Subgroups — C₁₅₁×#24989 #50329914

Order 38656.

620 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×#473×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	#2950×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2082×C₁₅₁	C₂	1	2	yes	maximal, complemented
4	#2049×C₁₅₁	C₂	1	2	yes	maximal
5	#1979×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1953×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1905×C₁₅₁	C₂	1	2	yes	maximal
8	#1833×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1830×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	#1814×C₁₅₁	C₂	1	1	yes	maximal, characteristic
11	#1757×C₁₅₁	C₂	1	1	yes	maximal, characteristic
12	C₂×#137×C₁₅₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
14	C₂×#131×C₁₅₁	C₂²	1	1	yes	characteristic
15	#519×C₁₅₁	C₂²	1	2	yes	—
16	#473×C₁₅₁	—	2	2	no	—
17	#473×C₁₅₁	—	2	2	no	—
18	#441×C₁₅₁	—	2	2	no	—
19	C₄×Q₁₆×C₁₅₁	—	2	2	no	—
20	#430×C₁₅₁	C₂²	1	2	yes	—
21	C₂×#108×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂×#108×C₁₅₁	C₂²	1	1	yes	characteristic
23	#427×C₁₅₁	C₂²	1	1	yes	characteristic
24	#421×C₁₅₁	C₂²	1	2	yes	—
25	#419×C₁₅₁	C₂²	1	2	yes	—
26	#419×C₁₅₁	C₂²	1	2	yes	—
27	#413×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₂×#101×C₁₅₁	C₂²	1	2	yes	—
29	C₂×#101×C₁₅₁	C₂²	1	2	yes	—
30	#410×C₁₅₁	C₂²	1	1	yes	characteristic
31	#405×C₁₅₁	C₂²	1	1	yes	characteristic
32	#405×C₁₅₁	C₂²	1	1	yes	characteristic
33	#344×C₁₅₁	C₂²	1	1	yes	characteristic
34	#344×C₁₅₁	C₂²	1	2	yes	—
35	#344×C₁₅₁	C₂²	1	1	yes	characteristic
36	#344×C₁₅₁	C₂²	1	2	yes	—
37	#344×C₁₅₁	C₂²	1	2	yes	—
38	H(3,ℤ/4)×C₁₅₁	C₂²	1	2	yes	—
39	C₂×#41×C₁₅₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₅₁	C₂³	1	2	yes	—
41	#137×C₁₅₁	—	2	4	no	—
42	#137×C₁₅₁	—	4	2	no	—
43	C₂×Q₁₆×C₁₅₁	—	2	1	no	—
44	C₂×Q₁₆×C₁₅₁	—	2	1	no	—
45	C₂×Q₁₆×C₁₅₁	—	2	1	no	—
46	C₂×Q₁₆×C₁₅₁	—	2	1	no	—
47	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
48	C₂×Q₁₆×C₁₅₁	D₄	1	2	yes	—
49	C₂×Q₁₆×C₁₅₁	D₄	1	2	yes	—
50	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
51	#131×C₁₅₁	—	2	1	no	—
52	#131×C₁₅₁	—	2	1	no	—
53	#131×C₁₅₁	—	2	1	no	—
54	#131×C₁₅₁	—	2	1	no	—
55	C₂×M₁₆×C₁₅₁	—	2	1	no	—
56	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
59	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₅₁	—	2	1	no	—
62	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₁₅₁	—	2	4	no	—
64	C₄×Q₈×C₁₅₁	—	4	2	no	—
65	#117×C₁₅₁	—	2	4	no	—
66	#117×C₁₅₁	C₂³	1	1	yes	characteristic
67	#117×C₁₅₁	C₂³	1	2	yes	—
68	#117×C₁₅₁	C₂³	1	1	yes	characteristic
69	#108×C₁₅₁	—	2	1	no	—
70	#108×C₁₅₁	—	2	1	no	—
71	#108×C₁₅₁	—	2	1	no	—
72	#108×C₁₅₁	—	2	1	no	—
73	#108×C₁₅₁	—	4	2	no	—
74	#107×C₁₅₁	—	2	1	no	—
75	#106×C₁₅₁	—	2	1	no	—
76	#104×C₁₅₁	—	4	2	no	—
77	#103×C₁₅₁	—	2	4	no	—
78	#103×C₁₅₁	—	4	2	no	—
79	#101×C₁₅₁	—	2	4	no	—
80	#101×C₁₅₁	—	2	1	no	—
81	#101×C₁₅₁	—	4	2	no	—
82	#100×C₁₅₁	—	2	1	no	—
83	#99×C₁₅₁	—	2	2	no	—
84	#97×C₁₅₁	—	2	1	no	—
85	#97×C₁₅₁	—	2	1	no	—
