Subgroups — #44564681

Order 32128.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632433	C₂	1	2	yes	maximal, complemented
2	#30632425	C₂	1	2	yes	maximal, complemented
3	#30632402	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632383	C₂	1	1	yes	maximal, characteristic, complemented
5	#30632377	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632364	C₂	1	2	yes	maximal, complemented
7	#30632358	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632341	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632333	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632333	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632326	C₂	1	2	yes	maximal, complemented
12	D₄×D₁₀₀₄	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632308	C₂	1	1	yes	maximal, characteristic, complemented
14	#30632292	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632289	C₂	1	2	yes	maximal, complemented
16	#30632273	C₂	1	2	yes	maximal, complemented
17	#30632265	C₂	1	1	yes	maximal, characteristic, complemented
18	#30632252	C₂	1	2	yes	maximal, complemented
19	#30632251	C₂	1	1	yes	maximal, characteristic, complemented
20	#30632247	C₂	1	2	yes	maximal, complemented
21	#30632198	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#22548689	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, complemented
25	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
26	C₂×#16860809	C₂²	1	2	yes	complemented
27	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic
28	C₂²×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
30	C₂×D₄×D₂₅₁	C₂²	1	2	yes	—
31	#22548715	C₂²	1	1	yes	characteristic, complemented
32	#22548712	C₂²	1	1	yes	characteristic, complemented
33	#22548711	C₂²	1	2	yes	complemented
34	#22548711	C₂²	1	2	yes	complemented
35	#22548710	C₂²	1	2	yes	complemented
36	#22548710	C₂²	1	2	yes	complemented
37	#22548708	C₂²	1	2	yes	complemented
38	#22548707	C₂²	1	1	yes	characteristic, complemented
39	#22548705	C₂²	1	2	yes	complemented
40	#22548704	C₂²	1	2	yes	complemented
41	#22548703	C₂²	1	1	yes	characteristic, complemented
42	#22548701	C₂²	1	2	yes	complemented
43	#22548701	C₂²	1	2	yes	complemented
44	#22548701	C₂²	1	2	yes	complemented
45	#22548700	C₂²	1	2	yes	complemented
46	#22548700	C₂²	1	2	yes	complemented
47	#22548700	C₂²	1	2	yes	complemented
48	#22548700	C₂²	1	2	yes	complemented
49	#22548699	C₂²	1	2	yes	complemented
50	#22548699	C₂²	1	2	yes	complemented
51	#22548698	C₂²	1	2	yes	complemented
52	#22548697	C₂²	1	2	yes	complemented
53	#22548697	C₂²	1	2	yes	complemented
54	#22548696	C₂²	1	2	yes	—
55	#22548695	C₂²	1	2	yes	complemented
56	#22548694	C₂²	1	1	yes	characteristic, complemented
57	#22548694	C₂²	1	1	yes	characteristic, complemented
58	#22548694	C₂²	1	1	yes	characteristic, complemented
59	#22548693	C₂²	1	2	yes	complemented
60	#22548691	C₂²	1	2	yes	complemented
61	#22548690	C₂²	1	2	yes	complemented
62	#22548689	C₂²	1	1	yes	characteristic
63	#22548689	C₂²	1	1	yes	characteristic
64	#22548689	C₂²	1	1	yes	characteristic
65	#22548689	C₂²	1	1	yes	characteristic, complemented
66	#22548689	C₂²	1	1	yes	characteristic, complemented
67	#22548689	C₂²	1	1	yes	characteristic, complemented
68	#22548689	C₂²	1	1	yes	characteristic, complemented
69	#22548689	C₂²	1	1	yes	characteristic, complemented
70	#22548689	C₂²	1	2	yes	complemented
71	#22548689	C₂²	1	1	yes	characteristic, complemented
72	#22548689	C₂²	1	2	yes	complemented
73	#22548688	C₂²	1	2	yes	complemented
74	#22548688	C₂²	1	2	yes	complemented
75	#22548688	C₂²	1	2	yes	complemented
