	16	no	—
933	H(5,𝔽₂)	—	106	32	no	—
934	H(5,𝔽₂)	—	106	16	no	—
935	H(5,𝔽₂)	—	106	16	no	—
936	H(5,𝔽₂)	—	106	16	no	—
937	C₂×#41	—	2	8	no	—
938	C₂×#41	—	53	4	no	—
939	C₂×#41	—	53	4	no	—
940	C₂×#41	—	53	8	no	—
941	C₂×#41	—	53	4	no	—
942	C₂×#41	—	53	8	no	—
943	C₂×#41	—	53	4	no	—
944	C₂×#41	—	53	16	no	—
945	C₂×#41	—	53	2	no	—
946	C₂×#41	—	53	2	no	—
947	C₂×#41	—	53	2	no	—
948	C₂×#41	—	53	2	no	—
949	C₂×#41	—	53	2	no	—
950	C₂×#41	—	53	8	no	—
951	C₂×#41	—	53	2	no	—
952	C₂×#41	—	53	2	no	—
953	C₂×#41	—	53	8	no	—
954	C₂×#41	—	53	2	no	—
955	C₂×#41	—	53	2	no	—
956	C₂×#41	—	53	2	no	—
957	C₂×#41	—	53	8	no	—
958	C₂×#41	—	53	2	no	—
959	C₂×#41	—	53	2	no	—
960	C₂×#41	—	53	4	no	—
961	C₂×#41	—	53	4	no	—
962	C₂×#41	—	53	8	no	—
963	C₂×#41	—	53	8	no	—
964	C₂×#41	—	53	4	no	—
965	C₂×#41	—	53	8	no	—
966	C₂×#41	—	53	4	no	—
967	C₂×#41	—	53	4	no	—
968	C₂×#41	—	53	4	no	—
969	C₂×#41	—	106	16	no	—
970	C₂×#41	—	106	16	no	—
971	C₂×#41	—	106	8	no	—
972	C₂×#41	—	106	8	no	—
973	C₂×#41	—	106	32	no	—
974	C₂×#41	—	106	32	no	—
975	C₂×#41	—	106	32	no	—
976	C₂×#41	—	106	32	no	—
977	C₂×#41	—	106	32	no	—
978	C₂×#41	—	106	32	no	—
979	C₂×#41	—	106	32	no	—
980	C₂×#41	—	106	8	no	—
981	C₂×#41	—	106	8	no	—
982	C₂×#41	C₂²×D₅₃	1	2	yes	—
983	C₂×#41	C₂²×D₅₃	1	2	yes	—
984	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
985	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
986	C₂²×Q₈	—	53	4	no	—
987	C₂²×Q₈	—	53	4	no	—
988	C₂²×Q₈	—	53	1	no	—
989	C₂²×Q₈	—	53	1	no	—
990	C₂²×Q₈	—	53	2	no	—
991	C₂²×Q₈	—	53	1	no	—
992	C₂²×Q₈	—	53	4	no	—
993	C₂²×Q₈	—	53	4	no	—
994	C₂²×Q₈	—	53	4	no	—
995	C₂²×Q₈	—	106	8	no	—
996	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
997	C₂²×D₄	—	53	2	no	—
998	C₂²×D₄	—	53	2	no	—
999	C₂²×D₄	—	53	2	no	—
1000	C₂²×D₄	—	53	2	no	—
1001	C₂²×D₄	—	53	2	no	—
1002	C₂²×D₄	—	53	8	no	—
1003	C₂²×D₄	—	53	8	no	—
1004	C₂²×D₄	—	53	8	no	—
1005	C₂²×D₄	—	53	4	no	—
1006	C₂²×D₄	—	53	8	no	—
1007	C₂²×D₄	—	53	4	no	—
1008	C₂²×D₄	—	53	8	no	—
1009	C₂²×D₄	—	53	4	no	—
1010	C₂²×D₄	—	53	16	no	—
1011	C₂²×D₄	—	53	1	no	—
1012	C₂²×D₄	—	53	1	no	—
1013	C₂²×D₄	—	53	2	no	—
1014	C₂²×D₄	—	53	1	no	—
1015	C₂²×D₄	—	53	4	no	—
1016	C₂²×D₄	—	53	4	no	—
1017	C₂²×D₄	—	53	4	no	—
1018	C₂²×D₄	—	106	8	no	—
1019	C₂²×D₄	—	106	16	no	—
1020	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
1021	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
1022	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1023	C₂³×C₄	—	2	8	no	—
1024	C₂³×C₄	—	53	2	no	—
1025	C₂³×C₄	—	53	2	no	—
1026	C₂³×C₄	—	53	8	no	—
1027	C₂³×C₄	—	53	8	no	—
1028	C₂³×C₄	—	53	2	no	—
1029	C₂³×C₄	—	53	8	no	—
1030	C₂³×C₄	—	53	2	no	—
1031	C₂³×C₄	—	53	2	no	—
1032	C₂³×C₄	—	53	2	no	—
1033	C₂³×C₄	—	106	16	no	—
1034	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
1035	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
1036	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
1037	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
1038	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1042	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1043	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1044	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
1045	C₄⋊Q₈	—	53	4	no	—
1046	C₄⋊Q₈	—	53	16	no	—
1047	C₄⋊Q₈	—	53	4	no	—
1048	#127	—	53	16	no	—
1049	#127	—	53	4	no	—
1050	#127	—	53	4	no	—
1051	#124	—	53	4	no	—
1052	#124	—	53	4	no	—
1053	#124	—	53	16	no	—
1054	#124	—	53	16	no	—
1055	#124	—	53	4	no	—
1056	#124	—	53	4	no	—
1057	#123	—	53	8	no	—
1058	#123	—	53	4	no	—
1059	#123	—	53	4	no	—
1060	#123	—	53	8	no	—
1061	#123	—	53	8	no	—
