Subgroups — C₁₅₁×#8026 #50312951

Order 38656.

742 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#431×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#2285×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#382×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#1294×C₁₅₁	C₂	1	4	yes	maximal
5	C₂×#117×C₁₅₁	—	2	1	no	—
6	C₂²×C₄⋊C₄×C₁₅₁	—	2	1	no	—
7	C₂²×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
8	#431×C₁₅₁	—	2	2	no	—
9	#431×C₁₅₁	C₄	1	4	yes	complemented
10	C₂×C₄⋊C₈×C₁₅₁	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₁₅₁	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₅₁	—	2	1	no	—
13	#384×C₁₅₁	C₄	1	2	yes	complemented
14	#382×C₁₅₁	—	2	2	no	—
15	#382×C₁₅₁	—	2	1	no	—
16	#382×C₁₅₁	C₄	1	4	yes	complemented
17	#380×C₁₅₁	—	2	1	no	—
18	#380×C₁₅₁	C₂²	1	2	yes	—
19	C₄×C₄⋊C₄×C₁₅₁	—	2	1	no	—
20	C₄×C₄⋊C₄×C₁₅₁	C₄	1	2	yes	complemented
21	C₂×#95×C₁₅₁	—	2	1	no	—
22	C₂×#95×C₁₅₁	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₅₁	—	2	2	no	—
24	C₂³×C₄×C₁₅₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₅₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₅₁	—	2	2	no	—
28	#117×C₁₅₁	—	4	2	no	—
29	#117×C₁₅₁	—	4	2	no	—
30	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₅₁	—	2	4	no	—
32	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₁₅₁	—	4	2	no	—
34	C₂×C₄⋊C₄×C₁₅₁	—	4	2	no	—
35	C₂×C₄⋊C₄×C₁₅₁	C₂×C₄	1	4	yes	—
36	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
37	C₂×C₄²×C₁₅₁	—	2	2	no	—
38	C₂×C₄²×C₁₅₁	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₅₁	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₅₁	D₄	1	2	yes	—
45	C₂×C₄²×C₁₅₁	Q₈	1	2	yes	—
46	C₄⋊C₈×C₁₅₁	—	2	4	no	—
47	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
48	C₂²⋊C₈×C₁₅₁	C₂×C₄	1	4	yes	—
49	C₄×C₈×C₁₅₁	—	2	4	no	—
50	#95×C₁₅₁	—	2	4	no	—
51	#95×C₁₅₁	—	2	2	no	—
52	#95×C₁₅₁	—	2	2	no	—
53	#95×C₁₅₁	—	2	2	no	—
54	#95×C₁₅₁	C₂×C₄	1	4	yes	—
55	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₅₁	—	2	4	no	—
57	C₂²×C₄×C₁₅₁	—	2	4	no	—
58	C₂²×C₄×C₁₅₁	—	4	2	no	—
59	C₂²×C₄×C₁₅₁	—	4	2	no	—
60	C₂²×C₄×C₁₅₁	—	4	4	no	—
61	C₂²×C₄×C₁₅₁	—	4	4	no	—
62	C₂²×C₄×C₁₅₁	—	4	2	no	—
63	C₂²×C₄×C₁₅₁	—	4	2	no	—
64	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	2	yes	—
72	C₂²×C₄×C₁₅₁	D₈	1	2	yes	—
73	C₂²×C₄×C₁₅₁	SD₁₆	1	2	yes	—
74	C₂²×C₄×C₁₅₁	SD₁₆	1	2	yes	—
75	C₂²×C₄×C₁₅₁	Q₁₆	1	2	yes	—
76	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
82	C₂×C₈×C₁₅₁	—	2	4	no	—
83	C₂×C₈×C₁₅₁	—	4	4	no	—
84	C₄⋊C₄×C₁₅₁	—	4	4	no	—
85	C₄⋊C₄×C₁₅₁	—	4	4	no	—
86	C₄⋊C₄×C₁₅₁	—	4	8	no	—
87	C₄⋊C₄×C₁₅₁	—	4	4	no	—
88	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
89	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
90	C₄²×C₁₅₁	—	4	4	no	—
91	C₄²×C₁₅₁	C₄²	1	2	yes	—
92	C₄²×C₁₅₁	C₄²	1	2	yes	—
93	C₄²×C₁₅₁	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₁₅₁	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₁₅₁	C₄⋊C₄	1	2	yes	—
