Subgroups — C₁₅₁×#19219 #50324144

Order 38656.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3212×C₁₅₁	C₂	1	2	yes	maximal, complemented
2	#3169×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#2966×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#1702×C₁₅₁	C₂	1	2	yes	maximal, complemented
5	#1701×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#1674×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1673×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1668×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1667×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1564×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1553×C₁₅₁	C₂	1	2	yes	maximal, complemented
12	#532×C₁₅₁	C₂²	1	2	yes	—
13	#529×C₁₅₁	C₂²	1	1	yes	characteristic
14	#500×C₁₅₁	C₂²	1	1	yes	characteristic
15	#495×C₁₅₁	—	2	2	no	—
16	#493×C₁₅₁	C₂²	1	1	yes	characteristic
17	#488×C₁₅₁	—	2	2	no	—
18	#486×C₁₅₁	C₂²	1	2	yes	—
19	#466×C₁₅₁	—	2	1	no	—
20	#466×C₁₅₁	—	2	1	no	—
21	#462×C₁₅₁	C₂²	1	2	yes	—
22	#461×C₁₅₁	C₂²	1	2	yes	—
23	#460×C₁₅₁	C₂²	1	2	yes	—
24	#459×C₁₅₁	C₂²	1	2	yes	—
25	#452×C₁₅₁	—	2	2	no	—
26	#449×C₁₅₁	—	2	2	no	—
27	#446×C₁₅₁	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₁₅₁	—	2	1	no	—
30	C₄×D₈×C₁₅₁	—	2	1	no	—
31	#436×C₁₅₁	C₂²	1	1	yes	characteristic
32	#435×C₁₅₁	—	2	1	no	—
33	C₈×D₄×C₁₅₁	—	2	1	no	—
34	C₈×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
35	#433×C₁₅₁	—	2	1	no	—
36	#432×C₁₅₁	C₂²	1	1	yes	characteristic
37	#431×C₁₅₁	C₂²	1	2	yes	—
38	#405×C₁₅₁	—	2	1	no	—
39	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
40	#335×C₁₅₁	C₂²	1	1	yes	characteristic
41	#335×C₁₅₁	C₂²	1	1	yes	characteristic
42	#334×C₁₅₁	C₂²	1	2	yes	—
43	#332×C₁₅₁	C₂²	1	2	yes	—
44	#332×C₁₅₁	C₂²	1	2	yes	—
45	#331×C₁₅₁	C₂²	1	2	yes	—
46	#331×C₁₅₁	C₂²	1	2	yes	—
47	C₂×#41×C₁₅₁	—	2	2	no	—
48	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
49	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
50	C₂×SD₁₆×C₁₅₁	—	2	2	no	—
51	C₂×D₈×C₁₅₁	—	2	2	no	—
52	C₂×D₈×C₁₅₁	—	2	1	no	—
53	C₂×D₈×C₁₅₁	—	2	1	no	—
54	C₂×M₁₆×C₁₅₁	—	2	1	no	—
55	C₂²×C₈×C₁₅₁	—	2	1	no	—
56	C₂²×C₈×C₁₅₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₅₁	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₁₅₁	C₂³	1	2	yes	—
59	#127×C₁₅₁	C₂³	1	2	yes	—
60	#126×C₁₅₁	—	2	1	no	—
61	#125×C₁₅₁	D₄	1	1	yes	characteristic
62	#124×C₁₅₁	—	2	2	no	—
63	#124×C₁₅₁	D₄	1	1	yes	characteristic
64	#123×C₁₅₁	—	2	1	no	—
65	C₂²⋊Q₈×C₁₅₁	D₄	1	1	yes	characteristic
66	#121×C₁₅₁	—	2	2	no	—
67	#121×C₁₅₁	—	2	2	no	—
