Subgroups — #44564927

Order 32128.

1032 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632441	C₂	1	1	yes	maximal, characteristic, complemented
2	#30632437	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632431	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632408	C₂	1	2	yes	maximal, complemented
5	#30632365	C₂	1	2	yes	maximal, complemented
6	#30632360	C₂	1	2	yes	maximal, complemented
7	#30632350	C₂	1	2	yes	maximal, complemented
8	#30632343	C₂	1	2	yes	maximal, complemented
9	#30632326	C₂	1	2	yes	maximal, complemented
10	#30632312	C₂	1	2	yes	maximal, complemented
11	#30632307	C₂	1	2	yes	maximal, complemented
12	#30632305	C₂	1	2	yes	maximal, complemented
13	#30632304	C₂	1	2	yes	maximal, complemented
14	#30632269	C₂	1	2	yes	maximal, complemented
15	#30632259	C₂	1	2	yes	maximal, complemented
16	#30632243	C₂	1	1	yes	maximal, characteristic, complemented
17	#30632216	C₂	1	1	yes	maximal, characteristic, complemented
18	#124×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
19	#562×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16860809	C₂²	1	2	yes	—
21	C₂²×Dic₅₀₂	C₂²	1	2	yes	complemented
22	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
23	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
24	#22548714	C₂²	1	1	yes	characteristic, complemented
25	#22548714	C₂²	1	1	yes	characteristic, complemented
26	#22548714	C₂²	1	2	yes	complemented
27	#22548714	C₂²	1	2	yes	complemented
28	#22548713	C₂²	1	2	yes	complemented
29	#22548710	C₂²	1	2	yes	complemented
30	#22548710	C₂²	1	2	yes	complemented
31	#22548710	C₂²	1	2	yes	complemented
32	#22548708	C₂²	1	2	yes	complemented
33	#22548708	C₂²	1	2	yes	complemented
34	#22548708	C₂²	1	2	yes	complemented
35	#22548708	C₂²	1	2	yes	complemented
36	#22548707	C₂²	1	1	yes	characteristic, complemented
37	#22548707	C₂²	1	1	yes	characteristic, complemented
38	#22548704	C₂²	1	1	yes	characteristic
39	#22548703	C₂²	1	1	yes	characteristic
40	#22548702	C₂²	1	1	yes	characteristic
41	#22548702	C₂²	1	2	yes	complemented
42	#22548702	C₂²	1	2	yes	complemented
43	#22548701	C₂²	1	2	yes	—
44	#22548701	C₂²	1	2	yes	—
45	#22548701	C₂²	1	2	yes	—
46	#22548701	C₂²	1	2	yes	complemented
47	#22548701	C₂²	1	2	yes	complemented
48	#22548700	C₂²	1	2	yes	—
49	#22548699	C₂²	1	2	yes	complemented
50	#22548698	C₂²	1	2	yes	complemented
51	#22548697	C₂²	1	2	yes	—
52	#22548697	C₂²	1	2	yes	complemented
53	#22548696	C₂²	1	2	yes	—
54	#22548696	C₂²	1	2	yes	complemented
55	#22548695	C₂²	1	2	yes	—
56	#22548695	C₂²	1	2	yes	complemented
57	#22548694	C₂²	1	2	yes	complemented
58	#22548693	C₂²	1	2	yes	—
59	#22548693	C₂²	1	2	yes	—
60	#22548693	C₂²	1	2	yes	—
61	#22548693	C₂²	1	2	yes	complemented
62	#22548693	C₂²	1	2	yes	complemented
63	#22548693	C₂²	1	2	yes	complemented
64	#22548692	C₂²	1	2	yes	complemented
65	#22548692	C₂²	1	2	yes	complemented
66	#22548692	C₂²	1	2	yes	complemented
67	#22548692	C₂²	1	2	yes	complemented
68	#22548692	C₂²	1	2	yes	complemented
69	#22548691	C₂²	1	1	yes	characteristic
70	#22548691	C₂²	1	2	yes	complemented
71	#22548688	C₂²	1	2	yes	—
72	#22548687	C₂²	1	2	yes	—
73	#22548687	C₂²	1	2	yes	complemented
74	#22548686	C₂²	1	1	yes	characteristic
75	#22548683	C₂²	1	2	yes	—
76	#22548683	C₂²	1	2	yes	—
77	Q₈×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
