Subgroups — C₃₁×#62244 #21519003

Order 7936.

1914 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3505	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3337	C₂	1	4	yes	maximal, complemented
3	C₃₁×#3300	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3297	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3282	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3191	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3189	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3186	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3168	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3050	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#465	C₂	1	2	yes	maximal, complemented
13	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
15	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
16	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
18	C₃₁×#553	—	2	4	no	—
19	C₃₁×#553	C₂²	1	4	yes	—
20	C₃₁×#552	C₂²	1	4	yes	complemented
21	C₃₁×#551	—	2	4	no	—
22	C₃₁×#548	C₂²	1	4	yes	—
23	C₃₁×#546	C₂²	1	4	yes	complemented
24	C₃₁×#539	—	2	2	no	—
25	C₃₁×#538	—	2	2	no	—
26	C₃₁×#534	—	2	2	no	—
27	C₃₁×#529	C₂²	1	4	yes	complemented
28	C₃₁×#525	C₂²	1	4	yes	complemented
29	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₃₁×#121	C₂²	1	2	yes	—
31	C₃₁×#518	—	2	2	no	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#499	C₂²	1	2	yes	complemented
34	C₃₁×#495	C₂²	1	2	yes	complemented
35	C₃₁×#488	C₂²	1	4	yes	complemented
36	C₃₁×#485	C₂²	1	4	yes	complemented
37	C₃₁×#484	C₂²	1	4	yes	complemented
38	C₃₁×#482	C₂²	1	4	yes	complemented
39	C₃₁×#480	C₂²	1	4	yes	complemented
40	C₃₁×#479	C₂²	1	4	yes	complemented
41	C₃₁×#478	C₂²	1	4	yes	complemented
42	C₃₁×#467	C₂²	1	2	yes	complemented
43	C₃₁×#467	C₂²	1	2	yes	complemented
44	C₃₁×#467	C₂²	1	2	yes	complemented
45	C₃₁×#466	C₂²	1	2	yes	—
46	C₃₁×#466	C₂²	1	2	yes	—
47	C₃₁×#466	C₂²	1	2	yes	complemented
48	C₃₁×#465	C₂²	1	4	yes	complemented
49	C₃₁×#465	C₂²	1	4	yes	complemented
50	C₃₁×#465	C₂²	1	4	yes	complemented
51	C₃₁×#465	C₂²	1	4	yes	complemented
52	C₃₁×#465	C₂²	1	4	yes	complemented
53	C₃₁×#464	C₂²	1	4	yes	complemented
54	C₃₁×#463	C₂²	1	4	yes	complemented
55	C₃₁×#452	C₂²	1	4	yes	complemented
56	C₃₁×#451	C₂²	1	4	yes	complemented
57	C₃₁×#449	C₂²	1	4	yes	complemented
58	C₃₁×#447	C₂²	1	4	yes	complemented
59	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
60	C₄×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
61	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
62	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
63	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
64	C₃₁×#427	C₂²	1	2	yes	complemented
65	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
66	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#416	C₂²	1	4	yes	complemented
68	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
69	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
70	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
