Subgroups — #44564568

Order 32128.

1038 conjugacy classes of subgroups.

The subgroup lattice has 590 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	#30632396	C₂	1	2	yes	maximal, complemented
4	#30632370	C₂	1	2	yes	maximal, complemented
5	#30632368	C₂	1	2	yes	maximal, complemented
6	#30632366	C₂	1	2	yes	maximal, complemented
7	#30632336	C₂	1	2	yes	maximal, complemented
8	#30632324	C₂	1	2	yes	maximal, complemented
9	#30632316	C₂	1	1	yes	maximal, characteristic, complemented
10	#30632312	C₂	1	1	yes	maximal, characteristic, complemented
11	#30632302	C₂	1	2	yes	maximal, complemented
12	#30632282	C₂	1	1	yes	maximal, characteristic, complemented
13	#30632281	C₂	1	2	yes	maximal, complemented
14	#30632279	C₂	1	2	yes	maximal, complemented
15	#30632274	C₂	1	1	yes	maximal, characteristic, complemented
16	#30632259	C₂	1	2	yes	maximal, complemented
17	C₂×#22548698	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#22548694	C₂	1	1	yes	maximal, characteristic, complemented
19	#525×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16860809	C₂²	1	2	yes	—
21	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
23	#22548714	C₂²	1	2	yes	complemented
24	#22548714	C₂²	1	2	yes	complemented
25	#22548713	C₂²	1	2	yes	complemented
26	#22548710	C₂²	1	2	yes	complemented
27	#22548710	C₂²	1	2	yes	complemented
28	#22548709	C₂²	1	2	yes	complemented
29	#22548708	C₂²	1	2	yes	complemented
30	#22548708	C₂²	1	2	yes	complemented
31	#22548708	C₂²	1	2	yes	complemented
32	#22548707	C₂²	1	2	yes	complemented
33	#22548706	C₂²	1	2	yes	complemented
34	#22548705	C₂²	1	2	yes	complemented
35	#22548705	C₂²	1	2	yes	complemented
36	#22548705	C₂²	1	2	yes	complemented
37	#22548702	C₂²	1	2	yes	complemented
38	#22548701	C₂²	1	2	yes	—
39	#22548701	C₂²	1	2	yes	complemented
40	#22548701	C₂²	1	2	yes	complemented
41	#22548699	C₂²	1	2	yes	—
42	#22548699	C₂²	1	2	yes	complemented
43	#22548698	C₂²	1	2	yes	—
44	#22548698	C₂²	1	2	yes	—
45	#22548698	C₂²	1	2	yes	—
46	#22548698	C₂²	1	2	yes	—
47	#22548698	C₂²	1	2	yes	complemented
48	#22548697	C₂²	1	2	yes	—
49	#22548697	C₂²	1	2	yes	complemented
50	#22548696	C₂²	1	2	yes	—
51	#22548696	C₂²	1	2	yes	complemented
52	#22548696	C₂²	1	2	yes	complemented
53	#22548696	C₂²	1	2	yes	complemented
54	#22548695	C₂²	1	2	yes	complemented
55	#22548694	C₂²	1	1	yes	characteristic
56	#22548694	C₂²	1	1	yes	characteristic
57	#22548694	C₂²	1	2	yes	—
58	#22548694	C₂²	1	1	yes	characteristic, complemented
59	#22548694	C₂²	1	1	yes	characteristic, complemented
60	#22548694	C₂²	1	2	yes	complemented
61	#22548694	C₂²	1	2	yes	complemented
62	#22548693	C₂²	1	2	yes	complemented
63	#22548693	C₂²	1	2	yes	complemented
64	#22548693	C₂²	1	2	yes	complemented
65	#22548692	C₂²	1	2	yes	—
66	#22548692	C₂²	1	2	yes	—
67	#22548692	C₂²	1	2	yes	complemented
68	#22548692	C₂²	1	2	yes	complemented
69	#22548692	C₂²	1	2	yes	complemented
70	#22548692	C₂²	1	2	yes	complemented
71	#22548691	C₂²	1	2	yes	complemented
72	#22548687	C₂²	1	2	yes	—
73	#22548687	C₂²	1	2	yes	—
74	#22548687	C₂²	1	2	yes	complemented
75	#22548686	C₂²	1	2	yes	—
76	#22548683	C₂²	1	2	yes	—
77	C₄×Dic₅₀₂	C₂²	1	2	yes	complemented
78	D₄×Dic₂₅₁	C₂²	1	2	yes	—
79	D₄×Dic₂₅₁	C₂²	1	2	yes	—
80	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
82	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
83	#22548672	C₂²	1	2	yes	complemented
84	#22548671	C₂²	1	2	yes	—
85	#22548671	C₂²	1	2	yes	complemented