78	#22548680	C₂²	1	2	yes	complemented
79	#22548680	C₂²	1	2	yes	complemented
80	#22548680	C₂²	1	2	yes	complemented
81	D₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₂₅₁	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
86	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
87	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	2	yes	—
88	#22548674	C₂²	1	2	yes	complemented
89	#22548673	C₂²	1	1	yes	characteristic
90	#22548673	C₂²	1	1	yes	characteristic
91	#22548673	C₂²	1	2	yes	complemented
92	#22548671	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	2	yes	—
94	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
95	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
96	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
97	C₄²×D₂₅₁	C₂²	1	1	yes	characteristic
98	#125×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
99	#124×C₂₅₁	C₂²	1	1	yes	characteristic
100	#124×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
101	#123×C₂₅₁	C₂²	1	2	yes	complemented
102	#123×C₂₅₁	C₂²	1	2	yes	complemented
103	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
105	#121×C₂₅₁	C₂²	1	2	yes	—
106	#121×C₂₅₁	C₂²	1	2	yes	complemented
107	C₂³×D₂₅₁	C₂³	1	2	yes	—
108	#16860809	—	4	4	no	—
109	C₂×Dic₅₀₂	—	4	4	no	—
110	C₂×Dic₅₀₂	C₂³	1	2	yes	—
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×Dic₅₀₂	C₂³	1	2	yes	—
116	Q₈×D₂₅₁	—	4	2	no	—
117	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
122	D₄×D₂₅₁	—	4	2	no	—
123	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
124	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
125	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
126	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
128	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
129	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
130	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
131	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
132	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
133	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
135	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
136	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
138	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
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	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	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
156	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
157	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
158	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₂₅₁)⋊C₄	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	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
170	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
171	C₄×Dic₂₅₁	C₂³	1	1	yes	characteristic
172	C₄×Dic₂₅₁	C₂³	1	2	yes	—
173	C₄×Dic₂₅₁	C₂³	1	2	yes	—
174	C₄×Dic₂₅₁	C₂³	1	2	yes	—
175	C₄×Dic₂₅₁	C₂³	1	2	yes	—
176	C₄×Dic₂₅₁	C₂³	1	2	yes	—
177	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
178	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
180	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
181	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
182	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
184	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
