Subgroups — C₂×#30632432 #44564489

Order 32128.

1152 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30632432	C₂	1	16	yes	maximal, direct product factor
2	C₂×#22548705	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#22548702	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×#22548696	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#22548694	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#22548693	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#22548692	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#22548692	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#22548687	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#22548687	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#22548686	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#121×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	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₂₅₁	C₂²	1	1	yes	characteristic
22	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic
23	C₂³×Dic₂₅₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₂₅₁	C₂²	1	1	yes	characteristic
25	#22548705	C₂²	1	8	yes	complemented
26	#22548702	C₂²	1	8	yes	complemented
27	#22548701	C₂²	1	8	yes	complemented
28	#22548698	C₂²	1	8	yes	complemented
29	#22548697	C₂²	1	8	yes	complemented
30	#22548696	C₂²	1	8	yes	complemented
31	#22548696	C₂²	1	8	yes	complemented
32	#22548694	C₂²	1	8	yes	complemented
33	#22548693	C₂²	1	8	yes	complemented
34	#22548692	C₂²	1	8	yes	complemented
35	#22548692	C₂²	1	8	yes	complemented
36	#22548687	C₂²	1	8	yes	complemented
37	#22548687	C₂²	1	8	yes	complemented
38	#22548686	C₂²	1	8	yes	complemented
39	C₂×C₄⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₂₅₁	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×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₂₅₁	C₂²	1	1	yes	characteristic
55	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×(C₂×D₂₅₁)⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₂₅₁	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₂₅₁	C₂²	1	1	yes	characteristic
62	C₂³×C₄×C₂₅₁	C₂²	1	1	yes	characteristic
63	#121×C₂₅₁	C₂²	1	8	yes	complemented
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	—	4	2	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	—	4	2	no	—
73	C₂×C₂²⋊D₂₅₁	—	4	2	no	—
74	C₂×C₂²⋊D₂₅₁	—	4	2	no	—
75	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₂₅₁	C₂³	1	4	yes	—
78	C₂²×Dic₂₅₁	—	4	2	no	—
79	C₂²×Dic₂₅₁	—	4	2	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	1	yes	characteristic
85	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
86	C₂²×Dic₂₅₁	C₂³	1	1	yes	characteristic
87	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
88	C₂²×Dic₂₅₁	C₂³	1	4	yes	—
89	C₂×C₄×D₂₅₁	—	4	2	no	—
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	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
101	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
102	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
103	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
104	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
105	C₂²⋊Dic₂₅₁	C₂³	1	4	yes	—
106	C₂²⋊Dic₂₅₁	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	—
