Subgroups — C₂×#30632366 #44563865

Order 32128.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632366	C₂	1	16	yes	maximal, direct product factor
2	C₂×#22548710	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22548701	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22548698	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548696	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22548694	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22548693	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#22548683	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#22548672	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#22548671	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×(C₂×D₂₅₁)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂²⋊C₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₄×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₂₅₁	C₂²	1	1	yes	characteristic
18	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
21	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
24	#22548710	C₂²	1	8	yes	complemented
25	#22548709	C₂²	1	8	yes	complemented
26	#22548701	C₂²	1	8	yes	complemented
27	#22548698	C₂²	1	8	yes	complemented
28	#22548697	C₂²	1	8	yes	complemented
29	#22548696	C₂²	1	8	yes	complemented
30	#22548694	C₂²	1	8	yes	complemented
31	#22548693	C₂²	1	8	yes	complemented
32	#22548683	C₂²	1	8	yes	—
33	C₄×C₂²⋊D₂₅₁	C₂²	1	8	yes	complemented
34	#22548672	C₂²	1	8	yes	complemented
35	#22548671	C₂²	1	8	yes	complemented
36	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
37	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
47	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	8	yes	complemented
56	C₂²⋊C₄×D₂₅₁	C₂²	1	8	yes	complemented
57	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
61	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
62	C₄×D₄×C₂₅₁	C₂²	1	8	yes	complemented
63	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄²×C₂₅₁	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₂₅₁	—	2	4	no	—
68	C₂³×D₂₅₁	—	2	4	no	—
69	C₂³×D₂₅₁	—	4	2	no	—
70	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
71	C₂³×D₂₅₁	C₂³	1	4	yes	—
72	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
73	C₂×Dic₅₀₂	—	4	2	no	—
74	C₂×Dic₅₀₂	C₂³	1	4	yes	complemented
75	C₂×C₂²⋊D₂₅₁	—	2	4	no	—
76	C₂×C₂²⋊D₂₅₁	—	4	2	no	—
77	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
78	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
79	C₂²×Dic₂₅₁	—	2	4	no	—
80	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
81	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
82	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
83	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
84	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
85	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
86	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₂₅₁	—	2	4	no	—
88	C₂×C₄×D₂₅₁	—	4	2	no	—
89	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
90	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
91	C₄⋊Dic₂₅₁	C₂³	1	4	yes	complemented
92	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
93	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
94	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
95	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
