Subgroups — C₂×C₃₁×#3093 #21517267

Order 7936.

2346 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3093	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#485	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#482	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#428	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#417	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
12	C₃₁×#525	—	2	4	no	—
13	C₃₁×#525	C₂²	1	8	yes	—
14	C₂×C₃₁×#123	—	2	1	no	—
15	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₃₁×#121	C₂²	1	2	yes	—
17	C₂×C₃₁×#120	—	2	1	no	—
18	C₂×C₄×D₄×C₃₁	—	2	2	no	—
19	C₂×C₃₁×#117	—	2	2	no	—
20	C₂×C₃₁×#117	—	2	4	no	—
21	C₂×C₃₁×#117	C₂²	1	4	yes	—
22	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#117	C₂²	1	8	yes	complemented
24	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
26	C₂²×C₄²×C₃₁	—	2	1	no	—
27	C₃₁×#485	C₂²	1	32	yes	complemented
28	C₃₁×#482	C₂²	1	32	yes	complemented
29	C₃₁×#428	C₂²	1	16	yes	complemented
30	C₂×C₃₁×#107	C₂²	1	4	yes	complemented
31	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
32	C₃₁×#417	C₂²	1	16	yes	complemented
33	C₂×C₃₁×#103	C₂²	1	4	yes	complemented
34	C₂×C₃₁×#102	C₂²	1	4	yes	complemented
35	C₃₁×#407	C₂²	1	8	yes	complemented
36	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
37	C₂⁵×C₃₁	D₄	1	1	yes	characteristic
38	C₂×#41×C₃₁	—	2	2	no	—
39	C₂×#41×C₃₁	—	2	8	no	—
40	C₂×#41×C₃₁	C₂³	1	4	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	—	2	2	no	—
43	C₂²×D₄×C₃₁	—	2	1	no	—
44	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₁	—	2	8	no	—
46	C₂³×C₄×C₃₁	—	2	2	no	—
47	C₂³×C₄×C₃₁	—	2	1	no	—
48	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₃₁	D₄	1	2	yes	—
50	C₂³×C₄×C₃₁	D₄	1	4	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
53	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₃₁	—	2	8	no	—
55	C₂×M₁₆×C₃₁	C₂³	1	8	yes	—
56	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
57	C₃₁×#123	—	2	8	no	—
58	C₃₁×C₂²⋊Q₈	—	2	4	no	—
59	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
60	C₃₁×#121	—	2	4	no	—
61	C₃₁×#121	C₂³	1	8	yes	—
62	C₃₁×#120	—	2	8	no	—
63	C₄×D₄×C₃₁	—	2	16	no	—
64	C₃₁×#117	—	2	8	no	—
65	C₃₁×#117	—	2	16	no	—
66	C₃₁×#117	—	2	2	no	—
67	C₃₁×#117	C₂³	1	4	yes	—
68	C₃₁×#117	C₂³	1	16	yes	—
69	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
70	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
80	C₂×C₄²×C₃₁	—	2	4	no	—
81	C₂×C₄²×C₃₁	—	2	8	no	—
82	C₂×C₄²×C₃₁	—	2	1	no	—
83	C₃₁×#107	C₂³	1	16	yes	complemented
84	C₃₁×#106	C₂³	1	16	yes	complemented
85	C₃₁×#103	C₂³	1	16	yes	complemented
86	C₃₁×#102	C₂³	1	16	yes	complemented
87	C₃₁×C₂²⋊C₈	C₂³	1	16	yes	—
88	C₂⁴×C₃₁	—	2	4	no	—
89	C₂⁴×C₃₁	—	2	1	no	—
90	C₂⁴×C₃₁	—	4	4	no	—
91	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
92	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
94	#41×C₃₁	—	2	16	no	—
95	#41×C₃₁	—	4	8	no	—
96	C₂×Q₈×C₃₁	—	2	1	no	—
97	C₂×Q₈×C₃₁	—	2	4	no	—
98	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
99	C₂×D₄×C₃₁	—	2	8	no	—
100	C₂×D₄×C₃₁	—	2	4	no	—
101	C₂×D₄×C₃₁	—	2	1	no	—
102	C₂×D₄×C₃₁	—	2	4	no	—
103	C₂×D₄×C₃₁	—	4	8	no	—
104	C₂×D₄×C₃₁	—	4	4	no	—
105	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₃₁	—	2	4	no	—
107	C₂²×C₄×C₃₁	—	2	8	no	—
108	C₂²×C₄×C₃₁	—	2	16	no	—
