Subgroups — C₂×#30632324 #44563807

Order 32128.

1900 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#16860809	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#30632324	C₂	1	16	yes	maximal, direct product factor
4	C₂×#22548701	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22548699	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22548687	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22548687	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#22548686	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#22548683	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₄×Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×(C₂²⋊D₂₅₁)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₂²⋊Dic₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊C₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#120×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₂₅₁	C₂²	1	1	yes	characteristic
18	C₂×#16860809	—	2	8	no	—
19	C₂×#16860809	C₂²	1	8	yes	complemented
20	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₂₅₁	—	2	8	no	—
22	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₂₅₁	C₂²	1	8	yes	complemented
27	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic, complemented
29	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic
30	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
31	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
32	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic, complemented
35	#22548701	C₂²	1	8	yes	complemented
36	#22548699	C₂²	1	8	yes	complemented
37	#22548697	C₂²	1	8	yes	complemented
38	#22548692	C₂²	1	8	yes	complemented
39	#22548687	C₂²	1	8	yes	complemented
40	#22548687	C₂²	1	8	yes	complemented
41	#22548686	C₂²	1	8	yes	complemented
42	#22548683	C₂²	1	8	yes	complemented
43	D₄×Dic₂₅₁	C₂²	1	8	yes	complemented
44	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	8	yes	complemented
45	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
47	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₂₅₁	C₂²	1	8	yes	complemented
52	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
55	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊C₄×D₂₅₁	C₂²	1	8	yes	complemented
60	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₂₅₁	C₂²	1	1	yes	characteristic
62	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
64	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
65	#120×C₂₅₁	C₂²	1	8	yes	complemented
66	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₂₅₁	—	2	4	no	—
70	C₂³×D₂₅₁	—	2	4	no	—
71	C₂³×D₂₅₁	—	4	2	no	—
72	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
73	C₂³×D₂₅₁	C₂³	1	4	yes	—
74	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
75	#16860809	—	2	32	no	—
76	C₂×Dic₅₀₂	—	2	4	no	—
77	C₂×Dic₅₀₂	C₂³	1	4	yes	complemented
78	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
79	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
80	C₂×C₂²⋊D₂₅₁	—	2	32	no	—
81	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
82	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
83	C₂×C₂²⋊D₂₅₁	—	4	2	no	—
84	C₂×C₂²⋊D₂₅₁	D₄	1	8	yes	complemented
85	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	complemented
90	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	complemented
91	C₂²×Dic₂₅₁	—	2	4	no	—
92	C₂²×Dic₂₅₁	—	2	4	no	—
