Subgroups — #536×D₂₅₁ #44563677

Order 32128.

1512 conjugacy classes of subgroups.

The subgroup lattice has 442 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	C₂²×Q₈×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632263	C₂	1	1	yes	maximal, characteristic, complemented
4	#30632262	C₂	1	2	yes	maximal, complemented
5	#30632261	C₂	1	1	yes	maximal, characteristic, complemented
6	#30632260	C₂	1	4	yes	maximal, complemented
7	#30632259	C₂	1	4	yes	maximal, complemented
8	#30632258	C₂	1	1	yes	maximal, characteristic, complemented
9	#30632257	C₂	1	2	yes	maximal, complemented
10	C₄⋊Q₈×D₂₅₁	C₂	1	2	yes	maximal, complemented
11	#124×D₂₅₁	C₂	1	2	yes	maximal, complemented
12	#123×D₂₅₁	C₂	1	4	yes	maximal, complemented
13	C₂²⋊Q₈×D₂₅₁	C₂	1	4	yes	maximal, complemented
14	#117×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#536×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16860811	C₂²	1	1	yes	characteristic
17	C₂×#16860810	C₂²	1	2	yes	—
18	C₂×#16860810	C₂²	1	1	yes	characteristic
19	C₂×#16860809	C₂²	1	1	yes	characteristic
20	C₂×#16860809	C₂²	1	2	yes	—
21	#41×D₂₅₁	—	2	8	no	—
22	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
23	C₂²×Dic₅₀₂	C₂²	1	2	yes	complemented
24	C₂×Q₈×D₂₅₁	—	2	8	no	—
25	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	—
26	C₂×Q₈×D₂₅₁	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	—
28	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	complemented
29	C₂×Q₈×D₂₅₁	C₂²	1	2	yes	complemented
30	C₂×D₄×D₂₅₁	C₂²	1	1	yes	characteristic
31	C₂×D₄×D₂₅₁	C₂²	1	2	yes	—
32	C₂²×C₄×D₂₅₁	C₂²	1	2	yes	—
33	C₂²×C₄×D₂₅₁	C₂²	1	2	yes	—
34	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
35	#22548715	C₂²	1	2	yes	complemented
36	#22548714	C₂²	1	8	yes	complemented
37	#22548713	C₂²	1	2	yes	complemented
38	#22548713	C₂²	1	2	yes	complemented
39	#22548704	C₂²	1	2	yes	complemented
40	#22548703	C₂²	1	2	yes	complemented
41	#22548702	C₂²	1	2	yes	complemented
42	#22548701	C₂²	1	8	yes	complemented
43	#22548700	C₂²	1	8	yes	complemented
44	#22548699	C₂²	1	4	yes	complemented
45	#22548698	C₂²	1	4	yes	complemented
46	#22548697	C₂²	1	8	yes	complemented
47	#22548696	C₂²	1	4	yes	complemented
48	#22548695	C₂²	1	4	yes	complemented
49	#22548694	C₂²	1	4	yes	complemented
50	#22548693	C₂²	1	8	yes	complemented
51	#22548692	C₂²	1	8	yes	complemented
52	#22548691	C₂²	1	4	yes	complemented
53	#22548674	C₂²	1	1	yes	characteristic, complemented
54	#22548673	C₂²	1	2	yes	complemented
55	#22548672	C₂²	1	2	yes	complemented
56	#22548671	C₂²	1	2	yes	complemented
57	C₄⋊C₄×D₂₅₁	C₂²	1	8	yes	—
58	C₄⋊C₄×D₂₅₁	C₂²	1	2	yes	—
59	C₂²⋊C₄×D₂₅₁	C₂²	1	8	yes	—
60	C₂²⋊C₄×D₂₅₁	C₂²	1	2	yes	—