73	C₂×#41×C₃₁	C₂³	1	4	yes	—
74	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
75	C₂²×D₄×C₃₁	—	2	2	no	—
76	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
77	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
78	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
80	C₃₁×#135	—	4	4	no	—
81	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
82	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
83	C₂×SD₁₆×C₃₁	—	4	4	no	—
84	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
85	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
86	C₂×D₈×C₃₁	C₂³	1	2	yes	—
87	C₂×D₈×C₃₁	C₂³	1	2	yes	—
88	C₂²×C₈×C₃₁	—	4	2	no	—
89	C₂²×C₈×C₃₁	—	4	2	no	—
90	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
97	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
98	C₃₁×#126	—	2	4	no	—
99	C₃₁×#126	—	2	4	no	—
100	C₃₁×#126	—	2	4	no	—
101	C₃₁×#125	—	2	4	no	—
102	C₃₁×#125	C₂³	1	4	yes	—
103	C₃₁×#124	—	2	4	no	—
104	C₃₁×#124	C₂³	1	4	yes	—
105	C₃₁×#123	—	2	4	no	—
106	C₃₁×#123	—	2	4	no	—
107	C₃₁×#123	—	2	4	no	—
108	C₃₁×#123	—	2	4	no	—
109	C₃₁×#123	—	2	4	no	—
110	C₃₁×C₂²⋊Q₈	—	2	2	no	—
111	C₃₁×C₂²⋊Q₈	—	2	2	no	—
112	C₃₁×C₂²⋊Q₈	—	2	4	no	—
113	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
114	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
116	C₃₁×#121	—	2	4	no	—
117	C₃₁×#121	—	2	4	no	—
118	C₃₁×#121	—	2	2	no	—
119	C₃₁×#121	—	2	2	no	—
120	C₃₁×#121	—	2	4	no	—
121	C₃₁×#121	C₂³	1	4	yes	—
122	C₃₁×#121	C₂³	1	4	yes	—
123	C₃₁×#121	C₂³	1	4	yes	—
124	C₃₁×#120	—	2	4	no	—
125	C₃₁×#120	—	2	4	no	—
126	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
127	C₄×D₄×C₃₁	—	2	4	no	—
128	C₄×D₄×C₃₁	—	2	4	no	—
129	C₄×D₄×C₃₁	—	2	4	no	—
130	C₄×D₄×C₃₁	—	2	4	no	—
131	C₄×D₄×C₃₁	—	2	4	no	—
132	C₄×D₄×C₃₁	D₄	1	4	yes	—
133	C₄×D₄×C₃₁	C₂³	1	4	yes	—
134	C₄×D₄×C₃₁	C₂³	1	4	yes	—
135	C₃₁×#117	—	2	4	no	—
136	C₃₁×#117	—	2	4	no	—
137	C₃₁×#117	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
139	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
148	C₃₁×#107	C₂³	1	2	yes	—
149	C₃₁×#107	C₂³	1	2	yes	—
150	C₃₁×#107	C₂³	1	2	yes	—
151	C₃₁×#107	C₂³	1	2	yes	—
152	C₃₁×#106	C₂³	1	4	yes	—
153	C₃₁×#106	C₂³	1	4	yes	—
154	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
155	C₃₁×#103	C₂³	1	4	yes	—
156	C₃₁×#103	C₂³	1	4	yes	—
157	C₃₁×#103	C₂³	1	4	yes	—
158	C₃₁×#103	C₂³	1	4	yes	—
159	C₃₁×#102	C₂³	1	4	yes	—
160	C₃₁×#102	C₂³	1	4	yes	—
161	C₃₁×#102	C₂³	1	4	yes	—
162	C₃₁×#102	C₂³	1	4	yes	—
163	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
165	C₄×C₈×C₃₁	C₂³	1	2	yes	—
166	C₄×C₈×C₃₁	C₂³	1	2	yes	—
167	C₂⁴×C₃₁	—	2	2	no	—
168	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
170	#41×C₃₁	—	4	4	no	—
171	#41×C₃₁	—	4	4	no	—
172	C₂×Q₈×C₃₁	—	2	2	no	—
173	C₂×Q₈×C₃₁	—	4	2	no	—
174	C₂×Q₈×C₃₁	—	4	2	no	—
175	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
176	C₂×D₄×C₃₁	—	2	4	no	—
177	C₂×D₄×C₃₁	—	2	4	no	—
178	C₂×D₄×C₃₁	—	2	4	no	—
179	C₂×D₄×C₃₁	—	2	4	no	—
180	C₂×D₄×C₃₁	—	2	4	no	—
