Subgroups — C₁₅₁×#17760 #50322685

Order 38656.

896 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3503×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#2989×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	#2925×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#1559×C₁₅₁	C₂	1	2	yes	maximal, complemented
5	#1558×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#1554×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	#1550×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1548×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1548×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1542×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#333×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₅₁	—	2	1	no	—
13	#557×C₁₅₁	C₄	1	2	yes	—
14	#554×C₁₅₁	—	2	2	no	—
15	#554×C₁₅₁	—	2	1	no	—
16	D₄×Q₈×C₁₅₁	C₄	1	2	yes	—
17	D₄×Q₈×C₁₅₁	C₄	1	4	yes	—
18	#544×C₁₅₁	—	2	1	no	—
19	#544×C₁₅₁	—	2	2	no	—
20	#533×C₁₅₁	C₂²	1	1	yes	characteristic
21	#533×C₁₅₁	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	2	yes	—
24	#520×C₁₅₁	—	2	1	no	—
25	C₄×#41×C₁₅₁	C₂²	1	1	yes	characteristic
26	#446×C₁₅₁	—	2	1	no	—
27	#436×C₁₅₁	—	2	1	no	—
28	#435×C₁₅₁	—	2	2	no	—
29	#433×C₁₅₁	—	2	2	no	—
30	#432×C₁₅₁	C₂²	1	2	yes	—
31	#432×C₁₅₁	C₂²	1	2	yes	—
32	#431×C₁₅₁	C₂²	1	2	yes	—
33	#431×C₁₅₁	C₂²	1	1	yes	characteristic
34	#423×C₁₅₁	C₂²	1	1	yes	characteristic
35	#423×C₁₅₁	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
38	#408×C₁₅₁	—	2	1	no	—
39	#405×C₁₅₁	—	2	1	no	—
40	#333×C₁₅₁	C₂²	1	2	yes	—
41	#333×C₁₅₁	C₂²	1	2	yes	—
42	#333×C₁₅₁	C₂²	1	1	yes	characteristic
43	#333×C₁₅₁	C₂²	1	1	yes	characteristic
44	#333×C₁₅₁	C₂²	1	2	yes	—
45	#333×C₁₅₁	C₂²	1	2	yes	—
46	#333×C₁₅₁	C₂²	1	2	yes	—
47	#332×C₁₅₁	C₂²	1	1	yes	characteristic
48	#332×C₁₅₁	C₂²	1	1	yes	characteristic
49	#332×C₁₅₁	C₂²	1	2	yes	—
50	C₂×#41×C₁₅₁	D₄	1	1	yes	characteristic
51	C₂²×Q₈×C₁₅₁	C₂×C₄	1	2	yes	—
52	C₂²×Q₈×C₁₅₁	C₂×C₄	1	4	yes	—
53	C₂×M₁₆×C₁₅₁	—	2	1	no	—
54	C₂×M₁₆×C₁₅₁	—	2	2	no	—
55	C₂²×C₈×C₁₅₁	—	2	1	no	—
56	C₂²×C₈×C₁₅₁	—	2	1	no	—
57	C₄⋊Q₈×C₁₅₁	—	2	4	no	—
58	C₄⋊Q₈×C₁₅₁	—	2	2	no	—
59	C₄⋊Q₈×C₁₅₁	—	2	2	no	—
60	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
61	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
62	C₄⋊Q₈×C₁₅₁	—	2	2	no	—
63	C₄⋊Q₈×C₁₅₁	C₂×C₄	1	2	yes	—
64	C₄⋊Q₈×C₁₅₁	C₂×C₄	1	4	yes	—
65	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₁₅₁	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
68	#125×C₁₅₁	—	2	4	no	—
69	#125×C₁₅₁	—	2	2	no	—
70	#125×C₁₅₁	—	2	2	no	—
71	#125×C₁₅₁	—	2	1	no	—
72	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
73	C₂²⋊Q₈×C₁₅₁	—	2	2	no	—
74	C₂²⋊Q₈×C₁₅₁	—	2	4	no	—
75	C₂²⋊Q₈×C₁₅₁	—	2	4	no	—
76	C₂²⋊Q₈×C₁₅₁	—	2	4	no	—
77	C₂²⋊Q₈×C₁₅₁	C₂×C₄	1	2	yes	—
78	C₂²⋊Q₈×C₁₅₁	C₂×C₄	1	4	yes	—
79	C₄×Q₈×C₁₅₁	—	2	1	no	—
80	C₄×Q₈×C₁₅₁	—	2	2	no	—
81	C₄×Q₈×C₁₅₁	—	2	2	no	—
82	C₄×Q₈×C₁₅₁	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₅₁	C₂×C₄	1	2	yes	—
84	C₄×Q₈×C₁₅₁	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₁₅₁	D₄	1	1	yes	characteristic
