Subgroups — C₂×C₃₁×#1986 #21478064

Order 7936.

1290 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1986	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#339	C₂	1	4	yes	maximal
6	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₃₁×#533	—	2	2	no	—
8	C₃₁×#533	—	2	2	no	—
9	C₃₁×#533	C₄	1	4	yes	complemented
10	C₃₁×#533	C₂²	1	4	yes	—
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃₁×#125	C₄	1	2	yes	complemented
14	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
16	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
18	C₂×C₃₁×#117	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
20	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
22	C₄×M₁₆×C₃₁	—	2	2	no	—
23	C₄×M₁₆×C₃₁	C₂²	1	4	yes	—
24	C₂×C₃₁×#97	—	2	1	no	—
25	C₂×C₄×C₈×C₃₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
27	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
28	C₂×C₃₁×#95	—	2	1	no	—
29	C₃₁×#339	C₂²	1	16	yes	—
30	C₂²×Q₈×C₃₁	—	2	1	no	—
31	C₂²×Q₈×C₃₁	—	2	1	no	—
32	C₂³×C₄×C₃₁	—	2	2	no	—
33	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₃₁	—	2	2	no	—
37	C₂×M₁₆×C₃₁	—	2	4	no	—
38	C₂×M₁₆×C₃₁	Q₈	1	8	yes	complemented
39	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
40	C₂²×C₈×C₃₁	—	2	2	no	—
41	C₃₁×C₄⋊Q₈	—	2	2	no	—
42	C₃₁×C₄⋊Q₈	—	2	2	no	—
43	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
44	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
45	C₃₁×#125	—	2	4	no	—
46	C₃₁×#125	C₂×C₄	1	8	yes	complemented
47	C₃₁×C₂²⋊Q₈	—	2	4	no	—
48	C₃₁×C₂²⋊Q₈	—	2	4	no	—
49	C₃₁×C₂²⋊Q₈	—	2	4	no	—
50	C₃₁×C₂²⋊Q₈	—	2	4	no	—
51	C₄×Q₈×C₃₁	—	2	4	no	—
52	C₄×Q₈×C₃₁	—	2	4	no	—
53	C₄×Q₈×C₃₁	—	2	4	no	—
54	C₄×Q₈×C₃₁	—	2	4	no	—
55	C₃₁×#117	—	2	2	no	—
56	C₃₁×#117	—	2	2	no	—
57	C₃₁×#117	C₂×C₄	1	4	yes	—
58	C₃₁×#117	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
68	C₂×C₄²×C₃₁	—	2	2	no	—
69	C₂×C₄²×C₃₁	—	2	8	no	—
70	C₂×C₄²×C₃₁	—	2	2	no	—
71	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₃₁	D₄	1	2	yes	—
75	C₂×C₄²×C₃₁	D₄	1	2	yes	—
76	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
79	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
80	C₃₁×#97	—	2	4	no	—
81	C₄×C₈×C₃₁	—	2	4	no	—
82	C₃₁×#95	—	2	4	no	—
83	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₃₁	—	2	4	no	—
85	C₂×Q₈×C₃₁	—	2	4	no	—
86	C₂×Q₈×C₃₁	—	4	4	no	—
87	C₂×Q₈×C₃₁	—	4	4	no	—
88	C₂²×C₄×C₃₁	—	2	4	no	—
89	C₂²×C₄×C₃₁	—	2	8	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	—	4	4	no	—
95	C₂²×C₄×C₃₁	—	4	4	no	—
96	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₃₁	#41	1	4	yes	—
111	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₃₁	—	2	8	no	—
113	M₁₆×C₃₁	—	2	4	no	—
114	M₁₆×C₃₁	C₂×Q₈	1	8	yes	complemented
115	C₂×C₈×C₃₁	—	2	8	no	—
116	C₂×C₈×C₃₁	—	2	4	no	—
117	C₄⋊C₄×C₃₁	—	2	16	no	—
118	C₄⋊C₄×C₃₁	—	2	8	no	—
119	C₄⋊C₄×C₃₁	—	2	8	no	—
120	C₄⋊C₄×C₃₁	—	2	4	no	—
121	C₄⋊C₄×C₃₁	—	2	4	no	—
122	C₄⋊C₄×C₃₁	—	2	2	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
125	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
126	C₂²⋊C₄×C₃₁	—	2	4	no	—
127	C₂²⋊C₄×C₃₁	—	2	4	no	—
128	C₄²×C₃₁	—	2	4	no	—
129	C₄²×C₃₁	—	2	4	no	—
130	C₄²×C₃₁	—	2	8	no	—
131	C₄²×C₃₁	—	4	4	no	—
132	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
133	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
134	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
135	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
136	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
137	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
138	C₄²×C₃₁	C₂×D₄	1	2	yes	—
139	C₄²×C₃₁	C₂×D₄	1	2	yes	—
140	C₂×#1986	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₃₁	—	2	2	no	—
142	C₂³×C₃₁	—	2	2	no	—
143	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₃₁	#124	1	2	yes	—
146	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
147	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₃₁	—	4	8	no	—
149	Q₈×C₃₁	—	4	8	no	—
150	C₂×C₄×C₃₁	—	2	2	no	—
151	C₂×C₄×C₃₁	—	2	2	no	—
152	C₂×C₄×C₃₁	—	2	2	no	—
153	C₂×C₄×C₃₁	—	2	4	no	—
