Subgroups — #44564726

Order 32128.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632426	C₂	1	2	yes	maximal, complemented
2	#30632425	C₂	1	2	yes	maximal, complemented
3	#30632406	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632380	C₂	1	2	yes	maximal, complemented
5	#30632357	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632357	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632356	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632336	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632331	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632330	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632324	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632308	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632306	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632272	C₂	1	2	yes	maximal, complemented
16	#30632269	C₂	1	2	yes	maximal, complemented
17	#30632264	C₂	1	2	yes	maximal, complemented
18	#30632252	C₂	1	2	yes	maximal, complemented
19	#30632250	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632236	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632235	C₂	1	1	yes	maximal, characteristic, complemented
22	#30632215	C₂	1	1	yes	maximal, characteristic, complemented
23	#535×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860811	C₂²	1	1	yes	characteristic, complemented
25	C₂×#16860809	C₂²	1	2	yes	complemented
26	C₂×#16860809	C₂²	1	1	yes	characteristic, complemented
27	C₂×#16860809	C₂²	1	1	yes	characteristic, complemented
28	C₂×#16860809	C₂²	1	2	yes	complemented
29	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
30	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
31	#22548715	C₂²	1	1	yes	characteristic, complemented
32	#22548713	C₂²	1	1	yes	characteristic, complemented
33	#22548711	C₂²	1	1	yes	characteristic
34	#22548711	C₂²	1	1	yes	characteristic, complemented
35	#22548711	C₂²	1	2	yes	complemented
36	#22548711	C₂²	1	2	yes	complemented
37	#22548710	C₂²	1	1	yes	characteristic, complemented
38	#22548710	C₂²	1	2	yes	complemented
39	#22548708	C₂²	1	1	yes	characteristic, complemented
40	#22548708	C₂²	1	2	yes	complemented
41	#22548708	C₂²	1	2	yes	complemented
42	#22548708	C₂²	1	2	yes	complemented
43	#22548705	C₂²	1	1	yes	characteristic, complemented
44	#22548703	C₂²	1	1	yes	characteristic, complemented
45	#22548702	C₂²	1	1	yes	characteristic
46	#22548702	C₂²	1	2	yes	complemented
47	#22548701	C₂²	1	1	yes	characteristic
48	#22548701	C₂²	1	2	yes	complemented
49	#22548701	C₂²	1	2	yes	complemented
50	#22548700	C₂²	1	1	yes	characteristic, complemented
51	#22548699	C₂²	1	2	yes	complemented
52	#22548698	C₂²	1	2	yes	complemented
53	#22548697	C₂²	1	1	yes	characteristic, complemented
54	#22548697	C₂²	1	2	yes	complemented
55	#22548697	C₂²	1	2	yes	complemented
56	#22548696	C₂²	1	2	yes	complemented
57	#22548696	C₂²	1	2	yes	complemented
58	#22548694	C₂²	1	1	yes	characteristic, complemented
