Subgroups — C₃₁×#25630 #21482389

Order 7936.

1186 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#460	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2548	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2013	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1880	C₂	1	4	yes	maximal, complemented
9	C₄×C₃₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	—
11	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
12	C₃₁×#557	—	2	4	no	—
13	C₃₁×#557	—	2	4	no	—
14	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#125	—	2	1	no	—
18	C₂×C₃₁×#125	—	2	2	no	—
19	C₂×C₃₁×#124	—	2	1	no	—
20	C₂×C₄×Q₈×C₃₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#492	—	2	4	no	—
25	C₃₁×#460	—	2	4	no	—
26	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#103	C₂²	1	2	yes	—
28	C₂×C₃₁×#103	C₂²	1	4	yes	—
29	C₂×C₃₁×#102	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
31	C₃₁×#394	—	2	2	no	—
32	C₃₁×#390	—	2	1	no	—
33	C₃₁×#390	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₃₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₃₁	—	2	1	no	—
41	C₂²×D₄×C₃₁	—	2	1	no	—
42	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
43	C₂×SD₁₆×C₃₁	—	2	4	no	—
44	C₂×SD₁₆×C₃₁	—	2	8	no	—
45	C₂×SD₁₆×C₃₁	—	2	8	no	—
46	C₂×SD₁₆×C₃₁	—	4	4	no	—
47	C₂×SD₁₆×C₃₁	—	4	4	no	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
50	C₃₁×C₄⋊Q₈	—	2	4	no	—
51	C₃₁×C₄⋊Q₈	—	2	4	no	—
52	C₃₁×C₄⋊Q₈	—	2	2	no	—
53	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
54	C₃₁×#127	—	2	2	no	—
55	C₃₁×#127	—	2	2	no	—
56	C₃₁×#125	—	2	16	no	—
57	C₃₁×#125	—	2	8	no	—
58	C₃₁×#124	—	4	4	no	—
59	C₄×Q₈×C₃₁	—	2	8	no	—
60	C₄×Q₈×C₃₁	—	2	4	no	—
61	C₄×Q₈×C₃₁	—	2	4	no	—
62	C₄×Q₈×C₃₁	—	2	2	no	—
63	C₄×Q₈×C₃₁	—	2	2	no	—
64	C₄×Q₈×C₃₁	—	2	2	no	—
65	C₄×Q₈×C₃₁	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
78	C₂×C₄²×C₃₁	—	2	2	no	—
79	C₂×C₄²×C₃₁	—	2	1	no	—
80	C₂×C₄²×C₃₁	—	2	1	no	—
81	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
83	C₃₁×C₄⋊C₈	—	2	2	no	—
84	C₃₁×#103	—	2	4	no	—
85	C₃₁×#103	—	4	4	no	—
86	C₃₁×#102	—	2	4	no	—
87	C₄×C₈×C₃₁	—	2	2	no	—
88	C₃₁×#95	—	2	1	no	—
89	C₂⁴×C₃₁	—	2	2	no	—
90	C₂×Q₈×C₃₁	—	2	2	no	—
91	C₂×Q₈×C₃₁	—	2	2	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	2	1	no	—
94	C₂×Q₈×C₃₁	—	2	2	no	—
95	C₂×Q₈×C₃₁	—	2	4	no	—
96	C₂×Q₈×C₃₁	—	2	4	no	—
97	C₂×Q₈×C₃₁	—	2	2	no	—
98	C₂×Q₈×C₃₁	SD₁₆	1	4	yes	complemented
99	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
100	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₃₁	—	2	2	no	—
102	C₂×D₄×C₃₁	—	2	2	no	—
103	C₂×D₄×C₃₁	—	2	4	no	—
104	C₂×D₄×C₃₁	—	2	4	no	—
105	C₂×D₄×C₃₁	—	4	2	no	—
106	C₂×D₄×C₃₁	—	4	2	no	—
107	C₂×D₄×C₃₁	—	4	2	no	—
108	C₂×D₄×C₃₁	—	4	2	no	—
109	C₂×D₄×C₃₁	—	8	2	no	—
110	C₂²×C₄×C₃₁	—	2	1	no	—
111	C₂²×C₄×C₃₁	—	2	2	no	—
112	C₂²×C₄×C₃₁	—	2	1	no	—
113	C₂²×C₄×C₃₁	—	2	2	no	—
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	2	yes	—
117	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₃₁	—	4	16	no	—
120	SD₁₆×C₃₁	—	4	8	no	—
121	C₂×C₈×C₃₁	—	2	2	no	—
122	C₂×C₈×C₃₁	—	2	2	no	—
123	C₂×C₈×C₃₁	—	2	2	no	—
124	C₂×C₈×C₃₁	—	2	4	no	—
125	C₂×C₈×C₃₁	#41	1	4	yes	—
126	C₄⋊C₄×C₃₁	—	2	8	no	—
127	C₄⋊C₄×C₃₁	—	2	8	no	—
128	C₄⋊C₄×C₃₁	—	2	8	no	—
129	C₄⋊C₄×C₃₁	—	2	4	no	—
130	C₄⋊C₄×C₃₁	—	2	4	no	—
131	C₄⋊C₄×C₃₁	—	2	4	no	—
132	C₄⋊C₄×C₃₁	—	2	4	no	—
133	C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₄⋊C₄×C₃₁	—	2	1	no	—
135	C₄⋊C₄×C₃₁	—	2	2	no	—
136	C₄⋊C₄×C₃₁	—	2	2	no	—
137	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₃₁	—	4	8	no	—
139	C₂²⋊C₄×C₃₁	—	8	4	no	—
140	C₄²×C₃₁	—	2	8	no	—
141	C₄²×C₃₁	—	2	4	no	—
142	C₄²×C₃₁	—	2	2	no	—
143	C₄²×C₃₁	—	2	2	no	—
144	C₄²×C₃₁	—	4	2	no	—