61	C₄²×D₂₅₁	C₂²	1	2	yes	—
62	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
64	C₄⋊Q₈×C₂₅₁	C₂²	1	2	yes	complemented
65	#124×C₂₅₁	C₂²	1	2	yes	complemented
66	#123×C₂₅₁	C₂²	1	4	yes	complemented
67	C₂²⋊Q₈×C₂₅₁	C₂²	1	4	yes	complemented
68	#117×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₂₅₁	C₂³	1	2	yes	—
70	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
71	#16860811	—	2	4	no	—
72	#16860810	—	2	8	no	—
73	#16860810	—	2	4	no	—
74	#16860809	—	2	8	no	—
75	#16860809	—	2	4	no	—
76	C₂×Dic₅₀₂	—	2	8	no	—
77	C₂×Dic₅₀₂	—	2	4	no	—
78	C₂×Dic₅₀₂	C₂³	1	4	yes	—
79	C₂×Dic₅₀₂	C₂³	1	2	yes	—
80	C₂×Dic₅₀₂	C₂³	1	4	yes	—
81	C₂×Dic₅₀₂	C₂³	1	2	yes	—
82	C₂×Dic₅₀₂	C₂³	1	1	yes	characteristic
83	C₂×Dic₅₀₂	C₂³	1	2	yes	—
84	Q₈×D₂₅₁	—	2	8	no	—
85	Q₈×D₂₅₁	—	2	8	no	—
86	Q₈×D₂₅₁	—	2	8	no	—
87	Q₈×D₂₅₁	—	2	8	no	—
88	Q₈×D₂₅₁	—	2	4	no	—
89	C₂×D₁₀₀₄	C₂³	1	2	yes	—
90	C₂×D₁₀₀₄	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₂₅₁	C₂³	1	2	yes	—
94	D₄×D₂₅₁	—	2	8	no	—
95	D₄×D₂₅₁	—	2	4	no	—
96	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
97	C₂²×Dic₂₅₁	C₂³	1	2	yes	—
98	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₂₅₁	—	2	8	no	—
100	C₂×C₄×D₂₅₁	—	2	8	no	—
101	C₂×C₄×D₂₅₁	D₄	1	8	yes	—
102	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
103	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
104	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
105	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
106	C₂×C₄×D₂₅₁	C₂³	1	2	yes	—
107	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
108	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
110	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₂₅₁	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₂₅₁	C₂³	1	2	yes	—
113	C₄⋊Dic₂₅₁	C₂³	1	8	yes	—
114	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
115	Dic₂₅₁⋊C₄	C₂³	1	8	yes	—
116	Dic₂₅₁⋊C₄	C₂³	1	8	yes	—
117	C₂²⋊Dic₂₅₁	C₂³	1	2	yes	—
118	C₂²⋊Dic₂₅₁	C₂³	1	8	yes	—
119	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	—
121	(C₂×D₂₅₁)⋊C₄	C₂³	1	8	yes	—
122	C₄×Dic₂₅₁	C₂³	1	4	yes	—
123	C₄×Dic₂₅₁	C₂³	1	2	yes	—
124	#41×C₂₅₁	—	2	4	no	—
125	C₂×Q₈×C₂₅₁	—	2	4	no	—
126	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
127	C₂×Q₈×C₂₅₁	C₂³	1	2	yes	—
128	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₂₅₁	C₂³	1	2	yes	—
130	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₂₅₁	C₂³	1	2	yes	—
133	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
134	C₄⋊C₄×C₂₅₁	C₂³	1	2	yes	—
135	C₄⋊C₄×C₂₅₁	C₂³	1	8	yes	—
136	C₂²⋊C₄×C₂₅₁	C₂³	1	2	yes	—
137	C₂²⋊C₄×C₂₅₁	C₂³	1	8	yes	—
138	C₄²×C₂₅₁	C₂³	1	2	yes	—
139	C₂²×D₂₅₁	—	2	4	no	—
140	C₂²×D₂₅₁	—	2	4	no	—
141	C₂²×D₂₅₁	—	2	8	no	—
