Subgroups — #28292127

Order 13568.

7998 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288765	C₂	1	4	yes	maximal, complemented
2	#20288748	C₂	1	4	yes	maximal, complemented
3	#20288658	C₂	1	8	yes	maximal, complemented
4	#20288569	C₂	1	2	yes	maximal, complemented
5	#20288556	C₂	1	4	yes	maximal, complemented
6	#20288479	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288425	C₂	1	2	yes	maximal, complemented
8	#20288405	C₂	1	4	yes	maximal, complemented
9	#20288351	C₂	1	2	yes	maximal, complemented
10	#20288326	C₂	1	8	yes	maximal, complemented
11	#20288281	C₂	1	4	yes	maximal, complemented
12	D₄×#11719949	C₂	1	4	yes	maximal, complemented
13	#20288138	C₂	1	2	yes	maximal, complemented
14	#20288127	C₂	1	4	yes	maximal, complemented
15	#20288012	C₂	1	2	yes	maximal, complemented
16	C₂×#16811136	C₂	1	4	yes	maximal, complemented
17	#20287919	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3501	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133262	C₂²	1	2	yes	—
21	C₂²×#11719949	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
24	#16811358	C₂²	1	8	yes	complemented
25	#16811346	C₂²	1	4	yes	complemented
26	#16811339	C₂²	1	4	yes	complemented
27	#16811334	C₂²	1	8	yes	complemented
28	#16811326	C₂²	1	8	yes	complemented
29	#16811326	C₂²	1	8	yes	complemented
30	#16811321	C₂²	1	8	yes	complemented
31	#16811321	C₂²	1	16	yes	complemented
32	#16811315	C₂²	1	8	yes	complemented
33	#16811311	C₂²	1	8	yes	complemented
34	#16811300	C₂²	1	16	yes	complemented
35	#16811300	C₂²	1	16	yes	complemented
36	#16811300	C₂²	1	16	yes	complemented
37	#16811295	C₂²	1	4	yes	complemented
38	#16811284	C₂²	1	8	yes	complemented
39	#16811277	C₂²	1	4	yes	complemented
40	#16811276	C₂²	1	8	yes	complemented
41	#16811276	C₂²	1	4	yes	complemented
42	#16811268	C₂²	1	8	yes	complemented
43	#16811268	C₂²	1	8	yes	complemented
44	#16811268	C₂²	1	8	yes	complemented
45	#16811264	C₂²	1	16	yes	complemented
46	#16811264	C₂²	1	16	yes	complemented
47	#16811264	C₂²	1	8	yes	complemented
48	D₄×D₂₁₂	C₂²	1	8	yes	complemented
49	D₄×D₂₁₂	C₂²	1	8	yes	complemented
50	D₄×D₂₁₂	C₂²	1	4	yes	complemented
51	#16811247	C₂²	1	8	yes	complemented
52	#16811229	C₂²	1	8	yes	complemented
53	#16811222	C₂²	1	8	yes	complemented
54	#16811222	C₂²	1	16	yes	complemented
55	#16811213	C₂²	1	8	yes	complemented
56	#16811213	C₂²	1	8	yes	complemented
57	#16811213	C₂²	1	16	yes	complemented
58	#16811204	C₂²	1	2	yes	complemented
59	#16811192	C₂²	1	4	yes	complemented
60	#16811185	C₂²	1	8	yes	complemented
61	#16811185	C₂²	1	4	yes	complemented
62	#16811178	C₂²	1	2	yes	complemented
63	#16811178	C₂²	1	2	yes	complemented
64	#16811174	C₂²	1	2	yes	complemented
65	#16811174	C₂²	1	2	yes	complemented
66	#16811174	C₂²	1	8	yes	complemented
67	#16811173	C₂²	1	2	yes	complemented
68	#16811160	C₂²	1	4	yes	complemented
69	#16811160	C₂²	1	4	yes	complemented
70	#16811159	C₂²	1	4	yes	complemented
71	#16811159	C₂²	1	4	yes	complemented
72	#16811159	C₂²	1	16	yes	complemented
73	#16811158	C₂²	1	4	yes	complemented
74	#16811158	C₂²	1	4	yes	complemented
75	#16811158	C₂²	1	8	yes	complemented
76	#16811136	C₂²	1	4	yes	complemented
77	#16811136	C₂²	1	4	yes	complemented
78	#16811136	C₂²	1	8	yes	complemented
79	#16811136	C₂²	1	8	yes	complemented
80	#16811136	C₂²	1	8	yes	complemented
81	#16811136	C₂²	1	8	yes	complemented
82	#16811136	C₂²	1	8	yes	complemented
83	#16811136	C₂²	1	16	yes	complemented
84	#16811136	C₂²	1	8	yes	complemented
85	#16811136	C₂²	1	8	yes	complemented
86	#16811135	C₂²	1	4	yes	complemented
87	C₂×#13133202	C₂²	1	8	yes	complemented
88	C₂×#13133193	C₂²	1	4	yes	complemented
89	C₂×#13133192	C₂²	1	4	yes	complemented
90	C₂×#13133191	C₂²	1	4	yes	complemented
91	C₂×#13133187	C₂²	1	8	yes	complemented
92	#16811103	C₂²	1	4	yes	complemented
93	#16811102	C₂²	1	8	yes	complemented
94	#16811096	C₂²	1	8	yes	complemented
95	#16811095	C₂²	1	8	yes	complemented
96	C₄×#11719949	C₂²	1	4	yes	complemented
97	C₄×#11719949	C₂²	1	4	yes	complemented
98	#16811091	C₂²	1	4	yes	complemented
99	C₄×#11719947	C₂²	1	8	yes	complemented
100	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
101	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
102	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13133179	C₂²	1	8	yes	complemented
104	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
105	C₂×#13133177	C₂²	1	2	yes	complemented
106	C₂×#13133177	C₂²	1	8	yes	complemented
107	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
108	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
109	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
110	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
111	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
112	C₂×#13133175	C₂²	1	4	yes	complemented
113	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
115	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#554	C₂²	1	4	yes	complemented
117	C₅₃×#554	C₂²	1	8	yes	complemented
118	D₄×Q₈×C₅₃	C₂²	1	4	yes	complemented
119	C₅₃×#544	C₂²	1	2	yes	complemented
120	C₅₃×#543	C₂²	1	4	yes	complemented
121	C₅₃×#533	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	4	yes	complemented
123	C₅₃×#518	C₂²	1	2	yes	—
124	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
125	C₂⁴×D₅₃	C₂³	1	2	yes	—
126	#13133262	—	2	16	no	—
127	C₂×#11719949	—	4	16	no	—
128	C₂×#11719949	C₂³	1	4	yes	—
129	C₂×#11719949	C₂³	1	4	yes	—
130	C₂×#11719949	C₂³	1	8	yes	—
131	C₂×#11719949	C₂³	1	8	yes	complemented
132	C₂×#11719949	C₂³	1	8	yes	complemented
133	C₂×#11719945	C₂³	1	4	yes	—
134	C₂×#11719947	C₂³	1	8	yes	—
135	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
136	C₂²×D₂₁₂	C₂³	1	8	yes	—
137	C₂²×D₂₁₂	C₂³	1	8	yes	—