181	C₂×D₄×C₃₁	—	2	2	no	—
182	C₂×D₄×C₃₁	—	4	2	no	—
183	C₂×D₄×C₃₁	—	4	2	no	—
184	C₂×D₄×C₃₁	—	4	8	no	—
185	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
186	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₃₁	—	2	2	no	—
188	C₂²×C₄×C₃₁	—	2	2	no	—
189	C₂²×C₄×C₃₁	—	2	2	no	—
190	C₂²×C₄×C₃₁	—	2	4	no	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	4	1	no	—
193	C₂²×C₄×C₃₁	—	4	1	no	—
194	C₂²×C₄×C₃₁	—	4	1	no	—
195	C₂²×C₄×C₃₁	—	4	1	no	—
196	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
205	Q₁₆×C₃₁	—	4	2	no	—
206	Q₁₆×C₃₁	—	4	2	no	—
207	SD₁₆×C₃₁	—	2	8	no	—
208	SD₁₆×C₃₁	—	4	4	no	—
209	D₈×C₃₁	—	4	2	no	—
210	D₈×C₃₁	—	4	2	no	—
211	C₂×C₈×C₃₁	—	2	2	no	—
212	C₂×C₈×C₃₁	—	2	4	no	—
213	C₂×C₈×C₃₁	—	2	4	no	—
214	C₂×C₈×C₃₁	—	4	2	no	—
215	C₂×C₈×C₃₁	—	4	2	no	—
216	C₂×C₈×C₃₁	—	4	1	no	—
217	C₂×C₈×C₃₁	—	4	1	no	—
218	C₂×C₈×C₃₁	—	4	1	no	—
219	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
220	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
222	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
223	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
224	C₄⋊C₄×C₃₁	—	2	4	no	—
225	C₄⋊C₄×C₃₁	—	2	4	no	—
226	C₄⋊C₄×C₃₁	—	2	2	no	—
227	C₄⋊C₄×C₃₁	—	2	2	no	—
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	2	4	no	—
230	C₄⋊C₄×C₃₁	—	2	4	no	—
231	C₄⋊C₄×C₃₁	—	2	4	no	—
232	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
235	C₂²⋊C₄×C₃₁	—	2	4	no	—
236	C₂²⋊C₄×C₃₁	—	2	4	no	—
237	C₂²⋊C₄×C₃₁	—	2	4	no	—
238	C₂²⋊C₄×C₃₁	—	2	4	no	—
239	C₂²⋊C₄×C₃₁	—	2	4	no	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	4	no	—
242	C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂²⋊C₄×C₃₁	—	2	4	no	—
244	C₂²⋊C₄×C₃₁	—	2	4	no	—
245	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
246	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
247	C₄²×C₃₁	—	2	4	no	—
248	C₄²×C₃₁	—	2	4	no	—
249	C₄²×C₃₁	C₂×D₄	1	2	yes	—
250	C₄²×C₃₁	C₂⁴	1	2	yes	—
251	#62244	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂³×C₃₁	—	2	2	no	—
253	C₂³×C₃₁	—	2	4	no	—
254	C₂³×C₃₁	—	4	1	no	—
255	C₂³×C₃₁	—	4	1	no	—
256	C₂³×C₃₁	—	4	1	no	—
257	C₂³×C₃₁	—	4	1	no	—
258	C₂³×C₃₁	—	4	4	no	—
259	C₂³×C₃₁	—	8	2	no	—
260	C₂³×C₃₁	—	8	2	no	—
261	C₂³×C₃₁	#135	1	4	yes	complemented
262	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
263	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
264	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
265	Q₈×C₃₁	—	2	4	no	—
266	Q₈×C₃₁	—	2	4	no	—
267	Q₈×C₃₁	—	8	2	no	—
268	D₄×C₃₁	—	2	8	no	—
269	D₄×C₃₁	—	2	4	no	—
270	D₄×C₃₁	—	2	4	no	—
271	D₄×C₃₁	—	4	8	no	—
272	D₄×C₃₁	—	4	8	no	—
273	D₄×C₃₁	—	8	2	no	—
274	D₄×C₃₁	—	8	4	no	—
275	D₄×C₃₁	—	8	4	no	—
276	C₂×C₄×C₃₁	—	2	2	no	—
277	C₂×C₄×C₃₁	—	2	1	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	1	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	4	no	—
284	C₂×C₄×C₃₁	—	2	4	no	—
285	C₂×C₄×C₃₁	—	2	4	no	—
286	C₂×C₄×C₃₁	—	4	2	no	—
287	C₂×C₄×C₃₁	—	4	2	no	—
288	C₂×C₄×C₃₁	—	4	1	no	—
289	C₂×C₄×C₃₁	—	4	1	no	—
290	C₂×C₄×C₃₁	—	4	1	no	—