142	C₂²×D₂₅₁	C₂×D₄	1	4	yes	—
143	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
144	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
145	C₂²×D₂₅₁	C₂⁴	1	1	yes	characteristic
146	Dic₅₀₂	—	2	4	no	—
147	Dic₅₀₂	—	2	4	no	—
148	Dic₅₀₂	—	2	2	no	—
149	Dic₅₀₂	—	2	8	no	—
150	Dic₅₀₂	—	2	8	no	—
151	Dic₅₀₂	—	2	4	no	—
152	D₁₀₀₄	—	2	4	no	—
153	D₁₀₀₄	—	2	2	no	—
154	C₂²⋊D₂₅₁	—	2	4	no	—
155	C₂²⋊D₂₅₁	—	2	4	no	—
156	C₂²⋊D₂₅₁	—	2	4	no	—
157	C₂×Dic₂₅₁	—	2	4	no	—
158	C₂×Dic₂₅₁	—	2	4	no	—
159	C₂×Dic₂₅₁	C₂×D₄	1	4	yes	—
160	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
161	C₂×Dic₂₅₁	C₂⁴	1	4	yes	—
162	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
163	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₂₅₁	C₂⁴	1	1	yes	characteristic
165	C₄×D₂₅₁	—	2	4	no	—
166	C₄×D₂₅₁	—	2	8	no	—
167	C₄×D₂₅₁	—	2	8	no	—
168	C₄×D₂₅₁	—	2	8	no	—
169	C₄×D₂₅₁	—	2	4	no	—
170	C₄×D₂₅₁	—	2	4	no	—
171	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
172	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
173	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
174	C₄×D₂₅₁	C₂×D₄	1	4	yes	—
175	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
176	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
177	Q₈×C₂₅₁	—	2	4	no	—
178	Q₈×C₂₅₁	—	2	4	no	—
179	Q₈×C₂₅₁	—	2	2	no	—
180	D₄×C₂₅₁	—	2	4	no	—
181	D₄×C₂₅₁	—	2	2	no	—
182	C₂×C₄×C₂₅₁	—	2	4	no	—
183	C₂×C₄×C₂₅₁	—	2	4	no	—
184	C₂×C₄×C₂₅₁	C₂×D₄	1	4	yes	—
185	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
186	C₂×C₄×C₂₅₁	C₂⁴	1	4	yes	—
187	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
188	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
189	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₂₅₁	—	2	2	no	—
191	C₂²×C₂₅₁	—	2	2	no	—
192	C₂²×C₂₅₁	—	2	4	no	—
193	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
194	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
195	C₂×D₂₅₁	—	2	2	no	—
196	C₂×D₂₅₁	—	2	8	no	—
197	C₂×D₂₅₁	—	2	2	no	—
198	C₂×D₂₅₁	—	2	4	no	—
199	C₂×D₂₅₁	—	4	8	no	—
200	C₂×D₂₅₁	C₂²×D₄	1	2	yes	—
201	C₂×D₂₅₁	C₂²×D₄	1	2	yes	—
202	C₂×D₂₅₁	2₋¹⁺⁴	1	4	yes	—
203	C₄×C₂₅₁	—	2	2	no	—
204	C₄×C₂₅₁	—	2	4	no	—
205	C₄×C₂₅₁	—	2	4	no	—
206	C₄×C₂₅₁	C₂²×D₄	1	2	yes	—
207	C₄×C₂₅₁	C₂²×D₄	1	2	yes	—
208	Dic₂₅₁	—	2	2	no	—
209	Dic₂₅₁	—	2	4	no	—
210	Dic₂₅₁	—	2	4	no	—
211	Dic₂₅₁	C₂²×D₄	1	2	yes	—
212	Dic₂₅₁	C₂²×D₄	1	2	yes	—
213	C₂×C₂₅₁	—	2	2	no	—
214	C₂×C₂₅₁	—	4	2	no	—
215	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
216	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	2	yes	—
217	D₂₅₁	—	2	2	no	—
218	D₂₅₁	—	4	2	no	—
219	D₂₅₁	#536	1	4	yes	direct product factor
220	C₂₅₁	C₂×#536	1	1	yes	characteristic, complemented, Sylow
