Subgroups — C₂×#20288749 #28292089

Order 13568.

8774 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288749	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16811338	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16811333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16811326	C₂	1	2	yes	maximal, complemented
5	C₂×#16811319	C₂	1	2	yes	maximal, complemented
6	C₂×#16811295	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16811266	C₂	1	2	yes	maximal, complemented
8	C₂×#16811265	C₂	1	4	yes	maximal, complemented
9	C₂×D₄×D₂₁₂	C₂	1	2	yes	maximal, complemented
10	C₂×D₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#16811228	C₂	1	2	yes	maximal, complemented
12	C₂×#16811212	C₂	1	4	yes	maximal, complemented
13	C₂×#16811173	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#16811136	C₂	1	2	yes	maximal, complemented
15	C₂×#121×D₅₃	C₂	1	2	yes	maximal, complemented
16	C₂×#16811097	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#11719949	C₂²	1	2	yes	complemented
20	C₂²×#11719945	C₂²	1	2	yes	complemented
21	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
22	C₂³×D₂₁₂	C₂²	1	2	yes	—
23	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
24	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
25	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
26	#16811338	C₂²	1	16	yes	complemented
27	#16811333	C₂²	1	16	yes	complemented
28	#16811326	C₂²	1	32	yes	complemented
29	#16811319	C₂²	1	32	yes	complemented
30	#16811295	C₂²	1	16	yes	complemented
31	#16811266	C₂²	1	32	yes	complemented
32	#16811265	C₂²	1	64	yes	complemented
33	D₄×D₂₁₂	C₂²	1	32	yes	complemented
34	D₄×D₂₁₂	C₂²	1	16	yes	complemented
35	#16811228	C₂²	1	32	yes	complemented
36	#16811212	C₂²	1	64	yes	complemented
37	#16811173	C₂²	1	16	yes	complemented
38	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133214	C₂²	1	2	yes	complemented
40	C₂×#13133214	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13133212	C₂²	1	4	yes	complemented
42	C₂×#13133209	C₂²	1	2	yes	complemented
43	C₂×#13133205	C₂²	1	2	yes	complemented
44	C₂×#13133203	C₂²	1	4	yes	complemented
45	#16811136	C₂²	1	32	yes	complemented
46	C₂×#13133202	C₂²	1	4	yes	complemented
47	C₂×#13133202	C₂²	1	4	yes	complemented
48	C₂×#13133199	C₂²	1	4	yes	complemented
49	C₂×#13133195	C₂²	1	4	yes	complemented
50	C₂×#13133193	C₂²	1	2	yes	complemented
51	C₂×#13133192	C₂²	1	4	yes	complemented
52	C₂×#13133192	C₂²	1	4	yes	complemented
53	C₂×#13133192	C₂²	1	2	yes	complemented
54	C₂×#13133192	C₂²	1	2	yes	complemented
55	C₂×#13133191	C₂²	1	2	yes	complemented
56	C₂×#13133191	C₂²	1	2	yes	complemented
57	C₂×#13133191	C₂²	1	2	yes	complemented
58	C₂×#13133191	C₂²	1	2	yes	complemented
59	C₂×#13133190	C₂²	1	4	yes	complemented
60	C₂×#13133190	C₂²	1	4	yes	complemented
61	C₂×#13133189	C₂²	1	4	yes	complemented
62	C₂×#13133188	C₂²	1	2	yes	complemented
63	#121×D₅₃	C₂²	1	32	yes	complemented
64	C₂×#13133187	C₂²	1	4	yes	complemented
65	C₂×#13133187	C₂²	1	4	yes	complemented
66	C₂×#13133187	C₂²	1	4	yes	complemented
67	#16811097	C₂²	1	32	yes	complemented
68	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₂₁₂	C₂²	1	2	yes	—
71	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
72	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
73	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
74	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
75	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
77	C₂×C₄×D₂₁₂	C₂²	1	2	yes	complemented
78	C₂×C₄×D₂₁₂	C₂²	1	16	yes	complemented
79	C₂×#13133179	C₂²	1	4	yes	complemented
80	C₂×#13133179	C₂²	1	4	yes	complemented
81	C₂×#13133177	C₂²	1	4	yes	complemented
82	C₂×#13133176	C₂²	1	2	yes	complemented
83	C₂×#13133175	C₂²	1	2	yes	complemented
84	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
86	C₂²×#11719921	C₂²	1	2	yes	complemented
87	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
88	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
89	C₅₃×#529	C₂²	1	16	yes	complemented
90	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
91	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
94	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
95	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
96	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
98	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×#117×C₅₃	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
101	C₂⁴×D₅₃	C₂³	1	2	yes	—
102	C₂⁴×D₅₃	C₂³	1	4	yes	—
103	C₂×#11719949	—	4	8	no	—
104	C₂×#11719949	C₂³	1	16	yes	complemented
105	C₂×#11719945	—	4	8	no	—
106	C₂×#11719945	C₂³	1	16	yes	complemented
107	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