291	C₂×C₄×C₃₁	—	4	4	no	—
292	C₂×C₄×C₃₁	—	8	4	no	—
293	C₂×C₄×C₃₁	—	8	4	no	—
294	C₂×C₄×C₃₁	—	8	2	no	—
295	C₂×C₄×C₃₁	—	8	2	no	—
296	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
298	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
300	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
302	C₈×C₃₁	—	2	1	no	—
303	C₈×C₃₁	—	2	2	no	—
304	C₈×C₃₁	—	2	2	no	—
305	C₈×C₃₁	—	2	2	no	—
306	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
307	#3505	C₂×C₃₁	1	2	yes	complemented
308	#3337	C₂×C₃₁	1	4	yes	complemented
309	#3300	C₂×C₃₁	1	4	yes	complemented
310	#3297	C₂×C₃₁	1	4	yes	complemented
311	#3282	C₂×C₃₁	1	4	yes	complemented
312	#3250	C₂×C₃₁	1	2	yes	complemented
313	#3191	C₂×C₃₁	1	2	yes	complemented
314	#3189	C₂×C₃₁	1	1	yes	characteristic, complemented
315	#3186	C₂×C₃₁	1	1	yes	characteristic, complemented
316	#3168	C₂×C₃₁	1	2	yes	complemented
317	#3050	C₂×C₃₁	1	2	yes	complemented
318	C₂×#465	C₂×C₃₁	1	2	yes	complemented
319	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
320	C₂²×C₃₁	—	2	1	no	—
321	C₂²×C₃₁	—	2	2	no	—
322	C₂²×C₃₁	—	2	1	no	—
323	C₂²×C₃₁	—	2	2	no	—
324	C₂²×C₃₁	—	2	2	no	—
325	C₂²×C₃₁	—	2	2	no	—
326	C₂²×C₃₁	—	2	2	no	—
327	C₂²×C₃₁	—	4	4	no	—
328	C₂²×C₃₁	—	4	4	no	—
329	C₂²×C₃₁	—	4	4	no	—
330	C₂²×C₃₁	—	4	4	no	—
331	C₂²×C₃₁	—	4	4	no	—
332	C₂²×C₃₁	—	16	4	no	—
333	C₂²×C₃₁	C₂×#135	1	2	yes	—
334	C₂²×C₃₁	C₂×#135	1	4	yes	—
335	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₃₁	—	2	2	no	—
337	C₄×C₃₁	—	2	1	no	—
338	C₄×C₃₁	—	2	2	no	—
339	C₄×C₃₁	—	2	2	no	—
340	C₄×C₃₁	—	2	2	no	—
341	C₄×C₃₁	—	4	4	no	—
342	C₄×C₃₁	—	4	4	no	—
343	C₄×C₃₁	—	4	4	no	—
344	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₄×C₃₁	#585	1	1	yes	characteristic
346	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
347	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
348	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
349	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
350	#553	—	2	4	no	—
351	#553	C₂²×C₃₁	1	4	yes	—
352	#552	C₂²×C₃₁	1	4	yes	complemented
353	#551	—	2	4	no	—
354	#548	C₂²×C₃₁	1	4	yes	—
355	#546	C₂²×C₃₁	1	4	yes	complemented
356	#539	—	2	2	no	—
357	#538	—	2	2	no	—
358	#534	—	2	2	no	—
359	#529	C₂²×C₃₁	1	4	yes	complemented
360	#525	C₂²×C₃₁	1	4	yes	complemented
361	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
362	C₂×#121	C₂²×C₃₁	1	2	yes	—
363	#518	—	2	2	no	—
364	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
365	#499	C₂²×C₃₁	1	2	yes	complemented
366	#495	C₂²×C₃₁	1	2	yes	complemented
367	#488	C₂²×C₃₁	1	4	yes	complemented
368	#485	C₂²×C₃₁	1	4	yes	complemented
369	#484	C₂²×C₃₁	1	4	yes	complemented
370	#482	C₂²×C₃₁	1	4	yes	complemented
371	#480	C₂²×C₃₁	1	4	yes	complemented
372	#479	C₂²×C₃₁	1	4	yes	complemented
373	#478	C₂²×C₃₁	1	4	yes	complemented
374	#467	C₂²×C₃₁	1	2	yes	complemented
375	#467	C₂²×C₃₁	1	2	yes	complemented
376	#467	C₂²×C₃₁	1	2	yes	complemented
377	#466	C₂²×C₃₁	1	2	yes	—
378	#466	C₂²×C₃₁	1	2	yes	—