185	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
186	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
187	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
188	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
189	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
190	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
191	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
192	C₂²⋊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	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
198	C₂²×D₂₅₁	—	2	4	no	—
199	C₂²×D₂₅₁	—	4	2	no	—
200	C₂²×D₂₅₁	—	4	2	no	—
201	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
202	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
203	Dic₅₀₂	—	2	4	no	—
204	Dic₅₀₂	—	2	4	no	—
205	Dic₅₀₂	—	4	1	no	—
206	Dic₅₀₂	—	4	2	no	—
207	Dic₅₀₂	—	4	2	no	—
208	Dic₅₀₂	—	4	2	no	—
209	D₁₀₀₄	—	4	1	no	—
210	C₂²⋊D₂₅₁	—	2	4	no	—
211	C₂²⋊D₂₅₁	—	2	4	no	—
212	C₂²⋊D₂₅₁	—	4	2	no	—
213	C₂²⋊D₂₅₁	—	4	2	no	—
214	C₂×Dic₂₅₁	—	2	4	no	—
215	C₂×Dic₂₅₁	—	4	2	no	—
216	C₂×Dic₂₅₁	—	4	2	no	—
217	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
218	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
219	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
225	C₄×D₂₅₁	—	2	2	no	—
226	C₄×D₂₅₁	—	2	2	no	—
227	C₄×D₂₅₁	—	4	2	no	—
228	C₄×D₂₅₁	—	4	1	no	—
229	C₄×D₂₅₁	—	4	2	no	—
230	C₄×D₂₅₁	—	4	2	no	—
231	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
232	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
233	Q₈×C₂₅₁	—	4	1	no	—
234	Q₈×C₂₅₁	—	4	1	no	—
235	D₄×C₂₅₁	—	4	2	no	—
236	D₄×C₂₅₁	—	4	1	no	—
237	D₄×C₂₅₁	—	4	1	no	—
238	D₄×C₂₅₁	—	4	2	no	—
239	C₂×C₄×C₂₅₁	—	4	2	no	—
240	C₂×C₄×C₂₅₁	—	4	2	no	—
241	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
245	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
246	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
248	C₂²×C₂₅₁	—	2	2	no	—
249	C₂²×C₂₅₁	—	2	2	no	—
250	C₂²×C₂₅₁	—	2	2	no	—
251	C₂²×C₂₅₁	—	2	2	no	—
252	C₂²×C₂₅₁	—	2	2	no	—
253	C₂²×C₂₅₁	—	2	2	no	—
254	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
255	C₂×D₂₅₁	—	2	1	no	—
256	C₂×D₂₅₁	—	2	1	no	—
257	C₂×D₂₅₁	—	2	2	no	—
258	C₂×D₂₅₁	—	2	2	no	—
259	C₂×D₂₅₁	—	2	2	no	—
260	C₂×D₂₅₁	—	8	4	no	—
261	C₂×D₂₅₁	2₋¹⁺⁴	1	2	yes	—
262	C₄×C₂₅₁	—	2	2	no	—
263	C₄×C₂₅₁	—	2	2	no	—
264	C₄×C₂₅₁	—	2	1	no	—
265	C₄×C₂₅₁	—	2	1	no	—
266	C₄×C₂₅₁	—	2	2	no	—
267	C₄×C₂₅₁	—	2	2	no	—
268	C₄×C₂₅₁	—	2	1	no	—
269	Dic₂₅₁	—	2	2	no	—
270	Dic₂₅₁	—	2	2	no	—
271	Dic₂₅₁	—	2	2	no	—
272	Dic₂₅₁	—	2	1	no	—
273	Dic₂₅₁	—	2	2	no	—
274	Dic₂₅₁	—	2	2	no	—
275	Dic₂₅₁	—	2	1	no	—
276	Dic₂₅₁	H(5,𝔽₂)	1	2	yes	—
277	C₂×C₂₅₁	—	4	2	no	—
278	C₂×C₂₅₁	—	4	2	no	—
279	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
281	C₂×C₂₅₁	#585	1	1	yes	characteristic
282	D₂₅₁	—	2	2	no	—
283	D₂₅₁	—	4	2	no	—
284	C₂₅₁	#3561	1	1	yes	characteristic, complemented, Sylow
285	#3561	—	251	1	no	maximal, Sylow
286	#563	—	251	1	no	—
287	#563	—	251	1	no	—
288	#562	—	251	1	no	—
289	#562	D₂₅₁	1	1	yes	characteristic, complemented
290	#556	—	251	2	no	—
291	#551	—	251	2	no	—
292	#551	—	251	2	no	—
293	D₄×Q₈	—	251	2	no	—
294	#548	—	251	2	no	—
295	#546	—	251	2	no	—
296	#543	—	251	2	no	—
297	#542	—	251	2	no	—
298	#542	—	251	2	no	—
299	#542	—	251	2	no	—
300	#538	—	251	2	no	—
301	#536	—	251	2	no	—
302	#533	—	251	1	no	—