86	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
87	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
88	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
89	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
90	C₂×Dic₂₅₁⋊C₄	C₂²	1	2	yes	complemented
91	C₂×C₂²⋊Dic₂₅₁	C₂²	1	2	yes	—
92	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
93	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
96	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
97	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
98	#123×C₂₅₁	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
100	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
101	#121×C₂₅₁	C₂²	1	1	yes	characteristic
102	#121×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
103	#120×C₂₅₁	C₂²	1	2	yes	—
104	C₄×D₄×C₂₅₁	C₂²	1	2	yes	—
105	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
106	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
108	#16860809	—	4	4	no	—
109	C₂×Dic₅₀₂	—	4	2	no	—
110	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
111	C₂×Dic₅₀₂	C₂³	1	2	yes	—
112	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
113	C₂×Dic₅₀₂	C₂³	1	2	yes	—
114	C₂×Dic₅₀₂	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₂₅₁	—	4	2	no	—
116	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
120	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
121	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
122	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
123	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
124	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
125	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
126	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
127	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
128	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
129	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
130	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
131	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
133	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
134	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
135	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
136	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
137	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
138	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
139	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
140	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
141	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
142	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
143	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
144	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
145	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
146	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
147	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
148	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
149	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
150	Dic₂₅₁⋊C₄	C₂³	1	2	yes	—
151	Dic₂₅₁⋊C₄	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	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
156	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
157	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
158	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
159	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
160	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