379	#466	C₂²×C₃₁	1	2	yes	complemented
380	#465	C₂²×C₃₁	1	4	yes	complemented
381	#465	C₂²×C₃₁	1	4	yes	complemented
382	#465	C₂²×C₃₁	1	4	yes	complemented
383	#465	C₂²×C₃₁	1	4	yes	complemented
384	#465	C₂²×C₃₁	1	4	yes	complemented
385	#464	C₂²×C₃₁	1	4	yes	complemented
386	#463	C₂²×C₃₁	1	4	yes	complemented
387	#452	C₂²×C₃₁	1	4	yes	complemented
388	#451	C₂²×C₃₁	1	4	yes	complemented
389	#449	C₂²×C₃₁	1	4	yes	complemented
390	#447	C₂²×C₃₁	1	4	yes	complemented
391	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
392	C₄×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
393	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
394	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
395	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
396	#427	C₂²×C₃₁	1	2	yes	complemented
397	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
398	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
399	#416	C₂²×C₃₁	1	4	yes	complemented
400	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
401	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
402	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
403	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
404	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	C₂×C₃₁	—	2	2	no	—
406	C₂×C₃₁	—	2	4	no	—
407	C₂×C₃₁	—	4	2	no	—
408	C₂×C₃₁	—	8	4	no	—
409	C₂×C₃₁	#3496	1	1	yes	characteristic
410	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
411	C₂×C₃₁	#3584	1	1	yes	characteristic
412	C₂×#41	C₂³×C₃₁	1	4	yes	—
413	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
417	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
419	#135	—	4	4	no	—
420	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
421	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
422	C₂×SD₁₆	—	4	4	no	—
423	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
424	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
425	C₂×D₈	C₂³×C₃₁	1	2	yes	—
426	C₂×D₈	C₂³×C₃₁	1	2	yes	—
427	C₂²×C₈	—	4	2	no	—
428	C₂²×C₈	—	4	2	no	—
429	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
431	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
432	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
434	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
436	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
437	#126	—	2	4	no	—
438	#126	—	2	4	no	—
439	#126	—	2	4	no	—
440	#125	—	2	4	no	—
441	#125	C₂³×C₃₁	1	4	yes	—
442	#124	—	2	4	no	—
443	#124	C₂³×C₃₁	1	4	yes	—
444	#123	—	2	4	no	—
445	#123	—	2	4	no	—
446	#123	—	2	4	no	—
447	#123	—	2	4	no	—
448	#123	—	2	4	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	—	2	4	no	—
452	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
453	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
454	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
455	#121	—	2	4	no	—
456	#121	—	2	4	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	—	2	4	no	—
460	#121	C₂³×C₃₁	1	4	yes	—
461	#121	C₂³×C₃₁	1	4	yes	—
462	#121	C₂³×C₃₁	1	4	yes	—