111	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
112	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
113	C₂⁴×C₂₅₁	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₂₅₁	—	4	2	no	—
115	C₂×D₄×C₂₅₁	—	4	2	no	—
116	C₂×D₄×C₂₅₁	—	4	2	no	—
117	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
118	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
119	C₂×D₄×C₂₅₁	C₂³	1	4	yes	—
120	C₂²×C₄×C₂₅₁	—	4	2	no	—
121	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₂₅₁	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₂₅₁	C₂³	1	4	yes	—
126	C₄⋊C₄×C₂₅₁	C₂³	1	4	yes	—
127	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
128	C₂²⋊C₄×C₂₅₁	C₂³	1	4	yes	—
129	C₂²×D₂₅₁	—	2	2	no	—
130	C₂²×D₂₅₁	—	2	2	no	—
131	C₂²×D₂₅₁	—	2	2	no	—
132	C₂²×D₂₅₁	C₂⁴	1	2	yes	—
133	Dic₅₀₂	—	4	4	no	—
134	Dic₅₀₂	—	4	4	no	—
135	C₂²⋊D₂₅₁	—	4	4	no	—
136	C₂²⋊D₂₅₁	—	4	4	no	—
137	C₂²⋊D₂₅₁	—	4	4	no	—
138	C₂×Dic₂₅₁	—	2	2	no	—
139	C₂×Dic₂₅₁	—	2	2	no	—
140	C₂×Dic₂₅₁	—	2	2	no	—
141	C₂×Dic₂₅₁	—	2	2	no	—
142	C₂×Dic₂₅₁	—	2	2	no	—
143	C₂×Dic₂₅₁	—	2	2	no	—
144	C₂×Dic₂₅₁	—	2	2	no	—
145	C₂×Dic₂₅₁	—	4	4	no	—
146	C₂×Dic₂₅₁	—	4	4	no	—
147	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
148	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
149	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
150	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
151	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
152	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
153	C₂×Dic₂₅₁	C₂⁴	1	2	yes	—
154	C₄×D₂₅₁	—	4	4	no	—
155	C₂³×C₂₅₁	—	2	2	no	—
156	C₂³×C₂₅₁	—	2	2	no	—
157	C₂³×C₂₅₁	—	2	2	no	—
158	C₂³×C₂₅₁	—	2	2	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	C₂⁴	1	2	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	—	4	4	no	—
169	D₄×C₂₅₁	—	4	4	no	—
170	D₄×C₂₅₁	—	4	4	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	—	2	2	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	C₂²×C₂₅₁	—	2	2	no	—
181	C₂²×C₂₅₁	—	2	2	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	—	2	2	no	—
188	C₂²×C₂₅₁	—	2	2	no	—
189	C₂²×C₂₅₁	—	4	4	no	—
190	C₂²×C₂₅₁	—	4	4	no	—
191	C₂²×C₂₅₁	—	4	4	no	—
192	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
193	C₂²×C₂₅₁	H(5,𝔽₂)	1	2	yes	—
194	C₂²×C₂₅₁	2₋¹⁺⁴	1	2	yes	—
195	C₂²×C₂₅₁	C₂⁵	1	1	yes	characteristic
196	C₂×D₂₅₁	—	2	2	no	—
197	C₂×D₂₅₁	—	2	2	no	—
198	C₂×D₂₅₁	—	2	2	no	—
199	C₂×D₂₅₁	—	4	4	no	—
200	C₄×C₂₅₁	—	2	2	no	—
201	C₄×C₂₅₁	—	2	2	no	—
202	C₄×C₂₅₁	—	2	2	no	—
203	C₄×C₂₅₁	—	2	2	no	—
204	Dic₂₅₁	—	2	2	no	—
205	Dic₂₅₁	—	2	2	no	—
206	Dic₂₅₁	—	2	2	no	—
207	Dic₂₅₁	—	2	2	no	—
208	Dic₂₅₁	—	2	2	no	—
209	Dic₂₅₁	—	2	2	no	—
210	Dic₂₅₁	—	2	2	no	—
211	C₂×C₂₅₁	—	4	2	no	—
212	C₂×C₂₅₁	—	4	2	no	—
213	C₂×C₂₅₁	—	4	2	no	—
214	C₂×C₂₅₁	#562	1	4	yes	complemented
215	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₂₅₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₂₅₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
218	D₂₅₁	—	4	2	no	—
219	C₂₅₁	C₂×#562	1	1	yes	characteristic, complemented, Sylow
220	C₂×#562	—	251	1	no	maximal, Sylow
221	#562	—	251	16	no	—
222	C₂×#125	—	251	1	no	—
223	C₂×#124	—	251	1	no	—
224	C₂×#124	—	251	1	no	—
