Subgroups — C₂×#23752721 #34082350

Order 19328.

1880 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14559004	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#23752721	C₂	1	16	yes	maximal, direct product factor
4	C₂×#18012724	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#18012721	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#18012717	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#18012716	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#18012712	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#18012711	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#18012709	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#18012707	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₆₀₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₄×C₂²⋊D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#18012696	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₁₅₁	C₂²	1	1	yes	characteristic
18	C₂×#14559004	—	2	8	no	—
19	C₂×#14559004	C₂²	1	8	yes	complemented
20	C₂²×Dic₃₀₂	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₆₀₄	C₂²	1	1	yes	characteristic
22	C₂²×D₆₀₄	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₅₁	C₂²	1	1	yes	characteristic, complemented
27	C₂³×Dic₁₅₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₅₁	—	2	8	no	—
29	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₁₅₁	C₂²	1	8	yes	complemented
34	C₂²×C₄×D₁₅₁	C₂²	1	1	yes	characteristic, complemented
35	#18012724	C₂²	1	8	yes	complemented
36	#18012721	C₂²	1	8	yes	complemented
37	#18012717	C₂²	1	8	yes	complemented
38	#18012716	C₂²	1	8	yes	complemented
39	#18012712	C₂²	1	8	yes	complemented
40	#18012711	C₂²	1	8	yes	complemented
41	#18012709	C₂²	1	8	yes	complemented
42	#18012707	C₂²	1	8	yes	complemented
43	C₄×D₆₀₄	C₂²	1	8	yes	complemented
44	C₄×C₂²⋊D₁₅₁	C₂²	1	8	yes	complemented
45	C₄×C₂²⋊D₁₅₁	C₂²	1	8	yes	complemented
46	#18012696	C₂²	1	8	yes	complemented
47	C₂×C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×Dic₁₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×Dic₁₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×Dic₁₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×Dic₁₅₁⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂²⋊Dic₁₅₁	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
54	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂×(C₂×D₁₅₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×Dic₁₅₁	C₂²	1	1	yes	characteristic, complemented
61	C₂²×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
62	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
