Subgroups — C₁₅₁×#23720 #50328645

Order 38656.

744 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#137×C₁₅₁	C₂	1	2	yes	maximal
2	C₂×#441×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2923×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2090×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2079×C₁₅₁	C₂	1	1	yes	maximal, characteristic
6	#2064×C₁₅₁	C₂	1	2	yes	maximal, complemented
7	#2052×C₁₅₁	C₂	1	2	yes	maximal
8	#2047×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#2020×C₁₅₁	C₂	1	1	yes	maximal, characteristic
10	#1778×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#101×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	C₂×#137×C₁₅₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₄×#41×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₅₁	C₂²	1	2	yes	—
16	#441×C₁₅₁	—	2	2	no	—
17	#441×C₁₅₁	—	2	2	no	—
18	#441×C₁₅₁	—	2	2	no	—
19	#440×C₁₅₁	—	2	2	no	—
20	C₄×Q₁₆×C₁₅₁	—	2	2	no	—
21	C₄×SD₁₆×C₁₅₁	—	2	2	no	—
22	#433×C₁₅₁	—	2	2	no	—
23	#432×C₁₅₁	—	2	2	no	—
24	C₂×#108×C₁₅₁	C₂²	1	2	yes	—
25	#428×C₁₅₁	C₂²	1	2	yes	—
26	C₂×#106×C₁₅₁	C₂²	1	1	yes	characteristic
27	#424×C₁₅₁	C₂²	1	1	yes	characteristic
28	#424×C₁₅₁	C₂²	1	1	yes	characteristic
29	#419×C₁₅₁	C₂²	1	2	yes	—
30	#417×C₁₅₁	C₂²	1	2	yes	—
31	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
32	C₂×#101×C₁₅₁	C₂²	1	2	yes	—
33	C₂×#101×C₁₅₁	C₂²	1	2	yes	—
34	#408×C₁₅₁	C₂²	1	1	yes	characteristic
35	#408×C₁₅₁	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₁₅₁	C₂²	1	2	yes	—
38	C₂×#97×C₁₅₁	C₂²	1	1	yes	characteristic
39	#343×C₁₅₁	C₂²	1	2	yes	—
40	#343×C₁₅₁	C₂²	1	2	yes	—
41	#341×C₁₅₁	C₂²	1	1	yes	characteristic
42	#341×C₁₅₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₁₅₁	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₅₁	C₂³	1	2	yes	—
45	#137×C₁₅₁	—	2	4	no	—
46	#137×C₁₅₁	—	2	4	no	—
47	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
48	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
49	C₂×Q₁₆×C₁₅₁	—	2	4	no	—
50	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
51	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
52	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
57	C₄×Q₈×C₁₅₁	—	2	2	no	—
58	C₄×Q₈×C₁₅₁	—	2	2	no	—
59	C₄×Q₈×C₁₅₁	—	2	2	no	—
60	C₄×Q₈×C₁₅₁	—	2	2	no	—
61	C₄×Q₈×C₁₅₁	D₄	1	2	yes	—
62	C₄×D₄×C₁₅₁	—	2	2	no	—
63	C₄×D₄×C₁₅₁	D₄	1	2	yes	—
64	#117×C₁₅₁	—	2	1	no	—
65	#117×C₁₅₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₅₁	—	2	1	no	—
69	C₂×C₄²×C₁₅₁	—	2	2	no	—
70	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
71	#108×C₁₅₁	—	2	4	no	—
72	#107×C₁₅₁	—	2	2	no	—
73	#106×C₁₅₁	—	2	2	no	—
74	#106×C₁₅₁	—	2	2	no	—
75	C₄⋊C₈×C₁₅₁	—	2	2	no	—
76	C₄⋊C₈×C₁₅₁	—	2	2	no	—