225	C₂×#123	—	251	1	no	—
226	C₂×#123	—	251	1	no	—
227	C₂×#123	—	251	1	no	—
228	C₂×#123	—	251	1	no	—
229	C₂×C₂²⋊Q₈	—	251	1	no	—
230	C₂×C₂²⋊Q₈	—	251	1	no	—
231	C₂×C₂²⋊Q₈	—	251	1	no	—
232	C₂×C₂²⋊Q₈	—	251	1	no	—
233	C₂×#121	—	251	1	no	—
234	C₂×#121	—	251	1	no	—
235	C₂×#121	—	251	1	no	—
236	C₂×#121	D₂₅₁	1	1	yes	characteristic, complemented
237	C₂²×Q₈	—	251	1	no	—
238	C₂²×Q₈	—	251	1	no	—
239	C₂²×D₄	—	251	1	no	—
240	C₂²×D₄	—	251	1	no	—
241	C₂²×D₄	—	251	1	no	—
242	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
243	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
244	C₂²×D₄	C₂×D₂₅₁	1	1	yes	characteristic
245	C₂³×C₄	—	251	1	no	—
246	C₂³×C₄	—	251	1	no	—
247	C₂³×C₄	—	251	1	no	—
248	C₂³×C₄	C₂×D₂₅₁	1	1	yes	characteristic
249	#125	—	251	8	no	—
250	#124	—	251	8	no	—
251	#124	—	251	8	no	—
252	#123	—	251	8	no	—
253	#123	—	251	8	no	—
254	#123	—	251	8	no	—
255	#123	—	251	8	no	—
256	C₂²⋊Q₈	—	251	8	no	—
257	C₂²⋊Q₈	—	251	8	no	—
258	C₂²⋊Q₈	—	251	8	no	—
259	C₂²⋊Q₈	—	251	8	no	—
260	#121	—	251	8	no	—
261	#121	—	251	8	no	—
262	#121	—	251	8	no	—
263	#121	C₂×D₂₅₁	1	8	yes	complemented
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	—	251	1	no	—
270	C₂×C₄⋊C₄	—	251	1	no	—
271	C₂×C₄⋊C₄	—	251	1	no	—
272	C₂×C₄⋊C₄	—	251	1	no	—
273	C₂×C₄⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
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	1	no	—
281	C₂×C₂²⋊C₄	—	251	1	no	—
282	C₂×C₂²⋊C₄	—	251	1	no	—
283	C₂×C₂²⋊C₄	—	251	1	no	—
284	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂×D₂₅₁	1	1	yes	characteristic
286	C₂×C₄²	—	251	1	no	—
287	C₂⁴	—	251	1	no	—
288	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
289	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
290	C₂⁴	C₂²×D₂₅₁	1	1	yes	characteristic
291	C₂×Q₈	—	1004	2	no	—
292	C₂×Q₈	—	1004	2	no	—
293	C₂×Q₈	—	251	4	no	—
294	C₂×Q₈	—	251	4	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	1004	2	no	—
299	C₂×D₄	—	1004	2	no	—
300	C₂×D₄	—	1004	2	no	—
301	C₂×D₄	—	251	4	no	—
302	C₂×D₄	—	251	4	no	—
303	C₂×D₄	—	251	4	no	—
304	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
305	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
306	C₂×D₄	C₂²×D₂₅₁	1	4	yes	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	1004	2	no	—
309	C₂²×C₄	—	1004	2	no	—
310	C₂²×C₄	—	1004	2	no	—
311	C₂²×C₄	—	251	4	no	—
312	C₂²×C₄	—	251	4	no	—
313	C₂²×C₄	—	251	4	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	1	no	—
319	C₂²×C₄	—	251	1	no	—
320	C₂²×C₄	—	251	1	no	—
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	1	yes	characteristic
325	C₂²×C₄	C₂²×D₂₅₁	1	4	yes	—
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	—	251	4	no	—
334	C₄⋊C₄	—	251	4	no	—
335	C₄⋊C₄	C₂²×D₂₅₁	1	4	yes	—
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	—
348	C₄²	—	251	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
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	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	502	2	no	—
359	C₂³	—	502	2	no	—
360	C₂³	—	502	2	no	—
361	C₂³	—	251	2	no	—
362	C₂³	C₂³×D₂₅₁	1	2	yes	—
363	C₂³	C₂³×D₂₅₁	1	2	yes	—
364	C₂³	C₂³×D₂₅₁	1	2	yes	—
365	C₂³	C₂³×D₂₅₁	1	1	yes	characteristic
366	Q₈	—	1004	4	no	—
