Subgroups — C₁₅₁×#19212 #50324137

Order 38656.

646 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3230×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3208×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#486×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2960×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1698×C₁₅₁	C₂	1	4	yes	maximal, complemented
6	#1678×C₁₅₁	C₂	1	4	yes	maximal, complemented
7	#1564×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1548×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1545×C₁₅₁	C₂	1	1	yes	maximal, characteristic
10	#533×C₁₅₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₅₁	C₂²	1	1	yes	characteristic
13	#500×C₁₅₁	—	2	1	no	—
14	#492×C₁₅₁	—	2	1	no	—
15	#487×C₁₅₁	—	2	1	no	—
16	#486×C₁₅₁	—	2	1	no	—
17	#486×C₁₅₁	—	2	1	no	—
18	#486×C₁₅₁	—	2	1	no	—
19	#486×C₁₅₁	C₂²	1	2	yes	—
20	#486×C₁₅₁	C₂²	1	2	yes	—
21	#484×C₁₅₁	—	2	2	no	—
22	#477×C₁₅₁	C₂²	1	4	yes	complemented
23	#460×C₁₅₁	C₂²	1	4	yes	—
24	#450×C₁₅₁	—	2	2	no	—
25	#446×C₁₅₁	—	2	1	no	—
26	#446×C₁₅₁	C₂²	1	2	yes	complemented
27	C₈×Q₈×C₁₅₁	—	2	1	no	—
28	C₈×Q₈×C₁₅₁	C₂²	1	2	yes	complemented
29	#431×C₁₅₁	C₂²	1	1	yes	characteristic
30	#431×C₁₅₁	C₂²	1	1	yes	characteristic
31	#424×C₁₅₁	—	2	1	no	—
32	#423×C₁₅₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₁₅₁	—	2	1	no	—
34	C₂×#102×C₁₅₁	—	2	1	no	—
35	#405×C₁₅₁	—	2	1	no	—
36	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
37	#335×C₁₅₁	C₂²	1	2	yes	complemented
38	#334×C₁₅₁	C₂²	1	2	yes	complemented
39	#333×C₁₅₁	C₂²	1	4	yes	complemented
40	#331×C₁₅₁	C₂²	1	4	yes	—
41	C₂²×Q₈×C₁₅₁	—	2	1	no	—
42	C₂²×D₄×C₁₅₁	—	2	1	no	—
43	C₂²×D₄×C₁₅₁	—	2	1	no	—
44	C₂²×D₄×C₁₅₁	—	2	1	no	—
45	C₂×SD₁₆×C₁₅₁	—	2	4	no	—
46	C₂×M₁₆×C₁₅₁	—	2	1	no	—
47	C₂²×C₈×C₁₅₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₅₁	D₄	1	1	yes	characteristic
49	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
50	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
51	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₅₁	D₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₁₅₁	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₁₅₁	C₂³	1	2	yes	—
55	#127×C₁₅₁	—	2	1	no	—
56	#127×C₁₅₁	—	2	1	no	—
57	#127×C₁₅₁	—	2	1	no	—
58	#127×C₁₅₁	C₂³	1	2	yes	—
59	#125×C₁₅₁	—	2	1	no	—
60	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
61	C₂²⋊Q₈×C₁₅₁	D₄	1	2	yes	—
62	C₄×Q₈×C₁₅₁	—	2	1	no	—
63	C₄×Q₈×C₁₅₁	C₂³	1	2	yes	—
64	#117×C₁₅₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
67	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
68	#107×C₁₅₁	—	2	4	no	—
69	C₄⋊C₈×C₁₅₁	—	2	2	no	—
70	C₄⋊C₈×C₁₅₁	—	2	2	no	—
71	C₄⋊C₈×C₁₅₁	—	2	1	no	—
72	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
74	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
75	#103×C₁₅₁	—	2	4	no	—
76	#102×C₁₅₁	—	2	2	no	—
77	#102×C₁₅₁	—	2	2	no	—
