Subgroups — #44564658

Order 32128.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632438	C₂	1	2	yes	maximal, complemented
2	#30632432	C₂	1	2	yes	maximal, complemented
3	#30632407	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632394	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632391	C₂	1	2	yes	maximal, complemented
6	#30632383	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632380	C₂	1	2	yes	maximal, complemented
8	#30632377	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Dic₅₀₂	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632346	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632346	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632342	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632308	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632305	C₂	1	2	yes	maximal, complemented
15	#30632299	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632280	C₂	1	2	yes	maximal, complemented
17	#30632272	C₂	1	2	yes	maximal, complemented
18	#30632272	C₂	1	2	yes	maximal, complemented
19	#30632265	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632258	C₂	1	1	yes	maximal, characteristic, complemented
21	#30632198	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#22548694	C₂	1	1	yes	maximal, characteristic, complemented
23	#525×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#16860810	C₂²	1	1	yes	characteristic
25	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
27	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
28	#22548715	C₂²	1	1	yes	characteristic, complemented
29	#22548715	C₂²	1	1	yes	characteristic, complemented
30	#22548714	C₂²	1	2	yes	complemented
31	#22548713	C₂²	1	2	yes	complemented
32	#22548710	C₂²	1	2	yes	complemented
33	#22548710	C₂²	1	2	yes	complemented
34	#22548708	C₂²	1	2	yes	—
35	#22548708	C₂²	1	2	yes	—
36	#22548708	C₂²	1	2	yes	—
37	#22548708	C₂²	1	2	yes	—
38	#22548708	C₂²	1	2	yes	complemented
39	#22548707	C₂²	1	1	yes	characteristic, complemented
40	#22548706	C₂²	1	2	yes	complemented
41	#22548705	C₂²	1	2	yes	complemented
42	#22548705	C₂²	1	2	yes	complemented
43	#22548705	C₂²	1	2	yes	complemented
44	#22548703	C₂²	1	1	yes	characteristic, complemented
45	#22548702	C₂²	1	2	yes	—
46	#22548702	C₂²	1	2	yes	—
47	#22548701	C₂²	1	2	yes	—
48	#22548701	C₂²	1	2	yes	—
49	#22548701	C₂²	1	2	yes	complemented
50	#22548698	C₂²	1	2	yes	—
51	#22548697	C₂²	1	2	yes	—
52	#22548697	C₂²	1	2	yes	—
53	#22548697	C₂²	1	2	yes	complemented
54	#22548697	C₂²	1	2	yes	complemented
55	#22548696	C₂²	1	2	yes	—
56	#22548696	C₂²	1	2	yes	—
57	#22548696	C₂²	1	2	yes	complemented
58	#22548694	C₂²	1	1	yes	characteristic
59	#22548694	C₂²	1	1	yes	characteristic
60	#22548694	C₂²	1	1	yes	characteristic
61	#22548694	C₂²	1	1	yes	characteristic
62	#22548694	C₂²	1	2	yes	—
63	#22548694	C₂²	1	1	yes	characteristic
64	#22548694	C₂²	1	1	yes	characteristic
65	#22548694	C₂²	1	2	yes	—
66	#22548694	C₂²	1	1	yes	characteristic, complemented
67	#22548694	C₂²	1	1	yes	characteristic, complemented
68	#22548694	C₂²	1	1	yes	characteristic, complemented
69	#22548693	C₂²	1	2	yes	complemented
70	#22548693	C₂²	1	2	yes	complemented
71	#22548693	C₂²	1	2	yes	complemented
72	#22548692	C₂²	1	2	yes	—
73	#22548692	C₂²	1	2	yes	—
74	#22548692	C₂²	1	2	yes	complemented
75	#22548692	C₂²	1	2	yes	complemented
76	#22548691	C₂²	1	2	yes	complemented
77	#22548689	C₂²	1	1	yes	characteristic
78	#22548689	C₂²	1	1	yes	characteristic
79	#22548689	C₂²	1	1	yes	characteristic, complemented
80	#22548687	C₂²	1	2	yes	—