145	C₄²×C₃₁	C₂×D₄	1	2	yes	—
146	C₄²×C₃₁	C₂×D₄	1	2	yes	—
147	#25630	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₃₁	—	4	2	no	—
149	C₂³×C₃₁	—	4	4	no	—
150	C₂³×C₃₁	—	4	2	no	—
151	C₂³×C₃₁	—	4	2	no	—
152	C₂³×C₃₁	—	4	4	no	—
153	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₃₁	—	2	8	no	—
155	Q₈×C₃₁	—	2	2	no	—
156	Q₈×C₃₁	—	2	2	no	—
157	Q₈×C₃₁	—	2	8	no	—
158	Q₈×C₃₁	—	4	2	no	—
159	Q₈×C₃₁	—	4	2	no	—
160	Q₈×C₃₁	—	4	2	no	—
161	D₄×C₃₁	—	4	2	no	—
162	D₄×C₃₁	—	4	2	no	—
163	D₄×C₃₁	—	4	4	no	—
164	D₄×C₃₁	—	8	4	no	—
165	D₄×C₃₁	—	8	4	no	—
166	C₂×C₄×C₃₁	—	2	2	no	—
167	C₂×C₄×C₃₁	—	2	2	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	2	no	—
171	C₂×C₄×C₃₁	—	2	4	no	—
172	C₂×C₄×C₃₁	—	2	2	no	—
173	C₂×C₄×C₃₁	—	2	4	no	—
174	C₂×C₄×C₃₁	—	4	2	no	—
175	C₂×C₄×C₃₁	—	4	4	no	—
176	C₂×C₄×C₃₁	—	4	2	no	—
177	C₂×C₄×C₃₁	—	4	2	no	—
178	C₂×C₄×C₃₁	—	4	2	no	—
179	C₂×C₄×C₃₁	—	4	2	no	—
180	C₂×C₄×C₃₁	#120	1	2	yes	—
181	C₂×C₄×C₃₁	#120	1	2	yes	—
182	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
183	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
184	C₂×C₄×C₃₁	#137	1	2	yes	—
185	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
188	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
189	C₈×C₃₁	—	2	4	no	—
190	C₈×C₃₁	—	4	2	no	—
191	C₂×#557	C₂×C₃₁	1	1	yes	characteristic, complemented
192	C₂×#492	C₂×C₃₁	1	1	yes	characteristic
193	C₂×#460	C₂×C₃₁	1	1	yes	characteristic
194	#2548	C₂×C₃₁	1	1	yes	characteristic
195	#2013	C₂×C₃₁	1	4	yes	complemented
196	#1984	C₂×C₃₁	1	1	yes	characteristic, complemented
197	#1981	C₂×C₃₁	1	1	yes	characteristic, complemented
198	#1880	C₂×C₃₁	1	4	yes	complemented
199	C₄×#103	C₂×C₃₁	1	1	yes	characteristic, complemented
200	C₂²×C₃₁	—	8	4	no	—
201	C₂²×C₃₁	—	8	4	no	—
202	C₂²×C₃₁	—	8	2	no	—
203	C₂²×C₃₁	—	8	2	no	—
204	C₂²×C₃₁	—	8	2	no	—
205	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
206	C₂²×C₃₁	#550	1	2	yes	—
207	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
208	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
209	C₂²×C₃₁	#577	1	2	yes	—
210	C₄×C₃₁	—	2	4	no	—
211	C₄×C₃₁	—	2	2	no	—
212	C₄×C₃₁	—	4	2	no	—
213	C₄×C₃₁	—	4	4	no	—
214	C₄×C₃₁	—	4	2	no	—
215	C₄×C₃₁	—	4	2	no	—
216	C₄×C₃₁	—	8	2	no	—
217	C₄×C₃₁	#448	1	4	yes	—
218	C₄×C₃₁	#532	1	1	yes	characteristic
219	C₄×C₃₁	#535	1	1	yes	characteristic
220	C₄×C₃₁	#546	1	2	yes	—
221	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	—
222	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
223	#557	—	2	4	no	—
224	#557	—	2	4	no	—
225	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
226	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
227	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
228	C₂×#125	—	2	1	no	—
229	C₂×#125	—	2	2	no	—
230	C₂×#124	—	2	1	no	—
231	C₂×C₄×Q₈	—	2	1	no	—
232	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
233	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
235	#492	—	2	4	no	—
236	#460	—	2	4	no	—
237	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
238	C₂×#103	C₂²×C₃₁	1	2	yes	—
239	C₂×#103	C₂²×C₃₁	1	4	yes	—
240	C₂×#102	C₂²×C₃₁	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
242	#394	—	2	2	no	—
243	#390	—	2	1	no	—
244	#390	C₂²×C₃₁	1	4	yes	—
245	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
246	#340	C₂²×C₃₁	1	2	yes	—
247	#336	C₂²×C₃₁	1	4	yes	—
248	C₂×C₃₁	—	16	2	no	—
249	C₂×C₃₁	#2431	1	1	yes	characteristic
250	C₂×C₃₁	C₂×#448	1	1	yes	characteristic
251	C₂×C₃₁	#3010	1	1	yes	characteristic
252	C₂×C₃₁	#3392	1	2	yes	—
253	C₂×C₃₁	#3400	1	2	yes	—
254	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
255	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
260	C₂×SD₁₆	—	2	4	no	—
