Subgroups — C₂×C₃₁×#1665 #21475857

Order 7936.

874 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×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1665	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₃₁	—	2	1	no	—
10	C₂²×SD₁₆×C₃₁	—	2	1	no	—
11	C₂²×D₈×C₃₁	—	2	1	no	—
12	C₂³×C₈×C₃₁	—	2	1	no	—
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#492	—	2	2	no	—
17	C₃₁×#492	C₂²	1	4	yes	complemented
18	C₃₁×#474	—	2	2	no	—
19	C₃₁×#474	C₂²	1	4	yes	complemented
20	C₃₁×#459	—	2	2	no	—
21	C₃₁×#459	C₂²	1	4	yes	—
22	C₈×D₄×C₃₁	—	2	2	no	—
23	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#107	—	2	1	no	—
25	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#102	—	2	1	no	—
29	C₂×C₃₁×#102	—	2	1	no	—
30	C₂×C₃₁×C₂²⋊C₈	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#334	C₂²	1	4	yes	complemented
33	C₃₁×#332	C₂²	1	4	yes	complemented
34	C₃₁×#331	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₃₁	—	2	1	no	—
36	C₂²×D₄×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	—	2	1	no	—
38	C₂²×D₄×C₃₁	—	2	1	no	—
39	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	—	2	1	no	—
41	C₂×SD₁₆×C₃₁	—	2	4	no	—
42	C₂×SD₁₆×C₃₁	—	2	4	no	—
43	C₂×SD₁₆×C₃₁	—	4	4	no	—
44	C₂×SD₁₆×C₃₁	—	4	4	no	—
45	C₂×D₈×C₃₁	—	2	4	no	—
46	C₂×D₈×C₃₁	—	4	4	no	—
47	C₂²×C₈×C₃₁	—	2	1	no	—
48	C₂²×C₈×C₃₁	—	2	1	no	—
49	C₂²×C₈×C₃₁	—	2	1	no	—
50	C₂²×C₈×C₃₁	—	2	4	no	—
51	C₂²×C₈×C₃₁	—	4	4	no	—
52	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
54	C₃₁×C₄⋊Q₈	—	2	1	no	—
55	C₃₁×C₄⋊Q₈	—	2	1	no	—
56	C₃₁×C₄⋊Q₈	—	2	1	no	—
57	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₃₁×#127	—	2	1	no	—
59	C₃₁×#127	—	2	1	no	—
60	C₃₁×#127	—	2	1	no	—
61	C₃₁×#127	C₂³	1	2	yes	—
62	C₄×D₄×C₃₁	—	2	1	no	—
63	C₄×D₄×C₃₁	—	2	1	no	—
64	C₄×D₄×C₃₁	D₄	1	2	yes	—
65	C₄×D₄×C₃₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
70	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
71	C₃₁×#107	—	2	4	no	—
72	C₃₁×C₄⋊C₈	—	2	1	no	—
73	C₃₁×C₄⋊C₈	—	2	1	no	—
74	C₃₁×C₄⋊C₈	—	2	1	no	—
75	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
76	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₃₁×#102	—	2	4	no	—
79	C₃₁×#102	—	2	4	no	—
80	C₃₁×C₂²⋊C₈	—	2	4	no	—
81	C₄×C₈×C₃₁	D₄	1	2	yes	—
82	C₄×C₈×C₃₁	C₂³	1	2	yes	—
83	C₂⁴×C₃₁	—	2	1	no	—
84	C₂⁴×C₃₁	—	4	1	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	—	4	1	no	—
87	C₂×Q₈×C₃₁	—	4	2	no	—
88	C₂×Q₈×C₃₁	—	4	2	no	—
89	C₂×D₄×C₃₁	—	2	1	no	—
90	C₂×D₄×C₃₁	—	2	2	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	2	2	no	—
93	C₂×D₄×C₃₁	—	2	2	no	—
94	C₂×D₄×C₃₁	—	4	1	no	—
95	C₂×D₄×C₃₁	—	4	1	no	—
96	C₂×D₄×C₃₁	—	4	1	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	2	no	—
100	C₂×D₄×C₃₁	—	4	2	no	—
101	C₂×D₄×C₃₁	—	8	2	no	—
102	C₂×D₄×C₃₁	SD₁₆	1	4	yes	complemented
103	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₃₁	—	2	1	no	—
105	C₂²×C₄×C₃₁	—	2	2	no	—
106	C₂²×C₄×C₃₁	—	2	2	no	—
107	C₂²×C₄×C₃₁	—	4	2	no	—
108	C₂²×C₄×C₃₁	—	4	2	no	—
109	C₂²×C₄×C₃₁	—	4	1	no	—
