Subgroups — #421×D₂₅₁ #44558904

Order 32128.

772 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₂₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#117×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#30631705	C₂	1	1	yes	maximal, characteristic, complemented
5	#30631704	C₂	1	1	yes	maximal, characteristic, complemented
6	#30631703	C₂	1	1	yes	maximal, characteristic, complemented
7	#30631702	C₂	1	4	yes	maximal, complemented
8	#104×D₂₅₁	C₂	1	4	yes	maximal, complemented
9	#421×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16860811	C₄	1	1	yes	characteristic, complemented
11	C₂×#16860810	—	2	1	no	—
12	C₂×#16860810	C₂²	1	1	yes	characteristic
13	C₂×#16860809	—	2	1	no	—
14	C₂×#16860809	C₄	1	1	yes	characteristic, complemented
15	#41×D₂₅₁	—	2	1	no	—
16	#41×D₂₅₁	—	2	1	no	—
17	#41×D₂₅₁	—	2	1	no	—
18	#41×D₂₅₁	—	2	1	no	—
19	#41×D₂₅₁	C₄	1	2	yes	complemented
20	#41×D₂₅₁	C₄	1	2	yes	complemented
21	#41×D₂₅₁	C₂²	1	2	yes	—
22	#41×D₂₅₁	C₂²	1	2	yes	—
23	C₂×Q₈×D₂₅₁	C₄	1	1	yes	characteristic, complemented
24	C₂×D₄×D₂₅₁	—	2	1	no	—
25	C₂×D₄×D₂₅₁	C₄	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₂₅₁	—	2	1	no	—
27	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
28	C₂×#16860794	C₂²	1	1	yes	characteristic, complemented
29	C₂×#16860793	—	2	1	no	—
30	M₁₆×D₂₅₁	—	2	1	no	—
31	M₁₆×D₂₅₁	—	2	1	no	—
32	M₁₆×D₂₅₁	C₂²	1	2	yes	complemented
33	M₁₆×D₂₅₁	C₂²	1	2	yes	complemented
34	C₂×C₈×D₂₅₁	—	2	1	no	—
35	#22548674	C₂²	1	1	yes	characteristic, complemented
36	#22548673	—	2	1	no	—
37	#22548672	C₂²	1	2	yes	complemented
38	#22548671	—	2	1	no	—
39	C₄⋊C₄×D₂₅₁	—	2	1	no	—
40	C₂²⋊C₄×D₂₅₁	—	2	1	no	—
41	C₄²×D₂₅₁	C₂²	1	2	yes	complemented
42	#22548643	C₂²	1	4	yes	complemented
43	#22548642	C₂²	1	4	yes	complemented
44	#22548641	C₂²	1	4	yes	complemented
45	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
46	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
47	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
48	#104×C₂₅₁	C₂²	1	4	yes	complemented
49	C₂³×D₂₅₁	—	2	1	no	—
50	C₂³×D₂₅₁	D₄	1	1	yes	characteristic
51	#16860811	—	2	1	no	—
52	#16860811	—	2	1	no	—
53	#16860811	C₂×C₄	1	2	yes	—
54	#16860811	C₂×C₄	1	2	yes	complemented
55	#16860810	—	2	2	no	—
56	#16860810	—	2	2	no	—
57	#16860810	—	2	2	no	—
58	#16860810	—	2	2	no	—
59	#16860810	—	2	1	no	—
60	#16860810	—	2	1	no	—
61	#16860810	C₂×C₄	1	2	yes	complemented
62	#16860810	C₂³	1	2	yes	—
63	#16860809	—	2	2	no	—
64	#16860809	—	2	2	no	—
65	#16860809	—	2	2	no	—
66	#16860809	—	2	2	no	—
67	#16860809	—	2	1	no	—