154	C₂×C₄×C₃₁	—	2	4	no	—
155	C₂×C₄×C₃₁	—	2	8	no	—
156	C₂×C₄×C₃₁	—	2	4	no	—
157	C₂×C₄×C₃₁	—	2	4	no	—
158	C₂×C₄×C₃₁	—	4	2	no	—
159	C₂×C₄×C₃₁	—	4	2	no	—
160	C₂×C₄×C₃₁	—	4	4	no	—
161	C₂×C₄×C₃₁	—	4	16	no	—
162	C₂×C₄×C₃₁	—	4	4	no	—
163	C₂×C₄×C₃₁	—	4	4	no	—
164	C₂×C₄×C₃₁	—	4	4	no	—
165	C₂×C₄×C₃₁	#104	1	4	yes	—
166	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
173	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
174	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
175	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
176	C₂×C₄×C₃₁	#124	1	2	yes	—
177	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
178	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
181	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
182	C₈×C₃₁	—	2	8	no	—
183	C₂×#533	C₂×C₃₁	1	1	yes	characteristic
184	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
185	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
186	#1986	C₂×C₃₁	1	8	yes	direct product factor
187	C₂×#339	C₂×C₃₁	1	4	yes	—
188	C₂²×C₃₁	—	2	1	no	—
189	C₂²×C₃₁	—	2	1	no	—
190	C₂²×C₃₁	—	2	1	no	—
191	C₂²×C₃₁	—	2	1	no	—
192	C₂²×C₃₁	—	2	4	no	—
193	C₂²×C₃₁	—	2	4	no	—
194	C₂²×C₃₁	#391	1	2	yes	—
195	C₂²×C₃₁	#391	1	2	yes	—
196	C₂²×C₃₁	C₂×#104	1	2	yes	—
197	C₂²×C₃₁	#421	1	2	yes	—
198	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
200	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
201	C₄×C₃₁	—	2	2	no	—
202	C₄×C₃₁	—	2	2	no	—
203	C₄×C₃₁	—	2	2	no	—
204	C₄×C₃₁	—	4	8	no	—
205	C₄×C₃₁	—	4	4	no	—
206	C₄×C₃₁	—	4	4	no	—
207	C₄×C₃₁	#391	1	2	yes	—
208	C₄×C₃₁	#391	1	2	yes	—
209	C₄×C₃₁	C₂×#104	1	4	yes	—
210	C₄×C₃₁	C₂×C₄×Q₈	1	2	yes	—
211	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
212	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
213	#533	—	2	2	no	—
214	#533	—	2	2	no	—
215	#533	C₄×C₃₁	1	4	yes	complemented
216	#533	C₂²×C₃₁	1	4	yes	—
217	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
218	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
219	C₂×#125	C₄×C₃₁	1	2	yes	complemented
220	C₂×C₂²⋊Q₈	—	2	1	no	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	C₂×C₄×Q₈	—	2	1	no	—
223	C₂×C₄×Q₈	—	2	1	no	—
224	C₂×#117	C₂²×C₃₁	1	2	yes	—
225	C₂²×C₄⋊C₄	—	2	1	no	—
226	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
227	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
228	C₄×M₁₆	—	2	2	no	—
229	C₄×M₁₆	C₂²×C₃₁	1	4	yes	—
230	C₂×#97	—	2	1	no	—
231	C₂×C₄×C₈	—	2	1	no	—
232	C₄×C₄⋊C₄	—	2	2	no	—
233	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
234	C₂×#95	—	2	1	no	—
235	#339	C₂²×C₃₁	1	16	yes	—
236	C₂×C₃₁	—	2	1	no	—
237	C₂×C₃₁	—	2	1	no	—
238	C₂×C₃₁	—	2	2	no	—
239	C₂×C₃₁	#1986	1	4	yes	direct product factor
240	C₂×C₃₁	C₂×#391	1	1	yes	characteristic
241	C₂×C₃₁	C₂²×#104	1	1	yes	characteristic
242	C₂×C₃₁	C₂×#421	1	1	yes	characteristic
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	4	no	—
251	C₂×M₁₆	Q₈×C₃₁	1	8	yes	complemented
252	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
253	C₂²×C₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
257	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
258	#125	—	2	4	no	—
259	#125	C₂×C₄×C₃₁	1	8	yes	complemented
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	4	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	2	4	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	C₂×C₄×C₃₁	1	4	yes	—
271	#117	C₂³×C₃₁	1	4	yes	—
272	C₂×C₄⋊C₄	—	2	8	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
279	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	2	8	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
286	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
287	C₂×C₄²	D₄×C₃₁	1	2	yes	—
288	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
289	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
290	C₂×C₄²	D₄×C₃₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
292	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
293	#97	—	2	4	no	—
294	C₄×C₈	—	2	4	no	—
295	#95	—	2	4	no	—