367	Q₈	—	1004	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	1004	4	no	—
372	D₄	—	1004	4	no	—
373	D₄	—	1004	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	1004	4	no	—
380	C₂×C₄	—	1004	4	no	—
381	C₂×C₄	—	1004	4	no	—
382	C₂×C₄	—	502	2	no	—
383	C₂×C₄	—	502	2	no	—
384	C₂×C₄	—	502	2	no	—
385	C₂×C₄	—	502	2	no	—
386	C₂×C₄	—	502	2	no	—
387	C₂×C₄	—	502	2	no	—
388	C₂×C₄	—	502	2	no	—
389	C₂×C₄	—	251	2	no	—
390	C₂×C₄	—	251	2	no	—
391	C₂×C₄	—	251	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	C₂³×D₂₅₁	1	2	yes	—
397	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
398	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
399	C₂×C₄	C₂³×D₂₅₁	1	2	yes	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	1004	4	no	—
413	C₂²	—	502	2	no	—
414	C₂²	—	502	2	no	—
415	C₂²	—	502	2	no	—
416	C₂²	#22548760	1	2	yes	—
417	C₂²	#22548760	1	2	yes	—
418	C₂²	#22548762	1	2	yes	—
419	C₂²	C₂⁴×D₂₅₁	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	502	2	no	—
425	C₄	—	502	2	no	—
426	C₄	—	502	2	no	—
427	C₄	—	502	2	no	—
428	C₄	—	502	2	no	—
429	C₄	—	502	2	no	—
430	C₄	—	502	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	4	2	no	—
433	C₂	—	4	2	no	—
434	C₂	—	1004	2	no	—
435	C₂	#30632432	1	4	yes	direct product factor
436	C₂	C₂×#22548760	1	1	yes	characteristic
437	C₂	C₂×#22548760	1	1	yes	characteristic
438	C₂	C₂×#22548762	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₅₁
commutator, cosocle	C₂²×C₂₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₂₅₁
Fitting	C₂×#121×C₂₅₁	C₂
socle	C₂³×C₂₅₁	C₂⁴
hypercenter	C₂×#121	D₂₅₁
hypocenter	C₂₅₁	C₂×#562
LCS	G ▷ C₂²×C₂₅₁ ▷ C₂₅₁
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. #30632432	C₂	direct (N × H)
2. C₂×#22548705	C₂	semidirect
3. C₂×#22548702	C₂	semidirect
4. C₂×#22548701	C₂	semidirect
5. C₂×#22548698	C₂	semidirect
6. C₂×#22548697	C₂	semidirect
7. C₂×#22548696	C₂	semidirect
8. C₂×#22548696	C₂	semidirect
9. C₂×#22548694	C₂	semidirect
10. C₂×#22548693	C₂	semidirect
11. C₂×#22548692	C₂	semidirect
12. C₂×#22548692	C₂	semidirect
13. C₂×#22548687	C₂	semidirect
14. C₂×#22548687	C₂	semidirect
15. C₂×#22548686	C₂	semidirect
16. C₂×#121×C₂₅₁	C₂	semidirect
25. #22548705	C₂²	semidirect
26. #22548702	C₂²	semidirect
27. #22548701	C₂²	semidirect
28. #22548698	C₂²	semidirect
29. #22548697	C₂²	semidirect
30. #22548696	C₂²	semidirect
31. #22548696	C₂²	semidirect
32. #22548694	C₂²	semidirect
33. #22548693	C₂²	semidirect
34. #22548692	C₂²	semidirect
35. #22548692	C₂²	semidirect
36. #22548687	C₂²	semidirect
37. #22548687	C₂²	semidirect
38. #22548686	C₂²	semidirect
63. #121×C₂₅₁	C₂²	semidirect
214. C₂×C₂₅₁	#562	semidirect
219. C₂₅₁	C₂×#562	semidirect
236. C₂×#121	D₂₅₁	semidirect
263. #121	C₂×D₂₅₁	semidirect
435. C₂	#30632432	direct (N × H)

Maximal subgroups

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

subgroup	index
#30632432	2
C₂×#22548705	2
C₂×#22548702	2
C₂×#22548701	2
C₂×#22548698	2
C₂×#22548697	2
C₂×#22548696	2
C₂×#22548694	2
C₂×#22548693	2
C₂×#22548692	2
C₂×#22548687	2
C₂×#22548686	2
C₂×#121×C₂₅₁	2
C₂×#562	251

Subgroups — C2×#30632432 #44564489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30632432 #44564489