68	#16860809	—	2	1	no	—
69	#16860809	C₂×C₄	1	2	yes	—
70	#16860809	C₂×C₄	1	2	yes	complemented
71	C₂×Dic₅₀₂	—	2	1	no	—
72	C₂×Dic₅₀₂	C₂×C₄	1	1	yes	characteristic, complemented
73	Q₈×D₂₅₁	—	2	1	no	—
74	Q₈×D₂₅₁	—	2	1	no	—
75	Q₈×D₂₅₁	C₂×C₄	1	2	yes	—
76	Q₈×D₂₅₁	C₂×C₄	1	2	yes	complemented
77	C₂×D₁₀₀₄	—	2	1	no	—
78	C₂×D₁₀₀₄	C₂×C₄	1	1	yes	characteristic, complemented
79	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
80	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
81	C₂×C₂²⋊D₂₅₁	—	2	1	no	—
82	D₄×D₂₅₁	—	2	2	no	—
83	D₄×D₂₅₁	—	2	2	no	—
84	D₄×D₂₅₁	—	2	2	no	—
85	D₄×D₂₅₁	—	2	2	no	—
86	D₄×D₂₅₁	—	2	1	no	—
87	D₄×D₂₅₁	—	2	1	no	—
88	D₄×D₂₅₁	C₂×C₄	1	2	yes	—
89	D₄×D₂₅₁	C₂×C₄	1	2	yes	complemented
90	C₂²×Dic₂₅₁	—	2	1	no	—
91	C₂²×Dic₂₅₁	D₄	1	1	yes	characteristic
92	C₂×C₄×D₂₅₁	—	2	1	no	—
93	C₂×C₄×D₂₅₁	—	2	1	no	—
94	C₂×C₄×D₂₅₁	—	2	2	no	—
95	C₂×C₄×D₂₅₁	—	2	2	no	—
96	C₂×C₄×D₂₅₁	—	2	2	no	—
97	C₂×C₄×D₂₅₁	—	2	2	no	—
98	C₂×C₄×D₂₅₁	—	2	2	no	—
99	C₂×C₄×D₂₅₁	—	2	1	no	—
100	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄×D₂₅₁	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
105	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
106	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
107	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
108	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
109	C₂×C₄×D₂₅₁	D₄	1	1	yes	characteristic
110	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
112	#16860794	—	2	1	no	—
113	#16860794	C₂³	1	2	yes	complemented
114	#16860793	—	2	2	no	—
115	#16860793	—	2	2	no	—
116	C₂×C₂₅₁⋊C₈	—	2	1	no	—
117	C₈×D₂₅₁	—	2	2	no	—
118	C₈×D₂₅₁	—	2	2	no	—
119	C₄⋊Dic₂₅₁	—	2	1	no	—
120	Dic₂₅₁⋊C₄	—	2	2	no	—
121	C₂²⋊Dic₂₅₁	—	2	1	no	—
122	(C₂×D₂₅₁)⋊C₄	—	2	2	no	—
123	C₄×Dic₂₅₁	—	2	2	no	—
124	C₄×Dic₂₅₁	C₂³	1	2	yes	complemented
125	#41×C₂₅₁	—	2	1	no	—
126	#41×C₂₅₁	—	2	1	no	—
127	#41×C₂₅₁	C₂×C₄	1	2	yes	complemented
128	#41×C₂₅₁	C₂³	1	2	yes	—
129	C₂×Q₈×C₂₅₁	C₂×C₄	1	1	yes	characteristic, complemented
130	C₂×D₄×C₂₅₁	—	2	1	no	—
131	C₂×D₄×C₂₅₁	C₂×C₄	1	1	yes	characteristic, complemented
132	C₂²×C₄×C₂₅₁	—	2	1	no	—
133	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
134	M₁₆×C₂₅₁	—	2	1	no	—
135	M₁₆×C₂₅₁	C₂³	1	2	yes	complemented
136	C₂×C₈×C₂₅₁	—	2	1	no	—
137	C₄⋊C₄×C₂₅₁	—	2	1	no	—
138	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
139	C₄²×C₂₅₁	C₂³	1	2	yes	complemented
140	C₂²×D₂₅₁	—	2	1	no	—
141	C₂²×D₂₅₁	—	2	2	no	—
142	C₂²×D₂₅₁	—	2	2	no	—
143	C₂²×D₂₅₁	—	4	2	no	—
144	C₂²×D₂₅₁	—	4	4	no	—