108	C₂²×D₂₁₂	—	2	8	no	—
109	C₂²×D₂₁₂	—	2	16	no	—
110	C₂²×D₂₁₂	C₂³	1	4	yes	—
111	C₂²×D₂₁₂	C₂³	1	2	yes	—
112	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
113	C₂²×D₂₁₂	C₂³	1	2	yes	—
114	C₂²×D₂₁₂	C₂³	1	8	yes	—
115	C₂²×D₂₁₂	C₂³	1	2	yes	—
116	C₂²×D₂₁₂	C₂³	1	16	yes	—
117	C₂²×D₂₁₂	C₂³	1	4	yes	—
118	C₂²×D₂₁₂	C₂³	1	2	yes	—
119	C₂²×D₂₁₂	C₂³	1	4	yes	—
120	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
121	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
123	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
124	C₂×D₄×D₅₃	—	4	8	no	—
125	C₂×D₄×D₅₃	—	4	16	no	—
126	C₂×D₄×D₅₃	C₂³	1	32	yes	complemented
127	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
128	C₂³×Dic₅₃	C₂³	1	2	yes	—
129	C₂²×C₄×D₅₃	—	4	8	no	—
130	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
131	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
132	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
133	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
134	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
135	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
136	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
137	C₂²×C₄×D₅₃	C₂³	1	16	yes	complemented
138	#13133217	C₂³	1	8	yes	complemented
139	#13133214	C₂³	1	8	yes	complemented
140	#13133214	C₂³	1	16	yes	complemented
141	#13133212	C₂³	1	32	yes	complemented
142	#13133209	C₂³	1	16	yes	complemented
143	#13133205	C₂³	1	16	yes	complemented
144	#13133203	C₂³	1	32	yes	complemented
145	#13133202	C₂³	1	32	yes	complemented
146	#13133202	C₂³	1	32	yes	complemented
147	#13133199	C₂³	1	32	yes	complemented
148	#13133195	C₂³	1	32	yes	complemented
149	#13133193	C₂³	1	16	yes	complemented
150	#13133192	C₂³	1	32	yes	complemented
151	#13133192	C₂³	1	16	yes	complemented
152	#13133192	C₂³	1	16	yes	complemented
153	#13133192	C₂³	1	32	yes	complemented
154	#13133191	C₂³	1	16	yes	complemented
155	#13133191	C₂³	1	16	yes	complemented
156	#13133191	C₂³	1	16	yes	complemented
157	#13133191	C₂³	1	16	yes	complemented
158	#13133190	C₂³	1	32	yes	complemented
159	#13133190	C₂³	1	32	yes	complemented
160	#13133189	C₂³	1	32	yes	complemented
161	#13133188	C₂³	1	16	yes	complemented
162	#13133187	C₂³	1	32	yes	complemented
163	#13133187	C₂³	1	32	yes	complemented
164	#13133187	C₂³	1	32	yes	complemented
165	C₄×D₂₁₂	C₂³	1	8	yes	—
166	C₄×D₂₁₂	C₂³	1	16	yes	—
167	C₄×D₂₁₂	C₂³	1	8	yes	—
168	C₄×D₂₁₂	C₂³	1	16	yes	complemented
169	C₄×D₂₁₂	C₂³	1	16	yes	complemented
170	C₄×D₂₁₂	C₂³	1	16	yes	complemented
171	C₄×D₂₁₂	C₂³	1	8	yes	complemented
172	C₄×D₂₁₂	C₂³	1	16	yes	complemented
173	C₄×D₂₁₂	C₂³	1	8	yes	complemented
174	C₄×D₂₁₂	C₂³	1	16	yes	complemented
175	#13133179	C₂³	1	32	yes	complemented
176	#13133179	C₂³	1	32	yes	complemented
177	#13133177	C₂³	1	32	yes	complemented
178	#13133176	C₂³	1	16	yes	complemented
179	#13133175	C₂³	1	16	yes	complemented
180	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
181	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
182	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
184	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
185	C₂×C₄⋊Dic₅₃	C₂³	1	8	yes	complemented
186	C₂×#11719919	C₂³	1	4	yes	—
187	C₂×#11719919	C₂³	1	4	yes	—
188	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
189	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
190	C₂×#11719921	C₂³	1	2	yes	—
191	C₂×#11719921	C₂³	1	4	yes	—
192	C₂×#11719921	C₂³	1	4	yes	—
193	C₂×#11719921	C₂³	1	4	yes	—
194	C₂×#11719921	C₂³	1	2	yes	—
195	C₂×#11719921	C₂³	1	2	yes	—
196	C₂×#11719921	C₂³	1	2	yes	—
197	C₂×#11719921	C₂³	1	4	yes	—
198	C₂×#11719921	C₂³	1	4	yes	—
199	C₂×#11719921	C₂³	1	4	yes	—
200	C₂×#11719921	C₂³	1	16	yes	complemented
201	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
202	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
203	C₂×C₄×Dic₅₃	C₂³	1	4	yes	—
204	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
206	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
211	#126×C₅₃	C₂³	1	16	yes	complemented
212	#125×C₅₃	C₂³	1	8	yes	complemented
213	#124×C₅₃	C₂³	1	8	yes	complemented
214	#123×C₅₃	C₂³	1	16	yes	complemented
215	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
216	#121×C₅₃	C₂³	1	8	yes	—
217	C₄×Q₈×C₅₃	C₂³	1	8	yes	complemented
218	C₄×D₄×C₅₃	C₂³	1	16	yes	complemented
219	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
220	#117×C₅₃	C₂³	1	16	yes	complemented
221	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
231	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
232	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
237	C₂×C₄²×C₅₃	C₂³	1	8	yes	complemented