96	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
97	Dic₂₅₁⋊C₄	C₂³	1	4	yes	complemented
98	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
99	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
100	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
101	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	complemented
102	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
103	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
104	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
105	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
106	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₂₅₁)⋊C₄	C₂³	1	4	yes	—
110	C₄×Dic₂₅₁	C₂³	1	4	yes	complemented
111	C₄×Dic₂₅₁	C₂³	1	4	yes	complemented
112	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
113	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₂₅₁	—	2	4	no	—
115	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
116	C₂²×C₄×C₂₅₁	—	4	2	no	—
117	C₂²×C₄×C₂₅₁	—	4	2	no	—
118	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
119	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
124	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	complemented
125	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	complemented
126	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	complemented
128	C₄²×C₂₅₁	C₂³	1	4	yes	complemented
129	C₂²×D₂₅₁	—	2	2	no	—
130	C₂²×D₂₅₁	—	2	2	no	—
131	C₂²×D₂₅₁	—	2	2	no	—
132	C₂²×D₂₅₁	—	2	8	no	—
133	C₂²×D₂₅₁	—	2	2	no	—
134	C₂²×D₂₅₁	—	2	2	no	—
135	C₂²×D₂₅₁	—	2	8	no	—
136	C₂²×D₂₅₁	—	4	4	no	—
137	C₂²×D₂₅₁	—	4	16	no	—
138	C₂²×D₂₅₁	#41	1	4	yes	—
139	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
140	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
141	Dic₅₀₂	—	4	4	no	—
142	C₂²⋊D₂₅₁	—	2	8	no	—
143	C₂²⋊D₂₅₁	—	4	4	no	—
144	C₂×Dic₂₅₁	—	2	2	no	—
145	C₂×Dic₂₅₁	—	2	8	no	—
146	C₂×Dic₂₅₁	—	2	2	no	—
147	C₂×Dic₂₅₁	—	2	2	no	—
148	C₂×Dic₂₅₁	—	2	2	no	—
149	C₂×Dic₂₅₁	—	2	2	no	—
150	C₂×Dic₂₅₁	—	2	2	no	—
151	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
152	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
153	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
154	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
155	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
156	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
157	C₄×D₂₅₁	—	2	8	no	—
158	C₄×D₂₅₁	—	4	4	no	—
159	C₂³×C₂₅₁	—	2	2	no	—
160	C₂³×C₂₅₁	—	2	2	no	—
161	C₂³×C₂₅₁	—	2	2	no	—
162	C₂³×C₂₅₁	—	2	2	no	—
163	C₂³×C₂₅₁	—	2	2	no	—
164	C₂³×C₂₅₁	#41	1	4	yes	—
165	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
166	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
167	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
168	D₄×C₂₅₁	—	2	8	no	—
169	C₂×C₄×C₂₅₁	—	2	2	no	—
170	C₂×C₄×C₂₅₁	—	2	2	no	—
171	C₂×C₄×C₂₅₁	—	2	2	no	—
172	C₂×C₄×C₂₅₁	—	2	2	no	—
173	C₂×C₄×C₂₅₁	—	2	2	no	—
174	C₂×C₄×C₂₅₁	—	4	4	no	—
175	C₂×C₄×C₂₅₁	—	4	4	no	—
176	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
177	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
178	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
179	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
180	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
181	C₂²×C₂₅₁	—	2	8	no	—
182	C₂²×C₂₅₁	—	2	2	no	—
183	C₂²×C₂₅₁	—	2	2	no	—
184	C₂²×C₂₅₁	—	2	2	no	—
