Subgroups — #28248743

Order 13568.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288273	C₂	1	1	yes	maximal, characteristic
2	#20283725	C₂	1	2	yes	maximal, complemented
3	#20283712	C₂	1	2	yes	maximal, complemented
4	#20283710	C₂	1	2	yes	maximal, complemented
5	#20283706	C₂	1	2	yes	maximal, complemented
6	#20283697	C₂	1	2	yes	maximal, complemented
7	#20283694	C₂	1	2	yes	maximal, complemented
8	#20283685	C₂	1	2	yes	maximal, complemented
9	#20283675	C₂	1	2	yes	maximal, complemented
10	#20283658	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283655	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#11719917	C₂	1	1	yes	maximal, characteristic, complemented
13	#20283436	C₂	1	1	yes	maximal, characteristic, complemented
14	#20283436	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283418	C₂	1	1	yes	maximal, characteristic, complemented
16	#20283409	C₂	1	1	yes	maximal, characteristic, complemented
17	#20283380	C₂	1	1	yes	maximal, characteristic, complemented
18	#20283369	C₂	1	1	yes	maximal, characteristic, complemented
19	#20283369	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283140	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283133	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16810578	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133223	C₂²	1	1	yes	characteristic
25	C₂×#13133223	C₂²	1	1	yes	characteristic
26	C₂²×#11719917	C₂²	1	1	yes	characteristic
27	C₂²×#11719917	C₂²	1	1	yes	characteristic
28	#16811343	C₄	1	1	yes	characteristic
29	#16811338	C₄	1	1	yes	characteristic
30	#16811330	C₄	1	1	yes	characteristic
31	#16811319	C₄	1	1	yes	characteristic
32	#16811319	C₄	1	1	yes	characteristic
33	#16811313	C₄	1	1	yes	characteristic
34	#16811313	C₄	1	1	yes	characteristic
35	#16811308	C₄	1	2	yes	—
36	#16811299	C₄	1	2	yes	—
37	#16811299	C₄	1	2	yes	—
38	#16811277	C₄	1	1	yes	characteristic
39	#16811267	C₄	1	2	yes	—
40	#16811180	C₂²	1	1	yes	characteristic
41	#16811155	C₂²	1	2	yes	—
42	#16811153	C₂²	1	2	yes	—
43	#16811153	C₂²	1	2	yes	—
44	#16811134	C₂²	1	1	yes	characteristic
45	#16811134	C₂²	1	1	yes	characteristic
46	C₄×#11719945	C₂²	1	1	yes	characteristic
47	C₄×#11719947	C₂²	1	2	yes	—
48	C₂×#13133176	C₂²	1	1	yes	characteristic
49	C₂×#13133176	C₂²	1	1	yes	characteristic
50	#16810752	C₂²	1	2	yes	complemented
51	#16810752	C₂²	1	2	yes	complemented
52	#16810751	C₂²	1	2	yes	complemented
53	#16810751	C₂²	1	2	yes	complemented
54	#16810751	C₂²	1	2	yes	complemented
55	#16810751	C₂²	1	2	yes	complemented
56	#16810750	C₂²	1	2	yes	complemented
57	#16810747	C₂²	1	2	yes	complemented
58	#16810701	C₂²	1	2	yes	—
59	#16810699	C₂²	1	2	yes	complemented
60	#16810699	C₂²	1	2	yes	complemented
61	#16810698	C₂²	1	2	yes	complemented
62	#16810698	C₂²	1	2	yes	complemented
63	#16810697	C₂²	1	2	yes	complemented
64	#16810697	C₂²	1	2	yes	complemented
65	#16810695	C₂²	1	2	yes	—
66	#16810695	C₂²	1	2	yes	—
67	#16810694	C₂²	1	2	yes	complemented
68	#16810694	C₂²	1	2	yes	complemented
69	#16810692	C₂²	1	2	yes	complemented
70	#16810692	C₂²	1	2	yes	complemented
71	#16810691	C₂²	1	2	yes	complemented
72	#16810691	C₂²	1	2	yes	complemented
73	D₄×#88322	C₂²	1	2	yes	—
74	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
75	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
76	#16810686	C₂²	1	2	yes	complemented
77	#16810686	C₂²	1	2	yes	complemented
78	#16810683	C₂²	1	2	yes	complemented
79	#16810683	C₂²	1	2	yes	complemented
80	#16810681	C₂²	1	2	yes	complemented
81	#16810681	C₂²	1	2	yes	complemented
82	#16810681	C₂²	1	2	yes	complemented
83	#16810681	C₂²	1	2	yes	complemented
84	#16810679	C₂²	1	2	yes	complemented
85	#16810677	C₂²	1	2	yes	complemented
86	#16810677	C₂²	1	2	yes	complemented
87	#16810675	C₂²	1	2	yes	complemented
88	#16810673	C₂²	1	2	yes	complemented
89	#16810673	C₂²	1	2	yes	complemented
90	#16810649	C₂²	1	1	yes	characteristic
91	#16810649	C₂²	1	1	yes	characteristic
92	#16810649	C₂²	1	1	yes	characteristic
93	#16810649	C₂²	1	1	yes	characteristic
94	#16810647	C₂²	1	1	yes	characteristic
95	#16810589	C₂²	1	1	yes	characteristic
96	#16810589	C₂²	1	1	yes	characteristic
97	#16810587	C₂²	1	1	yes	characteristic
98	#16810587	C₂²	1	1	yes	characteristic
99	#16810581	C₂²	1	2	yes	complemented
100	#16810581	C₂²	1	2	yes	complemented
101	#16810580	C₂²	1	2	yes	complemented
102	#16810580	C₂²	1	2	yes	complemented
103	#16810578	C₂²	1	1	yes	characteristic
104	#16810578	C₂²	1	1	yes	characteristic
105	#16810578	C₂²	1	1	yes	characteristic
106	#16810578	C₂²	1	1	yes	characteristic
107	#16810578	C₂²	1	1	yes	characteristic
108	#16810578	C₂²	1	1	yes	characteristic
109	#16810578	C₂²	1	1	yes	characteristic
110	#16810578	C₂²	1	1	yes	characteristic
111	#16810578	C₂²	1	2	yes	complemented
112	#16810578	C₂²	1	2	yes	complemented
