Subgroups — C₁₅₁×#23186 #50328111

Order 38656.

1038 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#495×C₁₅₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	#2367×C₁₅₁	C₂	1	2	yes	maximal, complemented
5	#1983×C₁₅₁	C₂	1	2	yes	maximal, complemented
6	#1970×C₁₅₁	C₂	1	1	yes	maximal, characteristic
7	#1969×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1880×C₁₅₁	C₂	1	2	yes	maximal, complemented
9	#1877×C₁₅₁	C₂	1	2	yes	maximal, complemented
10	C₄×#107×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₅₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₅₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₅₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₅₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₅₁	C₂²	1	2	yes	—
18	#495×C₁₅₁	C₄	1	8	yes	complemented
19	C₄×Q₁₆×C₁₅₁	—	2	4	no	—
20	C₄×D₈×C₁₅₁	—	2	4	no	—
21	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂×#107×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₁₅₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
25	C₂×#103×C₁₅₁	C₂²	1	2	yes	—
26	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
27	C₂×#102×C₁₅₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
31	#391×C₁₅₁	C₂²	1	2	yes	—
32	#390×C₁₅₁	C₂²	1	2	yes	—
33	#388×C₁₅₁	—	2	2	no	—
34	#388×C₁₅₁	—	2	2	no	—
35	#385×C₁₅₁	—	2	2	no	—
36	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
39	#340×C₁₅₁	C₂²	1	2	yes	—
40	#336×C₁₅₁	C₂²	1	1	yes	characteristic
41	#336×C₁₅₁	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₅₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₅₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₅₁	—	2	2	no	—
45	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
46	C₂×Q₁₆×C₁₅₁	—	2	2	no	—
47	C₂×Q₁₆×C₁₅₁	C₂×C₄	1	4	yes	complemented
48	C₂×SD₁₆×C₁₅₁	—	4	2	no	—
49	C₂×SD₁₆×C₁₅₁	—	4	2	no	—
50	C₂×SD₁₆×C₁₅₁	C₂×C₄	1	8	yes	complemented
51	C₂×D₈×C₁₅₁	—	2	2	no	—
52	C₂×D₈×C₁₅₁	—	2	2	no	—
53	C₂×D₈×C₁₅₁	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₅₁	C₂³	1	1	yes	characteristic
58	#124×C₁₅₁	—	2	4	no	—
59	#124×C₁₅₁	C₂×C₄	1	8	yes	complemented
60	C₄×Q₈×C₁₅₁	—	2	4	no	—
61	C₄×Q₈×C₁₅₁	—	4	2	no	—
62	C₄×D₄×C₁₅₁	—	2	4	no	—
63	C₄×D₄×C₁₅₁	—	4	2	no	—
64	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₅₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₅₁	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₁₅₁	—	2	2	no	—
74	C₂×C₄²×C₁₅₁	—	2	2	no	—
75	C₂×C₄²×C₁₅₁	—	2	2	no	—
76	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₅₁	C₂³	1	1	yes	characteristic
79	#107×C₁₅₁	—	2	2	no	—
80	#107×C₁₅₁	D₄	1	4	yes	—
81	C₄⋊C₈×C₁₅₁	—	2	2	no	—
82	#103×C₁₅₁	—	2	4	no	—
83	#103×C₁₅₁	—	4	2	no	—
84	#102×C₁₅₁	—	2	4	no	—
85	#102×C₁₅₁	—	4	2	no	—
86	C₄×C₈×C₁₅₁	—	2	2	no	—