63	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
64	C₄×D₄×C₁₅₁	C₂²	1	8	yes	complemented
65	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic, complemented
69	C₂³×D₁₅₁	—	2	4	no	—
70	C₂³×D₁₅₁	—	2	4	no	—
71	C₂³×D₁₅₁	—	2	4	no	—
72	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
73	C₂³×D₁₅₁	C₂³	1	4	yes	—
74	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
75	C₂³×D₁₅₁	C₂³	1	1	yes	characteristic
76	#14559004	—	2	32	no	—
77	C₂×Dic₃₀₂	—	2	4	no	—
78	C₂×Dic₃₀₂	C₂³	1	4	yes	complemented
79	C₂×D₆₀₄	—	2	4	no	—
80	C₂×D₆₀₄	—	2	4	no	—
81	C₂×D₆₀₄	C₂³	1	4	yes	—
82	C₂×D₆₀₄	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₅₁	—	2	4	no	—
84	C₂×C₂²⋊D₁₅₁	—	2	4	no	—
85	C₂×C₂²⋊D₁₅₁	—	2	4	no	—
86	C₂×C₂²⋊D₁₅₁	—	2	4	no	—
87	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
88	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₅₁	C₂³	1	4	yes	complemented
91	C₂²×Dic₁₅₁	—	2	4	no	—
92	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
93	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
94	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
96	C₂²×Dic₁₅₁	C₂³	1	4	yes	—
97	C₂²×Dic₁₅₁	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₅₁	—	2	4	no	—
99	C₂×C₄×D₁₅₁	—	2	4	no	—
100	C₂×C₄×D₁₅₁	—	2	32	no	—
101	C₂×C₄×D₁₅₁	—	2	4	no	—
102	C₂×C₄×D₁₅₁	—	2	4	no	—
103	C₂×C₄×D₁₅₁	D₄	1	8	yes	complemented
104	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
105	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
106	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
107	C₂×C₄×D₁₅₁	C₂³	1	4	yes	—
108	C₂×C₄×D₁₅₁	C₂³	1	4	yes	complemented
109	C₄⋊Dic₁₅₁	C₂³	1	4	yes	complemented
110	Dic₁₅₁⋊C₄	C₂³	1	4	yes	complemented
111	Dic₁₅₁⋊C₄	C₂³	1	4	yes	complemented
112	Dic₁₅₁⋊C₄	C₂³	1	4	yes	complemented
113	Dic₁₅₁⋊C₄	C₂³	1	4	yes	complemented
114	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₅₁	C₂³	1	4	yes	complemented
116	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
117	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	complemented
121	(C₂×D₁₅₁)⋊C₄	C₂³	1	4	yes	complemented
122	C₄×Dic₁₅₁	C₂³	1	4	yes	complemented
123	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
124	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₅₁	—	2	4	no	—
126	C₂×D₄×C₁₅₁	C₂³	1	4	yes	—
127	C₂²×C₄×C₁₅₁	—	2	4	no	—
128	C₂²×C₄×C₁₅₁	—	2	4	no	—
129	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₅₁	C₂³	1	4	yes	—
134	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₅₁	C₂³	1	4	yes	complemented
136	C₄⋊C₄×C₁₅₁	C₂³	1	4	yes	complemented
137	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	—
138	C₂²⋊C₄×C₁₅₁	C₂³	1	4	yes	complemented
