Subgroups — #3266×C₂₅₁ #44547853

Order 32128.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#137×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₁₆×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#546×C₂₅₁	C₂	1	1	yes	maximal, characteristic
5	#497×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#468×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#467×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#464×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#461×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#452×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#451×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#450×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#448×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#440×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	#435×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₂₅₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
20	#137×C₂₅₁	—	2	4	no	—
21	C₂×Q₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×Q₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×Q₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×SD₁₆×C₂₅₁	—	2	4	no	—
25	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
26	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
27	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
28	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
29	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
30	C₂×SD₁₆×C₂₅₁	C₂²	1	1	yes	characteristic
31	C₂×M₁₆×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₈×C₂₅₁	C₂²	1	1	yes	characteristic
33	C₄⋊Q₈×C₂₅₁	—	2	1	no	—
34	C₄⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
35	#124×C₂₅₁	C₂²	1	1	yes	characteristic
36	#123×C₂₅₁	—	2	1	no	—
37	C₂²⋊Q₈×C₂₅₁	—	2	1	no	—
38	C₂²⋊Q₈×C₂₅₁	—	2	1	no	—
39	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
40	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
41	C₂²⋊Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
42	#121×C₂₅₁	—	2	1	no	—
43	#121×C₂₅₁	C₂²	1	1	yes	characteristic
44	#120×C₂₅₁	—	2	1	no	—
45	C₄×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
46	C₄×D₄×C₂₅₁	—	2	1	no	—
47	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₂₅₁	—	2	1	no	—
50	#107×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
51	C₄⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
52	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
53	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
54	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
55	#103×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
56	#102×C₂₅₁	C₂²	1	1	yes	characteristic
57	#102×C₂₅₁	C₂²	1	1	yes	characteristic
58	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
60	#97×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₂₅₁	—	2	1	no	—
62	#41×C₂₅₁	—	2	2	no	—
63	#41×C₂₅₁	—	4	1	no	—
64	C₂×Q₈×C₂₅₁	—	2	1	no	—
65	C₂×Q₈×C₂₅₁	—	2	1	no	—
66	C₂×Q₈×C₂₅₁	—	2	2	no	—
67	C₂×Q₈×C₂₅₁	—	2	2	no	—
68	C₂×Q₈×C₂₅₁	—	4	1	no	—
69	C₂×Q₈×C₂₅₁	—	4	1	no	—
70	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