86	C₄×D₄×C₁₅₁	—	2	4	no	—
87	C₄×D₄×C₁₅₁	—	2	2	no	—
88	C₄×D₄×C₁₅₁	C₂×C₄	1	2	yes	—
89	C₄×D₄×C₁₅₁	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₁₅₁	D₄	1	2	yes	—
91	C₄×D₄×C₁₅₁	D₄	1	1	yes	characteristic
92	#117×C₁₅₁	—	2	2	no	—
93	#117×C₁₅₁	—	2	1	no	—
94	#117×C₁₅₁	D₄	1	1	yes	characteristic
95	#117×C₁₅₁	D₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
97	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
100	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
102	C₄⋊C₈×C₁₅₁	—	2	1	no	—
103	C₄⋊C₈×C₁₅₁	—	2	1	no	—
104	C₄⋊C₈×C₁₅₁	—	2	1	no	—
105	C₄⋊C₈×C₁₅₁	—	2	2	no	—
106	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
107	C₄⋊C₈×C₁₅₁	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₁₅₁	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₁₅₁	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
111	C₄⋊C₈×C₁₅₁	C₂³	1	1	yes	characteristic
112	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
113	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
114	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
115	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
116	#97×C₁₅₁	—	2	2	no	—
117	#97×C₁₅₁	—	2	2	no	—
118	C₄×C₈×C₁₅₁	—	2	2	no	—
119	C₄×C₈×C₁₅₁	—	2	1	no	—
120	#41×C₁₅₁	—	2	2	no	—
121	#41×C₁₅₁	—	2	2	no	—
122	C₂×Q₈×C₁₅₁	—	2	4	no	—
123	C₂×Q₈×C₁₅₁	—	2	2	no	—
124	C₂×Q₈×C₁₅₁	—	2	1	no	—
125	C₂×Q₈×C₁₅₁	—	8	2	no	—
126	C₂×Q₈×C₁₅₁	—	8	4	no	—
127	C₂×Q₈×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₅₁	C₂²×C₄	1	2	yes	—
129	C₂×Q₈×C₁₅₁	C₂²×C₄	1	4	yes	—
130	C₂×D₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
131	C₂×D₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₅₁	—	2	4	no	—
133	C₂²×C₄×C₁₅₁	—	2	2	no	—
134	C₂²×C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₅₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
140	M₁₆×C₁₅₁	—	4	2	no	—
141	M₁₆×C₁₅₁	—	8	2	no	—
142	C₂×C₈×C₁₅₁	—	2	1	no	—
143	C₂×C₈×C₁₅₁	—	2	1	no	—
144	C₂×C₈×C₁₅₁	—	2	2	no	—
145	C₂×C₈×C₁₅₁	—	2	1	no	—
146	C₂×C₈×C₁₅₁	—	2	1	no	—
147	C₂×C₈×C₁₅₁	—	2	2	no	—
148	C₂×C₈×C₁₅₁	—	4	2	no	—
149	C₂×C₈×C₁₅₁	—	8	1	no	—
150	C₄⋊C₄×C₁₅₁	—	2	4	no	—
151	C₄⋊C₄×C₁₅₁	—	2	2	no	—
152	C₄⋊C₄×C₁₅₁	—	2	4	no	—
153	C₄⋊C₄×C₁₅₁	—	2	2	no	—
154	C₄⋊C₄×C₁₅₁	—	2	4	no	—
155	C₄⋊C₄×C₁₅₁	—	2	2	no	—
156	C₄⋊C₄×C₁₅₁	—	2	4	no	—
157	C₄⋊C₄×C₁₅₁	—	2	2	no	—
158	C₄⋊C₄×C₁₅₁	—	2	1	no	—
159	C₄⋊C₄×C₁₅₁	—	2	2	no	—
160	C₄⋊C₄×C₁₅₁	—	2	2	no	—
161	C₄⋊C₄×C₁₅₁	—	2	1	no	—
162	C₄⋊C₄×C₁₅₁	—	2	1	no	—
163	C₄⋊C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
164	C₄⋊C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
166	C₄⋊C₄×C₁₅₁	C₂²⋊C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₅₁	C₂²×C₄	1	2	yes	—
168	C₂²⋊C₄×C₁₅₁	—	2	4	no	—
169	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
170	C₂²⋊C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
171	C₂²⋊C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
172	C₂²⋊C₄×C₁₅₁	C₂²⋊C₄	1	2	yes	—
173	C₄²×C₁₅₁	—	2	4	no	—
174	C₄²×C₁₅₁	—	2	2	no	—
175	C₄²×C₁₅₁	C₂²×C₄	1	2	yes	—
176	C₄²×C₁₅₁	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