139	C₄²×C₁₅₁	C₂³	1	4	yes	complemented
140	C₂²×D₁₅₁	—	2	32	no	—
141	C₂²×D₁₅₁	—	2	2	no	—
142	C₂²×D₁₅₁	—	2	2	no	—
143	C₂²×D₁₅₁	—	2	2	no	—
144	C₂²×D₁₅₁	—	2	2	no	—
145	C₂²×D₁₅₁	—	2	8	no	—
146	C₂²×D₁₅₁	—	2	8	no	—
147	C₂²×D₁₅₁	—	2	8	no	—
148	C₂²×D₁₅₁	—	2	2	no	—
149	C₂²×D₁₅₁	—	2	2	no	—
150	C₂²×D₁₅₁	—	2	2	no	—
151	C₂²×D₁₅₁	C₂×D₄	1	4	yes	—
152	C₂²×D₁₅₁	#41	1	4	yes	complemented
153	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
154	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
155	C₂²×D₁₅₁	C₂⁴	1	2	yes	—
156	Dic₃₀₂	—	2	8	no	—
157	D₆₀₄	—	2	8	no	—
158	D₆₀₄	—	2	8	no	—
159	C₂²⋊D₁₅₁	—	2	8	no	—
160	C₂²⋊D₁₅₁	—	2	8	no	—
161	C₂²⋊D₁₅₁	—	2	8	no	—
162	C₂²⋊D₁₅₁	—	2	8	no	—
163	C₂×Dic₁₅₁	—	2	2	no	—
164	C₂×Dic₁₅₁	—	2	2	no	—
165	C₂×Dic₁₅₁	—	2	2	no	—
166	C₂×Dic₁₅₁	—	2	2	no	—
167	C₂×Dic₁₅₁	—	2	8	no	—
168	C₂×Dic₁₅₁	C₂×D₄	1	4	yes	—
169	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
170	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
171	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
172	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
173	C₂×Dic₁₅₁	C₂⁴	1	2	yes	—
174	C₄×D₁₅₁	—	2	8	no	—
175	C₄×D₁₅₁	—	2	8	no	—
176	C₄×D₁₅₁	—	2	8	no	—
177	C₄×D₁₅₁	—	2	8	no	—
178	C₄×D₁₅₁	C₂×D₄	1	16	yes	complemented
179	C₂³×C₁₅₁	—	2	2	no	—
180	C₂³×C₁₅₁	—	2	2	no	—
181	C₂³×C₁₅₁	—	2	2	no	—
182	C₂³×C₁₅₁	—	2	2	no	—
183	C₂³×C₁₅₁	—	2	2	no	—
184	C₂³×C₁₅₁	#41	1	4	yes	complemented
185	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
186	C₂³×C₁₅₁	C₂⁴	1	2	yes	—
187	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
188	D₄×C₁₅₁	—	2	8	no	—
189	C₂×C₄×C₁₅₁	—	2	2	no	—
190	C₂×C₄×C₁₅₁	—	2	2	no	—
191	C₂×C₄×C₁₅₁	—	2	2	no	—
192	C₂×C₄×C₁₅₁	—	2	2	no	—
193	C₂×C₄×C₁₅₁	—	2	8	no	—
194	C₂×C₄×C₁₅₁	—	2	8	no	—
195	C₂×C₄×C₁₅₁	C₂×D₄	1	4	yes	—
196	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
197	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
198	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
199	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
200	C₂×C₄×C₁₅₁	C₂⁴	1	2	yes	—
201	C₂²×C₁₅₁	—	2	8	no	—
202	C₂²×C₁₅₁	—	2	2	no	—
203	C₂²×C₁₅₁	—	2	2	no	—
204	C₂²×C₁₅₁	—	2	2	no	—
205	C₂²×C₁₅₁	—	2	2	no	—
206	C₂²×C₁₅₁	—	2	2	no	—
207	C₂²×C₁₅₁	—	4	4	no	—
208	C₂²×C₁₅₁	C₂²×D₄	1	2	yes	—
209	C₂²×C₁₅₁	C₂×#41	1	2	yes	—
210	C₂²×C₁₅₁	C₂×#41	1	2	yes	—
211	C₂²×C₁₅₁	C₂×#41	1	4	yes	complemented
212	C₂²×C₁₅₁	C₂⁵	1	1	yes	characteristic
213	C₂×D₁₅₁	—	2	32	no	—
214	C₂×D₁₅₁	—	2	8	no	—
215	C₂×D₁₅₁	—	2	8	no	—
216	C₂×D₁₅₁	—	2	2	no	—
217	C₂×D₁₅₁	—	2	2	no	—
218	C₂×D₁₅₁	—	2	2	no	—
219	C₂×D₁₅₁	—	2	2	no	—
220	C₂×D₁₅₁	—	2	2	no	—
221	C₂×D₁₅₁	—	2	2	no	—
222	C₂×D₁₅₁	—	2	2	no	—