1062	#123	—	53	16	no	—
1063	#123	—	53	16	no	—
1064	#123	—	53	8	no	—
1065	#123	—	53	16	no	—
1066	#123	—	53	16	no	—
1067	#123	—	53	8	no	—
1068	#123	C₂²×D₅₃	1	4	yes	—
1069	#123	C₂²×D₅₃	1	4	yes	—
1070	#123	C₂²×D₅₃	1	8	yes	complemented
1071	C₂²⋊Q₈	—	53	8	no	—
1072	C₂²⋊Q₈	—	53	4	no	—
1073	C₂²⋊Q₈	—	53	4	no	—
1074	C₂²⋊Q₈	—	53	4	no	—
1075	C₂²⋊Q₈	—	53	4	no	—
1076	C₂²⋊Q₈	—	53	8	no	—
1077	C₂²⋊Q₈	—	53	8	no	—
1078	C₂²⋊Q₈	—	53	16	no	—
1079	C₂²⋊Q₈	—	53	16	no	—
1080	C₂²⋊Q₈	—	53	8	no	—
1081	C₂²⋊Q₈	—	53	16	no	—
1082	C₂²⋊Q₈	—	53	16	no	—
1083	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
1084	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
1085	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1086	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1087	#121	—	53	8	no	—
1088	#121	—	53	16	no	—
1089	#121	—	53	16	no	—
1090	#121	—	53	16	no	—
1091	#121	—	53	16	no	—
1092	#121	—	53	4	no	—
1093	#121	—	53	4	no	—
1094	#121	—	53	4	no	—
1095	#121	—	53	4	no	—
1096	#121	—	53	8	no	—
1097	#121	—	53	16	no	—
1098	#121	—	53	8	no	—
1099	#121	—	53	8	no	—
1100	#121	—	53	16	no	—
1101	#121	—	53	16	no	—
1102	#121	—	53	16	no	—
1103	#121	—	53	16	no	—
1104	#121	—	53	16	no	—
1105	#121	C₂²×D₅₃	1	4	yes	—
1106	#121	C₂²×D₅₃	1	4	yes	—
1107	#121	C₂²×D₅₃	1	4	yes	complemented
1108	#121	C₂²×D₅₃	1	4	yes	complemented
1109	#120	—	53	4	no	—
1110	#120	—	53	4	no	—
1111	#120	—	53	8	no	—
1112	#120	—	53	8	no	—
1113	#120	—	53	8	no	—
1114	#120	—	53	16	no	—
1115	#120	—	53	16	no	—
1116	#120	—	53	8	no	—
1117	#120	—	53	16	no	—
1118	#120	—	53	16	no	—
1119	#120	—	53	8	no	—
1120	#120	C₂²×D₅₃	1	4	yes	—
1121	#120	C₂²×D₅₃	1	4	yes	—
1122	#120	C₂²×D₅₃	1	8	yes	—
1123	C₄×Q₈	—	53	8	no	—
1124	C₄×Q₈	—	53	8	no	—
1125	C₄×D₄	—	53	16	no	—
1126	C₄×D₄	—	53	8	no	—
1127	C₄×D₄	—	53	16	no	—
1128	C₄×D₄	—	53	8	no	—
1129	C₄×D₄	—	53	8	no	—
1130	C₄×D₄	—	53	8	no	—
1131	C₄×D₄	—	53	16	no	—
1132	C₄×D₄	—	53	16	no	—
1133	C₄×D₄	—	53	8	no	—
1134	C₄×D₄	—	53	16	no	—
1135	C₄×D₄	—	53	16	no	—
1136	C₄×D₄	—	53	16	no	—
1137	C₄×D₄	—	53	16	no	—
1138	C₄×D₄	—	53	8	no	—
1139	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1140	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1141	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1142	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1143	#117	—	53	2	no	—
1144	#117	—	53	2	no	—
1145	#117	—	53	2	no	—
1146	#117	—	53	2	no	—
1147	#117	—	53	8	no	—
1148	#117	—	53	8	no	—
1149	#117	—	53	8	no	—
1150	#117	C₂²×D₅₃	1	2	yes	—
1151	#117	C₂²×D₅₃	1	2	yes	—
1152	#117	C₂²×D₅₃	1	2	yes	complemented
1153	#117	C₂²×D₅₃	1	2	yes	complemented
1154	C₂×C₄⋊C₄	—	53	2	no	—
1155	C₂×C₄⋊C₄	—	53	4	no	—
1156	C₂×C₄⋊C₄	—	53	8	no	—
1157	C₂×C₄⋊C₄	—	53	16	no	—
1158	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1159	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1160	C₂×C₂²⋊C₄	—	53	2	no	—
1161	C₂×C₂²⋊C₄	—	53	4	no	—
1162	C₂×C₂²⋊C₄	—	53	4	no	—
1163	C₂×C₂²⋊C₄	—	53	8	no	—
1164	C₂×C₂²⋊C₄	—	53	16	no	—
1165	C₂×C₂²⋊C₄	—	53	16	no	—
1166	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1167	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1168	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1169	C₂×C₄²	—	53	2	no	—
1170	C₂×C₄²	—	53	8	no	—
1171	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1172	C₂⁴	—	2	4	no	—
1173	C₂⁴	—	4	4	no	—
1174	C₂⁴	—	53	2	no	—
1175	C₂⁴	—	53	8	no	—
1176	C₂⁴	—	53	8	no	—
1177	C₂⁴	—	53	2	no	—
1178	C₂⁴	—	53	2	no	—
1179	C₂⁴	—	106	8	no	—
1180	C₂⁴	—	212	8	no	—
1181	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1182	C₂⁴	C₂³×D₅₃	1	2	yes	—
1183	C₂⁴	C₂³×D₅₃	1	2	yes	—
