Subgroups — C₂×#30632391 #44563893

Order 32128.

1200 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632391	C₂	1	16	yes	maximal, direct product factor
2	C₂×#22548713	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548705	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#22548705	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#22548693	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#22548693	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#22548692	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#22548692	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22548691	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#22548680	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₂²⋊D₂₅₁	C₂	1	1	yes	maximal, characteristic
12	C₂×(C₂²⋊D₂₅₁)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂×(C₂²⋊D₂₅₁)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₂²×Dic₂₅₁⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂²⋊Q₈×C₂₅₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
18	C₂²×Dic₅₀₂	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
20	C₂³×Dic₂₅₁	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	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
25	#22548713	C₂²	1	8	yes	complemented
26	#22548705	C₂²	1	8	yes	complemented
27	#22548705	C₂²	1	8	yes	complemented
28	#22548693	C₂²	1	8	yes	complemented
29	#22548693	C₂²	1	8	yes	complemented
30	#22548692	C₂²	1	8	yes	complemented
31	#22548692	C₂²	1	8	yes	complemented
32	#22548691	C₂²	1	8	yes	complemented
33	#22548680	C₂²	1	8	yes	complemented
34	C₄×C₂²⋊D₂₅₁	C₂²	1	8	yes	—
35	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	8	yes	—
36	(C₂²⋊D₂₅₁)⋊C₄	C₂²	1	8	yes	—
37	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
39	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×Dic₂₅₁⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×Dic₂₅₁⋊C₄	C₂²	1	8	yes	complemented
51	C₄⋊C₄×D₂₅₁	C₂²	1	8	yes	complemented
52	C₂×C₂²⋊Dic₂₅₁	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	1	yes	characteristic
56	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₅₁	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
61	C₂²⋊Q₈×C₂₅₁	C₂²	1	8	yes	complemented
62	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₂₅₁	C₂²	1	1	yes	characteristic
67	C₂³×D₂₅₁	C₂³	1	1	yes	characteristic
68	C₂×Dic₅₀₂	—	2	4	no	—
69	C₂×Dic₅₀₂	—	4	2	no	—
70	C₂×Dic₅₀₂	C₂³	1	4	yes	—
71	C₂×Dic₅₀₂	C₂³	1	4	yes	—
72	C₂×C₂²⋊D₂₅₁	Q₈	1	8	yes	complemented
73	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
74	C₂²×Dic₂₅₁	—	2	4	no	—
75	C₂²×Dic₂₅₁	—	4	2	no	—
76	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
78	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
79	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