223	C₂×D₁₅₁	—	4	4	no	—
224	C₂×D₁₅₁	C₂²×D₄	1	4	yes	—
225	C₂×D₁₅₁	C₂×#41	1	4	yes	complemented
226	C₄×C₁₅₁	—	2	2	no	—
227	C₄×C₁₅₁	—	2	2	no	—
228	C₄×C₁₅₁	—	2	2	no	—
229	C₄×C₁₅₁	—	2	2	no	—
230	C₄×C₁₅₁	C₂²×D₄	1	4	yes	—
231	Dic₁₅₁	—	2	2	no	—
232	Dic₁₅₁	—	2	2	no	—
233	Dic₁₅₁	—	2	2	no	—
234	Dic₁₅₁	—	2	2	no	—
235	Dic₁₅₁	C₂²×D₄	1	4	yes	—
236	C₂×C₁₅₁	—	2	4	no	—
237	C₂×C₁₅₁	—	4	2	no	—
238	C₂×C₁₅₁	#525	1	4	yes	complemented
239	C₂×C₁₅₁	C₂³×D₄	1	1	yes	characteristic
240	C₂×C₁₅₁	C₂²×#41	1	1	yes	characteristic
241	C₂×C₁₅₁	C₂²×#41	1	1	yes	characteristic
242	D₁₅₁	—	2	4	no	—
243	D₁₅₁	—	2	4	no	—
244	D₁₅₁	—	4	2	no	—
245	C₁₅₁	C₂×#525	1	1	yes	characteristic, complemented, Sylow
246	C₂×#525	—	151	1	no	maximal, Sylow
247	C₂²×#41	—	151	1	no	—
248	C₂⁴×C₄	—	151	1	no	—
249	#525	—	151	16	no	—
250	C₂×#123	—	151	1	no	—
251	C₂×#123	—	151	1	no	—
252	C₂×C₂²⋊Q₈	—	151	1	no	—
253	C₂×C₂²⋊Q₈	—	151	1	no	—
254	C₂×#121	—	151	1	no	—
255	C₂×#121	—	151	1	no	—
256	C₂×#120	—	151	1	no	—
257	C₂×#120	—	151	1	no	—
258	C₂×C₄×D₄	—	151	1	no	—
259	C₂×C₄×D₄	—	151	1	no	—
260	C₂×C₄×D₄	—	151	1	no	—
261	C₂×C₄×D₄	D₁₅₁	1	1	yes	characteristic, complemented
262	C₂×#117	—	151	1	no	—
263	C₂⁵	—	151	1	no	—
264	C₂×#41	—	302	8	no	—
265	C₂×#41	—	151	8	no	—
266	C₂²×Q₈	—	151	1	no	—
267	C₂²×D₄	—	151	1	no	—
268	C₂²×D₄	—	151	1	no	—
269	C₂²×D₄	—	151	1	no	—
270	C₂²×D₄	—	151	1	no	—
271	C₂²×D₄	—	151	1	no	—
272	C₂²×D₄	—	151	1	no	—
273	C₂²×D₄	C₂×D₁₅₁	1	1	yes	characteristic
274	C₂³×C₄	—	302	8	no	—
275	C₂³×C₄	—	151	1	no	—
276	C₂³×C₄	—	151	1	no	—
277	C₂³×C₄	—	151	1	no	—
278	C₂³×C₄	—	151	8	no	—
279	C₂³×C₄	—	151	1	no	—
280	C₂³×C₄	—	151	1	no	—
281	C₂³×C₄	—	151	1	no	—
282	C₂³×C₄	C₂×D₁₅₁	1	1	yes	characteristic
283	C₂³×C₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
284	#123	—	151	8	no	—
285	#123	—	151	8	no	—
286	C₂²⋊Q₈	—	151	8	no	—
287	C₂²⋊Q₈	—	151	8	no	—
288	#121	—	151	8	no	—
289	#121	—	151	8	no	—
290	#120	—	151	8	no	—
291	#120	—	151	8	no	—
292	C₄×D₄	—	151	8	no	—
293	C₄×D₄	—	151	8	no	—
294	C₄×D₄	—	151	8	no	—
295	C₄×D₄	C₂×D₁₅₁	1	8	yes	complemented
296	#117	—	151	8	no	—
297	C₂×C₄⋊C₄	—	151	1	no	—
298	C₂×C₄⋊C₄	—	151	1	no	—
299	C₂×C₄⋊C₄	—	151	1	no	—
300	C₂×C₄⋊C₄	—	151	1	no	—
301	C₂×C₄⋊C₄	—	151	1	no	—
302	C₂×C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
303	C₂×C₂²⋊C₄	—	151	1	no	—
304	C₂×C₂²⋊C₄	—	151	1	no	—
305	C₂×C₂²⋊C₄	—	151	1	no	—
306	C₂×C₂²⋊C₄	—	151	1	no	—
307	C₂×C₂²⋊C₄	—	151	1	no	—
308	C₂×C₂²⋊C₄	—	151	1	no	—
309	C₂×C₂²⋊C₄	—	151	1	no	—
310	C₂×C₂²⋊C₄	—	151	1	no	—
311	C₂×C₂²⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic, complemented
313	C₂×C₄²	—	151	1	no	—
