Subgroups — C₁₅₁×#19659 #50324584

Order 38656.

700 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3229×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3227×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	#3226×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#3209×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#3131×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#487×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1720×C₁₅₁	C₂	1	2	yes	maximal, complemented
8	#1718×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1711×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1707×C₁₅₁	C₂	1	2	yes	maximal, complemented
11	#1450×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#533×C₁₅₁	C₂²	1	1	yes	characteristic
13	#532×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
16	#500×C₁₅₁	C₂²	1	2	yes	—
17	#498×C₁₅₁	C₂²	1	2	yes	—
18	#498×C₁₅₁	C₂²	1	2	yes	—
19	#494×C₁₅₁	C₂²	1	2	yes	—
20	#488×C₁₅₁	—	2	2	no	—
21	#487×C₁₅₁	—	2	2	no	—
22	#487×C₁₅₁	C₂²	1	2	yes	—
23	#487×C₁₅₁	C₂²	1	2	yes	—
24	#487×C₁₅₁	C₂²	1	1	yes	characteristic
25	#487×C₁₅₁	C₂²	1	1	yes	characteristic
26	#487×C₁₅₁	C₂²	1	2	yes	—
27	#487×C₁₅₁	C₂²	1	2	yes	—
28	#486×C₁₅₁	C₂²	1	1	yes	characteristic
29	#486×C₁₅₁	C₂²	1	1	yes	characteristic
30	#486×C₁₅₁	C₂²	1	2	yes	—
31	#486×C₁₅₁	C₂²	1	2	yes	—
32	#483×C₁₅₁	—	2	2	no	—
33	#481×C₁₅₁	—	2	2	no	—
34	#480×C₁₅₁	—	2	2	no	—
35	#476×C₁₅₁	—	2	2	no	—
36	#475×C₁₅₁	—	2	2	no	—
37	#474×C₁₅₁	—	2	2	no	—
38	#462×C₁₅₁	—	2	2	no	—
39	#451×C₁₅₁	—	2	2	no	—
40	#431×C₁₅₁	C₂²	1	1	yes	characteristic
41	#431×C₁₅₁	C₂²	1	1	yes	characteristic
42	#416×C₁₅₁	—	2	2	no	—
43	C₂×#103×C₁₅₁	—	2	2	no	—
44	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
45	#322×C₁₅₁	C₂²	1	2	yes	—
46	C₈²×C₁₅₁	C₂²	1	2	yes	—
47	C₂×#41×C₁₅₁	—	2	1	no	—
48	C₂²×Q₈×C₁₅₁	—	2	1	no	—
49	C₂²×Q₈×C₁₅₁	—	2	1	no	—
50	C₂×Q₁₆×C₁₅₁	—	2	4	no	—
51	C₂²×C₈×C₁₅₁	D₄	1	2	yes	—
52	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
55	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
56	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
57	C₄⋊Q₈×C₁₅₁	—	2	1	no	—
58	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
59	C₄⋊Q₈×C₁₅₁	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₁₅₁	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
63	#127×C₁₅₁	C₂³	1	1	yes	characteristic
64	#125×C₁₅₁	—	2	1	no	—
65	#124×C₁₅₁	—	2	1	no	—
66	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
67	C₂²⋊Q₈×C₁₅₁	—	2	1	no	—
68	#121×C₁₅₁	—	2	1	no	—
69	#121×C₁₅₁	—	2	1	no	—
70	C₄×Q₈×C₁₅₁	—	2	1	no	—
71	C₄×Q₈×C₁₅₁	—	2	1	no	—
72	C₄×D₄×C₁₅₁	—	2	1	no	—
73	C₄×D₄×C₁₅₁	—	2	1	no	—
74	#117×C₁₅₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
79	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
80	#107×C₁₅₁	—	2	4	no	—
81	#106×C₁₅₁	—	2	4	no	—
82	#106×C₁₅₁	—	2	4	no	—