93	C₂²×Dic₂₅₁	—	2	4	no	—
94	C₂²×Dic₂₅₁	—	4	2	no	—
95	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
96	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
97	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
98	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
99	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
100	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
101	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
102	C₂²×Dic₂₅₁	C₂³	1	4	yes	complemented
103	C₂²×Dic₂₅₁	C₂³	1	4	yes	complemented
104	C₂²×Dic₂₅₁	C₂³	1	4	yes	complemented
105	C₂×C₄×D₂₅₁	—	2	4	no	—
106	C₂×C₄×D₂₅₁	—	4	2	no	—
107	C₂×C₄×D₂₅₁	C₂³	1	4	yes	complemented
108	C₂×C₄×D₂₅₁	C₂³	1	4	yes	complemented
109	C₄⋊Dic₂₅₁	C₂³	1	4	yes	complemented
110	C₄⋊Dic₂₅₁	C₂³	1	4	yes	complemented
111	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
112	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
113	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
114	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
115	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
116	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
117	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
118	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	complemented
119	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	complemented
120	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	complemented
121	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	complemented
122	C₄×Dic₂₅₁	C₂³	1	4	yes	complemented
123	C₂⁴×C₂₅₁	—	2	4	no	—
124	C₂⁴×C₂₅₁	—	2	4	no	—
125	C₂⁴×C₂₅₁	—	4	2	no	—
126	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
127	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
128	C₂⁴×C₂₅₁	C₂³	1	4	yes	—
129	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
130	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₂₅₁	—	2	4	no	—
132	C₂×D₄×C₂₅₁	—	2	4	no	—
133	C₂×D₄×C₂₅₁	—	4	2	no	—
134	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
135	C₂×D₄×C₂₅₁	C₂³	1	4	yes	complemented
136	C₂×D₄×C₂₅₁	C₂³	1	4	yes	complemented
137	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
140	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
141	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	complemented
142	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	complemented
143	C₂²×D₂₅₁	—	2	2	no	—
144	C₂²×D₂₅₁	—	2	2	no	—
145	C₂²×D₂₅₁	—	2	2	no	—
146	C₂²×D₂₅₁	—	2	2	no	—
147	C₂²×D₂₅₁	—	2	8	no	—
148	C₂²×D₂₅₁	—	2	2	no	—
149	C₂²×D₂₅₁	—	2	8	no	—
150	C₂²×D₂₅₁	—	4	4	no	—
151	C₂²×D₂₅₁	—	4	16	no	—
152	C₂²×D₂₅₁	C₂×D₄	1	4	yes	—
153	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
154	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
155	Dic₅₀₂	—	2	8	no	—
156	C₂²⋊D₂₅₁	—	2	8	no	—
157	C₂²⋊D₂₅₁	—	2	8	no	—
158	C₂²⋊D₂₅₁	—	2	8	no	—
159	C₂²⋊D₂₅₁	—	2	8	no	—
160	C₂²⋊D₂₅₁	—	4	4	no	—
161	C₂²⋊D₂₅₁	C₂×D₄	1	16	yes	complemented
162	C₂×Dic₂₅₁	—	2	2	no	—
163	C₂×Dic₂₅₁	—	2	2	no	—
164	C₂×Dic₂₅₁	—	2	2	no	—
165	C₂×Dic₂₅₁	—	2	8	no	—
166	C₂×Dic₂₅₁	—	2	2	no	—
167	C₂×Dic₂₅₁	—	2	2	no	—
168	C₂×Dic₂₅₁	—	2	8	no	—
169	C₂×Dic₂₅₁	—	2	8	no	—
170	C₂×Dic₂₅₁	—	4	4	no	—
171	C₂×Dic₂₅₁	C₂×D₄	1	4	yes	—
172	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
173	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
174	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