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
113	SD₁₆×C₃₁	—	4	8	no	—
114	SD₁₆×C₃₁	—	4	8	no	—
115	D₈×C₃₁	—	4	8	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	—	2	2	no	—
120	C₂×C₈×C₃₁	—	4	2	no	—
121	C₂×C₈×C₃₁	—	4	2	no	—
122	C₂×C₈×C₃₁	—	4	2	no	—
123	C₂×C₈×C₃₁	—	4	8	no	—
124	C₂×C₈×C₃₁	D₈	1	4	yes	complemented
125	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₃₁	—	2	1	no	—
128	C₄⋊C₄×C₃₁	—	2	2	no	—
129	C₄⋊C₄×C₃₁	—	2	2	no	—
130	C₄⋊C₄×C₃₁	—	4	1	no	—
131	C₄⋊C₄×C₃₁	—	4	1	no	—
132	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₂²⋊C₄×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₃₁	#41	1	1	yes	characteristic
138	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
139	C₂×#1665	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	2	2	no	—
141	C₂³×C₃₁	—	2	4	no	—
142	C₂³×C₃₁	—	4	2	no	—
143	C₂³×C₃₁	—	4	2	no	—
144	C₂³×C₃₁	—	4	2	no	—
145	C₂³×C₃₁	—	8	2	no	—
146	C₂³×C₃₁	—	8	2	no	—
147	C₂³×C₃₁	—	8	2	no	—
148	C₂³×C₃₁	#121	1	1	yes	characteristic
149	Q₈×C₃₁	—	4	2	no	—
150	Q₈×C₃₁	—	4	2	no	—
151	Q₈×C₃₁	—	8	2	no	—
152	D₄×C₃₁	—	2	2	no	—
153	D₄×C₃₁	—	2	4	no	—
154	D₄×C₃₁	—	4	2	no	—
155	D₄×C₃₁	—	4	2	no	—
156	D₄×C₃₁	—	4	2	no	—
157	D₄×C₃₁	—	4	2	no	—
158	D₄×C₃₁	—	8	2	no	—
159	D₄×C₃₁	—	8	2	no	—
160	D₄×C₃₁	—	8	2	no	—
161	D₄×C₃₁	—	8	2	no	—
162	D₄×C₃₁	C₂×SD₁₆	1	4	yes	complemented
163	C₂×C₄×C₃₁	—	2	2	no	—
164	C₂×C₄×C₃₁	—	2	2	no	—
165	C₂×C₄×C₃₁	—	4	2	no	—
166	C₂×C₄×C₃₁	—	4	2	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	4	no	—
169	C₂×C₄×C₃₁	—	4	2	no	—
170	C₂×C₄×C₃₁	—	8	2	no	—
171	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
172	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
173	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₃₁	#135	1	2	yes	—
177	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
178	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
181	C₈×C₃₁	—	2	2	no	—
182	C₈×C₃₁	—	4	2	no	—
183	C₈×C₃₁	—	4	2	no	—
184	C₈×C₃₁	—	4	2	no	—
185	C₈×C₃₁	C₂×D₈	1	4	yes	complemented
186	C₂×#492	C₂×C₃₁	1	1	yes	characteristic, complemented
187	C₂×#474	C₂×C₃₁	1	1	yes	characteristic, complemented
188	C₂×#459	C₂×C₃₁	1	1	yes	characteristic
189	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
190	#1665	C₂×C₃₁	1	8	yes	direct product factor
191	C₂×#334	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂×#332	C₂×C₃₁	1	1	yes	characteristic, complemented
193	C₂×#331	C₂×C₃₁	1	1	yes	characteristic, complemented
194	C₂²×C₃₁	—	2	4	no	—
195	C₂²×C₃₁	—	4	8	no	—
196	C₂²×C₃₁	—	4	2	no	—
197	C₂²×C₃₁	—	4	2	no	—
198	C₂²×C₃₁	—	8	2	no	—
199	C₂²×C₃₁	—	8	2	no	—
200	C₂²×C₃₁	—	8	2	no	—
201	C₂²×C₃₁	—	16	4	no	—
202	C₂²×C₃₁	#459	1	2	yes	—
203	C₂²×C₃₁	#465	1	2	yes	—
204	C₂²×C₃₁	#471	1	2	yes	—
205	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
206	C₄×C₃₁	—	2	1	no	—
207	C₄×C₃₁	—	2	1	no	—
208	C₄×C₃₁	—	4	2	no	—
209	C₄×C₃₁	—	8	2	no	—
210	C₄×C₃₁	#459	1	2	yes	—
211	C₄×C₃₁	#465	1	2	yes	—
212	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