59	#22548693	C₂²	1	1	yes	characteristic, complemented
60	#22548693	C₂²	1	2	yes	complemented
61	#22548692	C₂²	1	2	yes	complemented
62	#22548692	C₂²	1	2	yes	complemented
63	#22548691	C₂²	1	1	yes	characteristic, complemented
64	#22548689	C₂²	1	1	yes	characteristic
65	#22548689	C₂²	1	2	yes	complemented
66	#22548688	C₂²	1	1	yes	characteristic
67	#22548688	C₂²	1	2	yes	complemented
68	#22548688	C₂²	1	2	yes	complemented
69	#22548688	C₂²	1	2	yes	complemented
70	#22548687	C₂²	1	2	yes	—
71	#22548687	C₂²	1	2	yes	—
72	#22548687	C₂²	1	2	yes	complemented
73	#22548687	C₂²	1	2	yes	complemented
74	#22548687	C₂²	1	2	yes	complemented
75	#22548687	C₂²	1	2	yes	complemented
76	#22548687	C₂²	1	2	yes	complemented
77	#22548687	C₂²	1	2	yes	complemented
78	#22548687	C₂²	1	2	yes	complemented
79	#22548686	C₂²	1	1	yes	characteristic
80	#22548686	C₂²	1	1	yes	characteristic
81	#22548686	C₂²	1	1	yes	characteristic, complemented
82	#22548686	C₂²	1	2	yes	complemented
83	#22548686	C₂²	1	2	yes	complemented
84	#22548686	C₂²	1	2	yes	complemented
85	#22548685	C₂²	1	2	yes	complemented
86	#22548684	C₂²	1	2	yes	—
87	#22548684	C₂²	1	2	yes	complemented
88	#22548683	C₂²	1	2	yes	—
89	#22548683	C₂²	1	2	yes	complemented
90	#22548683	C₂²	1	2	yes	complemented
91	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
93	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
97	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
98	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
100	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
104	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
105	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
106	#22548672	C₂²	1	1	yes	characteristic, complemented
107	#22548671	C₂²	1	2	yes	complemented
108	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
109	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
111	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
114	#127×C₂₅₁	C₂²	1	1	yes	characteristic
115	#127×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
116	#124×C₂₅₁	C₂²	1	1	yes	characteristic
117	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
118	#121×C₂₅₁	C₂²	1	2	yes	complemented
119	#121×C₂₅₁	C₂²	1	2	yes	complemented
120	#120×C₂₅₁	C₂²	1	2	yes	complemented
121	#120×C₂₅₁	C₂²	1	2	yes	complemented
122	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₅₁	C₂³	1	2	yes	—
124	#16860811	—	4	2	no	—
125	#16860809	—	4	2	no	—
126	#16860809	—	4	2	no	—
127	#16860809	—	4	4	no	—
128	#16860809	—	4	4	no	—
129	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₅₀₂	C₂³	1	2	yes	—
132	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
133	C₂×D₁₀₀₄	C₂³	1	2	yes	—
134	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
136	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₂₅₁	C₂³	1	1	yes	characteristic
149	D₄×D₂₅₁	—	4	2	no	—
150	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
151	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