145	C₂²×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×D₂₅₁	C₂×D₄	1	1	yes	characteristic
151	Dic₅₀₂	—	2	1	no	—
152	Dic₅₀₂	—	2	2	no	—
153	Dic₅₀₂	—	2	2	no	—
154	Dic₅₀₂	C₂²×C₄	1	2	yes	—
155	D₁₀₀₄	—	2	2	no	—
156	D₁₀₀₄	—	2	2	no	—
157	D₁₀₀₄	—	2	1	no	—
158	D₁₀₀₄	C₂²×C₄	1	2	yes	—
159	C₂²⋊D₂₅₁	—	2	2	no	—
160	C₂²⋊D₂₅₁	—	2	2	no	—
161	C₂²⋊D₂₅₁	—	2	2	no	—
162	C₂²⋊D₂₅₁	—	2	2	no	—
163	C₂²⋊D₂₅₁	—	2	2	no	—
164	C₂²⋊D₂₅₁	—	2	2	no	—
165	C₂×Dic₂₅₁	—	2	1	no	—
166	C₂×Dic₂₅₁	—	2	2	no	—
167	C₂×Dic₂₅₁	—	2	2	no	—
168	C₂×Dic₂₅₁	—	2	2	no	—
169	C₂×Dic₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
170	C₂×Dic₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
171	C₂×Dic₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
172	C₂×Dic₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
173	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
174	C₂×Dic₂₅₁	C₂×D₄	1	1	yes	characteristic
175	C₄×D₂₅₁	—	2	2	no	—
176	C₄×D₂₅₁	—	2	2	no	—
177	C₄×D₂₅₁	—	2	2	no	—
178	C₄×D₂₅₁	—	2	2	no	—
179	C₄×D₂₅₁	—	2	2	no	—
180	C₄×D₂₅₁	—	2	2	no	—
181	C₄×D₂₅₁	—	4	4	no	—
182	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
183	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
184	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
185	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
186	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
187	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
188	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
189	C₄×D₂₅₁	C₂²⋊C₄	1	1	yes	characteristic
190	C₄×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
191	C₄×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
192	C₄×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
193	C₄×D₂₅₁	C₂²×C₄	1	1	yes	characteristic
194	C₄×D₂₅₁	C₂×D₄	1	1	yes	characteristic
195	C₄×D₂₅₁	C₂×D₄	1	1	yes	characteristic
196	C₄×D₂₅₁	C₂×D₄	1	1	yes	characteristic
197	C₄×D₂₅₁	C₂×D₄	1	1	yes	characteristic
198	C₂₅₁⋊C₈	—	2	2	no	—
199	C₂³×C₂₅₁	—	2	1	no	—
200	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
201	Q₈×C₂₅₁	—	2	1	no	—
202	Q₈×C₂₅₁	C₂²×C₄	1	2	yes	—
203	D₄×C₂₅₁	—	2	2	no	—
204	D₄×C₂₅₁	—	2	2	no	—
205	D₄×C₂₅₁	—	2	1	no	—
206	D₄×C₂₅₁	C₂²×C₄	1	2	yes	—
207	C₂×C₄×C₂₅₁	—	2	1	no	—
208	C₂×C₄×C₂₅₁	—	2	2	no	—
209	C₂×C₄×C₂₅₁	—	2	2	no	—
210	C₂×C₄×C₂₅₁	—	2	2	no	—
211	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₄×C₂₅₁	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
215	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
216	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
217	C₈×C₂₅₁	—	2	2	no	—
218	C₂²×C₂₅₁	—	2	2	no	—