113	C₄×#11719917	C₂²	1	1	yes	characteristic
114	#16810575	C₂²	1	2	yes	complemented
115	M₁₆×Dic₅₃	C₂²	1	2	yes	complemented
116	M₁₆×Dic₅₃	C₂²	1	2	yes	complemented
117	C₂×#13133127	C₂²	1	2	yes	complemented
118	#97×D₅₃	C₂²	1	2	yes	complemented
119	C₂×C₈×Dic₅₃	C₂²	1	2	yes	complemented
120	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
121	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
122	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
123	C₅₃×#435	C₂²	1	1	yes	characteristic
124	C₅₃×#435	C₂²	1	1	yes	characteristic
125	C₅₃×#435	C₂²	1	1	yes	characteristic
126	C₅₃×#435	C₂²	1	1	yes	characteristic
127	C₅₃×#435	C₂²	1	1	yes	characteristic
128	C₅₃×#435	C₂²	1	1	yes	characteristic
129	C₅₃×#435	C₂²	1	1	yes	characteristic
130	C₅₃×#435	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
134	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#11719945	C₂³	1	1	yes	characteristic
136	C₂×#11719947	C₂×C₄	1	2	yes	—
137	#13133223	—	2	4	no	—
138	#13133223	—	2	4	no	—
139	C₂×#11719917	—	2	4	no	—
140	C₂×#11719917	—	2	4	no	—
141	C₂×#11719917	C₂³	1	2	yes	—
142	C₂×#11719917	C₂³	1	1	yes	characteristic
143	C₂×#11719917	C₂³	1	1	yes	characteristic
144	C₂×#11719917	C₂³	1	1	yes	characteristic
145	C₂×#11719917	C₂³	1	2	yes	—
146	C₂×#11719917	C₂³	1	1	yes	characteristic
147	C₂×#11719912	C₂³	1	2	yes	—
148	C₂×#11719912	C₂³	1	2	yes	—
149	C₂²×#88322	C₂³	1	2	yes	—
150	C₂²×#88322	C₂³	1	2	yes	—
151	C₂×C₈×D₅₃	C₂³	1	2	yes	—
152	C₂×C₈×D₅₃	C₂³	1	2	yes	—
153	#13133217	C₂×C₄	1	1	yes	characteristic
154	#13133217	C₂×C₄	1	1	yes	characteristic
155	#13133212	C₂×C₄	1	2	yes	—
156	#13133212	C₂×C₄	1	2	yes	—
157	#13133210	C₂×C₄	1	2	yes	—
158	#13133210	C₂×C₄	1	2	yes	—
159	#13133210	C₂×C₄	1	2	yes	—
160	#13133210	C₂×C₄	1	2	yes	—
161	#13133209	C₂×C₄	1	1	yes	characteristic
162	#13133209	C₂×C₄	1	1	yes	characteristic
163	#13133208	C₂×C₄	1	2	yes	—
164	#13133207	C₂×C₄	1	2	yes	—
165	#13133207	C₂×C₄	1	2	yes	—
166	#13133204	C₂×C₄	1	2	yes	—
167	#13133203	C₂×C₄	1	2	yes	—
168	#13133203	C₂×C₄	1	2	yes	—
169	#13133201	C₂×C₄	1	2	yes	—
170	#13133201	C₂×C₄	1	2	yes	—
171	#13133200	C₂×C₄	1	2	yes	—
172	#13133200	C₂×C₄	1	2	yes	—
173	#13133199	C₂×C₄	1	2	yes	—
174	#13133199	C₂×C₄	1	2	yes	—
175	#13133198	C₂×C₄	1	2	yes	—
176	#13133198	C₂×C₄	1	2	yes	—
177	#13133197	C₂×C₄	1	2	yes	—
178	#13133196	C₂×C₄	1	2	yes	—
179	#13133196	C₂×C₄	1	2	yes	—
180	#13133196	C₂×C₄	1	1	yes	characteristic
181	#13133196	C₂×C₄	1	1	yes	characteristic
182	#13133196	C₂×C₄	1	1	yes	characteristic
183	#13133196	C₂×C₄	1	1	yes	characteristic
184	#13133194	C₂×C₄	1	2	yes	—
185	#13133194	C₂×C₄	1	2	yes	—
186	#13133191	C₂×C₄	1	1	yes	characteristic
187	#13133191	C₂×C₄	1	1	yes	characteristic
188	#13133191	C₂×C₄	1	1	yes	characteristic
189	#13133191	C₂×C₄	1	1	yes	characteristic
190	#13133189	C₂×C₄	1	2	yes	—
191	#13133189	C₂×C₄	1	2	yes	—
192	#13133188	C₂×C₄	1	2	yes	—
193	#13133186	C₂×C₄	1	2	yes	—
194	#13133186	C₂×C₄	1	2	yes	—
195	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
196	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
197	C₄×Dic₁₀₆	C₂³	1	2	yes	—
198	C₄×Dic₁₀₆	C₂³	1	2	yes	—
199	#13133182	C₂×C₄	1	2	yes	—
200	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
201	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
202	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
203	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
204	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
205	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
206	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
207	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
208	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
209	#13133177	C₂×C₄	1	2	yes	—
210	#13133177	C₂×C₄	1	2	yes	—
211	#13133176	C₂×C₄	1	2	yes	—
212	#13133176	C₂×C₄	1	2	yes	—
213	#13133176	C₂×C₄	1	1	yes	characteristic
214	#13133176	C₂×C₄	1	1	yes	characteristic
215	#13133176	C₂×C₄	1	1	yes	characteristic
216	#13133176	C₂×C₄	1	1	yes	characteristic
217	#13133176	C₂³	1	1	yes	characteristic
218	#13133176	C₂³	1	1	yes	characteristic
219	#13133176	C₂³	1	1	yes	characteristic
220	#13133176	C₂³	1	2	yes	—
221	#13133176	C₂³	1	2	yes	—
222	#13133175	C₂×C₄	1	2	yes	—
223	#13133174	C₂³	1	2	yes	—
224	#13133173	C₂×C₄	1	2	yes	—
225	#13133173	C₂×C₄	1	2	yes	—
226	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
228	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
229	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
230	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	2	yes	—
231	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	2	yes	—
232	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
233	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
234	C₄²×D₅₃	C₂³	1	2	yes	—
235	C₄⋊#88322	C₂³	1	2	yes	—