138	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
139	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
140	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
141	C₂×D₄×D₅₃	—	2	8	no	—
142	C₂×D₄×D₅₃	C₂³	1	4	yes	—
143	C₂×D₄×D₅₃	C₂³	1	4	yes	—
144	C₂×D₄×D₅₃	C₂³	1	8	yes	—
145	C₂³×Dic₅₃	C₂³	1	2	yes	—
146	C₂²×C₄×D₅₃	—	4	8	no	—
147	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
148	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
149	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
150	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
151	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
152	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
153	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
154	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
155	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
156	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
157	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
158	#13133217	C₂³	1	2	yes	complemented
159	#13133214	C₂³	1	8	yes	—
160	#13133214	C₂³	1	2	yes	complemented
161	#13133212	C₂³	1	16	yes	complemented
162	#13133212	C₂³	1	8	yes	complemented
163	#13133212	C₂³	1	16	yes	complemented
164	#13133212	C₂³	1	16	yes	complemented
165	#13133212	C₂³	1	8	yes	complemented
166	#13133208	C₂³	1	16	yes	complemented
167	#13133208	C₂³	1	4	yes	complemented
168	#13133208	C₂³	1	4	yes	complemented
169	#13133206	C₂³	1	4	yes	complemented
170	#13133206	C₂³	1	16	yes	complemented
171	#13133206	C₂³	1	16	yes	complemented
172	#13133206	C₂³	1	4	yes	complemented
173	#13133205	C₂³	1	8	yes	—
174	#13133205	C₂³	1	4	yes	complemented
175	#13133202	C₂³	1	8	yes	—
176	#13133202	C₂³	1	16	yes	—
177	#13133202	C₂³	1	8	yes	—
178	#13133202	C₂³	1	16	yes	complemented
179	#13133202	C₂³	1	16	yes	complemented
180	#13133202	C₂³	1	16	yes	complemented
181	#13133202	C₂³	1	16	yes	complemented
182	#13133202	C₂³	1	16	yes	complemented
183	#13133201	C₂³	1	16	yes	—
184	#13133201	C₂³	1	8	yes	—
185	#13133201	C₂³	1	16	yes	complemented
186	#13133197	C₂³	1	4	yes	—
187	#13133197	C₂³	1	4	yes	—
188	#13133197	C₂³	1	8	yes	complemented
189	#13133193	C₂³	1	4	yes	—
190	#13133193	C₂³	1	8	yes	—
191	#13133193	C₂³	1	4	yes	—
192	#13133193	C₂³	1	16	yes	complemented
193	#13133193	C₂³	1	8	yes	complemented
194	#13133193	C₂³	1	8	yes	complemented
195	#13133192	C₂³	1	4	yes	—
196	#13133192	C₂³	1	8	yes	—
197	#13133192	C₂³	1	8	yes	—
198	#13133192	C₂³	1	8	yes	—
199	#13133192	C₂³	1	4	yes	—
200	#13133192	C₂³	1	4	yes	—
201	#13133192	C₂³	1	4	yes	—
202	#13133192	C₂³	1	16	yes	complemented
203	#13133192	C₂³	1	16	yes	complemented
204	#13133192	C₂³	1	8	yes	complemented
205	#13133192	C₂³	1	8	yes	complemented
206	#13133192	C₂³	1	8	yes	complemented
207	#13133191	C₂³	1	16	yes	—
208	#13133191	C₂³	1	16	yes	—
209	#13133191	C₂³	1	4	yes	—
210	#13133191	C₂³	1	8	yes	—
211	#13133191	C₂³	1	4	yes	—
212	#13133191	C₂³	1	8	yes	complemented
213	#13133191	C₂³	1	8	yes	complemented
214	#13133187	C₂³	1	16	yes	—
215	#13133187	C₂³	1	16	yes	—
216	#13133187	C₂³	1	16	yes	—
217	#13133187	C₂³	1	8	yes	—
218	#13133187	C₂³	1	16	yes	—
219	#13133187	C₂³	1	16	yes	complemented
220	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
221	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
222	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
223	#13133182	C₂³	1	4	yes	complemented
224	#13133182	C₂³	1	4	yes	complemented
225	C₄×D₂₁₂	C₂³	1	8	yes	—
226	C₄×D₂₁₂	C₂³	1	8	yes	—
227	C₄×D₂₁₂	C₂³	1	4	yes	—
228	C₄×D₂₁₂	C₂³	1	4	yes	—
229	C₄×D₂₁₂	C₂³	1	4	yes	complemented
230	C₄×D₂₁₂	C₂³	1	4	yes	complemented
231	C₄×D₂₁₂	C₂³	1	8	yes	complemented
232	D₄×Dic₅₃	C₂³	1	4	yes	—
233	D₄×Dic₅₃	C₂³	1	4	yes	—
234	#13133179	C₂³	1	8	yes	—
235	#13133179	C₂³	1	16	yes	—
236	#13133179	C₂³	1	4	yes	—
237	#13133179	C₂³	1	4	yes	—
238	#13133179	C₂³	1	8	yes	—
239	#13133179	C₂³	1	4	yes	complemented
240	#13133179	C₂³	1	16	yes	complemented
241	#13133179	C₂³	1	4	yes	complemented
242	#13133179	C₂³	1	16	yes	complemented
243	#13133179	C₂³	1	4	yes	complemented
244	#13133179	C₂³	1	4	yes	complemented
245	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
246	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
247	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
248	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
249	#13133177	C₂³	1	8	yes	—
250	#13133177	C₂³	1	8	yes	—
251	#13133177	C₂³	1	8	yes	—
252	#13133177	C₂³	1	16	yes	—
253	#13133177	C₂³	1	8	yes	—
254	#13133177	C₂³	1	16	yes	complemented
255	#13133177	C₂³	1	16	yes	complemented
256	#13133175	C₂³	1	4	yes	—
257	#13133175	C₂³	1	8	yes	—
258	#13133175	C₂³	1	4	yes	—
259	#13133175	C₂³	1	8	yes	complemented
260	#13133175	C₂³	1	8	yes	complemented
261	#13133175	C₂³	1	8	yes	complemented
262	#13133175	C₂³	1	8	yes	complemented
263	#13133175	C₂³	1	8	yes	complemented
264	#13133174	C₂³	1	8	yes	complemented
265	#13133173	C₂³	1	16	yes	complemented
266	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
268	C₂×#11719919	C₂³	1	2	yes	—
269	C₂×#11719919	C₂³	1	8	yes	complemented
270	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
271	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
272	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
273	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
274	C₂×#11719921	C₂³	1	8	yes	—
275	C₂×#11719921	C₂³	1	8	yes	—
276	C₂×#11719921	C₂³	1	2	yes	—
277	C₂×#11719921	C₂³	1	2	yes	—
278	C₂×#11719921	C₂³	1	8	yes	complemented
279	C₂×#11719921	C₂³	1	8	yes	complemented
280	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
281	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
282	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
287	C₄²×D₅₃	C₂³	1	2	yes	—
