Subgroups — C₂×#2031×C₁₅₁ #50328396

Order 38656.

1234 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#421×C₁₅₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#104×C₁₅₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#410×C₁₅₁	C₂	1	1	yes	maximal, characteristic
5	#2031×C₁₅₁	C₂	1	8	yes	maximal, direct product factor
6	C₂×#344×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#339×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(3,ℤ/4)×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₅₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₅₁	C₂²	1	1	yes	characteristic
12	#533×C₁₅₁	—	2	2	no	—
13	#533×C₁₅₁	—	2	2	no	—
14	#533×C₁₅₁	—	2	2	no	—
15	#533×C₁₅₁	C₂²	1	4	yes	complemented
16	C₂×C₄⋊Q₈×C₁₅₁	—	2	1	no	—
17	C₂×#125×C₁₅₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₁₅₁	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₅₁	—	2	2	no	—
20	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₁₅₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
24	#421×C₁₅₁	—	2	2	no	—
25	#421×C₁₅₁	C₂²	1	4	yes	—
26	C₂×#104×C₁₅₁	—	2	1	no	—
27	C₂×#104×C₁₅₁	—	2	1	no	—
28	C₂×#104×C₁₅₁	—	2	2	no	—
29	C₂×#104×C₁₅₁	—	2	2	no	—
30	C₂×#104×C₁₅₁	C₂²	1	4	yes	—
31	#410×C₁₅₁	—	2	2	no	—
32	#410×C₁₅₁	C₂²	1	4	yes	—
33	C₂×#99×C₁₅₁	—	2	2	no	—
34	#344×C₁₅₁	C₂²	1	4	yes	complemented
35	#339×C₁₅₁	C₂²	1	4	yes	complemented
36	H(3,ℤ/4)×C₁₅₁	C₂²	1	4	yes	complemented
37	C₂×#41×C₁₅₁	—	2	1	no	—
38	C₂×#41×C₁₅₁	—	2	1	no	—
39	C₂×#41×C₁₅₁	—	2	1	no	—
40	C₂×#41×C₁₅₁	—	2	1	no	—
41	C₂×#41×C₁₅₁	—	2	1	no	—
42	C₂×#41×C₁₅₁	—	2	1	no	—
43	C₂×#41×C₁₅₁	—	2	1	no	—
44	C₂×#41×C₁₅₁	—	2	1	no	—
45	C₂×#41×C₁₅₁	—	2	1	no	—
46	C₂×#41×C₁₅₁	—	2	1	no	—
47	C₂×#41×C₁₅₁	Q₈	1	2	yes	complemented
48	C₂×#41×C₁₅₁	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₅₁	—	2	2	no	—
50	C₂²×Q₈×C₁₅₁	Q₈	1	1	yes	characteristic, complemented
51	C₂²×D₄×C₁₅₁	—	2	1	no	—
52	C₂²×D₄×C₁₅₁	Q₈	1	1	yes	characteristic, complemented
53	C₂³×C₄×C₁₅₁	—	2	1	no	—
54	C₂³×C₄×C₁₅₁	—	2	1	no	—
55	C₂³×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₁₅₁	—	2	1	no	—
57	C₂×M₁₆×C₁₅₁	—	2	1	no	—
58	C₂×M₁₆×C₁₅₁	—	2	1	no	—
59	C₂×M₁₆×C₁₅₁	—	2	1	no	—
60	C₂×M₁₆×C₁₅₁	—	2	1	no	—
61	C₂×M₁₆×C₁₅₁	—	2	1	no	—
62	C₂×M₁₆×C₁₅₁	—	2	1	no	—
63	C₂×M₁₆×C₁₅₁	—	2	1	no	—
64	C₂×M₁₆×C₁₅₁	—	2	1	no	—
65	C₂×M₁₆×C₁₅₁	—	2	1	no	—
66	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
67	C₂×M₁₆×C₁₅₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₅₁	—	2	1	no	—
69	C₂²×C₈×C₁₅₁	—	2	1	no	—
70	C₄⋊Q₈×C₁₅₁	—	2	4	no	—
71	C₄⋊Q₈×C₁₅₁	—	2	4	no	—