463	#120	—	2	4	no	—
464	#120	—	2	4	no	—
465	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
466	C₄×D₄	—	2	4	no	—
467	C₄×D₄	—	2	4	no	—
468	C₄×D₄	—	2	4	no	—
469	C₄×D₄	—	2	4	no	—
470	C₄×D₄	—	2	4	no	—
471	C₄×D₄	D₄×C₃₁	1	4	yes	—
472	C₄×D₄	C₂³×C₃₁	1	4	yes	—
473	C₄×D₄	C₂³×C₃₁	1	4	yes	—
474	#117	—	2	4	no	—
475	#117	—	2	4	no	—
476	#117	C₂³×C₃₁	1	4	yes	—
477	C₂×C₄⋊C₄	—	2	2	no	—
478	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
481	C₂×C₂²⋊C₄	—	2	2	no	—
482	C₂×C₂²⋊C₄	—	2	2	no	—
483	C₂×C₂²⋊C₄	—	2	4	no	—
484	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
486	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
487	#107	C₂³×C₃₁	1	2	yes	—
488	#107	C₂³×C₃₁	1	2	yes	—
489	#107	C₂³×C₃₁	1	2	yes	—
490	#107	C₂³×C₃₁	1	2	yes	—
491	#106	C₂³×C₃₁	1	4	yes	—
492	#106	C₂³×C₃₁	1	4	yes	—
493	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
494	#103	C₂³×C₃₁	1	4	yes	—
495	#103	C₂³×C₃₁	1	4	yes	—
496	#103	C₂³×C₃₁	1	4	yes	—
497	#103	C₂³×C₃₁	1	4	yes	—
498	#102	C₂³×C₃₁	1	4	yes	—
499	#102	C₂³×C₃₁	1	4	yes	—
500	#102	C₂³×C₃₁	1	4	yes	—
501	#102	C₂³×C₃₁	1	4	yes	—
502	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
503	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
504	C₄×C₈	C₂³×C₃₁	1	2	yes	—
505	C₄×C₈	C₂³×C₃₁	1	2	yes	—
506	C₃₁	#62244	1	1	yes	characteristic, direct product factor, Sylow
507	C₂⁴	—	2	2	no	—
508	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
509	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
510	#41	—	4	4	no	—
511	#41	—	4	4	no	—
512	C₂×Q₈	—	2	2	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂×Q₈	—	4	2	no	—
515	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
516	C₂×D₄	—	2	4	no	—
517	C₂×D₄	—	2	4	no	—
518	C₂×D₄	—	2	4	no	—
519	C₂×D₄	—	2	4	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	8	no	—
525	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
526	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	1	no	—
535	C₂²×C₄	—	4	1	no	—
536	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
539	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
543	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
544	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
545	Q₁₆	—	4	2	no	—
546	Q₁₆	—	4	2	no	—
547	SD₁₆	—	2	8	no	—
548	SD₁₆	—	4	4	no	—
549	D₈	—	4	2	no	—
550	D₈	—	4	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	2	4	no	—
553	C₂×C₈	—	2	4	no	—
554	C₂×C₈	—	4	2	no	—
555	C₂×C₈	—	4	2	no	—
556	C₂×C₈	—	4	1	no	—
557	C₂×C₈	—	4	1	no	—
558	C₂×C₈	—	4	1	no	—
559	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
560	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
561	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
562	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
563	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	4	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	2	4	no	—
570	C₄⋊C₄	—	2	4	no	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
573	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
