Subgroups — #2412×C₁₅₁ #34065744

Order 19328.

814 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#123×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#120×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₂²⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#397×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#394×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	#386×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#386×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#385×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#381×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#380×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	C₂⁵×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂²×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂²×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₅₁	C₂²	1	2	yes	—
18	C₂³×C₄×C₁₅₁	C₂²	1	1	yes	characteristic
19	#123×C₁₅₁	—	2	4	no	—
20	#120×C₁₅₁	—	2	4	no	—
21	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	complemented
22	C₂×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊C₄×C₁₅₁	—	2	4	no	—
24	C₂×C₂²⋊C₄×C₁₅₁	—	2	4	no	—
25	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	complemented
34	C₂×C₂²⋊C₄×C₁₅₁	C₂²	1	2	yes	complemented
35	#95×C₁₅₁	C₂²	1	2	yes	complemented
36	#95×C₁₅₁	C₂²	1	2	yes	complemented
37	#95×C₁₅₁	C₂²	1	2	yes	complemented
38	#95×C₁₅₁	C₂²	1	2	yes	complemented
39	C₂⁴×C₁₅₁	—	2	2	no	—
40	C₂⁴×C₁₅₁	—	2	2	no	—
41	C₂⁴×C₁₅₁	—	2	4	no	—
42	C₂⁴×C₁₅₁	—	4	2	no	—
43	C₂⁴×C₁₅₁	D₄	1	4	yes	—
44	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
45	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
46	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
47	C₂⁴×C₁₅₁	C₂³	1	1	yes	characteristic
48	C₂×D₄×C₁₅₁	—	2	2	no	—
49	C₂×D₄×C₁₅₁	—	2	2	no	—
50	C₂×D₄×C₁₅₁	—	2	2	no	—
51	C₂×D₄×C₁₅₁	—	2	2	no	—
52	C₂×D₄×C₁₅₁	—	2	2	no	—
53	C₂×D₄×C₁₅₁	—	2	4	no	—
54	C₂×D₄×C₁₅₁	—	4	2	no	—
55	C₂²×C₄×C₁₅₁	—	2	2	no	—
56	C₂²×C₄×C₁₅₁	—	2	2	no	—
57	C₂²×C₄×C₁₅₁	—	2	2	no	—
58	C₂²×C₄×C₁₅₁	—	2	4	no	—
59	C₂²×C₄×C₁₅₁	—	2	2	no	—
60	C₂²×C₄×C₁₅₁	—	2	4	no	—
61	C₂²×C₄×C₁₅₁	—	4	2	no	—
62	C₂²×C₄×C₁₅₁	—	4	2	no	—
63	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
65	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
66	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
67	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₅₁	C₂³	1	2	yes	—
70	C₄⋊C₄×C₁₅₁	—	2	4	no	—
71	C₄⋊C₄×C₁₅₁	—	4	2	no	—
72	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
73	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
74	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
75	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
76	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
77	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
78	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
79	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
80	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
81	C₂²⋊C₄×C₁₅₁	D₄	1	4	yes	complemented
82	C₂³×C₁₅₁	—	2	1	no	—
83	C₂³×C₁₅₁	—	2	1	no	—
84	C₂³×C₁₅₁	—	2	2	no	—
