Subgroups — C₂×C₄×C₃₁×#124 #21490791

Order 7936.

3790 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	C₂²×C₃₁×#124	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₄×C₃₁×#124	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₁×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×#390	C₂	1	1	yes	maximal, characteristic
7	C₂×C₃₁×#388	C₂	1	4	yes	maximal, complemented
8	C₂×C₃₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	4	yes	maximal, complemented
10	C₂×C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
14	C₂×C₃₁×#124	C₄	1	16	yes	direct product factor
15	C₂×C₃₁×#124	C₂²	1	8	yes	—
16	C₂×C₄×Q₈×C₃₁	—	2	8	no	—
17	C₂×C₄×Q₈×C₃₁	C₂²	1	8	yes	complemented
18	C₂×C₄×D₄×C₃₁	—	2	8	no	—
19	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	—
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
25	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
26	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
27	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
29	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
30	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#391	C₂²	1	8	yes	complemented
33	C₃₁×#390	C₂²	1	8	yes	—
34	C₃₁×#388	C₂²	1	32	yes	complemented
35	C₃₁×#382	C₂²	1	8	yes	complemented
36	C₄×C₂²⋊C₄×C₃₁	C₂²	1	32	yes	complemented
37	C₂×C₃₁×#95	C₂²	1	4	yes	—
38	C₂×C₃₁×#95	C₂²	1	4	yes	—
39	C₄³×C₃₁	C₂²	1	8	yes	complemented
40	C₂⁵×C₃₁	C₂³	1	2	yes	—
41	C₂²×Q₈×C₃₁	—	2	4	no	—
42	C₂²×Q₈×C₃₁	—	2	4	no	—
43	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
44	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
45	C₂²×D₄×C₃₁	—	2	4	no	—
46	C₂²×D₄×C₃₁	—	2	4	no	—
47	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
48	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
49	C₂³×C₄×C₃₁	—	2	8	no	—
50	C₂³×C₄×C₃₁	—	2	16	no	—
51	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
54	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₃₁×#124	C₂×C₄	1	64	yes	direct product factor
61	C₄×Q₈×C₃₁	—	2	32	no	—
62	C₄×D₄×C₃₁	—	2	32	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
66	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
71	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	32	yes	complemented
72	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
74	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
75	C₂×C₄²×C₃₁	—	2	8	no	—
76	C₂×C₄²×C₃₁	—	2	8	no	—
77	C₂×C₄²×C₃₁	—	2	4	no	—
78	C₂×C₄²×C₃₁	—	2	8	no	—
79	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	complemented
80	C₂×C₄²×C₃₁	D₄	1	8	yes	—
81	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
82	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
83	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
84	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
85	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
86	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
87	C₃₁×#95	C₂³	1	16	yes	—
88	C₃₁×#95	C₂³	1	16	yes	—
89	C₂⁴×C₃₁	—	2	4	no	—
90	C₂⁴×C₃₁	—	2	8	no	—
91	C₂⁴×C₃₁	—	2	8	no	—
92	C₂⁴×C₃₁	—	2	4	no	—
93	C₂⁴×C₃₁	C₂²×C₄	1	8	yes	—
94	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
95	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
96	C₂×Q₈×C₃₁	—	2	32	no	—
97	C₂×Q₈×C₃₁	—	2	8	no	—
98	C₂×Q₈×C₃₁	—	2	8	no	—
99	C₂×Q₈×C₃₁	C₂²×C₄	1	16	yes	complemented
100	C₂×D₄×C₃₁	—	2	32	no	—
101	C₂×D₄×C₃₁	—	2	8	no	—
102	C₂×D₄×C₃₁	—	2	8	no	—
103	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
104	C₂²×C₄×C₃₁	—	2	4	no	—
105	C₂²×C₄×C₃₁	—	2	4	no	—
106	C₂²×C₄×C₃₁	—	2	4	no	—
107	C₂²×C₄×C₃₁	—	2	4	no	—
108	C₂²×C₄×C₃₁	—	2	4	no	—
109	C₂²×C₄×C₃₁	—	2	4	no	—
110	C₂²×C₄×C₃₁	—	2	4	no	—
111	C₂²×C₄×C₃₁	—	2	4	no	—
112	C₂²×C₄×C₃₁	—	2	4	no	—
113	C₂²×C₄×C₃₁	—	2	8	no	—
114	C₂²×C₄×C₃₁	—	2	8	no	—
115	C₂²×C₄×C₃₁	—	2	16	no	—
116	C₂²×C₄×C₃₁	—	2	32	no	—
117	C₂²×C₄×C₃₁	—	4	32	no	—
118	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
119	C₂²×C₄×C₃₁	C₂²×C₄	1	8	yes	—
120	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₃₁	#41	1	8	yes	—
125	C₂²×C₄×C₃₁	#41	1	4	yes	—
126	C₂²×C₄×C₃₁	#41	1	8	yes	—
127	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