574	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	2	4	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
586	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	C₂×D₄×C₃₁	1	2	yes	—
590	C₄²	C₂⁴×C₃₁	1	2	yes	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	4	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	8	2	no	—
599	C₂³	—	8	2	no	—
600	C₂³	C₃₁×#135	1	4	yes	complemented
601	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
602	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
603	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
604	Q₈	—	2	4	no	—
605	Q₈	—	2	4	no	—
606	Q₈	—	8	2	no	—
607	D₄	—	2	8	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	4	no	—
610	D₄	—	4	8	no	—
611	D₄	—	4	8	no	—
612	D₄	—	8	2	no	—
613	D₄	—	8	4	no	—
614	D₄	—	8	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	4	no	—
631	C₂×C₄	—	8	4	no	—
632	C₂×C₄	—	8	4	no	—
633	C₂×C₄	—	8	2	no	—
634	C₂×C₄	—	8	2	no	—
635	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
636	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
637	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
639	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
640	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
641	C₈	—	2	1	no	—
642	C₈	—	2	2	no	—
643	C₈	—	2	2	no	—
644	C₈	—	2	2	no	—
645	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	4	4	no	—
655	C₂²	—	4	4	no	—
656	C₂²	—	4	4	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	16	4	no	—
659	C₂²	C₂×C₃₁×#135	1	2	yes	—
660	C₂²	C₂×C₃₁×#135	1	4	yes	—
661	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	4	4	no	—
668	C₄	—	4	4	no	—
669	C₄	—	4	4	no	—
670	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
671	C₄	C₃₁×#585	1	1	yes	characteristic
672	C₂	—	2	2	no	—
673	C₂	—	2	4	no	—
674	C₂	—	4	2	no	—
675	C₂	—	8	4	no	—
676	C₂	C₃₁×#3496	1	1	yes	characteristic
677	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
678	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
1. C₃₁×#3505	C₂	semidirect
2. C₃₁×#3337	C₂	semidirect
3. C₃₁×#3300	C₂	semidirect
4. C₃₁×#3297	C₂	semidirect
5. C₃₁×#3282	C₂	semidirect
6. C₃₁×#3250	C₂	semidirect
7. C₃₁×#3191	C₂	semidirect
8. C₃₁×#3189	C₂	semidirect
9. C₃₁×#3186	C₂	semidirect
10. C₃₁×#3168	C₂	semidirect
11. C₃₁×#3050	C₂	semidirect
12. C₂×C₃₁×#465	C₂	semidirect
13. C₂×C₈×D₄×C₃₁	C₂	semidirect
14. C₂×C₃₁×#135	C₂²	semidirect
15. C₂²×SD₁₆×C₃₁	C₂²	semidirect
17. C₂³×C₈×C₃₁	C₂²	semidirect
20. C₃₁×#552	C₂²	semidirect
23. C₃₁×#546	C₂²	semidirect
27. C₃₁×#529	C₂²	semidirect
28. C₃₁×#525	C₂²	semidirect
33. C₃₁×#499	C₂²	semidirect
34. C₃₁×#495	C₂²	semidirect
35. C₃₁×#488	C₂²	semidirect
36. C₃₁×#485	C₂²	semidirect
37. C₃₁×#484	C₂²	semidirect
38. C₃₁×#482	C₂²	semidirect
39. C₃₁×#480	C₂²	semidirect
40. C₃₁×#479	C₂²	semidirect
41. C₃₁×#478	C₂²	semidirect
42. C₃₁×#467	C₂²	semidirect
43. C₃₁×#467	C₂²	semidirect
44. C₃₁×#467	C₂²	semidirect
47. C₃₁×#466	C₂²	semidirect