1184	C₂⁴	C₂³×D₅₃	1	2	yes	—
1185	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1186	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1187	#41	—	2	8	no	—
1188	#41	—	2	8	no	—
1189	#41	—	2	8	no	—
1190	#41	—	2	8	no	—
1191	#41	—	53	16	no	—
1192	#41	—	53	16	no	—
1193	#41	—	53	16	no	—
1194	#41	—	53	16	no	—
1195	#41	—	106	32	no	—
1196	#41	—	106	32	no	—
1197	#41	—	106	32	no	—
1198	#41	—	106	32	no	—
1199	#41	—	106	32	no	—
1200	#41	—	106	16	no	—
1201	#41	—	106	16	no	—
1202	#41	—	106	32	no	—
1203	#41	—	106	16	no	—
1204	#41	—	106	16	no	—
1205	#41	—	106	16	no	—
1206	#41	—	106	16	no	—
1207	#41	—	106	32	no	—
1208	#41	—	106	16	no	—
1209	#41	—	106	16	no	—
1210	#41	—	106	32	no	—
1211	#41	—	106	16	no	—
1212	#41	—	106	16	no	—
1213	#41	—	106	8	no	—
1214	#41	—	106	8	no	—
1215	#41	—	106	8	no	—
1216	#41	—	106	8	no	—
1217	#41	—	106	8	no	—
1218	#41	—	106	8	no	—
1219	#41	—	106	8	no	—
1220	#41	—	106	8	no	—
1221	C₂×Q₈	—	2	4	no	—
1222	C₂×Q₈	—	53	8	no	—
1223	C₂×Q₈	—	53	2	no	—
1224	C₂×Q₈	—	53	2	no	—
1225	C₂×Q₈	—	53	2	no	—
1226	C₂×Q₈	—	53	8	no	—
1227	C₂×Q₈	—	53	8	no	—
1228	C₂×Q₈	—	53	2	no	—
1229	C₂×Q₈	—	53	2	no	—
1230	C₂×Q₈	—	53	2	no	—
1231	C₂×Q₈	—	106	8	no	—
1232	C₂×Q₈	—	106	16	no	—
1233	C₂×Q₈	—	106	16	no	—
1234	C₂×Q₈	—	106	16	no	—
1235	C₂×Q₈	—	106	16	no	—
1236	C₂×Q₈	—	106	16	no	—
1237	C₂×Q₈	—	106	4	no	—
1238	C₂×Q₈	—	106	4	no	—
1239	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1240	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1241	C₂×D₄	—	2	8	no	—
1242	C₂×D₄	—	2	4	no	—
1243	C₂×D₄	—	4	8	no	—
1244	C₂×D₄	—	53	16	no	—
1245	C₂×D₄	—	53	4	no	—
1246	C₂×D₄	—	53	4	no	—
1247	C₂×D₄	—	53	8	no	—
1248	C₂×D₄	—	53	4	no	—
1249	C₂×D₄	—	53	8	no	—
1250	C₂×D₄	—	53	8	no	—
1251	C₂×D₄	—	53	4	no	—
1252	C₂×D₄	—	53	4	no	—
1253	C₂×D₄	—	53	4	no	—
1254	C₂×D₄	—	53	8	no	—
1255	C₂×D₄	—	53	8	no	—
1256	C₂×D₄	—	53	16	no	—
1257	C₂×D₄	—	53	8	no	—
1258	C₂×D₄	—	53	8	no	—
1259	C₂×D₄	—	53	2	no	—
1260	C₂×D₄	—	53	2	no	—
1261	C₂×D₄	—	53	8	no	—
1262	C₂×D₄	—	53	8	no	—
1263	C₂×D₄	—	53	2	no	—
1264	C₂×D₄	—	53	2	no	—
1265	C₂×D₄	—	53	2	no	—
1266	C₂×D₄	—	53	2	no	—
1267	C₂×D₄	—	53	16	no	—
1268	C₂×D₄	—	106	16	no	—
1269	C₂×D₄	—	106	16	no	—
1270	C₂×D₄	—	106	16	no	—
1271	C₂×D₄	—	106	8	no	—
1272	C₂×D₄	—	106	16	no	—
1273	C₂×D₄	—	106	8	no	—
1274	C₂×D₄	—	106	32	no	—
1275	C₂×D₄	—	106	16	no	—
1276	C₂×D₄	—	106	32	no	—
1277	C₂×D₄	—	106	32	no	—
1278	C₂×D₄	—	106	32	no	—
1279	C₂×D₄	—	106	32	no	—
1280	C₂×D₄	—	106	8	no	—
1281	C₂×D₄	—	106	8	no	—
1282	C₂×D₄	—	106	8	no	—
1283	C₂×D₄	—	106	4	no	—
1284	C₂×D₄	—	106	4	no	—
1285	C₂×D₄	—	212	32	no	—
1286	C₂×D₄	—	212	8	no	—
1287	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1288	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1289	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1290	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1291	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1292	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1293	C₂²×C₄	—	2	4	no	—
1294	C₂²×C₄	—	2	4	no	—
1295	C₂²×C₄	—	2	4	no	—
1296	C₂²×C₄	—	2	4	no	—
1297	C₂²×C₄	—	2	4	no	—
1298	C₂²×C₄	—	2	8	no	—
1299	C₂²×C₄	—	2	8	no	—
1300	C₂²×C₄	—	2	8	no	—
1301	C₂²×C₄	—	2	8	no	—
1302	C₂²×C₄	—	2	8	no	—
1303	C₂²×C₄	—	53	2	no	—
1304	C₂²×C₄	—	53	16	no	—
1305	C₂²×C₄	—	53	4	no	—
1306	C₂²×C₄	—	53	4	no	—
1307	C₂²×C₄	—	53	2	no	—
1308	C₂²×C₄	—	53	8	no	—
1309	C₂²×C₄	—	53	8	no	—
1310	C₂²×C₄	—	53	2	no	—
1311	C₂²×C₄	—	53	4	no	—
1312	C₂²×C₄	—	53	8	no	—
1313	C₂²×C₄	—	53	8	no	—
1314	C₂²×C₄	—	53	8	no	—
1315	C₂²×C₄	—	53	8	no	—
1316	C₂²×C₄	—	53	4	no	—
1317	C₂²×C₄	—	53	4	no	—
