Subgroups — C₂×C₃₁×#3058 #21517205

Order 7936.

3062 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#535	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3058	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₁×#469	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#466	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#418	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
11	C₂²×D₈×C₃₁	—	2	8	no	—
12	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₃₁	C₂²	1	8	yes	complemented
15	C₂×C₃₁×#131	—	2	8	no	—
16	C₂×C₃₁×#131	C₂²	1	8	yes	complemented
17	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
19	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₃₁	C₂²	1	2	yes	complemented
21	C₃₁×#535	—	2	8	no	—
22	C₃₁×#535	C₂²	1	16	yes	complemented
23	C₂×C₃₁×#127	—	2	2	no	—
24	C₂×C₃₁×#124	—	2	2	no	—
25	C₂×C₃₁×#121	C₂²	1	8	yes	complemented
26	C₂×C₃₁×#120	—	2	4	no	—
27	C₂×C₃₁×#117	C₂²	1	2	yes	—
28	C₃₁×#469	C₂²	1	32	yes	complemented
29	C₃₁×#466	C₂²	1	32	yes	complemented
30	C₃₁×#427	C₂²	1	8	yes	complemented
31	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
32	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
33	C₃₁×#418	C₂²	1	16	yes	complemented
34	C₂×C₃₁×#102	C₂²	1	8	yes	complemented
35	C₂⁵×C₃₁	—	2	2	no	—
36	C₂×#41×C₃₁	—	2	4	no	—
37	C₂×#41×C₃₁	—	2	4	no	—
38	C₂×#41×C₃₁	D₄	1	4	yes	—
39	C₂×#41×C₃₁	C₂³	1	4	yes	—
40	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₃₁	—	2	8	no	—
42	C₂²×D₄×C₃₁	—	2	8	no	—
43	C₂²×D₄×C₃₁	—	2	2	no	—
44	C₂²×D₄×C₃₁	—	2	4	no	—
45	C₂²×D₄×C₃₁	—	2	8	no	—
46	C₂²×D₄×C₃₁	D₄	1	2	yes	—
47	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
49	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×D₈×C₃₁	—	2	8	no	—
53	C₂×D₈×C₃₁	—	2	8	no	—
54	C₂×D₈×C₃₁	—	2	32	no	—
55	C₂×D₈×C₃₁	C₂³	1	8	yes	—
56	C₂×D₈×C₃₁	C₂³	1	8	yes	—
57	C₃₁×#131	—	2	32	no	—
58	C₂×M₁₆×C₃₁	—	2	4	no	—
59	C₂×M₁₆×C₃₁	—	2	8	no	—
60	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
61	C₂×M₁₆×C₃₁	C₂³	1	8	yes	complemented
62	C₂²×C₈×C₃₁	—	2	8	no	—
63	C₂²×C₈×C₃₁	D₄	1	8	yes	complemented
64	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
68	C₂²×C₈×C₃₁	C₂³	1	8	yes	complemented
69	C₃₁×#127	—	2	16	no	—
70	C₃₁×#124	—	2	16	no	—
71	C₃₁×#121	—	2	16	no	—
72	C₃₁×#121	C₂³	1	32	yes	complemented
73	C₃₁×#120	—	2	32	no	—
74	C₃₁×#117	—	2	4	no	—
75	C₃₁×#117	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
79	C₂×C₄²×C₃₁	—	2	2	no	—
80	C₃₁×#107	C₂³	1	8	yes	complemented
81	C₃₁×#106	C₂³	1	8	yes	complemented
82	C₃₁×#102	C₂³	1	32	yes	complemented
83	C₂⁴×C₃₁	—	2	4	no	—
84	C₂⁴×C₃₁	—	2	8	no	—
85	C₂⁴×C₃₁	—	4	8	no	—
86	C₂⁴×C₃₁	—	8	8	no	—
87	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
88	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
89	#41×C₃₁	—	2	16	no	—
90	#41×C₃₁	—	2	8	no	—
91	#41×C₃₁	—	2	8	no	—
92	C₂×Q₈×C₃₁	—	2	4	no	—
93	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
94	C₂×D₄×C₃₁	—	2	8	no	—
95	C₂×D₄×C₃₁	—	2	32	no	—
96	C₂×D₄×C₃₁	—	2	4	no	—
97	C₂×D₄×C₃₁	—	2	8	no	—
98	C₂×D₄×C₃₁	—	2	16	no	—
99	C₂×D₄×C₃₁	—	2	4	no	—
100	C₂×D₄×C₃₁	—	2	8	no	—
101	C₂×D₄×C₃₁	—	2	8	no	—
102	C₂×D₄×C₃₁	—	2	16	no	—
103	C₂×D₄×C₃₁	—	4	8	no	—
104	C₂×D₄×C₃₁	—	4	16	no	—
105	C₂×D₄×C₃₁	—	8	16	no	—
106	C₂×D₄×C₃₁	C₂×D₄	1	8	yes	—
107	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
108	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
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	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₃₁	#41	1	4	yes	—
118	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