77	#103×C₁₅₁	—	2	4	no	—
78	#103×C₁₅₁	—	2	2	no	—
79	#103×C₁₅₁	—	2	2	no	—
80	#103×C₁₅₁	—	2	2	no	—
81	#102×C₁₅₁	—	2	2	no	—
82	#101×C₁₅₁	—	2	4	no	—
83	#101×C₁₅₁	—	2	4	no	—
84	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
85	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
86	#97×C₁₅₁	—	2	1	no	—
87	#97×C₁₅₁	—	2	2	no	—
88	#97×C₁₅₁	D₄	1	2	yes	—
89	#97×C₁₅₁	D₄	1	2	yes	—
90	C₄×C₈×C₁₅₁	—	2	1	no	—
91	C₄×C₈×C₁₅₁	—	2	2	no	—
92	#41×C₁₅₁	—	2	2	no	—
93	#41×C₁₅₁	—	2	2	no	—
94	C₂×Q₈×C₁₅₁	—	2	2	no	—
95	C₂×Q₈×C₁₅₁	—	2	2	no	—
96	C₂×Q₈×C₁₅₁	—	2	2	no	—
97	C₂×Q₈×C₁₅₁	—	2	2	no	—
98	C₂×Q₈×C₁₅₁	—	2	2	no	—
99	C₂×Q₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₁₅₁	#41	1	4	yes	—
101	C₂×D₄×C₁₅₁	—	2	1	no	—
102	C₂×D₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₅₁	—	2	2	no	—
104	C₂²×C₄×C₁₅₁	—	2	1	no	—
105	C₂²×C₄×C₁₅₁	—	2	2	no	—
106	C₂²×C₄×C₁₅₁	—	2	2	no	—
107	C₂²×C₄×C₁₅₁	#41	1	2	yes	—
108	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₁₅₁	—	2	8	no	—
110	Q₁₆×C₁₅₁	—	2	8	no	—
111	SD₁₆×C₁₅₁	—	2	8	no	—
112	M₁₆×C₁₅₁	—	2	2	no	—
113	M₁₆×C₁₅₁	—	2	2	no	—
114	M₁₆×C₁₅₁	—	2	2	no	—
115	M₁₆×C₁₅₁	—	2	2	no	—
116	M₁₆×C₁₅₁	—	2	2	no	—
117	M₁₆×C₁₅₁	#41	1	4	yes	—
118	C₂×C₈×C₁₅₁	—	2	2	no	—
119	C₂×C₈×C₁₅₁	—	2	2	no	—
120	C₂×C₈×C₁₅₁	—	2	2	no	—
121	C₂×C₈×C₁₅₁	—	2	1	no	—
122	C₂×C₈×C₁₅₁	—	2	1	no	—
123	C₂×C₈×C₁₅₁	—	2	2	no	—
124	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
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	2	no	—
130	C₄⋊C₄×C₁₅₁	—	4	2	no	—
131	C₄⋊C₄×C₁₅₁	C₂×D₄	1	2	yes	—
132	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
133	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
134	C₄²×C₁₅₁	—	2	2	no	—
135	C₄²×C₁₅₁	—	2	1	no	—
136	C₄²×C₁₅₁	—	4	2	no	—
137	C₄²×C₁₅₁	—	4	2	no	—
138	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
139	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₁₅₁	—	2	1	no	—
142	C₂³×C₁₅₁	C₂×#41	1	1	yes	characteristic
143	Q₈×C₁₅₁	—	2	4	no	—
144	Q₈×C₁₅₁	—	2	4	no	—
145	Q₈×C₁₅₁	—	2	2	no	—
146	Q₈×C₁₅₁	—	4	2	no	—
147	Q₈×C₁₅₁	—	4	2	no	—
148	D₄×C₁₅₁	—	2	2	no	—
149	D₄×C₁₅₁	—	4	2	no	—
150	C₂×C₄×C₁₅₁	—	2	1	no	—
151	C₂×C₄×C₁₅₁	—	2	2	no	—
152	C₂×C₄×C₁₅₁	—	2	4	no	—
153	C₂×C₄×C₁₅₁	—	4	2	no	—
154	C₂×C₄×C₁₅₁	—	4	2	no	—
155	C₂×C₄×C₁₅₁	—	4	2	no	—
156	C₂×C₄×C₁₅₁	—	4	1	no	—
157	C₂×C₄×C₁₅₁	—	4	1	no	—
158	C₂×C₄×C₁₅₁	—	4	2	no	—
159	C₂×C₄×C₁₅₁	—	8	2	no	—
160	C₂×C₄×C₁₅₁	—	8	2	no	—
161	C₂×C₄×C₁₅₁	#121	1	2	yes	—
162	C₂×C₄×C₁₅₁	#121	1	2	yes	—
163	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₅₁	C₂×#41	1	2	yes	—
166	C₂×C₄×C₁₅₁	C₂×#41	1	2	yes	—
167	C₈×C₁₅₁	—	2	2	no	—
168	C₈×C₁₅₁	—	2	4	no	—
169	C₈×C₁₅₁	—	2	2	no	—
170	C₈×C₁₅₁	—	4	1	no	—
171	C₈×C₁₅₁	—	4	2	no	—
172	C₈×C₁₅₁	—	4	1	no	—
