Subgroups — C₃₁×#17613 #21474372

Order 7936.

1350 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	C₃₁×#3496	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#2349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1519	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1517	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1502	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#327	C₂	1	4	yes	maximal, complemented
8	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
9	C₃₁×#547	C₄	1	4	yes	complemented
10	C₃₁×#546	—	2	4	no	—
11	D₄²×C₃₁	C₄	1	4	yes	complemented
12	C₃₁×#537	—	2	1	no	—
13	C₃₁×#534	—	2	2	no	—
14	C₃₁×#532	C₂²	1	2	yes	—
15	C₂×C₃₁×#121	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₃₁	—	2	1	no	—
17	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₈×D₄×C₃₁	—	2	4	no	—
19	C₃₁×#431	C₂²	1	2	yes	complemented
20	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
21	C₃₁×#389	—	2	1	no	—
22	C₃₁×#385	—	2	2	no	—
23	C₃₁×#382	C₂²	1	1	yes	characteristic, complemented
24	C₃₁×#380	C₂²	1	2	yes	complemented
25	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃₁×#95	C₂²	1	2	yes	complemented
27	C₃₁×#327	C₂²	1	4	yes	complemented
28	C₃₁×#327	C₂²	1	8	yes	complemented
29	C₃₁×#327	C₂²	1	4	yes	complemented
30	C₃₁×H(5,𝔽₂)	—	4	4	no	—
31	C₃₁×H(5,𝔽₂)	—	4	4	no	—
32	C₂×#41×C₃₁	—	2	4	no	—
33	C₂×#41×C₃₁	—	2	2	no	—
34	C₂²×D₄×C₃₁	—	2	4	no	—
35	C₂²×D₄×C₃₁	—	2	4	no	—
36	C₂²×D₄×C₃₁	C₂×C₄	1	4	yes	complemented
37	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₃₁	—	2	2	no	—
39	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₃₁	—	2	4	no	—
41	C₃₁×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
42	C₃₁×#127	C₂×C₄	1	2	yes	complemented
43	C₃₁×#124	—	2	2	no	—
44	C₃₁×#123	—	2	8	no	—
45	C₃₁×C₂²⋊Q₈	—	2	4	no	—
46	C₃₁×#121	—	2	4	no	—
47	C₃₁×#121	—	2	4	no	—
48	C₃₁×#121	—	2	2	no	—
49	C₃₁×#121	—	2	4	no	—
50	C₃₁×#121	C₂×C₄	1	8	yes	complemented
51	C₃₁×#121	C₂³	1	4	yes	—
52	C₃₁×#120	—	2	8	no	—
53	C₄×D₄×C₃₁	—	2	2	no	—
54	C₄×D₄×C₃₁	—	4	4	no	—
55	C₄×D₄×C₃₁	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₃₁	C₂×C₄	1	4	yes	complemented
57	C₄×D₄×C₃₁	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	complemented
62	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
66	C₂×C₄²×C₃₁	—	2	1	no	—
67	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
68	C₃₁×C₄⋊C₈	—	2	2	no	—
69	C₃₁×C₂²⋊C₈	—	2	4	no	—
70	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
71	C₄×C₈×C₃₁	—	2	2	no	—
72	C₃₁×#95	—	2	2	no	—
73	C₃₁×#95	—	2	1	no	—
74	C₃₁×#95	C₂³	1	1	yes	characteristic
75	C₃₁×#95	C₂³	1	2	yes	—
76	C₃₁×#95	C₂³	1	1	yes	characteristic
77	C₂⁴×C₃₁	—	2	4	no	—
78	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
79	#41×C₃₁	—	4	16	no	—
80	#41×C₃₁	—	4	4	no	—
81	#41×C₃₁	—	4	4	no	—
82	C₂×Q₈×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	8	no	—
84	C₂×D₄×C₃₁	—	2	4	no	—
85	C₂×D₄×C₃₁	—	2	2	no	—
86	C₂×D₄×C₃₁	—	2	2	no	—
87	C₂×D₄×C₃₁	—	2	4	no	—
88	C₂×D₄×C₃₁	—	4	8	no	—
89	C₂×D₄×C₃₁	—	4	8	no	—
90	C₂×D₄×C₃₁	—	4	16	no	—
91	C₂×D₄×C₃₁	—	8	4	no	—