236	C₄⋊#88322	C₂³	1	2	yes	—
237	#13133146	C₂³	1	2	yes	—
238	#13133146	C₂³	1	2	yes	—
239	#13133146	C₂³	1	2	yes	—
240	#13133146	C₂³	1	2	yes	—
241	#13133146	C₂³	1	2	yes	—
242	#13133146	C₂³	1	2	yes	—
243	#13133146	C₂³	1	2	yes	—
244	#13133146	C₂³	1	2	yes	—
245	C₂²⋊#88322	C₂³	1	2	yes	—
246	C₂²⋊#88322	C₂³	1	2	yes	—
247	C₂²⋊#88322	C₂³	1	2	yes	—
248	C₂²⋊#88322	C₂³	1	2	yes	—
249	#13133129	C₂³	1	2	yes	—
250	#13133129	C₂³	1	2	yes	—
251	#13133129	C₂³	1	2	yes	—
252	#13133129	C₂³	1	2	yes	—
253	#13133128	C₂³	1	2	yes	—
254	#13133127	C₂³	1	2	yes	—
255	#13133127	C₂³	1	2	yes	—
256	#13133127	C₂³	1	2	yes	—
257	#13133127	C₂³	1	2	yes	—
258	#13133127	C₂³	1	2	yes	—
259	#13133127	C₂³	1	2	yes	—
260	#13133127	C₂³	1	2	yes	—
261	#13133127	C₂³	1	2	yes	—
262	C₄×#88322	C₂³	1	2	yes	—
263	C₈×Dic₅₃	C₂³	1	2	yes	—
264	C₈×Dic₅₃	C₂³	1	2	yes	—
265	C₈×Dic₅₃	C₂³	1	2	yes	—
266	C₈×Dic₅₃	C₂³	1	2	yes	—
267	C₈×Dic₅₃	C₂³	1	2	yes	—
268	C₈×Dic₅₃	C₂³	1	2	yes	—
269	C₈×Dic₅₃	C₂³	1	2	yes	—
270	C₈×Dic₅₃	C₂³	1	2	yes	—
271	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
272	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×M₁₆×C₅₃	—	2	4	no	—
275	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₅₃	—	2	4	no	—
280	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
289	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
290	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
291	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
292	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
299	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
312	#97×C₅₃	C₂³	1	1	yes	characteristic
313	#97×C₅₃	C₂³	1	1	yes	characteristic
314	#97×C₅₃	C₂³	1	1	yes	characteristic
315	#97×C₅₃	C₂³	1	1	yes	characteristic
316	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
317	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×D₄×C₅₃	—	4	2	no	—
319	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
320	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
321	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
322	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
323	C₂²×C₄×C₅₃	—	2	2	no	—
324	C₂²×C₄×C₅₃	—	2	2	no	—
325	C₂²×C₄×C₅₃	—	2	2	no	—
326	C₂²×C₄×C₅₃	—	2	2	no	—
327	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
328	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
329	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
331	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
332	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
333	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
334	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
341	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
342	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
343	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
344	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
345	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
346	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
347	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
348	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
349	#11719947	—	4	4	no	—
350	#11719945	—	2	2	no	—
351	#11719945	—	2	2	no	—
352	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
353	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
354	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
355	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
356	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
357	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
358	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
359	M₁₆×C₅₃	—	2	2	no	—
360	M₁₆×C₅₃	—	2	2	no	—
361	M₁₆×C₅₃	—	2	2	no	—
362	M₁₆×C₅₃	—	2	2	no	—
363	C₂×C₈×C₅₃	—	2	2	no	—
364	C₂×C₈×C₅₃	—	2	2	no	—
365	C₂×C₈×C₅₃	—	2	2	no	—
366	C₂×C₈×C₅₃	—	2	2	no	—
367	C₂×C₈×C₅₃	—	2	2	no	—
368	C₂×C₈×C₅₃	—	2	2	no	—
369	C₂×C₈×C₅₃	—	2	2	no	—
370	C₂×C₈×C₅₃	#41	1	4	yes	complemented
371	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
382	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
383	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
384	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
385	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
386	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
387	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
388	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
389	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
390	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
391	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
392	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
393	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
396	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
397	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