288	C₄²×D₅₃	C₂³	1	2	yes	—
289	C₄²×D₅₃	C₂³	1	2	yes	—
290	C₄²×D₅₃	C₂³	1	2	yes	—
291	C₄²×D₅₃	C₂³	1	8	yes	complemented
292	C₂²×Q₈×C₅₃	C₂³	1	4	yes	complemented
293	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
295	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
296	C₄⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
297	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
298	#125×C₅₃	C₂³	1	8	yes	complemented
299	#125×C₅₃	C₂³	1	4	yes	complemented
300	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
301	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	—
302	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
303	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
304	C₂²⋊Q₈×C₅₃	C₂³	1	16	yes	complemented
305	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
306	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
307	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
308	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
309	C₄×D₄×C₅₃	C₂³	1	4	yes	—
310	C₄×D₄×C₅₃	C₂³	1	8	yes	—
311	C₄×D₄×C₅₃	C₂³	1	8	yes	—
312	C₄×D₄×C₅₃	C₂³	1	4	yes	—
313	#117×C₅₃	C₂³	1	4	yes	—
314	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
316	C₂×C₄⋊C₄×C₅₃	C₂³	1	8	yes	complemented
317	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	—
319	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
320	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
321	C₂³×D₅₃	—	2	8	no	—
322	C₂³×D₅₃	—	4	4	no	—
323	C₂³×D₅₃	—	4	4	no	—
324	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
325	C₂³×D₅₃	C₂⁴	1	4	yes	—
326	C₂³×D₅₃	C₂⁴	1	4	yes	—
327	C₂³×D₅₃	C₂⁴	1	8	yes	—
328	C₂³×D₅₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₅₃	—	4	8	no	—
330	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
331	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
332	C₂×Q₈×C₅₃	C₂⁴	1	8	yes	—
333	C₂×D₄×C₅₃	#41	1	8	yes	complemented
334	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
335	C₂²×C₄×C₅₃	—	4	4	no	—
336	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
341	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
342	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₂²⋊D₅₃	—	2	8	no	—
345	C₂×C₂²⋊D₅₃	—	2	32	no	—
346	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
347	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
348	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
349	C₂²×Dic₅₃	—	4	4	no	—
350	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
351	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
353	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
354	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
356	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
357	#11719949	—	2	16	no	—
358	#11719949	—	4	16	no	—
359	#11719949	—	4	16	no	—
360	#11719949	—	4	8	no	—
361	#11719949	—	4	16	no	—
362	#11719947	—	2	32	no	—
363	D₄×D₅₃	—	2	16	no	—
364	D₄×D₅₃	—	2	16	no	—
365	D₄×D₅₃	—	2	32	no	—
366	#11719945	—	2	16	no	—
367	C₂×D₂₁₂	—	2	4	no	—
368	C₂×D₂₁₂	—	4	8	no	—
369	C₂×D₂₁₂	—	4	16	no	—
370	C₂×D₂₁₂	—	4	16	no	—
371	C₂×D₂₁₂	C₂⁴	1	8	yes	—
372	C₂×D₂₁₂	C₂⁴	1	4	yes	—
373	C₂×D₂₁₂	C₂⁴	1	8	yes	—
374	C₂×D₂₁₂	C₂⁴	1	4	yes	—
375	C₂×D₂₁₂	C₂⁴	1	4	yes	—
376	C₂×D₂₁₂	C₂⁴	1	16	yes	—
377	C₂×D₂₁₂	C₂⁴	1	4	yes	—
378	C₂×D₂₁₂	C₂⁴	1	16	yes	—
379	C₂×D₂₁₂	C₂⁴	1	8	yes	—
380	C₂×C₄×D₅₃	—	2	4	no	—
381	C₂×C₄×D₅₃	—	2	4	no	—
382	C₂×C₄×D₅₃	—	2	16	no	—
383	C₂×C₄×D₅₃	—	4	8	no	—
384	C₂×C₄×D₅₃	—	4	4	no	—
385	C₂×C₄×D₅₃	—	4	16	no	—
386	C₂×C₄×D₅₃	—	4	8	no	—
387	C₂×C₄×D₅₃	—	4	4	no	—
388	C₂×C₄×D₅₃	—	4	8	no	—
389	C₂×C₄×D₅₃	—	4	4	no	—
390	C₂×C₄×D₅₃	—	4	2	no	—
391	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
392	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
393	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
394	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
398	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
399	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
400	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
401	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
402	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
403	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
404	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
405	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
406	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
407	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
408	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
410	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
411	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
412	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
413	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
414	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
416	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
417	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
418	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
419	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
420	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
421	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
422	C₄²×C₅₃	C₂⁴	1	2	yes	—
423	C₄²×C₅₃	C₂⁴	1	2	yes	—
424	C₄²×C₅₃	C₂⁴	1	8	yes	—
425	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
426	#11719921	C₂⁴	1	8	yes	—
427	#11719921	C₂⁴	1	8	yes	—
428	#11719921	C₂⁴	1	8	yes	—
429	#11719921	C₂⁴	1	16	yes	—
430	#11719921	C₂⁴	1	8	yes	—
431	#11719921	C₂⁴	1	8	yes	—
432	#11719921	C₂⁴	1	16	yes	—
433	#11719921	C₂⁴	1	16	yes	—
434	#11719921	C₂⁴	1	8	yes	—
435	#11719921	C₂⁴	1	8	yes	—
436	#11719921	C₂⁴	1	16	yes	—
437	#11719921	C₂⁴	1	8	yes	—
438	#11719921	C₂⁴	1	8	yes	—
439	#11719921	C₂⁴	1	8	yes	—