87	C₄×C₈×C₁₅₁	—	2	2	no	—
88	C₄×C₈×C₁₅₁	C₂×C₄	1	4	yes	complemented
89	#95×C₁₅₁	—	2	2	no	—
90	#95×C₁₅₁	—	2	2	no	—
91	#95×C₁₅₁	—	2	2	no	—
92	#95×C₁₅₁	D₄	1	1	yes	characteristic
93	#95×C₁₅₁	D₄	1	1	yes	characteristic
94	C₂⁴×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	—	2	2	no	—
100	C₂×Q₈×C₁₅₁	C₂²×C₄	1	4	yes	—
101	C₂×D₄×C₁₅₁	—	2	2	no	—
102	C₂×D₄×C₁₅₁	—	2	2	no	—
103	C₂×D₄×C₁₅₁	—	2	2	no	—
104	C₂×D₄×C₁₅₁	—	2	2	no	—
105	C₂×D₄×C₁₅₁	—	2	2	no	—
106	C₂×D₄×C₁₅₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₅₁	—	2	2	no	—
108	C₂²×C₄×C₁₅₁	—	2	2	no	—
109	C₂²×C₄×C₁₅₁	—	2	2	no	—
110	C₂²×C₄×C₁₅₁	—	4	4	no	—
111	C₂²×C₄×C₁₅₁	—	4	4	no	—
112	C₂²×C₄×C₁₅₁	—	8	2	no	—
113	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
120	Q₁₆×C₁₅₁	—	2	8	no	—
121	SD₁₆×C₁₅₁	—	4	8	no	—
122	D₈×C₁₅₁	—	2	8	no	—
123	C₂×C₈×C₁₅₁	—	2	1	no	—
124	C₂×C₈×C₁₅₁	—	2	1	no	—
125	C₂×C₈×C₁₅₁	—	2	1	no	—
126	C₂×C₈×C₁₅₁	—	2	1	no	—
127	C₂×C₈×C₁₅₁	—	2	1	no	—
128	C₂×C₈×C₁₅₁	—	2	1	no	—
129	C₂×C₈×C₁₅₁	—	2	1	no	—
130	C₂×C₈×C₁₅₁	—	2	1	no	—
131	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₅₁	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₅₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₅₁	#41	1	2	yes	—
135	C₄⋊C₄×C₁₅₁	—	2	2	no	—
136	C₄⋊C₄×C₁₅₁	—	2	2	no	—
137	C₄⋊C₄×C₁₅₁	—	2	2	no	—
138	C₄⋊C₄×C₁₅₁	—	2	2	no	—
139	C₄⋊C₄×C₁₅₁	—	2	2	no	—
140	C₄⋊C₄×C₁₅₁	—	4	4	no	—
141	C₄⋊C₄×C₁₅₁	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
143	C₂²⋊C₄×C₁₅₁	—	2	8	no	—
144	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
145	C₂²⋊C₄×C₁₅₁	—	4	4	no	—
146	C₂²⋊C₄×C₁₅₁	—	8	2	no	—
147	C₄²×C₁₅₁	—	2	1	no	—
148	C₄²×C₁₅₁	—	2	1	no	—
149	C₄²×C₁₅₁	—	2	1	no	—
150	C₄²×C₁₅₁	—	2	1	no	—
151	C₄²×C₁₅₁	—	4	4	no	—
152	C₄²×C₁₅₁	—	8	2	no	—
153	C₄²×C₁₅₁	C₂²×C₄	1	2	yes	—
154	C₄²×C₁₅₁	#41	1	2	yes	—
155	C₂³×C₁₅₁	—	2	4	no	—
156	C₂³×C₁₅₁	—	4	2	no	—
157	C₂³×C₁₅₁	—	4	2	no	—
158	C₂³×C₁₅₁	—	4	2	no	—
159	C₂³×C₁₅₁	—	4	2	no	—
160	C₂³×C₁₅₁	—	4	2	no	—
161	C₂³×C₁₅₁	—	4	2	no	—
162	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₅₁	—	2	4	no	—
164	Q₈×C₁₅₁	—	2	4	no	—
165	Q₈×C₁₅₁	—	4	2	no	—
166	Q₈×C₁₅₁	—	4	2	no	—
167	D₄×C₁₅₁	—	2	4	no	—
168	D₄×C₁₅₁	—	2	4	no	—
169	D₄×C₁₅₁	—	4	2	no	—
170	D₄×C₁₅₁	—	4	2	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	—	2	1	no	—
179	C₂×C₄×C₁₅₁	—	2	4	no	—
180	C₂×C₄×C₁₅₁	—	2	1	no	—
181	C₂×C₄×C₁₅₁	—	2	1	no	—
182	C₂×C₄×C₁₅₁	—	2	4	no	—
183	C₂×C₄×C₁₅₁	—	2	1	no	—
184	C₂×C₄×C₁₅₁	—	2	1	no	—
185	C₂×C₄×C₁₅₁	—	2	1	no	—
186	C₂×C₄×C₁₅₁	—	2	1	no	—
187	C₂×C₄×C₁₅₁	—	4	2	no	—
188	C₂×C₄×C₁₅₁	—	4	2	no	—
189	C₂×C₄×C₁₅₁	—	4	2	no	—
190	C₂×C₄×C₁₅₁	—	4	2	no	—
191	C₂×C₄×C₁₅₁	—	4	2	no	—
192	C₂×C₄×C₁₅₁	—	4	2	no	—
193	C₂×C₄×C₁₅₁	—	4	2	no	—
194	C₂×C₄×C₁₅₁	—	8	8	no	—