76	#22548688	C₂²	1	2	yes	complemented
77	#22548688	C₂²	1	2	yes	complemented
78	#22548688	C₂²	1	2	yes	complemented
79	#22548687	C₂²	1	2	yes	complemented
80	#22548687	C₂²	1	2	yes	complemented
81	#22548687	C₂²	1	2	yes	complemented
82	#22548686	C₂²	1	2	yes	complemented
83	#22548686	C₂²	1	2	yes	complemented
84	#22548685	C₂²	1	2	yes	—
85	#22548685	C₂²	1	2	yes	complemented
86	#22548684	C₂²	1	2	yes	complemented
87	#22548683	C₂²	1	2	yes	complemented
88	#22548683	C₂²	1	2	yes	complemented
89	#22548683	C₂²	1	2	yes	complemented
90	#22548683	C₂²	1	2	yes	complemented
91	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
92	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic, complemented
95	#22548677	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
98	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
99	#22548674	C₂²	1	1	yes	characteristic, complemented
100	#22548674	C₂²	1	1	yes	characteristic, complemented
101	#22548673	C₂²	1	2	yes	complemented
102	#22548671	C₂²	1	2	yes	complemented
103	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
105	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	complemented
108	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
109	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
110	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
111	#123×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
112	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
113	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
114	#121×C₂₅₁	C₂²	1	1	yes	characteristic
115	#121×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
116	#120×C₂₅₁	C₂²	1	1	yes	characteristic
117	#120×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
122	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₂₅₁	C₂³	1	2	yes	—
124	C₂³×D₂₅₁	C₂³	1	2	yes	—
125	#16860810	—	4	2	no	—
126	#16860810	—	4	2	no	—
127	#16860809	—	4	4	no	—
128	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
129	C₂×Dic₅₀₂	C₂³	1	2	yes	—
130	C₂×D₁₀₀₄	—	4	2	no	—
131	C₂×D₁₀₀₄	—	4	2	no	—
132	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
133	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
134	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
135	C₂×D₁₀₀₄	C₂³	1	2	yes	—
136	C₂×D₁₀₀₄	C₂³	1	2	yes	—
137	C₂×D₁₀₀₄	C₂³	1	2	yes	—
138	C₂×D₁₀₀₄	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₂₅₁	—	4	4	no	—
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	2	yes	—
149	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
151	D₄×D₂₅₁	—	4	4	no	—
152	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
153	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
154	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
155	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
156	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
157	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
158	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
159	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
163	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
164	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
165	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
166	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
167	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
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	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	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₂₅₁)⋊C₄	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	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