314	C₂×C₄²	C₂×D₁₅₁	1	1	yes	characteristic, complemented
315	C₂⁴	—	302	4	no	—
316	C₂⁴	—	302	4	no	—
317	C₂⁴	—	302	4	no	—
318	C₂⁴	—	151	1	no	—
319	C₂⁴	—	151	4	no	—
320	C₂⁴	—	151	1	no	—
321	C₂⁴	—	151	1	no	—
322	C₂⁴	C₂²×D₁₅₁	1	1	yes	characteristic
323	C₂⁴	C₂²×D₁₅₁	1	1	yes	characteristic
324	#41	—	302	32	no	—
325	C₂×Q₈	—	302	4	no	—
326	C₂×Q₈	—	151	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	302	4	no	—
329	C₂×D₄	—	302	4	no	—
330	C₂×D₄	—	302	4	no	—
331	C₂×D₄	—	302	4	no	—
332	C₂×D₄	—	302	4	no	—
333	C₂×D₄	—	302	4	no	—
334	C₂×D₄	—	151	4	no	—
335	C₂×D₄	—	151	4	no	—
336	C₂×D₄	—	151	4	no	—
337	C₂×D₄	—	151	4	no	—
338	C₂×D₄	—	151	4	no	—
339	C₂×D₄	—	151	4	no	—
340	C₂×D₄	C₂²×D₁₅₁	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	302	4	no	—
344	C₂²×C₄	—	302	4	no	—
345	C₂²×C₄	—	302	32	no	—
346	C₂²×C₄	—	302	4	no	—
347	C₂²×C₄	—	302	4	no	—
348	C₂²×C₄	—	302	4	no	—
349	C₂²×C₄	—	151	1	no	—
350	C₂²×C₄	—	151	1	no	—
351	C₂²×C₄	—	151	1	no	—
352	C₂²×C₄	—	151	1	no	—
353	C₂²×C₄	—	151	4	no	—
354	C₂²×C₄	—	151	4	no	—
355	C₂²×C₄	—	151	4	no	—
356	C₂²×C₄	—	151	4	no	—
357	C₂²×C₄	—	151	4	no	—
358	C₂²×C₄	—	151	1	no	—
359	C₂²×C₄	—	151	8	no	—
360	C₂²×C₄	—	151	4	no	—
361	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
362	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
363	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
364	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
365	C₂²×C₄	C₂²×D₁₅₁	1	4	yes	—
366	C₂²×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
367	C₂²×C₄	C₂²×D₁₅₁	1	4	yes	complemented
368	C₄⋊C₄	—	151	4	no	—
369	C₄⋊C₄	—	151	4	no	—
370	C₄⋊C₄	—	151	4	no	—
371	C₄⋊C₄	—	151	4	no	—
372	C₄⋊C₄	—	151	4	no	—
373	C₄⋊C₄	C₂²×D₁₅₁	1	4	yes	complemented
374	C₂²⋊C₄	—	151	4	no	—
375	C₂²⋊C₄	—	151	4	no	—
376	C₂²⋊C₄	—	151	4	no	—
377	C₂²⋊C₄	—	151	4	no	—
378	C₂²⋊C₄	—	151	4	no	—
379	C₂²⋊C₄	—	151	4	no	—
380	C₂²⋊C₄	—	151	4	no	—
381	C₂²⋊C₄	—	151	4	no	—
382	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	—
383	C₂²⋊C₄	C₂²×D₁₅₁	1	4	yes	complemented
384	C₄²	—	151	4	no	—
385	C₄²	C₂²×D₁₅₁	1	4	yes	complemented
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	302	32	no	—
392	C₂³	—	302	8	no	—
393	C₂³	—	302	8	no	—
394	C₂³	—	302	2	no	—
395	C₂³	—	302	2	no	—
396	C₂³	—	302	2	no	—
397	C₂³	—	302	2	no	—
398	C₂³	—	302	8	no	—
399	C₂³	—	302	2	no	—
400	C₂³	—	302	2	no	—
401	C₂³	—	302	2	no	—
402	C₂³	—	151	2	no	—
403	C₂³	—	151	4	no	—
404	C₂³	—	151	4	no	—
405	C₂³	—	151	2	no	—
406	C₂³	—	151	2	no	—
407	C₂³	#14559004	1	4	yes	complemented
408	C₂³	C₂³×D₁₅₁	1	2	yes	—
409	C₂³	C₂³×D₁₅₁	1	2	yes	—
410	C₂³	C₂³×D₁₅₁	1	1	yes	characteristic
411	Q₈	—	302	8	no	—