68	#121×C₁₅₁	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₅₁	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₅₁	—	2	1	no	—
71	C₄×D₄×C₁₅₁	—	2	2	no	—
72	C₄×D₄×C₁₅₁	—	2	2	no	—
73	C₄×D₄×C₁₅₁	C₂³	1	1	yes	characteristic
74	#117×C₁₅₁	—	2	1	no	—
75	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
76	#107×C₁₅₁	—	2	1	no	—
77	#107×C₁₅₁	—	2	1	no	—
78	C₄⋊C₈×C₁₅₁	—	2	1	no	—
79	C₄⋊C₈×C₁₅₁	—	2	1	no	—
80	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
81	C₄⋊C₈×C₁₅₁	C₂³	1	2	yes	—
82	C₄⋊C₈×C₁₅₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₁₅₁	C₂³	1	1	yes	characteristic
84	#103×C₁₅₁	—	2	2	no	—
85	#103×C₁₅₁	—	2	2	no	—
86	#102×C₁₅₁	—	2	2	no	—
87	#102×C₁₅₁	—	2	2	no	—
88	#102×C₁₅₁	—	2	2	no	—
89	#102×C₁₅₁	—	2	2	no	—
90	C₂²⋊C₈×C₁₅₁	—	2	2	no	—
91	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
92	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
93	C₂²⋊C₈×C₁₅₁	—	2	1	no	—
94	#97×C₁₅₁	—	2	1	no	—
95	#97×C₁₅₁	—	2	1	no	—
96	C₄×C₈×C₁₅₁	—	2	1	no	—
97	C₄×C₈×C₁₅₁	—	2	2	no	—
98	C₄×C₈×C₁₅₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₁₅₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
102	#41×C₁₅₁	—	8	2	no	—
103	#41×C₁₅₁	—	8	2	no	—
104	C₂×Q₈×C₁₅₁	—	2	2	no	—
105	C₂×Q₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₁₅₁	—	2	1	no	—
107	C₂×D₄×C₁₅₁	—	2	2	no	—
108	C₂×D₄×C₁₅₁	—	2	2	no	—
109	C₂×D₄×C₁₅₁	—	2	2	no	—
110	C₂×D₄×C₁₅₁	—	4	2	no	—
111	C₂×D₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₅₁	—	2	1	no	—
113	C₂²×C₄×C₁₅₁	—	4	2	no	—
114	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
117	Q₁₆×C₁₅₁	—	8	2	no	—
118	SD₁₆×C₁₅₁	—	8	2	no	—
119	SD₁₆×C₁₅₁	—	8	2	no	—
120	D₈×C₁₅₁	—	4	2	no	—
121	D₈×C₁₅₁	—	4	2	no	—
122	D₈×C₁₅₁	—	8	2	no	—
123	M₁₆×C₁₅₁	—	4	2	no	—
124	C₂×C₈×C₁₅₁	—	2	2	no	—
125	C₂×C₈×C₁₅₁	—	2	1	no	—
126	C₂×C₈×C₁₅₁	—	2	2	no	—
127	C₂×C₈×C₁₅₁	—	2	2	no	—
128	C₂×C₈×C₁₅₁	—	2	1	no	—
129	C₂×C₈×C₁₅₁	—	4	1	no	—
130	C₂×C₈×C₁₅₁	—	4	2	no	—
131	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
139	C₄⋊C₄×C₁₅₁	—	2	2	no	—
140	C₄⋊C₄×C₁₅₁	—	2	2	no	—
141	C₄⋊C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
144	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
145	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
146	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
147	C₂²⋊C₄×C₁₅₁	—	2	1	no	—
148	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
149	C₂²⋊C₄×C₁₅₁	—	4	2	no	—
150	C₄²×C₁₅₁	—	2	1	no	—
151	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₁₅₁	#41	1	1	yes	characteristic