152	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
153	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
154	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
155	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
159	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
160	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
165	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
167	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
169	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
170	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
171	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
174	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
175	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
177	Dic₂₅₁⋊C₄	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
181	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
182	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
189	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₂₅₁)⋊C₄	C₂³	1	1	yes	characteristic
200	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
201	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
202	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
203	C₄×Dic₂₅₁	C₂³	1	2	yes	—
204	C₄×Dic₂₅₁	C₂³	1	2	yes	—
205	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
206	C₂⁴×C₂₅₁	C₂³	1	2	yes	—
207	#41×C₂₅₁	—	4	2	no	—
208	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₂₅₁	—	4	2	no	—
210	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
214	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
215	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
216	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
217	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
218	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
219	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
221	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
229	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
230	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
231	C₂²×D₂₅₁	—	4	2	no	—
232	C₂²×D₂₅₁	—	4	2	no	—
233	C₂²×D₂₅₁	—	4	2	no	—
234	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
235	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
236	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
237	Dic₅₀₂	—	2	2	no	—
238	Dic₅₀₂	—	2	2	no	—
239	Dic₅₀₂	—	4	2	no	—
240	D₁₀₀₄	—	2	2	no	—
241	D₁₀₀₄	—	4	1	no	—
242	D₁₀₀₄	—	4	2	no	—
243	C₂²⋊D₂₅₁	—	2	2	no	—
244	C₂²⋊D₂₅₁	—	2	4	no	—
245	C₂²⋊D₂₅₁	—	4	2	no	—
246	C₂²⋊D₂₅₁	—	4	2	no	—
247	C₂²⋊D₂₅₁	—	4	2	no	—
248	C₂²⋊D₂₅₁	—	4	2	no	—
249	C₂²⋊D₂₅₁	—	4	1	no	—
250	C₂²⋊D₂₅₁	—	4	2	no	—
251	C₂²⋊D₂₅₁	—	4	2	no	—
252	C₂²⋊D₂₅₁	—	4	2	no	—
253	C₂²⋊D₂₅₁	—	4	2	no	—
254	C₂²⋊D₂₅₁	—	4	2	no	—
255	C₂²⋊D₂₅₁	—	4	2	no	—
256	C₂×Dic₂₅₁	—	2	4	no	—
257	C₂×Dic₂₅₁	—	2	4	no	—
258	C₂×Dic₂₅₁	—	4	2	no	—
259	C₂×Dic₂₅₁	—	4	2	no	—
260	C₂×Dic₂₅₁	—	4	2	no	—
261	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
265	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