81	#22548687	C₂²	1	2	yes	—
82	#22548687	C₂²	1	2	yes	—
83	#22548687	C₂²	1	2	yes	—
84	#22548687	C₂²	1	2	yes	complemented
85	#22548686	C₂²	1	2	yes	—
86	#22548686	C₂²	1	2	yes	—
87	#22548684	C₂²	1	2	yes	—
88	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
89	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
90	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
91	#22548680	C₂²	1	2	yes	complemented
92	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
93	D₄×Dic₂₅₁	C₂²	1	2	yes	—
94	D₄×Dic₂₅₁	C₂²	1	2	yes	—
95	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
97	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
98	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
99	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
100	#22548674	C₂²	1	1	yes	characteristic
101	#22548674	C₂²	1	1	yes	characteristic, complemented
102	#22548671	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
104	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
105	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	—
106	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	—
108	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
109	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
110	#123×C₂₅₁	C₂²	1	1	yes	characteristic
111	#123×C₂₅₁	C₂²	1	1	yes	characteristic
112	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
113	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
114	#121×C₂₅₁	C₂²	1	1	yes	characteristic
115	#121×C₂₅₁	C₂²	1	1	yes	characteristic
116	#120×C₂₅₁	C₂²	1	1	yes	characteristic
117	#120×C₂₅₁	C₂²	1	1	yes	characteristic
118	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
122	#117×C₂₅₁	C₂²	1	1	yes	characteristic
123	#16860810	—	4	2	no	—
124	#16860810	—	4	2	no	—
125	C₂×Dic₅₀₂	—	4	2	no	—
126	C₂×Dic₅₀₂	—	4	2	no	—
127	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
128	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
130	C₂×Dic₅₀₂	C₂³	1	2	yes	—
131	C₂×Dic₅₀₂	C₂³	1	2	yes	—
132	C₂×Dic₅₀₂	C₂³	1	2	yes	—
133	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
139	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
140	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
141	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
142	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
143	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
144	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
145	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
146	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
147	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
150	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
152	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
154	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
155	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
156	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
157	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
158	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
159	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
160	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
161	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
162	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
163	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
164	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
165	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
166	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
167	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
