Subgroups — C₁₅₁×#8079 #50313004

Order 38656.

634 conjugacy classes of subgroups.

The subgroup lattice has 406 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	C₂×#423×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#423×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#1301×C₁₅₁	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₁₅₁	—	2	1	no	—
6	C₂²×M₁₆×C₁₅₁	—	2	1	no	—
7	C₂²×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
8	#431×C₁₅₁	—	2	1	no	—
9	#431×C₁₅₁	—	2	1	no	—
10	#431×C₁₅₁	C₄	1	2	yes	—
11	#431×C₁₅₁	C₂²	1	2	yes	—
12	#423×C₁₅₁	—	2	1	no	—
13	#423×C₁₅₁	—	2	1	no	—
14	#423×C₁₅₁	—	2	1	no	—
15	#423×C₁₅₁	—	2	1	no	—
16	#423×C₁₅₁	C₄	1	2	yes	—
17	#423×C₁₅₁	C₄	1	2	yes	—
18	#423×C₁₅₁	C₄	1	2	yes	—
19	#423×C₁₅₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₁₅₁	—	2	1	no	—
21	C₂×C₄⋊C₈×C₁₅₁	—	2	1	no	—
22	C₂×C₄⋊C₈×C₁₅₁	—	2	1	no	—
23	C₂×C₄⋊C₈×C₁₅₁	C₄	1	2	yes	—
24	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₁₅₁	C₄	1	2	yes	—
26	C₂×C₄×C₈×C₁₅₁	—	2	1	no	—
27	C₂³×C₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₅₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₅₁	Q₈	1	1	yes	characteristic
30	C₂×M₁₆×C₁₅₁	—	2	2	no	—
31	C₂×M₁₆×C₁₅₁	—	2	2	no	—
32	C₂×M₁₆×C₁₅₁	—	2	2	no	—
33	C₂×M₁₆×C₁₅₁	—	2	2	no	—
34	C₂×M₁₆×C₁₅₁	—	4	2	no	—
35	C₂×M₁₆×C₁₅₁	—	4	2	no	—
36	C₂×M₁₆×C₁₅₁	—	4	2	no	—
37	C₂×M₁₆×C₁₅₁	—	4	2	no	—
38	C₂²×C₈×C₁₅₁	—	2	2	no	—
39	C₂²×C₈×C₁₅₁	—	2	2	no	—
40	C₂²×C₈×C₁₅₁	—	2	2	no	—
41	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₅₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₅₁	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
53	C₄⋊C₈×C₁₅₁	—	2	2	no	—
54	C₄⋊C₈×C₁₅₁	—	2	2	no	—
55	C₄⋊C₈×C₁₅₁	—	2	2	no	—
56	C₄⋊C₈×C₁₅₁	—	2	2	no	—
57	C₄⋊C₈×C₁₅₁	—	2	2	no	—
58	C₄⋊C₈×C₁₅₁	—	2	2	no	—
59	C₄⋊C₈×C₁₅₁	—	2	2	no	—
60	C₄⋊C₈×C₁₅₁	—	2	2	no	—
61	C₄⋊C₈×C₁₅₁	C₂×C₄	1	4	yes	—
62	C₄⋊C₈×C₁₅₁	C₂×C₄	1	4	yes	—
63	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
64	C₂²⋊C₈×C₁₅₁	C₂×C₄	1	4	yes	—
65	C₄×C₈×C₁₅₁	—	2	2	no	—
66	C₄×C₈×C₁₅₁	—	2	2	no	—
67	C₂⁴×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₅₁	—	4	2	no	—
69	C₂²×C₄×C₁₅₁	—	4	2	no	—
70	C₂²×C₄×C₁₅₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₅₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₅₁	D₈	1	2	yes	—
86	C₂²×C₄×C₁₅₁	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₁₅₁	SD₁₆	1	2	yes	—
88	C₂²×C₄×C₁₅₁	Q₁₆	1	2	yes	—
89	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
92	M₁₆×C₁₅₁	—	4	4	no	—
93	M₁₆×C₁₅₁	—	4	4	no	—
94	M₁₆×C₁₅₁	—	4	4	no	—
95	M₁₆×C₁₅₁	—	4	2	no	—
96	M₁₆×C₁₅₁	—	4	2	no	—
97	C₂×C₈×C₁₅₁	—	2	4	no	—
98	C₂×C₈×C₁₅₁	—	2	4	no	—
99	C₂×C₈×C₁₅₁	—	2	4	no	—
100	C₂×C₈×C₁₅₁	—	4	4	no	—
101	C₂×C₈×C₁₅₁	—	4	4	no	—
102	C₂×C₈×C₁₅₁	—	4	2	no	—
103	C₂×C₈×C₁₅₁	—	4	2	no	—
104	C₄²×C₁₅₁	C₄²	1	1	yes	characteristic
105	C₄²×C₁₅₁	C₄²	1	1	yes	characteristic
106	C₄²×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₄²×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₁₅₁	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