92	C₂×D₄×C₃₁	C₂²⋊C₄	1	4	yes	—
93	C₂×D₄×C₃₁	D₈	1	4	yes	—
94	C₂×D₄×C₃₁	SD₁₆	1	4	yes	—
95	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	—	2	1	no	—
98	C₂²×C₄×C₃₁	—	2	4	no	—
99	C₂²×C₄×C₃₁	—	2	2	no	—
100	C₂²×C₄×C₃₁	—	2	1	no	—
101	C₂²×C₄×C₃₁	—	4	4	no	—
102	C₂²×C₄×C₃₁	—	4	4	no	—
103	C₂²×C₄×C₃₁	—	8	2	no	—
104	C₂²×C₄×C₃₁	—	8	2	no	—
105	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₃₁	—	2	4	no	—
112	C₂×C₈×C₃₁	—	8	4	no	—
113	C₄⋊C₄×C₃₁	—	2	4	no	—
114	C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₄⋊C₄×C₃₁	—	4	2	no	—
116	C₄⋊C₄×C₃₁	—	4	2	no	—
117	C₄⋊C₄×C₃₁	—	8	2	no	—
118	C₄⋊C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
119	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₃₁	—	2	8	no	—
121	C₂²⋊C₄×C₃₁	—	2	4	no	—
122	C₂²⋊C₄×C₃₁	—	2	4	no	—
123	C₂²⋊C₄×C₃₁	—	4	4	no	—
124	C₂²⋊C₄×C₃₁	C₂²⋊C₄	1	8	yes	—
125	C₄²×C₃₁	—	4	2	no	—
126	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
127	C₄²×C₃₁	C₂×D₄	1	2	yes	—
128	#17613	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₃₁	—	2	4	no	—
130	C₂³×C₃₁	—	4	2	no	—
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	8	no	—
133	C₂³×C₃₁	—	8	4	no	—
134	C₂³×C₃₁	—	8	4	no	—
135	C₂³×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
136	C₂³×C₃₁	C₂×D₈	1	4	yes	—
137	C₂³×C₃₁	C₂×SD₁₆	1	4	yes	—
138	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₃₁	—	4	4	no	—
140	D₄×C₃₁	—	4	4	no	—
141	D₄×C₃₁	—	4	4	no	—
142	D₄×C₃₁	—	4	4	no	—
143	D₄×C₃₁	—	4	16	no	—
144	D₄×C₃₁	—	4	4	no	—
145	D₄×C₃₁	—	8	2	no	—
146	D₄×C₃₁	—	8	4	no	—
147	D₄×C₃₁	#102	1	16	yes	—
148	C₂×C₄×C₃₁	—	2	2	no	—
149	C₂×C₄×C₃₁	—	2	4	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	4	no	—
153	C₂×C₄×C₃₁	—	4	1	no	—
154	C₂×C₄×C₃₁	—	4	4	no	—
155	C₂×C₄×C₃₁	—	4	1	no	—
156	C₂×C₄×C₃₁	—	4	1	no	—
157	C₂×C₄×C₃₁	—	4	8	no	—
158	C₂×C₄×C₃₁	—	4	8	no	—
159	C₂×C₄×C₃₁	—	4	1	no	—
160	C₂×C₄×C₃₁	—	4	1	no	—
161	C₂×C₄×C₃₁	—	4	2	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	4	1	no	—
164	C₂×C₄×C₃₁	—	4	2	no	—
165	C₂×C₄×C₃₁	—	8	8	no	—
166	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
170	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
171	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₈×C₃₁	—	4	4	no	—
174	#3496	C₂×C₃₁	1	1	yes	characteristic
175	#2972	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2349	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#1519	C₂×C₃₁	1	4	yes	complemented
178	#1517	C₂×C₃₁	1	2	yes	complemented
179	#1502	C₂×C₃₁	1	2	yes	complemented
180	C₂×#327	C₂×C₃₁	1	4	yes	complemented
181	C₂²×C₃₁	—	2	1	no	—
182	C₂²×C₃₁	—	2	4	no	—
183	C₂²×C₃₁	—	2	1	no	—
184	C₂²×C₃₁	—	2	4	no	—
185	C₂²×C₃₁	—	4	4	no	—
186	C₂²×C₃₁	—	4	4	no	—
187	C₂²×C₃₁	—	4	4	no	—
188	C₂²×C₃₁	—	4	4	no	—
189	C₂²×C₃₁	—	4	4	no	—
190	C₂²×C₃₁	—	16	8	no	—
191	C₂²×C₃₁	C₂×#102	1	8	yes	—
192	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
194	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
195	C₄×C₃₁	—	2	1	no	—
196	C₄×C₃₁	—	2	1	no	—
197	C₄×C₃₁	—	2	4	no	—
198	C₄×C₃₁	—	2	2	no	—
199	C₄×C₃₁	—	4	2	no	—
200	C₄×C₃₁	—	4	4	no	—
201	C₄×C₃₁	—	8	1	no	—