296	C₃₁	C₂×#1986	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	4	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
312	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
314	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
315	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
323	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
324	C₂²×C₄	#41×C₃₁	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
326	M₁₆	—	2	8	no	—
327	M₁₆	—	2	4	no	—
328	M₁₆	C₂×Q₈×C₃₁	1	8	yes	complemented
329	C₂×C₈	—	2	8	no	—
330	C₂×C₈	—	2	4	no	—
331	C₄⋊C₄	—	2	16	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
339	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	8	no	—
345	C₄²	—	4	4	no	—
346	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
347	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
348	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
349	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
350	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
351	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
352	C₄²	C₂×D₄×C₃₁	1	2	yes	—
353	C₄²	C₂×D₄×C₃₁	1	2	yes	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
357	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
358	C₂³	C₃₁×#124	1	2	yes	—
359	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
360	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
361	Q₈	—	4	8	no	—
362	Q₈	—	4	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	C₃₁×#104	1	4	yes	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
384	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
385	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
386	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
387	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
388	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
389	C₂×C₄	C₃₁×#124	1	2	yes	—
390	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
394	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
395	C₈	—	2	8	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	C₃₁×#391	1	2	yes	—
403	C₂²	C₃₁×#391	1	2	yes	—
404	C₂²	C₂×C₃₁×#104	1	2	yes	—
405	C₂²	C₃₁×#421	1	2	yes	—
406	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
407	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
408	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	8	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	4	no	—
415	C₄	C₃₁×#391	1	2	yes	—
416	C₄	C₃₁×#391	1	2	yes	—
417	C₄	C₂×C₃₁×#104	1	4	yes	—
418	C₄	C₂×C₄×Q₈×C₃₁	1	2	yes	—
419	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	2	no	—
423	C₂	C₃₁×#1986	1	4	yes	direct product factor
424	C₂	C₂×C₃₁×#391	1	1	yes	characteristic
425	C₂	C₂²×C₃₁×#104	1	1	yes	characteristic
426	C₂	C₂×C₃₁×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1986	C₂	direct (N × H)
9. C₃₁×#533	C₄	semidirect
11. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
12. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
13. C₂×C₃₁×#125	C₄	semidirect
38. C₂×M₁₆×C₃₁	Q₈	semidirect
43. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
44. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
46. C₃₁×#125	C₂×C₄	semidirect
114. M₁₆×C₃₁	C₂×Q₈	semidirect
140. C₂×#1986	C₃₁	direct (N × H)
186. #1986	C₂×C₃₁	direct (N × H)
215. #533	C₄×C₃₁	semidirect
217. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
218. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
219. C₂×#125	C₄×C₃₁	semidirect
239. C₂×C₃₁	#1986	direct (N × H)
251. C₂×M₁₆	Q₈×C₃₁	semidirect
256. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
257. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
259. #125	C₂×C₄×C₃₁	semidirect
296. C₃₁	C₂×#1986	direct (N × H)
328. M₁₆	C₂×Q₈×C₃₁	semidirect
423. C₂	C₃₁×#1986	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×#533	2
C₂×C₄×M₁₆×C₃₁	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₃₁×#1986	2
C₂×C₃₁×#339	2
C₂×#1986	31

Subgroups — C2×C31×#1986 #21478064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1986 #21478064