96	C₄²×C₁₅₁	C₄⋊C₄	1	2	yes	—
97	C₄²×C₁₅₁	C₄⋊C₄	1	2	yes	—
98	C₄²×C₁₅₁	C₄⋊C₄	1	2	yes	—
99	C₂³×C₁₅₁	—	2	2	no	—
100	C₂³×C₁₅₁	—	2	2	no	—
101	C₂³×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂³×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂³×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
104	C₂³×C₁₅₁	C₂×D₈	1	1	yes	characteristic
105	C₂³×C₁₅₁	C₂×SD₁₆	1	1	yes	characteristic
106	C₂³×C₁₅₁	C₂×SD₁₆	1	1	yes	characteristic
107	C₂³×C₁₅₁	C₂×Q₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₅₁	—	2	2	no	—
109	C₂×C₄×C₁₅₁	—	2	2	no	—
110	C₂×C₄×C₁₅₁	—	2	2	no	—
111	C₂×C₄×C₁₅₁	—	2	2	no	—
112	C₂×C₄×C₁₅₁	—	4	2	no	—
113	C₂×C₄×C₁₅₁	—	4	2	no	—
114	C₂×C₄×C₁₅₁	—	4	1	no	—
115	C₂×C₄×C₁₅₁	—	4	1	no	—
116	C₂×C₄×C₁₅₁	—	4	1	no	—
117	C₂×C₄×C₁₅₁	—	4	1	no	—
118	C₂×C₄×C₁₅₁	—	4	4	no	—
119	C₂×C₄×C₁₅₁	—	4	4	no	—
120	C₂×C₄×C₁₅₁	—	4	4	no	—
121	C₂×C₄×C₁₅₁	—	4	4	no	—
122	C₂×C₄×C₁₅₁	—	4	4	no	—
123	C₂×C₄×C₁₅₁	—	4	4	no	—
124	C₂×C₄×C₁₅₁	—	8	4	no	—
125	C₂×C₄×C₁₅₁	—	8	4	no	—
126	C₂×C₄×C₁₅₁	#95	1	2	yes	—
127	C₂×C₄×C₁₅₁	#95	1	2	yes	—
128	C₂×C₄×C₁₅₁	#95	1	2	yes	—
129	C₂×C₄×C₁₅₁	#95	1	2	yes	—
130	C₂×C₄×C₁₅₁	#102	1	2	yes	—
131	C₂×C₄×C₁₅₁	#102	1	4	yes	—
132	C₂×C₄×C₁₅₁	#102	1	2	yes	—
133	C₂×C₄×C₁₅₁	#103	1	4	yes	—
134	C₂×C₄×C₁₅₁	#103	1	2	yes	—
135	C₂×C₄×C₁₅₁	#103	1	2	yes	—
136	C₂×C₄×C₁₅₁	#106	1	4	yes	—
137	C₂×C₄×C₁₅₁	#107	1	4	yes	—
138	C₂×C₄×C₁₅₁	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₈×C₁₅₁	—	4	4	no	—
143	C₂²×C₁₅₁	—	2	1	no	—
144	C₂²×C₁₅₁	—	2	1	no	—
145	C₂²×C₁₅₁	—	2	1	no	—
146	C₂²×C₁₅₁	—	2	1	no	—
147	C₂²×C₁₅₁	—	2	2	no	—
148	C₂²×C₁₅₁	—	2	2	no	—
149	C₂²×C₁₅₁	—	2	2	no	—
150	C₂²×C₁₅₁	—	2	2	no	—
151	C₂²×C₁₅₁	C₂×#95	1	1	yes	characteristic
152	C₂²×C₁₅₁	#410	1	2	yes	—
153	C₂²×C₁₅₁	C₂×#102	1	1	yes	characteristic
154	C₂²×C₁₅₁	C₂×#102	1	1	yes	characteristic
155	C₂²×C₁₅₁	C₂×#103	1	1	yes	characteristic
156	C₂²×C₁₅₁	C₂×#103	1	1	yes	characteristic
157	C₂²×C₁₅₁	#421	1	2	yes	—
158	C₂²×C₁₅₁	C₂×#106	1	1	yes	characteristic
159	C₂²×C₁₅₁	C₂×#107	1	1	yes	characteristic
160	C₄×C₁₅₁	—	2	2	no	—
161	C₄×C₁₅₁	—	2	2	no	—
162	C₄×C₁₅₁	—	2	1	no	—
163	C₄×C₁₅₁	—	2	1	no	—
164	C₄×C₁₅₁	—	2	1	no	—
165	C₄×C₁₅₁	—	2	1	no	—
166	C₄×C₁₅₁	—	8	4	no	—
167	C₄×C₁₅₁	—	8	4	no	—
168	C₄×C₁₅₁	#340	1	4	yes	—
169	C₄×C₁₅₁	#340	1	4	yes	—
170	C₂×C₁₅₁	—	2	1	no	—
171	C₂×C₁₅₁	—	2	1	no	—
172	C₂×C₁₅₁	—	2	1	no	—
173	C₂×C₁₅₁	—	2	1	no	—
174	C₂×C₁₅₁	#1517	1	2	yes	—
175	C₂×C₁₅₁	#1518	1	2	yes	—
176	C₂×C₁₅₁	#1733	1	1	yes	characteristic
177	C₂×C₁₅₁	C₂×#340	1	1	yes	characteristic
178	C₂×C₁₅₁	#1740	1	1	yes	characteristic
179	#8026	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₁₅₁	#8026	1	1	yes	characteristic, direct product factor, Sylow
181	C₂×#431	C₂×C₁₅₁	1	1	yes	characteristic
182	#2285	C₂×C₁₅₁	1	1	yes	characteristic
183	C₂×#382	C₂×C₁₅₁	1	1	yes	characteristic