266	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
268	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
270	C₄×D₂₅₁	—	2	2	no	—
271	C₄×D₂₅₁	—	2	2	no	—
272	C₄×D₂₅₁	—	2	2	no	—
273	C₄×D₂₅₁	—	4	1	no	—
274	C₄×D₂₅₁	—	4	2	no	—
275	C₄×D₂₅₁	—	4	2	no	—
276	C₂³×C₂₅₁	—	4	2	no	—
277	C₂³×C₂₅₁	—	4	2	no	—
278	C₂³×C₂₅₁	—	4	2	no	—
279	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
280	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
281	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
282	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
283	Q₈×C₂₅₁	—	2	2	no	—
284	D₄×C₂₅₁	—	2	2	no	—
285	D₄×C₂₅₁	—	2	2	no	—
286	D₄×C₂₅₁	—	2	2	no	—
287	D₄×C₂₅₁	—	4	2	no	—
288	D₄×C₂₅₁	—	4	2	no	—
289	D₄×C₂₅₁	—	4	2	no	—
290	D₄×C₂₅₁	—	4	2	no	—
291	D₄×C₂₅₁	—	4	2	no	—
292	D₄×C₂₅₁	—	4	2	no	—
293	C₂×C₄×C₂₅₁	—	2	2	no	—
294	C₂×C₄×C₂₅₁	—	4	2	no	—
295	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
298	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
300	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
302	C₂²×C₂₅₁	—	2	1	no	—
303	C₂²×C₂₅₁	—	2	2	no	—
304	C₂²×C₂₅₁	—	2	2	no	—
305	C₂²×C₂₅₁	—	2	2	no	—
306	C₂²×C₂₅₁	—	2	2	no	—
307	C₂²×C₂₅₁	—	2	2	no	—
308	C₂²×C₂₅₁	—	2	2	no	—
309	C₂²×C₂₅₁	—	2	1	no	—
310	C₂²×C₂₅₁	—	2	2	no	—
311	C₂²×C₂₅₁	—	2	2	no	—
312	C₂²×C₂₅₁	—	2	2	no	—
313	C₂²×C₂₅₁	—	2	1	no	—
314	C₂²×C₂₅₁	—	8	4	no	—
315	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
316	C₂×D₂₅₁	—	2	1	no	—
317	C₂×D₂₅₁	—	2	1	no	—
318	C₂×D₂₅₁	—	2	1	no	—
319	C₂×D₂₅₁	—	2	2	no	—
320	C₂×D₂₅₁	—	2	2	no	—
321	C₂×D₂₅₁	—	2	1	no	—
322	C₂×D₂₅₁	—	2	1	no	—
323	C₂×D₂₅₁	—	2	2	no	—
324	C₂×D₂₅₁	—	2	1	no	—
325	C₂×D₂₅₁	—	8	4	no	—
326	C₄×C₂₅₁	—	2	1	no	—
327	C₄×C₂₅₁	—	2	2	no	—
328	C₄×C₂₅₁	—	2	1	no	—
329	C₄×C₂₅₁	—	2	1	no	—
330	C₄×C₂₅₁	—	2	1	no	—
331	C₄×C₂₅₁	—	2	1	no	—
332	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
333	Dic₂₅₁	—	2	1	no	—
334	Dic₂₅₁	—	2	1	no	—
335	Dic₂₅₁	—	2	2	no	—
336	Dic₂₅₁	—	2	2	no	—
337	Dic₂₅₁	—	2	1	no	—
338	Dic₂₅₁	—	2	2	no	—
339	Dic₂₅₁	—	2	1	no	—
340	Dic₂₅₁	—	2	1	no	—
341	Dic₂₅₁	H(5,𝔽₂)	1	2	yes	—
342	C₂×C₂₅₁	—	4	2	no	—
343	C₂×C₂₅₁	—	4	2	no	—
344	C₂×C₂₅₁	—	4	2	no	—
345	C₂×C₂₅₁	—	4	1	no	—
346	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₂₅₁	#585	1	1	yes	characteristic
349	D₂₅₁	—	4	1	no	—
350	D₂₅₁	—	4	2	no	—
351	D₂₅₁	—	4	1	no	—
352	C₂₅₁	#3546	1	1	yes	characteristic, complemented, Sylow
353	#3546	—	251	1	no	maximal, Sylow
354	#560	—	251	2	no	—
355	#560	—	251	2	no	—
356	#556	—	251	1	no	—
357	#553	—	251	2	no	—
358	#550	—	251	1	no	—
359	#550	—	251	1	no	—
360	#550	—	251	1	no	—
361	#547	—	251	1	no	—
362	#546	—	251	1	no	—
363	#546	—	251	1	no	—
364	#546	—	251	2	no	—
365	D₄²	—	251	1	no	—
366	#542	—	251	1	no	—
367	#542	—	251	1	no	—
368	#538	—	251	2	no	—
369	#538	—	251	2	no	—
370	#537	—	251	2	no	—
371	#535	—	251	1	no	—
372	#535	—	251	2	no	—
373	#535	D₂₅₁	1	1	yes	characteristic, complemented
374	#532	—	251	1	no	—
375	#532	—	251	1	no	—
376	#529	—	251	1	no	—
377	C₂×#41	—	251	1	no	—