154	C₄²×C₁₅₁	C₂⁴	1	1	yes	characteristic
155	C₂³×C₁₅₁	—	2	1	no	—
156	C₂³×C₁₅₁	—	4	2	no	—
157	C₂³×C₁₅₁	#121	1	1	yes	characteristic
158	Q₈×C₁₅₁	—	2	1	no	—
159	Q₈×C₁₅₁	—	2	1	no	—
160	Q₈×C₁₅₁	—	4	2	no	—
161	Q₈×C₁₅₁	—	4	2	no	—
162	D₄×C₁₅₁	—	2	1	no	—
163	D₄×C₁₅₁	—	2	1	no	—
164	D₄×C₁₅₁	—	4	2	no	—
165	D₄×C₁₅₁	—	4	2	no	—
166	D₄×C₁₅₁	—	4	2	no	—
167	D₄×C₁₅₁	—	4	2	no	—
168	D₄×C₁₅₁	—	4	2	no	—
169	D₄×C₁₅₁	—	8	2	no	—
170	D₄×C₁₅₁	—	8	4	no	—
171	C₂×C₄×C₁₅₁	—	2	1	no	—
172	C₂×C₄×C₁₅₁	—	2	1	no	—
173	C₂×C₄×C₁₅₁	—	2	1	no	—
174	C₂×C₄×C₁₅₁	—	2	1	no	—
175	C₂×C₄×C₁₅₁	—	2	1	no	—
176	C₂×C₄×C₁₅₁	—	2	1	no	—
177	C₂×C₄×C₁₅₁	—	2	1	no	—
178	C₂×C₄×C₁₅₁	—	4	1	no	—
179	C₂×C₄×C₁₅₁	—	4	1	no	—
180	C₂×C₄×C₁₅₁	—	4	1	no	—
181	C₂×C₄×C₁₅₁	—	4	2	no	—
182	C₂×C₄×C₁₅₁	—	8	4	no	—
183	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₅₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₅₁	—	2	1	no	—
190	C₈×C₁₅₁	—	2	1	no	—
191	C₈×C₁₅₁	—	2	1	no	—
192	C₈×C₁₅₁	—	4	1	no	—
193	C₈×C₁₅₁	—	4	1	no	—
194	C₈×C₁₅₁	—	4	2	no	—
195	C₈×C₁₅₁	—	4	2	no	—
196	C₈×C₁₅₁	#135	1	2	yes	—
197	C₂²×C₁₅₁	—	2	1	no	—
198	C₂²×C₁₅₁	—	2	1	no	—
199	C₂²×C₁₅₁	—	2	1	no	—
200	C₂²×C₁₅₁	—	4	1	no	—
201	C₂²×C₁₅₁	—	4	1	no	—
202	C₂²×C₁₅₁	—	4	1	no	—
203	C₂²×C₁₅₁	—	8	2	no	—
204	C₂²×C₁₅₁	—	8	2	no	—
205	C₂²×C₁₅₁	—	8	2	no	—
206	C₂²×C₁₅₁	C₂×#121	1	1	yes	characteristic
207	C₄×C₁₅₁	—	2	1	no	—
208	C₄×C₁₅₁	—	2	1	no	—
209	C₄×C₁₅₁	—	2	1	no	—
210	C₄×C₁₅₁	—	2	1	no	—
211	C₄×C₁₅₁	—	4	1	no	—
212	C₄×C₁₅₁	—	4	1	no	—
213	C₄×C₁₅₁	—	4	1	no	—
214	C₄×C₁₅₁	—	8	2	no	—
215	C₄×C₁₅₁	C₂×#135	1	1	yes	characteristic
216	C₄×C₁₅₁	#575	1	1	yes	characteristic
217	C₄×C₁₅₁	#576	1	1	yes	characteristic
218	C₄×C₁₅₁	#576	1	1	yes	characteristic
219	C₂×C₁₅₁	—	4	1	no	—
220	C₂×C₁₅₁	—	8	1	no	—
221	C₂×C₁₅₁	—	16	2	no	—
222	C₂×C₁₅₁	#3035	1	1	yes	characteristic
223	C₂×C₁₅₁	#3058	1	1	yes	characteristic
224	C₂×C₁₅₁	#3067	1	1	yes	characteristic
225	#19219	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₁₅₁	#19219	1	1	yes	characteristic, direct product factor, Sylow
227	#3212	C₂×C₁₅₁	1	2	yes	complemented
228	#3169	C₂×C₁₅₁	1	1	yes	characteristic, complemented
229	#2966	C₂×C₁₅₁	1	1	yes	characteristic, complemented
230	#1702	C₂×C₁₅₁	1	2	yes	complemented
231	#1701	C₂×C₁₅₁	1	2	yes	complemented
232	#1674	C₂×C₁₅₁	1	1	yes	characteristic, complemented
233	#1673	C₂×C₁₅₁	1	1	yes	characteristic, complemented
234	#1668	C₂×C₁₅₁	1	1	yes	characteristic, complemented
235	#1667	C₂×C₁₅₁	1	1	yes	characteristic, complemented
236	#1564	C₂×C₁₅₁	1	1	yes	characteristic, complemented