161	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
162	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
170	C₄×Dic₂₅₁	C₂³	1	2	yes	—
171	C₄×Dic₂₅₁	C₂³	1	2	yes	—
172	C₄×Dic₂₅₁	C₂³	1	2	yes	—
173	C₄×Dic₂₅₁	C₂³	1	2	yes	—
174	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
175	#41×C₂₅₁	—	4	2	no	—
176	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
177	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
178	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
179	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
180	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₂₅₁	—	4	2	no	—
182	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
186	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
188	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
191	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
192	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
198	C₄²×C₂₅₁	C₂³	1	2	yes	—
199	C₂²×D₂₅₁	—	2	2	no	—
200	C₂²×D₂₅₁	—	4	1	no	—
201	C₂²×D₂₅₁	—	4	1	no	—
202	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
203	Dic₅₀₂	—	4	1	no	—
204	Dic₅₀₂	—	4	2	no	—
205	Dic₅₀₂	—	4	1	no	—
206	Dic₅₀₂	—	4	2	no	—
207	Dic₅₀₂	—	4	2	no	—
208	C₂²⋊D₂₅₁	—	2	4	no	—
209	C₂²⋊D₂₅₁	—	4	2	no	—
210	C₂²⋊D₂₅₁	—	4	2	no	—
211	C₂²⋊D₂₅₁	—	4	2	no	—
212	C₂×Dic₂₅₁	—	2	4	no	—
213	C₂×Dic₂₅₁	—	2	2	no	—
214	C₂×Dic₂₅₁	—	4	2	no	—
215	C₂×Dic₂₅₁	—	4	2	no	—
216	C₂×Dic₂₅₁	—	4	1	no	—
217	C₂×Dic₂₅₁	—	4	1	no	—
218	C₂×Dic₂₅₁	—	4	2	no	—
219	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
220	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
221	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
222	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
223	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
224	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
225	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
226	C₄×D₂₅₁	—	4	2	no	—
227	C₄×D₂₅₁	—	4	2	no	—
228	C₂³×C₂₅₁	—	2	2	no	—
229	C₂³×C₂₅₁	—	2	2	no	—
230	C₂³×C₂₅₁	—	4	1	no	—
231	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
232	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
233	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
234	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
235	Q₈×C₂₅₁	—	4	1	no	—
236	D₄×C₂₅₁	—	2	4	no	—
237	D₄×C₂₅₁	—	2	4	no	—
238	D₄×C₂₅₁	—	4	2	no	—
239	D₄×C₂₅₁	—	4	1	no	—
240	C₂×C₄×C₂₅₁	—	2	2	no	—
241	C₂×C₄×C₂₅₁	—	2	2	no	—
242	C₂×C₄×C₂₅₁	—	4	1	no	—
243	C₂×C₄×C₂₅₁	—	4	1	no	—
244	C₂×C₄×C₂₅₁	—	4	1	no	—
245	C₂×C₄×C₂₅₁	—	4	1	no	—
246	C₂×C₄×C₂₅₁	—	4	2	no	—
247	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₂₅₁	—	2	1	no	—
255	C₂²×C₂₅₁	—	2	1	no	—
256	C₂²×C₂₅₁	—	2	1	no	—
257	C₂²×C₂₅₁	—	2	1	no	—
258	C₂²×C₂₅₁	—	2	1	no	—
259	C₂²×C₂₅₁	—	2	2	no	—
260	C₂²×C₂₅₁	—	2	2	no	—
261	C₂²×C₂₅₁	—	2	1	no	—
262	C₂²×C₂₅₁	—	2	1	no	—
263	C₂²×C₂₅₁	—	2	2	no	—
264	C₂²×C₂₅₁	—	4	4	no	—
265	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
266	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
267	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
268	C₂×D₂₅₁	—	2	2	no	—
269	C₂×D₂₅₁	—	2	2	no	—
270	C₂×D₂₅₁	—	2	2	no	—
271	C₂×D₂₅₁	—	8	2	no	—
272	C₄×C₂₅₁	—	2	1	no	—
273	C₄×C₂₅₁	—	2	1	no	—
274	C₄×C₂₅₁	—	2	1	no	—
275	C₄×C₂₅₁	—	2	1	no	—
276	C₄×C₂₅₁	—	2	2	no	—
277	C₄×C₂₅₁	—	2	2	no	—
278	C₄×C₂₅₁	—	2	2	no	—
279	Dic₂₅₁	—	2	2	no	—
280	Dic₂₅₁	—	2	2	no	—
281	Dic₂₅₁	—	2	2	no	—
282	Dic₂₅₁	—	2	2	no	—
283	Dic₂₅₁	—	2	2	no	—
284	Dic₂₅₁	—	2	2	no	—
