Subgroups — #44564504

Order 32128.

1058 conjugacy classes of subgroups.

The subgroup lattice has 588 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	#30632439	C₂	1	2	yes	maximal, complemented
3	#30632435	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632434	C₂	1	2	yes	maximal, complemented
5	#30632433	C₂	1	2	yes	maximal, complemented
6	#30632431	C₂	1	1	yes	maximal, characteristic, complemented
7	#30632429	C₂	1	1	yes	maximal, characteristic, complemented
8	#30632428	C₂	1	2	yes	maximal, complemented
9	#30632427	C₂	1	2	yes	maximal, complemented
10	#30632425	C₂	1	2	yes	maximal, complemented
11	#30632237	C₂	1	1	yes	maximal, characteristic, complemented
12	#30632234	C₂	1	2	yes	maximal, complemented
13	#30632224	C₂	1	2	yes	maximal, complemented
14	#30632221	C₂	1	1	yes	maximal, characteristic, complemented
15	#30632215	C₂	1	2	yes	maximal, complemented
16	#30632199	C₂	1	2	yes	maximal, complemented
17	#30632196	C₂	1	2	yes	maximal, complemented
18	#30632196	C₂	1	2	yes	maximal, complemented
19	#529×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16860810	C₂²	1	1	yes	characteristic
21	C₂×#16860810	C₂²	1	2	yes	—
22	C₂×#16860810	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₄×D₂₅₁	C₂²	1	2	yes	complemented
24	#22548715	C₂²	1	1	yes	characteristic, complemented
25	#22548714	C₂²	1	2	yes	complemented
26	#22548712	C₂²	1	1	yes	characteristic
27	#22548711	C₂²	1	2	yes	—
28	#22548710	C₂²	1	2	yes	complemented
29	#22548710	C₂²	1	2	yes	complemented
30	#22548710	C₂²	1	2	yes	complemented
31	#22548709	C₂²	1	2	yes	complemented
32	#22548708	C₂²	1	2	yes	complemented
33	#22548707	C₂²	1	1	yes	characteristic, complemented
34	#22548706	C₂²	1	2	yes	complemented
35	#22548705	C₂²	1	2	yes	complemented
36	#22548704	C₂²	1	2	yes	—
37	#22548703	C₂²	1	1	yes	characteristic
38	#22548703	C₂²	1	1	yes	characteristic
39	#22548703	C₂²	1	1	yes	characteristic, complemented
40	#22548701	C₂²	1	2	yes	—
41	#22548701	C₂²	1	2	yes	—
42	#22548701	C₂²	1	2	yes	complemented
43	#22548700	C₂²	1	2	yes	—
44	#22548700	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	#22548699	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	#22548697	C₂²	1	2	yes	complemented
54	#22548695	C₂²	1	2	yes	complemented
55	#22548695	C₂²	1	2	yes	complemented
56	#22548694	C₂²	1	1	yes	characteristic, complemented
57	#22548693	C₂²	1	2	yes	complemented
58	#22548693	C₂²	1	2	yes	complemented
59	#22548693	C₂²	1	2	yes	complemented
60	#22548692	C₂²	1	2	yes	complemented
61	#22548692	C₂²	1	2	yes	complemented
62	#22548691	C₂²	1	2	yes	complemented
63	#22548690	C₂²	1	2	yes	—
64	#22548690	C₂²	1	2	yes	—
65	#22548690	C₂²	1	2	yes	—
66	#22548690	C₂²	1	2	yes	complemented
67	#22548689	C₂²	1	1	yes	characteristic
68	#22548689	C₂²	1	2	yes	complemented
69	#22548689	C₂²	1	2	yes	complemented
70	#22548688	C₂²	1	2	yes	—
71	#22548688	C₂²	1	2	yes	—
72	#22548688	C₂²	1	2	yes	—
73	#22548688	C₂²	1	2	yes	complemented
74	#22548688	C₂²	1	2	yes	complemented
75	#22548687	C₂²	1	2	yes	—
76	#22548687	C₂²	1	2	yes	—
77	#22548686	C₂²	1	2	yes	complemented
78	#22548685	C₂²	1	2	yes	—
79	#22548685	C₂²	1	2	yes	—