378	C₂×#41	—	251	2	no	—
379	C₂×#41	—	251	1	no	—
380	C₂×#41	—	251	1	no	—
381	C₂×#41	—	251	2	no	—
382	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
383	C₂²×D₄	—	251	2	no	—
384	C₂²×D₄	—	251	1	no	—
385	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
386	C₄⋊Q₈	—	251	1	no	—
387	C₄⋊Q₈	—	251	1	no	—
388	#127	—	251	1	no	—
389	#127	—	251	1	no	—
390	#127	—	251	2	no	—
391	#127	—	251	2	no	—
392	#127	C₂×D₂₅₁	1	1	yes	characteristic
393	#127	C₂×D₂₅₁	1	1	yes	characteristic, complemented
394	#126	—	251	1	no	—
395	#126	—	251	2	no	—
396	#126	—	251	1	no	—
397	#126	—	251	2	no	—
398	#126	—	251	2	no	—
399	#126	—	251	2	no	—
400	#125	—	251	1	no	—
401	#124	—	251	2	no	—
402	#124	—	251	1	no	—
403	#124	—	251	1	no	—
404	#124	—	251	2	no	—
405	#124	—	251	2	no	—
406	#124	—	251	1	no	—
407	#124	C₂×D₂₅₁	1	1	yes	characteristic
408	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
409	#123	—	251	2	no	—
410	#123	—	251	2	no	—
411	#123	—	251	2	no	—
412	#123	—	251	1	no	—
413	#123	—	251	1	no	—
414	#123	—	251	2	no	—
415	#123	—	251	2	no	—
416	#123	—	251	2	no	—
417	C₂²⋊Q₈	—	251	1	no	—
418	C₂²⋊Q₈	—	251	1	no	—
419	C₂²⋊Q₈	—	251	1	no	—
420	C₂²⋊Q₈	—	251	2	no	—
421	C₂²⋊Q₈	—	251	2	no	—
422	C₂²⋊Q₈	—	251	2	no	—
423	#121	—	251	1	no	—
424	#121	—	251	1	no	—
425	#121	—	251	2	no	—
426	#121	—	251	2	no	—
427	#121	—	251	2	no	—
428	#121	—	251	2	no	—
429	#121	—	251	2	no	—
430	#121	—	251	2	no	—
431	#121	—	251	2	no	—
432	#121	—	251	2	no	—
433	#121	—	251	2	no	—
434	#121	—	251	2	no	—
435	#121	—	251	2	no	—
436	#121	—	251	2	no	—
437	#121	—	251	1	no	—
438	#121	—	251	2	no	—
439	#121	—	251	1	no	—
440	#121	—	251	1	no	—
441	#121	—	251	2	no	—
442	#121	—	251	2	no	—
443	#121	—	251	2	no	—
444	#121	C₂×D₂₅₁	1	2	yes	complemented
445	#121	C₂×D₂₅₁	1	2	yes	complemented
446	#120	—	251	2	no	—
447	#120	—	251	2	no	—
448	#120	—	251	2	no	—
449	#120	—	251	2	no	—
450	#120	—	251	2	no	—
451	#120	—	251	2	no	—
452	#120	C₂×D₂₅₁	1	2	yes	complemented
453	#120	C₂×D₂₅₁	1	2	yes	complemented
454	C₄×Q₈	—	251	1	no	—
455	C₄×Q₈	—	251	1	no	—
456	C₄×Q₈	—	251	1	no	—
457	C₄×D₄	—	251	1	no	—
458	C₄×D₄	—	251	2	no	—
459	C₄×D₄	—	251	1	no	—
460	C₄×D₄	—	251	2	no	—
461	C₄×D₄	—	251	1	no	—
462	C₄×D₄	—	251	1	no	—
463	C₄×D₄	—	251	1	no	—
464	C₄×D₄	—	251	2	no	—
465	C₄×D₄	—	251	2	no	—
466	C₄×D₄	—	251	2	no	—
467	C₄×D₄	—	251	1	no	—
468	C₄×D₄	—	251	1	no	—
469	#117	—	251	2	no	—
470	#117	—	251	1	no	—
471	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
472	C₂×C₄⋊C₄	—	251	2	no	—
473	C₂×C₂²⋊C₄	—	251	2	no	—
474	C₂×C₂²⋊C₄	—	251	2	no	—
475	C₂×C₄²	—	251	1	no	—
476	C₂⁴	—	251	2	no	—
477	C₂⁴	C₂²×D₂₅₁	1	2	yes	—
478	#41	—	4	2	no	—
479	#41	—	1004	2	no	—
480	#41	—	1004	2	no	—
481	#41	—	1004	4	no	—
482	#41	—	1004	2	no	—
483	#41	—	1004	4	no	—
484	C₂×Q₈	—	251	2	no	—
485	C₂×Q₈	—	251	1	no	—
486	C₂×Q₈	—	251	1	no	—
487	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	1004	2	no	—
490	C₂×D₄	—	1004	4	no	—
491	C₂×D₄	—	251	2	no	—
492	C₂×D₄	—	251	1	no	—
493	C₂×D₄	—	251	2	no	—