219	C₂²×C₂₅₁	—	4	1	no	—
220	C₂²×C₂₅₁	—	4	2	no	—
221	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
224	C₂×D₂₅₁	—	2	2	no	—
225	C₂×D₂₅₁	—	2	2	no	—
226	C₂×D₂₅₁	—	2	2	no	—
227	C₂×D₂₅₁	—	2	2	no	—
228	C₂×D₂₅₁	—	4	1	no	—
229	C₂×D₂₅₁	—	4	1	no	—
230	C₂×D₂₅₁	—	4	1	no	—
231	C₂×D₂₅₁	—	4	4	no	—
232	C₂×D₂₅₁	—	4	2	no	—
233	C₂×D₂₅₁	—	4	4	no	—
234	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×D₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₄×C₂₅₁	—	2	2	no	—
239	C₄×C₂₅₁	—	4	2	no	—
240	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₄×C₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₄×C₂₅₁	C₂³×C₄	1	1	yes	characteristic
243	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
244	Dic₂₅₁	—	2	2	no	—
245	Dic₂₅₁	—	4	2	no	—
246	Dic₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
247	Dic₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	Dic₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	Dic₂₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂×C₂₅₁	—	2	1	no	—
251	C₂×C₂₅₁	—	2	1	no	—
252	C₂×C₂₅₁	—	2	1	no	—
253	C₂×C₂₅₁	—	4	2	no	—
254	C₂×C₂₅₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
255	D₂₅₁	—	2	1	no	—
256	D₂₅₁	—	2	1	no	—
257	D₂₅₁	—	2	1	no	—
258	D₂₅₁	—	4	2	no	—
259	D₂₅₁	#421	1	2	yes	direct product factor
260	C₂₅₁	C₂×#421	1	1	yes	characteristic, complemented, Sylow
261	C₂×#421	—	251	1	no	maximal, Sylow
262	C₂²×#41	—	251	1	no	—
263	C₂²×M₁₆	—	251	1	no	—
264	C₂×#117	—	251	1	no	—
265	#421	—	251	1	no	—
266	#421	—	251	1	no	—
267	#421	—	251	1	no	—
268	#421	—	251	4	no	—
269	#421	D₂₅₁	1	1	yes	characteristic, direct product factor
270	C₂×#104	—	251	4	no	—
271	C₂×#41	—	502	1	no	—
272	C₂×#41	—	502	1	no	—
273	C₂×#41	—	502	1	no	—
274	C₂×#41	—	502	1	no	—
275	C₂×#41	—	502	1	no	—
276	C₂×#41	—	502	1	no	—
277	C₂×#41	—	251	2	no	—
278	C₂×#41	—	251	2	no	—
279	C₂×#41	—	251	2	no	—
280	C₂×#41	—	251	2	no	—
281	C₂×#41	—	251	1	no	—
282	C₂×#41	—	251	1	no	—
283	C₂×#41	—	251	1	no	—
284	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
285	C₂²×Q₈	—	251	1	no	—
286	C₂²×D₄	—	502	1	no	—
287	C₂²×D₄	—	251	1	no	—
288	C₂³×C₄	—	502	1	no	—
289	C₂³×C₄	—	251	1	no	—
290	C₂×M₁₆	—	502	1	no	—
291	C₂×M₁₆	—	502	1	no	—
292	C₂×M₁₆	—	502	1	no	—
293	C₂×M₁₆	—	251	1	no	—
294	C₂×M₁₆	—	251	2	no	—
295	C₂×M₁₆	—	251	2	no	—
296	C₂×M₁₆	C₂×D₂₅₁	1	1	yes	characteristic, complemented
297	C₂²×C₈	—	502	1	no	—
298	#117	—	502	1	no	—
299	#117	—	502	1	no	—
300	#117	—	251	1	no	—
301	#117	—	251	2	no	—
302	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
303	C₂×C₄⋊C₄	—	502	1	no	—