80	#22548685	C₂²	1	2	yes	complemented
81	#22548685	C₂²	1	2	yes	complemented
82	#22548683	C₂²	1	2	yes	—
83	#22548683	C₂²	1	2	yes	complemented
84	C₄×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₁₀₀₄	C₂²	1	2	yes	—
86	C₄×D₁₀₀₄	C₂²	1	1	yes	characteristic
87	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
88	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
89	C₄×D₁₀₀₄	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
92	C₄×C₂²⋊D₂₅₁	C₂²	1	2	yes	complemented
93	#22548672	C₂²	1	2	yes	complemented
94	#22548672	C₂²	1	2	yes	complemented
95	C₄²×D₂₅₁	C₂²	1	2	yes	complemented
96	#126×C₂₅₁	C₂²	1	2	yes	complemented
97	#125×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
98	#124×C₂₅₁	C₂²	1	1	yes	characteristic
99	#123×C₂₅₁	C₂²	1	2	yes	complemented
100	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
101	#121×C₂₅₁	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₂₅₁	C₂²	1	2	yes	complemented
105	#117×C₂₅₁	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₂₅₁	C₂³	1	2	yes	—
108	#16860810	—	4	4	no	—
109	#16860810	—	4	2	no	—
110	#16860810	—	4	2	no	—
111	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
112	C₂×Dic₅₀₂	C₂³	1	2	yes	—
113	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
114	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
115	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
116	C₂×D₁₀₀₄	C₂³	1	2	yes	—
117	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
118	C₂×D₁₀₀₄	C₂³	1	2	yes	—
119	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
120	C₂×D₁₀₀₄	C₂³	1	2	yes	—
121	C₂×D₁₀₀₄	C₂³	1	2	yes	—
122	C₂×D₁₀₀₄	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
130	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
131	C₂×C₄×D₂₅₁	—	4	4	no	—
132	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
133	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
134	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
135	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
136	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
137	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
138	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
139	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
140	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
142	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
143	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
144	C₄⋊Dic₂₅₁	C₂³	1	1	yes	characteristic
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	Dic₂₅₁⋊C₄	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	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₂₅₁)⋊C₄	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	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
171	(C₂×D₂₅₁)⋊C₄	C₂³	1	2	yes	—
172	C₄×Dic₂₅₁	C₂³	1	2	yes	—
173	C₄×Dic₂₅₁	C₂³	1	2	yes	—
174	C₄×Dic₂₅₁	C₂³	1	2	yes	—
175	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
176	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
177	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
178	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