83	C₄⋊C₈×C₁₅₁	D₄	1	2	yes	—
84	C₄⋊C₈×C₁₅₁	D₄	1	2	yes	—
85	#103×C₁₅₁	—	2	4	no	—
86	#103×C₁₅₁	—	2	4	no	—
87	#103×C₁₅₁	—	2	2	no	—
88	#103×C₁₅₁	—	2	2	no	—
89	#103×C₁₅₁	—	2	4	no	—
90	#103×C₁₅₁	—	2	4	no	—
91	#102×C₁₅₁	—	2	2	no	—
92	#102×C₁₅₁	—	2	2	no	—
93	#102×C₁₅₁	—	2	4	no	—
94	#102×C₁₅₁	—	2	4	no	—
95	C₂²⋊C₈×C₁₅₁	D₄	1	2	yes	—
96	C₂²⋊C₈×C₁₅₁	D₄	1	2	yes	—
97	C₄×C₈×C₁₅₁	D₄	1	2	yes	—
98	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₅₁	C₂³	1	2	yes	—
101	C₄×C₈×C₁₅₁	C₂³	1	2	yes	—
102	#41×C₁₅₁	—	4	4	no	—
103	C₂×Q₈×C₁₅₁	—	2	1	no	—
104	C₂×Q₈×C₁₅₁	—	2	1	no	—
105	C₂×Q₈×C₁₅₁	—	2	2	no	—
106	C₂×Q₈×C₁₅₁	—	2	2	no	—
107	C₂×Q₈×C₁₅₁	—	2	1	no	—
108	C₂×Q₈×C₁₅₁	—	4	1	no	—
109	C₂×Q₈×C₁₅₁	—	4	1	no	—
110	C₂×Q₈×C₁₅₁	—	4	4	no	—
111	C₂×Q₈×C₁₅₁	—	8	2	no	—
112	C₂×D₄×C₁₅₁	—	2	1	no	—
113	C₂×D₄×C₁₅₁	—	2	1	no	—
114	C₂×D₄×C₁₅₁	—	2	1	no	—
115	C₂×D₄×C₁₅₁	—	4	1	no	—
116	C₂²×C₄×C₁₅₁	—	4	1	no	—
117	C₂²×C₄×C₁₅₁	—	4	1	no	—
118	C₂²×C₄×C₁₅₁	—	4	1	no	—
119	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
122	Q₁₆×C₁₅₁	—	8	4	no	—
123	C₂×C₈×C₁₅₁	—	2	4	no	—
124	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₅₁	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₁₅₁	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₁₅₁	—	2	1	no	—
129	C₄⋊C₄×C₁₅₁	—	2	1	no	—
130	C₄⋊C₄×C₁₅₁	—	2	2	no	—
131	C₄⋊C₄×C₁₅₁	—	2	2	no	—
132	C₄⋊C₄×C₁₅₁	—	2	2	no	—
133	C₄⋊C₄×C₁₅₁	—	2	1	no	—
134	C₄⋊C₄×C₁₅₁	—	2	2	no	—
135	C₄⋊C₄×C₁₅₁	—	2	1	no	—
136	C₄⋊C₄×C₁₅₁	—	2	1	no	—
137	C₄⋊C₄×C₁₅₁	—	2	1	no	—
138	C₄⋊C₄×C₁₅₁	—	4	1	no	—
139	C₄⋊C₄×C₁₅₁	—	4	1	no	—
140	C₄⋊C₄×C₁₅₁	—	4	1	no	—
141	C₄⋊C₄×C₁₅₁	—	4	1	no	—
142	C₄⋊C₄×C₁₅₁	—	4	1	no	—
143	C₄⋊C₄×C₁₅₁	—	4	1	no	—
144	C₂²⋊C₄×C₁₅₁	—	4	1	no	—
145	C₂²⋊C₄×C₁₅₁	—	4	1	no	—
146	C₂²⋊C₄×C₁₅₁	—	4	1	no	—
147	C₄²×C₁₅₁	—	4	1	no	—
148	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₁₅₁	C₂⁴	1	1	yes	characteristic
152	C₂³×C₁₅₁	—	4	1	no	—
153	C₂³×C₁₅₁	#127	1	1	yes	characteristic
154	Q₈×C₁₅₁	—	4	4	no	—
155	Q₈×C₁₅₁	—	4	2	no	—
156	Q₈×C₁₅₁	—	4	4	no	—
157	Q₈×C₁₅₁	—	4	2	no	—
158	Q₈×C₁₅₁	—	4	2	no	—
159	Q₈×C₁₅₁	—	8	2	no	—
160	Q₈×C₁₅₁	—	8	2	no	—
161	D₄×C₁₅₁	—	4	2	no	—
162	D₄×C₁₅₁	—	4	2	no	—
163	D₄×C₁₅₁	—	4	2	no	—
164	D₄×C₁₅₁	—	8	2	no	—
165	C₂×C₄×C₁₅₁	—	2	2	no	—
166	C₂×C₄×C₁₅₁	—	2	2	no	—
167	C₂×C₄×C₁₅₁	—	4	2	no	—
168	C₂×C₄×C₁₅₁	—	4	2	no	—
169	C₂×C₄×C₁₅₁	—	4	1	no	—
170	C₂×C₄×C₁₅₁	—	4	1	no	—
171	C₂×C₄×C₁₅₁	—	4	1	no	—
172	C₂×C₄×C₁₅₁	—	8	2	no	—
173	C₂×C₄×C₁₅₁	—	8	2	no	—
174	C₂×C₄×C₁₅₁	—	8	2	no	—
175	C₂×C₄×C₁₅₁	#127	1	1	yes	characteristic
176	C₂×C₄×C₁₅₁	#127	1	1	yes	characteristic
177	C₂×C₄×C₁₅₁	#127	1	1	yes	characteristic
178	C₂×C₄×C₁₅₁	#135	1	4	yes	—
179	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₅₁	—	2	2	no	—
183	C₈×C₁₅₁	—	2	2	no	—
184	C₈×C₁₅₁	—	2	4	no	—
185	C₈×C₁₅₁	—	2	4	no	—
186	C₂²×C₁₅₁	—	2	1	no	—
187	C₂²×C₁₅₁	—	2	1	no	—
188	C₂²×C₁₅₁	—	8	1	no	—