184	#1294	C₂×C₁₅₁	1	4	yes	—
185	C₂×#117	—	2	1	no	—
186	C₂²×C₄⋊C₄	—	2	1	no	—
187	C₂²×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
188	#431	—	2	2	no	—
189	#431	C₄×C₁₅₁	1	4	yes	complemented
190	C₂×C₄⋊C₈	—	2	1	no	—
191	C₂×C₂²⋊C₈	C₂²×C₁₅₁	1	2	yes	—
192	C₂×C₄×C₈	—	2	1	no	—
193	#384	C₄×C₁₅₁	1	2	yes	complemented
194	#382	—	2	2	no	—
195	#382	—	2	1	no	—
196	#382	C₄×C₁₅₁	1	4	yes	complemented
197	#380	—	2	1	no	—
198	#380	C₂²×C₁₅₁	1	2	yes	—
199	C₄×C₄⋊C₄	—	2	1	no	—
200	C₄×C₄⋊C₄	C₄×C₁₅₁	1	2	yes	complemented
201	C₂×#95	—	2	1	no	—
202	C₂×#95	C₂²×C₁₅₁	1	2	yes	—
203	C₂³×C₄	—	2	2	no	—
204	C₂³×C₄	D₄×C₁₅₁	1	1	yes	characteristic
205	C₂³×C₄	D₄×C₁₅₁	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
207	C₂²×C₈	—	2	2	no	—
208	#117	—	4	2	no	—
209	#117	—	4	2	no	—
210	C₂×C₄⋊C₄	—	2	4	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	2	no	—
213	C₂×C₄⋊C₄	—	4	2	no	—
214	C₂×C₄⋊C₄	—	4	2	no	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₅₁	1	4	yes	—
216	C₂×C₂²⋊C₄	—	2	2	no	—
217	C₂×C₄²	—	2	2	no	—
218	C₂×C₄²	C₂×C₄×C₁₅₁	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₁₅₁	1	2	yes	—
221	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
222	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
223	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
224	C₂×C₄²	D₄×C₁₅₁	1	2	yes	—
225	C₂×C₄²	Q₈×C₁₅₁	1	2	yes	—
226	C₄⋊C₈	—	2	4	no	—
227	C₂²⋊C₈	—	2	2	no	—
228	C₂²⋊C₈	C₂×C₄×C₁₅₁	1	4	yes	—
229	C₄×C₈	—	2	4	no	—
230	#95	—	2	4	no	—
231	#95	—	2	2	no	—
232	#95	—	2	2	no	—
233	#95	—	2	2	no	—
234	#95	C₂×C₄×C₁₅₁	1	4	yes	—
235	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	4	2	no	—
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	4	no	—
241	C₂²×C₄	—	4	4	no	—
242	C₂²×C₄	—	4	2	no	—
243	C₂²×C₄	—	4	2	no	—
244	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
246	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
247	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
248	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
249	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
250	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	2	yes	—
251	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	2	yes	—
252	C₂²×C₄	D₈×C₁₅₁	1	2	yes	—
253	C₂²×C₄	SD₁₆×C₁₅₁	1	2	yes	—
254	C₂²×C₄	SD₁₆×C₁₅₁	1	2	yes	—
255	C₂²×C₄	Q₁₆×C₁₅₁	1	2	yes	—
256	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
258	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
261	C₂²×C₄	C₂×Q₈×C₁₅₁	1	1	yes	characteristic
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	4	4	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₄⋊C₄	—	4	4	no	—
266	C₄⋊C₄	—	4	8	no	—
267	C₄⋊C₄	—	4	4	no	—
268	C₂²⋊C₄	—	4	2	no	—
269	C₂²⋊C₄	—	4	2	no	—
270	C₄²	—	4	4	no	—
271	C₄²	C₄²×C₁₅₁	1	2	yes	—
272	C₄²	C₄²×C₁₅₁	1	2	yes	—
273	C₄²	C₂²⋊C₄×C₁₅₁	1	2	yes	—
274	C₄²	C₂²⋊C₄×C₁₅₁	1	2	yes	—