71	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
73	C₂×Q₈×C₂₅₁	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₂₅₁	—	2	2	no	—
75	C₂×D₄×C₂₅₁	—	2	1	no	—
76	C₂×D₄×C₂₅₁	—	2	1	no	—
77	C₂×D₄×C₂₅₁	—	2	1	no	—
78	C₂×D₄×C₂₅₁	—	4	1	no	—
79	C₂×D₄×C₂₅₁	D₄	1	1	yes	characteristic
80	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
81	C₂×D₄×C₂₅₁	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₂₅₁	—	2	1	no	—
83	C₂²×C₄×C₂₅₁	—	2	1	no	—
84	C₂²×C₄×C₂₅₁	—	2	1	no	—
85	C₂²×C₄×C₂₅₁	—	2	1	no	—
86	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
88	Q₁₆×C₂₅₁	—	2	2	no	—
89	Q₁₆×C₂₅₁	—	2	2	no	—
90	Q₁₆×C₂₅₁	—	4	1	no	—
91	SD₁₆×C₂₅₁	—	2	2	no	—
92	SD₁₆×C₂₅₁	—	2	2	no	—
93	SD₁₆×C₂₅₁	—	2	2	no	—
94	SD₁₆×C₂₅₁	—	2	2	no	—
95	SD₁₆×C₂₅₁	—	4	1	no	—
96	SD₁₆×C₂₅₁	D₄	1	4	yes	complemented
97	M₁₆×C₂₅₁	—	2	2	no	—
98	C₂×C₈×C₂₅₁	—	2	2	no	—
99	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
100	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
101	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₂₅₁	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₂₅₁	—	2	1	no	—
104	C₄⋊C₄×C₂₅₁	—	2	1	no	—
105	C₄⋊C₄×C₂₅₁	—	2	1	no	—
106	C₄⋊C₄×C₂₅₁	—	2	1	no	—
107	C₄⋊C₄×C₂₅₁	—	2	1	no	—
108	C₄⋊C₄×C₂₅₁	—	2	1	no	—
109	C₄⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
110	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
111	C₄⋊C₄×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
113	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
114	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
115	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
116	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
117	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
118	C₂²⋊C₄×C₂₅₁	—	2	1	no	—
119	C₂²⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
120	C₂²⋊C₄×C₂₅₁	D₄	1	1	yes	characteristic
121	C₄²×C₂₅₁	—	2	1	no	—
122	C₄²×C₂₅₁	C₂³	1	1	yes	characteristic
123	C₂³×C₂₅₁	—	2	1	no	—
124	C₂³×C₂₅₁	—	2	1	no	—
125	C₂³×C₂₅₁	—	4	2	no	—
126	C₂³×C₂₅₁	—	4	2	no	—
127	C₂³×C₂₅₁	—	8	1	no	—
128	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
129	C₂³×C₂₅₁	C₂×D₄	1	1	yes	characteristic
130	Q₈×C₂₅₁	—	2	1	no	—
131	Q₈×C₂₅₁	—	2	1	no	—
132	Q₈×C₂₅₁	—	2	1	no	—
133	Q₈×C₂₅₁	—	2	1	no	—
134	Q₈×C₂₅₁	—	2	1	no	—
135	Q₈×C₂₅₁	—	2	1	no	—
136	Q₈×C₂₅₁	—	2	1	no	—
137	Q₈×C₂₅₁	—	4	2	no	—
138	Q₈×C₂₅₁	—	4	2	no	—
139	Q₈×C₂₅₁	C₂×D₄	1	2	yes	—
140	D₄×C₂₅₁	—	2	2	no	—
141	D₄×C₂₅₁	—	2	1	no	—
142	D₄×C₂₅₁	—	2	1	no	—
143	D₄×C₂₅₁	—	2	1	no	—
144	D₄×C₂₅₁	—	4	2	no	—
145	D₄×C₂₅₁	—	4	2	no	—
146	D₄×C₂₅₁	—	8	1	no	—
147	D₄×C₂₅₁	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₂₅₁	—	2	1	no	—
149	C₂×C₄×C₂₅₁	—	2	1	no	—
150	C₂×C₄×C₂₅₁	—	2	1	no	—
151	C₂×C₄×C₂₅₁	—	2	1	no	—
152	C₂×C₄×C₂₅₁	—	2	1	no	—
153	C₂×C₄×C₂₅₁	—	2	1	no	—
154	C₂×C₄×C₂₅₁	—	2	1	no	—
155	C₂×C₄×C₂₅₁	—	2	1	no	—
156	C₂×C₄×C₂₅₁	—	2	1	no	—
157	C₂×C₄×C₂₅₁	—	2	1	no	—
158	C₂×C₄×C₂₅₁	—	4	2	no	—
159	C₂×C₄×C₂₅₁	—	4	2	no	—
160	C₂×C₄×C₂₅₁	—	4	2	no	—
161	C₂×C₄×C₂₅₁	—	8	1	no	—
162	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×C₂₅₁	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×C₂₅₁	C₂⁴	1	1	yes	characteristic
167	C₈×C₂₅₁	—	2	1	no	—
168	C₈×C₂₅₁	—	2	1	no	—
