Subgroups — C₃₁×#60493 #21517252

Order 7936.

2030 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3428	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3084	C₂	1	4	yes	maximal, complemented
4	C₃₁×#3083	C₂	1	4	yes	maximal, complemented
5	C₃₁×#3082	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3081	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3080	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3079	C₂	1	4	yes	maximal, complemented
9	C₃₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#2896	C₂	1	1	yes	maximal, characteristic
13	C₂×C₃₁×#417	C₂	1	1	yes	maximal, characteristic
14	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
17	C₃₁×#544	—	2	2	no	—
18	C₃₁×#544	—	2	2	no	—
19	C₃₁×#544	C₂²	1	4	yes	—
20	C₃₁×#544	C₂²	1	4	yes	complemented
21	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#125	—	2	1	no	—
24	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
25	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
26	C₃₁×#520	—	2	1	no	—
27	C₃₁×#520	—	2	1	no	—
28	C₃₁×#520	C₂²	1	2	yes	—
29	C₃₁×#520	C₂²	1	2	yes	—
30	C₃₁×#519	C₂²	1	2	yes	—
31	C₃₁×#518	—	2	2	no	—
32	C₃₁×#518	C₂²	1	2	yes	—
33	C₄×#41×C₃₁	—	2	2	no	—
34	C₄×#41×C₃₁	C₂²	1	4	yes	—
35	C₂×C₃₁×#117	—	2	2	no	—
36	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
40	C₃₁×#479	C₂²	1	8	yes	complemented
41	C₃₁×#479	C₂²	1	8	yes	complemented
42	C₃₁×#478	C₂²	1	8	yes	complemented
43	C₃₁×#478	C₂²	1	8	yes	complemented
44	C₃₁×#477	C₂²	1	8	yes	complemented
45	C₃₁×#476	C₂²	1	8	yes	complemented
46	C₃₁×#475	C₂²	1	8	yes	complemented
47	C₃₁×#474	C₂²	1	8	yes	complemented
48	C₃₁×#428	C₂²	1	4	yes	—
49	C₃₁×#428	C₂²	1	2	yes	complemented
50	C₃₁×#428	C₂²	1	4	yes	complemented
51	C₃₁×#428	C₂²	1	2	yes	complemented
52	C₃₁×#428	C₂²	1	2	yes	complemented
53	C₃₁×#428	C₂²	1	2	yes	complemented
54	C₃₁×#427	C₂²	1	4	yes	—
55	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
57	C₃₁×#424	C₂²	1	4	yes	—
58	C₃₁×#424	C₂²	1	4	yes	complemented
59	C₃₁×#423	C₂²	1	4	yes	complemented
60	C₃₁×#419	C₂²	1	2	yes	—
61	C₃₁×#418	C₂²	1	2	yes	—
62	C₃₁×#417	C₂²	1	2	yes	—
63	C₃₁×#417	C₂²	1	4	yes	—
64	C₃₁×#417	C₂²	1	2	yes	—
65	C₃₁×#417	C₂²	1	4	yes	—
66	C₃₁×#416	C₂²	1	4	yes	—
67	C₂×C₃₁×#103	C₂²	1	2	yes	—
68	C₂×C₃₁×#102	C₂²	1	2	yes	—
69	C₂×#41×C₃₁	—	2	1	no	—
70	C₂×#41×C₃₁	—	2	1	no	—
71	C₂×#41×C₃₁	—	2	4	no	—
72	C₂×#41×C₃₁	Q₈	1	8	yes	complemented
73	C₂×#41×C₃₁	C₂³	1	2	yes	—
74	C₂×#41×C₃₁	C₂³	1	2	yes	—
75	C₂²×Q₈×C₃₁	—	2	2	no	—
76	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₃₁	—	2	1	no	—
78	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₃₁	—	2	1	no	—
80	C₂³×C₄×C₃₁	—	2	1	no	—
81	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₃₁	—	2	4	no	—
83	C₂×M₁₆×C₃₁	—	2	4	no	—
84	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
85	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
86	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
87	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
88	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
89	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
90	C₃₁×C₄⋊Q₈	—	2	4	no	—
91	C₃₁×C₄⋊Q₈	—	2	4	no	—
92	C₃₁×C₄⋊Q₈	—	2	4	no	—
93	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
94	C₃₁×#125	—	2	4	no	—
95	C₃₁×#125	—	2	4	no	—