398	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
399	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
400	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
401	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
402	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
403	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
404	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
405	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
406	#11719921	C₂²×C₄	1	2	yes	—
407	#11719921	C₂²×C₄	1	2	yes	—
408	#11719921	C₂²×C₄	1	2	yes	—
409	#11719921	C₂²×C₄	1	2	yes	—
410	#11719921	C₂²×C₄	1	2	yes	—
411	#11719921	C₂²×C₄	1	2	yes	—
412	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
414	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
415	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
416	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
417	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
418	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
419	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
420	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
421	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
422	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
423	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
424	#11719919	C₂²×C₄	1	2	yes	—
425	#11719919	C₂²×C₄	1	2	yes	—
426	#11719919	C₂²×C₄	1	2	yes	—
427	#11719919	C₂²×C₄	1	2	yes	—
428	#11719919	C₂²×C₄	1	2	yes	—
429	#11719919	C₂²×C₄	1	2	yes	—
430	#11719919	C₂²×C₄	1	2	yes	—
431	#11719919	C₂²×C₄	1	2	yes	—
432	#11719919	C₂²×C₄	1	2	yes	—
433	#11719919	C₂²×C₄	1	2	yes	—
434	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
435	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
436	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
437	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
438	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
439	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
440	C₄×Dic₅₃	C₂⁴	1	2	yes	—
441	C₄×Dic₅₃	C₂⁴	1	2	yes	—
442	C₄×Dic₅₃	C₂⁴	1	2	yes	—
443	#11719917	—	2	2	no	—
444	#11719917	—	2	2	no	—
445	#11719917	—	2	2	no	—
446	#11719917	—	2	4	no	—
447	#11719917	—	2	4	no	—
448	#11719917	#41	1	4	yes	complemented
449	C₂×#88322	—	2	4	no	—
450	C₂×#88322	—	2	4	no	—
451	C₂×#88322	C₂⁴	1	2	yes	—
452	C₂×#88322	C₂⁴	1	2	yes	—
453	C₂×#88322	C₂⁴	1	2	yes	—
454	C₂×#88322	C₂⁴	1	2	yes	—
455	#11719912	—	2	4	no	—
456	#11719912	—	2	4	no	—
457	C₈×D₅₃	—	2	4	no	—
458	C₈×D₅₃	—	2	4	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	2	no	—
461	C₂³×C₅₃	—	2	2	no	—
462	C₂³×C₅₃	—	4	1	no	—
463	C₂³×C₅₃	—	4	1	no	—
464	C₂³×C₅₃	—	4	1	no	—
465	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
466	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
468	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
469	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
470	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
471	D₄×C₅₃	—	2	2	no	—
472	D₄×C₅₃	—	2	2	no	—
473	D₄×C₅₃	—	4	1	no	—
474	D₄×C₅₃	—	4	1	no	—
475	C₂×C₄×C₅₃	—	2	2	no	—
476	C₂×C₄×C₅₃	—	2	2	no	—
477	C₂×C₄×C₅₃	—	2	2	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	2	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	1	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	2	1	no	—
485	C₂×C₄×C₅₃	—	2	1	no	—
486	C₂×C₄×C₅₃	—	2	1	no	—
487	C₂×C₄×C₅₃	—	2	1	no	—
488	C₂×C₄×C₅₃	—	2	1	no	—
489	C₂×C₄×C₅₃	—	4	1	no	—
490	C₂×C₄×C₅₃	—	4	1	no	—
491	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
499	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
500	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
501	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
502	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
503	C₂²⋊D₅₃	—	2	4	no	—
504	C₂²⋊D₅₃	—	2	4	no	—
505	C₂²⋊D₅₃	—	4	2	no	—
506	C₂²⋊D₅₃	—	4	2	no	—
507	C₂²⋊D₅₃	—	4	2	no	—
508	C₂×Dic₅₃	—	2	4	no	—
509	C₂×Dic₅₃	—	4	2	no	—
510	C₂×Dic₅₃	—	4	2	no	—
511	C₂×Dic₅₃	—	4	2	no	—
512	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
513	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
514	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
515	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
516	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
517	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
518	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
519	D₂₁₂	—	2	2	no	—
520	C₄×D₅₃	—	2	2	no	—
521	C₄×D₅₃	—	2	2	no	—
522	C₄×D₅₃	—	4	2	no	—
523	C₄×D₅₃	—	4	2	no	—
524	Dic₁₀₆	—	2	2	no	—
525	Dic₁₀₆	—	4	2	no	—
526	Dic₁₀₆	—	4	2	no	—
527	C₈×C₅₃	—	2	1	no	—
528	C₈×C₅₃	—	2	1	no	—
529	C₈×C₅₃	—	2	1	no	—
530	C₈×C₅₃	—	2	1	no	—
531	C₈×C₅₃	—	2	1	no	—
532	C₈×C₅₃	—	2	1	no	—
533	C₈×C₅₃	C₂×#41	1	2	yes	—
534	C₈×C₅₃	C₂×#41	1	2	yes	—