178	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
180	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₁₅₁	C₂⁴	1	1	yes	characteristic
182	C₂³×C₁₅₁	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂³×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	Q₈×C₁₅₁	—	2	2	no	—
185	Q₈×C₁₅₁	—	4	4	no	—
186	Q₈×C₁₅₁	—	4	2	no	—
187	Q₈×C₁₅₁	—	4	1	no	—
188	Q₈×C₁₅₁	—	4	1	no	—
189	Q₈×C₁₅₁	—	8	2	no	—
190	Q₈×C₁₅₁	—	8	4	no	—
191	D₄×C₁₅₁	—	2	4	no	—
192	D₄×C₁₅₁	—	2	2	no	—
193	C₂×C₄×C₁₅₁	—	2	2	no	—
194	C₂×C₄×C₁₅₁	—	2	2	no	—
195	C₂×C₄×C₁₅₁	—	2	1	no	—
196	C₂×C₄×C₁₅₁	—	2	2	no	—
197	C₂×C₄×C₁₅₁	—	2	1	no	—
198	C₂×C₄×C₁₅₁	—	2	2	no	—
199	C₂×C₄×C₁₅₁	—	2	4	no	—
200	C₂×C₄×C₁₅₁	—	2	2	no	—
201	C₂×C₄×C₁₅₁	—	2	2	no	—
202	C₂×C₄×C₁₅₁	—	4	1	no	—
203	C₂×C₄×C₁₅₁	—	4	2	no	—
204	C₂×C₄×C₁₅₁	—	8	2	no	—
205	C₂×C₄×C₁₅₁	—	8	4	no	—
206	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₅₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₅₁	#137	1	2	yes	—
213	C₂×C₄×C₁₅₁	#137	1	2	yes	—
214	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₁₅₁	—	4	1	no	—
218	C₈×C₁₅₁	—	4	1	no	—
219	C₈×C₁₅₁	—	4	2	no	—
220	C₈×C₁₅₁	—	4	2	no	—
221	C₈×C₁₅₁	—	4	1	no	—
222	C₈×C₁₅₁	—	4	1	no	—
223	C₂²×C₁₅₁	—	2	1	no	—
224	C₂²×C₁₅₁	—	2	1	no	—
225	C₂²×C₁₅₁	—	2	2	no	—
226	C₂²×C₁₅₁	—	2	2	no	—
227	C₂²×C₁₅₁	—	2	2	no	—
228	C₂²×C₁₅₁	#419	1	2	yes	—
229	C₂²×C₁₅₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₄×C₁₅₁	—	2	1	no	—
231	C₄×C₁₅₁	—	2	1	no	—
232	C₄×C₁₅₁	—	2	2	no	—
233	C₄×C₁₅₁	—	2	2	no	—
234	C₄×C₁₅₁	—	2	1	no	—
235	C₄×C₁₅₁	—	2	2	no	—
236	C₄×C₁₅₁	—	4	4	no	—
237	C₄×C₁₅₁	—	4	2	no	—
238	C₄×C₁₅₁	—	4	2	no	—
239	C₄×C₁₅₁	#419	1	2	yes	—
240	C₄×C₁₅₁	C₂×#137	1	1	yes	characteristic
241	C₄×C₁₅₁	C₂×#137	1	1	yes	characteristic
242	C₄×C₁₅₁	#577	1	1	yes	characteristic
243	C₄×C₁₅₁	#578	1	1	yes	characteristic
244	C₂×C₁₅₁	—	2	2	no	—
245	C₂×C₁₅₁	—	4	2	no	—
246	C₂×C₁₅₁	#2888	1	1	yes	characteristic
247	C₂×C₁₅₁	C₂×#419	1	1	yes	characteristic
248	C₂×C₁₅₁	#2898	1	1	yes	characteristic
249	#17760	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₁₅₁	#17760	1	1	yes	characteristic, direct product factor, Sylow
251	#3503	C₂×C₁₅₁	1	1	yes	characteristic
252	#2989	C₂×C₁₅₁	1	1	yes	characteristic
253	#2925	C₂×C₁₅₁	1	1	yes	characteristic
254	#1559	C₂×C₁₅₁	1	2	yes	complemented
255	#1558	C₂×C₁₅₁	1	2	yes	complemented
256	#1554	C₂×C₁₅₁	1	2	yes	complemented
257	#1550	C₂×C₁₅₁	1	1	yes	characteristic, complemented
258	#1548	C₂×C₁₅₁	1	1	yes	characteristic, complemented
259	#1548	C₂×C₁₅₁	1	2	yes	complemented
260	#1542	C₂×C₁₅₁	1	1	yes	characteristic, complemented
261	C₂×#333	C₂×C₁₅₁	1	1	yes	characteristic, complemented
262	Q₈²	—	2	1	no	—
263	#557	C₄×C₁₅₁	1	2	yes	—
264	#554	—	2	2	no	—
265	#554	—	2	1	no	—
266	D₄×Q₈	C₄×C₁₅₁	1	2	yes	—
267	D₄×Q₈	C₄×C₁₅₁	1	4	yes	—
268	#544	—	2	1	no	—
269	#544	—	2	2	no	—
270	#533	C₂²×C₁₅₁	1	1	yes	characteristic
271	#533	C₂²×C₁₅₁	1	2	yes	—
272	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	2	yes	—
274	#520	—	2	1	no	—
275	C₄×#41	C₂²×C₁₅₁	1	1	yes	characteristic
276	#446	—	2	1	no	—
277	#436	—	2	1	no	—