238	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
239	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂³×D₅₃	—	2	8	no	—
241	C₂³×D₅₃	—	2	8	no	—
242	C₂³×D₅₃	—	2	16	no	—
243	C₂³×D₅₃	—	4	4	no	—
244	C₂³×D₅₃	—	4	8	no	—
245	C₂³×D₅₃	—	4	8	no	—
246	C₂³×D₅₃	C₂⁴	1	2	yes	—
247	C₂³×D₅₃	C₂⁴	1	4	yes	—
248	C₂³×D₅₃	C₂⁴	1	8	yes	—
249	C₂³×D₅₃	C₂⁴	1	2	yes	—
250	C₂³×D₅₃	C₂⁴	1	16	yes	—
251	C₂×Q₈×C₅₃	—	2	4	no	—
252	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
253	C₂×D₄×C₅₃	—	2	8	no	—
254	C₂×D₄×C₅₃	—	2	4	no	—
255	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
256	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₅₃	—	2	4	no	—
258	C₂²×C₄×C₅₃	—	2	4	no	—
259	C₂²×C₄×C₅₃	—	2	8	no	—
260	C₂²×C₄×C₅₃	—	2	4	no	—
261	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
272	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
274	C₂×C₂²⋊D₅₃	—	2	16	no	—
275	C₂×C₂²⋊D₅₃	—	4	8	no	—
276	C₂×C₂²⋊D₅₃	—	4	8	no	—
277	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
280	C₂²×Dic₅₃	—	4	4	no	—
281	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
282	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
283	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
284	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
285	#11719949	—	4	32	no	—
286	D₄×D₅₃	—	4	32	no	—
287	D₄×D₅₃	—	4	64	no	—
288	#11719945	—	4	32	no	—
289	C₂×D₂₁₂	—	2	16	no	—
290	C₂×D₂₁₂	—	2	8	no	—
291	C₂×D₂₁₂	—	2	4	no	—
292	C₂×D₂₁₂	—	2	8	no	—
293	C₂×D₂₁₂	—	2	8	no	—
294	C₂×D₂₁₂	—	2	32	no	—
295	C₂×D₂₁₂	—	2	64	no	—
296	C₂×D₂₁₂	—	4	8	no	—
297	C₂×D₂₁₂	—	4	4	no	—
298	C₂×D₂₁₂	—	4	8	no	—
299	C₂×D₂₁₂	#41	1	8	yes	complemented
300	C₂×D₂₁₂	C₂⁴	1	16	yes	—
301	C₂×D₂₁₂	C₂⁴	1	8	yes	—
302	C₂×D₂₁₂	C₂⁴	1	8	yes	—
303	C₂×D₂₁₂	C₂⁴	1	4	yes	—
304	C₂×D₂₁₂	C₂⁴	1	8	yes	—
305	C₂×D₂₁₂	C₂⁴	1	16	yes	—
306	C₂×D₂₁₂	C₂⁴	1	8	yes	—
307	C₂×D₂₁₂	C₂⁴	1	16	yes	—
308	C₂×D₂₁₂	C₂⁴	1	4	yes	—
309	C₂×C₄×D₅₃	—	2	8	no	—
310	C₂×C₄×D₅₃	—	2	8	no	—
311	C₂×C₄×D₅₃	—	4	32	no	—
312	C₂×C₄×D₅₃	—	4	4	no	—
313	C₂×C₄×D₅₃	—	4	4	no	—
314	C₂×C₄×D₅₃	—	4	8	no	—
315	C₂×C₄×D₅₃	—	4	8	no	—
316	C₂×C₄×D₅₃	—	4	8	no	—
317	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
318	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
319	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
320	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
321	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
322	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
323	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
324	C₂×Dic₁₀₆	—	4	4	no	—
325	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
326	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
329	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
330	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
331	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
332	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
334	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
337	C₄²×C₅₃	C₂⁴	1	4	yes	—
338	C₄²×C₅₃	C₂⁴	1	4	yes	—
339	C₄²×C₅₃	C₂⁴	1	4	yes	—
340	C₄²×C₅₃	C₂⁴	1	4	yes	—
341	C₄²×C₅₃	C₂⁴	1	8	yes	—
342	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
343	#11719921	C₂⁴	1	8	yes	—
344	#11719921	C₂⁴	1	16	yes	—
345	#11719921	C₂⁴	1	16	yes	—
346	#11719921	C₂⁴	1	16	yes	—
347	#11719921	C₂⁴	1	8	yes	—
348	#11719921	C₂⁴	1	8	yes	—
349	#11719921	C₂⁴	1	8	yes	—
350	#11719921	C₂⁴	1	16	yes	—
351	#11719921	C₂⁴	1	16	yes	—
352	#11719921	C₂⁴	1	16	yes	—
353	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
354	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
355	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
356	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
357	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
358	#11719919	C₂⁴	1	16	yes	—
359	#11719919	C₂⁴	1	16	yes	—
360	C₄×Dic₅₃	C₂⁴	1	16	yes	—
361	C₂³×C₅₃	—	2	2	no	—
362	C₂³×C₅₃	—	2	2	no	—
363	C₂³×C₅₃	—	2	4	no	—
364	C₂³×C₅₃	—	2	4	no	—
365	C₂³×C₅₃	—	2	4	no	—
366	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₅₃	C₂⁵	1	4	yes	—
368	C₂³×C₅₃	C₂⁵	1	2	yes	—
369	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
370	C₂²×D₅₃	—	2	4	no	—
371	C₂²×D₅₃	—	2	4	no	—
372	C₂²×D₅₃	—	2	4	no	—
373	C₂²×D₅₃	—	2	8	no	—
374	C₂²×D₅₃	—	2	4	no	—
375	C₂²×D₅₃	—	2	8	no	—
376	C₂²×D₅₃	—	2	8	no	—
377	C₂²×D₅₃	—	2	4	no	—
378	C₂²×D₅₃	—	2	16	no	—
379	C₂²×D₅₃	—	2	16	no	—
380	C₂²×D₅₃	—	2	32	no	—
381	C₂²×D₅₃	—	4	8	no	—
382	C₂²×D₅₃	—	4	16	no	—
383	C₂²×D₅₃	—	4	16	no	—
384	C₂²×D₅₃	—	4	32	no	—
385	C₂²×D₅₃	—	8	32	no	—
386	C₂²×D₅₃	C₂×#41	1	8	yes	—
387	C₂²×D₅₃	C₂⁵	1	4	yes	—
388	C₂²×D₅₃	C₂⁵	1	8	yes	—
389	C₂²×D₅₃	C₂⁵	1	4	yes	—
390	Q₈×C₅₃	—	2	8	no	—
391	D₄×C₅₃	—	2	16	no	—
392	D₄×C₅₃	—	2	8	no	—
393	C₂×C₄×C₅₃	—	2	2	no	—