121	D₈×C₃₁	—	2	16	no	—
122	D₈×C₃₁	—	2	16	no	—
123	M₁₆×C₃₁	—	2	8	no	—
124	M₁₆×C₃₁	—	2	16	no	—
125	C₂×C₈×C₃₁	—	2	4	no	—
126	C₂×C₈×C₃₁	—	2	16	no	—
127	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
128	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₃₁	C₂×D₄	1	16	yes	complemented
130	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
131	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
132	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
133	C₄⋊C₄×C₃₁	—	2	4	no	—
134	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
135	C₂²⋊C₄×C₃₁	—	2	8	no	—
136	C₂²⋊C₄×C₃₁	—	2	32	no	—
137	C₄²×C₃₁	—	2	8	no	—
138	C₂×#3058	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₃₁	—	2	4	no	—
140	C₂³×C₃₁	—	2	4	no	—
141	C₂³×C₃₁	—	2	8	no	—
142	C₂³×C₃₁	—	2	8	no	—
143	C₂³×C₃₁	—	4	16	no	—
144	C₂³×C₃₁	—	4	8	no	—
145	C₂³×C₃₁	—	4	16	no	—
146	C₂³×C₃₁	—	8	16	no	—
147	C₂³×C₃₁	—	8	32	no	—
148	C₂³×C₃₁	#121	1	4	yes	—
149	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
150	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
151	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₃₁	—	2	8	no	—
153	D₄×C₃₁	—	2	16	no	—
154	D₄×C₃₁	—	2	8	no	—
155	D₄×C₃₁	—	2	8	no	—
156	D₄×C₃₁	—	2	8	no	—
157	D₄×C₃₁	—	4	8	no	—
158	D₄×C₃₁	—	4	16	no	—
159	D₄×C₃₁	—	8	32	no	—
160	C₂×C₄×C₃₁	—	2	4	no	—
161	C₂×C₄×C₃₁	—	2	8	no	—
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	2	4	no	—
164	C₂×C₄×C₃₁	—	2	8	no	—
165	C₂×C₄×C₃₁	—	4	8	no	—
166	C₂×C₄×C₃₁	#121	1	4	yes	—
167	C₂×C₄×C₃₁	#121	1	8	yes	—
168	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
174	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
175	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
176	C₈×C₃₁	—	2	4	no	—
177	C₈×C₃₁	C₂²×D₄	1	4	yes	—
178	C₈×C₃₁	C₂²×D₄	1	4	yes	—
179	C₂³×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
180	C₂²×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
181	C₂×#535	C₂×C₃₁	1	2	yes	complemented
182	#3058	C₂×C₃₁	1	16	yes	direct product factor
183	C₂×#469	C₂×C₃₁	1	4	yes	complemented
184	C₂×#466	C₂×C₃₁	1	4	yes	complemented
185	C₂×#427	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂×#418	C₂×C₃₁	1	2	yes	complemented
187	C₂²×C₃₁	—	2	8	no	—
188	C₂²×C₃₁	—	2	4	no	—
189	C₂²×C₃₁	—	2	4	no	—
190	C₂²×C₃₁	—	2	8	no	—
191	C₂²×C₃₁	—	4	8	no	—
192	C₂²×C₃₁	—	4	8	no	—
193	C₂²×C₃₁	—	4	16	no	—
194	C₂²×C₃₁	—	8	32	no	—
195	C₂²×C₃₁	—	8	16	no	—
196	C₂²×C₃₁	C₂×#121	1	4	yes	—
197	C₂²×C₃₁	C₂×#121	1	2	yes	—
198	C₂²×C₃₁	#576	1	4	yes	—
199	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
200	C₄×C₃₁	—	2	4	no	—
201	C₄×C₃₁	—	4	8	no	—
202	C₄×C₃₁	C₂×#121	1	2	yes	—
203	C₄×C₃₁	C₂×#121	1	4	yes	—
204	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
205	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
206	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
207	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
208	C₂²×D₈	—	2	8	no	—
209	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
210	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
211	C₂²×D₈	C₂²×C₃₁	1	8	yes	complemented
212	C₂×#131	—	2	8	no	—
213	C₂×#131	C₂²×C₃₁	1	8	yes	complemented
214	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
216	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₃₁	1	2	yes	complemented
218	#535	—	2	8	no	—
219	#535	C₂²×C₃₁	1	16	yes	complemented
220	C₂×#127	—	2	2	no	—
221	C₂×#124	—	2	2	no	—
222	C₂×#121	C₂²×C₃₁	1	8	yes	complemented
223	C₂×#120	—	2	4	no	—
224	C₂×#117	C₂²×C₃₁	1	2	yes	—
225	#469	C₂²×C₃₁	1	32	yes	complemented