169	C₈×C₂₅₁	—	2	1	no	—
170	C₈×C₂₅₁	C₂×D₄	1	2	yes	—
171	C₂²×C₂₅₁	—	2	1	no	—
172	C₂²×C₂₅₁	—	2	1	no	—
173	C₂²×C₂₅₁	—	2	1	no	—
174	C₂²×C₂₅₁	—	2	2	no	—
175	C₂²×C₂₅₁	—	2	1	no	—
176	C₂²×C₂₅₁	—	2	1	no	—
177	C₂²×C₂₅₁	—	4	1	no	—
178	C₂²×C₂₅₁	—	4	1	no	—
179	C₂²×C₂₅₁	—	4	1	no	—
180	C₂²×C₂₅₁	—	4	1	no	—
181	C₂²×C₂₅₁	—	4	1	no	—
182	C₂²×C₂₅₁	—	8	4	no	—
183	C₂²×C₂₅₁	#137	1	2	yes	complemented
184	C₂²×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
185	C₄×C₂₅₁	—	2	1	no	—
186	C₄×C₂₅₁	—	2	1	no	—
187	C₄×C₂₅₁	—	2	2	no	—
188	C₄×C₂₅₁	—	2	1	no	—
189	C₄×C₂₅₁	—	2	1	no	—
190	C₄×C₂₅₁	—	4	1	no	—
191	C₄×C₂₅₁	—	4	1	no	—
192	C₄×C₂₅₁	—	4	1	no	—
193	C₄×C₂₅₁	—	4	1	no	—
194	C₄×C₂₅₁	—	4	1	no	—
195	C₄×C₂₅₁	C₂²×D₄	1	1	yes	characteristic
196	C₄×C₂₅₁	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₂₅₁	—	2	2	no	—
198	C₂×C₂₅₁	—	4	1	no	—
199	C₂×C₂₅₁	—	4	2	no	—
200	C₂×C₂₅₁	—	8	1	no	—
201	C₂×C₂₅₁	D₄²	1	1	yes	characteristic
202	C₂×C₂₅₁	C₂×#137	1	1	yes	characteristic
203	C₂×C₂₅₁	#577	1	1	yes	characteristic
204	C₂₅₁	#3266	1	1	yes	characteristic, direct product factor, Sylow
205	#3266	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×#137	C₂×C₂₅₁	1	1	yes	characteristic, complemented
207	C₂²×SD₁₆	C₂×C₂₅₁	1	1	yes	characteristic, complemented
208	D₄×Q₈	C₂×C₂₅₁	1	1	yes	characteristic, complemented
209	#546	C₂×C₂₅₁	1	1	yes	characteristic
210	#497	C₂×C₂₅₁	1	1	yes	characteristic, complemented
211	#468	C₂×C₂₅₁	1	1	yes	characteristic, complemented
212	#467	C₂×C₂₅₁	1	1	yes	characteristic, complemented
213	#464	C₂×C₂₅₁	1	1	yes	characteristic, complemented
214	#461	C₂×C₂₅₁	1	1	yes	characteristic, complemented
215	#452	C₂×C₂₅₁	1	1	yes	characteristic, complemented
216	#451	C₂×C₂₅₁	1	1	yes	characteristic, complemented
217	#450	C₂×C₂₅₁	1	1	yes	characteristic, complemented
218	#448	C₂×C₂₅₁	1	1	yes	characteristic, complemented
219	#440	C₂×C₂₅₁	1	1	yes	characteristic, complemented
220	#435	C₂×C₂₅₁	1	1	yes	characteristic, complemented
221	C₂×#41	C₂²×C₂₅₁	1	1	yes	characteristic
222	C₂²×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
223	C₂²×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
224	C₂²×D₄	C₂²×C₂₅₁	1	1	yes	characteristic
225	#137	—	2	4	no	—
226	C₂×Q₁₆	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
227	C₂×Q₁₆	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
228	C₂×Q₁₆	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	2	4	no	—
230	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
231	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
232	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
233	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
234	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
235	C₂×SD₁₆	C₂²×C₂₅₁	1	1	yes	characteristic
236	C₂×M₁₆	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
237	C₂²×C₈	C₂²×C₂₅₁	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
240	#124	C₂²×C₂₅₁	1	1	yes	characteristic
241	#123	—	2	1	no	—
242	C₂²⋊Q₈	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
245	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic
246	C₂²⋊Q₈	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