535	#88322	—	2	2	no	—
536	#88322	—	2	2	no	—
537	#88322	—	2	2	no	—
538	#88322	C₂×#41	1	4	yes	—
539	#60216	—	53	1	no	maximal, Sylow
540	C₂²×C₅₃	—	2	1	no	—
541	C₂²×C₅₃	—	2	1	no	—
542	C₂²×C₅₃	—	2	1	no	—
543	C₂²×C₅₃	—	2	1	no	—
544	C₂²×C₅₃	—	2	1	no	—
545	C₂²×C₅₃	—	2	1	no	—
546	C₂²×C₅₃	—	2	1	no	—
547	C₂²×C₅₃	—	2	1	no	—
548	C₂²×C₅₃	—	2	1	no	—
549	C₂²×C₅₃	—	2	1	no	—
550	C₂²×C₅₃	—	2	1	no	—
551	C₂²×C₅₃	—	2	1	no	—
552	C₂²×C₅₃	—	2	1	no	—
553	C₂²×C₅₃	—	4	4	no	—
554	C₂²×C₅₃	—	8	2	no	—
555	C₂²×C₅₃	C₄×#41	1	2	yes	—
556	C₂²×C₅₃	#568	1	2	yes	—
557	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
558	C₂×D₅₃	—	2	2	no	—
559	C₂×D₅₃	—	2	2	no	—
560	C₂×D₅₃	—	2	2	no	—
561	C₄×C₅₃	—	2	1	no	—
562	C₄×C₅₃	—	2	1	no	—
563	C₄×C₅₃	—	2	1	no	—
564	C₄×C₅₃	—	2	1	no	—
565	C₄×C₅₃	—	2	1	no	—
566	C₄×C₅₃	—	2	1	no	—
567	C₄×C₅₃	—	2	1	no	—
568	C₄×C₅₃	—	2	1	no	—
569	C₄×C₅₃	C₄×#41	1	2	yes	—
570	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
571	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
572	Dic₅₃	—	2	2	no	—
573	Dic₅₃	—	2	2	no	—
574	Dic₅₃	—	2	2	no	—
575	Dic₅₃	—	2	2	no	—
576	Dic₅₃	—	2	2	no	—
577	Dic₅₃	—	2	2	no	—
578	Dic₅₃	—	2	2	no	—
579	#3475	—	53	1	no	—
580	#2970	—	53	2	no	—
581	#2969	—	53	2	no	—
582	#2968	—	53	2	no	—
583	#2968	—	53	2	no	—
584	#2967	—	53	2	no	—
585	#2967	—	53	2	no	—
586	#2966	—	53	2	no	—
587	#2965	—	53	2	no	—
588	#2962	—	53	1	no	—
589	#2961	—	53	1	no	—
590	D₄×M₁₆	—	53	1	no	—
591	#2933	—	53	1	no	—
592	#2933	—	53	1	no	—
593	#2930	—	53	1	no	—
594	#2929	—	53	1	no	—
595	C₂×#435	D₅₃	1	1	yes	characteristic, complemented
596	#2925	—	53	1	no	—
597	#2924	—	53	1	no	—
598	#2924	—	53	1	no	—
599	#2875	—	53	1	no	—
600	#2873	—	53	1	no	—
601	C₂×#405	—	53	1	no	—
602	C₂×C₅₃	—	2	2	no	—
603	C₂×C₅₃	—	2	2	no	—
604	C₂×C₅₃	—	4	1	no	—
605	C₂×C₅₃	—	4	1	no	—
606	C₂×C₅₃	—	4	1	no	—
607	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
608	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
609	C₂×C₅₃	#3573	1	1	yes	characteristic
610	D₅₃	—	4	2	no	—
611	C₂×#131	—	53	1	no	—
612	C₂×#131	—	53	1	no	—
613	C₂²×M₁₆	—	53	1	no	—
614	C₂²×M₁₆	—	53	1	no	—
615	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
616	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
617	#556	—	53	1	no	—
618	#555	—	53	1	no	—
619	#554	—	53	1	no	—
620	#553	—	53	1	no	—
621	#553	—	53	1	no	—
622	#552	—	53	1	no	—
623	#552	—	53	1	no	—
624	#552	—	53	2	no	—
625	#551	—	53	2	no	—
626	#551	—	53	2	no	—
627	#547	—	53	1	no	—
628	#546	—	53	2	no	—
629	#533	—	53	1	no	—
630	#529	—	53	2	no	—
631	#529	—	53	2	no	—
632	#529	—	53	2	no	—
633	#525	—	53	1	no	—
634	#525	—	53	1	no	—
635	C₄×#41	—	53	2	no	—
636	C₄×#41	—	53	1	no	—
637	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
638	C₂×#117	—	53	1	no	—
639	C₂×#117	—	53	1	no	—
640	#446	—	53	2	no	—
641	#446	—	53	2	no	—
642	#446	—	53	2	no	—
643	#446	—	53	2	no	—
644	#446	—	53	2	no	—
645	#446	—	53	2	no	—
646	#446	—	53	2	no	—
647	C₈×Q₈	—	53	2	no	—
648	#436	—	53	2	no	—
649	#436	—	53	2	no	—
650	#436	—	53	2	no	—
651	#436	—	53	2	no	—
652	#436	—	53	2	no	—
653	#435	—	53	2	no	—
654	#435	—	53	2	no	—
655	#435	—	53	2	no	—
656	#435	—	53	2	no	—
657	#435	—	53	2	no	—
658	#435	—	53	2	no	—
659	#435	—	53	2	no	—
660	#435	—	53	2	no	—
661	#435	—	53	2	no	—
662	#435	—	53	2	no	—
663	#435	C₂×D₅₃	1	1	yes	characteristic
664	#435	C₂×D₅₃	1	1	yes	characteristic
665	#435	C₂×D₅₃	1	1	yes	characteristic
666	#435	C₂×D₅₃	1	1	yes	characteristic
667	#435	C₂×D₅₃	1	1	yes	characteristic
668	#435	C₂×D₅₃	1	1	yes	characteristic
669	#435	C₂×D₅₃	1	1	yes	characteristic
670	#435	C₂×D₅₃	1	1	yes	characteristic
671	C₈×D₄	—	53	2	no	—
672	C₈×D₄	—	53	2	no	—
673	C₈×D₄	—	53	2	no	—
674	C₈×D₄	—	53	2	no	—
675	C₈×D₄	—	53	2	no	—
676	#433	—	53	2	no	—
677	#433	—	53	2	no	—
678	#433	—	53	2	no	—
679	#433	—	53	2	no	—
680	#433	—	53	2	no	—
681	#433	—	53	2	no	—
682	#432	—	53	2	no	—
683	#432	—	53	2	no	—
684	#432	—	53	2	no	—
685	#431	—	53	2	no	—
686	#431	—	53	2	no	—
687	#431	—	53	2	no	—
688	#424	—	53	1	no	—
689	#424	—	53	1	no	—
690	#424	—	53	1	no	—
691	#424	—	53	1	no	—
692	#423	—	53	1	no	—
693	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
694	#408	—	53	1	no	—
695	#408	—	53	1	no	—
696	#407	—	53	1	no	—
697	#407	—	53	1	no	—
698	C₂×C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic
699	C₂×C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic
700	#405	—	53	2	no	—
701	#405	—	53	2	no	—
702	#405	—	53	1	no	—
703	#405	—	53	1	no	—
704	#405	—	53	1	no	—
705	#405	—	53	1	no	—
706	#405	—	53	2	no	—
707	#405	—	53	2	no	—
708	#405	—	53	1	no	—
709	#405	—	53	1	no	—
710	#405	—	53	1	no	—
711	#405	—	53	1	no	—
712	#405	—	53	2	no	—
713	#405	—	53	2	no	—
714	C₄×M₁₆	—	53	2	no	—
715	C₄×M₁₆	—	53	2	no	—
716	C₄×M₁₆	—	53	1	no	—
717	C₄×M₁₆	—	53	2	no	—
718	C₂×#97	—	53	2	no	—
719	C₂×#97	—	53	2	no	—