394	C₂×C₄×C₅₃	—	2	4	no	—
395	C₂×C₄×C₅₃	—	2	2	no	—
396	C₂×C₄×C₅₃	—	2	2	no	—
397	C₂×C₄×C₅₃	—	2	2	no	—
398	C₂×C₄×C₅₃	—	2	4	no	—
399	C₂×C₄×C₅₃	—	2	4	no	—
400	C₂×C₄×C₅₃	—	2	8	no	—
401	C₂×C₄×C₅₃	—	2	8	no	—
402	C₂×C₄×C₅₃	—	2	16	no	—
403	C₂×C₄×C₅₃	—	2	8	no	—
404	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
405	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
406	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
407	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
408	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
409	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
410	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
411	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
412	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
413	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
414	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
415	C₂²⋊D₅₃	—	2	32	no	—
416	C₂²⋊D₅₃	—	4	16	no	—
417	C₂²⋊D₅₃	—	4	16	no	—
418	C₂×Dic₅₃	—	2	8	no	—
419	C₂×Dic₅₃	—	2	4	no	—
420	C₂×Dic₅₃	—	2	4	no	—
421	C₂×Dic₅₃	—	4	8	no	—
422	C₂×Dic₅₃	C₂⁵	1	8	yes	—
423	C₂×Dic₅₃	C₂⁵	1	4	yes	—
424	C₂×Dic₅₃	C₂⁵	1	4	yes	—
425	D₂₁₂	—	2	32	no	—
426	D₂₁₂	—	2	16	no	—
427	D₂₁₂	—	2	8	no	—
428	D₂₁₂	—	2	16	no	—
429	D₂₁₂	—	2	16	no	—
430	D₂₁₂	—	4	8	no	—
431	D₂₁₂	—	4	16	no	—
432	D₂₁₂	—	4	16	no	—
433	D₂₁₂	C₂×#41	1	16	yes	complemented
434	C₄×D₅₃	—	2	16	no	—
435	C₄×D₅₃	—	2	16	no	—
436	C₄×D₅₃	—	4	8	no	—
437	C₄×D₅₃	—	4	8	no	—
438	C₄×D₅₃	—	4	16	no	—
439	C₄×D₅₃	—	4	16	no	—
440	C₄×D₅₃	—	4	16	no	—
441	Dic₁₀₆	—	4	8	no	—
442	C₂×#3519	—	53	1	no	maximal, Sylow
443	C₂²×C₅₃	—	2	2	no	—
444	C₂²×C₅₃	—	2	2	no	—
445	C₂²×C₅₃	—	2	8	no	—
446	C₂²×C₅₃	—	2	4	no	—
447	C₂²×C₅₃	—	2	4	no	—
448	C₂²×C₅₃	—	2	4	no	—
449	C₂²×C₅₃	—	4	8	no	—
450	C₂²×C₅₃	C₂²×#41	1	2	yes	—
451	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
452	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
453	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
454	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
455	C₂×D₅₃	—	2	4	no	—
456	C₂×D₅₃	—	2	4	no	—
457	C₂×D₅₃	—	2	16	no	—
458	C₂×D₅₃	—	2	4	no	—
459	C₂×D₅₃	—	2	8	no	—
460	C₂×D₅₃	—	2	4	no	—
461	C₂×D₅₃	—	2	8	no	—
462	C₂×D₅₃	—	2	8	no	—
463	C₂×D₅₃	—	2	4	no	—
464	C₂×D₅₃	—	4	32	no	—
465	C₂×D₅₃	—	4	8	no	—
466	C₂×D₅₃	—	4	16	no	—
467	C₂×D₅₃	—	8	32	no	—
468	C₂×D₅₃	C₂²×#41	1	8	yes	—
469	C₄×C₅₃	—	2	4	no	—
470	C₄×C₅₃	—	2	2	no	—
471	C₄×C₅₃	—	2	2	no	—
472	C₄×C₅₃	—	2	2	no	—
473	C₄×C₅₃	—	2	2	no	—
474	C₄×C₅₃	—	2	4	no	—
475	C₄×C₅₃	—	2	4	no	—
476	C₄×C₅₃	C₂²×#41	1	4	yes	—
477	C₄×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
478	Dic₅₃	—	2	8	no	—
479	Dic₅₃	—	2	4	no	—
480	Dic₅₃	—	2	4	no	—
481	#3519	—	53	32	no	—
482	C₂×#555	—	53	1	no	—
483	C₂×#554	—	53	1	no	—
484	C₂×#553	—	53	2	no	—
485	C₂×#553	—	53	2	no	—
486	C₂×#550	—	53	1	no	—
487	C₂×#546	—	53	2	no	—
488	C₂×#546	—	53	4	no	—
489	C₂×D₄²	—	53	1	no	—
490	C₂×D₄²	—	53	2	no	—
491	C₂×#540	—	53	2	no	—
492	C₂×#538	—	53	4	no	—
493	C₂×#532	—	53	1	no	—
494	C₂×#529	D₅₃	1	1	yes	characteristic, complemented
495	C₂×#525	—	53	2	no	—
496	C₂²×#121	—	53	2	no	—
497	C₂×#518	—	53	2	no	—
498	C₂²×C₄×D₄	—	53	1	no	—
499	C₂×C₅₃	—	2	4	no	—
500	C₂×C₅₃	—	4	4	no	—
501	C₂×C₅₃	#3519	1	4	yes	complemented
502	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
503	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
505	D₅₃	—	2	8	no	—
506	D₅₃	—	4	4	no	—
507	D₅₃	—	4	8	no	—
508	C₂²×#41	—	53	2	no	—
509	C₂²×#41	—	53	2	no	—
510	C₂³×D₄	—	53	2	no	—
511	C₂³×D₄	—	53	4	no	—
512	C₂³×D₄	—	53	1	no	—
513	C₂³×D₄	—	53	2	no	—
514	C₂⁴×C₄	—	53	2	no	—
515	#555	—	53	16	no	—
516	#554	—	53	16	no	—
517	#553	—	53	32	no	—
518	#553	—	53	32	no	—
519	#550	—	53	16	no	—
520	#546	—	53	32	no	—
521	#546	—	53	64	no	—
522	D₄²	—	53	16	no	—
523	D₄²	—	53	32	no	—
524	#540	—	53	32	no	—
525	#538	—	53	64	no	—
526	#532	—	53	16	no	—
527	C₂×C₄⋊Q₈	—	53	1	no	—
528	C₂×#127	—	53	1	no	—
529	C₂×#127	—	53	2	no	—
530	#529	C₂×D₅₃	1	16	yes	complemented
531	C₂×#126	—	53	4	no	—
532	C₂×#126	C₂×D₅₃	1	2	yes	complemented
533	C₂×#125	—	53	2	no	—
534	C₂×#125	C₂×D₅₃	1	1	yes	characteristic, complemented
535	C₂×#124	—	53	4	no	—
536	C₂×#124	—	53	2	no	—
537	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
538	#525	—	53	32	no	—
539	C₂×#123	—	53	4	no	—
540	C₂×#123	—	53	4	no	—
541	C₂×#123	—	53	4	no	—
542	C₂×#123	C₂×D₅₃	1	2	yes	complemented
543	C₂×C₂²⋊Q₈	—	53	2	no	—
544	C₂×C₂²⋊Q₈	—	53	4	no	—
545	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
546	C₂×#121	—	53	2	no	—
547	C₂×#121	—	53	4	no	—
548	C₂×#121	—	53	2	no	—
549	C₂×#121	—	53	2	no	—
550	C₂×#121	—	53	2	no	—
551	C₂×#121	—	53	2	no	—
552	C₂×#121	—	53	32	no	—
553	C₂×#121	—	53	2	no	—