285	Dic₂₅₁	—	2	2	no	—
286	C₂×C₂₅₁	—	2	2	no	—
287	C₂×C₂₅₁	—	2	2	no	—
288	C₂×C₂₅₁	—	4	2	no	—
289	C₂×C₂₅₁	—	4	1	no	—
290	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
292	C₂×C₂₅₁	#585	1	1	yes	characteristic
293	D₂₅₁	—	4	2	no	—
294	C₂₅₁	#3535	1	1	yes	characteristic, complemented, Sylow
295	#3535	—	251	1	no	maximal, Sylow
296	#563	—	251	2	no	—
297	#562	—	251	2	no	—
298	#554	—	251	2	no	—
299	#552	—	251	2	no	—
300	#551	—	251	2	no	—
301	#551	—	251	2	no	—
302	#547	—	251	2	no	—
303	#546	—	251	2	no	—
304	#544	—	251	1	no	—
305	#543	—	251	1	no	—
306	#542	—	251	2	no	—
307	#539	—	251	2	no	—
308	#539	—	251	1	no	—
309	#539	—	251	2	no	—
310	#538	—	251	1	no	—
311	#536	—	251	2	no	—
312	#525	D₂₅₁	1	1	yes	characteristic, complemented
313	C₂×#123	—	251	1	no	—
314	C₂×C₂²⋊Q₈	—	251	1	no	—
315	C₂×#41	—	251	2	no	—
316	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic, complemented
317	C₂²×Q₈	—	251	1	no	—
318	C₂²×D₄	—	251	1	no	—
319	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
320	C₄⋊Q₈	—	251	2	no	—
321	C₄⋊Q₈	—	251	2	no	—
322	C₄⋊Q₈	—	251	2	no	—
323	#126	—	251	2	no	—
324	#126	—	251	2	no	—
325	#126	—	251	2	no	—
326	#126	—	251	2	no	—
327	#126	—	251	2	no	—
328	#126	—	251	2	no	—
329	#125	—	251	2	no	—
330	#125	—	251	2	no	—
331	#125	—	251	2	no	—
332	#125	—	251	2	no	—
333	#125	—	251	2	no	—
334	#124	—	251	2	no	—
335	#124	—	251	2	no	—
336	#124	—	251	2	no	—
337	#124	—	251	2	no	—
338	#123	—	251	2	no	—
339	#123	—	251	2	no	—
340	#123	—	251	2	no	—
341	#123	—	251	2	no	—
342	#123	—	251	2	no	—
343	#123	—	251	2	no	—
344	#123	—	251	2	no	—
345	#123	—	251	2	no	—
346	#123	—	251	2	no	—
347	#123	—	251	2	no	—
348	#123	—	251	2	no	—
349	#123	—	251	2	no	—
350	#123	—	251	2	no	—
351	#123	C₂×D₂₅₁	1	2	yes	complemented
352	C₂²⋊Q₈	—	251	2	no	—
353	C₂²⋊Q₈	—	251	1	no	—
354	C₂²⋊Q₈	—	251	1	no	—
355	C₂²⋊Q₈	—	251	1	no	—
356	C₂²⋊Q₈	—	251	1	no	—
357	C₂²⋊Q₈	—	251	2	no	—
358	C₂²⋊Q₈	—	251	2	no	—
359	C₂²⋊Q₈	—	251	2	no	—
360	C₂²⋊Q₈	—	251	2	no	—
361	C₂²⋊Q₈	—	251	2	no	—
362	C₂²⋊Q₈	—	251	2	no	—
363	C₂²⋊Q₈	—	251	2	no	—
364	C₂²⋊Q₈	—	251	2	no	—
365	C₂²⋊Q₈	—	251	2	no	—
366	C₂²⋊Q₈	—	251	2	no	—
367	C₂²⋊Q₈	—	251	2	no	—
368	C₂²⋊Q₈	—	251	2	no	—
369	C₂²⋊Q₈	—	251	2	no	—
370	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic
371	C₂²⋊Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
372	#121	—	251	2	no	—
373	#121	—	251	2	no	—
374	#121	—	251	2	no	—
375	#121	—	251	2	no	—
376	#121	C₂×D₂₅₁	1	1	yes	characteristic
377	#121	C₂×D₂₅₁	1	1	yes	characteristic, complemented
378	#120	—	251	2	no	—
379	#120	C₂×D₂₅₁	1	2	yes	—
380	C₄×Q₈	—	251	2	no	—
381	C₄×D₄	—	251	2	no	—
382	C₄×D₄	—	251	2	no	—
383	C₄×D₄	—	251	2	no	—
384	C₄×D₄	—	251	2	no	—
385	C₄×D₄	—	251	2	no	—
386	C₄×D₄	C₂×D₂₅₁	1	2	yes	—
387	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
388	#117	—	251	2	no	—
389	#117	—	251	2	no	—
390	#117	—	251	2	no	—
391	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
392	C₂×C₄⋊C₄	—	251	1	no	—
393	C₂×C₄⋊C₄	—	251	2	no	—
394	C₂×C₄⋊C₄	—	251	1	no	—
395	C₂×C₄⋊C₄	—	251	1	no	—
396	C₂×C₄⋊C₄	—	251	2	no	—
397	C₂×C₂²⋊C₄	—	251	2	no	—
398	C₂×C₂²⋊C₄	—	251	1	no	—
399	C₂×C₂²⋊C₄	—	251	1	no	—
400	C₂×C₂²⋊C₄	—	251	1	no	—
401	C₂×C₂²⋊C₄	—	251	2	no	—
402	C₂⁴	—	251	1	no	—
403	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
404	#41	—	4	2	no	—
405	#41	—	1004	4	no	—
406	C₂×Q₈	—	1004	2	no	—
407	C₂×Q₈	—	251	2	no	—
408	C₂×Q₈	—	251	1	no	—
409	C₂×Q₈	—	251	2	no	—
410	C₂×Q₈	—	251	1	no	—
411	C₂×Q₈	—	251	2	no	—