132	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
135	C₄⋊C₄×C₃₁	—	2	8	no	—
136	C₄⋊C₄×C₃₁	—	2	16	no	—
137	C₄⋊C₄×C₃₁	—	2	8	no	—
138	C₂²⋊C₄×C₃₁	—	2	16	no	—
139	C₂²⋊C₄×C₃₁	—	2	32	no	—
140	C₂²⋊C₄×C₃₁	C₂²×C₄	1	64	yes	complemented
141	C₄²×C₃₁	—	2	16	no	—
142	C₄²×C₃₁	—	2	16	no	—
143	C₄²×C₃₁	—	2	8	no	—
144	C₄²×C₃₁	—	2	16	no	—
145	C₄²×C₃₁	C₂²×C₄	1	16	yes	complemented
146	C₄²×C₃₁	C₂×D₄	1	16	yes	—
147	C₂×C₄×#124	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₃₁	—	2	16	no	—
149	C₂³×C₃₁	—	2	32	no	—
150	C₂³×C₃₁	—	2	4	no	—
151	C₂³×C₃₁	—	2	8	no	—
152	C₂³×C₃₁	—	2	8	no	—
153	C₂³×C₃₁	—	2	4	no	—
154	C₂³×C₃₁	—	4	8	no	—
155	C₂³×C₃₁	—	4	16	no	—
156	C₂³×C₃₁	—	4	8	no	—
157	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
158	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
159	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
160	C₂³×C₃₁	C₂×#41	1	2	yes	—
161	C₂³×C₃₁	C₂×#41	1	4	yes	—
162	C₂³×C₃₁	C₂×#41	1	4	yes	—
163	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
164	Q₈×C₃₁	—	2	32	no	—
165	D₄×C₃₁	—	2	32	no	—
166	C₂×C₄×C₃₁	—	2	16	no	—
167	C₂×C₄×C₃₁	—	2	16	no	—
168	C₂×C₄×C₃₁	—	2	16	no	—
169	C₂×C₄×C₃₁	—	2	8	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	2	4	no	—
172	C₂×C₄×C₃₁	—	2	4	no	—
173	C₂×C₄×C₃₁	—	2	4	no	—
174	C₂×C₄×C₃₁	—	2	4	no	—
175	C₂×C₄×C₃₁	—	2	4	no	—
176	C₂×C₄×C₃₁	—	2	4	no	—
177	C₂×C₄×C₃₁	—	2	4	no	—
178	C₂×C₄×C₃₁	—	2	4	no	—
179	C₂×C₄×C₃₁	—	2	8	no	—
180	C₂×C₄×C₃₁	—	2	8	no	—
181	C₂×C₄×C₃₁	—	4	8	no	—
182	C₂×C₄×C₃₁	—	4	8	no	—
183	C₂×C₄×C₃₁	—	4	32	no	—
184	C₂×C₄×C₃₁	C₄×D₄	1	16	yes	—
185	C₂×C₄×C₃₁	#124	1	16	yes	direct product factor
186	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
187	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
188	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
193	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
194	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
195	C₂²×#124	C₂×C₃₁	1	1	yes	characteristic
196	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
197	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic
198	C₄×#124	C₂×C₃₁	1	16	yes	direct product factor
199	C₂×#391	C₂×C₃₁	1	1	yes	characteristic, complemented
200	C₂×#390	C₂×C₃₁	1	1	yes	characteristic
201	C₂×#388	C₂×C₃₁	1	4	yes	complemented
202	C₂×#382	C₂×C₃₁	1	1	yes	characteristic, complemented
203	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	4	yes	complemented
204	C₂×C₄³	C₂×C₃₁	1	1	yes	characteristic, complemented
205	C₂²×C₃₁	—	2	8	no	—
206	C₂²×C₃₁	—	2	16	no	—
207	C₂²×C₃₁	—	4	4	no	—
208	C₂²×C₃₁	—	4	8	no	—
209	C₂²×C₃₁	—	4	4	no	—
210	C₂²×C₃₁	—	4	32	no	—
211	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
212	C₂²×C₃₁	C₄×#41	1	8	yes	—
213	C₂²×C₃₁	C₂×#124	1	4	yes	—
214	C₂²×C₃₁	#529	1	8	yes	—
215	C₂²×C₃₁	#532	1	4	yes	—
216	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
217	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
218	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
219	C₂²×C₃₁	C₂²×#41	1	2	yes	—
220	C₂²×C₃₁	C₂²×#41	1	2	yes	—
221	C₄×C₃₁	—	2	8	no	—
222	C₄×C₃₁	—	2	8	no	—
223	C₄×C₃₁	—	2	8	no	—
224	C₄×C₃₁	—	2	4	no	—
225	C₄×C₃₁	—	4	4	no	—
226	C₄×C₃₁	—	4	4	no	—
227	C₄×C₃₁	C₂×C₄×D₄	1	8	yes	—
228	C₄×C₃₁	C₂×#124	1	8	yes	direct product factor
229	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
230	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
231	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
232	C₂×#124	C₄×C₃₁	1	16	yes	direct product factor
233	C₂×#124	C₂²×C₃₁	1	8	yes	—
234	C₂×C₄×Q₈	—	2	8	no	—
235	C₂×C₄×Q₈	C₂²×C₃₁	1	8	yes	complemented
236	C₂×C₄×D₄	—	2	8	no	—
237	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	—
238	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
244	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
245	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
246	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
247	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
248	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
250	#391	C₂²×C₃₁	1	8	yes	complemented
251	#390	C₂²×C₃₁	1	8	yes	—
252	#388	C₂²×C₃₁	1	32	yes	complemented
253	#382	C₂²×C₃₁	1	8	yes	complemented