80	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
81	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
82	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
83	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
84	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
85	C₂×C₄×D₂₅₁	—	2	4	no	—
86	C₂×C₄×D₂₅₁	—	4	2	no	—
87	C₂×C₄×D₂₅₁	—	4	2	no	—
88	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
89	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
90	C₂×C₄×D₂₅₁	C₂³	1	4	yes	—
91	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
92	C₄⋊Dic₂₅₁	C₂³	1	4	yes	—
93	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
94	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
95	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
96	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
97	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
98	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
99	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
100	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
101	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
102	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
103	Dic₂₅₁⋊C₄	C₂³	1	4	yes	—
104	C₂²⋊Dic₂₅₁	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	C₄×Dic₂₅₁	C₂³	1	4	yes	—
109	C₄×Dic₂₅₁	C₂³	1	4	yes	—
110	C₄×Dic₂₅₁	C₂³	1	4	yes	—
111	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₂×Q₈×C₂₅₁	—	4	2	no	—
113	C₂×Q₈×C₂₅₁	C₂³	1	4	yes	—
114	C₂²×C₄×C₂₅₁	—	4	2	no	—
115	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
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	4	yes	—
122	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
123	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
124	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
125	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
127	C₂²×D₂₅₁	—	2	2	no	—
128	C₂²×D₂₅₁	—	2	2	no	—
129	C₂²×D₂₅₁	C₂×Q₈	1	4	yes	—
130	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
131	Dic₅₀₂	—	2	8	no	—
132	Dic₅₀₂	—	4	4	no	—
133	C₂²⋊D₂₅₁	C₂×Q₈	1	16	yes	complemented
134	C₂×Dic₂₅₁	—	2	2	no	—
135	C₂×Dic₂₅₁	—	2	2	no	—
136	C₂×Dic₂₅₁	—	2	2	no	—
137	C₂×Dic₂₅₁	—	2	2	no	—
138	C₂×Dic₂₅₁	—	2	2	no	—
139	C₂×Dic₂₅₁	—	2	8	no	—
140	C₂×Dic₂₅₁	—	4	4	no	—
141	C₂×Dic₂₅₁	C₂×Q₈	1	4	yes	—
142	C₂×Dic₂₅₁	#41	1	4	yes	—
143	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
144	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
145	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
146	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
147	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
148	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
149	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
150	C₄×D₂₅₁	—	2	8	no	—
151	C₄×D₂₅₁	—	4	4	no	—
152	C₄×D₂₅₁	—	4	4	no	—
153	C₂³×C₂₅₁	—	2	2	no	—