1318	C₂²×C₄	—	53	4	no	—
1319	C₂²×C₄	—	53	4	no	—
1320	C₂²×C₄	—	53	16	no	—
1321	C₂²×C₄	—	106	8	no	—
1322	C₂²×C₄	—	106	32	no	—
1323	C₂²×C₄	—	106	32	no	—
1324	C₂²×C₄	—	106	32	no	—
1325	C₂²×C₄	—	106	8	no	—
1326	C₂²×C₄	—	106	8	no	—
1327	C₂²×C₄	—	106	8	no	—
1328	C₂²×C₄	—	106	8	no	—
1329	C₂²×C₄	D₄×D₅₃	1	8	yes	complemented
1330	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1331	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1332	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1333	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1334	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1335	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1336	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1337	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1338	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1339	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1340	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1341	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1342	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1343	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1344	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1345	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1346	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1347	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1348	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1349	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1350	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1351	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1352	C₄⋊C₄	—	53	4	no	—
1353	C₄⋊C₄	—	53	8	no	—
1354	C₄⋊C₄	—	53	16	no	—
1355	C₄⋊C₄	—	53	4	no	—
1356	C₄⋊C₄	—	53	16	no	—
1357	C₄⋊C₄	—	53	8	no	—
1358	C₄⋊C₄	—	53	16	no	—
1359	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1360	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1361	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1362	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1363	C₂²⋊C₄	—	53	4	no	—
1364	C₂²⋊C₄	—	53	8	no	—
1365	C₂²⋊C₄	—	53	4	no	—
1366	C₂²⋊C₄	—	53	16	no	—
1367	C₂²⋊C₄	—	53	8	no	—
1368	C₂²⋊C₄	—	53	8	no	—
1369	C₂²⋊C₄	—	53	16	no	—
1370	C₂²⋊C₄	—	53	16	no	—
1371	C₂²⋊C₄	—	53	8	no	—
1372	C₂²⋊C₄	—	53	16	no	—
1373	C₂²⋊C₄	—	53	16	no	—
1374	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1375	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1376	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1377	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1378	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1379	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1380	C₄²	—	53	16	no	—
1381	C₄²	—	53	4	no	—
1382	C₄²	—	53	4	no	—
1383	C₄²	C₂³×D₅₃	1	4	yes	—
1384	C₄²	C₂³×D₅₃	1	4	yes	—
1385	C₂³	—	2	2	no	—
1386	C₂³	—	2	4	no	—
1387	C₂³	—	2	4	no	—
1388	C₂³	—	2	4	no	—
1389	C₂³	—	2	2	no	—
1390	C₂³	—	2	4	no	—
1391	C₂³	—	2	4	no	—
1392	C₂³	—	2	4	no	—
1393	C₂³	—	4	2	no	—
1394	C₂³	—	4	2	no	—
1395	C₂³	—	4	2	no	—
1396	C₂³	—	4	2	no	—
1397	C₂³	—	4	4	no	—
1398	C₂³	—	4	16	no	—
1399	C₂³	—	53	4	no	—
1400	C₂³	—	53	8	no	—
1401	C₂³	—	53	4	no	—
1402	C₂³	—	53	4	no	—
1403	C₂³	—	106	16	no	—
1404	C₂³	—	106	16	no	—
1405	C₂³	—	106	4	no	—
1406	C₂³	—	106	4	no	—
1407	C₂³	—	106	16	no	—
1408	C₂³	—	212	4	no	—
1409	C₂³	—	212	16	no	—
1410	C₂³	—	212	4	no	—
1411	C₂³	—	212	8	no	—
1412	C₂³	—	212	4	no	—
1413	C₂³	—	212	32	no	—
1414	C₂³	C₂×D₄×D₅₃	1	4	yes	—
1415	C₂³	C₂⁴×D₅₃	1	4	yes	—
1416	C₂³	C₂⁴×D₅₃	1	2	yes	—