185	C₂²×C₂₅₁	—	2	2	no	—
186	C₂²×C₂₅₁	—	2	2	no	—
187	C₂²×C₂₅₁	—	4	4	no	—
188	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
189	C₂²×C₂₅₁	C₂×#41	1	4	yes	—
190	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
191	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
192	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
193	C₂×D₂₅₁	—	2	8	no	—
194	C₂×D₂₅₁	—	2	2	no	—
195	C₂×D₂₅₁	—	2	2	no	—
196	C₂×D₂₅₁	—	2	2	no	—
197	C₂×D₂₅₁	—	2	2	no	—
198	C₂×D₂₅₁	—	2	2	no	—
199	C₂×D₂₅₁	—	4	16	no	—
200	C₂×D₂₅₁	—	4	4	no	—
201	C₂×D₂₅₁	C₂×#41	1	4	yes	—
202	C₄×C₂₅₁	—	2	2	no	—
203	C₄×C₂₅₁	—	2	2	no	—
204	C₄×C₂₅₁	—	2	2	no	—
205	C₄×C₂₅₁	—	2	2	no	—
206	C₄×C₂₅₁	—	2	2	no	—
207	Dic₂₅₁	—	2	2	no	—
208	Dic₂₅₁	—	2	2	no	—
209	Dic₂₅₁	—	2	2	no	—
210	Dic₂₅₁	—	2	2	no	—
211	Dic₂₅₁	—	2	2	no	—
212	Dic₂₅₁	—	2	2	no	—
213	C₂×C₂₅₁	—	2	4	no	—
214	C₂×C₂₅₁	—	4	2	no	—
215	C₂×C₂₅₁	#551	1	4	yes	complemented
216	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
217	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
218	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
219	D₂₅₁	—	2	4	no	—
220	D₂₅₁	—	4	2	no	—
221	C₂₅₁	C₂×#551	1	1	yes	characteristic, complemented, Sylow
222	C₂×#551	—	251	1	no	maximal, Sylow
223	#551	—	251	16	no	—
224	C₂×#126	—	251	1	no	—
225	C₂×#126	—	251	1	no	—
226	C₂×#124	—	251	1	no	—
227	C₂×#123	—	251	1	no	—
228	C₂×#123	—	251	1	no	—
229	C₂×#123	—	251	1	no	—
230	C₂×C₂²⋊Q₈	—	251	1	no	—
231	C₂×C₂²⋊Q₈	—	251	1	no	—
232	C₂×#120	—	251	1	no	—
233	C₂×C₄×D₄	—	251	1	no	—
234	C₂×C₄×D₄	D₂₅₁	1	1	yes	characteristic, complemented
235	C₂×#117	—	251	1	no	—
236	C₂×#117	—	251	1	no	—
237	C₂²×C₂²⋊C₄	—	251	1	no	—
238	C₂²×C₂²⋊C₄	—	251	1	no	—
239	C₂⁵	—	251	1	no	—
240	C₂²×Q₈	—	251	1	no	—
241	C₂²×D₄	—	251	1	no	—
242	C₂²×D₄	—	251	1	no	—
243	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
244	C₂³×C₄	—	251	1	no	—
245	C₂³×C₄	—	251	1	no	—
246	C₂³×C₄	—	251	1	no	—
247	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
248	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
249	#126	—	251	8	no	—
250	#126	—	251	8	no	—
251	#124	—	251	8	no	—
252	#123	—	251	8	no	—
253	#123	—	251	8	no	—
254	#123	—	251	8	no	—
255	C₂²⋊Q₈	—	251	8	no	—
256	C₂²⋊Q₈	—	251	8	no	—
257	#120	—	251	8	no	—
258	C₄×D₄	—	251	8	no	—
259	C₄×D₄	C₂×D₂₅₁	1	8	yes	complemented
260	#117	—	251	8	no	—
261	#117	—	251	8	no	—
262	C₂×C₄⋊C₄	—	251	1	no	—
263	C₂×C₄⋊C₄	—	251	1	no	—
264	C₂×C₄⋊C₄	—	251	1	no	—
265	C₂×C₄⋊C₄	—	251	1	no	—
266	C₂×C₄⋊C₄	—	251	1	no	—
267	C₂×C₄⋊C₄	—	251	1	no	—
268	C₂×C₄⋊C₄	—	251	1	no	—
269	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
270	C₂×C₂²⋊C₄	—	251	1	no	—
271	C₂×C₂²⋊C₄	—	251	1	no	—
272	C₂×C₂²⋊C₄	—	251	1	no	—
273	C₂×C₂²⋊C₄	—	251	1	no	—
274	C₂×C₂²⋊C₄	—	251	1	no	—
275	C₂×C₂²⋊C₄	—	251	1	no	—
276	C₂×C₂²⋊C₄	—	251	1	no	—
277	C₂×C₂²⋊C₄	—	251	1	no	—
278	C₂×C₂²⋊C₄	—	251	1	no	—
279	C₂×C₂²⋊C₄	—	251	1	no	—
280	C₂×C₂²⋊C₄	—	251	8	no	—
281	C₂×C₂²⋊C₄	—	251	1	no	—
282	C₂×C₂²⋊C₄	—	251	1	no	—
283	C₂×C₂²⋊C₄	—	251	8	no	—
284	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic, complemented
286	C₂×C₄²	—	251	1	no	—
287	C₂×C₄²	—	251	1	no	—
288	C₂×C₄²	C₂×D₂₅₁	1	1	yes	characteristic, complemented
289	C₂⁴	—	1004	2	no	—
290	C₂⁴	—	502	4	no	—
291	C₂⁴	—	502	4	no	—
292	C₂⁴	—	251	4	no	—
293	C₂⁴	—	251	1	no	—
294	C₂⁴	—	251	1	no	—
295	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
