Subgroups — C₃₁×#19277 #21476036

Order 7936.

638 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	C₂×C₃₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic
4	C₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1684	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1683	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#487	—	2	1	no	—
14	C₃₁×#487	—	2	1	no	—
15	C₃₁×#487	C₂²	1	4	yes	—
16	C₃₁×#477	—	2	1	no	—
17	C₃₁×#477	C₂²	1	2	yes	—
18	C₃₁×#476	—	2	1	no	—
19	C₃₁×#476	C₂²	1	2	yes	—
20	C₃₁×#475	—	2	1	no	—
21	C₃₁×#475	C₂²	1	2	yes	—
22	C₃₁×#474	—	2	1	no	—
23	C₃₁×#474	C₂²	1	2	yes	—
24	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
25	C₈×D₄×C₃₁	—	2	2	no	—
26	C₈×D₄×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#431	—	2	1	no	—
28	C₃₁×#431	C₂²	1	1	yes	characteristic
29	C₃₁×#428	—	2	1	no	—
30	C₃₁×#428	—	2	1	no	—
31	C₃₁×#423	C₂²	1	1	yes	characteristic
32	C₃₁×#423	C₂²	1	1	yes	characteristic
33	C₃₁×#417	—	2	1	no	—
34	C₃₁×#417	—	2	1	no	—
35	C₂×C₃₁×#103	—	2	2	no	—
36	C₂×C₄×C₈×C₃₁	—	2	1	no	—
37	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#335	C₂²	1	4	yes	—
39	C₃₁×#333	C₂²	1	4	yes	—
40	C₃₁×#332	C₂²	1	4	yes	—
41	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₃₁	—	2	1	no	—
43	C₂²×Q₈×C₃₁	—	2	1	no	—
44	C₂×M₁₆×C₃₁	—	2	1	no	—
45	C₂×M₁₆×C₃₁	—	2	1	no	—
46	C₂²×C₈×C₃₁	—	2	2	no	—
47	C₂²×C₈×C₃₁	D₄	1	2	yes	—
48	C₃₁×C₄⋊Q₈	—	2	1	no	—
49	C₃₁×C₄⋊Q₈	—	2	1	no	—
50	C₃₁×C₄⋊Q₈	—	2	1	no	—
51	C₃₁×C₄⋊Q₈	—	2	1	no	—
52	C₃₁×C₄⋊Q₈	—	2	1	no	—
53	C₃₁×C₄⋊Q₈	—	2	1	no	—
54	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
55	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
56	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
57	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₃₁	—	2	1	no	—
59	C₄×D₄×C₃₁	—	2	1	no	—
60	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
61	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#117	—	2	1	no	—
63	C₃₁×#117	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄²×C₃₁	—	2	1	no	—
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₃₁×#107	—	2	2	no	—
71	C₃₁×#107	—	2	2	no	—
72	C₃₁×#106	—	2	2	no	—
73	C₃₁×#106	—	2	2	no	—
74	C₃₁×C₄⋊C₈	—	2	2	no	—
75	C₃₁×C₄⋊C₈	—	2	1	no	—
76	C₃₁×C₄⋊C₈	—	2	1	no	—
77	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
78	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
79	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
80	C₃₁×#103	—	2	2	no	—
81	C₃₁×#103	—	2	2	no	—
82	C₃₁×#103	—	2	4	no	—
83	C₃₁×#103	—	2	4	no	—
84	C₃₁×#102	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×C₂²⋊C₈	—	2	1	no	—
87	C₃₁×C₂²⋊C₈	—	2	2	no	—
88	C₄×C₈×C₃₁	—	2	2	no	—
89	C₄×C₈×C₃₁	—	2	1	no	—
90	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
92	C₄×C₈×C₃₁	C₂³	1	2	yes	—
93	#41×C₃₁	—	2	2	no	—
94	#41×C₃₁	Q₁₆	1	4	yes	—
95	C₂×Q₈×C₃₁	—	2	2	no	—
96	C₂×Q₈×C₃₁	—	2	2	no	—
97	C₂×Q₈×C₃₁	—	4	4	no	—
98	C₂×Q₈×C₃₁	—	4	1	no	—
99	C₂×Q₈×C₃₁	—	4	1	no	—
100	C₂×Q₈×C₃₁	—	8	2	no	—
101	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₃₁	—	2	1	no	—
103	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	—	2	1	no	—
105	C₂²×C₄×C₃₁	—	2	1	no	—
106	C₂²×C₄×C₃₁	—	2	1	no	—
107	C₂²×C₄×C₃₁	—	4	1	no	—
108	C₂²×C₄×C₃₁	—	4	1	no	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
112	M₁₆×C₃₁	—	4	2	no	—
113	M₁₆×C₃₁	—	4	2	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	2	no	—
116	C₂×C₈×C₃₁	—	2	2	no	—
117	C₂×C₈×C₃₁	—	4	2	no	—
118	C₂×C₈×C₃₁	—	4	4	no	—
119	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₃₁	—	2	1	no	—