1417	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1418	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1419	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1420	C₂³	C₂⁴×D₅₃	1	2	yes	—
1421	Q₈	—	2	4	no	—
1422	Q₈	—	2	4	no	—
1423	Q₈	—	53	8	no	—
1424	Q₈	—	53	8	no	—
1425	Q₈	—	106	16	no	—
1426	Q₈	—	106	16	no	—
1427	Q₈	—	106	4	no	—
1428	Q₈	—	106	4	no	—
1429	Q₈	—	106	4	no	—
1430	Q₈	—	106	4	no	—
1431	D₄	—	2	8	no	—
1432	D₄	—	2	8	no	—
1433	D₄	—	2	16	no	—
1434	D₄	—	2	4	no	—
1435	D₄	—	2	4	no	—
1436	D₄	—	4	8	no	—
1437	D₄	—	53	16	no	—
1438	D₄	—	53	16	no	—
1439	D₄	—	53	8	no	—
1440	D₄	—	53	8	no	—
1441	D₄	—	106	16	no	—
1442	D₄	—	106	16	no	—
1443	D₄	—	106	16	no	—
1444	D₄	—	106	16	no	—
1445	D₄	—	106	16	no	—
1446	D₄	—	106	16	no	—
1447	D₄	—	106	8	no	—
1448	D₄	—	106	8	no	—
1449	D₄	—	106	8	no	—
1450	D₄	—	106	8	no	—
1451	D₄	—	106	16	no	—
1452	D₄	—	106	4	no	—
1453	D₄	—	106	4	no	—
1454	D₄	—	106	4	no	—
1455	D₄	—	106	4	no	—
1456	D₄	—	212	16	no	—
1457	D₄	—	212	16	no	—
1458	D₄	—	212	8	no	—
1459	C₂×C₄	—	2	2	no	—
1460	C₂×C₄	—	2	2	no	—
1461	C₂×C₄	—	2	4	no	—
1462	C₂×C₄	—	2	4	no	—
1463	C₂×C₄	—	2	4	no	—
1464	C₂×C₄	—	2	4	no	—
1465	C₂×C₄	—	2	4	no	—
1466	C₂×C₄	—	2	4	no	—
1467	C₂×C₄	—	2	4	no	—
1468	C₂×C₄	—	2	4	no	—
1469	C₂×C₄	—	2	4	no	—
1470	C₂×C₄	—	2	4	no	—
1471	C₂×C₄	—	2	4	no	—
1472	C₂×C₄	—	2	8	no	—
1473	C₂×C₄	—	2	8	no	—
1474	C₂×C₄	—	4	4	no	—
1475	C₂×C₄	—	53	8	no	—
1476	C₂×C₄	—	53	4	no	—
1477	C₂×C₄	—	53	16	no	—
1478	C₂×C₄	—	53	16	no	—
1479	C₂×C₄	—	53	8	no	—
1480	C₂×C₄	—	53	4	no	—
1481	C₂×C₄	—	53	4	no	—
1482	C₂×C₄	—	106	16	no	—
1483	C₂×C₄	—	106	16	no	—
1484	C₂×C₄	—	106	16	no	—
1485	C₂×C₄	—	106	16	no	—
1486	C₂×C₄	—	106	16	no	—
1487	C₂×C₄	—	106	16	no	—
1488	C₂×C₄	—	106	4	no	—
1489	C₂×C₄	—	106	4	no	—
1490	C₂×C₄	—	106	8	no	—
1491	C₂×C₄	—	106	8	no	—
1492	C₂×C₄	—	106	8	no	—
1493	C₂×C₄	—	106	8	no	—
1494	C₂×C₄	—	212	16	no	—
1495	C₂×C₄	—	212	4	no	—
1496	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1497	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1498	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1499	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1500	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1501	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1502	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1503	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1504	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1505	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1506	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1507	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1508	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1509	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1510	C₂²	—	2	8	no	—
1511	C₂²	—	2	2	no	—
1512	C₂²	—	2	2	no	—
1513	C₂²	—	2	2	no	—
1514	C₂²	—	2	2	no	—
1515	C₂²	—	2	2	no	—
1516	C₂²	—	2	2	no	—
1517	C₂²	—	2	4	no	—
1518	C₂²	—	2	8	no	—
1519	C₂²	—	2	2	no	—
1520	C₂²	—	2	2	no	—
1521	C₂²	—	4	4	no	—
1522	C₂²	—	4	8	no	—
1523	C₂²	—	4	8	no	—
1524	C₂²	—	4	4	no	—
1525	C₂²	—	8	4	no	—
1526	C₂²	—	53	8	no	—
1527	C₂²	—	106	8	no	—
1528	C₂²	—	106	4	no	—
1529	C₂²	—	106	4	no	—
1530	C₂²	—	106	8	no	—
1531	C₂²	—	106	8	no	—
1532	C₂²	—	424	4	no	—
1533	C₂²	—	424	16	no	—
1534	C₂²	—	212	8	no	—
1535	C₂²	—	212	32	no	—
1536	C₂²	—	212	8	no	—
1537	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1538	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1539	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1540	C₂²	#16811459	1	4	yes	complemented
1541	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1542	C₄	—	2	2	no	—
1543	C₄	—	2	2	no	—