554	C₂×#121	—	53	2	no	—
555	C₂×#121	—	53	4	no	—
556	C₂×#121	—	53	4	no	—
557	C₂×#121	—	53	4	no	—
558	C₂×#121	—	53	4	no	—
559	C₂×#121	C₂×D₅₃	1	1	yes	characteristic
560	C₂×#120	—	53	4	no	—
561	C₂×#120	—	53	4	no	—
562	C₂×#120	—	53	4	no	—
563	#518	—	53	32	no	—
564	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
565	C₂×C₄×D₄	—	53	4	no	—
566	C₂×C₄×D₄	—	53	4	no	—
567	C₂×C₄×D₄	—	53	4	no	—
568	C₂×C₄×D₄	—	53	1	no	—
569	C₂×C₄×D₄	—	53	1	no	—
570	C₂×C₄×D₄	—	53	2	no	—
571	C₂×C₄×D₄	—	53	2	no	—
572	C₂×C₄×D₄	—	53	1	no	—
573	C₂×C₄×D₄	—	53	2	no	—
574	C₂×C₄×D₄	—	53	1	no	—
575	C₂×C₄×D₄	—	53	2	no	—
576	C₂×C₄×D₄	—	53	2	no	—
577	C₂×C₄×D₄	—	53	2	no	—
578	C₂×C₄×D₄	—	53	16	no	—
579	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
580	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
581	C₂×#117	—	53	2	no	—
582	C₂×#117	—	53	2	no	—
583	C₂×#117	C₂×D₅₃	1	2	yes	complemented
584	C₂²×C₄⋊C₄	—	53	1	no	—
585	C₂²×C₄⋊C₄	—	53	2	no	—
586	C₂²×C₂²⋊C₄	—	53	2	no	—
587	C₂²×C₂²⋊C₄	—	53	4	no	—
588	C₂²×C₂²⋊C₄	—	53	4	no	—
589	C₂²×C₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
590	C₅₃	C₂×#3519	1	1	yes	characteristic, complemented, Sylow
591	C₂⁵	—	53	2	no	—
592	C₂⁵	—	53	4	no	—
593	C₂×#41	—	53	16	no	—
594	C₂×#41	—	53	16	no	—
595	C₂×#41	—	212	8	no	—
596	C₂×#41	—	212	8	no	—
597	C₂²×Q₈	—	53	2	no	—
598	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
599	C₂²×D₄	—	53	4	no	—
600	C₂²×D₄	—	53	4	no	—
601	C₂²×D₄	—	53	4	no	—
602	C₂²×D₄	—	53	16	no	—
603	C₂²×D₄	—	53	32	no	—
604	C₂²×D₄	—	53	1	no	—
605	C₂²×D₄	—	53	4	no	—
606	C₂²×D₄	—	53	2	no	—
607	C₂²×D₄	—	53	1	no	—
608	C₂²×D₄	—	53	2	no	—
609	C₂²×D₄	—	53	8	no	—
610	C₂²×D₄	—	53	2	no	—
611	C₂²×D₄	—	53	16	no	—
612	C₂²×D₄	—	53	4	no	—
613	C₂²×D₄	—	53	2	no	—
614	C₂²×D₄	—	53	4	no	—
615	C₂²×D₄	—	106	16	no	—
616	C₂²×D₄	—	106	8	no	—
617	C₂²×D₄	—	212	8	no	—
618	C₂²×D₄	—	212	16	no	—
619	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
620	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
621	C₂³×C₄	—	53	2	no	—
622	C₂³×C₄	—	53	2	no	—
623	C₂³×C₄	—	53	2	no	—
624	C₂³×C₄	—	53	2	no	—
625	C₂³×C₄	—	53	4	no	—
626	C₂³×C₄	—	53	4	no	—
627	C₂³×C₄	—	53	4	no	—
628	C₂³×C₄	—	53	2	no	—
629	C₂³×C₄	—	53	16	no	—
630	C₂³×C₄	—	212	8	no	—
631	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
632	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
633	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
634	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
635	C₄⋊Q₈	—	53	8	no	—
636	#127	—	53	8	no	—
637	#127	—	53	16	no	—
638	#126	—	53	32	no	—
639	#126	C₂²×D₅₃	1	16	yes	complemented
640	#125	—	53	16	no	—
641	#125	C₂²×D₅₃	1	8	yes	complemented
642	#124	—	53	32	no	—
643	#124	—	53	16	no	—
644	#124	C₂²×D₅₃	1	8	yes	complemented
645	#123	—	53	32	no	—
646	#123	—	53	32	no	—
647	#123	—	53	32	no	—
648	#123	C₂²×D₅₃	1	16	yes	complemented
649	C₂²⋊Q₈	—	53	16	no	—
650	C₂²⋊Q₈	—	53	32	no	—
651	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
652	#121	—	53	32	no	—
653	#121	—	53	16	no	—
654	#121	—	53	16	no	—
655	#121	—	53	16	no	—
656	#121	—	53	16	no	—
657	#121	—	53	16	no	—
658	#121	—	53	16	no	—
659	#121	—	53	16	no	—
660	#121	—	53	32	no	—
661	#121	—	53	32	no	—
662	#121	—	53	32	no	—
663	#121	—	53	32	no	—
664	#121	C₂²×D₅₃	1	8	yes	—
665	#120	—	53	32	no	—
666	#120	—	53	32	no	—
667	#120	—	53	32	no	—
668	C₄×Q₈	C₂²×D₅₃	1	8	yes	complemented
669	C₄×D₄	—	53	32	no	—
670	C₄×D₄	—	53	32	no	—
671	C₄×D₄	—	53	32	no	—
672	C₄×D₄	—	53	8	no	—
673	C₄×D₄	—	53	16	no	—
674	C₄×D₄	—	53	8	no	—
675	C₄×D₄	—	53	8	no	—
676	C₄×D₄	—	53	16	no	—
677	C₄×D₄	—	53	8	no	—
678	C₄×D₄	—	53	16	no	—
679	C₄×D₄	—	53	16	no	—
680	C₄×D₄	—	53	16	no	—
681	C₄×D₄	—	53	16	no	—
682	C₄×D₄	C₂²×D₅₃	1	16	yes	complemented
683	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
684	#117	—	53	16	no	—
685	#117	—	53	16	no	—
686	#117	C₂²×D₅₃	1	16	yes	complemented
687	C₂×C₄⋊C₄	—	53	1	no	—
688	C₂×C₄⋊C₄	—	53	2	no	—
689	C₂×C₄⋊C₄	—	53	1	no	—
690	C₂×C₄⋊C₄	—	53	2	no	—
691	C₂×C₄⋊C₄	—	53	8	no	—
692	C₂×C₄⋊C₄	—	53	4	no	—
693	C₂×C₄⋊C₄	—	53	2	no	—
694	C₂×C₄⋊C₄	—	53	4	no	—
695	C₂×C₄⋊C₄	—	53	16	no	—
696	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
700	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
701	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
702	C₂×C₂²⋊C₄	—	53	4	no	—
703	C₂×C₂²⋊C₄	—	53	2	no	—
704	C₂×C₂²⋊C₄	—	53	4	no	—
705	C₂×C₂²⋊C₄	—	53	2	no	—
706	C₂×C₂²⋊C₄	—	53	4	no	—
707	C₂×C₂²⋊C₄	—	53	2	no	—
708	C₂×C₂²⋊C₄	—	53	4	no	—
709	C₂×C₂²⋊C₄	—	53	2	no	—
710	C₂×C₂²⋊C₄	—	53	16	no	—
711	C₂×C₂²⋊C₄	—	53	4	no	—
712	C₂×C₂²⋊C₄	—	53	4	no	—
713	C₂×C₂²⋊C₄	—	53	4	no	—
714	C₂×C₂²⋊C₄	—	53	32	no	—
715	C₂×C₂²⋊C₄	—	53	32	no	—