720	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
721	C₂×C₄×C₈	—	53	2	no	—
722	C₅₃	#60216	1	1	yes	characteristic, complemented, Sylow
723	C₂×#41	—	53	2	no	—
724	C₂×#41	—	53	1	no	—
725	C₂²×D₄	C₄×D₅₃	1	1	yes	characteristic
726	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
727	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
728	#131	—	106	4	no	—
729	#131	—	106	4	no	—
730	C₂×M₁₆	—	2	4	no	—
731	C₂×M₁₆	—	53	1	no	—
732	C₂×M₁₆	—	53	2	no	—
733	C₂×M₁₆	—	53	1	no	—
734	C₂×M₁₆	—	53	1	no	—
735	C₂×M₁₆	—	53	2	no	—
736	C₂×M₁₆	—	53	1	no	—
737	C₂×M₁₆	—	53	2	no	—
738	C₂×M₁₆	—	53	2	no	—
739	C₂×M₁₆	—	106	4	no	—
740	C₂×M₁₆	—	106	4	no	—
741	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
742	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
743	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
744	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
745	C₂²×C₈	—	2	4	no	—
746	C₂²×C₈	—	53	2	no	—
747	C₂²×C₈	—	53	2	no	—
748	C₂²×C₈	—	53	2	no	—
749	C₂²×C₈	—	53	2	no	—
750	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
751	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
752	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
753	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
754	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
755	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
756	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
757	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
758	C₄⋊Q₈	—	53	1	no	—
759	C₄⋊Q₈	—	53	1	no	—
760	#126	—	53	2	no	—
761	#126	—	53	2	no	—
762	#126	—	53	2	no	—
763	#126	—	53	2	no	—
764	#126	—	53	2	no	—
765	#126	—	53	2	no	—
766	#125	—	53	2	no	—
767	#125	—	53	2	no	—
768	#125	—	53	2	no	—
769	#125	—	53	1	no	—
770	#125	—	53	1	no	—
771	#124	—	53	2	no	—
772	#124	—	53	2	no	—
773	#124	—	53	2	no	—
774	#123	—	53	2	no	—
775	#123	—	53	2	no	—
776	#123	—	53	2	no	—
777	#123	—	53	2	no	—
778	#123	—	53	2	no	—
779	#123	—	53	2	no	—
780	#123	—	53	2	no	—
781	#123	—	53	2	no	—
782	C₂²⋊Q₈	—	53	1	no	—
783	C₂²⋊Q₈	—	53	1	no	—
784	C₂²⋊Q₈	—	53	1	no	—
785	C₂²⋊Q₈	—	53	1	no	—
786	C₂²⋊Q₈	—	53	2	no	—
787	C₂²⋊Q₈	—	53	2	no	—
788	C₂²⋊Q₈	—	53	2	no	—
789	C₂²⋊Q₈	—	53	2	no	—
790	C₂²⋊Q₈	—	53	2	no	—
791	#121	—	53	2	no	—
792	#121	—	53	2	no	—
793	#121	—	53	2	no	—
794	#121	—	53	1	no	—
795	#121	—	53	1	no	—
796	#121	—	53	1	no	—
797	#121	—	53	1	no	—
798	#120	—	53	2	no	—
799	#120	—	53	2	no	—
800	C₄×Q₈	—	53	2	no	—
801	C₄×Q₈	—	53	1	no	—
802	C₄×Q₈	—	53	1	no	—
803	C₄×Q₈	—	53	2	no	—
804	C₄×Q₈	—	53	2	no	—
805	C₄×D₄	—	53	2	no	—
806	C₄×D₄	—	53	2	no	—
807	C₄×D₄	—	53	2	no	—
808	C₄×D₄	—	53	2	no	—
809	C₄×D₄	—	53	2	no	—
810	C₄×D₄	—	53	2	no	—
811	C₄×D₄	—	53	2	no	—
812	C₄×D₄	—	53	2	no	—
813	C₄×D₄	—	53	2	no	—
814	C₄×D₄	—	53	1	no	—
815	C₄×D₄	—	53	1	no	—
816	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
817	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
818	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
819	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
824	#117	—	53	2	no	—
825	#117	—	53	2	no	—
826	#117	—	53	1	no	—
827	#117	—	53	1	no	—
828	#117	—	53	1	no	—
829	#117	—	53	1	no	—
830	#117	—	53	1	no	—
831	#117	—	53	1	no	—
832	#117	—	53	1	no	—
833	#117	—	53	2	no	—
834	#117	—	53	2	no	—
835	#117	—	53	2	no	—
836	#117	—	53	2	no	—
837	#117	—	53	2	no	—
838	#117	—	53	2	no	—
839	C₂×C₄⋊C₄	—	53	1	no	—
840	C₂×C₄⋊C₄	—	53	1	no	—
841	C₂×C₄⋊C₄	—	53	1	no	—
842	C₂×C₄⋊C₄	—	53	1	no	—
843	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	53	2	no	—
845	C₂×C₂²⋊C₄	—	53	2	no	—
846	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
848	C₂×C₄²	—	53	2	no	—
849	C₂×C₄²	—	53	2	no	—
850	C₂×C₄²	—	53	2	no	—
851	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
852	C₄⋊C₈	—	53	2	no	—
853	C₄⋊C₈	—	53	2	no	—
854	C₄⋊C₈	—	53	2	no	—
855	C₄⋊C₈	—	53	2	no	—
856	C₄⋊C₈	—	53	2	no	—
857	C₄⋊C₈	—	53	2	no	—
858	C₄⋊C₈	—	53	2	no	—
859	C₄⋊C₈	—	53	2	no	—
860	C₄⋊C₈	—	53	2	no	—
861	C₄⋊C₈	—	53	2	no	—
862	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
863	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
864	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
865	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
866	C₂²⋊C₈	—	53	2	no	—
867	C₂²⋊C₈	—	53	2	no	—
868	C₂²⋊C₈	—	53	2	no	—
869	C₂²⋊C₈	—	53	2	no	—
870	C₂²⋊C₈	—	53	2	no	—
871	C₂²⋊C₈	—	53	2	no	—
872	C₂²⋊C₈	—	53	2	no	—
873	C₂²⋊C₈	—	53	2	no	—
874	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
875	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
877	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
878	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
879	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
880	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
881	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