195	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₅₁	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₅₁	#135	1	2	yes	—
198	C₂×C₄×C₁₅₁	#135	1	2	yes	—
199	C₂×C₄×C₁₅₁	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₅₁	H(5,𝔽₂)	1	1	yes	characteristic
205	C₈×C₁₅₁	—	2	2	no	—
206	C₈×C₁₅₁	—	4	1	no	—
207	C₈×C₁₅₁	—	4	1	no	—
208	C₈×C₁₅₁	C₄×D₄	1	4	yes	—
209	C₂²×C₁₅₁	—	4	4	no	—
210	C₂²×C₁₅₁	—	4	4	no	—
211	C₂²×C₁₅₁	—	4	4	no	—
212	C₂²×C₁₅₁	—	8	2	no	—
213	C₂²×C₁₅₁	—	8	2	no	—
214	C₂²×C₁₅₁	—	8	2	no	—
215	C₂²×C₁₅₁	—	8	2	no	—
216	C₂²×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₁₅₁	D₄²	1	1	yes	characteristic
218	C₂²×C₁₅₁	#550	1	1	yes	characteristic
219	C₂²×C₁₅₁	C₂×#135	1	1	yes	characteristic
220	C₂²×C₁₅₁	C₂×#135	1	1	yes	characteristic
221	C₂²×C₁₅₁	#576	1	1	yes	characteristic
222	C₂²×C₁₅₁	#578	1	1	yes	characteristic
223	C₄×C₁₅₁	—	2	2	no	—
224	C₄×C₁₅₁	—	2	2	no	—
225	C₄×C₁₅₁	—	2	2	no	—
226	C₄×C₁₅₁	—	2	2	no	—
227	C₄×C₁₅₁	—	4	4	no	—
228	C₄×C₁₅₁	—	4	1	no	—
229	C₄×C₁₅₁	—	4	4	no	—
230	C₄×C₁₅₁	—	4	1	no	—
231	C₄×C₁₅₁	—	8	2	no	—
232	C₄×C₁₅₁	C₂×C₄×D₄	1	1	yes	characteristic
233	C₄×C₁₅₁	#518	1	1	yes	characteristic
234	C₄×C₁₅₁	#550	1	1	yes	characteristic
235	C₄×C₁₅₁	#559	1	1	yes	characteristic
236	C₂×C₁₅₁	—	8	4	no	—
237	C₂×C₁₅₁	#2366	1	1	yes	characteristic
238	C₂×C₁₅₁	C₄×#135	1	1	yes	characteristic
239	C₂×C₁₅₁	#2951	1	1	yes	characteristic
240	C₂×C₁₅₁	#3280	1	1	yes	characteristic
241	C₂×C₁₅₁	#3285	1	1	yes	characteristic
242	C₂×C₁₅₁	#3393	1	1	yes	characteristic
243	C₂×C₁₅₁	#3396	1	1	yes	characteristic
244	#23186	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₁₅₁	#23186	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×#495	C₂×C₁₅₁	1	1	yes	characteristic
247	C₂×C₄×Q₁₆	C₂×C₁₅₁	1	1	yes	characteristic, complemented
248	C₂×C₄×D₈	C₂×C₁₅₁	1	1	yes	characteristic
249	#2367	C₂×C₁₅₁	1	2	yes	complemented
250	#1983	C₂×C₁₅₁	1	2	yes	complemented
251	#1970	C₂×C₁₅₁	1	1	yes	characteristic
252	#1969	C₂×C₁₅₁	1	1	yes	characteristic, complemented
253	#1880	C₂×C₁₅₁	1	2	yes	complemented
254	#1877	C₂×C₁₅₁	1	2	yes	complemented
255	C₄×#107	C₂×C₁₅₁	1	1	yes	characteristic, complemented
256	C₈×C₄⋊C₄	C₂×C₁₅₁	1	1	yes	characteristic, complemented
257	C₂²×Q₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂²×C₁₅₁	1	2	yes	—
259	C₂²×D₈	C₂²×C₁₅₁	1	1	yes	characteristic
260	C₂×#124	C₂²×C₁₅₁	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₁₅₁	1	2	yes	—
262	C₂×C₄×D₄	C₂²×C₁₅₁	1	2	yes	—
263	#495	C₄×C₁₅₁	1	8	yes	complemented
264	C₄×Q₁₆	—	2	4	no	—
265	C₄×D₈	—	2	4	no	—
266	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
267	C₂×#107	C₂²×C₁₅₁	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₁₅₁	1	1	yes	characteristic
269	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