78	#102×C₁₅₁	—	2	2	no	—
79	#102×C₁₅₁	—	2	2	no	—
80	#102×C₁₅₁	—	2	4	no	—
81	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
82	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
83	#97×C₁₅₁	—	2	2	no	—
84	C₄×C₈×C₁₅₁	—	2	2	no	—
85	C₄×C₈×C₁₅₁	—	2	1	no	—
86	C₄×C₈×C₁₅₁	—	2	1	no	—
87	C₄×C₈×C₁₅₁	D₄	1	1	yes	characteristic
88	C₄×C₈×C₁₅₁	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
91	C₂⁴×C₁₅₁	—	4	1	no	—
92	C₂×Q₈×C₁₅₁	—	2	1	no	—
93	C₂×Q₈×C₁₅₁	—	2	2	no	—
94	C₂×Q₈×C₁₅₁	—	4	1	no	—
95	C₂×Q₈×C₁₅₁	—	8	2	no	—
96	C₂×Q₈×C₁₅₁	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₁₅₁	—	2	2	no	—
98	C₂×D₄×C₁₅₁	—	2	2	no	—
99	C₂×D₄×C₁₅₁	—	2	2	no	—
100	C₂×D₄×C₁₅₁	—	4	1	no	—
101	C₂×D₄×C₁₅₁	—	4	1	no	—
102	C₂×D₄×C₁₅₁	—	4	1	no	—
103	C₂×D₄×C₁₅₁	—	4	2	no	—
104	C₂×D₄×C₁₅₁	—	4	2	no	—
105	C₂×D₄×C₁₅₁	—	8	2	no	—
106	C₂×D₄×C₁₅₁	—	8	2	no	—
107	C₂²×C₄×C₁₅₁	—	4	1	no	—
108	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
111	SD₁₆×C₁₅₁	—	8	4	no	—
112	M₁₆×C₁₅₁	—	4	2	no	—
113	C₂×C₈×C₁₅₁	—	2	2	no	—
114	C₂×C₈×C₁₅₁	—	2	2	no	—
115	C₂×C₈×C₁₅₁	—	2	2	no	—
116	C₂×C₈×C₁₅₁	—	2	2	no	—
117	C₂×C₈×C₁₅₁	—	2	2	no	—
118	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₁₅₁	—	2	1	no	—
123	C₄⋊C₄×C₁₅₁	—	2	1	no	—
124	C₄⋊C₄×C₁₅₁	—	2	1	no	—
125	C₄⋊C₄×C₁₅₁	—	2	2	no	—
126	C₄⋊C₄×C₁₅₁	—	2	2	no	—
127	C₄⋊C₄×C₁₅₁	—	2	2	no	—
128	C₄⋊C₄×C₁₅₁	—	2	2	no	—
129	C₄⋊C₄×C₁₅₁	—	4	1	no	—
130	C₄⋊C₄×C₁₅₁	—	4	1	no	—
131	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
132	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
133	C₄²×C₁₅₁	—	2	2	no	—
134	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₅₁	#41	1	1	yes	characteristic
137	C₄²×C₁₅₁	C₂⁴	1	1	yes	characteristic
138	C₂³×C₁₅₁	—	4	2	no	—
139	C₂³×C₁₅₁	—	8	2	no	—
140	C₂³×C₁₅₁	—	8	2	no	—
141	C₂³×C₁₅₁	—	8	2	no	—
142	C₂³×C₁₅₁	#121	1	1	yes	characteristic
143	Q₈×C₁₅₁	—	2	4	no	—
144	Q₈×C₁₅₁	—	4	2	no	—
145	Q₈×C₁₅₁	—	8	2	no	—
146	Q₈×C₁₅₁	—	8	2	no	—
147	D₄×C₁₅₁	—	4	2	no	—
148	D₄×C₁₅₁	—	4	2	no	—
149	D₄×C₁₅₁	—	4	4	no	—
150	D₄×C₁₅₁	—	8	2	no	—
151	D₄×C₁₅₁	—	8	2	no	—
152	D₄×C₁₅₁	—	8	2	no	—
153	D₄×C₁₅₁	—	8	2	no	—
154	C₂×C₄×C₁₅₁	—	2	2	no	—
155	C₂×C₄×C₁₅₁	—	2	2	no	—
156	C₂×C₄×C₁₅₁	—	2	2	no	—
157	C₂×C₄×C₁₅₁	—	2	2	no	—
158	C₂×C₄×C₁₅₁	—	4	2	no	—
159	C₂×C₄×C₁₅₁	—	8	2	no	—
160	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₅₁	#135	1	2	yes	—
164	C₂×C₄×C₁₅₁	#137	1	2	yes	—
165	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
168	C₈×C₁₅₁	—	2	1	no	—
169	C₈×C₁₅₁	—	2	1	no	—
170	C₈×C₁₅₁	—	2	1	no	—
171	C₈×C₁₅₁	—	2	1	no	—
172	C₈×C₁₅₁	—	4	2	no	—
173	C₈×C₁₅₁	—	4	2	no	—
174	C₈×C₁₅₁	—	4	2	no	—
175	C₂²×C₁₅₁	—	2	1	no	—
176	C₂²×C₁₅₁	—	2	1	no	—
177	C₂²×C₁₅₁	—	8	2	no	—
178	C₂²×C₁₅₁	—	8	2	no	—
179	C₂²×C₁₅₁	—	8	2	no	—
180	C₂²×C₁₅₁	—	16	4	no	—
181	C₂²×C₁₅₁	#464	1	2	yes	—
182	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
183	C₄×C₁₅₁	—	2	1	no	—