191	C₄×Dic₂₅₁	C₂³	1	2	yes	—
192	C₄×Dic₂₅₁	C₂³	1	2	yes	—
193	C₄×Dic₂₅₁	C₂³	1	2	yes	—
194	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
195	#41×C₂₅₁	—	4	2	no	—
196	C₂×Q₈×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	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
202	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
203	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
204	C₂²×C₄×C₂₅₁	—	4	2	no	—
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	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
212	C₂²×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	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
218	C₄⋊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	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
229	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
230	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
231	C₂²×D₂₅₁	—	2	4	no	—
232	C₂²×D₂₅₁	—	4	2	no	—
233	C₂²×D₂₅₁	—	4	2	no	—
234	C₂²×D₂₅₁	—	4	2	no	—
235	C₂²×D₂₅₁	—	4	2	no	—
236	C₂²×D₂₅₁	—	4	2	no	—
237	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
238	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
239	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
240	Dic₅₀₂	—	2	2	no	—
241	Dic₅₀₂	—	4	2	no	—
242	D₁₀₀₄	—	2	2	no	—
243	D₁₀₀₄	—	2	2	no	—
244	D₁₀₀₄	—	2	2	no	—
245	D₁₀₀₄	—	4	2	no	—
246	D₁₀₀₄	—	4	2	no	—
247	D₁₀₀₄	—	4	2	no	—
248	D₁₀₀₄	—	4	2	no	—
249	C₂²⋊D₂₅₁	—	2	4	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	C₂²⋊D₂₅₁	—	4	2	no	—
257	C₂²⋊D₂₅₁	—	4	2	no	—
258	C₂²⋊D₂₅₁	—	4	2	no	—
259	C₂²⋊D₂₅₁	—	4	2	no	—
260	C₂×Dic₂₅₁	—	2	4	no	—
261	C₂×Dic₂₅₁	—	4	2	no	—
262	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
263	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
264	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
265	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
266	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
267	C₄×D₂₅₁	—	4	2	no	—
268	C₄×D₂₅₁	—	4	2	no	—
269	C₄×D₂₅₁	—	4	2	no	—
270	C₄×D₂₅₁	—	4	2	no	—
271	C₄×D₂₅₁	—	4	2	no	—
272	C₂³×C₂₅₁	—	2	2	no	—
273	C₂³×C₂₅₁	—	4	1	no	—
274	C₂³×C₂₅₁	—	4	1	no	—
275	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
276	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
277	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
278	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
279	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
280	Q₈×C₂₅₁	—	4	1	no	—
281	D₄×C₂₅₁	—	2	2	no	—
282	D₄×C₂₅₁	—	2	2	no	—
283	D₄×C₂₅₁	—	4	1	no	—
284	D₄×C₂₅₁	—	4	1	no	—
285	D₄×C₂₅₁	—	4	1	no	—
286	D₄×C₂₅₁	—	4	1	no	—
287	D₄×C₂₅₁	—	4	1	no	—
288	C₂×C₄×C₂₅₁	—	2	2	no	—
289	C₂×C₄×C₂₅₁	—	2	2	no	—
290	C₂×C₄×C₂₅₁	—	2	2	no	—
291	C₂×C₄×C₂₅₁	—	2	2	no	—
292	C₂×C₄×C₂₅₁	—	2	2	no	—
293	C₂×C₄×C₂₅₁	—	4	1	no	—
294	C₂×C₄×C₂₅₁	—	4	1	no	—
295	C₂×C₄×C₂₅₁	—	4	1	no	—
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	1	yes	characteristic
300	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
302	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
303	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
305	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₂₅₁	—	2	1	no	—
307	C₂²×C₂₅₁	—	2	1	no	—
308	C₂²×C₂₅₁	—	2	1	no	—
309	C₂²×C₂₅₁	—	2	1	no	—
310	C₂²×C₂₅₁	—	2	1	no	—
311	C₂²×C₂₅₁	—	2	1	no	—
312	C₂²×C₂₅₁	—	2	1	no	—
313	C₂²×C₂₅₁	—	2	1	no	—
314	C₂²×C₂₅₁	—	2	1	no	—
315	C₂²×C₂₅₁	—	2	1	no	—
316	C₂²×C₂₅₁	—	2	1	no	—
317	C₂²×C₂₅₁	—	2	1	no	—
318	C₂²×C₂₅₁	—	2	1	no	—
319	C₂²×C₂₅₁	—	2	1	no	—
320	C₂²×C₂₅₁	—	4	4	no	—
321	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