882	#97	—	53	2	no	—
883	#97	—	53	2	no	—
884	#97	—	53	2	no	—
885	#97	—	53	2	no	—
886	#97	—	53	2	no	—
887	#97	—	53	2	no	—
888	#97	—	53	2	no	—
889	#97	—	53	2	no	—
890	#97	—	53	2	no	—
891	#97	C₂²×D₅₃	1	1	yes	characteristic
892	#97	C₂²×D₅₃	1	1	yes	characteristic
893	#97	C₂²×D₅₃	1	1	yes	characteristic
894	#97	C₂²×D₅₃	1	1	yes	characteristic
895	C₄×C₈	—	53	2	no	—
896	C₄×C₈	—	53	2	no	—
897	C₄×C₈	—	53	2	no	—
898	C₄×C₈	—	53	2	no	—
899	C₄×C₈	—	53	2	no	—
900	C₄×C₈	—	53	2	no	—
901	C₄×C₈	—	53	2	no	—
902	C₄×C₈	—	53	2	no	—
903	C₄×C₈	—	53	2	no	—
904	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
905	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
906	#41	—	106	2	no	—
907	#41	—	106	2	no	—
908	#41	—	212	4	no	—
909	C₂×Q₈	—	53	1	no	—
910	C₂×Q₈	—	53	2	no	—
911	C₂×Q₈	—	53	2	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	53	2	no	—
914	C₂×D₄	—	53	2	no	—
915	C₂×D₄	—	53	2	no	—
916	C₂×D₄	—	53	2	no	—
917	C₂×D₄	—	53	2	no	—
918	C₂×D₄	—	53	1	no	—
919	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
920	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
921	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
922	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	53	2	no	—
928	C₂²×C₄	—	53	2	no	—
929	C₂²×C₄	—	53	2	no	—
930	C₂²×C₄	—	53	2	no	—
931	C₂²×C₄	—	53	2	no	—
932	C₂²×C₄	—	53	2	no	—
933	C₂²×C₄	—	53	2	no	—
934	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
935	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
936	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
937	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
938	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
940	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
941	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
944	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
946	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	53	4	no	—
952	M₁₆	—	106	4	no	—
953	M₁₆	—	106	4	no	—
954	M₁₆	—	106	4	no	—
955	M₁₆	—	106	2	no	—
956	M₁₆	—	106	2	no	—
957	M₁₆	—	106	2	no	—
958	M₁₆	—	106	4	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	—	2	2	no	—
964	C₂×C₈	—	2	2	no	—
965	C₂×C₈	—	2	2	no	—
966	C₂×C₈	—	53	2	no	—
967	C₂×C₈	—	53	2	no	—
968	C₂×C₈	—	53	2	no	—
969	C₂×C₈	—	53	2	no	—
970	C₂×C₈	—	106	4	no	—
971	C₂×C₈	—	106	4	no	—
972	C₂×C₈	—	106	4	no	—
973	C₂×C₈	—	106	4	no	—
974	C₂×C₈	#11719947	1	4	yes	complemented
975	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
976	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
977	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
978	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
979	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
980	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
981	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
982	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
983	C₄⋊C₄	—	53	1	no	—
984	C₄⋊C₄	—	53	1	no	—
985	C₄⋊C₄	—	53	1	no	—
986	C₄⋊C₄	—	53	1	no	—
987	C₄⋊C₄	—	53	1	no	—
988	C₄⋊C₄	—	53	1	no	—
989	C₄⋊C₄	—	53	2	no	—
990	C₄⋊C₄	—	53	2	no	—
991	C₄⋊C₄	—	53	2	no	—
992	C₄⋊C₄	—	53	2	no	—
993	C₄⋊C₄	—	53	2	no	—
994	C₄⋊C₄	—	53	2	no	—
995	C₄⋊C₄	—	53	2	no	—
996	C₄⋊C₄	—	53	2	no	—
997	C₄⋊C₄	—	53	2	no	—
998	C₄⋊C₄	—	53	2	no	—
999	C₄⋊C₄	—	53	2	no	—
1000	C₄⋊C₄	—	53	2	no	—
1001	C₄⋊C₄	—	53	2	no	—
1002	C₄⋊C₄	—	53	2	no	—
1003	C₄⋊C₄	—	53	2	no	—
1004	C₄⋊C₄	—	53	2	no	—
1005	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1009	C₂²⋊C₄	—	53	2	no	—
1010	C₂²⋊C₄	—	53	2	no	—
1011	C₂²⋊C₄	—	53	2	no	—
1012	C₂²⋊C₄	—	53	2	no	—
1013	C₂²⋊C₄	—	53	2	no	—
1014	C₂²⋊C₄	—	53	2	no	—
1015	C₂²⋊C₄	—	53	2	no	—
1016	C₂²⋊C₄	—	53	2	no	—
1017	C₂²⋊C₄	—	53	2	no	—
1018	C₂²⋊C₄	—	53	2	no	—
1019	C₂²⋊C₄	—	53	2	no	—
1020	C₂²⋊C₄	—	53	2	no	—
1021	C₂²⋊C₄	—	53	2	no	—
1022	C₂²⋊C₄	—	53	2	no	—
1023	C₂²⋊C₄	—	53	2	no	—
1024	C₂²⋊C₄	—	53	2	no	—
1025	C₂²⋊C₄	—	53	2	no	—
1026	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1029	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1030	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1031	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1032	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1033	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1034	C₄²	—	53	2	no	—
1035	C₄²	—	53	2	no	—
1036	C₄²	—	53	2	no	—
1037	C₄²	—	53	2	no	—
1038	C₄²	—	53	2	no	—
1039	C₄²	—	53	2	no	—
1040	C₄²	—	53	2	no	—
1041	C₄²	—	53	2	no	—
1042	C₄²	—	53	2	no	—
1043	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1044	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1045	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1046	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	53	2	no	—