72	#125×C₁₅₁	—	2	4	no	—
73	#125×C₁₅₁	—	2	4	no	—
74	C₂²⋊Q₈×C₁₅₁	—	2	8	no	—
75	C₂²⋊Q₈×C₁₅₁	—	2	8	no	—
76	C₄×Q₈×C₁₅₁	—	2	8	no	—
77	C₄×Q₈×C₁₅₁	—	2	8	no	—
78	#117×C₁₅₁	—	2	1	no	—
79	#117×C₁₅₁	—	2	1	no	—
80	#117×C₁₅₁	—	2	1	no	—
81	#117×C₁₅₁	—	2	1	no	—
82	#117×C₁₅₁	—	2	1	no	—
83	#117×C₁₅₁	—	2	1	no	—
84	#117×C₁₅₁	—	2	1	no	—
85	#117×C₁₅₁	D₄	1	2	yes	—
86	#117×C₁₅₁	D₄	1	2	yes	—
87	#117×C₁₅₁	C₂³	1	2	yes	—
88	#117×C₁₅₁	C₂³	1	2	yes	—
89	#117×C₁₅₁	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₁₅₁	—	2	4	no	—
91	C₂×C₄⋊C₄×C₁₅₁	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₅₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₅₁	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₅₁	D₄	1	2	yes	—
98	C₂×C₄²×C₁₅₁	—	2	1	no	—
99	C₂×C₄²×C₁₅₁	—	2	1	no	—
100	C₂×C₄²×C₁₅₁	—	2	1	no	—
101	C₂×C₄²×C₁₅₁	—	2	1	no	—
102	C₂×C₄²×C₁₅₁	—	2	1	no	—
103	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₅₁	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₅₁	D₄	1	2	yes	—
106	C₂×C₄²×C₁₅₁	D₄	1	2	yes	—
107	C₂×C₄²×C₁₅₁	C₂³	1	2	yes	—
108	#104×C₁₅₁	—	2	4	no	—
109	#104×C₁₅₁	—	2	4	no	—
110	#104×C₁₅₁	—	2	8	no	—
111	#99×C₁₅₁	—	2	8	no	—
112	C₂⁴×C₁₅₁	—	2	1	no	—
113	C₂⁴×C₁₅₁	C₂×D₄	1	1	yes	characteristic
114	#41×C₁₅₁	—	2	2	no	—
115	#41×C₁₅₁	—	2	2	no	—
116	#41×C₁₅₁	—	2	2	no	—
117	#41×C₁₅₁	—	2	2	no	—
118	#41×C₁₅₁	—	2	2	no	—
119	#41×C₁₅₁	—	2	2	no	—
120	#41×C₁₅₁	—	2	2	no	—
121	#41×C₁₅₁	—	2	2	no	—
122	#41×C₁₅₁	—	4	1	no	—
123	#41×C₁₅₁	—	4	1	no	—
124	#41×C₁₅₁	—	4	1	no	—
125	#41×C₁₅₁	—	4	1	no	—
126	#41×C₁₅₁	—	4	1	no	—
127	#41×C₁₅₁	—	4	1	no	—
128	#41×C₁₅₁	—	4	1	no	—
129	#41×C₁₅₁	—	4	1	no	—
130	C₂×Q₈×C₁₅₁	—	2	8	no	—
131	C₂×Q₈×C₁₅₁	—	2	1	no	—
132	C₂×Q₈×C₁₅₁	—	2	1	no	—
133	C₂×Q₈×C₁₅₁	—	2	1	no	—
134	C₂×Q₈×C₁₅₁	—	2	1	no	—
135	C₂×Q₈×C₁₅₁	—	2	1	no	—
136	C₂×Q₈×C₁₅₁	—	4	8	no	—
137	C₂×Q₈×C₁₅₁	C₂×Q₈	1	2	yes	complemented
138	C₂×D₄×C₁₅₁	—	2	2	no	—
139	C₂×D₄×C₁₅₁	—	2	2	no	—
140	C₂×D₄×C₁₅₁	—	2	1	no	—
141	C₂×D₄×C₁₅₁	—	2	1	no	—
142	C₂×D₄×C₁₅₁	—	2	1	no	—
143	C₂×D₄×C₁₅₁	—	2	1	no	—
144	C₂×D₄×C₁₅₁	—	2	1	no	—
145	C₂×D₄×C₁₅₁	—	4	1	no	—
146	C₂×D₄×C₁₅₁	—	4	1	no	—
147	C₂×D₄×C₁₅₁	—	4	1	no	—
148	C₂×D₄×C₁₅₁	—	4	1	no	—
149	C₂×D₄×C₁₅₁	C₂×Q₈	1	2	yes	complemented
150	C₂²×C₄×C₁₅₁	—	2	1	no	—
151	C₂²×C₄×C₁₅₁	—	2	1	no	—
152	C₂²×C₄×C₁₅₁	—	2	2	no	—
153	C₂²×C₄×C₁₅₁	—	2	2	no	—
154	C₂²×C₄×C₁₅₁	—	2	2	no	—
155	C₂²×C₄×C₁₅₁	—	2	1	no	—
156	C₂²×C₄×C₁₅₁	—	2	2	no	—
157	C₂²×C₄×C₁₅₁	—	2	2	no	—
158	C₂²×C₄×C₁₅₁	—	2	2	no	—
159	C₂²×C₄×C₁₅₁	—	4	4	no	—
160	C₂²×C₄×C₁₅₁	—	4	1	no	—
161	C₂²×C₄×C₁₅₁	—	4	1	no	—