221	C₂×#536	—	251	1	no	maximal, Sylow
222	C₂²×#41	—	251	1	no	—
223	C₂³×Q₈	—	251	1	no	—
224	#536	—	251	1	no	—
225	#536	—	251	1	no	—
226	#536	—	251	2	no	—
227	#536	—	251	2	no	—
228	#536	—	251	4	no	—
229	#536	—	251	4	no	—
230	#536	—	251	1	no	—
231	#536	D₂₅₁	1	1	yes	characteristic, direct product factor
232	C₂×C₄⋊Q₈	—	251	2	no	—
233	C₂×#124	—	251	2	no	—
234	C₂×#123	—	251	4	no	—
235	C₂×C₂²⋊Q₈	—	251	4	no	—
236	C₂×#117	—	251	1	no	—
237	C₂×#41	—	502	8	no	—
238	C₂×#41	—	251	1	no	—
239	C₂×#41	—	251	1	no	—
240	C₂×#41	—	251	2	no	—
241	C₂×#41	—	251	1	no	—
242	C₂×#41	—	251	2	no	—
243	C₂×#41	C₂×D₂₅₁	1	1	yes	characteristic
244	C₂²×Q₈	—	502	8	no	—
245	C₂²×Q₈	—	251	2	no	—
246	C₂²×Q₈	—	251	2	no	—
247	C₂²×Q₈	—	251	1	no	—
248	C₂²×Q₈	—	251	2	no	—
249	C₂²×Q₈	—	251	2	no	—
250	C₂²×Q₈	—	251	1	no	—
251	C₂²×Q₈	—	251	2	no	—
252	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic, complemented
253	C₂²×D₄	—	251	2	no	—
254	C₂²×D₄	—	251	1	no	—
255	C₂³×C₄	—	251	2	no	—
256	C₂³×C₄	—	251	2	no	—
257	C₂³×C₄	—	251	1	no	—
258	C₄⋊Q₈	—	251	2	no	—
259	C₄⋊Q₈	—	251	2	no	—
260	C₄⋊Q₈	—	251	8	no	—
261	C₄⋊Q₈	—	251	2	no	—
262	C₄⋊Q₈	C₂×D₂₅₁	1	2	yes	complemented
263	#124	—	251	2	no	—
264	#124	—	251	2	no	—
265	#124	—	251	8	no	—
266	#124	—	251	2	no	—
267	#124	C₂×D₂₅₁	1	2	yes	complemented
268	#123	—	251	4	no	—
269	#123	—	251	4	no	—
270	#123	—	251	8	no	—
271	#123	—	251	8	no	—
272	#123	—	251	4	no	—
273	#123	C₂×D₂₅₁	1	4	yes	complemented
274	C₂²⋊Q₈	—	251	4	no	—
275	C₂²⋊Q₈	—	251	4	no	—
276	C₂²⋊Q₈	—	251	8	no	—
277	C₂²⋊Q₈	—	251	4	no	—
278	C₂²⋊Q₈	—	251	8	no	—
279	C₂²⋊Q₈	C₂×D₂₅₁	1	4	yes	complemented
280	#117	—	251	1	no	—
281	#117	—	251	2	no	—
282	#117	—	251	2	no	—
283	#117	—	251	2	no	—
284	#117	C₂×D₂₅₁	1	1	yes	characteristic, complemented
285	C₂×C₄⋊C₄	—	251	2	no	—
286	C₂×C₄⋊C₄	—	251	8	no	—
287	C₂×C₂²⋊C₄	—	251	2	no	—
288	C₂×C₂²⋊C₄	—	251	8	no	—
289	C₂×C₄²	—	251	2	no	—
290	C₂⁴	—	251	2	no	—
291	C₂⁴	—	251	1	no	—
292	#41	—	2	4	no	—
293	#41	—	502	8	no	—
294	#41	—	502	8	no	—
295	#41	—	502	4	no	—
296	#41	—	502	4	no	—
297	#41	—	502	4	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	502	8	no	—
300	C₂×Q₈	—	502	8	no	—
301	C₂×Q₈	—	502	8	no	—
302	C₂×Q₈	—	502	8	no	—
303	C₂×Q₈	—	502	8	no	—
304	C₂×Q₈	—	502	4	no	—
305	C₂×Q₈	—	502	4	no	—
306	C₂×Q₈	—	251	2	no	—
307	C₂×Q₈	—	251	4	no	—
308	C₂×Q₈	—	251	2	no	—
309	C₂×Q₈	—	251	4	no	—
310	C₂×Q₈	—	251	1	no	—
311	C₂×Q₈	—	251	2	no	—
312	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
313	C₂×Q₈	C₂²×D₂₅₁	1	2	yes	—
314	C₂×Q₈	C₂²×D₂₅₁	1	1	yes	characteristic
315	C₂×D₄	—	502	8	no	—
316	C₂×D₄	—	502	4	no	—
317	C₂×D₄	—	251	2	no	—
318	C₂×D₄	—	251	2	no	—
319	C₂×D₄	—	251	2	no	—
320	C₂×D₄	—	251	2	no	—
321	C₂×D₄	—	251	1	no	—