296	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
297	C₂×Q₈	—	1004	2	no	—
298	C₂×Q₈	—	251	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	1004	2	no	—
301	C₂×D₄	—	502	4	no	—
302	C₂×D₄	—	251	4	no	—
303	C₂×D₄	—	251	4	no	—
304	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	1004	2	no	—
308	C₂²×C₄	—	502	4	no	—
309	C₂²×C₄	—	502	4	no	—
310	C₂²×C₄	—	251	4	no	—
311	C₂²×C₄	—	251	4	no	—
312	C₂²×C₄	—	251	1	no	—
313	C₂²×C₄	—	251	1	no	—
314	C₂²×C₄	—	251	1	no	—
315	C₂²×C₄	—	251	1	no	—
316	C₂²×C₄	—	251	1	no	—
317	C₂²×C₄	—	251	1	no	—
318	C₂²×C₄	—	251	4	no	—
319	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	—
325	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	complemented
326	C₄⋊C₄	—	251	4	no	—
327	C₄⋊C₄	—	251	4	no	—
328	C₄⋊C₄	—	251	4	no	—
329	C₄⋊C₄	—	251	4	no	—
330	C₄⋊C₄	—	251	4	no	—
331	C₄⋊C₄	—	251	4	no	—
332	C₄⋊C₄	—	251	4	no	—
333	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	complemented
334	C₂²⋊C₄	—	251	4	no	—
335	C₂²⋊C₄	—	251	4	no	—
336	C₂²⋊C₄	—	251	4	no	—
337	C₂²⋊C₄	—	251	4	no	—
338	C₂²⋊C₄	—	251	4	no	—
339	C₂²⋊C₄	—	251	4	no	—
340	C₂²⋊C₄	—	251	4	no	—
341	C₂²⋊C₄	—	251	4	no	—
342	C₂²⋊C₄	—	251	4	no	—
343	C₂²⋊C₄	—	251	4	no	—
344	C₂²⋊C₄	—	251	4	no	—
345	C₂²⋊C₄	—	251	4	no	—
346	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
347	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	complemented
348	C₄²	—	251	4	no	—
349	C₄²	—	251	4	no	—
350	C₄²	C₂²×D₂₅₁	1	4	yes	complemented
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	1004	16	no	—
357	C₂³	—	1004	4	no	—
358	C₂³	—	502	8	no	—
359	C₂³	—	502	2	no	—
360	C₂³	—	502	8	no	—
361	C₂³	—	502	2	no	—
362	C₂³	—	502	2	no	—
363	C₂³	—	502	2	no	—
364	C₂³	—	502	2	no	—
365	C₂³	—	251	2	no	—
366	C₂³	—	251	4	no	—
367	C₂³	—	251	2	no	—
368	C₂³	#16860810	1	4	yes	—
369	C₂³	C₂³×D₂₅₁	1	2	yes	—
370	C₂³	C₂³×D₂₅₁	1	2	yes	—
371	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
372	Q₈	—	1004	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	1004	4	no	—
375	D₄	—	502	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	1004	4	no	—
384	C₂×C₄	—	502	8	no	—
385	C₂×C₄	—	502	2	no	—
386	C₂×C₄	—	502	2	no	—
387	C₂×C₄	—	502	8	no	—
388	C₂×C₄	—	502	2	no	—
389	C₂×C₄	—	502	2	no	—
390	C₂×C₄	—	502	2	no	—
391	C₂×C₄	—	502	2	no	—
392	C₂×C₄	—	251	2	no	—
393	C₂×C₄	—	251	2	no	—
394	C₂×C₄	—	251	2	no	—
395	C₂×C₄	—	251	2	no	—
396	C₂×C₄	—	251	2	no	—
397	C₂×C₄	—	251	2	no	—
398	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
399	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
400	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
401	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
402	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	1004	16	no	—
411	C₂²	—	1004	4	no	—
412	C₂²	—	502	2	no	—
413	C₂²	—	502	2	no	—
414	C₂²	—	502	2	no	—
415	C₂²	—	502	2	no	—
416	C₂²	—	502	2	no	—
417	C₂²	—	502	8	no	—
418	C₂²	—	251	4	no	—
419	C₂²	#41×D₂₅₁	1	2	yes	—
420	C₂²	C₂×#16860810	1	4	yes	—
421	C₂²	C₂×#16860810	1	2	yes	—
422	C₂²	#22548760	1	2	yes	—
423	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	502	2	no	—
430	C₄	—	502	2	no	—
431	C₄	—	502	2	no	—
432	C₄	—	502	2	no	—
433	C₄	—	502	2	no	—
434	C₄	—	502	2	no	—
435	C₂	—	2	4	no	—
436	C₂	—	4	2	no	—
437	C₂	—	1004	2	no	—
438	C₂	—	502	4	no	—
439	C₂	#30632366	1	4	yes	direct product factor