247	#121	—	2	1	no	—
248	#121	C₂²×C₂₅₁	1	1	yes	characteristic
249	#120	—	2	1	no	—
250	C₄×Q₈	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	C₂²×C₂₅₁	1	1	yes	characteristic
253	C₄×D₄	C₂²×C₂₅₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	#107	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
256	C₄⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
257	#103	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
258	#103	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
259	#103	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
260	#103	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
261	#102	C₂²×C₂₅₁	1	1	yes	characteristic
262	#102	C₂²×C₂₅₁	1	1	yes	characteristic
263	C₂²⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic
264	C₂²⋊C₈	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
265	#97	C₂²×C₂₅₁	1	1	yes	characteristic, complemented
266	C₂⁴	—	2	1	no	—
267	#41	—	2	2	no	—
268	#41	—	4	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	4	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
276	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
277	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
278	C₂×Q₈	C₂³×C₂₅₁	1	1	yes	characteristic
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	1	no	—
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	D₄×C₂₅₁	1	1	yes	characteristic
285	C₂×D₄	C₂³×C₂₅₁	1	1	yes	characteristic
286	C₂×D₄	C₂³×C₂₅₁	1	1	yes	characteristic
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	C₂³×C₂₅₁	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₂₅₁	1	1	yes	characteristic
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	2	2	no	—
295	Q₁₆	—	4	1	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	2	2	no	—
298	SD₁₆	—	2	2	no	—
299	SD₁₆	—	2	2	no	—
300	SD₁₆	—	4	1	no	—
301	SD₁₆	D₄×C₂₅₁	1	4	yes	complemented
302	M₁₆	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
305	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
306	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
307	C₂×C₈	C₂³×C₂₅₁	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
315	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
316	C₄⋊C₄	C₂³×C₂₅₁	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₂²⋊C₄	—	2	1	no	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
325	C₂²⋊C₄	D₄×C₂₅₁	1	1	yes	characteristic
326	C₄²	—	2	1	no	—
327	C₄²	C₂³×C₂₅₁	1	1	yes	characteristic
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	8	1	no	—
333	C₂³	C₂×D₄×C₂₅₁	1	1	yes	characteristic
334	C₂³	C₂×D₄×C₂₅₁	1	1	yes	characteristic
335	Q₈	—	2	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	2	1	no	—
340	Q₈	—	2	1	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	C₂×D₄×C₂₅₁	1	2	yes	—
345	D₄	—	2	2	no	—
346	D₄	—	2	1	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	8	1	no	—
352	D₄	C₂×D₄×C₂₅₁	1	2	yes	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	8	1	no	—
367	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
369	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
370	C₂×C₄	C₂×D₄×C₂₅₁	1	1	yes	characteristic
371	C₂×C₄	C₂⁴×C₂₅₁	1	1	yes	characteristic