237	#1553	C₂×C₁₅₁	1	2	yes	complemented
238	#532	C₂²×C₁₅₁	1	2	yes	—
239	#529	C₂²×C₁₅₁	1	1	yes	characteristic
240	#500	C₂²×C₁₅₁	1	1	yes	characteristic
241	#495	—	2	2	no	—
242	#493	C₂²×C₁₅₁	1	1	yes	characteristic
243	#488	—	2	2	no	—
244	#486	C₂²×C₁₅₁	1	2	yes	—
245	#466	—	2	1	no	—
246	#466	—	2	1	no	—
247	#462	C₂²×C₁₅₁	1	2	yes	—
248	#461	C₂²×C₁₅₁	1	2	yes	—
249	#460	C₂²×C₁₅₁	1	2	yes	—
250	#459	C₂²×C₁₅₁	1	2	yes	—
251	#452	—	2	2	no	—
252	#449	—	2	2	no	—
253	#446	C₂²×C₁₅₁	1	1	yes	characteristic
254	C₈×Q₈	C₂²×C₁₅₁	1	1	yes	characteristic
255	C₄×D₈	—	2	1	no	—
256	C₄×D₈	—	2	1	no	—
257	#436	C₂²×C₁₅₁	1	1	yes	characteristic
258	#435	—	2	1	no	—
259	C₈×D₄	—	2	1	no	—
260	C₈×D₄	C₂²×C₁₅₁	1	1	yes	characteristic
261	#433	—	2	1	no	—
262	#432	C₂²×C₁₅₁	1	1	yes	characteristic
263	#431	C₂²×C₁₅₁	1	2	yes	—
264	#405	—	2	1	no	—
265	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
266	#335	C₂²×C₁₅₁	1	1	yes	characteristic
267	#335	C₂²×C₁₅₁	1	1	yes	characteristic
268	#334	C₂²×C₁₅₁	1	2	yes	—
269	#332	C₂²×C₁₅₁	1	2	yes	—
270	#332	C₂²×C₁₅₁	1	2	yes	—
271	#331	C₂²×C₁₅₁	1	2	yes	—
272	#331	C₂²×C₁₅₁	1	2	yes	—
273	C₂×#41	—	2	2	no	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	D₄×C₁₅₁	1	1	yes	characteristic
283	C₂²×C₈	D₄×C₁₅₁	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₁₅₁	1	2	yes	—
285	#127	C₂³×C₁₅₁	1	2	yes	—
286	#126	—	2	1	no	—
287	#125	D₄×C₁₅₁	1	1	yes	characteristic
288	#124	—	2	2	no	—
289	#124	D₄×C₁₅₁	1	1	yes	characteristic
290	#123	—	2	1	no	—
291	C₂²⋊Q₈	D₄×C₁₅₁	1	1	yes	characteristic
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	D₄×C₁₅₁	1	1	yes	characteristic
295	C₄×Q₈	C₂³×C₁₅₁	1	1	yes	characteristic
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	C₂³×C₁₅₁	1	1	yes	characteristic
300	#117	—	2	1	no	—
301	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
302	#107	—	2	1	no	—
303	#107	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	C₂³×C₁₅₁	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₁₅₁	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
309	C₄⋊C₈	C₂³×C₁₅₁	1	2	yes	—
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	#97	—	2	1	no	—
321	#97	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	D₄×C₁₅₁	1	1	yes	characteristic
325	C₄×C₈	D₄×C₁₅₁	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
327	C₄×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
328	#41	—	8	2	no	—
329	#41	—	8	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
342	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
343	Q₁₆	—	8	2	no	—