175	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
176	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
177	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
178	C₄×D₂₅₁	—	2	8	no	—
179	C₄×D₂₅₁	—	4	4	no	—
180	C₂³×C₂₅₁	—	2	2	no	—
181	C₂³×C₂₅₁	—	2	2	no	—
182	C₂³×C₂₅₁	—	2	2	no	—
183	C₂³×C₂₅₁	—	2	2	no	—
184	C₂³×C₂₅₁	—	2	2	no	—
185	C₂³×C₂₅₁	—	2	8	no	—
186	C₂³×C₂₅₁	—	2	2	no	—
187	C₂³×C₂₅₁	—	2	2	no	—
188	C₂³×C₂₅₁	—	2	2	no	—
189	C₂³×C₂₅₁	—	2	8	no	—
190	C₂³×C₂₅₁	—	2	2	no	—
191	C₂³×C₂₅₁	—	2	2	no	—
192	C₂³×C₂₅₁	—	4	4	no	—
193	C₂³×C₂₅₁	—	4	16	no	—
194	C₂³×C₂₅₁	C₂×D₄	1	4	yes	—
195	C₂³×C₂₅₁	#41	1	4	yes	complemented
196	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
197	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
198	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
199	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
200	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
201	D₄×C₂₅₁	—	2	8	no	—
202	D₄×C₂₅₁	—	2	8	no	—
203	D₄×C₂₅₁	—	4	4	no	—
204	C₂×C₄×C₂₅₁	—	2	2	no	—
205	C₂×C₄×C₂₅₁	—	2	2	no	—
206	C₂×C₄×C₂₅₁	—	2	2	no	—
207	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
208	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
209	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
210	C₂²×C₂₅₁	—	2	8	no	—
211	C₂²×C₂₅₁	—	2	8	no	—
212	C₂²×C₂₅₁	—	2	2	no	—
213	C₂²×C₂₅₁	—	2	2	no	—
214	C₂²×C₂₅₁	—	2	2	no	—
215	C₂²×C₂₅₁	—	2	2	no	—
216	C₂²×C₂₅₁	—	2	2	no	—
217	C₂²×C₂₅₁	—	2	2	no	—
218	C₂²×C₂₅₁	—	2	2	no	—
219	C₂²×C₂₅₁	—	2	2	no	—
220	C₂²×C₂₅₁	—	2	2	no	—
221	C₂²×C₂₅₁	—	2	2	no	—
222	C₂²×C₂₅₁	—	4	16	no	—
223	C₂²×C₂₅₁	—	4	4	no	—
224	C₂²×C₂₅₁	—	4	4	no	—
225	C₂²×C₂₅₁	C₂²×D₄	1	4	yes	—
226	C₂²×C₂₅₁	C₂²×D₄	1	2	yes	—
227	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
228	C₂²×C₂₅₁	C₂×#41	1	4	yes	complemented
229	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
230	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
231	C₂×D₂₅₁	—	2	8	no	—
232	C₂×D₂₅₁	—	2	2	no	—
233	C₂×D₂₅₁	—	2	2	no	—
234	C₂×D₂₅₁	—	2	2	no	—
235	C₂×D₂₅₁	—	2	2	no	—
236	C₂×D₂₅₁	—	2	2	no	—
237	C₂×D₂₅₁	—	4	16	no	—
238	C₂×D₂₅₁	—	4	4	no	—
239	C₂×D₂₅₁	C₂²×D₄	1	4	yes	—
240	C₄×C₂₅₁	—	2	2	no	—
241	C₄×C₂₅₁	—	2	2	no	—
242	C₄×C₂₅₁	—	2	2	no	—
243	Dic₂₅₁	—	2	2	no	—
244	Dic₂₅₁	—	2	2	no	—
245	Dic₂₅₁	—	2	2	no	—
246	Dic₂₅₁	—	2	2	no	—
247	Dic₂₅₁	—	2	2	no	—
248	Dic₂₅₁	C₂²×D₄	1	4	yes	—
249	C₂×C₂₅₁	—	2	4	no	—
250	C₂×C₂₅₁	—	2	4	no	—
251	C₂×C₂₅₁	—	4	2	no	—
252	C₂×C₂₅₁	—	4	2	no	—
253	C₂×C₂₅₁	#546	1	4	yes	complemented
254	C₂×C₂₅₁	C₂³×D₄	1	1	yes	characteristic
255	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
256	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
257	D₂₅₁	—	2	4	no	—
258	D₂₅₁	—	4	2	no	—
259	C₂₅₁	C₂×#546	1	1	yes	characteristic, complemented, Sylow
260	C₂×#546	—	251	1	no	maximal, Sylow
261	C₂²×#41	—	251	1	no	—
262	C₂³×D₄	—	251	1	no	—
263	#546	—	251	16	no	—
264	C₂×#124	—	251	1	no	—
265	C₂×#123	—	251	1	no	—
266	C₂×#123	—	251	1	no	—
267	C₂×C₂²⋊Q₈	—	251	1	no	—
268	C₂×#121	—	251	1	no	—
269	C₂×#121	—	251	1	no	—
270	C₂×#121	—	251	1	no	—
271	C₂×#120	—	251	1	no	—
272	C₂×#120	D₂₅₁	1	1	yes	characteristic, complemented
273	C₂×C₄×D₄	—	251	1	no	—
274	C₂×C₄×D₄	—	251	1	no	—
275	C₂²×C₂²⋊C₄	—	251	1	no	—
276	C₂²×C₂²⋊C₄	—	251	1	no	—
277	C₂⁵	—	251	1	no	—
278	C₂⁵	C₂×D₂₅₁	1	1	yes	characteristic
279	C₂×#41	—	502	8	no	—
280	C₂×#41	—	251	8	no	—
281	C₂²×Q₈	—	251	1	no	—