154	C₂³×C₂₅₁	—	2	2	no	—
155	C₂³×C₂₅₁	C₂×Q₈	1	4	yes	—
156	C₂³×C₂₅₁	C₂⁴	1	2	yes	—
157	C₂³×C₂₅₁	C₂⁴	1	1	yes	characteristic
158	Q₈×C₂₅₁	—	4	4	no	—
159	C₂×C₄×C₂₅₁	—	2	2	no	—
160	C₂×C₄×C₂₅₁	—	2	2	no	—
161	C₂×C₄×C₂₅₁	—	2	2	no	—
162	C₂×C₄×C₂₅₁	—	2	2	no	—
163	C₂×C₄×C₂₅₁	—	2	2	no	—
164	C₂×C₄×C₂₅₁	—	2	2	no	—
165	C₂×C₄×C₂₅₁	—	4	4	no	—
166	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
167	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
168	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
169	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
170	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
171	C₂×C₄×C₂₅₁	C₂⁴	1	2	yes	—
172	C₂²×C₂₅₁	—	2	8	no	—
173	C₂²×C₂₅₁	—	2	2	no	—
174	C₂²×C₂₅₁	—	2	2	no	—
175	C₂²×C₂₅₁	C₂²×Q₈	1	4	yes	—
176	C₂²×C₂₅₁	C₂²×Q₈	1	2	yes	—
177	C₂²×C₂₅₁	C₂×#41	1	2	yes	—
178	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
179	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
180	C₂×D₂₅₁	—	2	8	no	—
181	C₂×D₂₅₁	—	2	2	no	—
182	C₂×D₂₅₁	—	2	2	no	—
183	C₂×D₂₅₁	C₂²×Q₈	1	4	yes	—
184	C₄×C₂₅₁	—	2	2	no	—
185	C₄×C₂₅₁	—	2	2	no	—
186	C₄×C₂₅₁	—	2	2	no	—
187	C₄×C₂₅₁	—	2	2	no	—
188	C₄×C₂₅₁	—	2	2	no	—
189	C₄×C₂₅₁	—	2	2	no	—
190	Dic₂₅₁	—	2	2	no	—
191	Dic₂₅₁	—	2	2	no	—
192	Dic₂₅₁	—	2	2	no	—
193	Dic₂₅₁	—	2	2	no	—
194	Dic₂₅₁	—	2	2	no	—
195	Dic₂₅₁	C₂²×Q₈	1	4	yes	—
196	Dic₂₅₁	C₂×#41	1	4	yes	—
197	C₂×C₂₅₁	—	2	4	no	—
198	C₂×C₂₅₁	#554	1	4	yes	complemented
199	C₂×C₂₅₁	C₂³×Q₈	1	1	yes	characteristic
200	C₂×C₂₅₁	C₂²×#41	1	1	yes	characteristic
201	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
202	D₂₅₁	—	2	4	no	—
203	C₂₅₁	C₂×#554	1	1	yes	characteristic, complemented, Sylow
204	C₂×#554	—	251	1	no	maximal, Sylow
205	#554	—	251	16	no	—
206	C₂×C₄⋊Q₈	—	251	1	no	—
207	C₂×#125	—	251	1	no	—
208	C₂×#125	—	251	1	no	—
209	C₂×C₂²⋊Q₈	—	251	1	no	—
210	C₂×C₂²⋊Q₈	—	251	1	no	—
211	C₂×C₂²⋊Q₈	—	251	1	no	—
212	C₂×C₂²⋊Q₈	—	251	1	no	—
213	C₂×C₂²⋊Q₈	—	251	1	no	—
214	C₂×C₂²⋊Q₈	D₂₅₁	1	1	yes	characteristic, complemented
215	C₂×C₄×Q₈	—	251	1	no	—
216	C₂×C₄×D₄	—	251	1	no	—
217	C₂×C₄×D₄	—	251	1	no	—
218	C₂×C₄×D₄	—	251	1	no	—
219	C₂²×C₄⋊C₄	—	251	1	no	—
220	C₂²×C₄⋊C₄	—	251	1	no	—
221	C₂²×Q₈	—	251	1	no	—
222	C₂²×Q₈	—	251	1	no	—
223	C₂²×Q₈	C₂×D₂₅₁	1	1	yes	characteristic
224	C₂²×D₄	—	251	1	no	—
225	C₂³×C₄	—	251	1	no	—
226	C₂³×C₄	—	251	1	no	—
227	C₂³×C₄	—	251	1	no	—
228	C₂³×C₄	—	251	1	no	—
229	C₂³×C₄	—	251	1	no	—
230	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
231	C₄⋊Q₈	—	251	8	no	—
232	#125	—	251	8	no	—
233	#125	—	251	8	no	—
234	C₂²⋊Q₈	—	251	8	no	—
235	C₂²⋊Q₈	—	251	8	no	—
236	C₂²⋊Q₈	—	251	8	no	—
237	C₂²⋊Q₈	—	251	8	no	—
238	C₂²⋊Q₈	—	251	8	no	—
239	C₂²⋊Q₈	C₂×D₂₅₁	1	8	yes	complemented
240	C₄×Q₈	—	251	8	no	—
241	C₄×D₄	—	251	8	no	—
242	C₄×D₄	—	251	8	no	—
243	C₄×D₄	—	251	8	no	—
244	C₂×C₄⋊C₄	—	251	1	no	—
245	C₂×C₄⋊C₄	—	251	1	no	—