184	C₄×C₁₅₁	—	2	1	no	—
185	C₄×C₁₅₁	—	4	2	no	—
186	C₄×C₁₅₁	—	4	2	no	—
187	C₄×C₁₅₁	—	8	2	no	—
188	C₄×C₁₅₁	#464	1	2	yes	—
189	C₄×C₁₅₁	#472	1	2	yes	—
190	C₄×C₁₅₁	C₂×#135	1	1	yes	characteristic
191	C₄×C₁₅₁	C₂×#137	1	1	yes	characteristic
192	C₄×C₁₅₁	#577	1	2	yes	—
193	C₂×C₁₅₁	—	2	2	no	—
194	C₂×C₁₅₁	—	16	2	no	—
195	C₂×C₁₅₁	C₂×#464	1	1	yes	characteristic
196	C₂×C₁₅₁	#3057	1	1	yes	characteristic
197	C₂×C₁₅₁	C₂×#472	1	1	yes	characteristic
198	#19212	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₁₅₁	#19212	1	1	yes	characteristic, direct product factor, Sylow
200	#3230	C₂×C₁₅₁	1	1	yes	characteristic, complemented
201	#3208	C₂×C₁₅₁	1	1	yes	characteristic
202	C₂×#486	C₂×C₁₅₁	1	1	yes	characteristic
203	#2960	C₂×C₁₅₁	1	1	yes	characteristic, complemented
204	#1698	C₂×C₁₅₁	1	4	yes	complemented
205	#1678	C₂×C₁₅₁	1	4	yes	complemented
206	#1564	C₂×C₁₅₁	1	1	yes	characteristic, complemented
207	#1548	C₂×C₁₅₁	1	1	yes	characteristic, complemented
208	#1545	C₂×C₁₅₁	1	1	yes	characteristic
209	#533	C₂²×C₁₅₁	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
211	C₂×#127	C₂²×C₁₅₁	1	1	yes	characteristic
212	#500	—	2	1	no	—
213	#492	—	2	1	no	—
214	#487	—	2	1	no	—
215	#486	—	2	1	no	—
216	#486	—	2	1	no	—
217	#486	—	2	1	no	—
218	#486	C₂²×C₁₅₁	1	2	yes	—
219	#486	C₂²×C₁₅₁	1	2	yes	—
220	#484	—	2	2	no	—
221	#477	C₂²×C₁₅₁	1	4	yes	complemented
222	#460	C₂²×C₁₅₁	1	4	yes	—
223	#450	—	2	2	no	—
224	#446	—	2	1	no	—
225	#446	C₂²×C₁₅₁	1	2	yes	complemented
226	C₈×Q₈	—	2	1	no	—
227	C₈×Q₈	C₂²×C₁₅₁	1	2	yes	complemented
228	#431	C₂²×C₁₅₁	1	1	yes	characteristic
229	#431	C₂²×C₁₅₁	1	1	yes	characteristic
230	#424	—	2	1	no	—
231	#423	C₂²×C₁₅₁	1	1	yes	characteristic
232	C₂×#102	—	2	1	no	—
233	C₂×#102	—	2	1	no	—
234	#405	—	2	1	no	—
235	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
236	#335	C₂²×C₁₅₁	1	2	yes	complemented
237	#334	C₂²×C₁₅₁	1	2	yes	complemented
238	#333	C₂²×C₁₅₁	1	4	yes	complemented
239	#331	C₂²×C₁₅₁	1	4	yes	—
240	C₂²×Q₈	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×M₁₆	—	2	1	no	—
246	C₂²×C₈	D₄×C₁₅₁	1	1	yes	characteristic
247	C₂²×C₈	D₄×C₁₅₁	1	1	yes	characteristic
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	D₄×C₁₅₁	1	1	yes	characteristic
252	C₄⋊Q₈	D₄×C₁₅₁	1	1	yes	characteristic
253	C₄⋊Q₈	C₂³×C₁₅₁	1	2	yes	—
254	#127	—	2	1	no	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	C₂³×C₁₅₁	1	2	yes	—
258	#125	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	D₄×C₁₅₁	1	2	yes	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	C₂³×C₁₅₁	1	2	yes	—
263	#117	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
267	#107	—	2	4	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
272	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
273	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