85	C₂³×C₁₅₁	—	2	2	no	—
86	C₂³×C₁₅₁	—	2	2	no	—
87	C₂³×C₁₅₁	—	2	8	no	—
88	C₂³×C₁₅₁	—	2	8	no	—
89	C₂³×C₁₅₁	—	2	1	no	—
90	C₂³×C₁₅₁	—	2	1	no	—
91	C₂³×C₁₅₁	—	2	2	no	—
92	C₂³×C₁₅₁	—	2	2	no	—
93	C₂³×C₁₅₁	—	2	1	no	—
94	C₂³×C₁₅₁	—	2	1	no	—
95	C₂³×C₁₅₁	—	2	1	no	—
96	C₂³×C₁₅₁	—	2	2	no	—
97	C₂³×C₁₅₁	—	2	2	no	—
98	C₂³×C₁₅₁	—	4	4	no	—
99	C₂³×C₁₅₁	—	4	8	no	—
100	C₂³×C₁₅₁	—	4	8	no	—
101	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
102	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
103	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
104	C₂³×C₁₅₁	C₂×D₄	1	2	yes	—
105	C₂³×C₁₅₁	#41	1	2	yes	—
106	C₂³×C₁₅₁	#41	1	4	yes	—
107	C₂³×C₁₅₁	C₂⁴	1	1	yes	characteristic
108	D₄×C₁₅₁	—	4	4	no	—
109	D₄×C₁₅₁	—	4	4	no	—
110	D₄×C₁₅₁	—	4	4	no	—
111	C₂×C₄×C₁₅₁	—	2	2	no	—
112	C₂×C₄×C₁₅₁	—	2	2	no	—
113	C₂×C₄×C₁₅₁	—	2	2	no	—
114	C₂×C₄×C₁₅₁	—	2	2	no	—
115	C₂×C₄×C₁₅₁	—	2	2	no	—
116	C₂×C₄×C₁₅₁	—	2	1	no	—
117	C₂×C₄×C₁₅₁	—	2	1	no	—
118	C₂×C₄×C₁₅₁	—	2	1	no	—
119	C₂×C₄×C₁₅₁	—	2	2	no	—
120	C₂×C₄×C₁₅₁	—	2	1	no	—
121	C₂×C₄×C₁₅₁	—	2	2	no	—
122	C₂×C₄×C₁₅₁	—	2	2	no	—
123	C₂×C₄×C₁₅₁	—	2	1	no	—
124	C₂×C₄×C₁₅₁	—	2	2	no	—
125	C₂×C₄×C₁₅₁	—	2	2	no	—
126	C₂×C₄×C₁₅₁	—	2	2	no	—
127	C₂×C₄×C₁₅₁	—	2	2	no	—
128	C₂×C₄×C₁₅₁	—	2	2	no	—
129	C₂×C₄×C₁₅₁	—	4	8	no	—
130	C₂×C₄×C₁₅₁	—	4	4	no	—
131	C₂×C₄×C₁₅₁	—	4	4	no	—
132	C₂×C₄×C₁₅₁	C₂×D₄	1	4	yes	—
133	C₂²×C₁₅₁	—	2	2	no	—
134	C₂²×C₁₅₁	—	2	2	no	—
135	C₂²×C₁₅₁	—	2	2	no	—
136	C₂²×C₁₅₁	—	2	2	no	—
137	C₂²×C₁₅₁	—	2	4	no	—
138	C₂²×C₁₅₁	—	2	4	no	—
139	C₂²×C₁₅₁	—	2	4	no	—
140	C₂²×C₁₅₁	—	2	4	no	—
141	C₂²×C₁₅₁	—	2	2	no	—
142	C₂²×C₁₅₁	—	2	2	no	—
143	C₂²×C₁₅₁	—	2	2	no	—
144	C₂²×C₁₅₁	—	4	16	no	—
145	C₂²×C₁₅₁	—	4	2	no	—
146	C₂²×C₁₅₁	—	4	2	no	—
147	C₂²×C₁₅₁	—	4	1	no	—
148	C₂²×C₁₅₁	—	4	1	no	—
149	C₂²×C₁₅₁	—	4	1	no	—
150	C₂²×C₁₅₁	—	4	2	no	—
151	C₂²×C₁₅₁	—	4	2	no	—
152	C₂²×C₁₅₁	#121	1	4	yes	—
153	C₂²×C₁₅₁	#123	1	4	yes	complemented
154	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
155	C₂²×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
156	C₂²×C₁₅₁	C₂×#41	1	1	yes	characteristic
157	C₂²×C₁₅₁	C₂×#41	1	2	yes	—
158	C₂²×C₁₅₁	H(5,𝔽₂)	1	2	yes	—
159	C₄×C₁₅₁	—	2	4	no	—
160	C₄×C₁₅₁	—	4	2	no	—
161	C₄×C₁₅₁	—	4	1	no	—
162	C₄×C₁₅₁	—	4	1	no	—
163	C₄×C₁₅₁	—	4	2	no	—
164	C₄×C₁₅₁	—	4	1	no	—
165	C₄×C₁₅₁	—	4	2	no	—
166	C₂×C₁₅₁	—	2	4	no	—
167	C₂×C₁₅₁	—	2	4	no	—
168	C₂×C₁₅₁	—	4	2	no	—
169	C₂×C₁₅₁	—	8	1	no	—
170	C₂×C₁₅₁	C₂×#121	1	1	yes	characteristic
171	C₂×C₁₅₁	C₂×#123	1	1	yes	characteristic
172	C₂×C₁₅₁	#534	1	1	yes	characteristic
173	C₂×C₁₅₁	#546	1	2	yes	—
174	C₂×C₁₅₁	#551	1	2	yes	—
175	C₁₅₁	#2412	1	1	yes	characteristic, direct product factor, Sylow
176	#2412	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂×#123	C₂×C₁₅₁	1	1	yes	characteristic, complemented
178	C₂×#120	C₂×C₁₅₁	1	1	yes	characteristic
179	C₂²×C₂²⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
180	C₂²×C₂²⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
181	#397	C₂×C₁₅₁	1	2	yes	complemented
182	#394	C₂×C₁₅₁	1	2	yes	complemented
183	#386	C₂×C₁₅₁	1	1	yes	characteristic, complemented
184	#386	C₂×C₁₅₁	1	2	yes	complemented