440	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
441	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
442	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
443	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
444	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
445	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
446	#11719919	C₂⁴	1	8	yes	—
447	#11719919	C₂⁴	1	16	yes	—
448	#11719919	C₂⁴	1	8	yes	—
449	#11719919	C₂⁴	1	8	yes	—
450	C₄×Dic₅₃	C₂⁴	1	2	yes	—
451	C₄×Dic₅₃	C₂⁴	1	2	yes	—
452	C₄×Dic₅₃	C₂⁴	1	2	yes	—
453	C₄×Dic₅₃	C₂⁴	1	2	yes	—
454	C₄×Dic₅₃	C₂⁴	1	2	yes	—
455	C₄×Dic₅₃	C₂⁴	1	2	yes	—
456	C₄×Dic₅₃	C₂⁴	1	8	yes	—
457	C₄×Dic₅₃	C₂⁴	1	8	yes	—
458	C₄×Dic₅₃	C₂⁴	1	16	yes	—
459	C₂³×C₅₃	—	4	2	no	—
460	C₂³×C₅₃	—	4	2	no	—
461	C₂³×C₅₃	C₂×#41	1	8	yes	complemented
462	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
463	C₂³×C₅₃	C₂⁵	1	4	yes	—
464	C₂²×D₅₃	—	2	2	no	—
465	C₂²×D₅₃	—	2	2	no	—
466	C₂²×D₅₃	—	2	2	no	—
467	C₂²×D₅₃	—	2	4	no	—
468	C₂²×D₅₃	—	2	8	no	—
469	C₂²×D₅₃	—	2	8	no	—
470	C₂²×D₅₃	—	2	16	no	—
471	C₂²×D₅₃	—	2	8	no	—
472	C₂²×D₅₃	—	2	8	no	—
473	C₂²×D₅₃	—	4	4	no	—
474	C₂²×D₅₃	—	4	2	no	—
475	C₂²×D₅₃	—	4	4	no	—
476	C₂²×D₅₃	—	4	2	no	—
477	C₂²×D₅₃	—	4	8	no	—
478	C₂²×D₅₃	—	4	8	no	—
479	C₂²×D₅₃	—	4	32	no	—
480	C₂²×D₅₃	C₂⁵	1	8	yes	—
481	C₂²×D₅₃	C₂⁵	1	4	yes	—
482	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
483	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
484	Q₈×C₅₃	—	2	8	no	—
485	Q₈×C₅₃	—	4	8	no	—
486	Q₈×C₅₃	—	4	4	no	—
487	D₄×C₅₃	C₂×#41	1	16	yes	complemented
488	C₂×C₄×C₅₃	—	2	2	no	—
489	C₂×C₄×C₅₃	—	2	8	no	—
490	C₂×C₄×C₅₃	—	4	4	no	—
491	C₂×C₄×C₅₃	—	4	2	no	—
492	C₂×C₄×C₅₃	—	4	8	no	—
493	C₂×C₄×C₅₃	—	4	1	no	—
494	C₂×C₄×C₅₃	—	4	8	no	—
495	C₂×C₄×C₅₃	C₂×#41	1	4	yes	complemented
496	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
498	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
499	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
500	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
501	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
502	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
503	C₂²⋊D₅₃	—	2	16	no	—
504	C₂²⋊D₅₃	—	2	16	no	—
505	C₂²⋊D₅₃	—	2	32	no	—
506	C₂×Dic₅₃	—	2	2	no	—
507	C₂×Dic₅₃	—	2	16	no	—
508	C₂×Dic₅₃	—	2	8	no	—
509	C₂×Dic₅₃	—	2	2	no	—
510	C₂×Dic₅₃	—	4	2	no	—
511	C₂×Dic₅₃	—	4	4	no	—
512	C₂×Dic₅₃	—	4	1	no	—
513	C₂×Dic₅₃	C₂⁵	1	8	yes	—
514	C₂×Dic₅₃	C₂⁵	1	4	yes	—
515	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
516	C₂×Dic₅₃	C₂⁵	1	2	yes	—
517	C₂×Dic₅₃	C₂⁵	1	2	yes	—
518	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
519	D₂₁₂	—	2	16	no	—
520	D₂₁₂	—	2	16	no	—
521	D₂₁₂	—	2	8	no	—
522	D₂₁₂	—	2	8	no	—
523	D₂₁₂	—	2	8	no	—
524	D₂₁₂	—	4	16	no	—
525	D₂₁₂	—	4	8	no	—
526	D₂₁₂	—	4	16	no	—
527	D₂₁₂	—	4	4	no	—
528	C₄×D₅₃	—	2	2	no	—
529	C₄×D₅₃	—	2	8	no	—
530	C₄×D₅₃	—	2	4	no	—
531	C₄×D₅₃	—	2	4	no	—
532	C₄×D₅₃	—	2	4	no	—
533	C₄×D₅₃	—	2	16	no	—
534	C₄×D₅₃	—	2	2	no	—
535	C₄×D₅₃	—	2	8	no	—
536	C₄×D₅₃	—	2	2	no	—
537	C₄×D₅₃	—	2	8	no	—
538	C₄×D₅₃	—	2	16	no	—
539	C₄×D₅₃	—	4	4	no	—
540	C₄×D₅₃	—	4	4	no	—
541	C₄×D₅₃	—	4	4	no	—
542	C₄×D₅₃	—	4	2	no	—
543	C₄×D₅₃	—	4	16	no	—
544	C₄×D₅₃	—	4	8	no	—
545	C₄×D₅₃	H(5,𝔽₂)	1	4	yes	complemented
546	Dic₁₀₆	—	2	8	no	—
547	#62773	—	53	1	no	maximal, Sylow
548	C₂²×C₅₃	—	2	1	no	—
549	C₂²×C₅₃	—	2	4	no	—
550	C₂²×C₅₃	—	2	1	no	—
551	C₂²×C₅₃	—	2	4	no	—
552	C₂²×C₅₃	—	4	8	no	—
553	C₂²×C₅₃	C₂²×#41	1	8	yes	—
554	C₂²×C₅₃	C₂²×#41	1	2	yes	—
555	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
556	C₂×D₅₃	—	2	8	no	—
557	C₂×D₅₃	—	2	1	no	—
558	C₂×D₅₃	—	2	1	no	—
559	C₂×D₅₃	—	2	1	no	—
560	C₂×D₅₃	—	2	1	no	—
561	C₂×D₅₃	—	2	8	no	—
562	C₂×D₅₃	—	2	4	no	—
563	C₂×D₅₃	—	2	4	no	—
564	C₂×D₅₃	—	2	8	no	—
565	C₂×D₅₃	—	2	8	no	—
566	C₂×D₅₃	—	2	4	no	—
567	C₂×D₅₃	—	4	16	no	—
568	C₂×D₅₃	—	4	16	no	—
569	C₂×D₅₃	—	4	8	no	—
570	C₂×D₅₃	—	8	16	no	—
571	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
572	C₂×D₅₃	#585	1	2	yes	—
573	C₄×C₅₃	—	2	1	no	—
574	C₄×C₅₃	—	2	4	no	—
575	C₄×C₅₃	—	2	8	no	—
576	C₄×C₅₃	—	2	2	no	—
577	C₄×C₅₃	—	2	8	no	—
578	C₄×C₅₃	C₂²×#41	1	4	yes	—
579	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
580	Dic₅₃	—	2	8	no	—
581	Dic₅₃	—	2	2	no	—
582	Dic₅₃	—	2	4	no	—
583	Dic₅₃	—	2	1	no	—
584	Dic₅₃	—	2	2	no	—
585	Dic₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
586	#3520	—	53	4	no	—
587	#3519	—	53	4	no	—
588	#3513	—	53	8	no	—
589	#3506	—	53	2	no	—
590	#3505	—	53	4	no	—
591	#3501	D₅₃	1	1	yes	characteristic, complemented
592	#3496	—	53	1	no	—
593	#3492	—	53	2	no	—
594	#3490	—	53	4	no	—
595	#3484	—	53	2	no	—
596	#3481	—	53	8	no	—
597	#3475	—	53	4	no	—
598	D₄×#41	—	53	4	no	—
599	#3460	—	53	2	no	—
600	#3459	—	53	4	no	—
601	#3444	—	53	2	no	—
602	C₂×#525	—	53	4	no	—
603	C₄×H(5,𝔽₂)	—	53	2	no	—
604	C₂²×C₄×D₄	—	53	1	no	—
605	C₂×C₅₃	—	2	2	no	—
606	C₂×C₅₃	—	2	8	no	—
607	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
608	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
609	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
610	D₅₃	—	2	2	no	—
611	D₅₃	—	2	2	no	—
612	D₅₃	—	4	4	no	—
613	D₅₃	—	4	8	no	—
614	C₂×H(5,𝔽₂)	—	53	2	no	—
615	C₂²×#41	—	53	4	no	—
616	C₂³×D₄	—	53	1	no	—
617	C₂⁴×C₄	—	53	2	no	—
618	#559	—	53	8	no	—
619	#556	—	53	4	no	—
620	#555	—	53	4	no	—
621	#554	—	53	8	no	—
622	#554	C₂×D₅₃	1	4	yes	complemented
623	#554	C₂×D₅₃	1	8	yes	complemented
624	#553	—	53	8	no	—
625	#553	—	53	8	no	—
626	#553	—	53	8	no	—
627	#553	—	53	16	no	—
628	#552	—	53	8	no	—
629	#552	—	53	8	no	—
630	#551	—	53	16	no	—
631	#551	—	53	16	no	—
632	#551	—	53	16	no	—
633	#550	—	53	4	no	—
634	D₄×Q₈	C₂×D₅₃	1	4	yes	complemented
635	#548	—	53	8	no	—
636	#547	—	53	8	no	—
637	#547	—	53	4	no	—
638	#547	—	53	4	no	—