173	C₂²×C₁₅₁	—	2	2	no	—
174	C₂²×C₁₅₁	—	4	1	no	—
175	C₂²×C₁₅₁	—	4	2	no	—
176	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
177	C₂²×C₁₅₁	#529	1	2	yes	—
178	C₄×C₁₅₁	—	2	2	no	—
179	C₄×C₁₅₁	—	2	2	no	—
180	C₄×C₁₅₁	—	4	1	no	—
181	C₄×C₁₅₁	—	4	4	no	—
182	C₄×C₁₅₁	—	4	2	no	—
183	C₄×C₁₅₁	—	8	2	no	—
184	C₄×C₁₅₁	#525	1	1	yes	characteristic
185	C₄×C₁₅₁	#525	1	2	yes	—
186	C₄×C₁₅₁	#532	1	1	yes	characteristic
187	C₂×C₁₅₁	—	2	2	no	—
188	C₂×C₁₅₁	—	8	1	no	—
189	C₂×C₁₅₁	#2392	1	1	yes	characteristic
190	C₂×C₁₅₁	#3069	1	2	yes	—
191	#23720	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₁₅₁	#23720	1	1	yes	characteristic, direct product factor, Sylow
193	C₄×#137	C₂×C₁₅₁	1	2	yes	—
194	C₂×#441	C₂×C₁₅₁	1	1	yes	characteristic, complemented
195	#2923	C₂×C₁₅₁	1	1	yes	characteristic
196	#2090	C₂×C₁₅₁	1	1	yes	characteristic, complemented
197	#2079	C₂×C₁₅₁	1	1	yes	characteristic
198	#2064	C₂×C₁₅₁	1	2	yes	complemented
199	#2052	C₂×C₁₅₁	1	2	yes	—
200	#2047	C₂×C₁₅₁	1	1	yes	characteristic, complemented
201	#2020	C₂×C₁₅₁	1	1	yes	characteristic
202	#1778	C₂×C₁₅₁	1	1	yes	characteristic, complemented
203	C₄×#101	C₂×C₁₅₁	1	2	yes	complemented
204	C₂×#137	C₂²×C₁₅₁	1	2	yes	—
205	C₂²×Q₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
206	C₄×#41	C₂²×C₁₅₁	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂²×C₁₅₁	1	2	yes	—
208	#441	—	2	2	no	—
209	#441	—	2	2	no	—
210	#441	—	2	2	no	—
211	#440	—	2	2	no	—
212	C₄×Q₁₆	—	2	2	no	—
213	C₄×SD₁₆	—	2	2	no	—
214	#433	—	2	2	no	—
215	#432	—	2	2	no	—
216	C₂×#108	C₂²×C₁₅₁	1	2	yes	—
217	#428	C₂²×C₁₅₁	1	2	yes	—
218	C₂×#106	C₂²×C₁₅₁	1	1	yes	characteristic
219	#424	C₂²×C₁₅₁	1	1	yes	characteristic
220	#424	C₂²×C₁₅₁	1	1	yes	characteristic
221	#419	C₂²×C₁₅₁	1	2	yes	—
222	#417	C₂²×C₁₅₁	1	2	yes	—
223	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
224	C₂×#101	C₂²×C₁₅₁	1	2	yes	—
225	C₂×#101	C₂²×C₁₅₁	1	2	yes	—
226	#408	C₂²×C₁₅₁	1	1	yes	characteristic
227	#408	C₂²×C₁₅₁	1	1	yes	characteristic
228	C₄×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
229	C₄×M₁₆	C₂²×C₁₅₁	1	2	yes	—
230	C₂×#97	C₂²×C₁₅₁	1	1	yes	characteristic
231	#343	C₂²×C₁₅₁	1	2	yes	—
232	#343	C₂²×C₁₅₁	1	2	yes	—
233	#341	C₂²×C₁₅₁	1	1	yes	characteristic
234	#341	C₂²×C₁₅₁	1	1	yes	characteristic
235	C₂×#41	C₂³×C₁₅₁	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
237	#137	—	2	4	no	—
238	#137	—	2	4	no	—
239	C₂×Q₁₆	—	2	4	no	—
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
244	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
245	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
246	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
247	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	D₄×C₁₅₁	1	2	yes	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	D₄×C₁₅₁	1	2	yes	—