96	C₃₁×#125	—	2	4	no	—
97	C₃₁×#125	C₂³	1	8	yes	—
98	C₃₁×C₂²⋊Q₈	—	2	8	no	—
99	C₃₁×C₂²⋊Q₈	—	2	8	no	—
100	C₄×Q₈×C₃₁	—	2	2	no	—
101	C₄×Q₈×C₃₁	—	2	2	no	—
102	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
103	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
104	C₄×D₄×C₃₁	—	2	4	no	—
105	C₄×D₄×C₃₁	—	2	4	no	—
106	C₄×D₄×C₃₁	—	2	2	no	—
107	C₄×D₄×C₃₁	—	2	2	no	—
108	C₄×D₄×C₃₁	—	2	4	no	—
109	C₄×D₄×C₃₁	—	2	4	no	—
110	C₄×D₄×C₃₁	C₂³	1	4	yes	—
111	C₄×D₄×C₃₁	C₂³	1	4	yes	—
112	C₃₁×#117	—	2	1	no	—
113	C₃₁×#117	—	2	1	no	—
114	C₃₁×#117	—	2	1	no	—
115	C₃₁×#117	—	2	1	no	—
116	C₃₁×#117	—	2	2	no	—
117	C₃₁×#117	—	2	2	no	—
118	C₃₁×#117	—	2	4	no	—
119	C₃₁×#117	—	2	4	no	—
120	C₃₁×#117	D₄	1	2	yes	—
121	C₃₁×#117	D₄	1	2	yes	—
122	C₃₁×#117	C₂³	1	2	yes	—
123	C₃₁×#117	C₂³	1	2	yes	—
124	C₃₁×#117	C₂³	1	2	yes	—
125	C₃₁×#117	C₂³	1	2	yes	—
126	C₃₁×#117	C₂³	1	2	yes	—
127	C₃₁×#117	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
129	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
130	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
131	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
132	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
133	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
134	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
135	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
136	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
148	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
149	C₂×C₄²×C₃₁	—	2	1	no	—
150	C₂×C₄²×C₃₁	—	2	1	no	—
151	C₂×C₄²×C₃₁	—	2	4	no	—
152	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
153	C₃₁×#107	C₂³	1	8	yes	—
154	C₃₁×#107	C₂³	1	4	yes	—
155	C₃₁×#107	C₂³	1	4	yes	—
156	C₃₁×#106	C₂³	1	8	yes	—
157	C₃₁×#106	C₂³	1	4	yes	—
158	C₃₁×#106	C₂³	1	4	yes	—
159	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
160	C₃₁×C₄⋊C₈	C₂³	1	8	yes	—
161	C₃₁×#103	C₂³	1	8	yes	—
162	C₃₁×#103	C₂³	1	4	yes	—
163	C₃₁×#103	C₂³	1	4	yes	—
164	C₃₁×#102	C₂³	1	8	yes	—
165	C₃₁×#102	C₂³	1	4	yes	—
166	C₃₁×#102	C₂³	1	4	yes	—
167	C₂⁴×C₃₁	—	2	1	no	—
168	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
169	#41×C₃₁	—	2	8	no	—
170	#41×C₃₁	—	2	8	no	—
171	#41×C₃₁	—	2	4	no	—
172	#41×C₃₁	—	2	4	no	—
173	#41×C₃₁	C₂×Q₈	1	8	yes	—
174	#41×C₃₁	C₂×Q₈	1	8	yes	complemented
175	C₂×Q₈×C₃₁	—	2	1	no	—
176	C₂×Q₈×C₃₁	—	2	8	no	—
177	C₂×Q₈×C₃₁	—	2	2	no	—
178	C₂×Q₈×C₃₁	—	8	4	no	—
179	C₂×Q₈×C₃₁	C₂×Q₈	1	4	yes	complemented
180	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
181	C₂×D₄×C₃₁	—	2	8	no	—
182	C₂×D₄×C₃₁	—	2	2	no	—
183	C₂×D₄×C₃₁	—	2	2	no	—
184	C₂×D₄×C₃₁	—	2	1	no	—
185	C₂×D₄×C₃₁	—	2	2	no	—
186	C₂×D₄×C₃₁	C₂×Q₈	1	4	yes	complemented
187	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₃₁	—	2	1	no	—
189	C₂²×C₄×C₃₁	—	2	8	no	—
190	C₂²×C₄×C₃₁	—	2	2	no	—
191	C₂²×C₄×C₃₁	—	2	2	no	—
192	C₂²×C₄×C₃₁	—	2	1	no	—
193	C₂²×C₄×C₃₁	—	2	1	no	—
194	C₂²×C₄×C₃₁	—	2	2	no	—
195	C₂²×C₄×C₃₁	—	2	1	no	—
196	C₂²×C₄×C₃₁	—	2	1	no	—
197	C₂²×C₄×C₃₁	—	2	2	no	—
198	C₂²×C₄×C₃₁	—	2	2	no	—
199	C₂²×C₄×C₃₁	—	2	4	no	—
200	C₂²×C₄×C₃₁	—	2	4	no	—
201	C₂²×C₄×C₃₁	—	8	2	no	—
202	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
208	C₂²×C₄×C₃₁	#41	1	4	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
210	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