109	C₂²×C₄×C₃₁	—	2	8	no	—
110	C₂²×C₄×C₃₁	—	2	16	no	—
111	C₂²×C₄×C₃₁	—	2	8	no	—
112	C₂²×C₄×C₃₁	—	2	4	no	—
113	C₂²×C₄×C₃₁	—	2	2	no	—
114	C₂²×C₄×C₃₁	—	2	1	no	—
115	C₂²×C₄×C₃₁	—	2	4	no	—
116	C₂²×C₄×C₃₁	—	4	8	no	—
117	C₂²×C₄×C₃₁	—	4	4	no	—
118	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
120	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₃₁	#41	1	8	yes	—
125	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₃₁	—	2	16	no	—
129	C₂×C₈×C₃₁	—	2	8	no	—
130	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
131	C₄⋊C₄×C₃₁	—	2	8	no	—
132	C₄⋊C₄×C₃₁	—	2	4	no	—
133	C₄⋊C₄×C₃₁	—	2	8	no	—
134	C₄⋊C₄×C₃₁	—	2	2	no	—
135	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
136	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
137	C₂²⋊C₄×C₃₁	—	2	16	no	—
138	C₂²⋊C₄×C₃₁	—	2	4	no	—
139	C₂²⋊C₄×C₃₁	—	2	8	no	—
140	C₂²⋊C₄×C₃₁	—	2	8	no	—
141	C₄²×C₃₁	—	2	16	no	—
142	C₄²×C₃₁	—	2	4	no	—
143	C₂×#3093	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₃₁	—	2	4	no	—
145	C₂³×C₃₁	—	2	8	no	—
146	C₂³×C₃₁	—	2	4	no	—
147	C₂³×C₃₁	—	2	4	no	—
148	C₂³×C₃₁	—	2	4	no	—
149	C₂³×C₃₁	—	2	2	no	—
150	C₂³×C₃₁	—	4	8	no	—
151	C₂³×C₃₁	—	4	16	no	—
152	C₂³×C₃₁	—	4	2	no	—
153	C₂³×C₃₁	—	4	4	no	—
154	C₂³×C₃₁	#123	1	4	yes	—
155	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
156	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
157	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₃₁	—	2	4	no	—
159	Q₈×C₃₁	—	4	2	no	—
160	D₄×C₃₁	—	2	4	no	—
161	D₄×C₃₁	—	4	16	no	—
162	D₄×C₃₁	—	4	8	no	—
163	D₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	2	8	no	—
165	C₂×C₄×C₃₁	—	2	4	no	—
166	C₂×C₄×C₃₁	—	2	16	no	—
167	C₂×C₄×C₃₁	—	2	8	no	—
168	C₂×C₄×C₃₁	—	2	8	no	—
169	C₂×C₄×C₃₁	—	2	8	no	—
170	C₂×C₄×C₃₁	—	2	4	no	—
171	C₂×C₄×C₃₁	—	2	2	no	—
172	C₂×C₄×C₃₁	—	4	16	no	—
173	C₂×C₄×C₃₁	—	4	2	no	—
174	C₂×C₄×C₃₁	—	4	8	no	—
175	C₂×C₄×C₃₁	—	4	4	no	—
176	C₂×C₄×C₃₁	—	4	8	no	—
177	C₂×C₄×C₃₁	#123	1	4	yes	—
178	C₂×C₄×C₃₁	#123	1	8	yes	—
179	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
181	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
183	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
184	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
185	C₈×C₃₁	—	2	8	no	—
186	C₂×#525	C₂×C₃₁	1	1	yes	characteristic
187	C₂²×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#3093	C₂×C₃₁	1	16	yes	direct product factor
189	C₂×#485	C₂×C₃₁	1	4	yes	complemented
190	C₂×#482	C₂×C₃₁	1	4	yes	complemented
191	C₂×#428	C₂×C₃₁	1	2	yes	complemented
192	C₂×#417	C₂×C₃₁	1	2	yes	complemented
193	C₂×#407	C₂×C₃₁	1	1	yes	characteristic, complemented
194	C₂²×C₃₁	—	2	8	no	—
195	C₂²×C₃₁	—	2	4	no	—
196	C₂²×C₃₁	—	2	4	no	—
197	C₂²×C₃₁	—	2	4	no	—
198	C₂²×C₃₁	—	2	4	no	—
199	C₂²×C₃₁	—	4	16	no	—
200	C₂²×C₃₁	—	4	8	no	—
201	C₂²×C₃₁	—	4	2	no	—
202	C₂²×C₃₁	—	4	4	no	—
203	C₂²×C₃₁	—	8	4	no	—
204	C₂²×C₃₁	C₂×#123	1	4	yes	—
205	C₂²×C₃₁	C₂×#123	1	2	yes	—
206	C₂²×C₃₁	#575	1	4	yes	—
207	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
208	C₄×C₃₁	—	2	4	no	—
209	C₄×C₃₁	—	4	2	no	—
210	C₄×C₃₁	—	4	8	no	—
211	C₄×C₃₁	—	4	4	no	—
212	C₄×C₃₁	C₂×#123	1	4	yes	—
213	C₄×C₃₁	C₂×#123	1	2	yes	—
214	C₄×C₃₁	C₂²×#41	1	2	yes	—
215	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
216	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