213	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
214	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
215	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂²×SD₁₆	—	2	1	no	—
217	C₂²×SD₁₆	—	2	1	no	—
218	C₂²×D₈	—	2	1	no	—
219	C₂³×C₈	—	2	1	no	—
220	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
221	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
222	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
223	#492	—	2	2	no	—
224	#492	C₂²×C₃₁	1	4	yes	complemented
225	#474	—	2	2	no	—
226	#474	C₂²×C₃₁	1	4	yes	complemented
227	#459	—	2	2	no	—
228	#459	C₂²×C₃₁	1	4	yes	—
229	C₈×D₄	—	2	2	no	—
230	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
231	C₂×#107	—	2	1	no	—
232	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
235	C₂×#102	—	2	1	no	—
236	C₂×#102	—	2	1	no	—
237	C₂×C₂²⋊C₈	—	2	1	no	—
238	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
239	#334	C₂²×C₃₁	1	4	yes	complemented
240	#332	C₂²×C₃₁	1	4	yes	complemented
241	#331	C₂²×C₃₁	1	4	yes	complemented
242	C₂×C₃₁	—	4	4	no	—
243	C₂×C₃₁	—	16	2	no	—
244	C₂×C₃₁	#1665	1	4	yes	direct product factor
245	C₂×C₃₁	C₂×#459	1	1	yes	characteristic
246	C₂×C₃₁	C₂×#465	1	1	yes	characteristic
247	C₂×C₃₁	C₂×#471	1	1	yes	characteristic
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
253	C₂³×C₄	—	2	1	no	—
254	C₂×SD₁₆	—	2	4	no	—
255	C₂×SD₁₆	—	2	4	no	—
256	C₂×SD₁₆	—	4	4	no	—
257	C₂×SD₁₆	—	4	4	no	—
258	C₂×D₈	—	2	4	no	—
259	C₂×D₈	—	4	4	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	2	4	no	—
264	C₂²×C₈	—	4	4	no	—
265	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
271	#127	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	2	1	no	—
274	#127	C₂³×C₃₁	1	2	yes	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	D₄×C₃₁	1	2	yes	—
278	C₄×D₄	C₂³×C₃₁	1	2	yes	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
284	#107	—	2	4	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
289	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
290	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
291	#102	—	2	4	no	—
292	#102	—	2	4	no	—
293	C₂²⋊C₈	—	2	4	no	—
294	C₄×C₈	D₄×C₃₁	1	2	yes	—
295	C₄×C₈	C₂³×C₃₁	1	2	yes	—
296	C₃₁	C₂×#1665	1	1	yes	characteristic, direct product factor, Sylow
297	C₂⁴	—	2	1	no	—
298	C₂⁴	—	4	1	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂×D₄	SD₁₆×C₃₁	1	4	yes	complemented
317	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
326	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
327	SD₁₆	—	4	8	no	—
328	SD₁₆	—	4	8	no	—
329	D₈	—	4	8	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	8	no	—
338	C₂×C₈	D₈×C₃₁	1	4	yes	complemented
339	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
350	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
351	C₄²	#41×C₃₁	1	1	yes	characteristic
352	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
353	C₂³	—	2	4	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	8	2	no	—