179	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
182	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
183	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
184	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
186	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
187	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
193	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
194	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
195	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
196	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
197	C₄²×C₂₅₁	C₂³	1	2	yes	—
198	C₂²×D₂₅₁	—	4	2	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	2	yes	—
203	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
204	Dic₅₀₂	—	4	1	no	—
205	Dic₅₀₂	—	4	1	no	—
206	Dic₅₀₂	—	4	2	no	—
207	Dic₅₀₂	—	4	1	no	—
208	D₁₀₀₄	—	4	2	no	—
209	D₁₀₀₄	—	4	2	no	—
210	D₁₀₀₄	—	4	1	no	—
211	D₁₀₀₄	—	4	2	no	—
212	D₁₀₀₄	—	4	2	no	—
213	D₁₀₀₄	—	4	2	no	—
214	D₁₀₀₄	—	4	1	no	—
215	D₁₀₀₄	—	4	1	no	—
216	C₂²⋊D₂₅₁	—	4	2	no	—
217	C₂²⋊D₂₅₁	—	4	2	no	—
218	C₂²⋊D₂₅₁	—	4	2	no	—
219	C₂²⋊D₂₅₁	—	4	2	no	—
220	C₂²⋊D₂₅₁	—	4	2	no	—
221	C₂²⋊D₂₅₁	—	4	2	no	—
222	C₂²⋊D₂₅₁	—	4	2	no	—
223	C₂×Dic₂₅₁	—	4	2	no	—
224	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
225	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
226	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
227	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
228	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
229	C₄×D₂₅₁	—	2	4	no	—
230	C₄×D₂₅₁	—	2	4	no	—
231	C₄×D₂₅₁	—	2	4	no	—
232	C₄×D₂₅₁	—	4	2	no	—
233	C₄×D₂₅₁	—	4	2	no	—
234	C₄×D₂₅₁	—	4	2	no	—
235	C₄×D₂₅₁	—	4	2	no	—
236	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
237	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
238	Q₈×C₂₅₁	—	4	1	no	—
239	D₄×C₂₅₁	—	4	1	no	—
240	D₄×C₂₅₁	—	4	2	no	—
241	C₂×C₄×C₂₅₁	—	2	4	no	—
242	C₂×C₄×C₂₅₁	—	2	2	no	—
243	C₂×C₄×C₂₅₁	—	4	1	no	—
244	C₂×C₄×C₂₅₁	—	4	1	no	—
245	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
254	C₂²×C₂₅₁	—	2	2	no	—
255	C₂²×C₂₅₁	—	2	1	no	—
256	C₂²×C₂₅₁	—	2	1	no	—
257	C₂²×C₂₅₁	—	2	1	no	—
258	C₂²×C₂₅₁	—	2	2	no	—
259	C₂²×C₂₅₁	—	2	2	no	—
260	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
261	C₂×D₂₅₁	—	2	2	no	—
262	C₂×D₂₅₁	—	2	2	no	—
263	C₂×D₂₅₁	—	2	2	no	—
264	C₂×D₂₅₁	—	2	2	no	—
265	C₂×D₂₅₁	—	2	2	no	—
266	C₂×D₂₅₁	—	2	2	no	—
267	C₂×D₂₅₁	—	2	2	no	—
268	C₂×D₂₅₁	—	2	2	no	—
269	C₂×D₂₅₁	—	2	2	no	—
270	C₂×D₂₅₁	—	4	8	no	—
271	C₄×C₂₅₁	—	2	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	1	no	—
277	C₄×C₂₅₁	—	2	2	no	—
278	C₄×C₂₅₁	—	2	2	no	—
279	C₄×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
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	C₂×C₂₅₁	—	4	2	no	—
286	C₂×C₂₅₁	—	4	1	no	—
287	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₂₅₁	#585	1	1	yes	characteristic
289	C₂×C₂₅₁	#585	1	1	yes	characteristic
290	D₂₅₁	—	4	2	no	—
291	D₂₅₁	—	4	2	no	—
292	D₂₅₁	—	4	2	no	—
293	C₂₅₁	#3529	1	1	yes	characteristic, complemented, Sylow
294	#3529	—	251	1	no	maximal, Sylow
295	#563	—	251	2	no	—
296	#563	—	251	1	no	—
297	#562	—	251	1	no	—
298	#562	—	251	1	no	—