162	C₂²×C₄×C₁₅₁	—	4	1	no	—
163	C₂²×C₄×C₁₅₁	—	4	1	no	—
164	C₂²×C₄×C₁₅₁	—	4	1	no	—
165	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₅₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₁₅₁	C₂×Q₈	1	1	yes	characteristic
172	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
173	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
174	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
175	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
176	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
177	C₂²×C₄×C₁₅₁	#41	1	1	yes	characteristic
178	C₂²×C₄×C₁₅₁	C₂⁴	1	1	yes	characteristic
179	M₁₆×C₁₅₁	—	2	2	no	—
180	M₁₆×C₁₅₁	—	2	2	no	—
181	M₁₆×C₁₅₁	—	2	2	no	—
182	M₁₆×C₁₅₁	—	2	2	no	—
183	M₁₆×C₁₅₁	—	4	1	no	—
184	M₁₆×C₁₅₁	—	4	1	no	—
185	M₁₆×C₁₅₁	—	4	1	no	—
186	M₁₆×C₁₅₁	—	4	1	no	—
187	C₂×C₈×C₁₅₁	—	2	2	no	—
188	C₂×C₈×C₁₅₁	—	2	2	no	—
189	C₂×C₈×C₁₅₁	—	4	1	no	—
190	C₂×C₈×C₁₅₁	—	4	1	no	—
191	C₂×C₈×C₁₅₁	—	4	1	no	—
192	C₂×C₈×C₁₅₁	—	4	1	no	—
193	C₄⋊C₄×C₁₅₁	—	2	16	no	—
194	C₄⋊C₄×C₁₅₁	—	2	8	no	—
195	C₄⋊C₄×C₁₅₁	—	2	2	no	—
196	C₄⋊C₄×C₁₅₁	—	2	2	no	—
197	C₄⋊C₄×C₁₅₁	—	2	2	no	—
198	C₄⋊C₄×C₁₅₁	—	2	2	no	—
199	C₄⋊C₄×C₁₅₁	—	2	2	no	—
200	C₄⋊C₄×C₁₅₁	—	4	1	no	—
201	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
202	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
203	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
204	C₂²⋊C₄×C₁₅₁	—	2	2	no	—
205	C₂²⋊C₄×C₁₅₁	—	4	1	no	—
206	C₂²⋊C₄×C₁₅₁	C₂×D₄	1	4	yes	—
207	C₄²×C₁₅₁	—	2	2	no	—
208	C₄²×C₁₅₁	—	2	1	no	—
209	C₄²×C₁₅₁	—	2	1	no	—
210	C₄²×C₁₅₁	—	2	2	no	—
211	C₄²×C₁₅₁	—	2	2	no	—
212	C₄²×C₁₅₁	—	2	2	no	—
213	C₄²×C₁₅₁	—	2	2	no	—
214	C₄²×C₁₅₁	—	2	2	no	—
215	C₄²×C₁₅₁	—	4	1	no	—
216	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
217	C₄²×C₁₅₁	C₂×D₄	1	2	yes	—
218	C₄²×C₁₅₁	C₂×D₄	1	4	yes	—
219	C₂³×C₁₅₁	—	2	2	no	—
220	C₂³×C₁₅₁	—	4	2	no	—
221	C₂³×C₁₅₁	—	4	1	no	—
222	C₂³×C₁₅₁	—	4	1	no	—
223	C₂³×C₁₅₁	—	8	2	no	—
224	C₂³×C₁₅₁	#120	1	1	yes	characteristic
225	C₂³×C₁₅₁	#120	1	1	yes	characteristic
226	C₂³×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂³×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
228	C₂³×C₁₅₁	#124	1	1	yes	characteristic
229	C₂³×C₁₅₁	#124	1	1	yes	characteristic
230	C₂³×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₅₁	—	2	2	no	—
232	Q₈×C₁₅₁	—	2	2	no	—
233	Q₈×C₁₅₁	—	4	16	no	—
234	Q₈×C₁₅₁	—	4	1	no	—
235	Q₈×C₁₅₁	—	4	1	no	—
236	D₄×C₁₅₁	—	2	2	no	—
237	D₄×C₁₅₁	—	2	2	no	—
238	D₄×C₁₅₁	—	4	2	no	—
239	D₄×C₁₅₁	—	4	2	no	—
240	D₄×C₁₅₁	—	4	2	no	—
241	D₄×C₁₅₁	—	4	2	no	—