304	C₂×C₂²⋊C₄	—	502	1	no	—
305	C₂×C₄²	—	251	2	no	—
306	#104	—	251	4	no	—
307	#104	—	251	4	no	—
308	#104	—	251	4	no	—
309	#104	C₂×D₂₅₁	1	4	yes	complemented
310	C₂⁴	—	502	1	no	—
311	C₂⁴	—	251	1	no	—
312	#41	—	2	1	no	—
313	#41	—	2	1	no	—
314	#41	—	502	2	no	—
315	#41	—	502	2	no	—
316	#41	—	502	2	no	—
317	#41	—	502	2	no	—
318	#41	—	502	2	no	—
319	#41	—	502	2	no	—
320	#41	—	502	2	no	—
321	#41	—	502	2	no	—
322	#41	—	502	1	no	—
323	#41	—	502	1	no	—
324	#41	—	502	1	no	—
325	#41	—	502	1	no	—
326	#41	—	502	1	no	—
327	#41	—	502	1	no	—
328	#41	—	251	2	no	—
329	#41	—	251	2	no	—
330	#41	—	251	2	no	—
331	#41	—	251	2	no	—
332	#41	—	251	2	no	—
333	#41	—	251	2	no	—
334	#41	C₄×D₂₅₁	1	2	yes	complemented
335	#41	C₂²×D₂₅₁	1	2	yes	—
336	C₂×Q₈	—	502	1	no	—
337	C₂×Q₈	—	502	1	no	—
338	C₂×Q₈	—	502	1	no	—
339	C₂×Q₈	—	251	2	no	—
340	C₂×Q₈	—	251	2	no	—
341	C₂×Q₈	—	251	1	no	—
342	C₂×Q₈	C₄×D₂₅₁	1	1	yes	characteristic, complemented
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	502	1	no	—
345	C₂×D₄	—	502	2	no	—
346	C₂×D₄	—	502	2	no	—
347	C₂×D₄	—	502	2	no	—
348	C₂×D₄	—	502	2	no	—
349	C₂×D₄	—	502	1	no	—
350	C₂×D₄	—	502	1	no	—
351	C₂×D₄	—	502	1	no	—
352	C₂×D₄	—	502	1	no	—
353	C₂×D₄	—	502	1	no	—
354	C₂×D₄	—	251	2	no	—
355	C₂×D₄	—	251	2	no	—
356	C₂×D₄	—	251	1	no	—
357	C₂×D₄	C₄×D₂₅₁	1	1	yes	characteristic, complemented
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	502	2	no	—
360	C₂²×C₄	—	502	1	no	—
361	C₂²×C₄	—	502	1	no	—
362	C₂²×C₄	—	502	2	no	—
363	C₂²×C₄	—	502	2	no	—
364	C₂²×C₄	—	502	2	no	—
365	C₂²×C₄	—	502	2	no	—
366	C₂²×C₄	—	502	1	no	—
367	C₂²×C₄	—	502	1	no	—
368	C₂²×C₄	—	251	1	no	—
369	C₂²×C₄	—	251	1	no	—
370	C₂²×C₄	—	251	1	no	—
371	C₂²×C₄	—	251	1	no	—
372	C₂²×C₄	—	251	1	no	—
373	C₂²×C₄	—	251	1	no	—
374	C₂²×C₄	—	251	1	no	—
375	C₂²×C₄	—	251	1	no	—
376	C₂²×C₄	—	251	1	no	—
377	C₂²×C₄	—	251	1	no	—
378	C₂²×C₄	—	251	1	no	—
379	C₂²×C₄	—	251	1	no	—
380	C₂²×C₄	—	251	1	no	—
381	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
382	M₁₆	—	2	1	no	—
383	M₁₆	—	502	2	no	—
384	M₁₆	—	502	2	no	—
385	M₁₆	—	502	1	no	—
386	M₁₆	—	251	2	no	—
387	M₁₆	C₂²×D₂₅₁	1	2	yes	complemented
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	502	2	no	—
390	C₂×C₈	—	502	2	no	—
391	C₂×C₈	—	502	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	502	2	no	—
394	C₄⋊C₄	—	502	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	502	2	no	—
397	C₂²⋊C₄	—	502	1	no	—
398	C₄²	—	502	2	no	—
399	C₄²	—	251	2	no	—
400	C₄²	C₂²×D₂₅₁	1	2	yes	complemented
401	C₂³	—	2	1	no	—
402	C₂³	—	1004	4	no	—