168	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
169	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
170	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
171	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
172	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
174	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
175	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
176	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
178	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
179	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
180	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
186	C₄×Dic₂₅₁	C₂³	1	2	yes	—
187	C₄×Dic₂₅₁	C₂³	1	2	yes	—
188	C₄×Dic₂₅₁	C₂³	1	2	yes	—
189	C₄×Dic₂₅₁	C₂³	1	2	yes	—
190	C₄×Dic₂₅₁	C₂³	1	2	yes	—
191	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
192	#41×C₂₅₁	—	4	2	no	—
193	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
197	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
198	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
199	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₂₅₁	—	4	2	no	—
202	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
222	C₂²⋊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	1	yes	characteristic
226	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
227	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
228	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
229	Dic₅₀₂	—	2	2	no	—
230	Dic₅₀₂	—	2	2	no	—
231	Dic₅₀₂	—	2	2	no	—
232	Dic₅₀₂	—	4	2	no	—
233	Dic₅₀₂	—	4	2	no	—
234	Dic₅₀₂	—	4	2	no	—
235	D₁₀₀₄	—	2	2	no	—
236	C₂²⋊D₂₅₁	—	2	4	no	—
237	C₂²⋊D₂₅₁	—	4	2	no	—
238	C₂²⋊D₂₅₁	—	4	2	no	—
239	C₂²⋊D₂₅₁	—	4	2	no	—
240	C₂²⋊D₂₅₁	—	4	2	no	—
241	C₂×Dic₂₅₁	—	4	2	no	—
242	C₂×Dic₂₅₁	—	4	2	no	—
243	C₂×Dic₂₅₁	—	4	2	no	—
244	C₂×Dic₂₅₁	—	4	2	no	—
245	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
246	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
247	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
248	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
249	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
250	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
251	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
252	C₄×D₂₅₁	—	4	2	no	—
253	C₄×D₂₅₁	—	4	2	no	—
254	C₄×D₂₅₁	—	4	2	no	—
255	C₂³×C₂₅₁	—	2	2	no	—
256	C₂³×C₂₅₁	—	4	1	no	—
257	C₂³×C₂₅₁	—	4	1	no	—
258	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
259	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
260	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
261	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
262	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
263	Q₈×C₂₅₁	—	4	1	no	—
264	D₄×C₂₅₁	—	2	2	no	—
265	D₄×C₂₅₁	—	2	2	no	—
266	D₄×C₂₅₁	—	4	1	no	—
267	D₄×C₂₅₁	—	4	1	no	—
268	D₄×C₂₅₁	—	4	1	no	—
269	D₄×C₂₅₁	—	4	1	no	—
270	D₄×C₂₅₁	—	4	1	no	—
271	C₂×C₄×C₂₅₁	—	2	2	no	—
272	C₂×C₄×C₂₅₁	—	2	2	no	—
273	C₂×C₄×C₂₅₁	—	2	2	no	—
274	C₂×C₄×C₂₅₁	—	2	2	no	—
275	C₂×C₄×C₂₅₁	—	2	2	no	—
276	C₂×C₄×C₂₅₁	—	4	1	no	—
277	C₂×C₄×C₂₅₁	—	4	1	no	—
278	C₂×C₄×C₂₅₁	—	4	1	no	—
279	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
288	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₂₅₁	—	2	1	no	—
290	C₂²×C₂₅₁	—	2	1	no	—
291	C₂²×C₂₅₁	—	2	1	no	—
292	C₂²×C₂₅₁	—	2	1	no	—
293	C₂²×C₂₅₁	—	2	1	no	—
294	C₂²×C₂₅₁	—	2	1	no	—
295	C₂²×C₂₅₁	—	2	1	no	—
296	C₂²×C₂₅₁	—	2	1	no	—
297	C₂²×C₂₅₁	—	2	1	no	—
298	C₂²×C₂₅₁	—	2	1	no	—
299	C₂²×C₂₅₁	—	2	1	no	—
300	C₂²×C₂₅₁	—	2	1	no	—
301	C₂²×C₂₅₁	—	2	1	no	—
302	C₂²×C₂₅₁	—	2	1	no	—