254	C₄×C₂²⋊C₄	C₂²×C₃₁	1	32	yes	complemented
255	C₂×#95	C₂²×C₃₁	1	4	yes	—
256	C₂×#95	C₂²×C₃₁	1	4	yes	—
257	C₄³	C₂²×C₃₁	1	8	yes	complemented
258	C₂×C₃₁	—	4	8	no	—
259	C₂×C₃₁	C₄×#124	1	8	yes	direct product factor
260	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
261	C₂×C₃₁	C₂×C₄×#41	1	2	yes	—
262	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
263	C₂×C₃₁	C₂×#529	1	2	yes	—
264	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
265	C₂⁵	C₂³×C₃₁	1	2	yes	—
266	C₂²×Q₈	—	2	4	no	—
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
269	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
273	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
274	C₂³×C₄	—	2	8	no	—
275	C₂³×C₄	—	2	16	no	—
276	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
277	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
278	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
279	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
280	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
281	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
283	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
285	#124	C₂×C₄×C₃₁	1	64	yes	direct product factor
286	C₄×Q₈	—	2	32	no	—
287	C₄×D₄	—	2	32	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	8	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
293	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
294	C₂×C₂²⋊C₄	—	2	8	no	—
295	C₂×C₂²⋊C₄	—	2	16	no	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	32	yes	complemented
297	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
299	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
300	C₂×C₄²	—	2	8	no	—
301	C₂×C₄²	—	2	8	no	—
302	C₂×C₄²	—	2	4	no	—
303	C₂×C₄²	—	2	8	no	—
304	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	complemented
305	C₂×C₄²	D₄×C₃₁	1	8	yes	—
306	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
307	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
308	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
309	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
310	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
311	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
312	#95	C₂³×C₃₁	1	16	yes	—
313	#95	C₂³×C₃₁	1	16	yes	—
314	C₃₁	C₂×C₄×#124	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	2	8	no	—
317	C₂⁴	—	2	8	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	C₂²×C₄×C₃₁	1	8	yes	—
320	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
321	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
322	C₂×Q₈	—	2	32	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	—	2	8	no	—
325	C₂×Q₈	C₂²×C₄×C₃₁	1	16	yes	complemented
326	C₂×D₄	—	2	32	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	16	no	—
342	C₂²×C₄	—	2	32	no	—
343	C₂²×C₄	—	4	32	no	—
344	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
345	C₂²×C₄	C₂²×C₄×C₃₁	1	8	yes	—
346	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
347	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
348	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
349	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
350	C₂²×C₄	#41×C₃₁	1	8	yes	—
351	C₂²×C₄	#41×C₃₁	1	4	yes	—
352	C₂²×C₄	#41×C₃₁	1	8	yes	—
353	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
356	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	16	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	16	no	—
365	C₂²⋊C₄	—	2	32	no	—
366	C₂²⋊C₄	C₂²×C₄×C₃₁	1	64	yes	complemented
367	C₄²	—	2	16	no	—
368	C₄²	—	2	16	no	—
369	C₄²	—	2	8	no	—
370	C₄²	—	2	16	no	—
371	C₄²	C₂²×C₄×C₃₁	1	16	yes	complemented
372	C₄²	C₂×D₄×C₃₁	1	16	yes	—
373	C₂³	—	2	16	no	—
374	C₂³	—	2	32	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	8	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	8	no	—
380	C₂³	—	4	16	no	—
381	C₂³	—	4	8	no	—
382	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
383	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
384	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
385	C₂³	C₂×#41×C₃₁	1	2	yes	—
386	C₂³	C₂×#41×C₃₁	1	4	yes	—
387	C₂³	C₂×#41×C₃₁	1	4	yes	—