322	C₂×D₄	C₂²×D₂₅₁	1	2	yes	—
323	C₂×D₄	C₂²×D₂₅₁	1	1	yes	characteristic
324	C₂²×C₄	—	502	8	no	—
325	C₂²×C₄	—	502	8	no	—
326	C₂²×C₄	—	251	2	no	—
327	C₂²×C₄	—	251	2	no	—
328	C₂²×C₄	—	251	4	no	—
329	C₂²×C₄	—	251	4	no	—
330	C₂²×C₄	—	251	2	no	—
331	C₂²×C₄	—	251	2	no	—
332	C₂²×C₄	—	251	2	no	—
333	C₂²×C₄	—	251	4	no	—
334	C₂²×C₄	—	251	1	no	—
335	C₂²×C₄	—	251	8	no	—
336	C₂²×C₄	—	251	1	no	—
337	C₂²×C₄	—	251	1	no	—
338	C₂²×C₄	—	251	1	no	—
339	C₂²×C₄	—	251	1	no	—
340	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
341	C₂²×C₄	C₂²×D₂₅₁	1	2	yes	—
342	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
343	C₄⋊C₄	—	251	4	no	—
344	C₄⋊C₄	—	251	2	no	—
345	C₄⋊C₄	—	251	8	no	—
346	C₄⋊C₄	—	251	8	no	—
347	C₄⋊C₄	—	251	8	no	—
348	C₄⋊C₄	C₂²×D₂₅₁	1	2	yes	—
349	C₄⋊C₄	C₂²×D₂₅₁	1	8	yes	—
350	C₂²⋊C₄	—	251	2	no	—
351	C₂²⋊C₄	—	251	8	no	—
352	C₂²⋊C₄	—	251	4	no	—
353	C₂²⋊C₄	—	251	8	no	—
354	C₂²⋊C₄	—	251	8	no	—
355	C₂²⋊C₄	C₂²×D₂₅₁	1	2	yes	—
356	C₂²⋊C₄	C₂²×D₂₅₁	1	8	yes	—
357	C₄²	—	251	2	no	—
358	C₄²	—	251	4	no	—
359	C₄²	C₂²×D₂₅₁	1	2	yes	—
360	C₂³	—	502	4	no	—
361	C₂³	—	502	8	no	—
362	C₂³	—	502	4	no	—
363	C₂³	—	251	2	no	—
364	C₂³	—	251	4	no	—
365	C₂³	—	251	1	no	—
366	C₂³	—	251	1	no	—
367	C₂³	C₂³×D₂₅₁	1	2	yes	—
368	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
369	Q₈	—	2	4	no	—
370	Q₈	—	2	4	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	502	8	no	—
373	Q₈	—	502	8	no	—
374	Q₈	—	502	4	no	—
375	Q₈	—	502	4	no	—
376	Q₈	—	502	4	no	—
377	Q₈	—	502	2	no	—
378	D₄	—	2	4	no	—
379	D₄	—	2	2	no	—
380	D₄	—	502	4	no	—
381	D₄	—	502	4	no	—
382	D₄	—	502	4	no	—
383	D₄	—	502	4	no	—
384	D₄	—	502	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	502	4	no	—
388	C₂×C₄	—	502	8	no	—
389	C₂×C₄	—	502	8	no	—
390	C₂×C₄	—	502	8	no	—
391	C₂×C₄	—	502	4	no	—
392	C₂×C₄	—	502	4	no	—
393	C₂×C₄	—	502	4	no	—
394	C₂×C₄	—	502	4	no	—
395	C₂×C₄	—	251	4	no	—
396	C₂×C₄	—	251	4	no	—
397	C₂×C₄	—	251	2	no	—
398	C₂×C₄	—	251	4	no	—
399	C₂×C₄	—	251	1	no	—
400	C₂×C₄	—	251	1	no	—
401	C₂×C₄	—	251	4	no	—
402	C₂×C₄	—	251	4	no	—
403	C₂×C₄	—	251	4	no	—
404	C₂×C₄	—	251	4	no	—
405	C₂×C₄	D₄×D₂₅₁	1	4	yes	—
406	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
407	C₂×C₄	C₂³×D₂₅₁	1	4	yes	—
408	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
409	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
410	C₂×C₄	C₂³×D₂₅₁	1	1	yes	characteristic
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	1004	8	no	—
415	C₂²	—	502	8	no	—
416	C₂²	—	502	2	no	—
417	C₂²	—	502	4	no	—
418	C₂²	—	502	2	no	—
419	C₂²	—	251	2	no	—
420	C₂²	—	251	2	no	—
421	C₂²	—	251	4	no	—
422	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