639	#546	—	53	16	no	—
640	#546	—	53	8	no	—
641	#546	—	53	16	no	—
642	#546	—	53	8	no	—
643	#546	—	53	8	no	—
644	#546	—	53	8	no	—
645	D₄²	—	53	8	no	—
646	D₄²	—	53	4	no	—
647	D₄²	—	53	8	no	—
648	#544	C₂×D₅₃	1	2	yes	complemented
649	#543	C₂×D₅₃	1	4	yes	complemented
650	#542	—	53	8	no	—
651	#540	—	53	8	no	—
652	#539	—	53	8	no	—
653	#539	—	53	16	no	—
654	#538	—	53	8	no	—
655	#538	—	53	8	no	—
656	#538	—	53	16	no	—
657	#537	—	53	2	no	—
658	#535	—	53	4	no	—
659	#534	—	53	8	no	—
660	#534	—	53	4	no	—
661	#533	—	53	2	no	—
662	#533	—	53	2	no	—
663	#533	C₂×D₅₃	1	2	yes	complemented
664	#532	—	53	2	no	—
665	#532	—	53	2	no	—
666	#532	—	53	8	no	—
667	#532	—	53	2	no	—
668	#529	—	53	4	no	—
669	#529	—	53	4	no	—
670	#529	—	53	8	no	—
671	#529	—	53	4	no	—
672	#529	—	53	4	no	—
673	#529	—	53	16	no	—
674	#529	—	53	4	no	—
675	#529	—	53	4	no	—
676	#525	—	53	4	no	—
677	#525	—	53	8	no	—
678	#525	—	53	8	no	—
679	#525	—	53	8	no	—
680	#525	—	53	4	no	—
681	#525	—	53	8	no	—
682	#525	—	53	8	no	—
683	#525	—	53	8	no	—
684	#525	—	53	8	no	—
685	#525	—	53	16	no	—
686	#525	—	53	4	no	—
687	C₂×#123	—	53	8	no	—
688	C₂×C₂²⋊Q₈	—	53	4	no	—
689	C₂×C₂²⋊Q₈	C₂×D₅₃	1	4	yes	complemented
690	C₂×#121	—	53	4	no	—
691	C₂×#121	—	53	4	no	—
692	C₂×#120	—	53	8	no	—
693	#520	—	53	8	no	—
694	#520	—	53	4	no	—
695	#518	—	53	8	no	—
696	#518	—	53	8	no	—
697	#518	C₂×D₅₃	1	2	yes	—
698	C₄×#41	—	53	4	no	—
699	C₄×#41	—	53	4	no	—
700	C₄×#41	—	53	8	no	—
701	C₄×#41	—	53	4	no	—
702	C₂×C₄×D₄	—	53	1	no	—
703	C₂×C₄×D₄	—	53	2	no	—
704	C₂×C₄×D₄	—	53	4	no	—
705	C₂×C₄×D₄	—	53	4	no	—
706	C₂×C₄×D₄	—	53	4	no	—
707	C₂×C₄×D₄	—	53	4	no	—
708	C₂×C₄×D₄	—	53	8	no	—
709	C₂×C₄×D₄	—	53	1	no	—
710	C₂×C₄×D₄	—	53	8	no	—
711	C₂×C₄×D₄	—	53	2	no	—
712	C₂×C₄×D₄	—	53	8	no	—
713	C₂×C₄×D₄	—	53	1	no	—
714	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
715	C₂×#117	—	53	4	no	—
716	C₂²×C₄⋊C₄	—	53	1	no	—
717	C₂²×C₂²⋊C₄	—	53	2	no	—
718	C₂²×C₄²	—	53	1	no	—
719	C₅₃	#62773	1	1	yes	characteristic, complemented, Sylow
720	C₂⁵	—	53	2	no	—
721	H(5,𝔽₂)	—	106	16	no	—
722	C₂×#41	—	53	4	no	—
723	C₂×#41	—	53	4	no	—
724	C₂×#41	—	53	8	no	—
725	C₂×#41	—	53	8	no	—
726	C₂×#41	—	53	8	no	—
727	C₂×#41	—	53	8	no	—
728	C₂×#41	—	53	4	no	—
729	C₂×#41	—	212	16	no	—
730	C₂²×Q₈	C₂²×D₅₃	1	4	yes	complemented
731	C₂²×D₄	—	53	2	no	—
732	C₂²×D₄	—	53	8	no	—
733	C₂²×D₄	—	53	4	no	—
734	C₂²×D₄	—	53	4	no	—
735	C₂²×D₄	—	53	8	no	—
736	C₂²×D₄	—	53	1	no	—
737	C₂²×D₄	—	53	8	no	—
738	C₂²×D₄	—	53	8	no	—
739	C₂²×D₄	—	53	4	no	—
740	C₂²×D₄	—	106	8	no	—
741	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
742	C₂³×C₄	—	53	2	no	—
743	C₂³×C₄	—	53	1	no	—
744	C₂³×C₄	—	53	4	no	—
745	C₂³×C₄	—	53	1	no	—
746	C₂³×C₄	—	53	1	no	—
747	C₂³×C₄	—	53	2	no	—
748	C₂³×C₄	—	53	4	no	—
749	C₂³×C₄	—	53	8	no	—
750	C₂³×C₄	—	53	4	no	—
751	C₂³×C₄	—	53	4	no	—
752	C₂³×C₄	—	53	2	no	—
753	C₂³×C₄	—	53	2	no	—
754	C₂³×C₄	—	212	8	no	—
755	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
756	C₄⋊Q₈	—	53	2	no	—
757	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
758	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
759	C₄⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
760	#127	—	53	2	no	—
761	#127	—	53	8	no	—
762	#126	—	53	8	no	—
763	#126	—	53	8	no	—
764	#126	—	53	16	no	—
765	#126	—	53	16	no	—
766	#126	—	53	16	no	—
767	#125	—	53	4	no	—
768	#125	—	53	4	no	—
769	#125	—	53	16	no	—
770	#125	C₂²×D₅₃	1	4	yes	complemented
771	#125	C₂²×D₅₃	1	8	yes	complemented
772	#124	—	53	4	no	—
773	#124	—	53	4	no	—
774	#124	—	53	16	no	—
775	#124	—	53	16	no	—
776	#124	—	53	4	no	—
777	#124	—	53	8	no	—
778	#123	—	53	8	no	—
779	#123	—	53	16	no	—
780	#123	—	53	16	no	—
781	#123	—	53	16	no	—
782	#123	—	53	8	no	—
783	#123	—	53	16	no	—
784	#123	—	53	16	no	—
785	#123	—	53	16	no	—
786	#123	—	53	8	no	—
787	#123	—	53	16	no	—
788	#123	—	53	16	no	—
789	C₂²⋊Q₈	—	53	4	no	—
790	C₂²⋊Q₈	—	53	8	no	—
791	C₂²⋊Q₈	—	53	8	no	—
792	C₂²⋊Q₈	—	53	8	no	—
793	C₂²⋊Q₈	—	53	4	no	—
794	C₂²⋊Q₈	—	53	16	no	—
795	C₂²⋊Q₈	—	53	4	no	—
796	C₂²⋊Q₈	—	53	4	no	—
797	C₂²⋊Q₈	—	53	8	no	—
798	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
799	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	—
800	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
801	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
802	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
803	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
804	C₂²⋊Q₈	C₂²×D₅₃	1	16	yes	complemented
805	#121	—	53	4	no	—
806	#121	—	53	8	no	—
807	#121	—	53	8	no	—
808	#121	—	53	8	no	—
809	#121	—	53	4	no	—
810	#121	—	53	16	no	—
811	#121	—	53	16	no	—
812	#121	—	53	4	no	—
813	#121	—	53	8	no	—
814	#121	—	53	8	no	—
815	#121	—	53	8	no	—
816	#121	—	53	4	no	—
817	#121	—	53	4	no	—
818	#121	—	53	4	no	—
819	#121	—	53	16	no	—
820	#121	—	53	8	no	—
821	#121	—	53	8	no	—
822	#121	—	53	8	no	—
823	#121	—	53	16	no	—
824	#120	—	53	8	no	—
825	#120	—	53	16	no	—
826	#120	—	53	16	no	—
827	#120	—	53	16	no	—
828	#120	—	53	16	no	—
829	#120	—	53	16	no	—
830	C₄×Q₈	—	53	4	no	—
831	C₄×Q₈	—	53	4	no	—
832	C₄×Q₈	—	53	4	no	—
833	C₄×Q₈	—	53	4	no	—
834	C₄×Q₈	—	53	8	no	—
835	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
836	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
837	C₄×D₄	—	53	4	no	—
838	C₄×D₄	—	53	4	no	—
839	C₄×D₄	—	53	8	no	—
840	C₄×D₄	—	53	8	no	—
841	C₄×D₄	—	53	16	no	—
842	C₄×D₄	—	53	16	no	—
843	C₄×D₄	—	53	4	no	—
844	C₄×D₄	—	53	4	no	—
845	C₄×D₄	—	53	8	no	—
846	C₄×D₄	—	53	4	no	—
847	C₄×D₄	—	53	16	no	—
848	C₄×D₄	—	53	16	no	—
849	C₄×D₄	—	53	16	no	—
850	C₄×D₄	—	53	4	no	—
851	C₄×D₄	—	53	4	no	—
852	C₄×D₄	—	53	8	no	—
853	C₄×D₄	—	53	4	no	—
854	C₄×D₄	—	53	8	no	—
855	C₄×D₄	—	53	8	no	—
856	C₄×D₄	—	53	8	no	—
857	C₄×D₄	—	53	16	no	—
858	C₄×D₄	—	53	16	no	—