242	D₄×C₁₅₁	—	4	1	no	—
243	D₄×C₁₅₁	—	4	1	no	—
244	C₂×C₄×C₁₅₁	—	2	4	no	—
245	C₂×C₄×C₁₅₁	—	2	2	no	—
246	C₂×C₄×C₁₅₁	—	2	4	no	—
247	C₂×C₄×C₁₅₁	—	2	4	no	—
248	C₂×C₄×C₁₅₁	—	2	2	no	—
249	C₂×C₄×C₁₅₁	—	2	2	no	—
250	C₂×C₄×C₁₅₁	—	4	4	no	—
251	C₂×C₄×C₁₅₁	—	4	4	no	—
252	C₂×C₄×C₁₅₁	—	4	4	no	—
253	C₂×C₄×C₁₅₁	—	4	4	no	—
254	C₂×C₄×C₁₅₁	—	4	2	no	—
255	C₂×C₄×C₁₅₁	—	4	1	no	—
256	C₂×C₄×C₁₅₁	—	4	1	no	—
257	C₂×C₄×C₁₅₁	—	4	2	no	—
258	C₂×C₄×C₁₅₁	—	4	2	no	—
259	C₂×C₄×C₁₅₁	—	4	2	no	—
260	C₂×C₄×C₁₅₁	—	4	2	no	—
261	C₂×C₄×C₁₅₁	—	4	2	no	—
262	C₂×C₄×C₁₅₁	—	8	2	no	—
263	C₂×C₄×C₁₅₁	#120	1	1	yes	characteristic
264	C₂×C₄×C₁₅₁	#120	1	1	yes	characteristic
265	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₁₅₁	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
276	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
277	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
278	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
279	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
280	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
281	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
282	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
283	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
284	C₂×C₄×C₁₅₁	#124	1	1	yes	characteristic
285	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₅₁	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₅₁	C₂²×Q₈	1	1	yes	characteristic
288	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₁₅₁	C₂×#41	1	1	yes	characteristic
291	C₈×C₁₅₁	—	4	2	no	—
292	C₈×C₁₅₁	—	4	2	no	—
293	C₂²×C₁₅₁	—	2	2	no	—
294	C₂²×C₁₅₁	—	2	2	no	—
295	C₂²×C₁₅₁	—	2	2	no	—
296	C₂²×C₁₅₁	—	4	1	no	—
297	C₂²×C₁₅₁	—	4	1	no	—
298	C₂²×C₁₅₁	—	4	1	no	—
299	C₂²×C₁₅₁	—	4	1	no	—
300	C₂²×C₁₅₁	—	4	2	no	—
301	C₂²×C₁₅₁	—	8	2	no	—
302	C₂²×C₁₅₁	—	8	2	no	—
303	C₂²×C₁₅₁	—	8	2	no	—
304	C₂²×C₁₅₁	#393	1	1	yes	characteristic
305	C₂²×C₁₅₁	#393	1	1	yes	characteristic
306	C₂²×C₁₅₁	#393	1	1	yes	characteristic
307	C₂²×C₁₅₁	#393	1	1	yes	characteristic
308	C₂²×C₁₅₁	C₂×#120	1	1	yes	characteristic
309	C₂²×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
310	C₂²×C₁₅₁	C₂×#124	1	1	yes	characteristic
311	C₄×C₁₅₁	—	2	4	no	—
312	C₄×C₁₅₁	—	4	2	no	—
313	C₄×C₁₅₁	—	4	4	no	—
314	C₄×C₁₅₁	—	4	4	no	—
315	C₄×C₁₅₁	—	4	2	no	—
316	C₄×C₁₅₁	—	8	2	no	—
317	C₄×C₁₅₁	#393	1	1	yes	characteristic
318	C₄×C₁₅₁	#393	1	1	yes	characteristic
319	C₄×C₁₅₁	#393	1	1	yes	characteristic
320	C₄×C₁₅₁	#393	1	1	yes	characteristic