278	#435	—	2	2	no	—
279	#433	—	2	2	no	—
280	#432	C₂²×C₁₅₁	1	2	yes	—
281	#432	C₂²×C₁₅₁	1	2	yes	—
282	#431	C₂²×C₁₅₁	1	1	yes	characteristic
283	#431	C₂²×C₁₅₁	1	2	yes	—
284	#423	C₂²×C₁₅₁	1	1	yes	characteristic
285	#423	C₂²×C₁₅₁	1	2	yes	—
286	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
288	#408	—	2	1	no	—
289	#405	—	2	1	no	—
290	#333	C₂²×C₁₅₁	1	2	yes	—
291	#333	C₂²×C₁₅₁	1	2	yes	—
292	#333	C₂²×C₁₅₁	1	1	yes	characteristic
293	#333	C₂²×C₁₅₁	1	1	yes	characteristic
294	#333	C₂²×C₁₅₁	1	2	yes	—
295	#333	C₂²×C₁₅₁	1	2	yes	—
296	#333	C₂²×C₁₅₁	1	2	yes	—
297	#332	C₂²×C₁₅₁	1	1	yes	characteristic
298	#332	C₂²×C₁₅₁	1	1	yes	characteristic
299	#332	C₂²×C₁₅₁	1	2	yes	—
300	C₂×#41	D₄×C₁₅₁	1	1	yes	characteristic
301	C₂²×Q₈	C₂×C₄×C₁₅₁	1	2	yes	—
302	C₂²×Q₈	C₂×C₄×C₁₅₁	1	4	yes	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	4	no	—
308	C₄⋊Q₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	C₂×C₄×C₁₅₁	1	2	yes	—
314	C₄⋊Q₈	C₂×C₄×C₁₅₁	1	4	yes	—
315	C₄⋊Q₈	C₂³×C₁₅₁	1	2	yes	—
316	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
317	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
318	#125	—	2	4	no	—
319	#125	—	2	2	no	—
320	#125	—	2	2	no	—
321	#125	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	2	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	4	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	C₂×C₄×C₁₅₁	1	2	yes	—
328	C₂²⋊Q₈	C₂×C₄×C₁₅₁	1	4	yes	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	C₂×C₄×C₁₅₁	1	2	yes	—
333	C₄×Q₈	C₂×C₄×C₁₅₁	1	4	yes	—
334	C₄×Q₈	C₂×C₄×C₁₅₁	1	1	yes	characteristic
335	C₄×Q₈	D₄×C₁₅₁	1	1	yes	characteristic
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	C₂×C₄×C₁₅₁	1	2	yes	—
339	C₄×D₄	C₂×C₄×C₁₅₁	1	1	yes	characteristic
340	C₄×D₄	D₄×C₁₅₁	1	2	yes	—
341	C₄×D₄	D₄×C₁₅₁	1	1	yes	characteristic
342	#117	—	2	2	no	—
343	#117	—	2	1	no	—
344	#117	D₄×C₁₅₁	1	1	yes	characteristic
345	#117	D₄×C₁₅₁	1	2	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	—	2	1	no	—
354	C₄⋊C₈	—	2	1	no	—
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
357	C₄⋊C₈	C₂³×C₁₅₁	1	1	yes	characteristic
358	C₄⋊C₈	C₂³×C₁₅₁	1	1	yes	characteristic
359	C₄⋊C₈	C₂³×C₁₅₁	1	1	yes	characteristic
360	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
361	C₄⋊C₈	C₂³×C₁₅₁	1	1	yes	characteristic
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	—	2	1	no	—
365	C₂²⋊C₈	—	2	2	no	—
366	#97	—	2	2	no	—
367	#97	—	2	2	no	—
368	C₄×C₈	—	2	2	no	—
369	C₄×C₈	—	2	1	no	—
370	#41	—	2	2	no	—
371	#41	—	2	2	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	8	2	no	—
376	C₂×Q₈	—	8	4	no	—
377	C₂×Q₈	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
378	C₂×Q₈	C₂²×C₄×C₁₅₁	1	2	yes	—
379	C₂×Q₈	C₂²×C₄×C₁₅₁	1	4	yes	—
380	C₂×D₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
381	C₂×D₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₅₁	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
390	M₁₆	—	4	2	no	—
391	M₁₆	—	8	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	8	1	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