412	D₄	—	2	8	no	—
413	D₄	—	302	8	no	—
414	D₄	—	302	8	no	—
415	D₄	—	302	8	no	—
416	D₄	—	302	8	no	—
417	D₄	—	302	8	no	—
418	D₄	—	302	8	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	302	8	no	—
426	C₂×C₄	—	302	8	no	—
427	C₂×C₄	—	302	2	no	—
428	C₂×C₄	—	302	2	no	—
429	C₂×C₄	—	302	2	no	—
430	C₂×C₄	—	302	2	no	—
431	C₂×C₄	—	302	8	no	—
432	C₂×C₄	—	302	8	no	—
433	C₂×C₄	—	302	8	no	—
434	C₂×C₄	—	151	2	no	—
435	C₂×C₄	—	151	2	no	—
436	C₂×C₄	—	151	2	no	—
437	C₂×C₄	—	151	2	no	—
438	C₂×C₄	—	151	4	no	—
439	C₂×C₄	—	151	2	no	—
440	C₂×C₄	—	151	16	no	—
441	C₂×C₄	D₄×D₁₅₁	1	4	yes	—
442	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
443	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
444	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
445	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
446	C₂×C₄	C₂³×D₁₅₁	1	2	yes	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	302	32	no	—
455	C₂²	—	302	8	no	—
456	C₂²	—	302	8	no	—
457	C₂²	—	302	2	no	—
458	C₂²	—	302	2	no	—
459	C₂²	—	302	2	no	—
460	C₂²	—	302	2	no	—
461	C₂²	—	302	2	no	—
462	C₂²	—	302	2	no	—
463	C₂²	—	302	2	no	—
464	C₂²	—	604	4	no	—
465	C₂²	—	151	4	no	—
466	C₂²	—	151	4	no	—
467	C₂²	C₂×D₄×D₁₅₁	1	2	yes	—
468	C₂²	#41×D₁₅₁	1	2	yes	—
469	C₂²	C₂×#14559004	1	2	yes	—
470	C₂²	C₂×#14559004	1	4	yes	complemented
471	C₂²	C₂⁴×D₁₅₁	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	302	2	no	—
477	C₄	—	302	2	no	—
478	C₄	—	302	2	no	—
479	C₄	—	302	2	no	—
480	C₄	—	151	4	no	—
481	C₄	C₂×D₄×D₁₅₁	1	4	yes	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	302	4	no	—
485	C₂	—	302	4	no	—
486	C₂	—	604	2	no	—
487	C₂	#23752721	1	4	yes	direct product factor
488	C₂	C₂²×D₄×D₁₅₁	1	1	yes	characteristic
489	C₂	C₂×#41×D₁₅₁	1	1	yes	characteristic
490	C₂	C₂²×#14559004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×D₁₅₁
commutator, cosocle	C₂²×C₁₅₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₅₁
Fitting	C₂×C₄×D₄×C₁₅₁	C₂
socle	C₂³×C₁₅₁	C₂⁴
hypercenter	C₂×C₄×D₄	D₁₅₁
hypocenter	C₁₅₁	C₂×#525
LCS	G ▷ C₂²×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#14559004	C₂	semidirect
2. C₂³×C₄×D₁₅₁	C₂	semidirect
3. #23752721	C₂	direct (N × H)
4. C₂×#18012724	C₂	semidirect
5. C₂×#18012721	C₂	semidirect
6. C₂×#18012717	C₂	semidirect
7. C₂×#18012716	C₂	semidirect
8. C₂×#18012712	C₂	semidirect
9. C₂×#18012711	C₂	semidirect
10. C₂×#18012709	C₂	semidirect
11. C₂×#18012707	C₂	semidirect
12. C₂×C₄×D₆₀₄	C₂	semidirect
13. C₂×C₄×C₂²⋊D₁₅₁	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₅₁	C₂	semidirect
15. C₂×#18012696	C₂	semidirect
16. C₂×C₄×D₄×C₁₅₁	C₂	semidirect
19. C₂×#14559004	C₂²	semidirect