388	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
389	Q₈	—	2	32	no	—
390	D₄	—	2	32	no	—
391	C₂×C₄	—	2	16	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	32	no	—
409	C₂×C₄	C₄×D₄×C₃₁	1	16	yes	—
410	C₂×C₄	C₃₁×#124	1	16	yes	direct product factor
411	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
412	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
413	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
414	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
415	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
416	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
417	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
418	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
419	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	16	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	8	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	32	no	—
426	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
427	C₂²	C₄×#41×C₃₁	1	8	yes	—
428	C₂²	C₂×C₃₁×#124	1	4	yes	—
429	C₂²	C₃₁×#529	1	8	yes	—
430	C₂²	C₃₁×#532	1	4	yes	—
431	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
432	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
433	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
434	C₂²	C₂²×#41×C₃₁	1	2	yes	—
435	C₂²	C₂²×#41×C₃₁	1	2	yes	—
436	C₄	—	2	8	no	—
437	C₄	—	2	8	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	4	no	—
442	C₄	C₂×C₄×D₄×C₃₁	1	8	yes	—
443	C₄	C₂×C₃₁×#124	1	8	yes	direct product factor
444	C₂	—	4	8	no	—
445	C₂	C₄×C₃₁×#124	1	8	yes	direct product factor
446	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
447	C₂	C₂×C₄×#41×C₃₁	1	2	yes	—
448	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
449	C₂	C₂×C₃₁×#529	1	2	yes	—
450	C₂	C₂×C₃₁×#532	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₃₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂⁴×C₃₁	C₂⁴
prime radical	C₂³×D₄×C₃₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₃₁	C₂	semidirect
4. C₄×C₃₁×#124	C₂	direct (N × H)
5. C₂×C₃₁×#391	C₂	semidirect
7. C₂×C₃₁×#388	C₂	semidirect
8. C₂×C₃₁×#382	C₂	semidirect
9. C₂×C₄×C₂²⋊C₄×C₃₁	C₂	semidirect
10. C₂×C₄³×C₃₁	C₂	semidirect
14. C₂×C₃₁×#124	C₄	direct (N × H)
17. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#391	C₂²	semidirect
34. C₃₁×#388	C₂²	semidirect
35. C₃₁×#382	C₂²	semidirect
36. C₄×C₂²⋊C₄×C₃₁	C₂²	semidirect
39. C₄³×C₃₁	C₂²	semidirect
43. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
60. C₃₁×#124	C₂×C₄	direct (N × H)
71. C₂×C₂²⋊C₄×C₃₁	C₂×C₄	semidirect
79. C₂×C₄²×C₃₁	C₂×C₄	semidirect
99. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
140. C₂²⋊C₄×C₃₁	C₂²×C₄	semidirect
145. C₄²×C₃₁	C₂²×C₄	semidirect
147. C₂×C₄×#124	C₃₁	direct (N × H)
185. C₂×C₄×C₃₁	#124	direct (N × H)
196. C₂²×C₄×Q₈	C₂×C₃₁	semidirect
198. C₄×#124	C₂×C₃₁	direct (N × H)
199. C₂×#391	C₂×C₃₁	semidirect
201. C₂×#388	C₂×C₃₁	semidirect
202. C₂×#382	C₂×C₃₁	semidirect
203. C₂×C₄×C₂²⋊C₄	C₂×C₃₁	semidirect
204. C₂×C₄³	C₂×C₃₁	semidirect
228. C₄×C₃₁	C₂×#124	direct (N × H)
232. C₂×#124	C₄×C₃₁	direct (N × H)
235. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
250. #391	C₂²×C₃₁	semidirect
252. #388	C₂²×C₃₁	semidirect
253. #382	C₂²×C₃₁	semidirect
254. C₄×C₂²⋊C₄	C₂²×C₃₁	semidirect
257. C₄³	C₂²×C₃₁	semidirect
259. C₂×C₃₁	C₄×#124	direct (N × H)
268. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
285. #124	C₂×C₄×C₃₁	direct (N × H)
296. C₂×C₂²⋊C₄	C₂×C₄×C₃₁	semidirect
304. C₂×C₄²	C₂×C₄×C₃₁	semidirect
314. C₃₁	C₂×C₄×#124	direct (N × H)
325. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
366. C₂²⋊C₄	C₂²×C₄×C₃₁	semidirect
371. C₄²	C₂²×C₄×C₃₁	semidirect
410. C₂×C₄	C₃₁×#124	direct (N × H)
443. C₄	C₂×C₃₁×#124	direct (N × H)
445. C₂	C₄×C₃₁×#124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#124	2
C₂²×C₄×Q₈×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₄×C₃₁×#124	2
C₂×C₃₁×#391	2
C₂×C₃₁×#390	2
C₂×C₃₁×#388	2
C₂×C₃₁×#382	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×C₄³×C₃₁	2
C₂×C₄×#124	31

Subgroups — C2×C4×C31×#124 #21490791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃₁×#124 #21490791