859	C₄×D₄	—	53	16	no	—
860	C₄×D₄	—	53	8	no	—
861	C₄×D₄	—	53	4	no	—
862	C₄×D₄	—	53	4	no	—
863	C₄×D₄	—	53	8	no	—
864	C₄×D₄	—	53	8	no	—
865	C₄×D₄	—	53	8	no	—
866	C₄×D₄	—	53	4	no	—
867	C₄×D₄	—	53	4	no	—
868	C₄×D₄	C₂²×D₅₃	1	4	yes	—
869	C₄×D₄	C₂²×D₅₃	1	4	yes	—
870	C₄×D₄	C₂²×D₅₃	1	8	yes	—
871	C₄×D₄	C₂²×D₅₃	1	8	yes	—
872	#117	—	53	4	no	—
873	#117	—	53	8	no	—
874	#117	—	53	8	no	—
875	#117	—	53	8	no	—
876	#117	—	53	8	no	—
877	#117	—	53	8	no	—
878	#117	—	53	4	no	—
879	#117	—	53	8	no	—
880	#117	—	53	16	no	—
881	#117	—	53	8	no	—
882	#117	C₂²×D₅₃	1	4	yes	—
883	C₂×C₄⋊C₄	—	53	1	no	—
884	C₂×C₄⋊C₄	—	53	2	no	—
885	C₂×C₄⋊C₄	—	53	4	no	—
886	C₂×C₄⋊C₄	—	53	8	no	—
887	C₂×C₄⋊C₄	—	53	4	no	—
888	C₂×C₄⋊C₄	—	53	4	no	—
889	C₂×C₄⋊C₄	—	53	8	no	—
890	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
892	C₂×C₄⋊C₄	C₂²×D₅₃	1	8	yes	complemented
893	C₂×C₂²⋊C₄	—	53	2	no	—
894	C₂×C₂²⋊C₄	—	53	2	no	—
895	C₂×C₂²⋊C₄	—	53	2	no	—
896	C₂×C₂²⋊C₄	—	53	8	no	—
897	C₂×C₂²⋊C₄	—	53	8	no	—
898	C₂×C₂²⋊C₄	—	53	8	no	—
899	C₂×C₂²⋊C₄	—	53	8	no	—
900	C₂×C₂²⋊C₄	—	53	8	no	—
901	C₂×C₂²⋊C₄	—	53	8	no	—
902	C₂×C₂²⋊C₄	—	53	16	no	—
903	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
904	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	—
905	C₂×C₄²	—	53	8	no	—
906	C₂×C₄²	—	53	1	no	—
907	C₂×C₄²	—	53	1	no	—
908	C₂×C₄²	—	53	1	no	—
909	C₂×C₄²	—	53	2	no	—
910	C₂×C₄²	—	53	2	no	—
911	C₂×C₄²	—	53	2	no	—
912	C₂×C₄²	—	53	2	no	—
913	C₂×C₄²	—	53	8	no	—
914	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
915	C₂⁴	—	53	1	no	—
916	C₂⁴	—	53	4	no	—
917	C₂⁴	—	53	4	no	—
918	C₂⁴	—	53	8	no	—
919	C₂⁴	—	53	2	no	—
920	C₂⁴	—	106	8	no	—
921	C₂⁴	—	212	4	no	—
922	C₂⁴	—	212	4	no	—
923	C₂⁴	C₂³×D₅₃	1	2	yes	—
924	#41	—	106	16	no	—
925	#41	—	106	32	no	—
926	#41	—	106	16	no	—
927	#41	—	212	16	no	—
928	#41	—	212	8	no	—
929	#41	—	212	16	no	—
930	#41	—	212	16	no	—
931	C₂×Q₈	—	4	8	no	—
932	C₂×Q₈	—	53	4	no	—
933	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
934	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
935	C₂×Q₈	C₂³×D₅₃	1	8	yes	—
936	C₂×D₄	—	53	16	no	—
937	C₂×D₄	—	53	8	no	—
938	C₂×D₄	—	53	8	no	—
939	C₂×D₄	—	53	8	no	—
940	C₂×D₄	—	53	4	no	—
941	C₂×D₄	—	53	4	no	—
942	C₂×D₄	—	53	8	no	—
943	C₂×D₄	—	53	4	no	—
944	C₂×D₄	—	53	4	no	—
945	C₂×D₄	—	53	16	no	—
946	C₂×D₄	—	53	16	no	—
947	C₂×D₄	—	53	8	no	—
948	C₂×D₄	—	106	8	no	—
949	C₂×D₄	—	106	32	no	—
950	C₂×D₄	—	106	16	no	—
951	C₂×D₄	—	106	16	no	—
952	C₂×D₄	—	106	32	no	—
953	C₂×D₄	—	106	4	no	—
954	C₂×D₄	—	212	8	no	—
955	C₂×D₄	—	212	16	no	—
956	C₂×D₄	—	212	16	no	—
957	C₂×D₄	#11719949	1	8	yes	complemented
958	C₂×D₄	C₂³×D₅₃	1	4	yes	—
959	C₂²×C₄	—	4	4	no	—
960	C₂²×C₄	—	53	1	no	—
961	C₂²×C₄	—	53	1	no	—
962	C₂²×C₄	—	53	4	no	—
963	C₂²×C₄	—	53	1	no	—
964	C₂²×C₄	—	53	8	no	—
965	C₂²×C₄	—	53	1	no	—
966	C₂²×C₄	—	53	4	no	—
967	C₂²×C₄	—	53	2	no	—
968	C₂²×C₄	—	53	2	no	—
969	C₂²×C₄	—	53	2	no	—
970	C₂²×C₄	—	53	2	no	—
971	C₂²×C₄	—	53	1	no	—
972	C₂²×C₄	—	53	1	no	—
973	C₂²×C₄	—	53	1	no	—
974	C₂²×C₄	—	53	8	no	—
975	C₂²×C₄	—	53	8	no	—
976	C₂²×C₄	—	53	4	no	—
977	C₂²×C₄	—	53	4	no	—
978	C₂²×C₄	—	53	4	no	—
979	C₂²×C₄	—	53	2	no	—
980	C₂²×C₄	—	53	8	no	—
981	C₂²×C₄	—	53	4	no	—
982	C₂²×C₄	—	53	16	no	—
983	C₂²×C₄	—	53	4	no	—
984	C₂²×C₄	—	53	4	no	—
985	C₂²×C₄	—	106	4	no	—
986	C₂²×C₄	—	106	16	no	—
987	C₂²×C₄	—	106	4	no	—
988	C₂²×C₄	—	212	4	no	—
989	C₂²×C₄	—	212	8	no	—
990	C₂²×C₄	—	212	8	no	—
991	C₂²×C₄	—	212	4	no	—
992	C₂²×C₄	—	212	16	no	—
993	C₂²×C₄	—	212	2	no	—
994	C₂²×C₄	—	212	8	no	—
995	C₂²×C₄	—	212	4	no	—
996	C₂²×C₄	—	212	4	no	—
997	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
998	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
999	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1001	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1002	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1003	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1004	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1005	C₄⋊C₄	—	53	4	no	—
1006	C₄⋊C₄	—	53	8	no	—
1007	C₄⋊C₄	—	53	4	no	—
1008	C₄⋊C₄	—	53	8	no	—
1009	C₄⋊C₄	—	53	16	no	—
1010	C₄⋊C₄	—	53	8	no	—
1011	C₄⋊C₄	—	53	8	no	—
1012	C₄⋊C₄	—	53	8	no	—
1013	C₄⋊C₄	—	53	8	no	—
1014	C₄⋊C₄	—	53	4	no	—
1015	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1016	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1017	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1018	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1019	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1020	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
1021	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1022	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1023	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1024	C₂²⋊C₄	—	53	8	no	—
1025	C₂²⋊C₄	—	53	8	no	—
1026	C₂²⋊C₄	—	53	8	no	—
1027	C₂²⋊C₄	—	53	8	no	—
1028	C₂²⋊C₄	—	53	8	no	—
1029	C₂²⋊C₄	—	53	8	no	—
1030	C₂²⋊C₄	—	53	8	no	—
1031	C₂²⋊C₄	—	53	16	no	—
1032	C₂²⋊C₄	—	53	8	no	—
1033	C₂²⋊C₄	—	53	16	no	—
1034	C₂²⋊C₄	—	53	16	no	—
1035	C₂²⋊C₄	—	53	16	no	—
1036	C₂²⋊C₄	—	53	8	no	—
1037	C₂²⋊C₄	—	53	8	no	—
1038	C₂²⋊C₄	—	53	8	no	—
1039	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1040	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1041	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1042	C₄²	—	53	2	no	—
1043	C₄²	—	53	8	no	—
1044	C₄²	—	53	2	no	—
1045	C₄²	—	53	2	no	—
1046	C₄²	—	53	2	no	—
1047	C₄²	—	53	2	no	—
1048	C₄²	—	53	2	no	—
1049	C₄²	—	53	16	no	—
1050	C₄²	—	53	8	no	—
1051	C₄²	C₂³×D₅₃	1	2	yes	—
1052	C₄²	C₂³×D₅₃	1	2	yes	—
1053	C₄²	C₂³×D₅₃	1	8	yes	—
1054	C₂³	—	4	2	no	—
1055	C₂³	—	4	2	no	—
1056	C₂³	—	53	1	no	—
1057	C₂³	—	53	1	no	—
1058	C₂³	—	53	4	no	—
1059	C₂³	—	53	8	no	—
1060	C₂³	—	106	2	no	—