86	C₄×C₈×C₁₅₁	—	2	1	no	—
87	C₄×C₈×C₁₅₁	—	2	1	no	—
88	#41×C₁₅₁	—	2	1	no	—
89	#41×C₁₅₁	—	2	1	no	—
90	#41×C₁₅₁	—	2	1	no	—
91	#41×C₁₅₁	—	2	1	no	—
92	C₂×Q₈×C₁₅₁	—	2	2	no	—
93	C₂×Q₈×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	C₂×D₄	1	4	yes	—
98	C₂×Q₈×C₁₅₁	#41	1	1	yes	characteristic
99	C₂×D₄×C₁₅₁	—	2	1	no	—
100	C₂×D₄×C₁₅₁	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₅₁	—	2	2	no	—
102	C₂²×C₄×C₁₅₁	—	2	1	no	—
103	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
104	Q₁₆×C₁₅₁	—	2	2	no	—
105	Q₁₆×C₁₅₁	—	2	2	no	—
106	Q₁₆×C₁₅₁	—	2	2	no	—
107	Q₁₆×C₁₅₁	—	2	2	no	—
108	Q₁₆×C₁₅₁	—	4	4	no	—
109	SD₁₆×C₁₅₁	—	4	4	no	—
110	M₁₆×C₁₅₁	—	2	1	no	—
111	M₁₆×C₁₅₁	—	2	2	no	—
112	M₁₆×C₁₅₁	—	2	1	no	—
113	M₁₆×C₁₅₁	—	2	1	no	—
114	M₁₆×C₁₅₁	—	2	2	no	—
115	M₁₆×C₁₅₁	—	2	1	no	—
116	M₁₆×C₁₅₁	—	2	1	no	—
117	M₁₆×C₁₅₁	—	2	2	no	—
118	M₁₆×C₁₅₁	—	2	1	no	—
119	M₁₆×C₁₅₁	—	2	2	no	—
120	M₁₆×C₁₅₁	—	4	1	no	—
121	M₁₆×C₁₅₁	—	4	1	no	—
122	C₂×C₈×C₁₅₁	—	2	1	no	—
123	C₂×C₈×C₁₅₁	—	2	1	no	—
124	C₂×C₈×C₁₅₁	—	2	1	no	—
125	C₂×C₈×C₁₅₁	—	2	2	no	—
126	C₂×C₈×C₁₅₁	—	2	2	no	—
127	C₂×C₈×C₁₅₁	—	4	1	no	—
128	C₂×C₈×C₁₅₁	—	4	1	no	—
129	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₅₁	#41	1	1	yes	characteristic
132	C₂×C₈×C₁₅₁	#41	1	1	yes	characteristic
133	C₂×C₈×C₁₅₁	#41	1	1	yes	characteristic
134	C₂×C₈×C₁₅₁	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₁₅₁	—	2	1	no	—
136	C₄⋊C₄×C₁₅₁	—	2	2	no	—
137	C₄⋊C₄×C₁₅₁	—	2	1	no	—
138	C₄⋊C₄×C₁₅₁	—	4	4	no	—
139	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
140	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
141	C₂²⋊C₄×C₁₅₁	#41	1	2	yes	—
142	C₄²×C₁₅₁	—	2	1	no	—
143	C₄²×C₁₅₁	—	2	1	no	—
144	C₄²×C₁₅₁	—	2	2	no	—
145	C₄²×C₁₅₁	—	4	4	no	—
146	C₂³×C₁₅₁	—	2	1	no	—
147	C₂³×C₁₅₁	C₂×#41	1	1	yes	characteristic
148	Q₈×C₁₅₁	—	2	4	no	—
149	Q₈×C₁₅₁	—	2	4	no	—
150	Q₈×C₁₅₁	—	2	1	no	—
151	Q₈×C₁₅₁	—	2	1	no	—
152	Q₈×C₁₅₁	—	4	2	no	—
153	Q₈×C₁₅₁	—	4	2	no	—
154	D₄×C₁₅₁	—	2	1	no	—
155	D₄×C₁₅₁	—	2	1	no	—
156	D₄×C₁₅₁	—	4	1	no	—
157	D₄×C₁₅₁	—	4	1	no	—
158	C₂×C₄×C₁₅₁	—	2	1	no	—
159	C₂×C₄×C₁₅₁	—	2	4	no	—
160	C₂×C₄×C₁₅₁	—	2	2	no	—
161	C₂×C₄×C₁₅₁	—	4	2	no	—
162	C₂×C₄×C₁₅₁	—	4	2	no	—
163	C₂×C₄×C₁₅₁	—	4	1	no	—
164	C₂×C₄×C₁₅₁	—	4	1	no	—
165	C₂×C₄×C₁₅₁	—	4	2	no	—
166	C₂×C₄×C₁₅₁	—	4	1	no	—
167	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₈×C₁₅₁	—	4	1	no	—
174	C₈×C₁₅₁	—	4	2	no	—
175	C₈×C₁₅₁	—	4	1	no	—
176	C₈×C₁₅₁	—	4	2	no	—
177	C₈×C₁₅₁	—	4	1	no	—
178	C₈×C₁₅₁	#123	1	1	yes	characteristic
179	C₈×C₁₅₁	#123	1	1	yes	characteristic
180	C₈×C₁₅₁	#123	1	1	yes	characteristic
181	C₈×C₁₅₁	#123	1	1	yes	characteristic
182	C₂²×C₁₅₁	—	4	1	no	—
183	C₂²×C₁₅₁	—	4	1	no	—
184	C₂²×C₁₅₁	—	8	1	no	—
185	C₂²×C₁₅₁	#529	1	1	yes	characteristic
186	C₂²×C₁₅₁	#546	1	1	yes	characteristic
187	C₂²×C₁₅₁	#555	1	1	yes	characteristic
188	C₄×C₁₅₁	—	4	2	no	—
189	C₄×C₁₅₁	—	4	1	no	—
190	C₄×C₁₅₁	—	4	4	no	—
191	C₄×C₁₅₁	—	8	2	no	—
192	C₄×C₁₅₁	—	8	1	no	—