344	SD₁₆	—	8	2	no	—
345	SD₁₆	—	8	2	no	—
346	D₈	—	4	2	no	—
347	D₈	—	4	2	no	—
348	D₈	—	8	2	no	—
349	M₁₆	—	4	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
358	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
359	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
360	C₂×C₈	C₂×D₄×C₁₅₁	1	1	yes	characteristic
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
368	C₄⋊C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	2	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₁₅₁	1	1	yes	characteristic
379	C₄²	#41×C₁₅₁	1	1	yes	characteristic
380	C₄²	C₂⁴×C₁₅₁	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	#121×C₁₅₁	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
410	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
411	C₂×C₄	#121×C₁₅₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	4	2	no	—
421	C₈	—	4	2	no	—
422	C₈	#135×C₁₅₁	1	2	yes	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₂×#121×C₁₅₁	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×#135×C₁₅₁	1	1	yes	characteristic
442	C₄	#575×C₁₅₁	1	1	yes	characteristic
443	C₄	#576×C₁₅₁	1	1	yes	characteristic
444	C₄	#576×C₁₅₁	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	8	1	no	—
447	C₂	—	16	2	no	—
448	C₂	#3035×C₁₅₁	1	1	yes	characteristic
449	C₂	#3058×C₁₅₁	1	1	yes	characteristic
450	C₂	#3067×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₅₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₅₁
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. #3212×C₁₅₁	C₂	semidirect
2. #3169×C₁₅₁	C₂	semidirect
3. #2966×C₁₅₁	C₂	semidirect
4. #1702×C₁₅₁	C₂	semidirect
5. #1701×C₁₅₁	C₂	semidirect
6. #1674×C₁₅₁	C₂	semidirect
7. #1673×C₁₅₁	C₂	semidirect
8. #1668×C₁₅₁	C₂	semidirect
9. #1667×C₁₅₁	C₂	semidirect
10. #1564×C₁₅₁	C₂	semidirect
11. #1553×C₁₅₁	C₂	semidirect
225. #19219	C₁₅₁	direct (N × H)
226. C₁₅₁	#19219	direct (N × H)
227. #3212	C₂×C₁₅₁	semidirect
228. #3169	C₂×C₁₅₁	semidirect
229. #2966	C₂×C₁₅₁	semidirect
230. #1702	C₂×C₁₅₁	semidirect
231. #1701	C₂×C₁₅₁	semidirect
232. #1674	C₂×C₁₅₁	semidirect
233. #1673	C₂×C₁₅₁	semidirect
234. #1668	C₂×C₁₅₁	semidirect
235. #1667	C₂×C₁₅₁	semidirect
236. #1564	C₂×C₁₅₁	semidirect
237. #1553	C₂×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#3212×C₁₅₁	2
#3169×C₁₅₁	2
#2966×C₁₅₁	2
#1702×C₁₅₁	2
#1701×C₁₅₁	2
#1674×C₁₅₁	2
#1673×C₁₅₁	2
#1668×C₁₅₁	2
#1667×C₁₅₁	2
#1564×C₁₅₁	2
#1553×C₁₅₁	2
#19219	151

Subgroups — C151×#19219 #50324144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#19219 #50324144