299	#562	—	251	2	no	—
300	#562	—	251	2	no	—
301	H(3,𝔽₄)	—	251	1	no	—
302	#560	—	251	2	no	—
303	#560	—	251	2	no	—
304	#560	—	251	2	no	—
305	#532	—	251	2	no	—
306	#532	—	251	1	no	—
307	#529	—	251	2	no	—
308	#529	—	251	2	no	—
309	#529	—	251	1	no	—
310	#529	D₂₅₁	1	1	yes	characteristic, complemented
311	#525	—	251	2	no	—
312	#525	—	251	2	no	—
313	#525	—	251	2	no	—
314	C₂×#41	—	251	2	no	—
315	C₂×#41	—	251	1	no	—
316	C₂×#41	—	251	1	no	—
317	C₂³×C₄	—	251	2	no	—
318	C₄⋊Q₈	—	251	2	no	—
319	C₄⋊Q₈	—	251	1	no	—
320	#127	—	251	2	no	—
321	#127	—	251	1	no	—
322	#126	—	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	C₂×D₂₅₁	1	2	yes	complemented
328	#125	—	251	2	no	—
329	#125	—	251	2	no	—
330	#125	—	251	1	no	—
331	#125	C₂×D₂₅₁	1	1	yes	characteristic, complemented
332	#124	—	251	2	no	—
333	#124	—	251	2	no	—
334	#124	—	251	2	no	—
335	#124	—	251	2	no	—
336	#124	—	251	1	no	—
337	#124	—	251	1	no	—
338	#124	—	251	1	no	—
339	#124	C₂×D₂₅₁	1	1	yes	characteristic
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	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	1	yes	characteristic, complemented
362	#121	—	251	2	no	—
363	#121	—	251	2	no	—
364	#121	—	251	2	no	—
365	#121	—	251	1	no	—
366	#121	—	251	2	no	—
367	#121	—	251	2	no	—
368	#121	—	251	2	no	—
369	#121	—	251	2	no	—
370	#121	—	251	2	no	—
371	#121	—	251	2	no	—
372	#121	—	251	2	no	—
373	#121	—	251	2	no	—
374	#121	—	251	2	no	—
375	#121	—	251	2	no	—
376	#121	—	251	2	no	—
377	#121	C₂×D₂₅₁	1	1	yes	characteristic
378	#120	—	251	2	no	—
379	#120	—	251	2	no	—
380	#120	—	251	2	no	—
381	#120	—	251	2	no	—
382	#120	—	251	2	no	—
383	#120	—	251	2	no	—
384	C₄×Q₈	—	251	1	no	—
385	C₄×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
386	C₄×D₄	—	251	2	no	—
387	C₄×D₄	—	251	2	no	—
388	C₄×D₄	—	251	2	no	—
389	C₄×D₄	—	251	2	no	—
390	C₄×D₄	—	251	1	no	—
391	C₄×D₄	—	251	2	no	—
392	C₄×D₄	—	251	2	no	—
393	C₄×D₄	—	251	2	no	—
394	C₄×D₄	C₂×D₂₅₁	1	1	yes	characteristic
395	C₄×D₄	C₂×D₂₅₁	1	2	yes	complemented
396	#117	—	251	2	no	—
397	#117	—	251	2	no	—
398	#117	C₂×D₂₅₁	1	2	yes	complemented
399	C₂×C₄²	—	251	2	no	—
400	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
401	C₂⁴	—	251	2	no	—
402	#41	—	1004	4	no	—
403	#41	—	1004	2	no	—
404	#41	—	1004	2	no	—
405	C₂×Q₈	—	251	1	no	—
406	C₂×Q₈	—	251	2	no	—
407	C₂×Q₈	—	251	1	no	—
408	C₂×Q₈	—	251	1	no	—
409	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
410	C₂×D₄	—	251	2	no	—
411	C₂×D₄	—	251	2	no	—
412	C₂×D₄	—	251	2	no	—
413	C₂×D₄	—	251	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	—	251	1	no	—
419	C₂×D₄	—	251	2	no	—
420	C₂×D₄	—	251	2	no	—
421	C₂×D₄	—	251	2	no	—
422	C₂×D₄	—	251	1	no	—
423	C₂×D₄	—	251	2	no	—
424	C₂×D₄	—	251	1	no	—
425	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
426	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
427	C₂²×C₄	—	1004	4	no	—
428	C₂²×C₄	—	251	2	no	—
429	C₂²×C₄	—	251	2	no	—
430	C₂²×C₄	—	251	2	no	—
431	C₂²×C₄	—	251	2	no	—
432	C₂²×C₄	—	251	2	no	—
433	C₂²×C₄	—	251	2	no	—
434	C₂²×C₄	—	251	2	no	—
435	C₂²×C₄	—	251	2	no	—
436	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
437	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