494	C₂×D₄	—	251	2	no	—
495	C₂×D₄	—	251	2	no	—
496	C₂×D₄	—	251	2	no	—
497	C₂×D₄	—	251	2	no	—
498	C₂×D₄	—	251	2	no	—
499	C₂×D₄	—	251	2	no	—
500	C₂×D₄	—	251	2	no	—
501	C₂×D₄	—	251	2	no	—
502	C₂×D₄	—	251	1	no	—
503	C₂×D₄	—	251	2	no	—
504	C₂×D₄	—	251	1	no	—
505	C₂×D₄	—	251	2	no	—
506	C₂×D₄	—	251	1	no	—
507	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
510	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
511	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
512	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
513	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
514	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
515	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
516	C₂²×C₄	—	251	2	no	—
517	C₂²×C₄	—	251	2	no	—
518	C₂²×C₄	—	251	2	no	—
519	C₂²×C₄	—	251	1	no	—
520	C₂²×C₄	—	251	2	no	—
521	C₂²×C₄	—	251	2	no	—
522	C₂²×C₄	—	251	2	no	—
523	C₂²×C₄	—	251	2	no	—
524	C₂²×C₄	—	251	1	no	—
525	C₂²×C₄	—	251	1	no	—
526	C₂²×C₄	—	251	1	no	—
527	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
528	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
529	C₄⋊C₄	—	251	1	no	—
530	C₄⋊C₄	—	251	2	no	—
531	C₄⋊C₄	—	251	2	no	—
532	C₄⋊C₄	—	251	2	no	—
533	C₄⋊C₄	—	251	1	no	—
534	C₄⋊C₄	—	251	1	no	—
535	C₄⋊C₄	—	251	1	no	—
536	C₄⋊C₄	—	251	1	no	—
537	C₄⋊C₄	—	251	2	no	—
538	C₄⋊C₄	—	251	2	no	—
539	C₄⋊C₄	—	251	1	no	—
540	C₄⋊C₄	—	251	1	no	—
541	C₄⋊C₄	—	251	1	no	—
542	C₄⋊C₄	—	251	1	no	—
543	C₄⋊C₄	—	251	2	no	—
544	C₄⋊C₄	—	251	2	no	—
545	C₄⋊C₄	—	251	1	no	—
546	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
548	C₂²⋊C₄	—	251	1	no	—
549	C₂²⋊C₄	—	251	2	no	—
550	C₂²⋊C₄	—	251	2	no	—
551	C₂²⋊C₄	—	251	2	no	—
552	C₂²⋊C₄	—	251	2	no	—
553	C₂²⋊C₄	—	251	2	no	—
554	C₂²⋊C₄	—	251	2	no	—
555	C₂²⋊C₄	—	251	1	no	—
556	C₂²⋊C₄	—	251	2	no	—
557	C₂²⋊C₄	—	251	2	no	—
558	C₂²⋊C₄	—	251	2	no	—
559	C₂²⋊C₄	—	251	1	no	—
560	C₂²⋊C₄	—	251	2	no	—
561	C₂²⋊C₄	—	251	1	no	—
562	C₂²⋊C₄	—	251	1	no	—
563	C₂²⋊C₄	—	251	1	no	—
564	C₂²⋊C₄	—	251	2	no	—
565	C₂²⋊C₄	—	251	2	no	—
566	C₂²⋊C₄	—	251	2	no	—
567	C₂²⋊C₄	—	251	2	no	—
568	C₂²⋊C₄	—	251	1	no	—
569	C₂²⋊C₄	—	251	1	no	—
570	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
571	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
572	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
574	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
576	C₄²	—	251	1	no	—
577	C₄²	—	251	1	no	—
578	C₄²	—	251	1	no	—
579	C₄²	—	251	1	no	—
580	C₄²	—	251	2	no	—
581	C₄²	—	251	2	no	—
582	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
583	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
584	C₂³	—	4	2	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	4	2	no	—
587	C₂³	—	1004	2	no	—
588	C₂³	—	1004	2	no	—
589	C₂³	—	1004	2	no	—
590	C₂³	—	251	1	no	—
591	C₂³	—	251	2	no	—
592	C₂³	—	251	1	no	—
593	C₂³	C₂³×D₂₅₁	1	2	yes	—
594	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
595	C₂³	C₂³×D₂₅₁	1	2	yes	—
596	C₂³	C₂³×D₂₅₁	1	2	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	1004	2	no	—