360	C₂³	—	8	2	no	—
361	C₂³	C₃₁×#121	1	1	yes	characteristic
362	Q₈	—	4	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	8	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	8	2	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	8	2	no	—
375	D₄	C₂×SD₁₆×C₃₁	1	4	yes	complemented
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
385	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
386	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
387	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
388	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
389	C₂×C₄	C₃₁×#135	1	2	yes	—
390	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₈	C₂×D₈×C₃₁	1	4	yes	complemented
399	C₂²	—	2	4	no	—
400	C₂²	—	4	8	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	16	4	no	—
407	C₂²	C₃₁×#459	1	2	yes	—
408	C₂²	C₃₁×#465	1	2	yes	—
409	C₂²	C₃₁×#471	1	2	yes	—
410	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₃₁×#459	1	2	yes	—
416	C₄	C₃₁×#465	1	2	yes	—
417	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
418	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
419	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
420	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂	—	4	4	no	—
422	C₂	—	16	2	no	—
423	C₂	C₃₁×#1665	1	4	yes	direct product factor
424	C₂	C₂×C₃₁×#459	1	1	yes	characteristic
425	C₂	C₂×C₃₁×#465	1	1	yes	characteristic
426	C₂	C₂×C₃₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#492	C₂	semidirect
2. C₂×C₃₁×#474	C₂	semidirect
4. C₂×C₈×D₄×C₃₁	C₂	semidirect
5. C₃₁×#1665	C₂	direct (N × H)
6. C₂×C₃₁×#334	C₂	semidirect
7. C₂×C₃₁×#332	C₂	semidirect
8. C₂×C₃₁×#331	C₂	semidirect
17. C₃₁×#492	C₂²	semidirect
19. C₃₁×#474	C₂²	semidirect
23. C₈×D₄×C₃₁	C₂²	semidirect
32. C₃₁×#334	C₂²	semidirect
33. C₃₁×#332	C₂²	semidirect
34. C₃₁×#331	C₂²	semidirect
102. C₂×D₄×C₃₁	SD₁₆	semidirect
124. C₂×C₈×C₃₁	D₈	semidirect
139. C₂×#1665	C₃₁	direct (N × H)
162. D₄×C₃₁	C₂×SD₁₆	semidirect
185. C₈×C₃₁	C₂×D₈	semidirect
186. C₂×#492	C₂×C₃₁	semidirect
187. C₂×#474	C₂×C₃₁	semidirect
189. C₂×C₈×D₄	C₂×C₃₁	semidirect
190. #1665	C₂×C₃₁	direct (N × H)
191. C₂×#334	C₂×C₃₁	semidirect
192. C₂×#332	C₂×C₃₁	semidirect
193. C₂×#331	C₂×C₃₁	semidirect
224. #492	C₂²×C₃₁	semidirect
226. #474	C₂²×C₃₁	semidirect
230. C₈×D₄	C₂²×C₃₁	semidirect
239. #334	C₂²×C₃₁	semidirect
240. #332	C₂²×C₃₁	semidirect
241. #331	C₂²×C₃₁	semidirect
244. C₂×C₃₁	#1665	direct (N × H)
296. C₃₁	C₂×#1665	direct (N × H)
316. C₂×D₄	SD₁₆×C₃₁	semidirect
338. C₂×C₈	D₈×C₃₁	semidirect
375. D₄	C₂×SD₁₆×C₃₁	semidirect
398. C₈	C₂×D₈×C₃₁	semidirect
423. C₂	C₃₁×#1665	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×#492	2
C₂×C₃₁×#474	2
C₂×C₃₁×#459	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1665	2
C₂×C₃₁×#334	2
C₂×C₃₁×#332	2
C₂×C₃₁×#331	2
C₂×#1665	31

Subgroups — C2×C31×#1665 #21475857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1665 #21475857