322	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
323	C₂×D₂₅₁	—	2	2	no	—
324	C₂×D₂₅₁	—	2	2	no	—
325	C₂×D₂₅₁	—	2	2	no	—
326	C₂×D₂₅₁	—	2	2	no	—
327	C₂×D₂₅₁	—	2	2	no	—
328	C₂×D₂₅₁	—	2	2	no	—
329	C₂×D₂₅₁	—	2	2	no	—
330	C₂×D₂₅₁	—	2	2	no	—
331	C₂×D₂₅₁	—	2	2	no	—
332	C₂×D₂₅₁	—	8	4	no	—
333	C₂×D₂₅₁	—	8	4	no	—
334	C₄×C₂₅₁	—	2	1	no	—
335	C₄×C₂₅₁	—	2	1	no	—
336	C₄×C₂₅₁	—	2	1	no	—
337	C₄×C₂₅₁	—	2	1	no	—
338	C₄×C₂₅₁	—	2	1	no	—
339	C₄×C₂₅₁	—	2	1	no	—
340	C₄×C₂₅₁	—	2	1	no	—
341	C₄×C₂₅₁	—	2	1	no	—
342	C₄×C₂₅₁	—	2	1	no	—
343	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
344	Dic₂₅₁	—	2	2	no	—
345	Dic₂₅₁	—	2	2	no	—
346	Dic₂₅₁	—	2	2	no	—
347	Dic₂₅₁	—	2	2	no	—
348	Dic₂₅₁	—	2	2	no	—
349	C₂×C₂₅₁	—	2	2	no	—
350	C₂×C₂₅₁	—	4	1	no	—
351	C₂×C₂₅₁	—	4	1	no	—
352	C₂×C₂₅₁	—	4	1	no	—
353	C₂×C₂₅₁	—	4	1	no	—
354	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
356	C₂×C₂₅₁	#585	1	1	yes	characteristic
357	D₂₅₁	—	4	2	no	—
358	D₂₅₁	—	4	2	no	—
359	D₂₅₁	—	4	2	no	—
360	C₂₅₁	#3542	1	1	yes	characteristic, complemented, Sylow
361	#3542	—	251	1	no	maximal, Sylow
362	#562	—	251	2	no	—
363	#560	—	251	2	no	—
364	#555	—	251	1	no	—
365	#553	—	251	1	no	—
366	#552	—	251	1	no	—
367	#551	—	251	2	no	—
368	#550	—	251	1	no	—
369	#547	—	251	1	no	—
370	#546	—	251	2	no	—
371	#546	—	251	1	no	—
372	#546	—	251	1	no	—
373	D₄²	—	251	1	no	—
374	#542	—	251	1	no	—
375	#540	—	251	2	no	—
376	#540	—	251	1	no	—
377	#538	—	251	2	no	—
378	#537	—	251	1	no	—
379	#535	—	251	1	no	—
380	#535	—	251	2	no	—
381	#534	—	251	2	no	—
382	#525	—	251	1	no	—
383	#525	D₂₅₁	1	1	yes	characteristic, complemented
384	C₂×#121	—	251	1	no	—
385	C₂×#41	—	251	2	no	—
386	C₂×#41	—	251	1	no	—
387	C₂×#41	—	251	1	no	—
388	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
389	C₂²×D₄	—	251	2	no	—
390	C₂²×D₄	—	251	2	no	—
391	C₂²×D₄	—	251	1	no	—
392	C₂²×D₄	—	251	1	no	—
393	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
394	C₄⋊Q₈	—	251	1	no	—
395	#127	—	251	2	no	—
396	#127	—	251	2	no	—
397	#127	—	251	1	no	—
398	#126	—	251	2	no	—
399	#126	—	251	2	no	—
400	#126	—	251	2	no	—
401	#125	—	251	2	no	—
402	#125	—	251	1	no	—
403	#124	—	251	2	no	—
404	#124	—	251	2	no	—
405	#124	—	251	2	no	—
406	#124	—	251	2	no	—
407	#124	—	251	1	no	—
408	#123	—	251	2	no	—
409	#123	—	251	2	no	—
410	#123	—	251	2	no	—
411	#123	—	251	2	no	—
412	#123	—	251	2	no	—
413	#123	—	251	2	no	—
414	#123	—	251	2	no	—
415	#123	—	251	2	no	—
416	#123	—	251	2	no	—
417	#123	—	251	2	no	—
418	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
419	#123	C₂×D₂₅₁	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	—	251	2	no	—
421	C₂²⋊Q₈	—	251	1	no	—
422	C₂²⋊Q₈	—	251	1	no	—
423	C₂²⋊Q₈	—	251	1	no	—
424	C₂²⋊Q₈	—	251	2	no	—
425	C₂²⋊Q₈	—	251	2	no	—
426	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
427	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
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	1	no	—
434	#121	—	251	1	no	—
435	#121	—	251	2	no	—
436	#121	—	251	1	no	—
437	#121	—	251	1	no	—
438	#121	—	251	2	no	—
439	#121	—	251	1	no	—
440	#121	—	251	1	no	—
441	#121	—	251	1	no	—
442	#121	—	251	1	no	—
443	#121	—	251	1	no	—
444	#121	—	251	2	no	—
445	#121	—	251	2	no	—
446	#121	—	251	2	no	—
447	#121	—	251	2	no	—
448	#121	—	251	2	no	—
449	#121	—	251	2	no	—
450	#121	—	251	2	no	—
451	#121	C₂×D₂₅₁	1	1	yes	characteristic
452	#121	C₂×D₂₅₁	1	1	yes	characteristic, complemented
453	#120	—	251	2	no	—
454	#120	—	251	2	no	—
455	#120	—	251	2	no	—
456	#120	—	251	2	no	—
457	#120	—	251	2	no	—
458	#120	—	251	2	no	—
459	#120	—	251	2	no	—
460	#120	C₂×D₂₅₁	1	1	yes	characteristic