303	C₂²×C₂₅₁	—	4	4	no	—
304	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
305	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
306	C₂×D₂₅₁	—	2	2	no	—
307	C₂×D₂₅₁	—	2	2	no	—
308	C₂×D₂₅₁	—	2	2	no	—
309	C₄×C₂₅₁	—	2	1	no	—
310	C₄×C₂₅₁	—	2	1	no	—
311	C₄×C₂₅₁	—	2	1	no	—
312	C₄×C₂₅₁	—	2	1	no	—
313	C₄×C₂₅₁	—	2	1	no	—
314	C₄×C₂₅₁	—	2	1	no	—
315	C₄×C₂₅₁	—	2	1	no	—
316	C₄×C₂₅₁	—	2	1	no	—
317	C₄×C₂₅₁	—	2	1	no	—
318	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
319	Dic₂₅₁	—	2	2	no	—
320	Dic₂₅₁	—	2	2	no	—
321	Dic₂₅₁	—	2	2	no	—
322	Dic₂₅₁	—	2	2	no	—
323	Dic₂₅₁	—	2	2	no	—
324	Dic₂₅₁	—	2	2	no	—
325	Dic₂₅₁	—	2	2	no	—
326	C₂×C₂₅₁	—	2	2	no	—
327	C₂×C₂₅₁	—	4	1	no	—
328	C₂×C₂₅₁	—	4	1	no	—
329	C₂×C₂₅₁	—	4	1	no	—
330	C₂×C₂₅₁	—	4	1	no	—
331	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂×C₂₅₁	#585	1	1	yes	characteristic
334	D₂₅₁	—	4	2	no	—
335	C₂₅₁	#3541	1	1	yes	characteristic, complemented, Sylow
336	#3541	—	251	1	no	maximal, Sylow
337	#563	—	251	2	no	—
338	#562	—	251	2	no	—
339	#556	—	251	1	no	—
340	#554	—	251	2	no	—
341	#554	—	251	1	no	—
342	#553	—	251	2	no	—
343	#553	—	251	1	no	—
344	#552	—	251	1	no	—
345	D₄×Q₈	—	251	1	no	—
346	#548	—	251	1	no	—
347	#548	—	251	1	no	—
348	#547	—	251	1	no	—
349	#542	—	251	2	no	—
350	#542	—	251	1	no	—
351	#541	—	251	1	no	—
352	#539	—	251	2	no	—
353	#538	—	251	2	no	—
354	#538	—	251	2	no	—
355	#537	—	251	1	no	—
356	#536	—	251	1	no	—
357	#525	—	251	1	no	—
358	#525	D₂₅₁	1	1	yes	characteristic, complemented
359	C₂×C₂²⋊Q₈	—	251	1	no	—
360	C₂×#41	—	251	1	no	—
361	C₂×#41	—	251	1	no	—
362	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
363	C₂²×Q₈	—	251	1	no	—
364	C₂²×Q₈	—	251	1	no	—
365	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
366	C₄⋊Q₈	—	251	2	no	—
367	C₄⋊Q₈	—	251	2	no	—
368	C₄⋊Q₈	—	251	1	no	—
369	C₄⋊Q₈	—	251	1	no	—
370	#126	—	251	2	no	—
371	#126	—	251	2	no	—
372	#126	—	251	2	no	—
373	#126	—	251	2	no	—
374	#126	—	251	2	no	—
375	#126	—	251	2	no	—
376	#126	—	251	2	no	—
377	#125	—	251	2	no	—
378	#125	—	251	2	no	—
379	#125	—	251	2	no	—
380	#125	—	251	2	no	—
381	#125	—	251	1	no	—
382	#124	—	251	2	no	—
383	#124	—	251	2	no	—
384	#124	—	251	2	no	—
385	#124	—	251	2	no	—
386	#124	—	251	2	no	—
387	#124	—	251	1	no	—
388	#123	—	251	2	no	—
389	#123	—	251	2	no	—
390	#123	—	251	2	no	—
391	#123	—	251	2	no	—
392	#123	—	251	2	no	—
393	#123	—	251	2	no	—
394	#123	—	251	2	no	—
395	#123	—	251	2	no	—
396	#123	C₂×D₂₅₁	1	1	yes	characteristic
397	#123	C₂×D₂₅₁	1	1	yes	characteristic
398	C₂²⋊Q₈	—	251	2	no	—
399	C₂²⋊Q₈	—	251	1	no	—
400	C₂²⋊Q₈	—	251	1	no	—
401	C₂²⋊Q₈	—	251	2	no	—
402	C₂²⋊Q₈	—	251	1	no	—
403	C₂²⋊Q₈	—	251	1	no	—
404	C₂²⋊Q₈	—	251	2	no	—
405	C₂²⋊Q₈	—	251	1	no	—
406	C₂²⋊Q₈	—	251	1	no	—
407	C₂²⋊Q₈	—	251	1	no	—
408	C₂²⋊Q₈	—	251	1	no	—
409	C₂²⋊Q₈	—	251	1	no	—
410	C₂²⋊Q₈	—	251	2	no	—
411	C₂²⋊Q₈	—	251	2	no	—
412	C₂²⋊Q₈	—	251	2	no	—
413	C₂²⋊Q₈	—	251	2	no	—
414	C₂²⋊Q₈	—	251	2	no	—
415	C₂²⋊Q₈	—	251	2	no	—
416	C₂²⋊Q₈	—	251	2	no	—
417	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
419	#121	—	251	2	no	—
420	#121	—	251	2	no	—
421	#121	—	251	2	no	—
422	#121	—	251	2	no	—
423	#121	—	251	2	no	—
424	#121	—	251	2	no	—
425	#121	—	251	2	no	—
426	#121	—	251	1	no	—
427	#121	—	251	1	no	—
428	#121	—	251	1	no	—
429	#121	C₂×D₂₅₁	1	1	yes	characteristic
430	#121	C₂×D₂₅₁	1	1	yes	characteristic
431	#120	—	251	2	no	—
432	#120	C₂×D₂₅₁	1	1	yes	characteristic
433	#120	C₂×D₂₅₁	1	1	yes	characteristic
434	C₄×Q₈	—	251	2	no	—
435	C₄×Q₈	—	251	1	no	—
436	C₄×Q₈	—	251	1	no	—
437	C₄×Q₈	—	251	1	no	—