282	C₂²×D₄	—	502	8	no	—
283	C₂²×D₄	—	251	1	no	—
284	C₂²×D₄	—	251	1	no	—
285	C₂²×D₄	—	251	1	no	—
286	C₂²×D₄	—	251	1	no	—
287	C₂²×D₄	—	251	1	no	—
288	C₂²×D₄	—	251	8	no	—
289	C₂²×D₄	—	251	1	no	—
290	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
291	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
292	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
293	C₂³×C₄	—	251	1	no	—
294	C₂³×C₄	—	251	1	no	—
295	C₂³×C₄	—	251	1	no	—
296	C₂³×C₄	—	251	1	no	—
297	C₂³×C₄	—	251	1	no	—
298	C₂³×C₄	—	251	1	no	—
299	#124	—	251	8	no	—
300	#123	—	251	8	no	—
301	#123	—	251	8	no	—
302	C₂²⋊Q₈	—	251	8	no	—
303	#121	—	251	8	no	—
304	#121	—	251	8	no	—
305	#121	—	251	8	no	—
306	#120	—	251	8	no	—
307	#120	C₂×D₂₅₁	1	8	yes	complemented
308	C₄×D₄	—	251	8	no	—
309	C₄×D₄	—	251	8	no	—
310	C₂×C₄⋊C₄	—	251	1	no	—
311	C₂×C₄⋊C₄	—	251	1	no	—
312	C₂×C₄⋊C₄	—	251	1	no	—
313	C₂×C₄⋊C₄	—	251	1	no	—
314	C₂×C₂²⋊C₄	—	251	1	no	—
315	C₂×C₂²⋊C₄	—	251	1	no	—
316	C₂×C₂²⋊C₄	—	251	1	no	—
317	C₂×C₂²⋊C₄	—	251	1	no	—
318	C₂×C₂²⋊C₄	—	251	8	no	—
319	C₂×C₂²⋊C₄	—	251	1	no	—
320	C₂×C₂²⋊C₄	—	251	1	no	—
321	C₂×C₂²⋊C₄	—	251	1	no	—
322	C₂×C₂²⋊C₄	—	251	1	no	—
323	C₂×C₂²⋊C₄	—	251	1	no	—
324	C₂×C₂²⋊C₄	—	251	8	no	—
325	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
327	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
328	C₂×C₄²	—	251	1	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	4	2	no	—
332	C₂⁴	—	1004	2	no	—
333	C₂⁴	—	502	4	no	—
334	C₂⁴	—	502	4	no	—
335	C₂⁴	—	251	4	no	—
336	C₂⁴	—	251	1	no	—
337	C₂⁴	—	251	1	no	—
338	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
339	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
340	C₂⁴	C₂²×D₂₅₁	1	4	yes	—
341	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
342	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
343	#41	—	502	32	no	—
344	C₂×Q₈	—	502	4	no	—
345	C₂×Q₈	—	251	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	1004	2	no	—
350	C₂×D₄	—	502	4	no	—
351	C₂×D₄	—	502	4	no	—
352	C₂×D₄	—	502	4	no	—
353	C₂×D₄	—	502	32	no	—
354	C₂×D₄	—	502	4	no	—
355	C₂×D₄	—	251	4	no	—
356	C₂×D₄	—	251	4	no	—
357	C₂×D₄	—	251	4	no	—
358	C₂×D₄	—	251	4	no	—
359	C₂×D₄	—	251	4	no	—
360	C₂×D₄	—	251	8	no	—
361	C₂×D₄	—	251	4	no	—
362	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
363	C₂×D₄	C₂²×D₂₅₁	1	4	yes	complemented
364	C₂×D₄	C₂²×D₂₅₁	1	4	yes	complemented
365	C₂²×C₄	—	1004	2	no	—
366	C₂²×C₄	—	1004	2	no	—
367	C₂²×C₄	—	502	4	no	—
368	C₂²×C₄	—	502	4	no	—
369	C₂²×C₄	—	502	4	no	—
370	C₂²×C₄	—	502	4	no	—
371	C₂²×C₄	—	251	4	no	—
372	C₂²×C₄	—	251	4	no	—
373	C₂²×C₄	—	251	4	no	—
374	C₂²×C₄	—	251	4	no	—
375	C₂²×C₄	—	251	4	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	—	251	4	no	—
382	C₂²×C₄	—	251	1	no	—
383	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
384	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
385	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
386	C₄⋊C₄	—	251	4	no	—
387	C₄⋊C₄	—	251	4	no	—
388	C₄⋊C₄	—	251	4	no	—
389	C₄⋊C₄	—	251	4	no	—
390	C₂²⋊C₄	—	251	4	no	—
391	C₂²⋊C₄	—	251	4	no	—
392	C₂²⋊C₄	—	251	4	no	—
393	C₂²⋊C₄	—	251	4	no	—
394	C₂²⋊C₄	—	251	4	no	—
395	C₂²⋊C₄	—	251	4	no	—
396	C₂²⋊C₄	—	251	4	no	—
397	C₂²⋊C₄	—	251	4	no	—
398	C₂²⋊C₄	—	251	4	no	—
399	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
400	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	complemented