303	#529	—	251	1	no	—
304	C₂×#124	—	251	1	no	—
305	C₂×#41	—	251	2	no	—
306	C₂²×Q₈	—	251	1	no	—
307	C₂²×Q₈	—	251	2	no	—
308	C₂²×D₄	—	251	1	no	—
309	C₄⋊Q₈	—	251	2	no	—
310	C₄⋊Q₈	—	251	1	no	—
311	C₄⋊Q₈	—	251	1	no	—
312	C₄⋊Q₈	—	251	2	no	—
313	C₄⋊Q₈	—	251	2	no	—
314	#126	—	251	2	no	—
315	#126	—	251	2	no	—
316	#126	—	251	2	no	—
317	#126	—	251	2	no	—
318	#126	—	251	2	no	—
319	#126	—	251	2	no	—
320	#126	—	251	2	no	—
321	#125	—	251	1	no	—
322	#125	—	251	1	no	—
323	#125	C₂×D₂₅₁	1	1	yes	characteristic, complemented
324	#124	—	251	1	no	—
325	#124	—	251	1	no	—
326	#124	—	251	2	no	—
327	#124	—	251	2	no	—
328	#124	—	251	2	no	—
329	#124	—	251	2	no	—
330	#124	—	251	2	no	—
331	#124	—	251	2	no	—
332	#124	—	251	2	no	—
333	#124	—	251	1	no	—
334	#124	C₂×D₂₅₁	1	1	yes	characteristic
335	#124	C₂×D₂₅₁	1	1	yes	characteristic, complemented
336	#123	—	251	2	no	—
337	#123	—	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	C₂×D₂₅₁	1	2	yes	complemented
344	#123	C₂×D₂₅₁	1	2	yes	complemented
345	C₂²⋊Q₈	—	251	1	no	—
346	C₂²⋊Q₈	—	251	2	no	—
347	C₂²⋊Q₈	—	251	2	no	—
348	C₂²⋊Q₈	—	251	2	no	—
349	C₂²⋊Q₈	—	251	2	no	—
350	C₂²⋊Q₈	—	251	2	no	—
351	C₂²⋊Q₈	—	251	2	no	—
352	C₂²⋊Q₈	—	251	2	no	—
353	C₂²⋊Q₈	—	251	2	no	—
354	C₂²⋊Q₈	—	251	2	no	—
355	C₂²⋊Q₈	—	251	2	no	—
356	C₂²⋊Q₈	—	251	2	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	C₂×D₂₅₁	1	2	yes	complemented
362	C₂²⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
363	#121	—	251	1	no	—
364	#121	—	251	2	no	—
365	#121	—	251	2	no	—
366	#121	—	251	2	no	—
367	#121	C₂×D₂₅₁	1	2	yes	—
368	#121	C₂×D₂₅₁	1	2	yes	complemented
369	#120	—	251	2	no	—
370	#120	—	251	2	no	—
371	C₄×Q₈	—	251	1	no	—
372	C₄×Q₈	—	251	2	no	—
373	C₄×Q₈	—	251	2	no	—
374	C₄×Q₈	—	251	2	no	—
375	C₄×D₄	—	251	1	no	—
376	C₄×D₄	—	251	2	no	—
377	C₄×D₄	—	251	2	no	—
378	C₄×D₄	—	251	2	no	—
379	C₄×D₄	—	251	2	no	—
380	C₄×D₄	—	251	2	no	—
381	C₄×D₄	—	251	2	no	—
382	#117	—	251	2	no	—
383	#117	—	251	1	no	—
384	#117	—	251	1	no	—
385	#117	—	251	2	no	—
386	#117	—	251	2	no	—
387	C₂×C₂²⋊C₄	—	251	2	no	—
388	C₂×C₂²⋊C₄	—	251	2	no	—
389	C₂×C₂²⋊C₄	—	251	2	no	—
390	C₂×C₂²⋊C₄	—	251	2	no	—
391	C₂×C₄²	—	251	1	no	—
392	C₂⁴	—	251	2	no	—
393	#41	—	1004	4	no	—
394	C₂×Q₈	—	1004	4	no	—
395	C₂×Q₈	—	1004	2	no	—
396	C₂×Q₈	—	251	2	no	—
397	C₂×Q₈	—	251	2	no	—
398	C₂×Q₈	—	251	2	no	—
399	C₂×Q₈	—	251	1	no	—
400	C₂×Q₈	—	251	2	no	—
401	C₂×Q₈	—	251	2	no	—
402	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
403	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
404	C₂×D₄	—	1004	2	no	—
405	C₂×D₄	—	251	2	no	—
406	C₂×D₄	—	251	2	no	—
407	C₂×D₄	—	251	2	no	—
408	C₂×D₄	—	251	2	no	—
409	C₂×D₄	—	251	1	no	—
410	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
411	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
412	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
413	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
414	C₂²×C₄	—	251	2	no	—
415	C₂²×C₄	—	251	2	no	—
416	C₂²×C₄	—	251	1	no	—
417	C₂²×C₄	—	251	2	no	—
418	C₂²×C₄	—	251	2	no	—
419	C₂²×C₄	—	251	2	no	—
420	C₂²×C₄	—	251	2	no	—
421	C₂²×C₄	—	251	1	no	—
422	C₂²×C₄	—	251	1	no	—
423	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
424	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
425	C₄⋊C₄	—	251	2	no	—
426	C₄⋊C₄	—	251	2	no	—
427	C₄⋊C₄	—	251	2	no	—
428	C₄⋊C₄	—	251	2	no	—