246	C₂×C₄⋊C₄	—	251	1	no	—
247	C₂×C₄⋊C₄	—	251	1	no	—
248	C₂×C₄⋊C₄	—	251	1	no	—
249	C₂×C₄⋊C₄	—	251	1	no	—
250	C₂×C₄⋊C₄	—	251	8	no	—
251	C₂×C₄⋊C₄	—	251	1	no	—
252	C₂×C₄⋊C₄	—	251	1	no	—
253	C₂×C₄⋊C₄	—	251	1	no	—
254	C₂×C₄⋊C₄	—	251	1	no	—
255	C₂×C₄⋊C₄	—	251	1	no	—
256	C₂×C₄⋊C₄	—	251	1	no	—
257	C₂×C₄⋊C₄	—	251	1	no	—
258	C₂×C₄⋊C₄	—	251	8	no	—
259	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	251	1	no	—
263	C₂×C₂²⋊C₄	—	251	1	no	—
264	C₂×C₂²⋊C₄	—	251	1	no	—
265	C₂×C₂²⋊C₄	—	251	1	no	—
266	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
268	C₂×C₄²	—	251	1	no	—
269	C₂×C₄²	—	251	1	no	—
270	C₂×C₄²	—	251	1	no	—
271	C₂⁴	—	251	1	no	—
272	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	1004	2	no	—
275	C₂×Q₈	—	502	4	no	—
276	C₂×Q₈	—	251	4	no	—
277	C₂×Q₈	—	251	4	no	—
278	C₂×Q₈	C₂²×D₂₅₁	1	4	yes	—
279	C₂×D₄	—	251	8	no	—
280	C₂×D₄	—	251	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	1004	2	no	—
283	C₂²×C₄	—	1004	2	no	—
284	C₂²×C₄	—	1004	2	no	—
285	C₂²×C₄	—	502	4	no	—
286	C₂²×C₄	—	502	4	no	—
287	C₂²×C₄	—	251	4	no	—
288	C₂²×C₄	—	251	4	no	—
289	C₂²×C₄	—	251	4	no	—
290	C₂²×C₄	—	251	4	no	—
291	C₂²×C₄	—	251	1	no	—
292	C₂²×C₄	—	251	1	no	—
293	C₂²×C₄	—	251	1	no	—
294	C₂²×C₄	—	251	1	no	—
295	C₂²×C₄	—	251	1	no	—
296	C₂²×C₄	—	251	4	no	—
297	C₂²×C₄	—	251	1	no	—
298	C₂²×C₄	—	251	1	no	—
299	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
300	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₂₅₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	—
306	C₄⋊C₄	—	251	4	no	—
307	C₄⋊C₄	—	251	4	no	—
308	C₄⋊C₄	—	251	4	no	—
309	C₄⋊C₄	—	251	4	no	—
310	C₄⋊C₄	—	251	4	no	—
311	C₄⋊C₄	—	251	4	no	—
312	C₄⋊C₄	—	251	4	no	—
313	C₄⋊C₄	—	251	4	no	—
314	C₄⋊C₄	—	251	4	no	—
315	C₄⋊C₄	—	251	4	no	—
316	C₄⋊C₄	—	251	4	no	—
317	C₄⋊C₄	—	251	4	no	—
318	C₄⋊C₄	—	251	4	no	—
319	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
320	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
321	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
322	C₂²⋊C₄	—	251	4	no	—
323	C₂²⋊C₄	—	251	4	no	—
324	C₂²⋊C₄	—	251	4	no	—
325	C₂²⋊C₄	—	251	4	no	—
326	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
327	C₂²⋊C₄	C₂²×D₂₅₁	1	4	yes	—
328	C₄²	—	251	4	no	—
329	C₄²	—	251	4	no	—
330	C₄²	—	251	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	502	2	no	—
334	C₂³	—	502	2	no	—
335	C₂³	—	251	4	no	—
336	C₂³	—	251	2	no	—
337	C₂³	Q₈×D₂₅₁	1	4	yes	—
338	C₂³	C₂³×D₂₅₁	1	2	yes	—
339	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
340	Q₈	—	4	4	no	—
341	Q₈	—	1004	4	no	—
342	Q₈	—	502	8	no	—
343	D₄	—	251	16	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	1004	4	no	—
352	C₂×C₄	—	1004	4	no	—
353	C₂×C₄	—	1004	4	no	—
354	C₂×C₄	—	502	8	no	—
355	C₂×C₄	—	502	2	no	—
356	C₂×C₄	—	502	2	no	—
357	C₂×C₄	—	502	2	no	—
358	C₂×C₄	—	502	2	no	—