189	C₂²×C₁₅₁	—	8	1	no	—
190	C₂²×C₁₅₁	—	8	1	no	—
191	C₂²×C₁₅₁	#495	1	2	yes	—
192	C₂²×C₁₅₁	C₂×#127	1	1	yes	characteristic
193	C₄×C₁₅₁	—	2	1	no	—
194	C₄×C₁₅₁	—	2	1	no	—
195	C₄×C₁₅₁	—	8	1	no	—
196	C₄×C₁₅₁	—	8	2	no	—
197	C₄×C₁₅₁	—	8	2	no	—
198	C₄×C₁₅₁	—	8	1	no	—
199	C₄×C₁₅₁	—	8	1	no	—
200	C₄×C₁₅₁	#495	1	2	yes	—
201	C₄×C₁₅₁	C₂×#135	1	2	yes	—
202	C₄×C₁₅₁	#577	1	2	yes	—
203	C₄×C₁₅₁	#578	1	2	yes	—
204	C₂×C₁₅₁	—	2	2	no	—
205	C₂×C₁₅₁	—	16	1	no	—
206	C₂×C₁₅₁	C₂×#495	1	1	yes	characteristic
207	C₂×C₁₅₁	#3154	1	1	yes	characteristic
208	C₂×C₁₅₁	#3156	1	1	yes	characteristic
209	#19659	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₁₅₁	#19659	1	1	yes	characteristic, direct product factor, Sylow
211	#3229	C₂×C₁₅₁	1	1	yes	characteristic, complemented
212	#3227	C₂×C₁₅₁	1	1	yes	characteristic
213	#3226	C₂×C₁₅₁	1	1	yes	characteristic
214	#3209	C₂×C₁₅₁	1	1	yes	characteristic, complemented
215	#3131	C₂×C₁₅₁	1	1	yes	characteristic
216	C₂×#487	C₂×C₁₅₁	1	1	yes	characteristic, complemented
217	#1720	C₂×C₁₅₁	1	2	yes	complemented
218	#1718	C₂×C₁₅₁	1	2	yes	complemented
219	#1711	C₂×C₁₅₁	1	2	yes	complemented
220	#1707	C₂×C₁₅₁	1	2	yes	complemented
221	#1450	C₂×C₁₅₁	1	1	yes	characteristic, complemented
222	#533	C₂²×C₁₅₁	1	1	yes	characteristic
223	#532	C₂²×C₁₅₁	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
226	#500	C₂²×C₁₅₁	1	2	yes	—
227	#498	C₂²×C₁₅₁	1	2	yes	—
228	#498	C₂²×C₁₅₁	1	2	yes	—
229	#494	C₂²×C₁₅₁	1	2	yes	—
230	#488	—	2	2	no	—
231	#487	—	2	2	no	—
232	#487	C₂²×C₁₅₁	1	2	yes	—
233	#487	C₂²×C₁₅₁	1	2	yes	—
234	#487	C₂²×C₁₅₁	1	1	yes	characteristic
235	#487	C₂²×C₁₅₁	1	1	yes	characteristic
236	#487	C₂²×C₁₅₁	1	2	yes	—
237	#487	C₂²×C₁₅₁	1	2	yes	—
238	#486	C₂²×C₁₅₁	1	1	yes	characteristic
239	#486	C₂²×C₁₅₁	1	1	yes	characteristic
240	#486	C₂²×C₁₅₁	1	2	yes	—
241	#486	C₂²×C₁₅₁	1	2	yes	—
242	#483	—	2	2	no	—
243	#481	—	2	2	no	—
244	#480	—	2	2	no	—
245	#476	—	2	2	no	—
246	#475	—	2	2	no	—
247	#474	—	2	2	no	—
248	#462	—	2	2	no	—
249	#451	—	2	2	no	—
250	#431	C₂²×C₁₅₁	1	1	yes	characteristic
251	#431	C₂²×C₁₅₁	1	1	yes	characteristic
252	#416	—	2	2	no	—
253	C₂×#103	—	2	2	no	—
254	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
255	#322	C₂²×C₁₅₁	1	2	yes	—
256	C₈²	C₂²×C₁₅₁	1	2	yes	—
257	C₂×#41	—	2	1	no	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂×Q₁₆	—	2	4	no	—
261	C₂²×C₈	D₄×C₁₅₁	1	2	yes	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	C₂³×C₁₅₁	1	2	yes	—
269	C₄⋊Q₈	C₂³×C₁₅₁	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
271	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
272	C₄⋊Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
273	#127	C₂³×C₁₅₁	1	1	yes	characteristic
274	#125	—	2	1	no	—
275	#124	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	#117	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