412	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
413	C₂×D₄	—	1004	2	no	—
414	C₂×D₄	—	251	2	no	—
415	C₂×D₄	—	251	2	no	—
416	C₂×D₄	—	251	2	no	—
417	C₂×D₄	—	251	2	no	—
418	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
419	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
420	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
421	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	251	1	no	—
424	C₂²×C₄	—	251	2	no	—
425	C₂²×C₄	—	251	1	no	—
426	C₂²×C₄	—	251	2	no	—
427	C₂²×C₄	—	251	2	no	—
428	C₂²×C₄	—	251	2	no	—
429	C₂²×C₄	—	251	2	no	—
430	C₂²×C₄	—	251	1	no	—
431	C₂²×C₄	—	251	2	no	—
432	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
433	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
434	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
435	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
437	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
439	C₄⋊C₄	—	251	2	no	—
440	C₄⋊C₄	—	251	2	no	—
441	C₄⋊C₄	—	251	2	no	—
442	C₄⋊C₄	—	251	2	no	—
443	C₄⋊C₄	—	251	2	no	—
444	C₄⋊C₄	—	251	2	no	—
445	C₄⋊C₄	—	251	2	no	—
446	C₄⋊C₄	—	251	2	no	—
447	C₄⋊C₄	—	251	2	no	—
448	C₄⋊C₄	—	251	2	no	—
449	C₄⋊C₄	—	251	1	no	—
450	C₄⋊C₄	—	251	2	no	—
451	C₄⋊C₄	—	251	1	no	—
452	C₄⋊C₄	—	251	2	no	—
453	C₄⋊C₄	—	251	2	no	—
454	C₄⋊C₄	—	251	2	no	—
455	C₄⋊C₄	—	251	2	no	—
456	C₄⋊C₄	—	251	2	no	—
457	C₄⋊C₄	—	251	2	no	—
458	C₄⋊C₄	—	251	2	no	—
459	C₄⋊C₄	—	251	2	no	—
460	C₄⋊C₄	—	251	2	no	—
461	C₄⋊C₄	—	251	2	no	—
462	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
463	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
465	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
466	C₂²⋊C₄	—	251	2	no	—
467	C₂²⋊C₄	—	251	2	no	—
468	C₂²⋊C₄	—	251	2	no	—
469	C₂²⋊C₄	—	251	2	no	—
470	C₂²⋊C₄	—	251	2	no	—
471	C₂²⋊C₄	—	251	2	no	—
472	C₂²⋊C₄	—	251	2	no	—
473	C₂²⋊C₄	—	251	2	no	—
474	C₂²⋊C₄	—	251	2	no	—
475	C₂²⋊C₄	—	251	2	no	—
476	C₂²⋊C₄	—	251	2	no	—
477	C₂²⋊C₄	—	251	2	no	—
478	C₂²⋊C₄	—	251	2	no	—
479	C₂²⋊C₄	—	251	2	no	—
480	C₂²⋊C₄	—	251	2	no	—
481	C₂²⋊C₄	—	251	2	no	—
482	C₂²⋊C₄	—	251	2	no	—
483	C₂²⋊C₄	—	251	2	no	—
484	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
487	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
489	C₄²	—	251	2	no	—
490	C₄²	—	251	2	no	—
491	C₄²	—	251	2	no	—
492	C₄²	—	251	2	no	—
493	C₄²	C₂²×D₂₅₁	1	2	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	1004	1	no	—
498	C₂³	—	1004	1	no	—
499	C₂³	—	502	2	no	—
500	C₂³	—	251	2	no	—
501	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
502	C₂³	C₂³×D₂₅₁	1	2	yes	—
503	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
504	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	1004	1	no	—
507	Q₈	—	1004	2	no	—
508	Q₈	—	1004	1	no	—
509	Q₈	—	1004	2	no	—
510	Q₈	—	1004	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	2	no	—
515	D₄	—	1004	2	no	—
516	D₄	—	1004	2	no	—
517	D₄	—	1004	2	no	—
518	D₄	—	502	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	1004	2	no	—
527	C₂×C₄	—	1004	2	no	—
528	C₂×C₄	—	1004	1	no	—
529	C₂×C₄	—	1004	2	no	—
530	C₂×C₄	—	1004	2	no	—
531	C₂×C₄	—	1004	2	no	—
532	C₂×C₄	—	1004	1	no	—
533	C₂×C₄	—	502	4	no	—
534	C₂×C₄	—	502	2	no	—
535	C₂×C₄	—	251	2	no	—
536	C₂×C₄	—	251	2	no	—
537	C₂×C₄	—	251	2	no	—
538	C₂×C₄	—	251	2	no	—
539	C₂×C₄	—	251	2	no	—
540	C₂×C₄	—	251	2	no	—
541	C₂×C₄	—	251	2	no	—
542	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
543	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
544	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