438	C₄×D₄	—	251	2	no	—
439	C₄×D₄	—	251	2	no	—
440	C₄×D₄	—	251	2	no	—
441	C₄×D₄	—	251	2	no	—
442	C₄×D₄	—	251	2	no	—
443	C₄×D₄	—	251	2	no	—
444	C₄×D₄	—	251	2	no	—
445	C₄×D₄	—	251	1	no	—
446	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
447	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
448	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
449	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
450	#117	—	251	1	no	—
451	#117	—	251	1	no	—
452	#117	—	251	2	no	—
453	#117	C₂×D₂₅₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	—	251	2	no	—
455	C₂×C₄⋊C₄	—	251	1	no	—
456	C₂×C₄⋊C₄	—	251	1	no	—
457	C₂×C₄⋊C₄	—	251	2	no	—
458	C₂×C₂²⋊C₄	—	251	2	no	—
459	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
460	#41	—	4	2	no	—
461	#41	—	1004	2	no	—
462	#41	—	1004	2	no	—
463	C₂×Q₈	—	1004	2	no	—
464	C₂×Q₈	—	1004	2	no	—
465	C₂×Q₈	—	251	2	no	—
466	C₂×Q₈	—	251	2	no	—
467	C₂×Q₈	—	251	2	no	—
468	C₂×Q₈	—	251	1	no	—
469	C₂×Q₈	—	251	1	no	—
470	C₂×Q₈	—	251	1	no	—
471	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
472	C₂×D₄	—	251	2	no	—
473	C₂×D₄	—	251	2	no	—
474	C₂×D₄	—	251	2	no	—
475	C₂×D₄	—	251	2	no	—
476	C₂×D₄	—	251	2	no	—
477	C₂×D₄	—	251	1	no	—
478	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	251	2	no	—
487	C₂²×C₄	—	251	2	no	—
488	C₂²×C₄	—	251	2	no	—
489	C₂²×C₄	—	251	2	no	—
490	C₂²×C₄	—	251	2	no	—
491	C₂²×C₄	—	251	2	no	—
492	C₂²×C₄	—	251	2	no	—
493	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
501	C₄⋊C₄	—	251	2	no	—
502	C₄⋊C₄	—	251	1	no	—
503	C₄⋊C₄	—	251	2	no	—
504	C₄⋊C₄	—	251	1	no	—
505	C₄⋊C₄	—	251	1	no	—
506	C₄⋊C₄	—	251	2	no	—
507	C₄⋊C₄	—	251	2	no	—
508	C₄⋊C₄	—	251	2	no	—
509	C₄⋊C₄	—	251	2	no	—
510	C₄⋊C₄	—	251	2	no	—
511	C₄⋊C₄	—	251	2	no	—
512	C₄⋊C₄	—	251	1	no	—
513	C₄⋊C₄	—	251	2	no	—
514	C₄⋊C₄	—	251	2	no	—
515	C₄⋊C₄	—	251	2	no	—
516	C₄⋊C₄	—	251	2	no	—
517	C₄⋊C₄	—	251	2	no	—
518	C₄⋊C₄	—	251	2	no	—
519	C₄⋊C₄	—	251	2	no	—
520	C₄⋊C₄	—	251	2	no	—
521	C₄⋊C₄	—	251	2	no	—
522	C₄⋊C₄	—	251	2	no	—
523	C₄⋊C₄	—	251	2	no	—
524	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
530	C₂²⋊C₄	—	251	2	no	—
531	C₂²⋊C₄	—	251	2	no	—
532	C₂²⋊C₄	—	251	2	no	—
533	C₂²⋊C₄	—	251	2	no	—
534	C₂²⋊C₄	—	251	2	no	—
535	C₂²⋊C₄	—	251	2	no	—
536	C₂²⋊C₄	—	251	2	no	—
537	C₂²⋊C₄	—	251	2	no	—
538	C₂²⋊C₄	—	251	2	no	—
539	C₂²⋊C₄	—	251	2	no	—
540	C₂²⋊C₄	—	251	2	no	—
541	C₂²⋊C₄	—	251	2	no	—
542	C₂²⋊C₄	—	251	2	no	—
543	C₂²⋊C₄	—	251	2	no	—
544	C₂²⋊C₄	—	251	2	no	—
545	C₂²⋊C₄	—	251	2	no	—
546	C₂²⋊C₄	—	251	2	no	—
547	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
548	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
549	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
552	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
555	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
557	C₄²	—	251	2	no	—
558	C₄²	—	251	2	no	—
559	C₄²	—	251	2	no	—
560	C₄²	—	251	2	no	—
561	C₄²	—	251	2	no	—
562	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
563	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
564	C₂³	—	2	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	251	2	no	—
568	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
569	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
570	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
571	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
572	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
573	Q₈	—	4	1	no	—
574	Q₈	—	1004	2	no	—
575	Q₈	—	1004	2	no	—
576	Q₈	—	1004	2	no	—
577	Q₈	—	502	2	no	—
578	Q₈	—	502	2	no	—