438	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
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	2	no	—
450	C₄⋊C₄	—	251	2	no	—
451	C₄⋊C₄	—	251	2	no	—
452	C₄⋊C₄	—	251	1	no	—
453	C₄⋊C₄	—	251	1	no	—
454	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
455	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
456	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
457	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
458	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
459	C₄⋊C₄	C₂²×D₂₅₁	1	1	yes	characteristic
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	—	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	C₂²×D₂₅₁	1	2	yes	—
480	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
484	C₄²	—	251	2	no	—
485	C₄²	—	251	2	no	—
486	C₄²	—	251	2	no	—
487	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
488	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
489	C₄²	C₂²×D₂₅₁	1	2	yes	—
490	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
491	C₄²	C₂²×D₂₅₁	1	1	yes	characteristic
492	C₂³	—	1004	2	no	—
493	C₂³	—	1004	2	no	—
494	C₂³	—	1004	2	no	—
495	C₂³	—	251	2	no	—
496	C₂³	—	251	2	no	—
497	C₂³	—	251	2	no	—
498	C₂³	C₂³×D₂₅₁	1	2	yes	—
499	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
500	Q₈	—	4	1	no	—
501	Q₈	—	1004	2	no	—
502	Q₈	—	1004	1	no	—
503	Q₈	—	1004	1	no	—
504	Q₈	—	1004	1	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	2	no	—
507	D₄	—	1004	2	no	—
508	D₄	—	1004	1	no	—
509	D₄	—	1004	1	no	—
510	D₄	—	1004	2	no	—
511	D₄	—	1004	2	no	—
512	D₄	—	1004	1	no	—
513	D₄	—	1004	2	no	—
514	D₄	—	1004	2	no	—
515	D₄	—	1004	2	no	—
516	D₄	—	1004	2	no	—
517	D₄	—	1004	2	no	—
518	D₄	—	1004	2	no	—
519	D₄	—	1004	2	no	—
520	D₄	—	1004	2	no	—
521	D₄	—	1004	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	1004	2	no	—
527	C₂×C₄	—	1004	2	no	—
528	C₂×C₄	—	1004	2	no	—
529	C₂×C₄	—	1004	2	no	—
530	C₂×C₄	—	1004	2	no	—
531	C₂×C₄	—	502	4	no	—
532	C₂×C₄	—	502	4	no	—
533	C₂×C₄	—	502	4	no	—
534	C₂×C₄	—	251	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	C₂³×D₂₅₁	1	2	yes	—
540	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
541	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
542	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
546	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
547	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
548	C₂²	—	2	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	1004	8	no	—
555	C₂²	—	502	2	no	—
556	C₂²	—	502	2	no	—
557	C₂²	—	502	2	no	—
558	C₂²	—	502	2	no	—
559	C₂²	—	502	2	no	—
560	C₂²	—	502	2	no	—
561	C₂²	—	502	2	no	—
562	C₂²	—	502	2	no	—
563	C₂²	—	502	2	no	—
564	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
565	C₄	—	2	2	no	—
566	C₄	—	2	1	no	—
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	—	502	2	no	—
574	C₄	—	502	2	no	—
575	C₄	—	502	2	no	—
576	C₄	—	502	2	no	—
577	C₄	—	502	2	no	—
578	C₄	#22548761	1	2	yes	—
579	C₂	—	4	2	no	—
580	C₂	—	4	1	no	—
581	C₂	—	1004	2	no	—
582	C₂	—	1004	2	no	—
583	C₂	—	1004	2	no	—
584	C₂	C₂×#22548761	1	1	yes	characteristic
585	C₂	#30632523	1	1	yes	characteristic