1061	C₂³	—	106	2	no	—
1062	C₂³	—	106	8	no	—
1063	C₂³	—	106	8	no	—
1064	C₂³	—	106	2	no	—
1065	C₂³	—	106	16	no	—
1066	C₂³	—	106	8	no	—
1067	C₂³	—	106	8	no	—
1068	C₂³	—	106	4	no	—
1069	C₂³	—	212	8	no	—
1070	C₂³	—	212	8	no	—
1071	C₂³	—	212	4	no	—
1072	C₂³	—	212	2	no	—
1073	C₂³	—	212	4	no	—
1074	C₂³	—	212	2	no	—
1075	C₂³	—	212	32	no	—
1076	C₂³	C₂×#11719949	1	8	yes	complemented
1077	C₂³	C₂⁴×D₅₃	1	4	yes	—
1078	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1079	Q₈	—	2	8	no	—
1080	Q₈	—	4	8	no	—
1081	Q₈	—	4	4	no	—
1082	Q₈	—	106	8	no	—
1083	D₄	—	106	16	no	—
1084	D₄	—	106	16	no	—
1085	D₄	—	106	16	no	—
1086	D₄	—	106	32	no	—
1087	D₄	—	106	16	no	—
1088	D₄	—	106	8	no	—
1089	D₄	—	106	8	no	—
1090	D₄	—	106	8	no	—
1091	D₄	—	212	16	no	—
1092	D₄	—	212	8	no	—
1093	D₄	—	212	16	no	—
1094	D₄	—	212	4	no	—
1095	D₄	C₂×#11719949	1	16	yes	complemented
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	8	no	—
1098	C₂×C₄	—	4	4	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	8	no	—
1102	C₂×C₄	—	4	8	no	—
1103	C₂×C₄	—	53	1	no	—
1104	C₂×C₄	—	53	4	no	—
1105	C₂×C₄	—	53	2	no	—
1106	C₂×C₄	—	53	8	no	—
1107	C₂×C₄	—	53	2	no	—
1108	C₂×C₄	—	53	4	no	—
1109	C₂×C₄	—	53	1	no	—
1110	C₂×C₄	—	106	2	no	—
1111	C₂×C₄	—	106	8	no	—
1112	C₂×C₄	—	106	16	no	—
1113	C₂×C₄	—	106	2	no	—
1114	C₂×C₄	—	106	8	no	—
1115	C₂×C₄	—	106	4	no	—
1116	C₂×C₄	—	106	8	no	—
1117	C₂×C₄	—	106	2	no	—
1118	C₂×C₄	—	106	2	no	—
1119	C₂×C₄	—	106	16	no	—
1120	C₂×C₄	—	106	4	no	—
1121	C₂×C₄	—	106	4	no	—
1122	C₂×C₄	—	106	16	no	—
1123	C₂×C₄	—	106	2	no	—
1124	C₂×C₄	—	106	8	no	—
1125	C₂×C₄	—	212	2	no	—
1126	C₂×C₄	—	212	4	no	—
1127	C₂×C₄	—	212	4	no	—
1128	C₂×C₄	—	212	4	no	—
1129	C₂×C₄	—	212	16	no	—
1130	C₂×C₄	—	212	8	no	—
1131	C₂×C₄	—	212	1	no	—
1132	C₂×C₄	—	212	4	no	—
1133	C₂×C₄	—	212	2	no	—
1134	C₂×C₄	C₂×#11719949	1	4	yes	complemented
1135	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1136	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1137	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1138	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1139	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1140	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1141	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1142	C₂²	—	2	4	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	4	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	4	8	no	—
1147	C₂²	—	53	2	no	—
1148	C₂²	—	53	2	no	—
1149	C₂²	—	106	8	no	—
1150	C₂²	—	106	1	no	—
1151	C₂²	—	106	1	no	—
1152	C₂²	—	106	1	no	—
1153	C₂²	—	106	1	no	—
1154	C₂²	—	106	8	no	—
1155	C₂²	—	106	4	no	—
1156	C₂²	—	106	4	no	—
1157	C₂²	—	106	8	no	—
1158	C₂²	—	106	8	no	—
1159	C₂²	—	106	4	no	—
1160	C₂²	—	424	16	no	—
1161	C₂²	—	212	16	no	—
1162	C₂²	—	212	16	no	—
1163	C₂²	—	212	8	no	—
1164	C₂²	C₂²×#11719949	1	8	yes	—
1165	C₂²	C₂²×#11719949	1	2	yes	—
1166	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1167	C₄	—	2	1	no	—
1168	C₄	—	2	4	no	—
1169	C₄	—	2	8	no	—
1170	C₄	—	2	8	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	53	2	no	—
1173	C₄	—	106	2	no	—
1174	C₄	—	106	8	no	—
1175	C₄	—	106	1	no	—
1176	C₄	—	106	4	no	—
1177	C₄	—	106	2	no	—
1178	C₄	C₂²×#11719949	1	4	yes	—
1179	C₄	H(5,𝔽₂)×D₅₃	1	2	yes	—
1180	C₂	—	2	2	no	—
1181	C₂	—	2	8	no	—
1182	C₂	—	106	2	no	—
1183	C₂	—	106	2	no	—
1184	C₂	—	212	8	no	—
1185	C₂	—	212	4	no	—
1186	C₂	C₂³×#11719949	1	1	yes	characteristic
1187	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1188	C₂	#585×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3501	C₂
hypercenter	#3501	D₅₃
hypocenter	C₅₃	#62773
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3501

Complements

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

N	H ≅ G/N	type
1. #20288765	C₂	semidirect
2. #20288748	C₂	semidirect
3. #20288658	C₂	semidirect
4. #20288569	C₂	semidirect
5. #20288556	C₂	semidirect
6. #20288479	C₂	semidirect
7. #20288425	C₂	semidirect
8. #20288405	C₂	semidirect
9. #20288351	C₂	semidirect
10. #20288326	C₂	semidirect
11. #20288281	C₂	semidirect
12. D₄×#11719949	C₂	semidirect
13. #20288138	C₂	semidirect
14. #20288127	C₂	semidirect
15. #20288012	C₂	semidirect
16. C₂×#16811136	C₂	semidirect
17. #20287919	C₂	semidirect
18. C₂×C₄×D₄×D₅₃	C₂	semidirect
19. C₅₃×#3501	C₂	semidirect
21. C₂²×#11719949	C₂²	semidirect
23. C₂³×C₄×D₅₃	C₂²	semidirect
24. #16811358	C₂²	semidirect
25. #16811346	C₂²	semidirect
26. #16811339	C₂²	semidirect
27. #16811334	C₂²	semidirect
28. #16811326	C₂²	semidirect
29. #16811326	C₂²	semidirect
30. #16811321	C₂²	semidirect
31. #16811321	C₂²	semidirect
32. #16811315	C₂²	semidirect
33. #16811311	C₂²	semidirect
34. #16811300	C₂²	semidirect
35. #16811300	C₂²	semidirect
36. #16811300	C₂²	semidirect
37. #16811295	C₂²	semidirect
38. #16811284	C₂²	semidirect
39. #16811277	C₂²	semidirect
40. #16811276	C₂²	semidirect
41. #16811276	C₂²	semidirect
42. #16811268	C₂²	semidirect
43. #16811268	C₂²	semidirect
44. #16811268	C₂²	semidirect
45. #16811264	C₂²	semidirect
46. #16811264	C₂²	semidirect
47. #16811264	C₂²	semidirect
48. D₄×D₂₁₂	C₂²	semidirect
49. D₄×D₂₁₂	C₂²	semidirect
50. D₄×D₂₁₂	C₂²	semidirect
51. #16811247	C₂²	semidirect
52. #16811229	C₂²	semidirect
53. #16811222	C₂²	semidirect
54. #16811222	C₂²	semidirect
55. #16811213	C₂²	semidirect
56. #16811213	C₂²	semidirect
57. #16811213	C₂²	semidirect
58. #16811204	C₂²	semidirect
59. #16811192	C₂²	semidirect
60. #16811185	C₂²	semidirect
61. #16811185	C₂²	semidirect
62. #16811178	C₂²	semidirect
63. #16811178	C₂²	semidirect
64. #16811174	C₂²	semidirect
65. #16811174	C₂²	semidirect
66. #16811174	C₂²	semidirect
67. #16811173	C₂²	semidirect
68. #16811160	C₂²	semidirect
69. #16811160	C₂²	semidirect
70. #16811159	C₂²	semidirect