403	C₂³	—	1004	2	no	—
404	C₂³	—	502	2	no	—
405	C₂³	—	502	2	no	—
406	C₂³	—	502	1	no	—
407	C₂³	—	251	1	no	—
408	C₂³	—	251	1	no	—
409	C₂³	—	251	1	no	—
410	C₂³	—	251	1	no	—
411	C₂³	—	251	1	no	—
412	C₂³	—	251	1	no	—
413	C₂³	D₄×D₂₅₁	1	1	yes	characteristic
414	Q₈	—	2	1	no	—
415	Q₈	—	502	2	no	—
416	Q₈	—	502	2	no	—
417	Q₈	—	502	1	no	—
418	Q₈	—	251	2	no	—
419	Q₈	C₂×C₄×D₂₅₁	1	2	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	1	no	—
423	D₄	—	502	2	no	—
424	D₄	—	502	2	no	—
425	D₄	—	502	2	no	—
426	D₄	—	502	2	no	—
427	D₄	—	502	2	no	—
428	D₄	—	502	2	no	—
429	D₄	—	502	2	no	—
430	D₄	—	502	2	no	—
431	D₄	—	502	1	no	—
432	D₄	—	251	2	no	—
433	D₄	C₂×C₄×D₂₅₁	1	2	yes	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	1004	4	no	—
439	C₂×C₄	—	502	2	no	—
440	C₂×C₄	—	502	2	no	—
441	C₂×C₄	—	502	2	no	—
442	C₂×C₄	—	502	2	no	—
443	C₂×C₄	—	502	2	no	—
444	C₂×C₄	—	502	1	no	—
445	C₂×C₄	—	502	2	no	—
446	C₂×C₄	—	502	2	no	—
447	C₂×C₄	—	502	2	no	—
448	C₂×C₄	—	502	2	no	—
449	C₂×C₄	—	251	1	no	—
450	C₂×C₄	—	251	1	no	—
451	C₂×C₄	—	251	1	no	—
452	C₂×C₄	—	251	1	no	—
453	C₂×C₄	—	251	1	no	—
454	C₂×C₄	—	251	1	no	—
455	C₂×C₄	—	251	1	no	—
456	C₂×C₄	—	251	1	no	—
457	C₂×C₄	—	251	1	no	—
458	C₂×C₄	—	251	1	no	—
459	C₂×C₄	—	251	1	no	—
460	C₂×C₄	—	251	1	no	—
461	C₂×C₄	—	251	1	no	—
462	C₂×C₄	—	251	1	no	—
463	C₂×C₄	—	251	1	no	—
464	C₂×C₄	—	251	1	no	—
465	C₂×C₄	—	251	1	no	—
466	C₂×C₄	—	251	1	no	—
467	C₂×C₄	—	251	1	no	—
468	C₂×C₄	—	251	1	no	—
469	C₂×C₄	—	251	1	no	—
470	C₂×C₄	—	251	1	no	—
471	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
472	C₂×C₄	C₂×C₄×D₂₅₁	1	1	yes	characteristic
473	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
474	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
475	C₂×C₄	D₄×D₂₅₁	1	1	yes	characteristic
476	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	502	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	1004	2	no	—
483	C₂²	—	1004	1	no	—
484	C₂²	—	1004	1	no	—
485	C₂²	—	1004	1	no	—
486	C₂²	—	1004	4	no	—
487	C₂²	—	1004	4	no	—
488	C₂²	—	502	2	no	—
489	C₂²	—	502	2	no	—
490	C₂²	—	502	2	no	—
491	C₂²	—	502	2	no	—
492	C₂²	—	251	1	no	—
493	C₂²	—	251	1	no	—
494	C₂²	—	251	1	no	—
495	C₂²	—	251	1	no	—
496	C₂²	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
497	C₂²	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
498	C₂²	C₂×D₄×D₂₅₁	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	1004	2	no	—
502	C₄	—	502	2	no	—
503	C₄	—	251	1	no	—
504	C₄	—	251	1	no	—
505	C₄	—	251	1	no	—
506	C₄	—	251	1	no	—
507	C₄	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