461	#120	C₂×D₂₅₁	1	1	yes	characteristic, complemented
462	C₄×Q₈	—	251	1	no	—
463	C₄×D₄	—	251	2	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	C₄×D₄	—	251	1	no	—
470	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
471	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
472	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
473	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
474	#117	—	251	1	no	—
475	#117	—	251	1	no	—
476	#117	—	251	2	no	—
477	#117	—	251	2	no	—
478	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
479	C₂×C₄⋊C₄	—	251	1	no	—
480	C₂×C₄⋊C₄	—	251	1	no	—
481	C₂×C₂²⋊C₄	—	251	2	no	—
482	C₂×C₂²⋊C₄	—	251	2	no	—
483	C₂×C₂²⋊C₄	—	251	2	no	—
484	C₂⁴	—	251	2	no	—
485	C₂⁴	—	251	2	no	—
486	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
487	#41	—	4	2	no	—
488	#41	—	1004	2	no	—
489	#41	—	1004	2	no	—
490	#41	—	1004	4	no	—
491	C₂×Q₈	—	251	2	no	—
492	C₂×Q₈	—	251	1	no	—
493	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
494	C₂×D₄	—	1004	2	no	—
495	C₂×D₄	—	1004	2	no	—
496	C₂×D₄	—	1004	4	no	—
497	C₂×D₄	—	1004	4	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	2	no	—
503	C₂×D₄	—	251	2	no	—
504	C₂×D₄	—	251	2	no	—
505	C₂×D₄	—	251	2	no	—
506	C₂×D₄	—	251	2	no	—
507	C₂×D₄	—	251	2	no	—
508	C₂×D₄	—	251	2	no	—
509	C₂×D₄	—	251	2	no	—
510	C₂×D₄	—	251	2	no	—
511	C₂×D₄	—	251	2	no	—
512	C₂×D₄	—	251	2	no	—
513	C₂×D₄	—	251	1	no	—
514	C₂×D₄	—	251	1	no	—
515	C₂×D₄	—	251	1	no	—
516	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
517	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
518	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
519	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	251	2	no	—
525	C₂²×C₄	—	251	2	no	—
526	C₂²×C₄	—	251	2	no	—
527	C₂²×C₄	—	251	2	no	—
528	C₂²×C₄	—	251	2	no	—
529	C₂²×C₄	—	251	2	no	—
530	C₂²×C₄	—	251	2	no	—
531	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
532	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
533	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
534	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
535	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
539	C₄⋊C₄	—	251	1	no	—
540	C₄⋊C₄	—	251	1	no	—
541	C₄⋊C₄	—	251	1	no	—
542	C₄⋊C₄	—	251	2	no	—
543	C₄⋊C₄	—	251	2	no	—
544	C₄⋊C₄	—	251	1	no	—
545	C₄⋊C₄	—	251	2	no	—
546	C₄⋊C₄	—	251	2	no	—
547	C₄⋊C₄	—	251	2	no	—
548	C₄⋊C₄	—	251	2	no	—
549	C₄⋊C₄	—	251	2	no	—
550	C₄⋊C₄	—	251	2	no	—
551	C₄⋊C₄	—	251	2	no	—
552	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
556	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
558	C₂²⋊C₄	—	251	2	no	—
559	C₂²⋊C₄	—	251	2	no	—
560	C₂²⋊C₄	—	251	2	no	—
561	C₂²⋊C₄	—	251	2	no	—
562	C₂²⋊C₄	—	251	2	no	—
563	C₂²⋊C₄	—	251	2	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	2	no	—
569	C₂²⋊C₄	—	251	2	no	—
570	C₂²⋊C₄	—	251	2	no	—
571	C₂²⋊C₄	—	251	2	no	—
572	C₂²⋊C₄	—	251	2	no	—
573	C₂²⋊C₄	—	251	2	no	—
574	C₂²⋊C₄	—	251	2	no	—
575	C₂²⋊C₄	—	251	2	no	—
576	C₂²⋊C₄	—	251	2	no	—
577	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
579	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
580	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
581	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
582	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
583	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
584	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
585	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
586	C₂²⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
587	C₄²	—	251	2	no	—
588	C₄²	—	251	2	no	—
589	C₄²	—	251	2	no	—