217	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
218	#525	—	2	4	no	—
219	#525	C₂²×C₃₁	1	8	yes	—
220	C₂×#123	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
222	C₂×#121	C₂²×C₃₁	1	2	yes	—
223	C₂×#120	—	2	1	no	—
224	C₂×C₄×D₄	—	2	2	no	—
225	C₂×#117	—	2	2	no	—
226	C₂×#117	—	2	4	no	—
227	C₂×#117	C₂²×C₃₁	1	4	yes	—
228	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
229	C₂×#117	C₂²×C₃₁	1	8	yes	complemented
230	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
231	C₂²×C₂²⋊C₄	—	2	1	no	—
232	C₂²×C₄²	—	2	1	no	—
233	#485	C₂²×C₃₁	1	32	yes	complemented
234	#482	C₂²×C₃₁	1	32	yes	complemented
235	#428	C₂²×C₃₁	1	16	yes	complemented
236	C₂×#107	C₂²×C₃₁	1	4	yes	complemented
237	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
238	#417	C₂²×C₃₁	1	16	yes	complemented
239	C₂×#103	C₂²×C₃₁	1	4	yes	complemented
240	C₂×#102	C₂²×C₃₁	1	4	yes	complemented
241	#407	C₂²×C₃₁	1	8	yes	complemented
242	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
243	C₂×C₃₁	—	2	4	no	—
244	C₂×C₃₁	—	4	4	no	—
245	C₂×C₃₁	—	8	2	no	—
246	C₂×C₃₁	#3093	1	4	yes	direct product factor
247	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
248	C₂×C₃₁	C₂×#575	1	2	yes	—
249	C₂⁵	D₄×C₃₁	1	1	yes	characteristic
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	8	no	—
252	C₂×#41	C₂³×C₃₁	1	4	yes	—
253	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
257	C₂³×C₄	—	2	8	no	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	D₄×C₃₁	1	2	yes	—
261	C₂³×C₄	D₄×C₃₁	1	4	yes	—
262	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
264	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
265	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
266	C₂×M₁₆	—	2	8	no	—
267	C₂×M₁₆	C₂³×C₃₁	1	8	yes	—
268	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
269	#123	—	2	8	no	—
270	C₂²⋊Q₈	—	2	4	no	—
271	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
272	#121	—	2	4	no	—
273	#121	C₂³×C₃₁	1	8	yes	—
274	#120	—	2	8	no	—
275	C₄×D₄	—	2	16	no	—
276	#117	—	2	8	no	—
277	#117	—	2	16	no	—
278	#117	—	2	2	no	—
279	#117	C₂³×C₃₁	1	16	yes	—
280	#117	C₂³×C₃₁	1	4	yes	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
286	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	4	no	—
293	C₂×C₄²	—	2	8	no	—
294	C₂×C₄²	—	2	1	no	—
295	#107	C₂³×C₃₁	1	16	yes	complemented
296	#106	C₂³×C₃₁	1	16	yes	complemented
297	#103	C₂³×C₃₁	1	16	yes	complemented
298	#102	C₂³×C₃₁	1	16	yes	complemented
299	C₂²⋊C₈	C₂³×C₃₁	1	16	yes	—
300	C₃₁	C₂×#3093	1	1	yes	characteristic, direct product factor, Sylow
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
305	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
307	#41	—	2	16	no	—
308	#41	—	4	8	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	4	8	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	16	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	16	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	4	8	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
334	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
335	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
337	C₂²×C₄	#41×C₃₁	1	8	yes	—
338	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
341	M₁₆	—	2	16	no	—
342	C₂×C₈	—	2	8	no	—