401	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	complemented
402	C₄²	—	251	4	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	8	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	16	no	—
417	C₂³	—	1004	16	no	—
418	C₂³	—	1004	4	no	—
419	C₂³	—	502	8	no	—
420	C₂³	—	502	2	no	—
421	C₂³	—	502	2	no	—
422	C₂³	—	502	8	no	—
423	C₂³	—	502	2	no	—
424	C₂³	—	502	2	no	—
425	C₂³	—	502	2	no	—
426	C₂³	—	251	2	no	—
427	C₂³	—	251	4	no	—
428	C₂³	—	251	2	no	—
429	C₂³	D₄×D₂₅₁	1	4	yes	—
430	C₂³	#16860809	1	4	yes	complemented
431	C₂³	C₂³×D₂₅₁	1	2	yes	—
432	C₂³	C₂³×D₂₅₁	1	2	yes	—
433	C₂³	C₂³×D₂₅₁	1	2	yes	—
434	C₂³	C₂³×D₂₅₁	1	2	yes	—
435	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
436	Q₈	—	502	8	no	—
437	D₄	—	2	8	no	—
438	D₄	—	2	8	no	—
439	D₄	—	4	4	no	—
440	D₄	—	1004	4	no	—
441	D₄	—	502	8	no	—
442	D₄	—	502	8	no	—
443	D₄	—	502	8	no	—
444	D₄	—	502	8	no	—
445	D₄	—	251	16	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	1004	4	no	—
450	C₂×C₄	—	1004	4	no	—
451	C₂×C₄	—	502	8	no	—
452	C₂×C₄	—	502	2	no	—
453	C₂×C₄	—	502	2	no	—
454	C₂×C₄	—	502	2	no	—
455	C₂×C₄	—	502	8	no	—
456	C₂×C₄	—	502	2	no	—
457	C₂×C₄	—	502	2	no	—
458	C₂×C₄	—	502	8	no	—
459	C₂×C₄	—	502	8	no	—
460	C₂×C₄	—	251	2	no	—
461	C₂×C₄	—	251	2	no	—
462	C₂×C₄	—	251	2	no	—
463	C₂×C₄	—	251	2	no	—
464	C₂×C₄	—	251	2	no	—
465	C₂×C₄	—	251	4	no	—
466	C₂×C₄	—	251	2	no	—
467	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
468	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
469	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	16	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	1004	16	no	—
486	C₂²	—	1004	4	no	—
487	C₂²	—	502	2	no	—
488	C₂²	—	502	2	no	—
489	C₂²	—	502	2	no	—
490	C₂²	—	502	2	no	—
491	C₂²	—	502	2	no	—
492	C₂²	—	502	8	no	—
493	C₂²	—	251	4	no	—
494	C₂²	C₂×D₄×D₂₅₁	1	4	yes	—
495	C₂²	C₂×D₄×D₂₅₁	1	2	yes	—
496	C₂²	C₂×#16860809	1	2	yes	—
497	C₂²	C₂×#16860809	1	4	yes	complemented
498	C₂²	#22548760	1	2	yes	—
499	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	502	2	no	—
504	C₄	—	502	2	no	—
505	C₄	—	502	2	no	—
506	C₄	—	502	2	no	—
507	C₄	—	502	2	no	—
508	C₄	—	251	4	no	—
509	C₂	—	2	4	no	—
510	C₂	—	2	4	no	—
511	C₂	—	4	2	no	—
512	C₂	—	4	2	no	—
513	C₂	—	1004	2	no	—
514	C₂	—	502	4	no	—
515	C₂	#30632324	1	4	yes	direct product factor
516	C₂	C₂²×D₄×D₂₅₁	1	1	yes	characteristic
517	C₂	C₂²×#16860809	1	1	yes	characteristic
518	C₂	C₂×#22548760	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂×#120×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
hypercenter	C₂×#120	D₂₅₁
hypocenter	C₂₅₁	C₂×#546
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×#16860809	C₂	semidirect
2. C₂³×C₂²⋊D₂₅₁	C₂	semidirect
3. #30632324	C₂	direct (N × H)
4. C₂×#22548701	C₂	semidirect
5. C₂×#22548699	C₂	semidirect
6. C₂×#22548697	C₂	semidirect
7. C₂×#22548692	C₂	semidirect
8. C₂×#22548687	C₂	semidirect
9. C₂×#22548687	C₂	semidirect
10. C₂×#22548686	C₂	semidirect
11. C₂×#22548683	C₂	semidirect
12. C₂×D₄×Dic₂₅₁	C₂	semidirect
13. C₂×(C₂²⋊D₂₅₁)⋊C₄	C₂	semidirect
14. C₂²×C₂²⋊Dic₂₅₁	C₂	semidirect
15. C₂×C₂²⋊C₄×D₂₅₁	C₂	semidirect
16. C₂×#120×C₂₅₁	C₂	semidirect
19. C₂×#16860809	C₂²	semidirect
20. C₂²×Dic₅₀₂	C₂²	semidirect
26. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
27. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
28. C₂²×C₂²⋊D₂₅₁	C₂²	semidirect
30. C₂³×Dic₂₅₁	C₂²	semidirect