716	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
721	C₂×C₄²	—	53	4	no	—
722	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
723	C₂×C₄²	C₂²×D₅₃	1	2	yes	—
724	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
725	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
726	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
727	C₂×C₄²	C₂²×D₅₃	1	8	yes	complemented
728	C₂⁴	—	53	2	no	—
729	C₂⁴	—	53	2	no	—
730	C₂⁴	—	53	4	no	—
731	C₂⁴	—	53	8	no	—
732	C₂⁴	—	53	16	no	—
733	C₂⁴	—	106	16	no	—
734	C₂⁴	—	106	8	no	—
735	C₂⁴	—	106	8	no	—
736	C₂⁴	—	212	8	no	—
737	C₂⁴	—	212	8	no	—
738	C₂⁴	—	212	4	no	—
739	C₂⁴	C₂³×D₅₃	1	2	yes	—
740	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
741	#41	—	212	32	no	—
742	#41	—	212	32	no	—
743	C₂×Q₈	—	2	4	no	—
744	C₂×Q₈	—	53	8	no	—
745	C₂×Q₈	—	212	4	no	—
746	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
747	C₂×D₄	—	2	8	no	—
748	C₂×D₄	—	2	4	no	—
749	C₂×D₄	—	53	16	no	—
750	C₂×D₄	—	53	16	no	—
751	C₂×D₄	—	53	16	no	—
752	C₂×D₄	—	53	8	no	—
753	C₂×D₄	—	53	4	no	—
754	C₂×D₄	—	53	16	no	—
755	C₂×D₄	—	53	8	no	—
756	C₂×D₄	—	53	4	no	—
757	C₂×D₄	—	53	8	no	—
758	C₂×D₄	—	53	8	no	—
759	C₂×D₄	—	53	16	no	—
760	C₂×D₄	—	53	8	no	—
761	C₂×D₄	—	53	16	no	—
762	C₂×D₄	—	106	64	no	—
763	C₂×D₄	—	106	32	no	—
764	C₂×D₄	—	106	16	no	—
765	C₂×D₄	—	106	8	no	—
766	C₂×D₄	—	106	16	no	—
767	C₂×D₄	—	106	8	no	—
768	C₂×D₄	—	106	4	no	—
769	C₂×D₄	—	106	8	no	—
770	C₂×D₄	—	212	8	no	—
771	C₂×D₄	—	212	4	no	—
772	C₂×D₄	—	212	8	no	—
773	C₂×D₄	—	212	32	no	—
774	C₂×D₄	—	212	8	no	—
775	C₂×D₄	—	212	8	no	—
776	C₂×D₄	—	212	64	no	—
777	C₂×D₄	C₂³×D₅₃	1	8	yes	—
778	C₂×D₄	C₂³×D₅₃	1	4	yes	—
779	C₂²×C₄	—	2	4	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	2	8	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	53	2	no	—
784	C₂²×C₄	—	53	4	no	—
785	C₂²×C₄	—	53	2	no	—
786	C₂²×C₄	—	53	8	no	—
787	C₂²×C₄	—	53	8	no	—
788	C₂²×C₄	—	53	8	no	—
789	C₂²×C₄	—	53	8	no	—
790	C₂²×C₄	—	53	16	no	—
791	C₂²×C₄	—	53	16	no	—
792	C₂²×C₄	—	53	16	no	—
793	C₂²×C₄	—	53	8	no	—
794	C₂²×C₄	—	106	8	no	—
795	C₂²×C₄	—	106	8	no	—
796	C₂²×C₄	—	212	32	no	—
797	C₂²×C₄	—	212	4	no	—
798	C₂²×C₄	—	212	4	no	—
799	C₂²×C₄	—	212	8	no	—
800	C₂²×C₄	—	212	8	no	—
801	C₂²×C₄	—	212	8	no	—
802	C₂²×C₄	—	212	4	no	—
803	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
804	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
805	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
806	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
807	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
808	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
809	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
810	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
811	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
812	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
813	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
814	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
815	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
816	C₄⋊C₄	—	53	4	no	—
817	C₄⋊C₄	—	53	8	no	—
818	C₄⋊C₄	—	53	4	no	—
819	C₄⋊C₄	—	53	8	no	—
820	C₄⋊C₄	—	53	16	no	—
821	C₄⋊C₄	—	53	8	no	—
822	C₄⋊C₄	—	53	16	no	—
823	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
824	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
825	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
826	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
827	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
828	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
829	C₂²⋊C₄	—	53	16	no	—
830	C₂²⋊C₄	—	53	8	no	—
831	C₂²⋊C₄	—	53	16	no	—
832	C₂²⋊C₄	—	53	8	no	—
833	C₂²⋊C₄	—	53	16	no	—
834	C₂²⋊C₄	—	53	8	no	—
835	C₂²⋊C₄	—	53	16	no	—
836	C₂²⋊C₄	—	53	8	no	—
837	C₂²⋊C₄	—	53	16	no	—
838	C₂²⋊C₄	—	53	16	no	—
839	C₂²⋊C₄	—	53	16	no	—
840	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
841	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
842	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
843	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
844	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
845	C₄²	—	53	16	no	—
846	C₄²	C₂³×D₅₃	1	4	yes	—
847	C₄²	C₂³×D₅₃	1	4	yes	—
848	C₄²	C₂³×D₅₃	1	4	yes	—
849	C₄²	C₂³×D₅₃	1	4	yes	—
850	C₄²	C₂³×D₅₃	1	8	yes	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	2	4	no	—
855	C₂³	—	2	4	no	—
856	C₂³	—	53	8	no	—
857	C₂³	—	53	4	no	—
858	C₂³	—	53	4	no	—
859	C₂³	—	53	8	no	—
860	C₂³	—	106	32	no	—
861	C₂³	—	106	16	no	—
862	C₂³	—	106	4	no	—
863	C₂³	—	106	4	no	—
864	C₂³	—	106	8	no	—
865	C₂³	—	106	4	no	—
866	C₂³	—	106	4	no	—
867	C₂³	—	106	8	no	—
868	C₂³	—	106	8	no	—
869	C₂³	—	106	16	no	—
870	C₂³	—	106	4	no	—
871	C₂³	—	424	32	no	—