256	#117	—	2	1	no	—
257	#117	C₂³×C₁₅₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
263	#108	—	2	4	no	—
264	#107	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	4	no	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#102	—	2	2	no	—
274	#101	—	2	4	no	—
275	#101	—	2	4	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	#97	—	2	1	no	—
279	#97	—	2	2	no	—
280	#97	D₄×C₁₅₁	1	2	yes	—
281	#97	D₄×C₁₅₁	1	2	yes	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
292	C₂×Q₈	#41×C₁₅₁	1	4	yes	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	#41×C₁₅₁	1	2	yes	—
300	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
301	Q₁₆	—	2	8	no	—
302	Q₁₆	—	2	8	no	—
303	SD₁₆	—	2	8	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	2	no	—
309	M₁₆	#41×C₁₅₁	1	4	yes	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	C₂×D₄×C₁₅₁	1	2	yes	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	4	2	no	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
331	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
333	C₂³	—	2	1	no	—
334	C₂³	C₂×#41×C₁₅₁	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	2	4	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	#121×C₁₅₁	1	2	yes	—
354	C₂×C₄	#121×C₁₅₁	1	2	yes	—
355	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₁₅₁	1	2	yes	—
358	C₂×C₄	C₂×#41×C₁₅₁	1	2	yes	—
359	C₈	—	2	2	no	—
360	C₈	—	2	4	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
369	C₂²	#529×C₁₅₁	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	4	no	—
374	C₄	—	4	2	no	—
375	C₄	—	8	2	no	—
376	C₄	#525×C₁₅₁	1	1	yes	characteristic
377	C₄	#525×C₁₅₁	1	2	yes	—
378	C₄	#532×C₁₅₁	1	1	yes	characteristic
379	C₂	—	2	2	no	—
380	C₂	—	8	1	no	—
381	C₂	#2392×C₁₅₁	1	1	yes	characteristic
382	C₂	#3069×C₁₅₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂×#41×C₁₅₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
2. C₂×#441×C₁₅₁	C₂	semidirect
4. #2090×C₁₅₁	C₂	semidirect
6. #2064×C₁₅₁	C₂	semidirect
8. #2047×C₁₅₁	C₂	semidirect
10. #1778×C₁₅₁	C₂	semidirect
11. C₄×#101×C₁₅₁	C₂	semidirect
191. #23720	C₁₅₁	direct (N × H)
192. C₁₅₁	#23720	direct (N × H)
194. C₂×#441	C₂×C₁₅₁	semidirect
196. #2090	C₂×C₁₅₁	semidirect
198. #2064	C₂×C₁₅₁	semidirect
200. #2047	C₂×C₁₅₁	semidirect
202. #1778	C₂×C₁₅₁	semidirect
203. C₄×#101	C₂×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×#137×C₁₅₁	2
C₂×#441×C₁₅₁	2
#2923×C₁₅₁	2
#2090×C₁₅₁	2
#2079×C₁₅₁	2
#2064×C₁₅₁	2
#2052×C₁₅₁	2
#2047×C₁₅₁	2
#2020×C₁₅₁	2
#1778×C₁₅₁	2
C₄×#101×C₁₅₁	2
#23720	151

Subgroups — C151×#23720 #50328645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23720 #50328645