120	C₂³×C₁₅₁	—	4	1	no	—
121	C₂³×C₁₅₁	—	4	1	no	—
122	C₂³×C₁₅₁	#95	1	1	yes	characteristic
123	C₂³×C₁₅₁	#95	1	1	yes	characteristic
124	C₂³×C₁₅₁	#106	1	2	yes	—
125	C₂³×C₁₅₁	#107	1	2	yes	—
126	C₂³×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₅₁	—	2	2	no	—
128	C₂×C₄×C₁₅₁	—	2	2	no	—
129	C₂×C₄×C₁₅₁	—	2	2	no	—
130	C₂×C₄×C₁₅₁	—	2	2	no	—
131	C₂×C₄×C₁₅₁	—	2	2	no	—
132	C₂×C₄×C₁₅₁	—	2	2	no	—
133	C₂×C₄×C₁₅₁	—	4	1	no	—
134	C₂×C₄×C₁₅₁	—	4	1	no	—
135	C₂×C₄×C₁₅₁	—	4	1	no	—
136	C₂×C₄×C₁₅₁	—	4	1	no	—
137	C₂×C₄×C₁₅₁	—	4	1	no	—
138	C₂×C₄×C₁₅₁	—	4	1	no	—
139	C₂×C₄×C₁₅₁	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₅₁	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₅₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₅₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₅₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₅₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₅₁	#102	1	2	yes	—
146	C₂×C₄×C₁₅₁	#102	1	2	yes	—
147	C₂×C₄×C₁₅₁	#102	1	2	yes	—
148	C₂×C₄×C₁₅₁	#102	1	2	yes	—
149	C₂×C₄×C₁₅₁	#103	1	2	yes	—
150	C₂×C₄×C₁₅₁	#103	1	2	yes	—
151	C₂×C₄×C₁₅₁	#103	1	2	yes	—
152	C₂×C₄×C₁₅₁	#103	1	2	yes	—
153	C₂×C₄×C₁₅₁	#106	1	2	yes	—
154	C₂×C₄×C₁₅₁	#107	1	2	yes	—
155	C₂×C₄×C₁₅₁	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₅₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₅₁	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₅₁	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₅₁	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₅₁	C₂×Q₁₆	1	1	yes	characteristic
165	C₈×C₁₅₁	—	4	4	no	—
166	C₈×C₁₅₁	—	4	4	no	—
167	C₈×C₁₅₁	—	4	4	no	—
168	C₂²×C₁₅₁	—	2	1	no	—
169	C₂²×C₁₅₁	—	2	1	no	—
170	C₂²×C₁₅₁	—	2	1	no	—
171	C₂²×C₁₅₁	—	2	1	no	—
172	C₂²×C₁₅₁	—	2	1	no	—
173	C₂²×C₁₅₁	—	2	1	no	—
174	C₂²×C₁₅₁	—	4	2	no	—
175	C₂²×C₁₅₁	—	4	2	no	—
176	C₂²×C₁₅₁	#340	1	2	yes	—
177	C₂²×C₁₅₁	#340	1	2	yes	—
178	C₂²×C₁₅₁	C₂×#95	1	1	yes	characteristic
179	C₂²×C₁₅₁	C₂×#106	1	1	yes	characteristic
180	C₂²×C₁₅₁	C₂×#107	1	1	yes	characteristic
181	C₄×C₁₅₁	—	2	1	no	—
182	C₄×C₁₅₁	—	2	1	no	—
183	C₄×C₁₅₁	—	2	1	no	—
184	C₄×C₁₅₁	—	2	1	no	—
185	C₄×C₁₅₁	—	2	1	no	—
186	C₄×C₁₅₁	—	2	1	no	—
187	C₄×C₁₅₁	#340	1	2	yes	—
188	C₄×C₁₅₁	#340	1	2	yes	—
189	C₄×C₁₅₁	#344	1	2	yes	—
190	C₄×C₁₅₁	C₂×#102	1	1	yes	characteristic
191	C₄×C₁₅₁	C₂×#102	1	1	yes	characteristic
192	C₄×C₁₅₁	C₂×#103	1	1	yes	characteristic
193	C₄×C₁₅₁	C₂×#103	1	1	yes	characteristic
194	C₄×C₁₅₁	#430	1	2	yes	—
195	C₂×C₁₅₁	—	2	2	no	—
196	C₂×C₁₅₁	—	2	2	no	—
197	C₂×C₁₅₁	—	2	1	no	—
198	C₂×C₁₅₁	—	2	1	no	—
199	C₂×C₁₅₁	C₂×#340	1	1	yes	characteristic
200	C₂×C₁₅₁	#1738	1	1	yes	characteristic
201	C₂×C₁₅₁	C₂×#344	1	1	yes	characteristic
202	#8079	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₅₁	#8079	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×#431	C₂×C₁₅₁	1	1	yes	characteristic
205	C₂×#423	C₂×C₁₅₁	1	1	yes	characteristic