122	C₄⋊C₄×C₃₁	—	2	1	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	—	2	2	no	—
125	C₄⋊C₄×C₃₁	—	2	2	no	—
126	C₄⋊C₄×C₃₁	—	2	2	no	—
127	C₄⋊C₄×C₃₁	—	4	1	no	—
128	C₄⋊C₄×C₃₁	—	4	1	no	—
129	C₄⋊C₄×C₃₁	—	4	1	no	—
130	C₄⋊C₄×C₃₁	—	4	1	no	—
131	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₃₁	—	2	1	no	—
134	C₂²⋊C₄×C₃₁	—	2	1	no	—
135	C₂²⋊C₄×C₃₁	—	2	1	no	—
136	C₄²×C₃₁	—	2	1	no	—
137	C₄²×C₃₁	—	2	1	no	—
138	C₄²×C₃₁	—	2	1	no	—
139	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₃₁	#41	1	1	yes	characteristic
142	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
143	#19277	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
144	C₂³×C₃₁	—	2	1	no	—
145	C₂³×C₃₁	#121	1	1	yes	characteristic
146	Q₈×C₃₁	—	2	1	no	—
147	Q₈×C₃₁	—	4	4	no	—
148	Q₈×C₃₁	—	8	2	no	—
149	Q₈×C₃₁	—	8	2	no	—
150	Q₈×C₃₁	—	8	2	no	—
151	Q₈×C₃₁	C₂×Q₁₆	1	2	yes	—
152	D₄×C₃₁	—	2	4	no	—
153	D₄×C₃₁	—	2	1	no	—
154	D₄×C₃₁	C₂×Q₁₆	1	2	yes	—
155	C₂×C₄×C₃₁	—	2	1	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	4	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	1	no	—
160	C₂×C₄×C₃₁	—	2	1	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	8	2	no	—
166	C₂×C₄×C₃₁	—	8	2	no	—
167	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
168	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
169	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂×Q₁₆	1	2	yes	—
171	C₂×C₄×C₃₁	#135	1	2	yes	—
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
175	C₈×C₃₁	—	2	2	no	—
176	C₈×C₃₁	—	2	2	no	—
177	C₈×C₃₁	—	4	2	no	—
178	C₈×C₃₁	—	4	2	no	—
179	C₈×C₃₁	—	4	2	no	—
180	C₂×#487	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#3079	C₂×C₃₁	1	1	yes	characteristic
182	#3079	C₂×C₃₁	1	1	yes	characteristic
183	C₈×#41	C₂×C₃₁	1	1	yes	characteristic
184	#1684	C₂×C₃₁	1	4	yes	complemented
185	#1683	C₂×C₃₁	1	4	yes	complemented
186	#1567	C₂×C₃₁	1	1	yes	characteristic, complemented
187	#1549	C₂×C₃₁	1	1	yes	characteristic, complemented
188	#1548	C₂×C₃₁	1	1	yes	characteristic, complemented
189	C₂²×C₃₁	—	2	1	no	—
190	C₂²×C₃₁	—	2	1	no	—
191	C₂²×C₃₁	—	2	2	no	—
192	C₂²×C₃₁	—	4	1	no	—
193	C₂²×C₃₁	—	4	1	no	—
194	C₂²×C₃₁	#467	1	2	yes	—
195	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
196	C₄×C₃₁	—	2	1	no	—
197	C₄×C₃₁	—	2	2	no	—
198	C₄×C₃₁	—	2	1	no	—
199	C₄×C₃₁	—	4	1	no	—
200	C₄×C₃₁	—	4	1	no	—
201	C₄×C₃₁	—	8	2	no	—
202	C₄×C₃₁	—	8	2	no	—
203	C₄×C₃₁	#467	1	2	yes	—
204	C₄×C₃₁	#471	1	2	yes	—
205	C₄×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
206	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
207	C₄×C₃₁	#575	1	2	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
210	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
211	#487	—	2	1	no	—
212	#487	—	2	1	no	—
213	#487	C₂²×C₃₁	1	4	yes	—
214	#477	—	2	1	no	—
215	#477	C₂²×C₃₁	1	2	yes	—
216	#476	—	2	1	no	—
217	#476	C₂²×C₃₁	1	2	yes	—
218	#475	—	2	1	no	—
219	#475	C₂²×C₃₁	1	2	yes	—
220	#474	—	2	1	no	—
221	#474	C₂²×C₃₁	1	2	yes	—
222	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
223	C₈×D₄	—	2	2	no	—
224	C₈×D₄	C₂²×C₃₁	1	2	yes	—
225	#431	—	2	1	no	—
226	#431	C₂²×C₃₁	1	1	yes	characteristic
227	#428	—	2	1	no	—
228	#428	—	2	1	no	—
229	#423	C₂²×C₃₁	1	1	yes	characteristic
230	#423	C₂²×C₃₁	1	1	yes	characteristic
231	#417	—	2	1	no	—
232	#417	—	2	1	no	—
233	C₂×#103	—	2	2	no	—
234	C₂×C₄×C₈	—	2	1	no	—
235	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
236	#335	C₂²×C₃₁	1	4	yes	—
237	#333	C₂²×C₃₁	1	4	yes	—
238	#332	C₂²×C₃₁	1	4	yes	—