31. C₂³×Dic₂₅₁	C₂²	semidirect
32. C₂³×Dic₂₅₁	C₂²	semidirect
33. C₂²×C₄×D₂₅₁	C₂²	semidirect
34. C₂²×C₄×D₂₅₁	C₂²	semidirect
35. #22548701	C₂²	semidirect
36. #22548699	C₂²	semidirect
37. #22548697	C₂²	semidirect
38. #22548692	C₂²	semidirect
39. #22548687	C₂²	semidirect
40. #22548687	C₂²	semidirect
41. #22548686	C₂²	semidirect
42. #22548683	C₂²	semidirect
43. D₄×Dic₂₅₁	C₂²	semidirect
44. (C₂²⋊D₂₅₁)⋊C₄	C₂²	semidirect
45. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
46. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
47. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
48. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
51. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
52. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
53. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
54. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
55. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
56. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
57. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
58. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
59. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
60. C₂×C₄×Dic₂₅₁	C₂²	semidirect
63. C₂²×D₄×C₂₅₁	C₂²	semidirect
64. C₂²×D₄×C₂₅₁	C₂²	semidirect
65. #120×C₂₅₁	C₂²	semidirect
67. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
68. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
77. C₂×Dic₅₀₂	C₂³	semidirect
84. C₂×C₂²⋊D₂₅₁	D₄	semidirect
89. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
90. C₂×C₂²⋊D₂₅₁	C₂³	semidirect
102. C₂²×Dic₂₅₁	C₂³	semidirect
103. C₂²×Dic₂₅₁	C₂³	semidirect
104. C₂²×Dic₂₅₁	C₂³	semidirect
107. C₂×C₄×D₂₅₁	C₂³	semidirect
108. C₂×C₄×D₂₅₁	C₂³	semidirect
109. C₄⋊Dic₂₅₁	C₂³	semidirect
110. C₄⋊Dic₂₅₁	C₂³	semidirect
111. Dic₂₅₁⋊C₄	C₂³	semidirect
112. Dic₂₅₁⋊C₄	C₂³	semidirect
115. C₂²⋊Dic₂₅₁	C₂³	semidirect
116. C₂²⋊Dic₂₅₁	C₂³	semidirect
117. C₂²⋊Dic₂₅₁	C₂³	semidirect
118. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
119. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
120. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
121. (C₂×D₂₅₁)⋊C₄	C₂³	semidirect
122. C₄×Dic₂₅₁	C₂³	semidirect
135. C₂×D₄×C₂₅₁	C₂³	semidirect
136. C₂×D₄×C₂₅₁	C₂³	semidirect
141. C₂²⋊C₄×C₂₅₁	C₂³	semidirect
142. C₂²⋊C₄×C₂₅₁	C₂³	semidirect
161. C₂²⋊D₂₅₁	C₂×D₄	semidirect
195. C₂³×C₂₅₁	#41	semidirect
228. C₂²×C₂₅₁	C₂×#41	semidirect
253. C₂×C₂₅₁	#546	semidirect
259. C₂₅₁	C₂×#546	semidirect
272. C₂×#120	D₂₅₁	semidirect
291. C₂²×D₄	C₂×D₂₅₁	semidirect
292. C₂²×D₄	C₂×D₂₅₁	semidirect
307. #120	C₂×D₂₅₁	semidirect
326. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
327. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
363. C₂×D₄	C₂²×D₂₅₁	semidirect
364. C₂×D₄	C₂²×D₂₅₁	semidirect
400. C₂²⋊C₄	C₂²×D₂₅₁	semidirect
401. C₂²⋊C₄	C₂²×D₂₅₁	semidirect
430. C₂³	#16860809	semidirect
497. C₂²	C₂×#16860809	semidirect
515. C₂	#30632324	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#16860809	2
C₂³×C₂²⋊D₂₅₁	2
#30632324	2
C₂×#22548701	2
C₂×#22548699	2
C₂×#22548697	2
C₂×#22548692	2
C₂×#22548687	2
C₂×#22548686	2
C₂×#22548683	2
C₂×D₄×Dic₂₅₁	2
C₂×(C₂²⋊D₂₅₁)⋊C₄	2
C₂²×C₂²⋊Dic₂₅₁	2
C₂×C₂²⋊C₄×D₂₅₁	2
C₂×#120×C₂₅₁	2
C₂×#546	251

Subgroups — C2×#30632324 #44563807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632324 #44563807