590	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
591	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
592	C₂³	—	2	2	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	1004	2	no	—
596	C₂³	—	1004	2	no	—
597	C₂³	—	1004	2	no	—
598	C₂³	—	1004	2	no	—
599	C₂³	—	1004	2	no	—
600	C₂³	—	502	4	no	—
601	C₂³	—	251	2	no	—
602	C₂³	—	251	2	no	—
603	C₂³	—	251	2	no	—
604	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
605	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
606	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
607	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
608	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
609	Q₈	—	4	1	no	—
610	Q₈	—	1004	2	no	—
611	Q₈	—	502	2	no	—
612	D₄	—	2	2	no	—
613	D₄	—	2	2	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	4	1	no	—
619	D₄	—	1004	2	no	—
620	D₄	—	1004	2	no	—
621	D₄	—	1004	2	no	—
622	D₄	—	1004	2	no	—
623	D₄	—	1004	2	no	—
624	D₄	—	1004	2	no	—
625	D₄	—	1004	2	no	—
626	D₄	—	1004	2	no	—
627	D₄	—	1004	2	no	—
628	D₄	—	1004	2	no	—
629	D₄	—	1004	2	no	—
630	D₄	—	1004	2	no	—
631	D₄	—	1004	2	no	—
632	D₄	—	1004	2	no	—
633	D₄	—	502	4	no	—
634	D₄	—	502	2	no	—
635	D₄	—	502	2	no	—
636	D₄	—	502	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	1004	2	no	—
646	C₂×C₄	—	1004	2	no	—
647	C₂×C₄	—	1004	2	no	—
648	C₂×C₄	—	1004	2	no	—
649	C₂×C₄	—	1004	2	no	—
650	C₂×C₄	—	1004	2	no	—
651	C₂×C₄	—	502	4	no	—
652	C₂×C₄	—	251	2	no	—
653	C₂×C₄	—	251	2	no	—
654	C₂×C₄	—	251	2	no	—
655	C₂×C₄	—	251	2	no	—
656	C₂×C₄	—	251	2	no	—
657	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
658	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
659	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
663	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
666	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	2	1	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	2008	4	no	—
683	C₂²	—	2008	4	no	—
684	C₂²	—	502	2	no	—
685	C₂²	—	502	2	no	—
686	C₂²	—	502	2	no	—
687	C₂²	—	502	2	no	—
688	C₂²	—	502	2	no	—
689	C₂²	—	502	2	no	—
690	C₂²	—	502	2	no	—
691	C₂²	—	502	2	no	—
692	C₂²	—	502	2	no	—
693	C₂²	#22548761	1	2	yes	—
694	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	2	1	no	—
703	C₄	—	2	1	no	—
704	C₄	—	502	2	no	—
705	C₄	—	502	2	no	—
706	C₄	—	502	2	no	—
707	C₄	—	502	2	no	—
708	C₄	—	502	2	no	—
709	C₄	#22548760	1	2	yes	—
710	C₂	—	2	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	4	1	no	—
714	C₂	—	4	1	no	—
715	C₂	—	1004	2	no	—
716	C₂	—	1004	2	no	—
717	C₂	—	1004	2	no	—
718	C₂	C₂×#22548760	1	1	yes	characteristic
719	C₂	C₂×#22548761	1	1	yes	characteristic
720	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	#3542
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. #30632433	C₂	semidirect
2. #30632425	C₂	semidirect
3. #30632402	C₂	semidirect
4. #30632383	C₂	semidirect
5. #30632377	C₂	semidirect
6. #30632364	C₂	semidirect
7. #30632358	C₂	semidirect
8. #30632341	C₂	semidirect
9. #30632333	C₂	semidirect
10. #30632333	C₂	semidirect
11. #30632326	C₂	semidirect
12. D₄×D₁₀₀₄	C₂	semidirect
13. #30632308	C₂	semidirect
14. #30632292	C₂	semidirect
15. #30632289	C₂	semidirect
16. #30632273	C₂	semidirect
17. #30632265	C₂	semidirect
18. #30632252	C₂	semidirect
19. #30632251	C₂	semidirect
20. #30632247	C₂	semidirect
21. #30632198	C₂	semidirect
22. C₂×#22548689	C₂	semidirect
23. #525×C₂₅₁	C₂	semidirect
24. C₂×#16860810	C₂²	semidirect
25. C₂×#16860810	C₂²	semidirect
26. C₂×#16860809	C₂²	semidirect
28. C₂²×D₁₀₀₄	C₂²	semidirect
29. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
31. #22548715	C₂²	semidirect