193	C₄×C₁₅₁	C₂×#123	1	1	yes	characteristic
194	C₄×C₁₅₁	#540	1	1	yes	characteristic
195	C₄×C₁₅₁	#546	1	1	yes	characteristic
196	C₄×C₁₅₁	#553	1	1	yes	characteristic
197	C₂×C₁₅₁	—	2	1	no	—
198	C₂×C₁₅₁	—	2	1	no	—
199	C₂×C₁₅₁	—	2	1	no	—
200	C₂×C₁₅₁	—	8	1	no	—
201	C₂×C₁₅₁	#2420	1	1	yes	characteristic
202	#24989	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₁₅₁	#24989	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×#473	C₂×C₁₅₁	1	1	yes	characteristic
205	#2950	C₂×C₁₅₁	1	1	yes	characteristic, complemented
206	#2082	C₂×C₁₅₁	1	2	yes	complemented
207	#2049	C₂×C₁₅₁	1	2	yes	—
208	#1979	C₂×C₁₅₁	1	1	yes	characteristic, complemented
209	#1953	C₂×C₁₅₁	1	1	yes	characteristic, complemented
210	#1905	C₂×C₁₅₁	1	2	yes	—
211	#1833	C₂×C₁₅₁	1	1	yes	characteristic, complemented
212	#1830	C₂×C₁₅₁	1	2	yes	complemented
213	#1814	C₂×C₁₅₁	1	1	yes	characteristic
214	#1757	C₂×C₁₅₁	1	1	yes	characteristic
215	C₂×#137	C₂²×C₁₅₁	1	2	yes	—
216	C₂²×Q₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
217	C₂×#131	C₂²×C₁₅₁	1	1	yes	characteristic
218	#519	C₂²×C₁₅₁	1	2	yes	—
219	#473	—	2	2	no	—
220	#473	—	2	2	no	—
221	#441	—	2	2	no	—
222	C₄×Q₁₆	—	2	2	no	—
223	#430	C₂²×C₁₅₁	1	2	yes	—
224	C₂×#108	C₂²×C₁₅₁	1	1	yes	characteristic
225	C₂×#108	C₂²×C₁₅₁	1	1	yes	characteristic
226	#427	C₂²×C₁₅₁	1	1	yes	characteristic
227	#421	C₂²×C₁₅₁	1	2	yes	—
228	#419	C₂²×C₁₅₁	1	2	yes	—
229	#419	C₂²×C₁₅₁	1	2	yes	—
230	#413	C₂²×C₁₅₁	1	1	yes	characteristic
231	C₂×#101	C₂²×C₁₅₁	1	2	yes	—
232	C₂×#101	C₂²×C₁₅₁	1	2	yes	—
233	#410	C₂²×C₁₅₁	1	1	yes	characteristic
234	#405	C₂²×C₁₅₁	1	1	yes	characteristic
235	#405	C₂²×C₁₅₁	1	1	yes	characteristic
236	#344	C₂²×C₁₅₁	1	2	yes	—
237	#344	C₂²×C₁₅₁	1	2	yes	—
238	#344	C₂²×C₁₅₁	1	1	yes	characteristic
239	#344	C₂²×C₁₅₁	1	1	yes	characteristic
240	#344	C₂²×C₁₅₁	1	2	yes	—
241	H(3,ℤ/4)	C₂²×C₁₅₁	1	2	yes	—
242	C₂×#41	C₂³×C₁₅₁	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
244	#137	—	2	4	no	—
245	#137	—	4	2	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	—	2	1	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	D₄×C₁₅₁	1	2	yes	—
252	C₂×Q₁₆	D₄×C₁₅₁	1	2	yes	—
253	C₂×SD₁₆	—	2	2	no	—
254	#131	—	2	1	no	—
255	#131	—	2	1	no	—
256	#131	—	2	1	no	—
257	#131	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
260	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
261	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
262	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
263	C₂×M₁₆	C₂³×C₁₅₁	1	1	yes	characteristic
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	4	2	no	—
268	#117	—	2	4	no	—
269	#117	C₂³×C₁₅₁	1	2	yes	—
270	#117	C₂³×C₁₅₁	1	1	yes	characteristic
271	#117	C₂³×C₁₅₁	1	1	yes	characteristic
272	#108	—	2	1	no	—
273	#108	—	2	1	no	—
274	#108	—	2	1	no	—
275	#108	—	2	1	no	—
276	#108	—	4	2	no	—
277	#107	—	2	1	no	—
278	#106	—	2	1	no	—
279	#104	—	4	2	no	—
280	#103	—	2	4	no	—
281	#103	—	4	2	no	—
282	#101	—	2	1	no	—
283	#101	—	2	4	no	—