270	C₂×#103	C₂²×C₁₅₁	1	2	yes	—
271	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
272	C₂×#102	C₂²×C₁₅₁	1	2	yes	—
273	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂²×C₁₅₁	1	1	yes	characteristic
276	#391	C₂²×C₁₅₁	1	2	yes	—
277	#390	C₂²×C₁₅₁	1	2	yes	—
278	#388	—	2	2	no	—
279	#388	—	2	2	no	—
280	#385	—	2	2	no	—
281	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	2	yes	—
282	C₄×C₄⋊C₄	C₂²×C₁₅₁	1	1	yes	characteristic
283	C₄×C₂²⋊C₄	—	2	2	no	—
284	#340	C₂²×C₁₅₁	1	2	yes	—
285	#336	C₂²×C₁₅₁	1	1	yes	characteristic
286	#336	C₂²×C₁₅₁	1	1	yes	characteristic
287	C₂²×Q₈	C₂³×C₁₅₁	1	2	yes	—
288	C₂²×D₄	C₂³×C₁₅₁	1	2	yes	—
289	C₂³×C₄	—	2	2	no	—
290	C₂×Q₁₆	—	2	2	no	—
291	C₂×Q₁₆	—	2	2	no	—
292	C₂×Q₁₆	C₂×C₄×C₁₅₁	1	4	yes	complemented
293	C₂×SD₁₆	—	4	2	no	—
294	C₂×SD₁₆	—	4	2	no	—
295	C₂×SD₁₆	C₂×C₄×C₁₅₁	1	8	yes	complemented
296	C₂×D₈	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	C₂×C₄×C₁₅₁	1	4	yes	—
299	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
302	C₂²×C₈	C₂³×C₁₅₁	1	1	yes	characteristic
303	#124	—	2	4	no	—
304	#124	C₂×C₄×C₁₅₁	1	8	yes	complemented
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	4	2	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	4	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₁₅₁	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₁₅₁	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₅₁	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#107	D₄×C₁₅₁	1	4	yes	—
326	C₄⋊C₈	—	2	2	no	—
327	#103	—	2	4	no	—
328	#103	—	4	2	no	—
329	#102	—	2	4	no	—
330	#102	—	4	2	no	—
331	C₄×C₈	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	C₂×C₄×C₁₅₁	1	4	yes	complemented
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	D₄×C₁₅₁	1	1	yes	characteristic
338	#95	D₄×C₁₅₁	1	1	yes	characteristic
339	C₂⁴	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂²×C₄×C₁₅₁	1	4	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	C₂²×C₄×C₁₅₁	1	4	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	8	2	no	—
358	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
365	Q₁₆	—	2	8	no	—
366	SD₁₆	—	4	8	no	—
367	D₈	—	2	8	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
377	C₂×C₈	C₂²×C₄×C₁₅₁	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₁₅₁	1	2	yes	—
379	C₂×C₈	#41×C₁₅₁	1	2	yes	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	C₂×D₄×C₁₅₁	1	4	yes	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	8	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	4	no	—
397	C₄²	—	8	2	no	—
398	C₄²	C₂²×C₄×C₁₅₁	1	2	yes	—
399	C₄²	#41×C₁₅₁	1	2	yes	—
400	C₂³	—	2	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
408	Q₈	—	2	4	no	—
409	Q₈	—	2	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	8	no	—