508	C₄	C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic
509	C₄	C₂²×C₄×D₂₅₁	1	1	yes	characteristic
510	C₄	C₂×D₄×D₂₅₁	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	4	2	no	—
515	C₂	—	1004	2	no	—
516	C₂	—	502	1	no	—
517	C₂	—	502	1	no	—
518	C₂	—	502	1	no	—
519	C₂	—	251	2	no	—
520	C₂	C₂×C₂²⋊C₄×D₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×D₂₅₁
commutator	C₄×C₂₅₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₂₅₁
Fitting	#421×C₂₅₁	C₂
socle	C₂×C₂₅₁	C₂²×C₂²⋊C₄
prime radical	C₂×#41×D₂₅₁	C₂
cosocle	C₂×C₄×C₂₅₁	C₂⁴
hypercenter	#421	D₂₅₁
hypocenter	C₂₅₁	C₂×#421
LCS	G ▷ C₄×C₂₅₁ ▷ C₂×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #421

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×D₂₅₁	C₂	semidirect
3. #117×D₂₅₁	C₂	semidirect
4. #30631705	C₂	semidirect
5. #30631704	C₂	semidirect
6. #30631703	C₂	semidirect
7. #30631702	C₂	semidirect
8. #104×D₂₅₁	C₂	semidirect
9. #421×C₂₅₁	C₂	semidirect
10. C₂×#16860811	C₄	semidirect
14. C₂×#16860809	C₄	semidirect
19. #41×D₂₅₁	C₄	semidirect
20. #41×D₂₅₁	C₄	semidirect
23. C₂×Q₈×D₂₅₁	C₄	semidirect
25. C₂×D₄×D₂₅₁	C₄	semidirect
28. C₂×#16860794	C₂²	semidirect
32. M₁₆×D₂₅₁	C₂²	semidirect
33. M₁₆×D₂₅₁	C₂²	semidirect
35. #22548674	C₂²	semidirect
37. #22548672	C₂²	semidirect
41. C₄²×D₂₅₁	C₂²	semidirect
42. #22548643	C₂²	semidirect
43. #22548642	C₂²	semidirect
44. #22548641	C₂²	semidirect
46. C₂×M₁₆×C₂₅₁	C₂²	semidirect
47. #117×C₂₅₁	C₂²	semidirect
48. #104×C₂₅₁	C₂²	semidirect
54. #16860811	C₂×C₄	semidirect
61. #16860810	C₂×C₄	semidirect
70. #16860809	C₂×C₄	semidirect
72. C₂×Dic₅₀₂	C₂×C₄	semidirect
76. Q₈×D₂₅₁	C₂×C₄	semidirect
78. C₂×D₁₀₀₄	C₂×C₄	semidirect
89. D₄×D₂₅₁	C₂×C₄	semidirect
113. #16860794	C₂³	semidirect
124. C₄×Dic₂₅₁	C₂³	semidirect
127. #41×C₂₅₁	C₂×C₄	semidirect
129. C₂×Q₈×C₂₅₁	C₂×C₄	semidirect
131. C₂×D₄×C₂₅₁	C₂×C₄	semidirect
135. M₁₆×C₂₅₁	C₂³	semidirect
139. C₄²×C₂₅₁	C₂³	semidirect
259. D₂₅₁	#421	direct (N × H)
260. C₂₅₁	C₂×#421	semidirect
269. #421	D₂₅₁	direct (N × H)
296. C₂×M₁₆	C₂×D₂₅₁	semidirect
302. #117	C₂×D₂₅₁	semidirect
309. #104	C₂×D₂₅₁	semidirect
334. #41	C₄×D₂₅₁	semidirect
342. C₂×Q₈	C₄×D₂₅₁	semidirect
357. C₂×D₄	C₄×D₂₅₁	semidirect
387. M₁₆	C₂²×D₂₅₁	semidirect
400. C₄²	C₂²×D₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₂₅₁	2
C₂×M₁₆×D₂₅₁	2
#117×D₂₅₁	2
#30631705	2
#30631704	2
#30631703	2
#30631702	2
#104×D₂₅₁	2
#421×C₂₅₁	2
C₂×#421	251

Subgroups — #421×D251 #44558904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #421×D₂₅₁ #44558904