239	C₂×C₃₁	—	2	2	no	—
240	C₂×C₃₁	—	4	2	no	—
241	C₂×C₃₁	#3040	1	1	yes	characteristic
242	C₂×C₃₁	C₂×#467	1	1	yes	characteristic
243	C₂×C₃₁	C₂×#471	1	1	yes	characteristic
244	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	D₄×C₃₁	1	2	yes	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
258	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
259	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
260	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
264	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
265	#117	—	2	1	no	—
266	#117	D₄×C₃₁	1	1	yes	characteristic
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
273	#107	—	2	2	no	—
274	#107	—	2	2	no	—
275	#106	—	2	2	no	—
276	#106	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
281	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
282	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
283	#103	—	2	2	no	—
284	#103	—	2	2	no	—
285	#103	—	2	4	no	—
286	#103	—	2	4	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
294	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₃₁	1	2	yes	—
296	C₃₁	#19277	1	1	yes	characteristic, direct product factor, Sylow
297	#41	—	2	2	no	—
298	#41	Q₁₆×C₃₁	1	4	yes	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×Q₈	—	8	2	no	—
305	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
324	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
336	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
344	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
345	C₄²	#41×C₃₁	1	1	yes	characteristic
346	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
347	C₂³	—	2	1	no	—
348	C₂³	C₃₁×#121	1	1	yes	characteristic
349	Q₈	—	2	1	no	—
350	Q₈	—	4	4	no	—
351	Q₈	—	8	2	no	—
352	Q₈	—	8	2	no	—
353	Q₈	—	8	2	no	—
354	Q₈	C₂×Q₁₆×C₃₁	1	2	yes	—
355	D₄	—	2	4	no	—
356	D₄	—	2	1	no	—
357	D₄	C₂×Q₁₆×C₃₁	1	2	yes	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	2	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
371	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
372	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
373	C₂×C₄	C₂×Q₁₆×C₃₁	1	2	yes	—
374	C₂×C₄	C₃₁×#135	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	—	4	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	C₃₁×#467	1	2	yes	—
389	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₃₁×#467	1	2	yes	—
398	C₄	C₃₁×#471	1	2	yes	—
399	C₄	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
400	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
401	C₄	C₃₁×#575	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	4	2	no	—
404	C₂	C₃₁×#3040	1	1	yes	characteristic
405	C₂	C₂×C₃₁×#467	1	1	yes	characteristic
406	C₂	C₂×C₃₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
prime radical	C₂×#41×C₃₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#487	C₂	semidirect
5. C₃₁×#1684	C₂	semidirect
6. C₃₁×#1683	C₂	semidirect
7. C₃₁×#1567	C₂	semidirect
8. C₃₁×#1549	C₂	semidirect
9. C₃₁×#1548	C₂	semidirect
143. #19277	C₃₁	direct (N × H)
180. C₂×#487	C₂×C₃₁	semidirect
184. #1684	C₂×C₃₁	semidirect
185. #1683	C₂×C₃₁	semidirect
186. #1567	C₂×C₃₁	semidirect
187. #1549	C₂×C₃₁	semidirect
188. #1548	C₂×C₃₁	semidirect
296. C₃₁	#19277	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×#487	2
C₃₁×#3079	2
C₈×#41×C₃₁	2
C₃₁×#1684	2
C₃₁×#1683	2
C₃₁×#1567	2
C₃₁×#1549	2
C₃₁×#1548	2
#19277	31

Subgroups — C31×#19277 #21476036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19277 #21476036