599	Q₈	—	502	2	no	—
600	Q₈	—	502	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	1004	2	no	—
611	D₄	—	1004	1	no	—
612	D₄	—	1004	2	no	—
613	D₄	—	1004	2	no	—
614	D₄	—	1004	2	no	—
615	D₄	—	1004	2	no	—
616	D₄	—	1004	2	no	—
617	D₄	—	1004	2	no	—
618	D₄	—	1004	2	no	—
619	D₄	—	1004	2	no	—
620	D₄	—	1004	2	no	—
621	D₄	—	1004	2	no	—
622	D₄	—	1004	1	no	—
623	D₄	—	502	2	no	—
624	D₄	—	502	4	no	—
625	D₄	—	502	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	1004	2	no	—
629	C₂×C₄	—	1004	2	no	—
630	C₂×C₄	—	1004	1	no	—
631	C₂×C₄	—	1004	2	no	—
632	C₂×C₄	—	1004	2	no	—
633	C₂×C₄	—	1004	2	no	—
634	C₂×C₄	—	502	2	no	—
635	C₂×C₄	—	502	4	no	—
636	C₂×C₄	—	502	4	no	—
637	C₂×C₄	—	502	2	no	—
638	C₂×C₄	—	502	2	no	—
639	C₂×C₄	—	251	1	no	—
640	C₂×C₄	—	251	1	no	—
641	C₂×C₄	—	251	1	no	—
642	C₂×C₄	—	251	2	no	—
643	C₂×C₄	—	251	1	no	—
644	C₂×C₄	—	251	2	no	—
645	C₂×C₄	—	251	2	no	—
646	C₂×C₄	—	251	1	no	—
647	C₂×C₄	—	251	1	no	—
648	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
652	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	8	4	no	—
668	C₂²	—	2008	4	no	—
669	C₂²	—	502	2	no	—
670	C₂²	—	502	1	no	—
671	C₂²	—	502	1	no	—
672	C₂²	—	502	2	no	—
673	C₂²	—	502	1	no	—
674	C₂²	—	502	1	no	—
675	C₂²	—	502	1	no	—
676	C₂²	—	502	2	no	—
677	C₂²	—	502	1	no	—
678	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	502	2	no	—
686	C₄	—	502	1	no	—
687	C₄	—	502	2	no	—
688	C₄	—	502	1	no	—
689	C₄	—	502	1	no	—
690	C₄	—	502	2	no	—
691	C₄	—	502	1	no	—
692	C₄	—	502	1	no	—
693	C₄	—	251	2	no	—
694	C₄	#22548760	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	4	2	no	—
698	C₂	—	4	2	no	—
699	C₂	—	1004	1	no	—
700	C₂	—	1004	2	no	—
701	C₂	—	1004	1	no	—
702	C₂	H(5,𝔽₂)×D₂₅₁	1	1	yes	characteristic
703	C₂	C₂×#22548760	1	1	yes	characteristic
704	C₂	#30632522	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#535×C₂₅₁	C₂
hypercenter	#535	D₂₅₁
hypocenter	C₂₅₁	#3546
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #535

Complements

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

N	H ≅ G/N	type
1. #30632426	C₂	semidirect
2. #30632425	C₂	semidirect
3. #30632406	C₂	semidirect
4. #30632380	C₂	semidirect
5. #30632357	C₂	semidirect
6. #30632357	C₂	semidirect
7. #30632356	C₂	semidirect
8. #30632336	C₂	semidirect
9. #30632331	C₂	semidirect
10. #30632330	C₂	semidirect
11. #30632324	C₂	semidirect
12. D₄×C₂²⋊D₂₅₁	C₂	semidirect
13. #30632308	C₂	semidirect
14. #30632306	C₂	semidirect
15. #30632272	C₂	semidirect
16. #30632269	C₂	semidirect
17. #30632264	C₂	semidirect
18. #30632252	C₂	semidirect
19. #30632250	C₂	semidirect
20. #30632236	C₂	semidirect
21. #30632235	C₂	semidirect
22. #30632215	C₂	semidirect
23. #535×C₂₅₁	C₂	semidirect
24. C₂×#16860811	C₂²	semidirect
25. C₂×#16860809	C₂²	semidirect
26. C₂×#16860809	C₂²	semidirect
27. C₂×#16860809	C₂²	semidirect
28. C₂×#16860809	C₂²	semidirect
31. #22548715	C₂²	semidirect
32. #22548713	C₂²	semidirect
34. #22548711	C₂²	semidirect