359	C₂×C₄	—	502	2	no	—
360	C₂×C₄	—	502	8	no	—
361	C₂×C₄	—	251	2	no	—
362	C₂×C₄	—	251	2	no	—
363	C₂×C₄	—	251	2	no	—
364	C₂×C₄	—	251	2	no	—
365	C₂×C₄	—	251	2	no	—
366	C₂×C₄	—	251	4	no	—
367	C₂×C₄	—	251	4	no	—
368	C₂×C₄	—	251	2	no	—
369	C₂×C₄	—	251	2	no	—
370	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
371	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
372	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
373	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
374	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
375	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	502	2	no	—
380	C₂²	—	502	2	no	—
381	C₂²	—	502	8	no	—
382	C₂²	—	251	4	no	—
383	C₂²	C₂×Q₈×D₂₅₁	1	4	yes	—
384	C₂²	C₂×Q₈×D₂₅₁	1	2	yes	—
385	C₂²	#41×D₂₅₁	1	2	yes	—
386	C₂²	#22548760	1	2	yes	—
387	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	502	2	no	—
395	C₄	—	502	2	no	—
396	C₄	—	502	2	no	—
397	C₄	—	502	2	no	—
398	C₄	—	502	2	no	—
399	C₄	—	251	4	no	—
400	C₄	—	251	4	no	—
401	C₂	—	2	4	no	—
402	C₂	—	502	4	no	—
403	C₂	#30632391	1	4	yes	direct product factor
404	C₂	C₂²×Q₈×D₂₅₁	1	1	yes	characteristic
405	C₂	C₂×#41×D₂₅₁	1	1	yes	characteristic
406	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×C₂²⋊Q₈×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
prime radical	C₂²×C₂²⋊D₂₅₁	C₂²
hypercenter	C₂×C₂²⋊Q₈	D₂₅₁
hypocenter	C₂₅₁	C₂×#554
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #30632391	C₂	direct (N × H)
2. C₂×#22548713	C₂	semidirect
3. C₂×#22548705	C₂	semidirect
4. C₂×#22548705	C₂	semidirect
5. C₂×#22548693	C₂	semidirect
6. C₂×#22548693	C₂	semidirect
7. C₂×#22548692	C₂	semidirect
8. C₂×#22548692	C₂	semidirect
9. C₂×#22548691	C₂	semidirect
10. C₂×#22548680	C₂	semidirect
14. C₂²×Dic₂₅₁⋊C₄	C₂	semidirect
15. C₂×C₄⋊C₄×D₂₅₁	C₂	semidirect
16. C₂×C₂²⋊Q₈×C₂₅₁	C₂	semidirect
25. #22548713	C₂²	semidirect
26. #22548705	C₂²	semidirect
27. #22548705	C₂²	semidirect
28. #22548693	C₂²	semidirect
29. #22548693	C₂²	semidirect
30. #22548692	C₂²	semidirect
31. #22548692	C₂²	semidirect
32. #22548691	C₂²	semidirect
33. #22548680	C₂²	semidirect
50. C₂×Dic₂₅₁⋊C₄	C₂²	semidirect
51. C₄⋊C₄×D₂₅₁	C₂²	semidirect
61. C₂²⋊Q₈×C₂₅₁	C₂²	semidirect
72. C₂×C₂²⋊D₂₅₁	Q₈	semidirect
133. C₂²⋊D₂₅₁	C₂×Q₈	semidirect
198. C₂×C₂₅₁	#554	semidirect
203. C₂₅₁	C₂×#554	semidirect
214. C₂×C₂²⋊Q₈	D₂₅₁	semidirect
239. C₂²⋊Q₈	C₂×D₂₅₁	semidirect
403. C₂	#30632391	direct (N × H)

Maximal subgroups

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

subgroup	index
#30632391	2
C₂×#22548713	2
C₂×#22548705	2
C₂×#22548693	2
C₂×#22548692	2
C₂×#22548691	2
C₂×#22548680	2
C₂×C₄×C₂²⋊D₂₅₁	2
C₂×(C₂²⋊D₂₅₁)⋊C₄	2
C₂²×Dic₂₅₁⋊C₄	2
C₂×C₄⋊C₄×D₂₅₁	2
C₂×C₂²⋊Q₈×C₂₅₁	2
C₂×#554	251

Subgroups — C2×#30632391 #44563893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632391 #44563893