202	C₄×C₃₁	—	8	2	no	—
203	C₄×C₃₁	C₂×#102	1	4	yes	—
204	C₂×H(5,𝔽₂)	—	2	1	no	—
205	#547	C₄×C₃₁	1	4	yes	complemented
206	#546	—	2	4	no	—
207	D₄²	C₄×C₃₁	1	4	yes	complemented
208	#537	—	2	1	no	—
209	#534	—	2	2	no	—
210	#532	C₂²×C₃₁	1	2	yes	—
211	C₂×#121	C₂²×C₃₁	1	4	yes	—
212	C₂×C₄×D₄	—	2	1	no	—
213	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
214	C₈×D₄	—	2	4	no	—
215	#431	C₂²×C₃₁	1	2	yes	complemented
216	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	complemented
217	#389	—	2	1	no	—
218	#385	—	2	2	no	—
219	#382	C₂²×C₃₁	1	1	yes	characteristic, complemented
220	#380	C₂²×C₃₁	1	2	yes	complemented
221	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
222	C₂×#95	C₂²×C₃₁	1	2	yes	complemented
223	#327	C₂²×C₃₁	1	4	yes	complemented
224	#327	C₂²×C₃₁	1	8	yes	complemented
225	#327	C₂²×C₃₁	1	4	yes	complemented
226	C₂×C₃₁	—	2	1	no	—
227	C₂×C₃₁	—	2	1	no	—
228	C₂×C₃₁	—	2	8	no	—
229	C₂×C₃₁	—	8	4	no	—
230	C₂×C₃₁	#2883	1	1	yes	characteristic
231	C₂×C₃₁	C₂²×#102	1	1	yes	characteristic
232	C₂×C₃₁	#2901	1	1	yes	characteristic
233	H(5,𝔽₂)	—	4	4	no	—
234	H(5,𝔽₂)	—	4	4	no	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	—	2	2	no	—
237	C₂²×D₄	—	2	4	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	C₂×C₄×C₃₁	1	4	yes	complemented
240	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
243	C₂²×C₈	—	2	4	no	—
244	C₄⋊Q₈	C₂×C₄×C₃₁	1	2	yes	complemented
245	#127	C₂×C₄×C₃₁	1	2	yes	complemented
246	#124	—	2	2	no	—
247	#123	—	2	8	no	—
248	C₂²⋊Q₈	—	2	4	no	—
249	#121	—	2	4	no	—
250	#121	—	2	4	no	—
251	#121	—	2	2	no	—
252	#121	—	2	4	no	—
253	#121	C₂×C₄×C₃₁	1	8	yes	complemented
254	#121	C₂³×C₃₁	1	4	yes	—
255	#120	—	2	8	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	4	4	no	—
258	C₄×D₄	C₂×C₄×C₃₁	1	4	yes	—
259	C₄×D₄	C₂×C₄×C₃₁	1	4	yes	complemented
260	C₄×D₄	D₄×C₃₁	1	4	yes	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	complemented
265	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
271	C₄⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	4	no	—
273	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
274	C₄×C₈	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	1	no	—
277	#95	C₂³×C₃₁	1	1	yes	characteristic
278	#95	C₂³×C₃₁	1	2	yes	—
279	#95	C₂³×C₃₁	1	1	yes	characteristic
280	C₃₁	#17613	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴	—	2	4	no	—
282	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
283	#41	—	4	16	no	—
284	#41	—	4	4	no	—
285	#41	—	4	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	16	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	C₂²⋊C₄×C₃₁	1	4	yes	—
297	C₂×D₄	D₈×C₃₁	1	4	yes	—
298	C₂×D₄	SD₁₆×C₃₁	1	4	yes	—
299	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	8	2	no	—
308	C₂²×C₄	—	8	2	no	—
309	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
313	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	8	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	8	2	no	—
322	C₄⋊C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
323	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	C₂²⋊C₄×C₃₁	1	8	yes	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