414	C₄⋊C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
415	C₄⋊C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
416	C₄⋊C₄	C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
417	C₄⋊C₄	C₂²×C₄×C₁₅₁	1	2	yes	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
421	C₂²⋊C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
422	C₂²⋊C₄	C₂²⋊C₄×C₁₅₁	1	2	yes	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	2	no	—
425	C₄²	C₂²×C₄×C₁₅₁	1	2	yes	—
426	C₄²	C₂²×C₄×C₁₅₁	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
428	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
430	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
431	C₄²	C₂⁴×C₁₅₁	1	1	yes	characteristic
432	C₂³	C₂×C₂²⋊C₄×C₁₅₁	1	2	yes	—
433	C₂³	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
434	Q₈	—	2	2	no	—
435	Q₈	—	4	4	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	8	2	no	—
440	Q₈	—	8	4	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	2	yes	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	2	yes	—
458	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
459	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	2	yes	—
460	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
461	C₂×C₄	C₂×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
462	C₂×C₄	#137×C₁₅₁	1	2	yes	—
463	C₂×C₄	#137×C₁₅₁	1	2	yes	—
464	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
466	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
467	C₈	—	4	1	no	—
468	C₈	—	4	1	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	2	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	#419×C₁₅₁	1	2	yes	—
479	C₂²	C₂²×C₂²⋊C₄×C₁₅₁	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	#419×C₁₅₁	1	2	yes	—
490	C₄	C₂×#137×C₁₅₁	1	1	yes	characteristic
491	C₄	C₂×#137×C₁₅₁	1	1	yes	characteristic
492	C₄	#577×C₁₅₁	1	1	yes	characteristic
493	C₄	#578×C₁₅₁	1	1	yes	characteristic
494	C₂	—	2	2	no	—
495	C₂	—	4	2	no	—
496	C₂	#2888×C₁₅₁	1	1	yes	characteristic
497	C₂	C₂×#419×C₁₅₁	1	1	yes	characteristic
498	C₂	#2898×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₄²	C₂⁴×C₁₅₁
prime radical	C₂×#41×C₁₅₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₄×#41×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1559×C₁₅₁	C₂	semidirect
5. #1558×C₁₅₁	C₂	semidirect
6. #1554×C₁₅₁	C₂	semidirect
7. #1550×C₁₅₁	C₂	semidirect
8. #1548×C₁₅₁	C₂	semidirect
9. #1548×C₁₅₁	C₂	semidirect
10. #1542×C₁₅₁	C₂	semidirect
11. C₂×#333×C₁₅₁	C₂	semidirect
249. #17760	C₁₅₁	direct (N × H)
250. C₁₅₁	#17760	direct (N × H)
254. #1559	C₂×C₁₅₁	semidirect
255. #1558	C₂×C₁₅₁	semidirect
256. #1554	C₂×C₁₅₁	semidirect
257. #1550	C₂×C₁₅₁	semidirect
258. #1548	C₂×C₁₅₁	semidirect
259. #1548	C₂×C₁₅₁	semidirect
260. #1542	C₂×C₁₅₁	semidirect
261. C₂×#333	C₂×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3503×C₁₅₁	2
#2989×C₁₅₁	2
#2925×C₁₅₁	2
#1559×C₁₅₁	2
#1558×C₁₅₁	2
#1554×C₁₅₁	2
#1550×C₁₅₁	2
#1548×C₁₅₁	2
#1542×C₁₅₁	2
C₂×#333×C₁₅₁	2
#17760	151

Subgroups — C151×#17760 #50322685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#17760 #50322685