20. C₂²×Dic₃₀₂	C₂²	semidirect
26. C₂²×C₂²⋊D₁₅₁	C₂²	semidirect
33. C₂²×C₄×D₁₅₁	C₂²	semidirect
34. C₂²×C₄×D₁₅₁	C₂²	semidirect
35. #18012724	C₂²	semidirect
36. #18012721	C₂²	semidirect
37. #18012717	C₂²	semidirect
38. #18012716	C₂²	semidirect
39. #18012712	C₂²	semidirect
40. #18012711	C₂²	semidirect
41. #18012709	C₂²	semidirect
42. #18012707	C₂²	semidirect
43. C₄×D₆₀₄	C₂²	semidirect
44. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
45. C₄×C₂²⋊D₁₅₁	C₂²	semidirect
46. #18012696	C₂²	semidirect
47. C₂×C₄⋊Dic₁₅₁	C₂²	semidirect
48. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
49. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
50. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
51. C₂×Dic₁₅₁⋊C₄	C₂²	semidirect
53. C₂×C₂²⋊Dic₁₅₁	C₂²	semidirect
58. C₂×(C₂×D₁₅₁)⋊C₄	C₂²	semidirect
59. C₂×(C₂×D₁₅₁)⋊C₄	C₂²	semidirect
60. C₂×C₄×Dic₁₅₁	C₂²	semidirect
63. C₂³×C₄×C₁₅₁	C₂²	semidirect
64. C₄×D₄×C₁₅₁	C₂²	semidirect
65. C₂×C₄⋊C₄×C₁₅₁	C₂²	semidirect
67. C₂×C₂²⋊C₄×C₁₅₁	C₂²	semidirect
68. C₂×C₄²×C₁₅₁	C₂²	semidirect
78. C₂×Dic₃₀₂	C₂³	semidirect
90. C₂×C₂²⋊D₁₅₁	C₂³	semidirect
103. C₂×C₄×D₁₅₁	D₄	semidirect
108. C₂×C₄×D₁₅₁	C₂³	semidirect
109. C₄⋊Dic₁₅₁	C₂³	semidirect
110. Dic₁₅₁⋊C₄	C₂³	semidirect
111. Dic₁₅₁⋊C₄	C₂³	semidirect
112. Dic₁₅₁⋊C₄	C₂³	semidirect
113. Dic₁₅₁⋊C₄	C₂³	semidirect
115. C₂²⋊Dic₁₅₁	C₂³	semidirect
120. (C₂×D₁₅₁)⋊C₄	C₂³	semidirect
121. (C₂×D₁₅₁)⋊C₄	C₂³	semidirect
122. C₄×Dic₁₅₁	C₂³	semidirect
135. C₂²×C₄×C₁₅₁	C₂³	semidirect
136. C₄⋊C₄×C₁₅₁	C₂³	semidirect
138. C₂²⋊C₄×C₁₅₁	C₂³	semidirect
139. C₄²×C₁₅₁	C₂³	semidirect
152. C₂²×D₁₅₁	#41	semidirect
178. C₄×D₁₅₁	C₂×D₄	semidirect
184. C₂³×C₁₅₁	#41	semidirect
211. C₂²×C₁₅₁	C₂×#41	semidirect
225. C₂×D₁₅₁	C₂×#41	semidirect
238. C₂×C₁₅₁	#525	semidirect
245. C₁₅₁	C₂×#525	semidirect
261. C₂×C₄×D₄	D₁₅₁	semidirect
283. C₂³×C₄	C₂×D₁₅₁	semidirect
295. C₄×D₄	C₂×D₁₅₁	semidirect
302. C₂×C₄⋊C₄	C₂×D₁₅₁	semidirect
312. C₂×C₂²⋊C₄	C₂×D₁₅₁	semidirect
314. C₂×C₄²	C₂×D₁₅₁	semidirect
367. C₂²×C₄	C₂²×D₁₅₁	semidirect
373. C₄⋊C₄	C₂²×D₁₅₁	semidirect
383. C₂²⋊C₄	C₂²×D₁₅₁	semidirect
385. C₄²	C₂²×D₁₅₁	semidirect
407. C₂³	#14559004	semidirect
470. C₂²	C₂×#14559004	semidirect
487. C₂	#23752721	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×#14559004	2
C₂³×C₄×D₁₅₁	2
#23752721	2
C₂×#18012724	2
C₂×#18012721	2
C₂×#18012717	2
C₂×#18012716	2
C₂×#18012712	2
C₂×#18012711	2
C₂×#18012709	2
C₂×#18012707	2
C₂×C₄×D₆₀₄	2
C₂×C₄×C₂²⋊D₁₅₁	2
C₂×#18012696	2
C₂×C₄×D₄×C₁₅₁	2
C₂×#525	151

Subgroups — C2×#23752721 #34082350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23752721 #34082350