226	#466	C₂²×C₃₁	1	32	yes	complemented
227	#427	C₂²×C₃₁	1	8	yes	complemented
228	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
229	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
230	#418	C₂²×C₃₁	1	16	yes	complemented
231	C₂×#102	C₂²×C₃₁	1	8	yes	complemented
232	C₂×C₃₁	—	2	4	no	—
233	C₂×C₃₁	—	4	4	no	—
234	C₂×C₃₁	—	8	8	no	—
235	C₂×C₃₁	#3058	1	4	yes	direct product factor
236	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
237	C₂×C₃₁	C₂×#576	1	2	yes	—
238	C₂⁵	—	2	2	no	—
239	C₂×#41	—	2	4	no	—
240	C₂×#41	—	2	4	no	—
241	C₂×#41	D₄×C₃₁	1	4	yes	—
242	C₂×#41	C₂³×C₃₁	1	4	yes	—
243	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
244	C₂²×D₄	—	2	8	no	—
245	C₂²×D₄	—	2	8	no	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	—	2	8	no	—
249	C₂²×D₄	D₄×C₃₁	1	2	yes	—
250	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
252	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
253	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
254	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
255	C₂×D₈	—	2	8	no	—
256	C₂×D₈	—	2	8	no	—
257	C₂×D₈	—	2	32	no	—
258	C₂×D₈	C₂³×C₃₁	1	8	yes	—
259	C₂×D₈	C₂³×C₃₁	1	8	yes	—
260	#131	—	2	32	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	8	no	—
263	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
264	C₂×M₁₆	C₂³×C₃₁	1	8	yes	complemented
265	C₂²×C₈	—	2	8	no	—
266	C₂²×C₈	D₄×C₃₁	1	8	yes	complemented
267	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
268	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
271	C₂²×C₈	C₂³×C₃₁	1	8	yes	complemented
272	#127	—	2	16	no	—
273	#124	—	2	16	no	—
274	#121	—	2	16	no	—
275	#121	C₂³×C₃₁	1	32	yes	complemented
276	#120	—	2	32	no	—
277	#117	—	2	4	no	—
278	#117	C₂³×C₃₁	1	8	yes	—
279	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₄²	—	2	2	no	—
283	#107	C₂³×C₃₁	1	8	yes	complemented
284	#106	C₂³×C₃₁	1	8	yes	complemented
285	#102	C₂³×C₃₁	1	32	yes	complemented
286	C₃₁	C₂×#3058	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	2	4	no	—
288	C₂⁴	—	2	8	no	—
289	C₂⁴	—	4	8	no	—
290	C₂⁴	—	8	8	no	—
291	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
292	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
293	#41	—	2	16	no	—
294	#41	—	2	8	no	—
295	#41	—	2	8	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	32	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	2	8	no	—
306	C₂×D₄	—	2	16	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	4	16	no	—
309	C₂×D₄	—	8	16	no	—
310	C₂×D₄	C₂×D₄×C₃₁	1	8	yes	—
311	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
312	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
318	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
321	C₂²×C₄	#41×C₃₁	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
325	D₈	—	2	16	no	—
326	D₈	—	2	16	no	—
327	M₁₆	—	2	8	no	—
328	M₁₆	—	2	16	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	16	no	—
331	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
332	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
333	C₂×C₈	C₂×D₄×C₃₁	1	16	yes	complemented
334	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
335	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
336	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	32	no	—
341	C₄²	—	2	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	4	16	no	—
347	C₂³	—	4	8	no	—
348	C₂³	—	4	16	no	—
349	C₂³	—	8	16	no	—
350	C₂³	—	8	32	no	—
351	C₂³	C₃₁×#121	1	4	yes	—
352	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
353	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