331	C₄²	C₂×D₄×C₃₁	1	2	yes	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	8	4	no	—
337	C₂³	—	8	4	no	—
338	C₂³	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
339	C₂³	C₂×D₈×C₃₁	1	4	yes	—
340	C₂³	C₂×SD₁₆×C₃₁	1	4	yes	—
341	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
342	Q₈	—	4	4	no	—
343	D₄	—	4	4	no	—
344	D₄	—	4	16	no	—
345	D₄	—	4	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	4	no	—
350	D₄	C₃₁×#102	1	16	yes	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
372	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
373	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	16	8	no	—
387	C₂²	C₂×C₃₁×#102	1	8	yes	—
388	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
389	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
390	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	C₂×C₃₁×#102	1	4	yes	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	8	no	—
403	C₂	—	8	4	no	—
404	C₂	C₃₁×#2883	1	1	yes	characteristic
405	C₂	C₂²×C₃₁×#102	1	1	yes	characteristic
406	C₂	C₃₁×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₃₁×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2972	C₂	semidirect
3. C₃₁×#2349	C₂	semidirect
4. C₃₁×#1519	C₂	semidirect
5. C₃₁×#1517	C₂	semidirect
6. C₃₁×#1502	C₂	semidirect
7. C₂×C₃₁×#327	C₂	semidirect
9. C₃₁×#547	C₄	semidirect
11. D₄²×C₃₁	C₄	semidirect
19. C₃₁×#431	C₂²	semidirect
20. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
23. C₃₁×#382	C₂²	semidirect
24. C₃₁×#380	C₂²	semidirect
25. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
26. C₂×C₃₁×#95	C₂²	semidirect
27. C₃₁×#327	C₂²	semidirect
28. C₃₁×#327	C₂²	semidirect
29. C₃₁×#327	C₂²	semidirect
36. C₂²×D₄×C₃₁	C₂×C₄	semidirect
41. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
42. C₃₁×#127	C₂×C₄	semidirect
50. C₃₁×#121	C₂×C₄	semidirect
56. C₄×D₄×C₃₁	C₂×C₄	semidirect
61. C₂×C₄⋊C₄×C₃₁	C₂×C₄	semidirect
128. #17613	C₃₁	direct (N × H)
175. #2972	C₂×C₃₁	semidirect
176. #2349	C₂×C₃₁	semidirect
177. #1519	C₂×C₃₁	semidirect
178. #1517	C₂×C₃₁	semidirect
179. #1502	C₂×C₃₁	semidirect
180. C₂×#327	C₂×C₃₁	semidirect
205. #547	C₄×C₃₁	semidirect
207. D₄²	C₄×C₃₁	semidirect
215. #431	C₂²×C₃₁	semidirect
216. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
219. #382	C₂²×C₃₁	semidirect
220. #380	C₂²×C₃₁	semidirect
221. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
222. C₂×#95	C₂²×C₃₁	semidirect
223. #327	C₂²×C₃₁	semidirect
224. #327	C₂²×C₃₁	semidirect
225. #327	C₂²×C₃₁	semidirect
239. C₂²×D₄	C₂×C₄×C₃₁	semidirect
244. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
245. #127	C₂×C₄×C₃₁	semidirect
253. #121	C₂×C₄×C₃₁	semidirect
259. C₄×D₄	C₂×C₄×C₃₁	semidirect
264. C₂×C₄⋊C₄	C₂×C₄×C₃₁	semidirect
280. C₃₁	#17613	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3496	2
C₃₁×#2972	2
C₃₁×#2349	2
C₃₁×#1519	2
C₃₁×#1517	2
C₃₁×#1502	2
C₂×C₃₁×#327	2
#17613	31

Subgroups — C31×#17613 #21474372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17613 #21474372