579	Q₈	—	502	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	1004	2	no	—
588	D₄	—	1004	2	no	—
589	D₄	—	1004	2	no	—
590	D₄	—	1004	2	no	—
591	D₄	—	502	4	no	—
592	D₄	—	502	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	1004	2	no	—
602	C₂×C₄	—	1004	2	no	—
603	C₂×C₄	—	1004	2	no	—
604	C₂×C₄	—	1004	2	no	—
605	C₂×C₄	—	1004	2	no	—
606	C₂×C₄	—	1004	2	no	—
607	C₂×C₄	—	1004	2	no	—
608	C₂×C₄	—	251	2	no	—
609	C₂×C₄	—	251	2	no	—
610	C₂×C₄	—	251	2	no	—
611	C₂×C₄	—	251	2	no	—
612	C₂×C₄	—	251	2	no	—
613	C₂×C₄	—	251	2	no	—
614	C₂×C₄	—	251	2	no	—
615	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
616	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	502	2	no	—
641	C₂²	—	502	2	no	—
642	C₂²	—	502	2	no	—
643	C₂²	#22548762	1	2	yes	—
644	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	502	2	no	—
655	C₄	—	502	2	no	—
656	C₄	—	502	2	no	—
657	C₄	—	502	2	no	—
658	C₄	—	502	2	no	—
659	C₄	—	502	2	no	—
660	C₄	—	502	2	no	—
661	C₄	#22548760	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	1	no	—
667	C₂	—	1004	2	no	—
668	C₂	C₂×#22548760	1	1	yes	characteristic
669	C₂	C₂×#22548762	1	1	yes	characteristic
670	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#525×C₂₅₁	C₂
hypercenter	#525	D₂₅₁
hypocenter	C₂₅₁	#3541
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #30632438	C₂	semidirect
2. #30632432	C₂	semidirect
3. #30632407	C₂	semidirect
4. #30632394	C₂	semidirect
5. #30632391	C₂	semidirect
6. #30632383	C₂	semidirect
7. #30632380	C₂	semidirect
8. #30632377	C₂	semidirect
9. D₄×Dic₅₀₂	C₂	semidirect
10. #30632346	C₂	semidirect
11. #30632346	C₂	semidirect
12. #30632342	C₂	semidirect
13. #30632308	C₂	semidirect
14. #30632305	C₂	semidirect
15. #30632299	C₂	semidirect
16. #30632280	C₂	semidirect
17. #30632272	C₂	semidirect
18. #30632272	C₂	semidirect
19. #30632265	C₂	semidirect
20. #30632258	C₂	semidirect
21. #30632198	C₂	semidirect
22. C₂×#22548694	C₂	semidirect
23. #525×C₂₅₁	C₂	semidirect
25. C₂×#16860810	C₂²	semidirect
27. C₂²×Dic₅₀₂	C₂²	semidirect
28. #22548715	C₂²	semidirect
29. #22548715	C₂²	semidirect
30. #22548714	C₂²	semidirect
31. #22548713	C₂²	semidirect
32. #22548710	C₂²	semidirect
33. #22548710	C₂²	semidirect
38. #22548708	C₂²	semidirect
39. #22548707	C₂²	semidirect
40. #22548706	C₂²	semidirect
41. #22548705	C₂²	semidirect
42. #22548705	C₂²	semidirect
43. #22548705	C₂²	semidirect
44. #22548703	C₂²	semidirect
49. #22548701	C₂²	semidirect
53. #22548697	C₂²	semidirect
54. #22548697	C₂²	semidirect
57. #22548696	C₂²	semidirect
66. #22548694	C₂²	semidirect
67. #22548694	C₂²	semidirect
68. #22548694	C₂²	semidirect
69. #22548693	C₂²	semidirect
70. #22548693	C₂²	semidirect
71. #22548693	C₂²	semidirect
74. #22548692	C₂²	semidirect
75. #22548692	C₂²	semidirect
76. #22548691	C₂²	semidirect
79. #22548689	C₂²	semidirect
84. #22548687	C₂²	semidirect
88. C₄×Dic₅₀₂	C₂²	semidirect
89. C₄×Dic₅₀₂	C₂²	semidirect
90. C₄×Dic₅₀₂	C₂²	semidirect
91. #22548680	C₂²	semidirect
92. C₄×D₁₀₀₄	C₂²	semidirect
99. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
101. #22548674	C₂²	semidirect
102. #22548671	C₂²	semidirect
104. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
106. C₄⋊C₄×D₂₅₁	C₂²	semidirect
335. C₂₅₁	#3541	semidirect
358. #525	D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632438	2
#30632432	2
#30632407	2
#30632394	2
#30632391	2
#30632383	2
#30632380	2
#30632377	2
D₄×Dic₅₀₂	2
#30632346	2
#30632342	2
#30632308	2
#30632305	2
#30632299	2
#30632280	2
#30632272	2
#30632265	2
#30632258	2
#30632198	2
C₂×#22548694	2
#525×C₂₅₁	2
#3541	251