284	#101	—	4	2	no	—
285	#100	—	2	1	no	—
286	#99	—	2	2	no	—
287	#97	—	2	1	no	—
288	#97	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	—	2	1	no	—
293	#41	—	2	1	no	—
294	#41	—	2	1	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	C₂×D₄×C₁₅₁	1	4	yes	—
301	C₂×Q₈	#41×C₁₅₁	1	1	yes	characteristic
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	#41×C₁₅₁	1	1	yes	characteristic
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
307	Q₁₆	—	2	2	no	—
308	Q₁₆	—	2	2	no	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	4	4	no	—
312	SD₁₆	—	4	4	no	—
313	M₁₆	—	2	1	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	1	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
334	C₂×C₈	#41×C₁₅₁	1	1	yes	characteristic
335	C₂×C₈	#41×C₁₅₁	1	1	yes	characteristic
336	C₂×C₈	#41×C₁₅₁	1	1	yes	characteristic
337	C₂×C₈	#41×C₁₅₁	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	#41×C₁₅₁	1	2	yes	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	4	4	no	—
349	C₂³	—	2	1	no	—
350	C₂³	C₂×#41×C₁₅₁	1	1	yes	characteristic
351	Q₈	—	2	4	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	2	1	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
375	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
376	C₈	—	4	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	#123×C₁₅₁	1	1	yes	characteristic
382	C₈	#123×C₁₅₁	1	1	yes	characteristic
383	C₈	#123×C₁₅₁	1	1	yes	characteristic
384	C₈	#123×C₁₅₁	1	1	yes	characteristic
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	#529×C₁₅₁	1	1	yes	characteristic
389	C₂²	#546×C₁₅₁	1	1	yes	characteristic
390	C₂²	#555×C₁₅₁	1	1	yes	characteristic
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	4	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	1	no	—
396	C₄	C₂×#123×C₁₅₁	1	1	yes	characteristic
397	C₄	#540×C₁₅₁	1	1	yes	characteristic
398	C₄	#546×C₁₅₁	1	1	yes	characteristic
399	C₄	#553×C₁₅₁	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	#2420×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₅₁	#2420
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂×#41×C₁₅₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₅₁ ◁ C₂²×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #2950×C₁₅₁	C₂	semidirect
3. #2082×C₁₅₁	C₂	semidirect
5. #1979×C₁₅₁	C₂	semidirect
6. #1953×C₁₅₁	C₂	semidirect
8. #1833×C₁₅₁	C₂	semidirect
9. #1830×C₁₅₁	C₂	semidirect
202. #24989	C₁₅₁	direct (N × H)
203. C₁₅₁	#24989	direct (N × H)
205. #2950	C₂×C₁₅₁	semidirect
206. #2082	C₂×C₁₅₁	semidirect
208. #1979	C₂×C₁₅₁	semidirect
209. #1953	C₂×C₁₅₁	semidirect
211. #1833	C₂×C₁₅₁	semidirect
212. #1830	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×#473×C₁₅₁	2
#2950×C₁₅₁	2
#2082×C₁₅₁	2
#2049×C₁₅₁	2
#1979×C₁₅₁	2
#1953×C₁₅₁	2
#1905×C₁₅₁	2
#1833×C₁₅₁	2
#1830×C₁₅₁	2
#1814×C₁₅₁	2
#1757×C₁₅₁	2
#24989	151

Subgroups — C151×#24989 #50329914

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#24989 #50329914