440	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₁₅₁	1	2	yes	—
442	C₂×C₄	#135×C₁₅₁	1	2	yes	—
443	C₂×C₄	#135×C₁₅₁	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₁₅₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
449	C₂×C₄	H(5,𝔽₂)×C₁₅₁	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	4	1	no	—
452	C₈	—	4	1	no	—
453	C₈	C₄×D₄×C₁₅₁	1	4	yes	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
462	C₂²	D₄²×C₁₅₁	1	1	yes	characteristic
463	C₂²	#550×C₁₅₁	1	1	yes	characteristic
464	C₂²	C₂×#135×C₁₅₁	1	1	yes	characteristic
465	C₂²	C₂×#135×C₁₅₁	1	1	yes	characteristic
466	C₂²	#576×C₁₅₁	1	1	yes	characteristic
467	C₂²	#578×C₁₅₁	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	1	no	—
476	C₄	—	8	2	no	—
477	C₄	C₂×C₄×D₄×C₁₅₁	1	1	yes	characteristic
478	C₄	#518×C₁₅₁	1	1	yes	characteristic
479	C₄	#550×C₁₅₁	1	1	yes	characteristic
480	C₄	#559×C₁₅₁	1	1	yes	characteristic
481	C₂	—	8	4	no	—
482	C₂	#2366×C₁₅₁	1	1	yes	characteristic
483	C₂	C₄×#135×C₁₅₁	1	1	yes	characteristic
484	C₂	#2951×C₁₅₁	1	1	yes	characteristic
485	C₂	#3280×C₁₅₁	1	1	yes	characteristic
486	C₂	#3285×C₁₅₁	1	1	yes	characteristic
487	C₂	#3393×C₁₅₁	1	1	yes	characteristic
488	C₂	#3396×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₅₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₅₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
prime radical	C₂²×D₈×C₁₅₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₅₁ ◁ C₄×C₄⋊C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₁₅₁	C₂	semidirect
4. #2367×C₁₅₁	C₂	semidirect
5. #1983×C₁₅₁	C₂	semidirect
7. #1969×C₁₅₁	C₂	semidirect
8. #1880×C₁₅₁	C₂	semidirect
9. #1877×C₁₅₁	C₂	semidirect
10. C₄×#107×C₁₅₁	C₂	semidirect
11. C₈×C₄⋊C₄×C₁₅₁	C₂	semidirect
18. #495×C₁₅₁	C₄	semidirect
47. C₂×Q₁₆×C₁₅₁	C₂×C₄	semidirect
50. C₂×SD₁₆×C₁₅₁	C₂×C₄	semidirect
59. #124×C₁₅₁	C₂×C₄	semidirect
88. C₄×C₈×C₁₅₁	C₂×C₄	semidirect
244. #23186	C₁₅₁	direct (N × H)
245. C₁₅₁	#23186	direct (N × H)
247. C₂×C₄×Q₁₆	C₂×C₁₅₁	semidirect
249. #2367	C₂×C₁₅₁	semidirect
250. #1983	C₂×C₁₅₁	semidirect
252. #1969	C₂×C₁₅₁	semidirect
253. #1880	C₂×C₁₅₁	semidirect
254. #1877	C₂×C₁₅₁	semidirect
255. C₄×#107	C₂×C₁₅₁	semidirect
256. C₈×C₄⋊C₄	C₂×C₁₅₁	semidirect
263. #495	C₄×C₁₅₁	semidirect
292. C₂×Q₁₆	C₂×C₄×C₁₅₁	semidirect
295. C₂×SD₁₆	C₂×C₄×C₁₅₁	semidirect
304. #124	C₂×C₄×C₁₅₁	semidirect
333. C₄×C₈	C₂×C₄×C₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#495×C₁₅₁	2
C₂×C₄×Q₁₆×C₁₅₁	2
C₂×C₄×D₈×C₁₅₁	2
#2367×C₁₅₁	2
#1983×C₁₅₁	2
#1970×C₁₅₁	2
#1969×C₁₅₁	2
#1880×C₁₅₁	2
#1877×C₁₅₁	2
C₄×#107×C₁₅₁	2
C₈×C₄⋊C₄×C₁₅₁	2
#23186	151

Subgroups — C151×#23186 #50328111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×#23186 #50328111