872	C₂³	—	212	16	no	—
873	C₂³	—	212	16	no	—
874	C₂³	—	212	8	no	—
875	C₂³	—	212	32	no	—
876	C₂³	#13133263	1	4	yes	—
877	C₂³	C₂⁴×D₅₃	1	4	yes	—
878	C₂³	C₂⁴×D₅₃	1	2	yes	—
879	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
880	Q₈	—	2	8	no	—
881	Q₈	—	212	8	no	—
882	D₄	—	2	16	no	—
883	D₄	—	2	8	no	—
884	D₄	—	53	16	no	—
885	D₄	—	106	32	no	—
886	D₄	—	106	16	no	—
887	D₄	—	106	32	no	—
888	D₄	—	106	16	no	—
889	D₄	—	106	8	no	—
890	D₄	—	106	16	no	—
891	D₄	—	212	16	no	—
892	D₄	—	212	8	no	—
893	D₄	—	212	16	no	—
894	D₄	—	212	16	no	—
895	D₄	—	212	16	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	8	no	—
902	C₂×C₄	—	2	4	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	16	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	53	4	no	—
908	C₂×C₄	—	53	8	no	—
909	C₂×C₄	—	53	4	no	—
910	C₂×C₄	—	106	4	no	—
911	C₂×C₄	—	106	4	no	—
912	C₂×C₄	—	106	8	no	—
913	C₂×C₄	—	106	16	no	—
914	C₂×C₄	—	106	16	no	—
915	C₂×C₄	—	212	8	no	—
916	C₂×C₄	—	212	8	no	—
917	C₂×C₄	—	212	16	no	—
918	C₂×C₄	—	212	16	no	—
919	C₂×C₄	—	212	16	no	—
920	C₂×C₄	—	212	8	no	—
921	C₂×C₄	#41×D₅₃	1	4	yes	—
922	C₂×C₄	#13133263	1	4	yes	—
923	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
924	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
925	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
926	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
927	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
928	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
929	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
930	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
931	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	8	no	—
934	C₂²	—	2	2	no	—
935	C₂²	—	2	4	no	—
936	C₂²	—	2	4	no	—
937	C₂²	—	2	4	no	—
938	C₂²	—	4	8	no	—
939	C₂²	—	53	8	no	—
940	C₂²	—	106	16	no	—
941	C₂²	—	106	4	no	—
942	C₂²	—	106	4	no	—
943	C₂²	—	106	8	no	—
944	C₂²	—	106	4	no	—
945	C₂²	—	106	4	no	—
946	C₂²	—	106	8	no	—
947	C₂²	—	106	8	no	—
948	C₂²	—	106	4	no	—
949	C₂²	—	424	32	no	—
950	C₂²	—	212	32	no	—
951	C₂²	—	212	16	no	—
952	C₂²	—	212	8	no	—
953	C₂²	C₂×#41×D₅₃	1	2	yes	—
954	C₂²	C₂×#13133263	1	4	yes	—
955	C₂²	C₂×#13133263	1	2	yes	—
956	C₂²	C₂×#13133263	1	2	yes	—
957	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
958	C₄	—	2	4	no	—
959	C₄	—	2	2	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	2	no	—
963	C₄	—	2	4	no	—
964	C₄	—	2	4	no	—
965	C₄	—	106	4	no	—
966	C₄	—	106	4	no	—
967	C₄	—	106	8	no	—
968	C₄	C₂×#41×D₅₃	1	4	yes	—
969	C₄	C₂×#13133263	1	4	yes	—
970	C₂	—	2	4	no	—
971	C₂	—	4	4	no	—
972	C₂	—	106	8	no	—
973	C₂	—	212	8	no	—
974	C₂	—	212	4	no	—
975	C₂	#20288749	1	4	yes	direct product factor
976	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
977	C₂	C₂²×#13133263	1	1	yes	characteristic
978	C₂	C₂²×#13133263	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅₃
commutator, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₂×C₅₃×#529	C₂
socle	C₂³×C₅₃	C₂⁵
hypercenter	C₂×#529	D₅₃
hypocenter	C₅₃	C₂×#3519
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #20288749	C₂	direct (N × H)
2. C₂×#16811338	C₂	semidirect
3. C₂×#16811333	C₂	semidirect
4. C₂×#16811326	C₂	semidirect
5. C₂×#16811319	C₂	semidirect
6. C₂×#16811295	C₂	semidirect
7. C₂×#16811266	C₂	semidirect
8. C₂×#16811265	C₂	semidirect
9. C₂×D₄×D₂₁₂	C₂	semidirect
10. C₂×D₄×D₂₁₂	C₂	semidirect
11. C₂×#16811228	C₂	semidirect
12. C₂×#16811212	C₂	semidirect
13. C₂×#16811173	C₂	semidirect
14. C₂×#16811136	C₂	semidirect
15. C₂×#121×D₅₃	C₂	semidirect
16. C₂×#16811097	C₂	semidirect
17. C₂²×C₄×D₂₁₂	C₂	semidirect
18. C₂×C₅₃×#529	C₂	semidirect
19. C₂²×#11719949	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
23. C₂²×D₄×D₅₃	C₂²	semidirect
24. C₂²×D₄×D₅₃	C₂²	semidirect
25. C₂³×C₄×D₅₃	C₂²	semidirect
26. #16811338	C₂²	semidirect
27. #16811333	C₂²	semidirect
28. #16811326	C₂²	semidirect
29. #16811319	C₂²	semidirect
30. #16811295	C₂²	semidirect
31. #16811266	C₂²	semidirect
32. #16811265	C₂²	semidirect
33. D₄×D₂₁₂	C₂²	semidirect
34. D₄×D₂₁₂	C₂²	semidirect
35. #16811228	C₂²	semidirect
36. #16811212	C₂²	semidirect
37. #16811173	C₂²	semidirect
38. C₂×#13133217	C₂²	semidirect
39. C₂×#13133214	C₂²	semidirect
40. C₂×#13133214	C₂²	semidirect
41. C₂×#13133212	C₂²	semidirect
42. C₂×#13133209	C₂²	semidirect
43. C₂×#13133205	C₂²	semidirect
44. C₂×#13133203	C₂²	semidirect
45. #16811136	C₂²	semidirect
46. C₂×#13133202	C₂²	semidirect
47. C₂×#13133202	C₂²	semidirect
48. C₂×#13133199	C₂²	semidirect
49. C₂×#13133195	C₂²	semidirect
50. C₂×#13133193	C₂²	semidirect
51. C₂×#13133192	C₂²	semidirect
52. C₂×#13133192	C₂²	semidirect
53. C₂×#13133192	C₂²	semidirect