206	C₂×#423	C₂×C₁₅₁	1	1	yes	characteristic
207	#1301	C₂×C₁₅₁	1	4	yes	complemented
208	C₂²×M₁₆	—	2	1	no	—
209	C₂²×M₁₆	—	2	1	no	—
210	C₂²×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
211	#431	—	2	1	no	—
212	#431	—	2	1	no	—
213	#431	C₄×C₁₅₁	1	2	yes	—
214	#431	C₂²×C₁₅₁	1	2	yes	—
215	#423	—	2	1	no	—
216	#423	—	2	1	no	—
217	#423	—	2	1	no	—
218	#423	—	2	1	no	—
219	#423	C₄×C₁₅₁	1	2	yes	—
220	#423	C₄×C₁₅₁	1	2	yes	—
221	#423	C₄×C₁₅₁	1	2	yes	—
222	#423	C₂²×C₁₅₁	1	2	yes	—
223	C₂×C₄⋊C₈	—	2	1	no	—
224	C₂×C₄⋊C₈	—	2	1	no	—
225	C₂×C₄⋊C₈	—	2	1	no	—
226	C₂×C₄⋊C₈	C₄×C₁₅₁	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	2	yes	—
228	C₂×C₂²⋊C₈	C₄×C₁₅₁	1	2	yes	—
229	C₂×C₄×C₈	—	2	1	no	—
230	C₂³×C₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
231	C₂³×C₄	D₄×C₁₅₁	1	1	yes	characteristic
232	C₂³×C₄	Q₈×C₁₅₁	1	1	yes	characteristic
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	4	2	no	—
238	C₂×M₁₆	—	4	2	no	—
239	C₂×M₁₆	—	4	2	no	—
240	C₂×M₁₆	—	4	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
246	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
247	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₄×C₁₅₁	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
252	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
254	C₂×C₄²	Q₈×C₁₅₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
256	C₄⋊C₈	—	2	2	no	—
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	C₂×C₄×C₁₅₁	1	4	yes	—
265	C₄⋊C₈	C₂×C₄×C₁₅₁	1	4	yes	—
266	C₂²⋊C₈	—	2	2	no	—
267	C₂²⋊C₈	C₂×C₄×C₁₅₁	1	4	yes	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₂⁴	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₄²×C₁₅₁	1	1	yes	characteristic
274	C₂²×C₄	C₄²×C₁₅₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
281	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
282	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
286	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
287	C₂²×C₄	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
288	C₂²×C₄	D₈×C₁₅₁	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₁₅₁	1	2	yes	—
290	C₂²×C₄	SD₁₆×C₁₅₁	1	2	yes	—
291	C₂²×C₄	Q₁₆×C₁₅₁	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
294	C₂²×C₄	C₂×Q₈×C₁₅₁	1	1	yes	characteristic
295	M₁₆	—	4	4	no	—
296	M₁₆	—	4	4	no	—
297	M₁₆	—	4	4	no	—
298	M₁₆	—	4	2	no	—
299	M₁₆	—	4	2	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	4	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₄²	C₄²×C₁₅₁	1	1	yes	characteristic
308	C₄²	C₄²×C₁₅₁	1	1	yes	characteristic
309	C₄²	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
310	C₄²	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
311	C₄²	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
312	C₄²	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
313	C₄²	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
314	C₄²	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