32. #22548712	C₂²	semidirect
33. #22548711	C₂²	semidirect
34. #22548711	C₂²	semidirect
35. #22548710	C₂²	semidirect
36. #22548710	C₂²	semidirect
37. #22548708	C₂²	semidirect
38. #22548707	C₂²	semidirect
39. #22548705	C₂²	semidirect
40. #22548704	C₂²	semidirect
41. #22548703	C₂²	semidirect
42. #22548701	C₂²	semidirect
43. #22548701	C₂²	semidirect
44. #22548701	C₂²	semidirect
45. #22548700	C₂²	semidirect
46. #22548700	C₂²	semidirect
47. #22548700	C₂²	semidirect
48. #22548700	C₂²	semidirect
49. #22548699	C₂²	semidirect
50. #22548699	C₂²	semidirect
51. #22548698	C₂²	semidirect
52. #22548697	C₂²	semidirect
53. #22548697	C₂²	semidirect
55. #22548695	C₂²	semidirect
56. #22548694	C₂²	semidirect
57. #22548694	C₂²	semidirect
58. #22548694	C₂²	semidirect
59. #22548693	C₂²	semidirect
60. #22548691	C₂²	semidirect
61. #22548690	C₂²	semidirect
65. #22548689	C₂²	semidirect
66. #22548689	C₂²	semidirect
67. #22548689	C₂²	semidirect
68. #22548689	C₂²	semidirect
69. #22548689	C₂²	semidirect
70. #22548689	C₂²	semidirect
71. #22548689	C₂²	semidirect
72. #22548689	C₂²	semidirect
73. #22548688	C₂²	semidirect
74. #22548688	C₂²	semidirect
75. #22548688	C₂²	semidirect
76. #22548688	C₂²	semidirect
77. #22548688	C₂²	semidirect
78. #22548688	C₂²	semidirect
79. #22548687	C₂²	semidirect
80. #22548687	C₂²	semidirect
81. #22548687	C₂²	semidirect
82. #22548686	C₂²	semidirect
83. #22548686	C₂²	semidirect
85. #22548685	C₂²	semidirect
86. #22548684	C₂²	semidirect
87. #22548683	C₂²	semidirect
88. #22548683	C₂²	semidirect
89. #22548683	C₂²	semidirect
90. #22548683	C₂²	semidirect
91. C₄×Dic₅₀₂	C₂²	semidirect
92. C₄×D₁₀₀₄	C₂²	semidirect
93. C₄×D₁₀₀₄	C₂²	semidirect
94. C₄×D₁₀₀₄	C₂²	semidirect
95. #22548677	C₂²	semidirect
96. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
97. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
98. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
99. #22548674	C₂²	semidirect
100. #22548674	C₂²	semidirect
101. #22548673	C₂²	semidirect
102. #22548671	C₂²	semidirect
103. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
104. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
105. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
106. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
107. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
108. C₂×#41×C₂₅₁	C₂²	semidirect
109. C₂³×C₄×C₂₅₁	C₂²	semidirect
110. #123×C₂₅₁	C₂²	semidirect
111. #123×C₂₅₁	C₂²	semidirect
112. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
113. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
115. #121×C₂₅₁	C₂²	semidirect
117. #120×C₂₅₁	C₂²	semidirect
119. C₄×D₄×C₂₅₁	C₂²	semidirect
120. C₄×D₄×C₂₅₁	C₂²	semidirect
121. C₄×D₄×C₂₅₁	C₂²	semidirect
122. #117×C₂₅₁	C₂²	semidirect
360. C₂₅₁	#3542	semidirect
383. #525	D₂₅₁	semidirect
388. C₂×#41	C₂×D₂₅₁	semidirect
393. C₂³×C₄	C₂×D₂₅₁	semidirect
418. #123	C₂×D₂₅₁	semidirect
419. #123	C₂×D₂₅₁	semidirect
426. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
427. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
452. #121	C₂×D₂₅₁	semidirect
461. #120	C₂×D₂₅₁	semidirect
471. C₄×D₄	C₂×D₂₅₁	semidirect
472. C₄×D₄	C₂×D₂₅₁	semidirect
473. C₄×D₄	C₂×D₂₅₁	semidirect
478. #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
#30632433	2
#30632425	2
#30632402	2
#30632383	2
#30632377	2
#30632364	2
#30632358	2
#30632341	2
#30632333	2
#30632326	2
D₄×D₁₀₀₄	2
#30632308	2
#30632292	2
#30632289	2
#30632273	2
#30632265	2
#30632252	2
#30632251	2
#30632247	2
#30632198	2
C₂×#22548689	2
#525×C₂₅₁	2
#3542	251