423	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	4	no	—
426	C₄	—	2	4	no	—
427	C₄	—	502	2	no	—
428	C₄	—	502	4	no	—
429	C₄	—	502	4	no	—
430	C₄	—	251	2	no	—
431	C₄	—	251	2	no	—
432	C₄	C₂×D₄×D₂₅₁	1	2	yes	—
433	C₄	C₂×D₄×D₂₅₁	1	2	yes	—
434	C₂	—	2	2	no	—
435	C₂	—	4	2	no	—
436	C₂	—	1004	2	no	—
437	C₂	—	502	2	no	—
438	C₂	—	251	4	no	—
439	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic
440	C₂	2₋¹⁺⁴×D₂₅₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₂₅₁
commutator, socle, cosocle	C₂²×C₂₅₁	C₂⁵
Fitting	#536×C₂₅₁	C₂
prime radical	C₂×#41×D₂₅₁	C₂
hypercenter	#536	D₂₅₁
hypocenter	C₂₅₁	C₂×#536
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
2. C₂²×Q₈×D₂₅₁	C₂	semidirect
3. #30632263	C₂	semidirect
4. #30632262	C₂	semidirect
5. #30632261	C₂	semidirect
6. #30632260	C₂	semidirect
7. #30632259	C₂	semidirect
8. #30632258	C₂	semidirect
9. #30632257	C₂	semidirect
10. C₄⋊Q₈×D₂₅₁	C₂	semidirect
11. #124×D₂₅₁	C₂	semidirect
12. #123×D₂₅₁	C₂	semidirect
13. C₂²⋊Q₈×D₂₅₁	C₂	semidirect
14. #117×D₂₅₁	C₂	semidirect
15. #536×C₂₅₁	C₂	semidirect
22. C₂²×Dic₅₀₂	C₂²	semidirect
23. C₂²×Dic₅₀₂	C₂²	semidirect
28. C₂×Q₈×D₂₅₁	C₂²	semidirect
29. C₂×Q₈×D₂₅₁	C₂²	semidirect
35. #22548715	C₂²	semidirect
36. #22548714	C₂²	semidirect
37. #22548713	C₂²	semidirect
38. #22548713	C₂²	semidirect
39. #22548704	C₂²	semidirect
40. #22548703	C₂²	semidirect
41. #22548702	C₂²	semidirect
42. #22548701	C₂²	semidirect
43. #22548700	C₂²	semidirect
44. #22548699	C₂²	semidirect
45. #22548698	C₂²	semidirect
46. #22548697	C₂²	semidirect
47. #22548696	C₂²	semidirect
48. #22548695	C₂²	semidirect
49. #22548694	C₂²	semidirect
50. #22548693	C₂²	semidirect
51. #22548692	C₂²	semidirect
52. #22548691	C₂²	semidirect
53. #22548674	C₂²	semidirect
54. #22548673	C₂²	semidirect
55. #22548672	C₂²	semidirect
56. #22548671	C₂²	semidirect
63. C₂²×Q₈×C₂₅₁	C₂²	semidirect
64. C₄⋊Q₈×C₂₅₁	C₂²	semidirect
65. #124×C₂₅₁	C₂²	semidirect
66. #123×C₂₅₁	C₂²	semidirect
67. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
68. #117×C₂₅₁	C₂²	semidirect
219. D₂₅₁	#536	direct (N × H)
220. C₂₅₁	C₂×#536	semidirect
231. #536	D₂₅₁	direct (N × H)
252. C₂²×Q₈	C₂×D₂₅₁	semidirect
262. C₄⋊Q₈	C₂×D₂₅₁	semidirect
267. #124	C₂×D₂₅₁	semidirect
273. #123	C₂×D₂₅₁	semidirect
279. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
284. #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
C₂×#41×D₂₅₁	2
C₂²×Q₈×D₂₅₁	2
#30632263	2
#30632262	2
#30632261	2
#30632260	2
#30632259	2
#30632258	2
#30632257	2
C₄⋊Q₈×D₂₅₁	2
#124×D₂₅₁	2
#123×D₂₅₁	2
C₂²⋊Q₈×D₂₅₁	2
#117×D₂₅₁	2
#536×C₂₅₁	2
C₂×#536	251

Subgroups — #536×D251 #44563677

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #536×D₂₅₁ #44563677