440	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
441	C₂	C₂²×#16860810	1	1	yes	characteristic
442	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×C₄×D₄×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
prime radical	C₂×#22548683	C₂
hypercenter	C₂×C₄×D₄	D₂₅₁
hypocenter	C₂₅₁	C₂×#551
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #30632366	C₂	direct (N × H)
2. C₂×#22548710	C₂	semidirect
3. C₂×#22548709	C₂	semidirect
4. C₂×#22548701	C₂	semidirect
5. C₂×#22548698	C₂	semidirect
6. C₂×#22548697	C₂	semidirect
7. C₂×#22548696	C₂	semidirect
8. C₂×#22548694	C₂	semidirect
9. C₂×#22548693	C₂	semidirect
11. C₂×C₄×C₂²⋊D₂₅₁	C₂	semidirect
12. C₂×#22548672	C₂	semidirect
13. C₂×#22548671	C₂	semidirect
14. C₂²×(C₂×D₂₅₁)⋊C₄	C₂	semidirect
15. C₂×C₂²⋊C₄×D₂₅₁	C₂	semidirect
16. C₂×C₄×D₄×C₂₅₁	C₂	semidirect
18. C₂²×Dic₅₀₂	C₂²	semidirect
24. #22548710	C₂²	semidirect
25. #22548709	C₂²	semidirect
26. #22548701	C₂²	semidirect
27. #22548698	C₂²	semidirect
28. #22548697	C₂²	semidirect
29. #22548696	C₂²	semidirect
30. #22548694	C₂²	semidirect
31. #22548693	C₂²	semidirect
33. C₄×C₂²⋊D₂₅₁	C₂²	semidirect
34. #22548672	C₂²	semidirect
35. #22548671	C₂²	semidirect
36. C₂×C₄⋊Dic₂₅₁	C₂²	semidirect
37. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
38. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
39. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
40. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
41. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
42. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
45. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
46. C₂×C₂²⋊Dic₂₅₁	C₂²	semidirect
55. C₂×(C₂×D₂₅₁)⋊C₄	C₂²	semidirect
56. C₂²⋊C₄×D₂₅₁	C₂²	semidirect
57. C₂×C₄×Dic₂₅₁	C₂²	semidirect
58. C₂×C₄×Dic₂₅₁	C₂²	semidirect
61. C₂³×C₄×C₂₅₁	C₂²	semidirect
62. C₄×D₄×C₂₅₁	C₂²	semidirect
63. C₂×C₄⋊C₄×C₂₅₁	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₂₅₁	C₂²	semidirect
66. C₂×C₄²×C₂₅₁	C₂²	semidirect
74. C₂×Dic₅₀₂	C₂³	semidirect
91. C₄⋊Dic₂₅₁	C₂³	semidirect
92. Dic₂₅₁⋊C₄	C₂³	semidirect
93. Dic₂₅₁⋊C₄	C₂³	semidirect
94. Dic₂₅₁⋊C₄	C₂³	semidirect
95. Dic₂₅₁⋊C₄	C₂³	semidirect
96. Dic₂₅₁⋊C₄	C₂³	semidirect
97. Dic₂₅₁⋊C₄	C₂³	semidirect
100. C₂²⋊Dic₂₅₁	C₂³	semidirect
101. C₂²⋊Dic₂₅₁	C₂³	semidirect
110. C₄×Dic₂₅₁	C₂³	semidirect
111. C₄×Dic₂₅₁	C₂³	semidirect
124. C₂²×C₄×C₂₅₁	C₂³	semidirect
125. C₄⋊C₄×C₂₅₁	C₂³	semidirect
127. C₂²⋊C₄×C₂₅₁	C₂³	semidirect
128. C₄²×C₂₅₁	C₂³	semidirect
215. C₂×C₂₅₁	#551	semidirect
221. C₂₅₁	C₂×#551	semidirect
234. C₂×C₄×D₄	D₂₅₁	semidirect
248. C₂³×C₄	C₂×D₂₅₁	semidirect
259. C₄×D₄	C₂×D₂₅₁	semidirect
269. C₂×C₄⋊C₄	C₂×D₂₅₁	semidirect
285. C₂×C₂²⋊C₄	C₂×D₂₅₁	semidirect
288. C₂×C₄²	C₂×D₂₅₁	semidirect
325. C₂²×C₄	C₂²×D₂₅₁	semidirect
333. C₄⋊C₄	C₂²×D₂₅₁	semidirect
347. C₂²⋊C₄	C₂²×D₂₅₁	semidirect
350. C₄²	C₂²×D₂₅₁	semidirect
439. C₂	#30632366	direct (N × H)

Maximal subgroups

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

subgroup	index
#30632366	2
C₂×#22548710	2
C₂×#22548709	2
C₂×#22548701	2
C₂×#22548698	2
C₂×#22548697	2
C₂×#22548696	2
C₂×#22548694	2
C₂×#22548693	2
C₂×#22548683	2
C₂×C₄×C₂²⋊D₂₅₁	2
C₂×#22548672	2
C₂×#22548671	2
C₂²×(C₂×D₂₅₁)⋊C₄	2
C₂×C₂²⋊C₄×D₂₅₁	2
C₂×C₄×D₄×C₂₅₁	2
C₂×#551	251

Subgroups — C2×#30632366 #44563865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632366 #44563865