35. #22548711	C₂²	semidirect
36. #22548711	C₂²	semidirect
37. #22548710	C₂²	semidirect
38. #22548710	C₂²	semidirect
39. #22548708	C₂²	semidirect
40. #22548708	C₂²	semidirect
41. #22548708	C₂²	semidirect
42. #22548708	C₂²	semidirect
43. #22548705	C₂²	semidirect
44. #22548703	C₂²	semidirect
46. #22548702	C₂²	semidirect
48. #22548701	C₂²	semidirect
49. #22548701	C₂²	semidirect
50. #22548700	C₂²	semidirect
51. #22548699	C₂²	semidirect
52. #22548698	C₂²	semidirect
53. #22548697	C₂²	semidirect
54. #22548697	C₂²	semidirect
55. #22548697	C₂²	semidirect
56. #22548696	C₂²	semidirect
57. #22548696	C₂²	semidirect
58. #22548694	C₂²	semidirect
59. #22548693	C₂²	semidirect
60. #22548693	C₂²	semidirect
61. #22548692	C₂²	semidirect
62. #22548692	C₂²	semidirect
63. #22548691	C₂²	semidirect
65. #22548689	C₂²	semidirect
67. #22548688	C₂²	semidirect
68. #22548688	C₂²	semidirect
69. #22548688	C₂²	semidirect
72. #22548687	C₂²	semidirect
73. #22548687	C₂²	semidirect
74. #22548687	C₂²	semidirect
75. #22548687	C₂²	semidirect
76. #22548687	C₂²	semidirect
77. #22548687	C₂²	semidirect
78. #22548687	C₂²	semidirect
81. #22548686	C₂²	semidirect
82. #22548686	C₂²	semidirect
83. #22548686	C₂²	semidirect
84. #22548686	C₂²	semidirect
85. #22548685	C₂²	semidirect
87. #22548684	C₂²	semidirect
89. #22548683	C₂²	semidirect
90. #22548683	C₂²	semidirect
91. Q₈×Dic₂₅₁	C₂²	semidirect
92. C₄×Dic₅₀₂	C₂²	semidirect
93. C₄×Dic₅₀₂	C₂²	semidirect
94. C₄×D₁₀₀₄	C₂²	semidirect
95. C₄×D₁₀₀₄	C₂²	semidirect
97. D₄×Dic₂₅₁	C₂²	semidirect
98. D₄×Dic₂₅₁	C₂²	semidirect
99. D₄×Dic₂₅₁	C₂²	semidirect
100. D₄×Dic₂₅₁	C₂²	semidirect
102. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
103. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
104. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
105. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
106. #22548672	C₂²	semidirect
107. #22548671	C₂²	semidirect
108. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
109. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
110. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
111. C₄²×D₂₅₁	C₂²	semidirect
112. C₂×#41×C₂₅₁	C₂²	semidirect
115. #127×C₂₅₁	C₂²	semidirect
117. #124×C₂₅₁	C₂²	semidirect
118. #121×C₂₅₁	C₂²	semidirect
119. #121×C₂₅₁	C₂²	semidirect
120. #120×C₂₅₁	C₂²	semidirect
121. #120×C₂₅₁	C₂²	semidirect
122. #117×C₂₅₁	C₂²	semidirect
352. C₂₅₁	#3546	semidirect
373. #535	D₂₅₁	semidirect
382. C₂×#41	C₂×D₂₅₁	semidirect
393. #127	C₂×D₂₅₁	semidirect
408. #124	C₂×D₂₅₁	semidirect
444. #121	C₂×D₂₅₁	semidirect
445. #121	C₂×D₂₅₁	semidirect
452. #120	C₂×D₂₅₁	semidirect
453. #120	C₂×D₂₅₁	semidirect
471. #117	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632426	2
#30632425	2
#30632406	2
#30632380	2
#30632357	2
#30632356	2
#30632336	2
#30632331	2
#30632330	2
#30632324	2
D₄×C₂²⋊D₂₅₁	2
#30632308	2
#30632306	2
#30632272	2
#30632269	2
#30632264	2
#30632252	2
#30632250	2
#30632236	2
#30632235	2
#30632215	2
#535×C₂₅₁	2
#3546	251