71. #16811159	C₂²	semidirect
72. #16811159	C₂²	semidirect
73. #16811158	C₂²	semidirect
74. #16811158	C₂²	semidirect
75. #16811158	C₂²	semidirect
76. #16811136	C₂²	semidirect
77. #16811136	C₂²	semidirect
78. #16811136	C₂²	semidirect
79. #16811136	C₂²	semidirect
80. #16811136	C₂²	semidirect
81. #16811136	C₂²	semidirect
82. #16811136	C₂²	semidirect
83. #16811136	C₂²	semidirect
84. #16811136	C₂²	semidirect
85. #16811136	C₂²	semidirect
86. #16811135	C₂²	semidirect
87. C₂×#13133202	C₂²	semidirect
88. C₂×#13133193	C₂²	semidirect
89. C₂×#13133192	C₂²	semidirect
90. C₂×#13133191	C₂²	semidirect
91. C₂×#13133187	C₂²	semidirect
92. #16811103	C₂²	semidirect
93. #16811102	C₂²	semidirect
94. #16811096	C₂²	semidirect
95. #16811095	C₂²	semidirect
96. C₄×#11719949	C₂²	semidirect
97. C₄×#11719949	C₂²	semidirect
98. #16811091	C₂²	semidirect
99. C₄×#11719947	C₂²	semidirect
100. C₂×C₄×D₂₁₂	C₂²	semidirect
102. C₂×#13133179	C₂²	semidirect
103. C₂×#13133179	C₂²	semidirect
104. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
105. C₂×#13133177	C₂²	semidirect
106. C₂×#13133177	C₂²	semidirect
107. C₄×D₄×D₅₃	C₂²	semidirect
108. C₄×D₄×D₅₃	C₂²	semidirect
109. C₄×D₄×D₅₃	C₂²	semidirect
110. C₄×D₄×D₅₃	C₂²	semidirect
111. C₄×D₄×D₅₃	C₂²	semidirect
112. C₂×#13133175	C₂²	semidirect
113. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
115. C₂×C₄²×D₅₃	C₂²	semidirect
116. C₅₃×#554	C₂²	semidirect
117. C₅₃×#554	C₂²	semidirect
118. D₄×Q₈×C₅₃	C₂²	semidirect
119. C₅₃×#544	C₂²	semidirect
120. C₅₃×#543	C₂²	semidirect
121. C₅₃×#533	C₂²	semidirect
122. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
131. C₂×#11719949	C₂³	semidirect
132. C₂×#11719949	C₂³	semidirect
138. C₂²×D₂₁₂	C₂³	semidirect
157. C₂²×C₄×D₅₃	C₂³	semidirect
158. #13133217	C₂³	semidirect
160. #13133214	C₂³	semidirect
161. #13133212	C₂³	semidirect
162. #13133212	C₂³	semidirect
163. #13133212	C₂³	semidirect
164. #13133212	C₂³	semidirect
165. #13133212	C₂³	semidirect
166. #13133208	C₂³	semidirect
167. #13133208	C₂³	semidirect
168. #13133208	C₂³	semidirect
169. #13133206	C₂³	semidirect
170. #13133206	C₂³	semidirect
171. #13133206	C₂³	semidirect
172. #13133206	C₂³	semidirect
174. #13133205	C₂³	semidirect
178. #13133202	C₂³	semidirect
179. #13133202	C₂³	semidirect
180. #13133202	C₂³	semidirect
181. #13133202	C₂³	semidirect
182. #13133202	C₂³	semidirect
185. #13133201	C₂³	semidirect
188. #13133197	C₂³	semidirect
192. #13133193	C₂³	semidirect
193. #13133193	C₂³	semidirect
194. #13133193	C₂³	semidirect
202. #13133192	C₂³	semidirect
203. #13133192	C₂³	semidirect
204. #13133192	C₂³	semidirect
205. #13133192	C₂³	semidirect
206. #13133192	C₂³	semidirect
212. #13133191	C₂³	semidirect
213. #13133191	C₂³	semidirect
219. #13133187	C₂³	semidirect
220. Q₈×Dic₅₃	C₂³	semidirect
221. Q₈×Dic₅₃	C₂³	semidirect
222. C₄×Dic₁₀₆	C₂³	semidirect
223. #13133182	C₂³	semidirect
224. #13133182	C₂³	semidirect
229. C₄×D₂₁₂	C₂³	semidirect
230. C₄×D₂₁₂	C₂³	semidirect
231. C₄×D₂₁₂	C₂³	semidirect
239. #13133179	C₂³	semidirect
240. #13133179	C₂³	semidirect
241. #13133179	C₂³	semidirect
242. #13133179	C₂³	semidirect
243. #13133179	C₂³	semidirect
244. #13133179	C₂³	semidirect
247. C₄×C₂²⋊D₅₃	C₂³	semidirect
248. C₄×C₂²⋊D₅₃	C₂³	semidirect
254. #13133177	C₂³	semidirect
255. #13133177	C₂³	semidirect
259. #13133175	C₂³	semidirect
260. #13133175	C₂³	semidirect
261. #13133175	C₂³	semidirect
262. #13133175	C₂³	semidirect
263. #13133175	C₂³	semidirect
264. #13133174	C₂³	semidirect
265. #13133173	C₂³	semidirect
267. C₂×C₄⋊Dic₅₃	C₂³	semidirect
269. C₂×#11719919	C₂³	semidirect
272. C₄⋊C₄×D₅₃	C₂³	semidirect
278. C₂×#11719921	C₂³	semidirect
279. C₂×#11719921	C₂³	semidirect
282. C₂²⋊C₄×D₅₃	C₂³	semidirect
286. C₂×C₄×Dic₅₃	C₂³	semidirect
291. C₄²×D₅₃	C₂³	semidirect
292. C₂²×Q₈×C₅₃	C₂³	semidirect
295. C₄⋊Q₈×C₅₃	C₂³	semidirect
296. C₄⋊Q₈×C₅₃	C₂³	semidirect
297. C₄⋊Q₈×C₅₃	C₂³	semidirect
298. #125×C₅₃	C₂³	semidirect
299. #125×C₅₃	C₂³	semidirect
303. C₂²⋊Q₈×C₅₃	C₂³	semidirect
304. C₂²⋊Q₈×C₅₃	C₂³	semidirect
305. C₂²⋊Q₈×C₅₃	C₂³	semidirect
306. C₂²⋊Q₈×C₅₃	C₂³	semidirect
307. C₄×Q₈×C₅₃	C₂³	semidirect
308. C₄×Q₈×C₅₃	C₂³	semidirect
315. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
316. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
333. C₂×D₄×C₅₃	#41	semidirect
461. C₂³×C₅₃	C₂×#41	semidirect
487. D₄×C₅₃	C₂×#41	semidirect
495. C₂×C₄×C₅₃	C₂×#41	semidirect
545. C₄×D₅₃	H(5,𝔽₂)	semidirect
591. #3501	D₅₃	semidirect
622. #554	C₂×D₅₃	semidirect
623. #554	C₂×D₅₃	semidirect
634. D₄×Q₈	C₂×D₅₃	semidirect
648. #544	C₂×D₅₃	semidirect
649. #543	C₂×D₅₃	semidirect
663. #533	C₂×D₅₃	semidirect
689. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
719. C₅₃	#62773	semidirect
730. C₂²×Q₈	C₂²×D₅₃	semidirect
757. C₄⋊Q₈	C₂²×D₅₃	semidirect
758. C₄⋊Q₈	C₂²×D₅₃	semidirect
759. C₄⋊Q₈	C₂²×D₅₃	semidirect
770. #125	C₂²×D₅₃	semidirect
771. #125	C₂²×D₅₃	semidirect
801. C₂²⋊Q₈	C₂²×D₅₃	semidirect
802. C₂²⋊Q₈	C₂²×D₅₃	semidirect
803. C₂²⋊Q₈	C₂²×D₅₃	semidirect
804. C₂²⋊Q₈	C₂²×D₅₃	semidirect
835. C₄×Q₈	C₂²×D₅₃	semidirect
836. C₄×Q₈	C₂²×D₅₃	semidirect
891. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
892. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
957. C₂×D₄	#11719949	semidirect
1076. C₂³	C₂×#11719949	semidirect
1095. D₄	C₂×#11719949	semidirect
1134. C₂×C₄	C₂×#11719949	semidirect

Maximal subgroups

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

subgroup	index
#20288765	2
#20288748	2
#20288658	2
#20288569	2
#20288556	2
#20288479	2
#20288425	2
#20288405	2
#20288351	2
#20288326	2
#20288281	2
D₄×#11719949	2
#20288138	2
#20288127	2
#20288012	2
C₂×#16811136	2
#20287919	2
C₂×C₄×D₄×D₅₃	2
C₅₃×#3501	2
#62773	53