315	C₄²	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
316	C₄²	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
317	C₄²	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
318	C₄²	C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
319	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
320	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
321	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
323	C₂³	—	4	1	no	—
324	C₂³	—	4	1	no	—
325	C₂³	#95×C₁₅₁	1	1	yes	characteristic
326	C₂³	#95×C₁₅₁	1	1	yes	characteristic
327	C₂³	#106×C₁₅₁	1	2	yes	—
328	C₂³	#107×C₁₅₁	1	2	yes	—
329	C₂³	C₂×C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	#95×C₁₅₁	1	1	yes	characteristic
343	C₂×C₄	#95×C₁₅₁	1	1	yes	characteristic
344	C₂×C₄	#95×C₁₅₁	1	1	yes	characteristic
345	C₂×C₄	#95×C₁₅₁	1	1	yes	characteristic
346	C₂×C₄	#95×C₁₅₁	1	1	yes	characteristic
347	C₂×C₄	#95×C₁₅₁	1	1	yes	characteristic
348	C₂×C₄	#102×C₁₅₁	1	2	yes	—
349	C₂×C₄	#102×C₁₅₁	1	2	yes	—
350	C₂×C₄	#102×C₁₅₁	1	2	yes	—
351	C₂×C₄	#102×C₁₅₁	1	2	yes	—
352	C₂×C₄	#103×C₁₅₁	1	2	yes	—
353	C₂×C₄	#103×C₁₅₁	1	2	yes	—
354	C₂×C₄	#103×C₁₅₁	1	2	yes	—
355	C₂×C₄	#103×C₁₅₁	1	2	yes	—
356	C₂×C₄	#106×C₁₅₁	1	2	yes	—
357	C₂×C₄	#107×C₁₅₁	1	2	yes	—
358	C₂×C₄	C₂×C₄²×C₁₅₁	1	1	yes	characteristic
359	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
361	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄⋊C₄×C₁₅₁	1	1	yes	characteristic
364	C₂×C₄	C₂×D₈×C₁₅₁	1	1	yes	characteristic
365	C₂×C₄	C₂×SD₁₆×C₁₅₁	1	1	yes	characteristic
366	C₂×C₄	C₂×SD₁₆×C₁₅₁	1	1	yes	characteristic
367	C₂×C₄	C₂×Q₁₆×C₁₅₁	1	1	yes	characteristic
368	C₈	—	4	4	no	—
369	C₈	—	4	4	no	—
370	C₈	—	4	4	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	#340×C₁₅₁	1	2	yes	—
380	C₂²	#340×C₁₅₁	1	2	yes	—
381	C₂²	C₂×#95×C₁₅₁	1	1	yes	characteristic
382	C₂²	C₂×#106×C₁₅₁	1	1	yes	characteristic
383	C₂²	C₂×#107×C₁₅₁	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	#340×C₁₅₁	1	2	yes	—
391	C₄	#340×C₁₅₁	1	2	yes	—
392	C₄	#344×C₁₅₁	1	2	yes	—
393	C₄	C₂×#102×C₁₅₁	1	1	yes	characteristic
394	C₄	C₂×#102×C₁₅₁	1	1	yes	characteristic
395	C₄	C₂×#103×C₁₅₁	1	1	yes	characteristic
396	C₄	C₂×#103×C₁₅₁	1	1	yes	characteristic
397	C₄	#430×C₁₅₁	1	2	yes	—
398	C₂	—	2	2	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	C₂×#340×C₁₅₁	1	1	yes	characteristic
403	C₂	#1738×C₁₅₁	1	1	yes	characteristic
404	C₂	C₂×#344×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₁₅₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₅₁
socle	C₂²×C₁₅₁	C₂×#95
prime radical	C₂⁴×C₁₅₁	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₅₁ ◁ C₂²×C₄²×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1301×C₁₅₁	C₂	semidirect
202. #8079	C₁₅₁	direct (N × H)
203. C₁₅₁	#8079	direct (N × H)
207. #1301	C₂×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
C₂×#423×C₁₅₁	2
#1301×C₁₅₁	2
#8079	151

Subgroups — C151×#8079 #50313004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#8079 #50313004