290	#107	—	2	4	no	—
291	#106	—	2	4	no	—
292	#106	—	2	4	no	—
293	C₄⋊C₈	D₄×C₁₅₁	1	2	yes	—
294	C₄⋊C₈	D₄×C₁₅₁	1	2	yes	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	4	no	—
300	#103	—	2	4	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	C₂²⋊C₈	D₄×C₁₅₁	1	2	yes	—
306	C₂²⋊C₈	D₄×C₁₅₁	1	2	yes	—
307	C₄×C₈	D₄×C₁₅₁	1	2	yes	—
308	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
309	C₄×C₈	C₂³×C₁₅₁	1	2	yes	—
310	C₄×C₈	C₂³×C₁₅₁	1	2	yes	—
311	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
312	#41	—	4	4	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	4	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
332	Q₁₆	—	8	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₁₅₁	1	4	yes	—
337	C₂×C₈	C₂×D₄×C₁₅₁	1	4	yes	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
361	C₄²	C₂⁴×C₁₅₁	1	1	yes	characteristic
362	C₂³	—	4	1	no	—
363	C₂³	#127×C₁₅₁	1	1	yes	characteristic
364	Q₈	—	4	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	8	2	no	—
370	Q₈	—	8	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	#127×C₁₅₁	1	1	yes	characteristic
386	C₂×C₄	#127×C₁₅₁	1	1	yes	characteristic
387	C₂×C₄	#127×C₁₅₁	1	1	yes	characteristic
388	C₂×C₄	#135×C₁₅₁	1	4	yes	—
389	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
392	C₈	—	2	2	no	—
393	C₈	—	2	2	no	—
394	C₈	—	2	4	no	—
395	C₈	—	2	4	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	#495×C₁₅₁	1	2	yes	—
402	C₂²	C₂×#127×C₁₅₁	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	2	no	—
407	C₄	—	8	2	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	1	no	—
410	C₄	#495×C₁₅₁	1	2	yes	—
411	C₄	C₂×#135×C₁₅₁	1	2	yes	—
412	C₄	#577×C₁₅₁	1	2	yes	—
413	C₄	#578×C₁₅₁	1	2	yes	—
414	C₂	—	2	2	no	—
415	C₂	—	16	1	no	—
416	C₂	C₂×#495×C₁₅₁	1	1	yes	characteristic
417	C₂	#3154×C₁₅₁	1	1	yes	characteristic
418	C₂	#3156×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₅₁
prime radical	#532×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. #3229×C₁₅₁	C₂	semidirect
4. #3209×C₁₅₁	C₂	semidirect
6. C₂×#487×C₁₅₁	C₂	semidirect
7. #1720×C₁₅₁	C₂	semidirect
8. #1718×C₁₅₁	C₂	semidirect
9. #1711×C₁₅₁	C₂	semidirect
10. #1707×C₁₅₁	C₂	semidirect
11. #1450×C₁₅₁	C₂	semidirect
209. #19659	C₁₅₁	direct (N × H)
210. C₁₅₁	#19659	direct (N × H)
211. #3229	C₂×C₁₅₁	semidirect
214. #3209	C₂×C₁₅₁	semidirect
216. C₂×#487	C₂×C₁₅₁	semidirect
217. #1720	C₂×C₁₅₁	semidirect
218. #1718	C₂×C₁₅₁	semidirect
219. #1711	C₂×C₁₅₁	semidirect
220. #1707	C₂×C₁₅₁	semidirect
221. #1450	C₂×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3229×C₁₅₁	2
#3227×C₁₅₁	2
#3226×C₁₅₁	2
#3209×C₁₅₁	2
#3131×C₁₅₁	2
C₂×#487×C₁₅₁	2
#1720×C₁₅₁	2
#1718×C₁₅₁	2
#1711×C₁₅₁	2
#1707×C₁₅₁	2
#1450×C₁₅₁	2
#19659	151

Subgroups — C151×#19659 #50324584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#19659 #50324584