274	#103	—	2	4	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	—	2	4	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	D₄×C₁₅₁	1	1	yes	characteristic
287	C₄×C₈	D₄×C₁₅₁	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
290	C₂⁴	—	4	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	8	2	no	—
295	C₂×Q₈	C₂×D₄×C₁₅₁	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
309	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
310	SD₁₆	—	8	4	no	—
311	M₁₆	—	4	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
335	C₄²	#41×C₁₅₁	1	1	yes	characteristic
336	C₄²	C₂⁴×C₁₅₁	1	1	yes	characteristic
337	C₂³	—	4	2	no	—
338	C₂³	—	8	2	no	—
339	C₂³	—	8	2	no	—
340	C₂³	—	8	2	no	—
341	C₂³	#121×C₁₅₁	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	2	no	—
345	Q₈	—	8	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	4	no	—
349	D₄	—	8	2	no	—
350	D₄	—	8	2	no	—
351	D₄	—	8	2	no	—
352	D₄	—	8	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
360	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
361	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
362	C₂×C₄	#135×C₁₅₁	1	2	yes	—
363	C₂×C₄	#137×C₁₅₁	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	16	4	no	—
380	C₂²	#464×C₁₅₁	1	2	yes	—
381	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	8	2	no	—
387	C₄	#464×C₁₅₁	1	2	yes	—
388	C₄	#472×C₁₅₁	1	2	yes	—
389	C₄	C₂×#135×C₁₅₁	1	1	yes	characteristic
390	C₄	C₂×#137×C₁₅₁	1	1	yes	characteristic
391	C₄	#577×C₁₅₁	1	2	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	16	2	no	—
394	C₂	C₂×#464×C₁₅₁	1	1	yes	characteristic
395	C₂	#3057×C₁₅₁	1	1	yes	characteristic
396	C₂	C₂×#472×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₅₁
prime radical	C₂×#127×C₁₅₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₅₁ ◁ C₂×C₄²×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3230×C₁₅₁	C₂	semidirect
4. #2960×C₁₅₁	C₂	semidirect
5. #1698×C₁₅₁	C₂	semidirect
6. #1678×C₁₅₁	C₂	semidirect
7. #1564×C₁₅₁	C₂	semidirect
8. #1548×C₁₅₁	C₂	semidirect
22. #477×C₁₅₁	C₂²	semidirect
26. #446×C₁₅₁	C₂²	semidirect
28. C₈×Q₈×C₁₅₁	C₂²	semidirect
37. #335×C₁₅₁	C₂²	semidirect
38. #334×C₁₅₁	C₂²	semidirect
39. #333×C₁₅₁	C₂²	semidirect
198. #19212	C₁₅₁	direct (N × H)
199. C₁₅₁	#19212	direct (N × H)
200. #3230	C₂×C₁₅₁	semidirect
203. #2960	C₂×C₁₅₁	semidirect
204. #1698	C₂×C₁₅₁	semidirect
205. #1678	C₂×C₁₅₁	semidirect
206. #1564	C₂×C₁₅₁	semidirect
207. #1548	C₂×C₁₅₁	semidirect
221. #477	C₂²×C₁₅₁	semidirect
225. #446	C₂²×C₁₅₁	semidirect
227. C₈×Q₈	C₂²×C₁₅₁	semidirect
236. #335	C₂²×C₁₅₁	semidirect
237. #334	C₂²×C₁₅₁	semidirect
238. #333	C₂²×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3230×C₁₅₁	2
#3208×C₁₅₁	2
C₂×#486×C₁₅₁	2
#2960×C₁₅₁	2
#1698×C₁₅₁	2
#1678×C₁₅₁	2
#1564×C₁₅₁	2
#1548×C₁₅₁	2
#1545×C₁₅₁	2
#19212	151

Subgroups — C151×#19212 #50324137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#19212 #50324137