429	C₄⋊C₄	—	251	1	no	—
430	C₄⋊C₄	—	251	1	no	—
431	C₄⋊C₄	—	251	2	no	—
432	C₄⋊C₄	—	251	2	no	—
433	C₄⋊C₄	—	251	2	no	—
434	C₄⋊C₄	—	251	2	no	—
435	C₄⋊C₄	—	251	2	no	—
436	C₄⋊C₄	—	251	2	no	—
437	C₄⋊C₄	—	251	2	no	—
438	C₄⋊C₄	—	251	2	no	—
439	C₄⋊C₄	—	251	2	no	—
440	C₄⋊C₄	—	251	1	no	—
441	C₄⋊C₄	—	251	2	no	—
442	C₄⋊C₄	—	251	1	no	—
443	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
444	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
445	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
446	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
447	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
448	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
449	C₂²⋊C₄	—	251	2	no	—
450	C₂²⋊C₄	—	251	2	no	—
451	C₂²⋊C₄	—	251	2	no	—
452	C₂²⋊C₄	—	251	2	no	—
453	C₂²⋊C₄	—	251	2	no	—
454	C₂²⋊C₄	—	251	2	no	—
455	C₂²⋊C₄	—	251	2	no	—
456	C₂²⋊C₄	—	251	2	no	—
457	C₂²⋊C₄	—	251	2	no	—
458	C₂²⋊C₄	—	251	2	no	—
459	C₂²⋊C₄	—	251	2	no	—
460	C₂²⋊C₄	—	251	2	no	—
461	C₂²⋊C₄	—	251	2	no	—
462	C₂²⋊C₄	—	251	2	no	—
463	C₂²⋊C₄	—	251	2	no	—
464	C₂²⋊C₄	—	251	2	no	—
465	C₂²⋊C₄	—	251	2	no	—
466	C₂²⋊C₄	—	251	2	no	—
467	C₂²⋊C₄	—	251	2	no	—
468	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
469	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
470	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
471	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
472	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
473	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
474	C₄²	—	251	1	no	—
475	C₄²	—	251	1	no	—
476	C₄²	—	251	1	no	—
477	C₄²	—	251	2	no	—
478	C₄²	—	251	2	no	—
479	C₄²	—	251	2	no	—
480	C₄²	—	251	2	no	—
481	C₄²	—	251	2	no	—
482	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
483	C₂³	—	1004	2	no	—
484	C₂³	—	1004	2	no	—
485	C₂³	—	502	4	no	—
486	C₂³	—	251	2	no	—
487	C₂³	—	251	1	no	—
488	C₂³	C₂³×D₂₅₁	1	2	yes	—
489	C₂³	C₂³×D₂₅₁	1	2	yes	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	1004	2	no	—
493	Q₈	—	1004	2	no	—
494	Q₈	—	1004	1	no	—
495	Q₈	—	1004	2	no	—
496	Q₈	—	502	4	no	—
497	Q₈	—	502	4	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	1	no	—
502	D₄	—	1004	1	no	—
503	D₄	—	1004	2	no	—
504	D₄	—	1004	2	no	—
505	D₄	—	502	4	no	—
506	D₄	—	502	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	1004	2	no	—
510	C₂×C₄	—	1004	2	no	—
511	C₂×C₄	—	1004	2	no	—
512	C₂×C₄	—	1004	1	no	—
513	C₂×C₄	—	1004	2	no	—
514	C₂×C₄	—	1004	2	no	—
515	C₂×C₄	—	502	2	no	—
516	C₂×C₄	—	502	2	no	—
517	C₂×C₄	—	502	4	no	—
518	C₂×C₄	—	251	1	no	—
519	C₂×C₄	—	251	2	no	—
520	C₂×C₄	—	251	1	no	—
521	C₂×C₄	—	251	2	no	—
522	C₂×C₄	—	251	2	no	—
523	C₂×C₄	—	251	2	no	—
524	C₂×C₄	—	251	2	no	—
525	C₂×C₄	—	251	1	no	—
526	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
527	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
529	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
530	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
531	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
532	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2008	4	no	—
540	C₂²	—	502	2	no	—
541	C₂²	—	502	2	no	—
542	C₂²	—	502	2	no	—
543	C₂²	—	502	1	no	—
544	C₂²	—	502	1	no	—
545	C₂²	—	251	2	no	—
546	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	2	1	no	—
554	C₄	—	502	2	no	—
555	C₄	—	502	2	no	—
556	C₄	—	502	2	no	—