321	C₄×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₄×C₁₅₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
323	C₄×C₁₅₁	C₂×#124	1	1	yes	characteristic
324	C₄×C₁₅₁	C₂×#124	1	1	yes	characteristic
325	C₂×C₁₅₁	—	2	1	no	—
326	C₂×C₁₅₁	—	2	1	no	—
327	C₂×C₁₅₁	—	2	1	no	—
328	C₂×C₁₅₁	—	2	1	no	—
329	C₂×C₁₅₁	—	2	1	no	—
330	C₂×C₁₅₁	—	2	1	no	—
331	C₂×C₁₅₁	—	8	2	no	—
332	C₂×C₁₅₁	#2031	1	2	yes	direct product factor
333	C₂×C₁₅₁	C₂×#393	1	1	yes	characteristic
334	C₂×#2031	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₁₅₁	C₂×#2031	1	1	yes	characteristic, direct product factor, Sylow
336	C₂×#533	C₂×C₁₅₁	1	1	yes	characteristic, complemented
337	C₂×#421	C₂×C₁₅₁	1	1	yes	characteristic
338	C₂²×#104	C₂×C₁₅₁	1	1	yes	characteristic
339	C₂×#410	C₂×C₁₅₁	1	1	yes	characteristic
340	#2031	C₂×C₁₅₁	1	8	yes	direct product factor
341	C₂×#344	C₂×C₁₅₁	1	1	yes	characteristic, complemented
342	C₂×#339	C₂×C₁₅₁	1	1	yes	characteristic, complemented
343	C₂×H(3,ℤ/4)	C₂×C₁₅₁	1	1	yes	characteristic, complemented
344	C₂²×#41	C₂²×C₁₅₁	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
346	C₂²×M₁₆	C₂²×C₁₅₁	1	1	yes	characteristic
347	#533	—	2	2	no	—
348	#533	—	2	2	no	—
349	#533	—	2	2	no	—
350	#533	C₂²×C₁₅₁	1	4	yes	complemented
351	C₂×C₄⋊Q₈	—	2	1	no	—
352	C₂×#125	—	2	1	no	—
353	C₂×C₂²⋊Q₈	—	2	2	no	—
354	C₂×C₄×Q₈	—	2	2	no	—
355	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
356	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
357	C₂×#117	C₂²×C₁₅₁	1	1	yes	characteristic
358	C₂²×C₄²	C₂²×C₁₅₁	1	1	yes	characteristic
359	#421	—	2	2	no	—
360	#421	C₂²×C₁₅₁	1	4	yes	—
361	C₂×#104	—	2	1	no	—
362	C₂×#104	—	2	1	no	—
363	C₂×#104	—	2	2	no	—
364	C₂×#104	—	2	2	no	—
365	C₂×#104	C₂²×C₁₅₁	1	4	yes	—
366	#410	—	2	2	no	—
367	#410	C₂²×C₁₅₁	1	4	yes	—
368	C₂×#99	—	2	2	no	—
369	#344	C₂²×C₁₅₁	1	4	yes	complemented
370	#339	C₂²×C₁₅₁	1	4	yes	complemented
371	H(3,ℤ/4)	C₂²×C₁₅₁	1	4	yes	complemented
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	C₂×#41	—	2	1	no	—
379	C₂×#41	—	2	1	no	—
380	C₂×#41	—	2	1	no	—
381	C₂×#41	—	2	1	no	—
382	C₂×#41	Q₈×C₁₅₁	1	2	yes	complemented
383	C₂×#41	C₂³×C₁₅₁	1	2	yes	—
384	C₂²×Q₈	—	2	2	no	—
385	C₂²×Q₈	Q₈×C₁₅₁	1	1	yes	characteristic, complemented
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	Q₈×C₁₅₁	1	1	yes	characteristic, complemented
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	C₂³×C₁₅₁	1	1	yes	characteristic
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	2	1	no	—
397	C₂×M₁₆	—	2	1	no	—
398	C₂×M₁₆	—	2	1	no	—
399	C₂×M₁₆	—	2	1	no	—
400	C₂×M₁₆	—	2	1	no	—