275	C₄²	C₄⋊C₄×C₁₅₁	1	2	yes	—
276	C₄²	C₄⋊C₄×C₁₅₁	1	2	yes	—
277	C₄²	C₄⋊C₄×C₁₅₁	1	2	yes	—
278	C₄²	C₄⋊C₄×C₁₅₁	1	2	yes	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
282	C₂³	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
283	C₂³	C₂×C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
284	C₂³	C₂×D₈×C₁₅₁	1	1	yes	characteristic
285	C₂³	C₂×SD₁₆×C₁₅₁	1	1	yes	characteristic
286	C₂³	C₂×SD₁₆×C₁₅₁	1	1	yes	characteristic
287	C₂³	C₂×Q₁₆×C₁₅₁	1	1	yes	characteristic
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	—	4	1	no	—
293	C₂×C₄	—	4	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	1	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	1	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	4	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	—	8	4	no	—
305	C₂×C₄	—	8	4	no	—
306	C₂×C₄	#95×C₁₅₁	1	2	yes	—
307	C₂×C₄	#95×C₁₅₁	1	2	yes	—
308	C₂×C₄	#95×C₁₅₁	1	2	yes	—
309	C₂×C₄	#95×C₁₅₁	1	2	yes	—
310	C₂×C₄	#102×C₁₅₁	1	2	yes	—
311	C₂×C₄	#102×C₁₅₁	1	4	yes	—
312	C₂×C₄	#102×C₁₅₁	1	2	yes	—
313	C₂×C₄	#103×C₁₅₁	1	4	yes	—
314	C₂×C₄	#103×C₁₅₁	1	2	yes	—
315	C₂×C₄	#103×C₁₅₁	1	2	yes	—
316	C₂×C₄	#106×C₁₅₁	1	4	yes	—
317	C₂×C₄	#107×C₁₅₁	1	4	yes	—
318	C₂×C₄	C₂×C₄²×C₁₅₁	1	1	yes	characteristic
319	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
322	C₈	—	4	4	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	C₂×#95×C₁₅₁	1	1	yes	characteristic
332	C₂²	#410×C₁₅₁	1	2	yes	—
333	C₂²	C₂×#102×C₁₅₁	1	1	yes	characteristic
334	C₂²	C₂×#102×C₁₅₁	1	1	yes	characteristic
335	C₂²	C₂×#103×C₁₅₁	1	1	yes	characteristic
336	C₂²	C₂×#103×C₁₅₁	1	1	yes	characteristic
337	C₂²	#421×C₁₅₁	1	2	yes	—
338	C₂²	C₂×#106×C₁₅₁	1	1	yes	characteristic
339	C₂²	C₂×#107×C₁₅₁	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	8	4	no	—
347	C₄	—	8	4	no	—
348	C₄	#340×C₁₅₁	1	4	yes	—
349	C₄	#340×C₁₅₁	1	4	yes	—
350	C₂	—	2	1	no	—
351	C₂	—	2	1	no	—
352	C₂	—	2	1	no	—
353	C₂	—	2	1	no	—
354	C₂	#1517×C₁₅₁	1	2	yes	—
355	C₂	#1518×C₁₅₁	1	2	yes	—
356	C₂	#1733×C₁₅₁	1	1	yes	characteristic
357	C₂	C₂×#340×C₁₅₁	1	1	yes	characteristic
358	C₂	#1740×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₁₅₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₅₁
prime radical	C₂⁴×C₁₅₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₂²×C₄²×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. #431×C₁₅₁	C₄	semidirect
13. #384×C₁₅₁	C₄	semidirect
16. #382×C₁₅₁	C₄	semidirect
20. C₄×C₄⋊C₄×C₁₅₁	C₄	semidirect
179. #8026	C₁₅₁	direct (N × H)
180. C₁₅₁	#8026	direct (N × H)
189. #431	C₄×C₁₅₁	semidirect
193. #384	C₄×C₁₅₁	semidirect
196. #382	C₄×C₁₅₁	semidirect
200. C₄×C₄⋊C₄	C₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#431×C₁₅₁	2
#2285×C₁₅₁	2
C₂×#382×C₁₅₁	2
#1294×C₁₅₁	2
#8026	151

Subgroups — C151×#8026 #50312951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#8026 #50312951