1544	C₄	—	2	4	no	—
1545	C₄	—	2	8	no	—
1546	C₄	—	53	8	no	—
1547	C₄	—	106	4	no	—
1548	C₄	—	106	4	no	—
1549	C₄	—	106	8	no	—
1550	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1551	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1552	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1553	C₄	C₂²×D₄×D₅₃	1	2	yes	—
1554	C₂	—	2	2	no	—
1555	C₂	—	2	4	no	—
1556	C₂	—	2	2	no	—
1557	C₂	—	2	2	no	—
1558	C₂	—	4	2	no	—
1559	C₂	—	4	4	no	—
1560	C₂	—	106	8	no	—
1561	C₂	—	212	4	no	—
1562	C₂	—	212	4	no	—
1563	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1564	C₂	C₂×#16811459	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#525	C₂
hypercenter	C₂×#525	D₅₃
hypocenter	C₅₃	#62811
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. C₂×#16811459	C₂	semidirect
2. C₂³×#11719945	C₂	semidirect
3. #20288391	C₂	semidirect
4. #20288387	C₂	semidirect
5. #20288380	C₂	semidirect
6. #20288376	C₂	semidirect
7. #20288369	C₂	semidirect
8. #20288362	C₂	semidirect
9. #20288357	C₂	semidirect
10. #20288353	C₂	semidirect
11. #20288348	C₂	semidirect
12. #20288344	C₂	semidirect
13. D₄×#11719945	C₂	semidirect
14. #20288198	C₂	semidirect
15. #20288048	C₂	semidirect
16. #20288045	C₂	semidirect
17. #20288044	C₂	semidirect
18. C₂×#16811134	C₂	semidirect
19. #525×D₅₃	C₂	semidirect
20. #20287916	C₂	semidirect
21. C₂×C₅₃×#525	C₂	semidirect
23. C₂×#13133265	C₂²	semidirect
24. C₂×#13133264	C₂²	semidirect
25. C₂×#13133264	C₂²	semidirect
26. C₂×#13133263	C₂²	semidirect
27. C₂×#13133263	C₂²	semidirect
28. C₂×#13133262	C₂²	semidirect
29. C₂×#13133262	C₂²	semidirect
32. C₂²×#11719945	C₂²	semidirect
33. C₂²×#11719945	C₂²	semidirect
34. C₂²×#11719945	C₂²	semidirect
35. C₂²×#11719945	C₂²	semidirect
36. C₂²×#11719945	C₂²	semidirect
37. C₂²×#11719945	C₂²	semidirect
38. C₂²×#11719945	C₂²	semidirect
39. C₂²×#11719945	C₂²	semidirect
40. C₂²×#11719945	C₂²	semidirect
41. C₂²×#11719945	C₂²	semidirect
42. C₂²×#11719945	C₂²	semidirect
43. C₂×#41×D₅₃	C₂²	semidirect
44. C₂×#41×D₅₃	C₂²	semidirect
45. C₂³×Dic₁₀₆	C₂²	semidirect
46. C₂³×D₂₁₂	C₂²	semidirect
47. C₂³×C₂²⋊D₅₃	C₂²	semidirect
48. C₂³×C₄×D₅₃	C₂²	semidirect
49. #16811294	C₂²	semidirect
50. #16811291	C₂²	semidirect
51. D₄×Dic₁₀₆	C₂²	semidirect
52. #16811286	C₂²	semidirect
53. #16811283	C₂²	semidirect
54. #16811282	C₂²	semidirect
55. #16811282	C₂²	semidirect
56. #16811279	C₂²	semidirect
57. #16811278	C₂²	semidirect
58. #16811275	C₂²	semidirect
59. #16811274	C₂²	semidirect
60. #16811271	C₂²	semidirect
61. #16811270	C₂²	semidirect
62. #16811269	C₂²	semidirect
63. #16811269	C₂²	semidirect
64. #16811265	C₂²	semidirect
65. #16811264	C₂²	semidirect
66. #16811263	C₂²	semidirect
67. #16811263	C₂²	semidirect
68. #16811260	C₂²	semidirect
69. D₄×D₂₁₂	C₂²	semidirect
70. #16811257	C₂²	semidirect
71. D₄×C₂²⋊D₅₃	C₂²	semidirect
72. #16811255	C₂²	semidirect
73. #16811204	C₂²	semidirect
74. #16811203	C₂²	semidirect
75. #16811202	C₂²	semidirect
76. #16811201	C₂²	semidirect
77. #16811199	C₂²	semidirect
78. #16811199	C₂²	semidirect
79. #16811197	C₂²	semidirect
80. #16811196	C₂²	semidirect
81. #16811195	C₂²	semidirect
82. #16811194	C₂²	semidirect
83. #16811192	C₂²	semidirect
84. #16811192	C₂²	semidirect
85. #16811190	C₂²	semidirect
86. #16811189	C₂²	semidirect
87. #16811188	C₂²	semidirect
88. #16811187	C₂²	semidirect
89. #16811185	C₂²	semidirect
90. #16811184	C₂²	semidirect
91. #16811183	C₂²	semidirect
92. #16811182	C₂²	semidirect
93. #16811173	C₂²	semidirect
94. #16811170	C₂²	semidirect
95. #16811169	C₂²	semidirect
96. #16811136	C₂²	semidirect