54. C₂×#13133192	C₂²	semidirect
55. C₂×#13133191	C₂²	semidirect
56. C₂×#13133191	C₂²	semidirect
57. C₂×#13133191	C₂²	semidirect
58. C₂×#13133191	C₂²	semidirect
59. C₂×#13133190	C₂²	semidirect
60. C₂×#13133190	C₂²	semidirect
61. C₂×#13133189	C₂²	semidirect
62. C₂×#13133188	C₂²	semidirect
63. #121×D₅₃	C₂²	semidirect
64. C₂×#13133187	C₂²	semidirect
65. C₂×#13133187	C₂²	semidirect
66. C₂×#13133187	C₂²	semidirect
67. #16811097	C₂²	semidirect
71. C₂×C₄×D₂₁₂	C₂²	semidirect
72. C₂×C₄×D₂₁₂	C₂²	semidirect
73. C₂×C₄×D₂₁₂	C₂²	semidirect
74. C₂×C₄×D₂₁₂	C₂²	semidirect
75. C₂×C₄×D₂₁₂	C₂²	semidirect
76. C₂×C₄×D₂₁₂	C₂²	semidirect
77. C₂×C₄×D₂₁₂	C₂²	semidirect
78. C₂×C₄×D₂₁₂	C₂²	semidirect
79. C₂×#13133179	C₂²	semidirect
80. C₂×#13133179	C₂²	semidirect
81. C₂×#13133177	C₂²	semidirect
82. C₂×#13133176	C₂²	semidirect
83. C₂×#13133175	C₂²	semidirect
84. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
85. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
86. C₂²×#11719921	C₂²	semidirect
87. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
88. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
89. C₅₃×#529	C₂²	semidirect
90. C₂×#126×C₅₃	C₂²	semidirect
91. C₂×#125×C₅₃	C₂²	semidirect
92. C₂×#124×C₅₃	C₂²	semidirect
93. C₂×#123×C₅₃	C₂²	semidirect
94. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
96. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
97. C₂×C₄×D₄×C₅₃	C₂²	semidirect
98. C₂×C₄×D₄×C₅₃	C₂²	semidirect
99. C₂×#117×C₅₃	C₂²	semidirect
100. C₂²×C₄²×C₅₃	C₂²	semidirect
104. C₂×#11719949	C₂³	semidirect
106. C₂×#11719945	C₂³	semidirect
126. C₂×D₄×D₅₃	C₂³	semidirect
127. C₂×D₄×D₅₃	C₂³	semidirect
137. C₂²×C₄×D₅₃	C₂³	semidirect
138. #13133217	C₂³	semidirect
139. #13133214	C₂³	semidirect
140. #13133214	C₂³	semidirect
141. #13133212	C₂³	semidirect
142. #13133209	C₂³	semidirect
143. #13133205	C₂³	semidirect
144. #13133203	C₂³	semidirect
145. #13133202	C₂³	semidirect
146. #13133202	C₂³	semidirect
147. #13133199	C₂³	semidirect
148. #13133195	C₂³	semidirect
149. #13133193	C₂³	semidirect
150. #13133192	C₂³	semidirect
151. #13133192	C₂³	semidirect
152. #13133192	C₂³	semidirect
153. #13133192	C₂³	semidirect
154. #13133191	C₂³	semidirect
155. #13133191	C₂³	semidirect
156. #13133191	C₂³	semidirect
157. #13133191	C₂³	semidirect
158. #13133190	C₂³	semidirect
159. #13133190	C₂³	semidirect
160. #13133189	C₂³	semidirect
161. #13133188	C₂³	semidirect
162. #13133187	C₂³	semidirect
163. #13133187	C₂³	semidirect
164. #13133187	C₂³	semidirect
168. C₄×D₂₁₂	C₂³	semidirect
169. C₄×D₂₁₂	C₂³	semidirect
170. C₄×D₂₁₂	C₂³	semidirect
171. C₄×D₂₁₂	C₂³	semidirect
172. C₄×D₂₁₂	C₂³	semidirect
173. C₄×D₂₁₂	C₂³	semidirect
174. C₄×D₂₁₂	C₂³	semidirect
175. #13133179	C₂³	semidirect
176. #13133179	C₂³	semidirect
177. #13133177	C₂³	semidirect
178. #13133176	C₂³	semidirect
179. #13133175	C₂³	semidirect
185. C₂×C₄⋊Dic₅₃	C₂³	semidirect
188. C₄⋊C₄×D₅₃	C₂³	semidirect
200. C₂×#11719921	C₂³	semidirect
201. C₂²⋊C₄×D₅₃	C₂³	semidirect
202. C₂²⋊C₄×D₅₃	C₂³	semidirect
211. #126×C₅₃	C₂³	semidirect
212. #125×C₅₃	C₂³	semidirect
213. #124×C₅₃	C₂³	semidirect
214. #123×C₅₃	C₂³	semidirect
215. C₂²⋊Q₈×C₅₃	C₂³	semidirect
217. C₄×Q₈×C₅₃	C₂³	semidirect
218. C₄×D₄×C₅₃	C₂³	semidirect
219. C₄×D₄×C₅₃	C₂³	semidirect
220. #117×C₅₃	C₂³	semidirect
237. C₂×C₄²×C₅₃	C₂³	semidirect
299. C₂×D₂₁₂	#41	semidirect
433. D₂₁₂	C₂×#41	semidirect
494. C₂×#529	D₅₃	semidirect
501. C₂×C₅₃	#3519	semidirect
530. #529	C₂×D₅₃	semidirect
532. C₂×#126	C₂×D₅₃	semidirect
534. C₂×#125	C₂×D₅₃	semidirect
537. C₂×#124	C₂×D₅₃	semidirect
542. C₂×#123	C₂×D₅₃	semidirect
545. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
564. C₂×C₄×Q₈	C₂×D₅₃	semidirect
579. C₂×C₄×D₄	C₂×D₅₃	semidirect
580. C₂×C₄×D₄	C₂×D₅₃	semidirect
583. C₂×#117	C₂×D₅₃	semidirect
589. C₂²×C₄²	C₂×D₅₃	semidirect
590. C₅₃	C₂×#3519	semidirect
639. #126	C₂²×D₅₃	semidirect
641. #125	C₂²×D₅₃	semidirect
644. #124	C₂²×D₅₃	semidirect
648. #123	C₂²×D₅₃	semidirect
651. C₂²⋊Q₈	C₂²×D₅₃	semidirect
668. C₄×Q₈	C₂²×D₅₃	semidirect
682. C₄×D₄	C₂²×D₅₃	semidirect
683. C₄×D₄	C₂²×D₅₃	semidirect
686. #117	C₂²×D₅₃	semidirect
727. C₂×C₄²	C₂²×D₅₃	semidirect
975. C₂	#20288749	direct (N × H)

Maximal subgroups

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

subgroup	index
#20288749	2
C₂×#16811338	2
C₂×#16811333	2
C₂×#16811326	2
C₂×#16811319	2
C₂×#16811295	2
C₂×#16811266	2
C₂×#16811265	2
C₂×D₄×D₂₁₂	2
C₂×#16811228	2
C₂×#16811212	2
C₂×#16811173	2
C₂×#16811136	2
C₂×#121×D₅₃	2
C₂×#16811097	2
C₂²×C₄×D₂₁₂	2
C₂×C₅₃×#529	2
C₂×#3519	53

Subgroups — C2×#20288749 #28292089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20288749 #28292089