212	M₁₆×C₃₁	—	2	4	no	—
213	M₁₆×C₃₁	—	2	4	no	—
214	M₁₆×C₃₁	—	2	4	no	—
215	M₁₆×C₃₁	—	2	4	no	—
216	C₂×C₈×C₃₁	—	2	4	no	—
217	C₂×C₈×C₃₁	—	2	4	no	—
218	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
219	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
220	C₄⋊C₄×C₃₁	—	2	1	no	—
221	C₄⋊C₄×C₃₁	—	2	1	no	—
222	C₄⋊C₄×C₃₁	—	2	2	no	—
223	C₄⋊C₄×C₃₁	—	2	2	no	—
224	C₄⋊C₄×C₃₁	—	2	2	no	—
225	C₄⋊C₄×C₃₁	—	2	4	no	—
226	C₄⋊C₄×C₃₁	—	2	4	no	—
227	C₄⋊C₄×C₃₁	—	2	8	no	—
228	C₄⋊C₄×C₃₁	—	2	8	no	—
229	C₄⋊C₄×C₃₁	—	2	8	no	—
230	C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₄⋊C₄×C₃₁	—	2	1	no	—
232	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
233	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
234	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
236	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
238	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
241	C₂²⋊C₄×C₃₁	—	2	2	no	—
242	C₂²⋊C₄×C₃₁	—	2	2	no	—
243	C₂²⋊C₄×C₃₁	—	2	2	no	—
244	C₂²⋊C₄×C₃₁	—	2	2	no	—
245	C₂²⋊C₄×C₃₁	—	2	4	no	—
246	C₂²⋊C₄×C₃₁	—	2	4	no	—
247	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
248	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
249	C₄²×C₃₁	—	2	2	no	—
250	C₄²×C₃₁	—	2	4	no	—
251	C₄²×C₃₁	—	2	4	no	—
252	C₄²×C₃₁	—	2	2	no	—
253	C₄²×C₃₁	—	2	2	no	—
254	C₄²×C₃₁	—	2	2	no	—
255	C₄²×C₃₁	C₂×D₄	1	4	yes	—
256	C₄²×C₃₁	C₂⁴	1	4	yes	—
257	#60493	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂³×C₃₁	—	2	2	no	—
259	C₂³×C₃₁	—	2	4	no	—
260	C₂³×C₃₁	—	4	1	no	—
261	C₂³×C₃₁	—	4	1	no	—
262	C₂³×C₃₁	—	8	1	no	—
263	C₂³×C₃₁	—	8	1	no	—
264	C₂³×C₃₁	C₂²⋊Q₈	1	4	yes	—
265	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
266	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
267	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
268	Q₈×C₃₁	—	2	4	no	—
269	Q₈×C₃₁	—	2	2	no	—
270	Q₈×C₃₁	—	8	8	no	—
271	Q₈×C₃₁	C₂²×Q₈	1	4	yes	—
272	D₄×C₃₁	—	2	8	no	—
273	D₄×C₃₁	—	2	8	no	—
274	D₄×C₃₁	—	2	4	no	—
275	D₄×C₃₁	—	2	2	no	—
276	D₄×C₃₁	C₂²×Q₈	1	4	yes	—
277	C₂×C₄×C₃₁	—	2	4	no	—
278	C₂×C₄×C₃₁	—	2	2	no	—
279	C₂×C₄×C₃₁	—	2	8	no	—
280	C₂×C₄×C₃₁	—	2	8	no	—
281	C₂×C₄×C₃₁	—	2	2	no	—
282	C₂×C₄×C₃₁	—	2	2	no	—
283	C₂×C₄×C₃₁	—	2	2	no	—
284	C₂×C₄×C₃₁	—	2	2	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	2	no	—
289	C₂×C₄×C₃₁	—	4	4	no	—
290	C₂×C₄×C₃₁	—	4	2	no	—
291	C₂×C₄×C₃₁	—	8	4	no	—
292	C₂×C₄×C₃₁	—	8	4	no	—
293	C₂×C₄×C₃₁	—	8	1	no	—
294	C₂×C₄×C₃₁	—	8	1	no	—
295	C₂×C₄×C₃₁	—	8	2	no	—
296	C₂×C₄×C₃₁	—	8	2	no	—
297	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
298	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
299	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
300	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
301	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
306	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
307	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
309	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
310	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
311	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
312	C₈×C₃₁	—	2	4	no	—
313	C₈×C₃₁	—	2	4	no	—
314	C₂×#544	C₂×C₃₁	1	1	yes	characteristic, complemented
315	#3428	C₂×C₃₁	1	1	yes	characteristic
316	#3084	C₂×C₃₁	1	4	yes	complemented