401	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
402	C₂×M₁₆	C₂³×C₁₅₁	1	2	yes	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₄⋊Q₈	—	2	4	no	—
406	C₄⋊Q₈	—	2	4	no	—
407	#125	—	2	4	no	—
408	#125	—	2	4	no	—
409	C₂²⋊Q₈	—	2	8	no	—
410	C₂²⋊Q₈	—	2	8	no	—
411	C₄×Q₈	—	2	8	no	—
412	C₄×Q₈	—	2	8	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	2	1	no	—
416	#117	—	2	1	no	—
417	#117	—	2	1	no	—
418	#117	—	2	1	no	—
419	#117	—	2	1	no	—
420	#117	D₄×C₁₅₁	1	2	yes	—
421	#117	D₄×C₁₅₁	1	2	yes	—
422	#117	C₂³×C₁₅₁	1	2	yes	—
423	#117	C₂³×C₁₅₁	1	2	yes	—
424	#117	C₂³×C₁₅₁	1	2	yes	—
425	C₂×C₄⋊C₄	—	2	4	no	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	D₄×C₁₅₁	1	2	yes	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	D₄×C₁₅₁	1	2	yes	—
439	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
440	C₂×C₄²	D₄×C₁₅₁	1	1	yes	characteristic
441	C₂×C₄²	D₄×C₁₅₁	1	2	yes	—
442	C₂×C₄²	C₂³×C₁₅₁	1	2	yes	—
443	#104	—	2	4	no	—
444	#104	—	2	4	no	—
445	#104	—	2	8	no	—
446	#99	—	2	8	no	—
447	C₂⁴	—	2	1	no	—
448	C₂⁴	C₂×D₄×C₁₅₁	1	1	yes	characteristic
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	4	1	no	—
458	#41	—	4	1	no	—
459	#41	—	4	1	no	—
460	#41	—	4	1	no	—
461	#41	—	4	1	no	—
462	#41	—	4	1	no	—
463	#41	—	4	1	no	—
464	#41	—	4	1	no	—
465	C₂×Q₈	—	2	8	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	4	8	no	—
472	C₂×Q₈	C₂×Q₈×C₁₅₁	1	2	yes	complemented
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	—	4	1	no	—
484	C₂×D₄	C₂×Q₈×C₁₅₁	1	2	yes	complemented
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	4	4	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₅₁	1	1	yes	characteristic
505	C₂²×C₄	C₂×Q₈×C₁₅₁	1	1	yes	characteristic
506	C₂²×C₄	C₂×Q₈×C₁₅₁	1	1	yes	characteristic
507	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
508	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
509	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
510	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
511	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
512	C₂²×C₄	#41×C₁₅₁	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₁₅₁	1	1	yes	characteristic
514	M₁₆	—	2	2	no	—
515	M₁₆	—	2	2	no	—
516	M₁₆	—	2	2	no	—
517	M₁₆	—	2	2	no	—
518	M₁₆	—	4	1	no	—
519	M₁₆	—	4	1	no	—
520	M₁₆	—	4	1	no	—
521	M₁₆	—	4	1	no	—
522	C₂×C₈	—	2	2	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	4	1	no	—
525	C₂×C₈	—	4	1	no	—
526	C₂×C₈	—	4	1	no	—
527	C₂×C₈	—	4	1	no	—
528	C₄⋊C₄	—	2	16	no	—
529	C₄⋊C₄	—	2	8	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	4	1	no	—