343	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
349	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
350	C₂²⋊C₄	—	2	16	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₄²	—	2	16	no	—
355	C₄²	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	16	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	C₃₁×#123	1	4	yes	—
367	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
368	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
369	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	4	16	no	—
374	D₄	—	4	8	no	—
375	D₄	—	4	2	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	C₃₁×#123	1	4	yes	—
390	C₂×C₄	C₃₁×#123	1	8	yes	—
391	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
392	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
395	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
396	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
397	C₈	—	2	8	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	4	16	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	4	no	—
408	C₂²	C₂×C₃₁×#123	1	4	yes	—
409	C₂²	C₂×C₃₁×#123	1	2	yes	—
410	C₂²	C₃₁×#575	1	4	yes	—
411	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	8	no	—
415	C₄	—	4	4	no	—
416	C₄	C₂×C₃₁×#123	1	4	yes	—
417	C₄	C₂×C₃₁×#123	1	2	yes	—
418	C₄	C₂²×#41×C₃₁	1	2	yes	—
419	C₂	—	2	4	no	—
420	C₂	—	4	4	no	—
421	C₂	—	8	2	no	—
422	C₂	C₃₁×#3093	1	4	yes	direct product factor
423	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
424	C₂	C₂×C₃₁×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂⁴×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₁×#117	C₂	semidirect
3. C₃₁×#3093	C₂	direct (N × H)
4. C₂×C₃₁×#485	C₂	semidirect
5. C₂×C₃₁×#482	C₂	semidirect
6. C₂×C₃₁×#428	C₂	semidirect
7. C₂×C₃₁×#417	C₂	semidirect
8. C₂×C₃₁×#407	C₂	semidirect
23. C₂×C₃₁×#117	C₂²	semidirect
27. C₃₁×#485	C₂²	semidirect
28. C₃₁×#482	C₂²	semidirect
29. C₃₁×#428	C₂²	semidirect
30. C₂×C₃₁×#107	C₂²	semidirect
31. C₂×C₃₁×#106	C₂²	semidirect
32. C₃₁×#417	C₂²	semidirect
33. C₂×C₃₁×#103	C₂²	semidirect
34. C₂×C₃₁×#102	C₂²	semidirect
35. C₃₁×#407	C₂²	semidirect
83. C₃₁×#107	C₂³	semidirect
84. C₃₁×#106	C₂³	semidirect
85. C₃₁×#103	C₂³	semidirect
86. C₃₁×#102	C₂³	semidirect
143. C₂×#3093	C₃₁	direct (N × H)
187. C₂²×#117	C₂×C₃₁	semidirect
188. #3093	C₂×C₃₁	direct (N × H)
189. C₂×#485	C₂×C₃₁	semidirect
190. C₂×#482	C₂×C₃₁	semidirect
191. C₂×#428	C₂×C₃₁	semidirect
192. C₂×#417	C₂×C₃₁	semidirect
193. C₂×#407	C₂×C₃₁	semidirect
229. C₂×#117	C₂²×C₃₁	semidirect
233. #485	C₂²×C₃₁	semidirect
234. #482	C₂²×C₃₁	semidirect
235. #428	C₂²×C₃₁	semidirect
236. C₂×#107	C₂²×C₃₁	semidirect
237. C₂×#106	C₂²×C₃₁	semidirect
238. #417	C₂²×C₃₁	semidirect
239. C₂×#103	C₂²×C₃₁	semidirect
240. C₂×#102	C₂²×C₃₁	semidirect
241. #407	C₂²×C₃₁	semidirect
246. C₂×C₃₁	#3093	direct (N × H)
295. #107	C₂³×C₃₁	semidirect
296. #106	C₂³×C₃₁	semidirect
297. #103	C₂³×C₃₁	semidirect
298. #102	C₂³×C₃₁	semidirect
300. C₃₁	C₂×#3093	direct (N × H)
422. C₂	C₃₁×#3093	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×C₃₁×#525	2
C₂²×C₃₁×#117	2
C₃₁×#3093	2
C₂×C₃₁×#485	2
C₂×C₃₁×#482	2
C₂×C₃₁×#428	2
C₂×C₃₁×#417	2
C₂×C₃₁×#407	2
C₂×#3093	31

Subgroups — C2×C31×#3093 #21517267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3093 #21517267