586	C₂	#30632523	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	#529×C₂₅₁	C₂
hypercenter	#529	D₂₅₁
hypocenter	C₂₅₁	#3529
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #30632441	C₂	semidirect
2. #30632439	C₂	semidirect
3. #30632435	C₂	semidirect
4. #30632434	C₂	semidirect
5. #30632433	C₂	semidirect
6. #30632431	C₂	semidirect
7. #30632429	C₂	semidirect
8. #30632428	C₂	semidirect
9. #30632427	C₂	semidirect
10. #30632425	C₂	semidirect
11. #30632237	C₂	semidirect
12. #30632234	C₂	semidirect
13. #30632224	C₂	semidirect
14. #30632221	C₂	semidirect
15. #30632215	C₂	semidirect
16. #30632199	C₂	semidirect
17. #30632196	C₂	semidirect
18. #30632196	C₂	semidirect
19. #529×C₂₅₁	C₂	semidirect
22. C₂×#16860810	C₂²	semidirect
23. C₂²×C₄×D₂₅₁	C₂²	semidirect
24. #22548715	C₂²	semidirect
25. #22548714	C₂²	semidirect
28. #22548710	C₂²	semidirect
29. #22548710	C₂²	semidirect
30. #22548710	C₂²	semidirect
31. #22548709	C₂²	semidirect
32. #22548708	C₂²	semidirect
33. #22548707	C₂²	semidirect
34. #22548706	C₂²	semidirect
35. #22548705	C₂²	semidirect
39. #22548703	C₂²	semidirect
42. #22548701	C₂²	semidirect
44. #22548700	C₂²	semidirect
45. #22548700	C₂²	semidirect
46. #22548700	C₂²	semidirect
47. #22548700	C₂²	semidirect
49. #22548699	C₂²	semidirect
50. #22548698	C₂²	semidirect
52. #22548697	C₂²	semidirect
53. #22548697	C₂²	semidirect
54. #22548695	C₂²	semidirect
55. #22548695	C₂²	semidirect
56. #22548694	C₂²	semidirect
57. #22548693	C₂²	semidirect
58. #22548693	C₂²	semidirect
59. #22548693	C₂²	semidirect
60. #22548692	C₂²	semidirect
61. #22548692	C₂²	semidirect
62. #22548691	C₂²	semidirect
66. #22548690	C₂²	semidirect
68. #22548689	C₂²	semidirect
69. #22548689	C₂²	semidirect
73. #22548688	C₂²	semidirect
74. #22548688	C₂²	semidirect
77. #22548686	C₂²	semidirect
80. #22548685	C₂²	semidirect
81. #22548685	C₂²	semidirect
83. #22548683	C₂²	semidirect
84. C₄×Dic₅₀₂	C₂²	semidirect
87. C₄×D₁₀₀₄	C₂²	semidirect
88. C₄×D₁₀₀₄	C₂²	semidirect
89. C₄×D₁₀₀₄	C₂²	semidirect
91. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
92. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
93. #22548672	C₂²	semidirect
94. #22548672	C₂²	semidirect
95. C₄²×D₂₅₁	C₂²	semidirect
96. #126×C₂₅₁	C₂²	semidirect
97. #125×C₂₅₁	C₂²	semidirect
99. #123×C₂₅₁	C₂²	semidirect
100. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
102. C₄×Q₈×C₂₅₁	C₂²	semidirect
104. C₄×D₄×C₂₅₁	C₂²	semidirect
105. #117×C₂₅₁	C₂²	semidirect
106. C₂×C₄²×C₂₅₁	C₂²	semidirect
293. C₂₅₁	#3529	semidirect
310. #529	D₂₅₁	semidirect
327. #126	C₂×D₂₅₁	semidirect
331. #125	C₂×D₂₅₁	semidirect
351. #123	C₂×D₂₅₁	semidirect
361. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
385. C₄×Q₈	C₂×D₂₅₁	semidirect
395. C₄×D₄	C₂×D₂₅₁	semidirect
398. #117	C₂×D₂₅₁	semidirect
400. C₂×C₄²	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
#30632439	2
#30632435	2
#30632434	2
#30632433	2
#30632431	2
#30632429	2
#30632428	2
#30632427	2
#30632425	2
#30632237	2
#30632234	2
#30632224	2
#30632221	2
#30632215	2
#30632199	2
#30632196	2
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