541	C₂²⋊C₄	C₂×D₄×C₁₅₁	1	4	yes	—
542	C₄²	—	2	2	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	2	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	2	no	—
550	C₄²	—	4	1	no	—
551	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
552	C₄²	C₂×D₄×C₁₅₁	1	2	yes	—
553	C₄²	C₂×D₄×C₁₅₁	1	4	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	8	2	no	—
559	C₂³	#120×C₁₅₁	1	1	yes	characteristic
560	C₂³	#120×C₁₅₁	1	1	yes	characteristic
561	C₂³	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
562	C₂³	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
563	C₂³	#124×C₁₅₁	1	1	yes	characteristic
564	C₂³	#124×C₁₅₁	1	1	yes	characteristic
565	C₂³	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	4	16	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	D₄	—	2	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	8	2	no	—
598	C₂×C₄	#120×C₁₅₁	1	1	yes	characteristic
599	C₂×C₄	#120×C₁₅₁	1	1	yes	characteristic
600	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
601	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
602	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
603	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
604	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
605	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
606	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
607	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
608	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
609	C₂×C₄	C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
610	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
611	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
612	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
613	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
614	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
615	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
616	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
617	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
618	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
619	C₂×C₄	#124×C₁₅₁	1	1	yes	characteristic
620	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₁₅₁	1	1	yes	characteristic
622	C₂×C₄	C₂²×Q₈×C₁₅₁	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
625	C₂×C₄	C₂×#41×C₁₅₁	1	1	yes	characteristic
626	C₈	—	4	2	no	—
627	C₈	—	4	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	2	no	—
639	C₂²	#393×C₁₅₁	1	1	yes	characteristic
640	C₂²	#393×C₁₅₁	1	1	yes	characteristic