185	#385	C₂×C₁₅₁	1	1	yes	characteristic, complemented
186	#381	C₂×C₁₅₁	1	1	yes	characteristic, complemented
187	#380	C₂×C₁₅₁	1	2	yes	complemented
188	C₂⁵	C₂²×C₁₅₁	1	1	yes	characteristic
189	C₂²×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
190	C₂²×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
191	C₂²×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
192	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
193	C₂³×C₄	C₂²×C₁₅₁	1	2	yes	—
194	C₂³×C₄	C₂²×C₁₅₁	1	1	yes	characteristic
195	#123	—	2	4	no	—
196	#120	—	2	4	no	—
197	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	complemented
198	C₂×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	complemented
199	C₂×C₂²⋊C₄	—	2	4	no	—
200	C₂×C₂²⋊C₄	—	2	4	no	—
201	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
202	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
206	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
207	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
208	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
209	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	complemented
210	C₂×C₂²⋊C₄	C₂²×C₁₅₁	1	2	yes	complemented
211	#95	C₂²×C₁₅₁	1	2	yes	complemented
212	#95	C₂²×C₁₅₁	1	2	yes	complemented
213	#95	C₂²×C₁₅₁	1	2	yes	complemented
214	#95	C₂²×C₁₅₁	1	2	yes	complemented
215	C₂⁴	—	2	2	no	—
216	C₂⁴	—	2	4	no	—
217	C₂⁴	—	2	2	no	—
218	C₂⁴	—	4	2	no	—
219	C₂⁴	D₄×C₁₅₁	1	4	yes	—
220	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
221	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
222	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
223	C₂⁴	C₂³×C₁₅₁	1	1	yes	characteristic
224	C₂×D₄	—	2	2	no	—
225	C₂×D₄	—	2	4	no	—
226	C₂×D₄	—	2	2	no	—
227	C₂×D₄	—	2	2	no	—
228	C₂×D₄	—	2	2	no	—
229	C₂×D₄	—	2	2	no	—
230	C₂×D₄	—	4	2	no	—
231	C₂²×C₄	—	2	4	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	4	2	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
240	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
241	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
242	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
243	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₁₅₁	1	2	yes	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₂²⋊C₄	—	2	4	no	—
249	C₂²⋊C₄	—	2	2	no	—
250	C₂²⋊C₄	—	2	4	no	—
251	C₂²⋊C₄	—	2	2	no	—
252	C₂²⋊C₄	—	2	2	no	—
253	C₂²⋊C₄	—	2	2	no	—
254	C₂²⋊C₄	—	2	4	no	—
255	C₂²⋊C₄	—	2	4	no	—
256	C₂²⋊C₄	—	4	2	no	—
257	C₂²⋊C₄	D₄×C₁₅₁	1	4	yes	complemented
258	C₂³	—	2	1	no	—
259	C₂³	—	2	1	no	—
260	C₂³	—	2	2	no	—
261	C₂³	—	2	2	no	—
262	C₂³	—	2	2	no	—
263	C₂³	—	2	8	no	—
264	C₂³	—	2	8	no	—
265	C₂³	—	2	1	no	—
266	C₂³	—	2	1	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	—	2	1	no	—
270	C₂³	—	2	1	no	—
271	C₂³	—	2	1	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	2	no	—
274	C₂³	—	4	4	no	—
275	C₂³	—	4	8	no	—
276	C₂³	—	4	8	no	—
277	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
278	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
279	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
280	C₂³	C₂×D₄×C₁₅₁	1	2	yes	—