1054	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1055	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1056	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1057	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1058	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1059	Q₈	—	106	2	no	—
1060	Q₈	—	212	2	no	—
1061	Q₈	—	212	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	4	1	no	—
1066	D₄	—	106	4	no	—
1067	D₄	—	106	4	no	—
1068	D₄	—	106	2	no	—
1069	D₄	—	212	2	no	—
1070	D₄	—	212	2	no	—
1071	D₄	—	212	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	53	2	no	—
1089	C₂×C₄	—	53	2	no	—
1090	C₂×C₄	—	53	2	no	—
1091	C₂×C₄	—	53	2	no	—
1092	C₂×C₄	—	53	2	no	—
1093	C₂×C₄	—	53	2	no	—
1094	C₂×C₄	—	53	2	no	—
1095	C₂×C₄	—	106	4	no	—
1096	C₂×C₄	—	106	2	no	—
1097	C₂×C₄	—	106	2	no	—
1098	C₂×C₄	—	212	2	no	—
1099	C₂×C₄	—	212	2	no	—
1100	C₂×C₄	—	212	2	no	—
1101	C₂×C₄	—	212	2	no	—
1102	C₂×C₄	—	212	2	no	—
1103	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1106	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1109	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1112	C₂×C₄	#41×D₅₃	1	2	yes	—
1113	C₂×C₄	C₂×#11719947	1	2	yes	—
1114	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	53	4	no	—
1122	C₈	—	106	2	no	—
1123	C₈	—	106	2	no	—
1124	C₈	—	106	2	no	—
1125	C₈	C₂×#11719947	1	2	yes	—
1126	C₈	C₂×#11719947	1	2	yes	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	4	4	no	—
1141	C₂²	—	8	2	no	—
1142	C₂²	—	106	2	no	—
1143	C₂²	—	106	2	no	—
1144	C₂²	—	106	2	no	—
1145	C₂²	C₄×#11719947	1	2	yes	—
1146	C₂²	#16811389	1	2	yes	—
1147	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	106	2	no	—
1157	C₄	—	106	2	no	—
1158	C₄	—	106	2	no	—
1159	C₄	—	106	2	no	—
1160	C₄	—	106	2	no	—
1161	C₄	—	106	2	no	—
1162	C₄	—	106	2	no	—
1163	C₄	C₄×#11719947	1	2	yes	—
1164	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1165	C₄	C₂²×#11719947	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	212	2	no	—
1172	C₂	C₂×C₄×#11719947	1	1	yes	characteristic
1173	C₂	C₂×#16811389	1	1	yes	characteristic
1174	C₂	#20289426	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₂×C₅₃×#435	C₂
prime radical	#20288273	C₂
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	C₂×#435	D₅₃
hypocenter	C₅₃	#60216
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. #20283725	C₂	semidirect
3. #20283712	C₂	semidirect
4. #20283710	C₂	semidirect
5. #20283706	C₂	semidirect
6. #20283697	C₂	semidirect
7. #20283694	C₂	semidirect
8. #20283685	C₂	semidirect
9. #20283675	C₂	semidirect
10. #20283658	C₂	semidirect
11. #20283655	C₂	semidirect
12. D₄×#11719917	C₂	semidirect
13. #20283436	C₂	semidirect
14. #20283436	C₂	semidirect
15. #20283418	C₂	semidirect
16. #20283409	C₂	semidirect
17. #20283380	C₂	semidirect
18. #20283369	C₂	semidirect
19. #20283369	C₂	semidirect
20. #20283140	C₂	semidirect
21. #20283133	C₂	semidirect
22. C₂×#16810578	C₂	semidirect
23. C₂×C₅₃×#435	C₂	semidirect
50. #16810752	C₂²	semidirect
51. #16810752	C₂²	semidirect
52. #16810751	C₂²	semidirect
53. #16810751	C₂²	semidirect
54. #16810751	C₂²	semidirect
55. #16810751	C₂²	semidirect
56. #16810750	C₂²	semidirect
57. #16810747	C₂²	semidirect
59. #16810699	C₂²	semidirect
60. #16810699	C₂²	semidirect
61. #16810698	C₂²	semidirect
62. #16810698	C₂²	semidirect
63. #16810697	C₂²	semidirect
64. #16810697	C₂²	semidirect
67. #16810694	C₂²	semidirect
68. #16810694	C₂²	semidirect
69. #16810692	C₂²	semidirect
70. #16810692	C₂²	semidirect
71. #16810691	C₂²	semidirect
72. #16810691	C₂²	semidirect
74. C₈×C₂²⋊D₅₃	C₂²	semidirect
75. C₈×C₂²⋊D₅₃	C₂²	semidirect
76. #16810686	C₂²	semidirect
77. #16810686	C₂²	semidirect
78. #16810683	C₂²	semidirect
79. #16810683	C₂²	semidirect
80. #16810681	C₂²	semidirect
81. #16810681	C₂²	semidirect
82. #16810681	C₂²	semidirect
83. #16810681	C₂²	semidirect
84. #16810679	C₂²	semidirect
85. #16810677	C₂²	semidirect
86. #16810677	C₂²	semidirect
87. #16810675	C₂²	semidirect
88. #16810673	C₂²	semidirect
89. #16810673	C₂²	semidirect
99. #16810581	C₂²	semidirect
100. #16810581	C₂²	semidirect
101. #16810580	C₂²	semidirect
102. #16810580	C₂²	semidirect
111. #16810578	C₂²	semidirect
112. #16810578	C₂²	semidirect
114. #16810575	C₂²	semidirect
115. M₁₆×Dic₅₃	C₂²	semidirect
116. M₁₆×Dic₅₃	C₂²	semidirect
117. C₂×#13133127	C₂²	semidirect
118. #97×D₅₃	C₂²	semidirect
119. C₂×C₈×Dic₅₃	C₂²	semidirect
370. C₂×C₈×C₅₃	#41	semidirect
448. #11719917	#41	semidirect
595. C₂×#435	D₅₃	semidirect
722. C₅₃	#60216	semidirect
974. C₂×C₈	#11719947	semidirect

Maximal subgroups

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

subgroup	index
#20288273	2
#20283725	2
#20283712	2
#20283710	2
#20283706	2
#20283697	2
#20283694	2
#20283685	2
#20283675	2
#20283658	2
#20283655	2
D₄×#11719917	2
#20283436	2
#20283418	2
#20283409	2
#20283380	2
#20283369	2
#20283140	2
#20283133	2
C₂×#16810578	2
C₂×C₅₃×#435	2
#60216	53