557	C₄	—	502	1	no	—
558	C₄	—	502	2	no	—
559	C₄	—	502	2	no	—
560	C₄	—	502	1	no	—
561	C₄	—	251	2	no	—
562	C₂	—	4	2	no	—
563	C₂	—	4	2	no	—
564	C₂	—	1004	2	no	—
565	C₂	—	502	2	no	—
566	C₂	H(5,𝔽₂)×D₂₅₁	1	1	yes	characteristic
567	C₂	2₋¹⁺⁴×D₂₅₁	1	1	yes	characteristic
568	C₂	#30632522	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#562×C₂₅₁	C₂
hypercenter	#562	D₂₅₁
hypocenter	C₂₅₁	#3561
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #562

Complements

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

N	H ≅ G/N	type
1. #30632441	C₂	semidirect
2. #30632437	C₂	semidirect
3. #30632431	C₂	semidirect
4. #30632408	C₂	semidirect
5. #30632365	C₂	semidirect
6. #30632360	C₂	semidirect
7. #30632350	C₂	semidirect
8. #30632343	C₂	semidirect
9. #30632326	C₂	semidirect
10. #30632312	C₂	semidirect
11. #30632307	C₂	semidirect
12. #30632305	C₂	semidirect
13. #30632304	C₂	semidirect
14. #30632269	C₂	semidirect
15. #30632259	C₂	semidirect
16. #30632243	C₂	semidirect
17. #30632216	C₂	semidirect
18. #124×D₂₅₁	C₂	semidirect
19. #562×C₂₅₁	C₂	semidirect
21. C₂²×Dic₅₀₂	C₂²	semidirect
24. #22548714	C₂²	semidirect
25. #22548714	C₂²	semidirect
26. #22548714	C₂²	semidirect
27. #22548714	C₂²	semidirect
28. #22548713	C₂²	semidirect
29. #22548710	C₂²	semidirect
30. #22548710	C₂²	semidirect
31. #22548710	C₂²	semidirect
32. #22548708	C₂²	semidirect
33. #22548708	C₂²	semidirect
34. #22548708	C₂²	semidirect
35. #22548708	C₂²	semidirect
36. #22548707	C₂²	semidirect
37. #22548707	C₂²	semidirect
41. #22548702	C₂²	semidirect
42. #22548702	C₂²	semidirect
46. #22548701	C₂²	semidirect
47. #22548701	C₂²	semidirect
49. #22548699	C₂²	semidirect
50. #22548698	C₂²	semidirect
52. #22548697	C₂²	semidirect
54. #22548696	C₂²	semidirect
56. #22548695	C₂²	semidirect
57. #22548694	C₂²	semidirect
61. #22548693	C₂²	semidirect
62. #22548693	C₂²	semidirect
63. #22548693	C₂²	semidirect
64. #22548692	C₂²	semidirect
65. #22548692	C₂²	semidirect
66. #22548692	C₂²	semidirect
67. #22548692	C₂²	semidirect
68. #22548692	C₂²	semidirect
70. #22548691	C₂²	semidirect
73. #22548687	C₂²	semidirect
77. Q₈×Dic₂₅₁	C₂²	semidirect
78. #22548680	C₂²	semidirect
79. #22548680	C₂²	semidirect
80. #22548680	C₂²	semidirect
81. D₄×Dic₂₅₁	C₂²	semidirect
82. D₄×Dic₂₅₁	C₂²	semidirect
85. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
88. #22548674	C₂²	semidirect
91. #22548673	C₂²	semidirect
92. #22548671	C₂²	semidirect
98. #125×C₂₅₁	C₂²	semidirect
100. #124×C₂₅₁	C₂²	semidirect
101. #123×C₂₅₁	C₂²	semidirect
102. #123×C₂₅₁	C₂²	semidirect
103. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
104. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
106. #121×C₂₅₁	C₂²	semidirect
284. C₂₅₁	#3561	semidirect
289. #562	D₂₅₁	semidirect
323. #125	C₂×D₂₅₁	semidirect
335. #124	C₂×D₂₅₁	semidirect
343. #123	C₂×D₂₅₁	semidirect
344. #123	C₂×D₂₅₁	semidirect
361. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
362. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
368. #121	C₂×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30632441	2
#30632437	2
#30632431	2
#30632408	2
#30632365	2
#30632360	2
#30632350	2
#30632343	2
#30632326	2
#30632312	2
#30632307	2
#30632305	2
#30632304	2
#30632269	2
#30632259	2
#30632243	2
#30632216	2
#124×D₂₅₁	2
#562×C₂₅₁	2
#3561	251