261	C₂×SD₁₆	—	2	8	no	—
262	C₂×SD₁₆	—	2	8	no	—
263	C₂×SD₁₆	—	4	4	no	—
264	C₂×SD₁₆	—	4	4	no	—
265	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
266	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	—	2	4	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
271	#127	—	2	2	no	—
272	#127	—	2	2	no	—
273	#125	—	2	16	no	—
274	#125	—	2	8	no	—
275	#124	—	4	4	no	—
276	C₄×Q₈	—	2	8	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	2	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	D₄×C₃₁	1	4	yes	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	4	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
299	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
300	C₄⋊C₈	—	2	2	no	—
301	#103	—	2	4	no	—
302	#103	—	4	4	no	—
303	#102	—	2	4	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	1	no	—
306	C₃₁	#25630	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁴	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	SD₁₆×C₃₁	1	4	yes	complemented
317	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
318	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
337	SD₁₆	—	4	16	no	—
338	SD₁₆	—	4	8	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	4	no	—
343	C₂×C₈	#41×C₃₁	1	4	yes	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
356	C₂²⋊C₄	—	4	8	no	—
357	C₂²⋊C₄	—	8	4	no	—
358	C₄²	—	2	8	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	4	2	no	—
363	C₄²	C₂×D₄×C₃₁	1	2	yes	—
364	C₄²	C₂×D₄×C₃₁	1	2	yes	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	4	no	—
370	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	Q₈	—	2	8	no	—
372	Q₈	—	2	2	no	—
373	Q₈	—	2	2	no	—
374	Q₈	—	2	8	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	8	4	no	—
382	D₄	—	8	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	C₃₁×#120	1	2	yes	—
398	C₂×C₄	C₃₁×#120	1	2	yes	—
399	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
400	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
401	C₂×C₄	C₃₁×#137	1	2	yes	—
402	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
404	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
405	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
406	C₈	—	2	4	no	—
407	C₈	—	4	2	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
414	C₂²	C₃₁×#550	1	2	yes	—
415	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
416	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
417	C₂²	C₃₁×#577	1	2	yes	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₃₁×#448	1	4	yes	—
426	C₄	C₃₁×#532	1	1	yes	characteristic
427	C₄	C₃₁×#535	1	1	yes	characteristic
428	C₄	C₃₁×#546	1	2	yes	—
429	C₂	—	16	2	no	—
430	C₂	C₃₁×#2431	1	1	yes	characteristic
431	C₂	C₂×C₃₁×#448	1	1	yes	characteristic
432	C₂	C₃₁×#3010	1	1	yes	characteristic
433	C₂	C₃₁×#3392	1	2	yes	—
434	C₂	C₃₁×#3400	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×Q₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#557	C₂	semidirect
5. C₃₁×#2013	C₂	semidirect
6. C₃₁×#1984	C₂	semidirect
7. C₃₁×#1981	C₂	semidirect
8. C₃₁×#1880	C₂	semidirect
9. C₄×C₃₁×#103	C₂	semidirect
98. C₂×Q₈×C₃₁	SD₁₆	semidirect
147. #25630	C₃₁	direct (N × H)
191. C₂×#557	C₂×C₃₁	semidirect
195. #2013	C₂×C₃₁	semidirect
196. #1984	C₂×C₃₁	semidirect
197. #1981	C₂×C₃₁	semidirect
198. #1880	C₂×C₃₁	semidirect
199. C₄×#103	C₂×C₃₁	semidirect
306. C₃₁	#25630	direct (N × H)
316. C₂×Q₈	SD₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#557	2
C₂×C₃₁×#492	2
C₂×C₃₁×#460	2
C₃₁×#2548	2
C₃₁×#2013	2
C₃₁×#1984	2
C₃₁×#1981	2
C₃₁×#1880	2
C₄×C₃₁×#103	2
#25630	31

Subgroups — C31×#25630 #21482389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25630 #21482389