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	C₂×D₄×C₂₅₁	1	2	yes	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	8	4	no	—
388	C₂²	#137×C₂₅₁	1	2	yes	complemented
389	C₂²	C₂²×D₄×C₂₅₁	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	C₂²×D₄×C₂₅₁	1	1	yes	characteristic
401	C₄	H(5,𝔽₂)×C₂₅₁	1	1	yes	characteristic
402	C₂	—	2	2	no	—
403	C₂	—	4	1	no	—
404	C₂	—	4	2	no	—
405	C₂	—	8	1	no	—
406	C₂	D₄²×C₂₅₁	1	1	yes	characteristic
407	C₂	C₂×#137×C₂₅₁	1	1	yes	characteristic
408	C₂	#577×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₅₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₅₁
prime radical	#546×C₂₅₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₅₁ ◁ C₄×D₄×C₂₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#137×C₂₅₁	C₂	semidirect
2. C₂²×SD₁₆×C₂₅₁	C₂	semidirect
3. D₄×Q₈×C₂₅₁	C₂	semidirect
5. #497×C₂₅₁	C₂	semidirect
6. #468×C₂₅₁	C₂	semidirect
7. #467×C₂₅₁	C₂	semidirect
8. #464×C₂₅₁	C₂	semidirect
9. #461×C₂₅₁	C₂	semidirect
10. #452×C₂₅₁	C₂	semidirect
11. #451×C₂₅₁	C₂	semidirect
12. #450×C₂₅₁	C₂	semidirect
13. #448×C₂₅₁	C₂	semidirect
14. #440×C₂₅₁	C₂	semidirect
15. #435×C₂₅₁	C₂	semidirect
18. C₂²×Q₈×C₂₅₁	C₂²	semidirect
21. C₂×Q₁₆×C₂₅₁	C₂²	semidirect
22. C₂×Q₁₆×C₂₅₁	C₂²	semidirect
23. C₂×Q₁₆×C₂₅₁	C₂²	semidirect
31. C₂×M₁₆×C₂₅₁	C₂²	semidirect
34. C₄⋊Q₈×C₂₅₁	C₂²	semidirect
41. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
45. C₄×Q₈×C₂₅₁	C₂²	semidirect
50. #107×C₂₅₁	C₂²	semidirect
51. C₄⋊C₈×C₂₅₁	C₂²	semidirect
52. #103×C₂₅₁	C₂²	semidirect
53. #103×C₂₅₁	C₂²	semidirect
54. #103×C₂₅₁	C₂²	semidirect
55. #103×C₂₅₁	C₂²	semidirect
59. C₂²⋊C₈×C₂₅₁	C₂²	semidirect
60. #97×C₂₅₁	C₂²	semidirect
96. SD₁₆×C₂₅₁	D₄	semidirect
183. C₂²×C₂₅₁	#137	semidirect
204. C₂₅₁	#3266	direct (N × H)
205. #3266	C₂₅₁	direct (N × H)
206. C₂×#137	C₂×C₂₅₁	semidirect
207. C₂²×SD₁₆	C₂×C₂₅₁	semidirect
208. D₄×Q₈	C₂×C₂₅₁	semidirect
210. #497	C₂×C₂₅₁	semidirect
211. #468	C₂×C₂₅₁	semidirect
212. #467	C₂×C₂₅₁	semidirect
213. #464	C₂×C₂₅₁	semidirect
214. #461	C₂×C₂₅₁	semidirect
215. #452	C₂×C₂₅₁	semidirect
216. #451	C₂×C₂₅₁	semidirect
217. #450	C₂×C₂₅₁	semidirect
218. #448	C₂×C₂₅₁	semidirect
219. #440	C₂×C₂₅₁	semidirect
220. #435	C₂×C₂₅₁	semidirect
223. C₂²×Q₈	C₂²×C₂₅₁	semidirect
226. C₂×Q₁₆	C₂²×C₂₅₁	semidirect
227. C₂×Q₁₆	C₂²×C₂₅₁	semidirect
228. C₂×Q₁₆	C₂²×C₂₅₁	semidirect
236. C₂×M₁₆	C₂²×C₂₅₁	semidirect
239. C₄⋊Q₈	C₂²×C₂₅₁	semidirect
246. C₂²⋊Q₈	C₂²×C₂₅₁	semidirect
250. C₄×Q₈	C₂²×C₂₅₁	semidirect
255. #107	C₂²×C₂₅₁	semidirect
256. C₄⋊C₈	C₂²×C₂₅₁	semidirect
257. #103	C₂²×C₂₅₁	semidirect
258. #103	C₂²×C₂₅₁	semidirect
259. #103	C₂²×C₂₅₁	semidirect
260. #103	C₂²×C₂₅₁	semidirect
264. C₂²⋊C₈	C₂²×C₂₅₁	semidirect
265. #97	C₂²×C₂₅₁	semidirect
301. SD₁₆	D₄×C₂₅₁	semidirect
388. C₂²	#137×C₂₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#137×C₂₅₁	2
C₂²×SD₁₆×C₂₅₁	2
D₄×Q₈×C₂₅₁	2
#546×C₂₅₁	2
#497×C₂₅₁	2
#468×C₂₅₁	2
#467×C₂₅₁	2
#464×C₂₅₁	2
#461×C₂₅₁	2
#452×C₂₅₁	2
#451×C₂₅₁	2
#450×C₂₅₁	2
#448×C₂₅₁	2
#440×C₂₅₁	2
#435×C₂₅₁	2
#3266	251

Subgroups — #3266×C251 #44547853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3266×C₂₅₁ #44547853