281	C₂³	#41×C₁₅₁	1	2	yes	—
282	C₂³	#41×C₁₅₁	1	4	yes	—
283	C₂³	C₂⁴×C₁₅₁	1	1	yes	characteristic
284	D₄	—	4	4	no	—
285	D₄	—	4	4	no	—
286	D₄	—	4	4	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	1	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	4	8	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	C₂×D₄×C₁₅₁	1	4	yes	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	4	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	4	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	4	16	no	—
321	C₂²	—	4	2	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	4	1	no	—
324	C₂²	—	4	1	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	2	no	—
328	C₂²	#121×C₁₅₁	1	4	yes	—
329	C₂²	#123×C₁₅₁	1	4	yes	complemented
330	C₂²	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
331	C₂²	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
332	C₂²	C₂×#41×C₁₅₁	1	1	yes	characteristic
333	C₂²	C₂×#41×C₁₅₁	1	2	yes	—
334	C₂²	H(5,𝔽₂)×C₁₅₁	1	2	yes	—
335	C₄	—	2	4	no	—
336	C₄	—	4	2	no	—
337	C₄	—	4	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	4	2	no	—
340	C₄	—	4	1	no	—
341	C₄	—	4	2	no	—
342	C₂	—	2	4	no	—
343	C₂	—	2	4	no	—
344	C₂	—	4	2	no	—
345	C₂	—	8	1	no	—
346	C₂	C₂×#121×C₁₅₁	1	1	yes	characteristic
347	C₂	C₂×#123×C₁₅₁	1	1	yes	characteristic
348	C₂	#534×C₁₅₁	1	1	yes	characteristic
349	C₂	#546×C₁₅₁	1	2	yes	—
350	C₂	#551×C₁₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₅₁
prime radical	C₂×#120×C₁₅₁	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#123×C₁₅₁	C₂	semidirect
3. C₂²×C₂²⋊C₄×C₁₅₁	C₂	semidirect
4. C₂²×C₂²⋊C₄×C₁₅₁	C₂	semidirect
5. #397×C₁₅₁	C₂	semidirect
6. #394×C₁₅₁	C₂	semidirect
7. #386×C₁₅₁	C₂	semidirect
8. #386×C₁₅₁	C₂	semidirect
9. #385×C₁₅₁	C₂	semidirect
10. #381×C₁₅₁	C₂	semidirect
11. #380×C₁₅₁	C₂	semidirect
21. C₂×C₄⋊C₄×C₁₅₁	C₂²	semidirect
22. C₂×C₄⋊C₄×C₁₅₁	C₂²	semidirect
33. C₂×C₂²⋊C₄×C₁₅₁	C₂²	semidirect
34. C₂×C₂²⋊C₄×C₁₅₁	C₂²	semidirect
35. #95×C₁₅₁	C₂²	semidirect
36. #95×C₁₅₁	C₂²	semidirect
37. #95×C₁₅₁	C₂²	semidirect
38. #95×C₁₅₁	C₂²	semidirect
81. C₂²⋊C₄×C₁₅₁	D₄	semidirect
153. C₂²×C₁₅₁	#123	semidirect
175. C₁₅₁	#2412	direct (N × H)
176. #2412	C₁₅₁	direct (N × H)
177. C₂×#123	C₂×C₁₅₁	semidirect
179. C₂²×C₂²⋊C₄	C₂×C₁₅₁	semidirect
180. C₂²×C₂²⋊C₄	C₂×C₁₅₁	semidirect
181. #397	C₂×C₁₅₁	semidirect
182. #394	C₂×C₁₅₁	semidirect
183. #386	C₂×C₁₅₁	semidirect
184. #386	C₂×C₁₅₁	semidirect
185. #385	C₂×C₁₅₁	semidirect
186. #381	C₂×C₁₅₁	semidirect
187. #380	C₂×C₁₅₁	semidirect
197. C₂×C₄⋊C₄	C₂²×C₁₅₁	semidirect
198. C₂×C₄⋊C₄	C₂²×C₁₅₁	semidirect
209. C₂×C₂²⋊C₄	C₂²×C₁₅₁	semidirect
210. C₂×C₂²⋊C₄	C₂²×C₁₅₁	semidirect
211. #95	C₂²×C₁₅₁	semidirect
212. #95	C₂²×C₁₅₁	semidirect
213. #95	C₂²×C₁₅₁	semidirect
214. #95	C₂²×C₁₅₁	semidirect
257. C₂²⋊C₄	D₄×C₁₅₁	semidirect
329. C₂²	#123×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#123×C₁₅₁	2
C₂×#120×C₁₅₁	2
C₂²×C₂²⋊C₄×C₁₅₁	2
#397×C₁₅₁	2
#394×C₁₅₁	2
#386×C₁₅₁	2
#385×C₁₅₁	2
#381×C₁₅₁	2
#380×C₁₅₁	2
#2412	151

Subgroups — #2412×C151 #34065744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2412×C₁₅₁ #34065744