354	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
355	Q₈	—	2	8	no	—
356	D₄	—	2	16	no	—
357	D₄	—	2	8	no	—
358	D₄	—	2	8	no	—
359	D₄	—	2	8	no	—
360	D₄	—	4	8	no	—
361	D₄	—	4	16	no	—
362	D₄	—	8	32	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	C₃₁×#121	1	4	yes	—
370	C₂×C₄	C₃₁×#121	1	8	yes	—
371	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
372	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
376	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
377	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
378	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	C₂²×D₄×C₃₁	1	4	yes	—
381	C₈	C₂²×D₄×C₃₁	1	4	yes	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	8	32	no	—
390	C₂²	—	8	16	no	—
391	C₂²	C₂×C₃₁×#121	1	4	yes	—
392	C₂²	C₂×C₃₁×#121	1	2	yes	—
393	C₂²	C₃₁×#576	1	4	yes	—
394	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
395	C₄	—	2	4	no	—
396	C₄	—	4	8	no	—
397	C₄	C₂×C₃₁×#121	1	2	yes	—
398	C₄	C₂×C₃₁×#121	1	4	yes	—
399	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
400	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
401	C₂	—	2	4	no	—
402	C₂	—	4	4	no	—
403	C₂	—	8	8	no	—
404	C₂	C₃₁×#3058	1	4	yes	direct product factor
405	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic
406	C₂	C₂×C₃₁×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₃₁	C₂	semidirect
2. C₂²×C₃₁×#131	C₂	semidirect
3. C₂×C₃₁×#535	C₂	semidirect
4. C₃₁×#3058	C₂	direct (N × H)
5. C₂×C₃₁×#469	C₂	semidirect
6. C₂×C₃₁×#466	C₂	semidirect
7. C₂×C₃₁×#427	C₂	semidirect
8. C₂×C₃₁×#418	C₂	semidirect
14. C₂²×D₈×C₃₁	C₂²	semidirect
16. C₂×C₃₁×#131	C₂²	semidirect
18. C₂²×M₁₆×C₃₁	C₂²	semidirect
20. C₂³×C₈×C₃₁	C₂²	semidirect
22. C₃₁×#535	C₂²	semidirect
25. C₂×C₃₁×#121	C₂²	semidirect
28. C₃₁×#469	C₂²	semidirect
29. C₃₁×#466	C₂²	semidirect
30. C₃₁×#427	C₂²	semidirect
31. C₂×C₃₁×#107	C₂²	semidirect
32. C₂×C₃₁×#106	C₂²	semidirect
33. C₃₁×#418	C₂²	semidirect
34. C₂×C₃₁×#102	C₂²	semidirect
61. C₂×M₁₆×C₃₁	C₂³	semidirect
63. C₂²×C₈×C₃₁	D₄	semidirect
68. C₂²×C₈×C₃₁	C₂³	semidirect
72. C₃₁×#121	C₂³	semidirect
80. C₃₁×#107	C₂³	semidirect
81. C₃₁×#106	C₂³	semidirect
82. C₃₁×#102	C₂³	semidirect
129. C₂×C₈×C₃₁	C₂×D₄	semidirect
138. C₂×#3058	C₃₁	direct (N × H)
179. C₂³×D₈	C₂×C₃₁	semidirect
180. C₂²×#131	C₂×C₃₁	semidirect
181. C₂×#535	C₂×C₃₁	semidirect
182. #3058	C₂×C₃₁	direct (N × H)
183. C₂×#469	C₂×C₃₁	semidirect
184. C₂×#466	C₂×C₃₁	semidirect
185. C₂×#427	C₂×C₃₁	semidirect
186. C₂×#418	C₂×C₃₁	semidirect
211. C₂²×D₈	C₂²×C₃₁	semidirect
213. C₂×#131	C₂²×C₃₁	semidirect
215. C₂²×M₁₆	C₂²×C₃₁	semidirect
217. C₂³×C₈	C₂²×C₃₁	semidirect
219. #535	C₂²×C₃₁	semidirect
222. C₂×#121	C₂²×C₃₁	semidirect
225. #469	C₂²×C₃₁	semidirect
226. #466	C₂²×C₃₁	semidirect
227. #427	C₂²×C₃₁	semidirect
228. C₂×#107	C₂²×C₃₁	semidirect
229. C₂×#106	C₂²×C₃₁	semidirect
230. #418	C₂²×C₃₁	semidirect
231. C₂×#102	C₂²×C₃₁	semidirect
235. C₂×C₃₁	#3058	direct (N × H)
264. C₂×M₁₆	C₂³×C₃₁	semidirect
266. C₂²×C₈	D₄×C₃₁	semidirect
271. C₂²×C₈	C₂³×C₃₁	semidirect
275. #121	C₂³×C₃₁	semidirect
283. #107	C₂³×C₃₁	semidirect
284. #106	C₂³×C₃₁	semidirect
285. #102	C₂³×C₃₁	semidirect
286. C₃₁	C₂×#3058	direct (N × H)
333. C₂×C₈	C₂×D₄×C₃₁	semidirect
404. C₂	C₃₁×#3058	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₃₁	2
C₂²×C₃₁×#131	2
C₂×C₃₁×#535	2
C₃₁×#3058	2
C₂×C₃₁×#469	2
C₂×C₃₁×#466	2
C₂×C₃₁×#427	2
C₂×C₃₁×#418	2
C₂×#3058	31

Subgroups — C2×C31×#3058 #21517205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3058 #21517205