641	C₂²	#393×C₁₅₁	1	1	yes	characteristic
642	C₂²	#393×C₁₅₁	1	1	yes	characteristic
643	C₂²	C₂×#120×C₁₅₁	1	1	yes	characteristic
644	C₂²	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
645	C₂²	C₂×#124×C₁₅₁	1	1	yes	characteristic
646	C₄	—	2	4	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	4	no	—
649	C₄	—	4	4	no	—
650	C₄	—	4	2	no	—
651	C₄	—	8	2	no	—
652	C₄	#393×C₁₅₁	1	1	yes	characteristic
653	C₄	#393×C₁₅₁	1	1	yes	characteristic
654	C₄	#393×C₁₅₁	1	1	yes	characteristic
655	C₄	#393×C₁₅₁	1	1	yes	characteristic
656	C₄	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
657	C₄	C₂×C₂²⋊Q₈×C₁₅₁	1	1	yes	characteristic
658	C₄	C₂×#124×C₁₅₁	1	1	yes	characteristic
659	C₄	C₂×#124×C₁₅₁	1	1	yes	characteristic
660	C₂	—	2	1	no	—
661	C₂	—	2	1	no	—
662	C₂	—	2	1	no	—
663	C₂	—	2	1	no	—
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	8	2	no	—
667	C₂	#2031×C₁₅₁	1	2	yes	direct product factor
668	C₂	C₂×#393×C₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₅₁	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₅₁
socle	C₂²×C₁₅₁	#393
prime radical	C₂²×#41×C₁₅₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₅₁ ◁ C₂³×C₄×C₁₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₁₅₁	C₂	semidirect
5. #2031×C₁₅₁	C₂	direct (N × H)
6. C₂×#344×C₁₅₁	C₂	semidirect
7. C₂×#339×C₁₅₁	C₂	semidirect
8. C₂×H(3,ℤ/4)×C₁₅₁	C₂	semidirect
15. #533×C₁₅₁	C₂²	semidirect
34. #344×C₁₅₁	C₂²	semidirect
35. #339×C₁₅₁	C₂²	semidirect
36. H(3,ℤ/4)×C₁₅₁	C₂²	semidirect
47. C₂×#41×C₁₅₁	Q₈	semidirect
50. C₂²×Q₈×C₁₅₁	Q₈	semidirect
52. C₂²×D₄×C₁₅₁	Q₈	semidirect
137. C₂×Q₈×C₁₅₁	C₂×Q₈	semidirect
149. C₂×D₄×C₁₅₁	C₂×Q₈	semidirect
332. C₂×C₁₅₁	#2031	direct (N × H)
334. C₂×#2031	C₁₅₁	direct (N × H)
335. C₁₅₁	C₂×#2031	direct (N × H)
336. C₂×#533	C₂×C₁₅₁	semidirect
340. #2031	C₂×C₁₅₁	direct (N × H)
341. C₂×#344	C₂×C₁₅₁	semidirect
342. C₂×#339	C₂×C₁₅₁	semidirect
343. C₂×H(3,ℤ/4)	C₂×C₁₅₁	semidirect
350. #533	C₂²×C₁₅₁	semidirect
369. #344	C₂²×C₁₅₁	semidirect
370. #339	C₂²×C₁₅₁	semidirect
371. H(3,ℤ/4)	C₂²×C₁₅₁	semidirect
382. C₂×#41	Q₈×C₁₅₁	semidirect
385. C₂²×Q₈	Q₈×C₁₅₁	semidirect
387. C₂²×D₄	Q₈×C₁₅₁	semidirect
472. C₂×Q₈	C₂×Q₈×C₁₅₁	semidirect
484. C₂×D₄	C₂×Q₈×C₁₅₁	semidirect
667. C₂	#2031×C₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#533×C₁₅₁	2
C₂×#421×C₁₅₁	2
C₂²×#104×C₁₅₁	2
C₂×#410×C₁₅₁	2
#2031×C₁₅₁	2
C₂×#344×C₁₅₁	2
C₂×#339×C₁₅₁	2
C₂×H(3,ℤ/4)×C₁₅₁	2
C₂×#2031	151

Subgroups — C2×#2031×C151 #50328396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2031×C₁₅₁ #50328396