97. #16811135	C₂²	semidirect
98. #16811135	C₂²	semidirect
99. #16811134	C₂²	semidirect
100. #16811134	C₂²	semidirect
101. #16811134	C₂²	semidirect
102. #16811134	C₂²	semidirect
103. #16811134	C₂²	semidirect
104. #16811134	C₂²	semidirect
105. #16811134	C₂²	semidirect
106. #16811133	C₂²	semidirect
107. #16811132	C₂²	semidirect
108. #16811132	C₂²	semidirect
109. #16811131	C₂²	semidirect
110. #16811130	C₂²	semidirect
111. #16811129	C₂²	semidirect
112. C₂×#13133200	C₂²	semidirect
113. #123×D₅₃	C₂²	semidirect
114. C₂×#13133196	C₂²	semidirect
115. C₂²⋊Q₈×D₅₃	C₂²	semidirect
116. C₂×#13133191	C₂²	semidirect
117. #121×D₅₃	C₂²	semidirect
118. C₂×#13133186	C₂²	semidirect
119. #120×D₅₃	C₂²	semidirect
120. #16811104	C₂²	semidirect
121. #16811103	C₂²	semidirect
122. #16811100	C₂²	semidirect
123. #16811097	C₂²	semidirect
124. #16811096	C₂²	semidirect
125. C₄×#11719945	C₂²	semidirect
126. #16811091	C₂²	semidirect
127. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
128. C₄×D₄×D₅₃	C₂²	semidirect
129. C₂×#13133176	C₂²	semidirect
130. #117×D₅₃	C₂²	semidirect
131. C₂²×#41×C₅₃	C₂²	semidirect
132. C₂⁴×C₄×C₅₃	C₂²	semidirect
133. C₅₃×#525	C₂²	semidirect
134. C₅₃×#525	C₂²	semidirect
135. C₅₃×#525	C₂²	semidirect
136. C₅₃×#525	C₂²	semidirect
137. C₅₃×#525	C₂²	semidirect
138. C₅₃×#525	C₂²	semidirect
139. C₂×#123×C₅₃	C₂²	semidirect
140. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
141. C₂×#121×C₅₃	C₂²	semidirect
142. C₂×#120×C₅₃	C₂²	semidirect
143. C₂×C₄×D₄×C₅₃	C₂²	semidirect
144. C₂×#117×C₅₃	C₂²	semidirect
153. C₂×#11719949	C₂³	semidirect
154. C₂×#11719949	C₂³	semidirect
166. C₂×#11719945	D₄	semidirect
185. C₂×#11719945	C₂³	semidirect
186. C₂×#11719945	C₂³	semidirect
187. C₂×#11719945	C₂³	semidirect
188. C₂×#11719945	C₂³	semidirect
189. C₂×#11719945	C₂³	semidirect
190. C₂×#11719945	C₂³	semidirect
192. C₂×#11719947	C₂³	semidirect
193. C₂×#11719947	C₂³	semidirect
194. C₂×#11719947	C₂³	semidirect
203. C₂²×Dic₁₀₆	C₂³	semidirect
204. C₂²×Dic₁₀₆	C₂³	semidirect
205. C₂×Q₈×D₅₃	C₂³	semidirect
206. C₂×Q₈×D₅₃	C₂³	semidirect
213. C₂²×D₂₁₂	C₂³	semidirect
214. C₂²×D₂₁₂	C₂³	semidirect
224. C₂²×C₂²⋊D₅₃	C₂³	semidirect
227. C₂×D₄×D₅₃	C₂³	semidirect
228. C₂×D₄×D₅₃	C₂³	semidirect
229. C₂×D₄×D₅₃	C₂³	semidirect
238. C₂²×C₄×D₅₃	C₂³	semidirect
239. C₂²×C₄×D₅₃	C₂³	semidirect
240. #13133217	C₂³	semidirect
241. #13133216	C₂³	semidirect
242. #13133215	C₂³	semidirect
243. #13133214	C₂³	semidirect
244. #13133213	C₂³	semidirect
245. #13133213	C₂³	semidirect
246. #13133206	C₂³	semidirect
247. #13133205	C₂³	semidirect
248. #13133205	C₂³	semidirect
249. #13133204	C₂³	semidirect
250. #13133203	C₂³	semidirect
251. #13133203	C₂³	semidirect
252. #13133202	C₂³	semidirect
253. #13133202	C₂³	semidirect
255. #13133201	C₂³	semidirect
258. #13133200	C₂³	semidirect
259. #13133200	C₂³	semidirect
260. #13133199	C₂³	semidirect
261. #13133199	C₂³	semidirect
263. #13133197	C₂³	semidirect
264. #13133197	C₂³	semidirect
267. #13133196	C₂³	semidirect
268. #13133196	C₂³	semidirect
269. #13133196	C₂³	semidirect
270. #13133195	C₂³	semidirect
271. #13133195	C₂³	semidirect
273. #13133194	C₂³	semidirect
274. #13133193	C₂³	semidirect
275. #13133192	C₂³	semidirect
276. #13133192	C₂³	semidirect
277. #13133192	C₂³	semidirect
280. #13133191	C₂³	semidirect
281. #13133191	C₂³	semidirect
282. #13133191	C₂³	semidirect
283. #13133191	C₂³	semidirect
284. #13133190	C₂³	semidirect
285. #13133190	C₂³	semidirect
286. #13133190	C₂³	semidirect
287. #13133190	C₂³	semidirect
289. #13133189	C₂³	semidirect