545	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
547	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	2008	2	no	—
561	C₂²	—	502	2	no	—
562	C₂²	—	502	2	no	—
563	C₂²	—	502	2	no	—
564	C₂²	#22548760	1	2	yes	—
565	C₂²	#22548762	1	2	yes	—
566	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	502	2	no	—
575	C₄	—	502	2	no	—
576	C₄	—	502	2	no	—
577	C₄	—	502	2	no	—
578	C₄	—	502	2	no	—
579	C₄	—	502	2	no	—
580	C₄	—	502	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	1004	2	no	—
586	C₂	C₂×#22548760	1	1	yes	characteristic
587	C₂	C₂×#22548762	1	1	yes	characteristic
588	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	#3535
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. #30632396	C₂	semidirect
4. #30632370	C₂	semidirect
5. #30632368	C₂	semidirect
6. #30632366	C₂	semidirect
7. #30632336	C₂	semidirect
8. #30632324	C₂	semidirect
9. #30632316	C₂	semidirect
10. #30632312	C₂	semidirect
11. #30632302	C₂	semidirect
12. #30632282	C₂	semidirect
13. #30632281	C₂	semidirect
14. #30632279	C₂	semidirect
15. #30632274	C₂	semidirect
16. #30632259	C₂	semidirect
17. C₂×#22548698	C₂	semidirect
18. C₂×#22548694	C₂	semidirect
19. #525×C₂₅₁	C₂	semidirect
21. C₂²×Dic₅₀₂	C₂²	semidirect
23. #22548714	C₂²	semidirect
24. #22548714	C₂²	semidirect
25. #22548713	C₂²	semidirect
26. #22548710	C₂²	semidirect
27. #22548710	C₂²	semidirect
28. #22548709	C₂²	semidirect
29. #22548708	C₂²	semidirect
30. #22548708	C₂²	semidirect
31. #22548708	C₂²	semidirect
32. #22548707	C₂²	semidirect
33. #22548706	C₂²	semidirect
34. #22548705	C₂²	semidirect
35. #22548705	C₂²	semidirect
36. #22548705	C₂²	semidirect
37. #22548702	C₂²	semidirect
39. #22548701	C₂²	semidirect
40. #22548701	C₂²	semidirect
42. #22548699	C₂²	semidirect
47. #22548698	C₂²	semidirect
49. #22548697	C₂²	semidirect
51. #22548696	C₂²	semidirect
52. #22548696	C₂²	semidirect
53. #22548696	C₂²	semidirect
54. #22548695	C₂²	semidirect
58. #22548694	C₂²	semidirect
59. #22548694	C₂²	semidirect
60. #22548694	C₂²	semidirect
61. #22548694	C₂²	semidirect
62. #22548693	C₂²	semidirect
63. #22548693	C₂²	semidirect
64. #22548693	C₂²	semidirect
67. #22548692	C₂²	semidirect
68. #22548692	C₂²	semidirect
69. #22548692	C₂²	semidirect
70. #22548692	C₂²	semidirect
71. #22548691	C₂²	semidirect
74. #22548687	C₂²	semidirect
77. C₄×Dic₅₀₂	C₂²	semidirect
80. D₄×Dic₂₅₁	C₂²	semidirect
81. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
83. #22548672	C₂²	semidirect
85. #22548671	C₂²	semidirect
86. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
89. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
90. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
96. C₂×#41×C₂₅₁	C₂²	semidirect
98. #123×C₂₅₁	C₂²	semidirect
100. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
102. #121×C₂₅₁	C₂²	semidirect
105. C₄×D₄×C₂₅₁	C₂²	semidirect
106. #117×C₂₅₁	C₂²	semidirect
294. C₂₅₁	#3535	semidirect
312. #525	D₂₅₁	semidirect
316. C₂×#41	C₂×D₂₅₁	semidirect
351. #123	C₂×D₂₅₁	semidirect
371. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
377. #121	C₂×D₂₅₁	semidirect
387. C₄×D₄	C₂×D₂₅₁	semidirect
391. #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
#30632438	2
#30632432	2
#30632396	2
#30632370	2
#30632368	2
#30632366	2
#30632336	2
#30632324	2
#30632316	2
#30632312	2
#30632302	2
#30632282	2
#30632281	2
#30632279	2
#30632274	2
#30632259	2
C₂×#22548698	2
C₂×#22548694	2
#525×C₂₅₁	2
#3535	251