48. C₃₁×#465	C₂²	semidirect
49. C₃₁×#465	C₂²	semidirect
50. C₃₁×#465	C₂²	semidirect
51. C₃₁×#465	C₂²	semidirect
52. C₃₁×#465	C₂²	semidirect
53. C₃₁×#464	C₂²	semidirect
54. C₃₁×#463	C₂²	semidirect
55. C₃₁×#452	C₂²	semidirect
56. C₃₁×#451	C₂²	semidirect
57. C₃₁×#449	C₂²	semidirect
58. C₃₁×#447	C₂²	semidirect
59. C₄×Q₁₆×C₃₁	C₂²	semidirect
60. C₄×SD₁₆×C₃₁	C₂²	semidirect
61. C₄×D₈×C₃₁	C₂²	semidirect
62. C₈×D₄×C₃₁	C₂²	semidirect
63. C₈×D₄×C₃₁	C₂²	semidirect
64. C₃₁×#427	C₂²	semidirect
65. C₂×C₃₁×#106	C₂²	semidirect
66. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
67. C₃₁×#416	C₂²	semidirect
68. C₂×C₃₁×#103	C₂²	semidirect
69. C₂×C₃₁×#102	C₂²	semidirect
71. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
72. C₂×C₄×C₈×C₃₁	C₂²	semidirect
251. #62244	C₃₁	direct (N × H)
261. C₂³×C₃₁	#135	semidirect
307. #3505	C₂×C₃₁	semidirect
308. #3337	C₂×C₃₁	semidirect
309. #3300	C₂×C₃₁	semidirect
310. #3297	C₂×C₃₁	semidirect
311. #3282	C₂×C₃₁	semidirect
312. #3250	C₂×C₃₁	semidirect
313. #3191	C₂×C₃₁	semidirect
314. #3189	C₂×C₃₁	semidirect
315. #3186	C₂×C₃₁	semidirect
316. #3168	C₂×C₃₁	semidirect
317. #3050	C₂×C₃₁	semidirect
318. C₂×#465	C₂×C₃₁	semidirect
319. C₂×C₈×D₄	C₂×C₃₁	semidirect
346. C₂×#135	C₂²×C₃₁	semidirect
347. C₂²×SD₁₆	C₂²×C₃₁	semidirect
349. C₂³×C₈	C₂²×C₃₁	semidirect
352. #552	C₂²×C₃₁	semidirect
355. #546	C₂²×C₃₁	semidirect
359. #529	C₂²×C₃₁	semidirect
360. #525	C₂²×C₃₁	semidirect
365. #499	C₂²×C₃₁	semidirect
366. #495	C₂²×C₃₁	semidirect
367. #488	C₂²×C₃₁	semidirect
368. #485	C₂²×C₃₁	semidirect
369. #484	C₂²×C₃₁	semidirect
370. #482	C₂²×C₃₁	semidirect
371. #480	C₂²×C₃₁	semidirect
372. #479	C₂²×C₃₁	semidirect
373. #478	C₂²×C₃₁	semidirect
374. #467	C₂²×C₃₁	semidirect
375. #467	C₂²×C₃₁	semidirect
376. #467	C₂²×C₃₁	semidirect
379. #466	C₂²×C₃₁	semidirect
380. #465	C₂²×C₃₁	semidirect
381. #465	C₂²×C₃₁	semidirect
382. #465	C₂²×C₃₁	semidirect
383. #465	C₂²×C₃₁	semidirect
384. #465	C₂²×C₃₁	semidirect
385. #464	C₂²×C₃₁	semidirect
386. #463	C₂²×C₃₁	semidirect
387. #452	C₂²×C₃₁	semidirect
388. #451	C₂²×C₃₁	semidirect
389. #449	C₂²×C₃₁	semidirect
390. #447	C₂²×C₃₁	semidirect
391. C₄×Q₁₆	C₂²×C₃₁	semidirect
392. C₄×SD₁₆	C₂²×C₃₁	semidirect
393. C₄×D₈	C₂²×C₃₁	semidirect
394. C₈×D₄	C₂²×C₃₁	semidirect
395. C₈×D₄	C₂²×C₃₁	semidirect
396. #427	C₂²×C₃₁	semidirect
397. C₂×#106	C₂²×C₃₁	semidirect
398. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
399. #416	C₂²×C₃₁	semidirect
400. C₂×#103	C₂²×C₃₁	semidirect
401. C₂×#102	C₂²×C₃₁	semidirect
403. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
404. C₂×C₄×C₈	C₂²×C₃₁	semidirect
506. C₃₁	#62244	direct (N × H)
600. C₂³	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3505	2
C₃₁×#3337	2
C₃₁×#3300	2
C₃₁×#3297	2
C₃₁×#3282	2
C₃₁×#3250	2
C₃₁×#3191	2
C₃₁×#3189	2
C₃₁×#3186	2
C₃₁×#3168	2
C₃₁×#3050	2
C₂×C₃₁×#465	2
C₂×C₈×D₄×C₃₁	2
#62244	31

Subgroups — C31×#62244 #21519003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62244 #21519003