290. #13133189	C₂³	semidirect
291. #13133188	C₂³	semidirect
292. #13133188	C₂³	semidirect
295. #13133187	C₂³	semidirect
296. #13133187	C₂³	semidirect
300. #13133186	C₂³	semidirect
303. #13133185	C₂³	semidirect
304. C₄×Dic₁₀₆	C₂³	semidirect
305. #13133182	C₂³	semidirect
306. C₄×D₂₁₂	C₂³	semidirect
307. C₄×D₂₁₂	C₂³	semidirect
309. #13133179	C₂³	semidirect
310. #13133179	C₂³	semidirect
313. C₄×C₂²⋊D₅₃	C₂³	semidirect
314. C₄×C₂²⋊D₅₃	C₂³	semidirect
315. C₄×C₂²⋊D₅₃	C₂³	semidirect
316. C₄×C₂²⋊D₅₃	C₂³	semidirect
318. #13133177	C₂³	semidirect
319. #13133177	C₂³	semidirect
322. #13133176	C₂³	semidirect
323. #13133176	C₂³	semidirect
324. #13133175	C₂³	semidirect
325. #13133174	C₂³	semidirect
327. C₂×C₄⋊Dic₅₃	C₂³	semidirect
328. C₂×#11719919	C₂³	semidirect
329. C₄⋊C₄×D₅₃	C₂³	semidirect
330. C₄⋊C₄×D₅₃	C₂³	semidirect
333. C₂×#11719921	C₂³	semidirect
336. C₂²⋊C₄×D₅₃	C₂³	semidirect
337. C₂×C₄×Dic₅₃	C₂³	semidirect
338. C₄²×D₅₃	C₂³	semidirect
343. C₂×#41×C₅₃	C₂³	semidirect
344. C₂×#41×C₅₃	C₂³	semidirect
345. C₂²×Q₈×C₅₃	C₂³	semidirect
348. C₂²×D₄×C₅₃	C₂³	semidirect
360. C₂³×C₄×C₅₃	C₂³	semidirect
363. #123×C₅₃	C₂³	semidirect
366. C₂²⋊Q₈×C₅₃	C₂³	semidirect
367. C₂²⋊Q₈×C₅₃	C₂³	semidirect
370. #121×C₅₃	C₂³	semidirect
371. #121×C₅₃	C₂³	semidirect
377. C₄×D₄×C₅₃	C₂³	semidirect
378. C₄×D₄×C₅₃	C₂³	semidirect
381. #117×C₅₃	C₂³	semidirect
382. #117×C₅₃	C₂³	semidirect
383. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
384. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
387. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
388. C₂×C₄²×C₅₃	C₂³	semidirect
430. C₂²×C₄×C₅₃	C₂×D₄	semidirect
461. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
515. #11719945	C₂×D₄	semidirect
516. #11719945	C₂×D₄	semidirect
517. #11719945	C₂×D₄	semidirect
518. #11719945	C₂×D₄	semidirect
525. C₂×D₂₁₂	C₂×D₄	semidirect
542. C₂×C₄×D₅₃	C₂×D₄	semidirect
560. C₂×Dic₁₀₆	C₂×D₄	semidirect
747. C₂²×C₅₃	#585	semidirect
791. C₂×#525	D₅₃	semidirect
827. C₂²×#41	C₂×D₅₃	semidirect
832. C₂⁴×C₄	C₂×D₅₃	semidirect
896. #525	C₂×D₅₃	semidirect
897. #525	C₂×D₅₃	semidirect
898. #525	C₂×D₅₃	semidirect
899. #525	C₂×D₅₃	semidirect
900. #525	C₂×D₅₃	semidirect
901. #525	C₂×D₅₃	semidirect
904. C₂×#123	C₂×D₅₃	semidirect
907. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
910. C₂×#121	C₂×D₅₃	semidirect
913. C₂×#120	C₂×D₅₃	semidirect
923. C₂×C₄×D₄	C₂×D₅₃	semidirect
926. C₂×#117	C₂×D₅₃	semidirect
927. C₅₃	#62811	semidirect
984. C₂×#41	C₂²×D₅₃	semidirect
985. C₂×#41	C₂²×D₅₃	semidirect
996. C₂²×Q₈	C₂²×D₅₃	semidirect
1022. C₂²×D₄	C₂²×D₅₃	semidirect
1044. C₂³×C₄	C₂²×D₅₃	semidirect
1070. #123	C₂²×D₅₃	semidirect
1085. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1086. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1107. #121	C₂²×D₅₃	semidirect
1108. #121	C₂²×D₅₃	semidirect
1141. C₄×D₄	C₂²×D₅₃	semidirect
1142. C₄×D₄	C₂²×D₅₃	semidirect
1152. #117	C₂²×D₅₃	semidirect
1153. #117	C₂²×D₅₃	semidirect
1158. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1159. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1168. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1171. C₂×C₄²	C₂²×D₅₃	semidirect
1329. C₂²×C₄	D₄×D₅₃	semidirect
1540. C₂²	#16811459	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811459	2
C₂³×#11719945	2
#20288391	2
#20288387	2
#20288380	2
#20288376	2
#20288369	2
#20288362	2
#20288357	2
#20288353	2
#20288348	2
#20288344	2
D₄×#11719945	2
#20288198	2
#20288048	2
#20288045	2
#20288044	2
C₂×#16811134	2
#525×D₅₃	2
#20287916	2
C₂×C₅₃×#525	2
#62811	53