317	#3083	C₂×C₃₁	1	4	yes	complemented
318	#3082	C₂×C₃₁	1	4	yes	complemented
319	#3081	C₂×C₃₁	1	4	yes	complemented
320	#3080	C₂×C₃₁	1	4	yes	complemented
321	#3079	C₂×C₃₁	1	4	yes	complemented
322	#2911	C₂×C₃₁	1	1	yes	characteristic, complemented
323	C₂×#428	C₂×C₃₁	1	1	yes	characteristic, complemented
324	#2905	C₂×C₃₁	1	1	yes	characteristic, complemented
325	#2896	C₂×C₃₁	1	1	yes	characteristic
326	C₂×#417	C₂×C₃₁	1	1	yes	characteristic
327	C₂²×C₃₁	—	2	1	no	—
328	C₂²×C₃₁	—	2	1	no	—
329	C₂²×C₃₁	—	2	1	no	—
330	C₂²×C₃₁	—	2	1	no	—
331	C₂²×C₃₁	—	2	1	no	—
332	C₂²×C₃₁	—	2	1	no	—
333	C₂²×C₃₁	—	2	4	no	—
334	C₂²×C₃₁	—	4	4	no	—
335	C₂²×C₃₁	—	4	2	no	—
336	C₂²×C₃₁	—	4	2	no	—
337	C₂²×C₃₁	—	8	4	no	—
338	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
339	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
340	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
341	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
342	C₄×C₃₁	—	2	4	no	—
343	C₄×C₃₁	—	2	4	no	—
344	C₄×C₃₁	—	2	4	no	—
345	C₄×C₃₁	—	4	4	no	—
346	C₄×C₃₁	—	4	2	no	—
347	C₄×C₃₁	—	4	2	no	—
348	C₄×C₃₁	—	4	2	no	—
349	C₄×C₃₁	—	4	2	no	—
350	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
351	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
352	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
353	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
354	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
355	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
356	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
357	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
358	#544	—	2	2	no	—
359	#544	—	2	2	no	—
360	#544	C₂²×C₃₁	1	4	yes	—
361	#544	C₂²×C₃₁	1	4	yes	complemented
362	C₂×C₄⋊Q₈	—	2	1	no	—
363	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
364	C₂×#125	—	2	1	no	—
365	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
366	C₂×C₂²⋊Q₈	—	2	2	no	—
367	#520	—	2	1	no	—
368	#520	—	2	1	no	—
369	#520	C₂²×C₃₁	1	2	yes	—
370	#520	C₂²×C₃₁	1	2	yes	—
371	#519	C₂²×C₃₁	1	2	yes	—
372	#518	—	2	2	no	—
373	#518	C₂²×C₃₁	1	2	yes	—
374	C₄×#41	—	2	2	no	—
375	C₄×#41	C₂²×C₃₁	1	4	yes	—
376	C₂×#117	—	2	2	no	—
377	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
378	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
379	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
380	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
381	#479	C₂²×C₃₁	1	8	yes	complemented
382	#479	C₂²×C₃₁	1	8	yes	complemented
383	#478	C₂²×C₃₁	1	8	yes	complemented
384	#478	C₂²×C₃₁	1	8	yes	complemented
385	#477	C₂²×C₃₁	1	8	yes	complemented
386	#476	C₂²×C₃₁	1	8	yes	complemented
387	#475	C₂²×C₃₁	1	8	yes	complemented
388	#474	C₂²×C₃₁	1	8	yes	complemented
389	#428	C₂²×C₃₁	1	4	yes	—
390	#428	C₂²×C₃₁	1	2	yes	complemented
391	#428	C₂²×C₃₁	1	4	yes	complemented
392	#428	C₂²×C₃₁	1	2	yes	complemented
393	#428	C₂²×C₃₁	1	2	yes	complemented
394	#428	C₂²×C₃₁	1	2	yes	complemented
395	#427	C₂²×C₃₁	1	4	yes	—
396	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
397	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
398	#424	C₂²×C₃₁	1	4	yes	—
399	#424	C₂²×C₃₁	1	4	yes	complemented
400	#423	C₂²×C₃₁	1	4	yes	complemented
401	#419	C₂²×C₃₁	1	2	yes	—
402	#418	C₂²×C₃₁	1	2	yes	—
403	#417	C₂²×C₃₁	1	2	yes	—
404	#417	C₂²×C₃₁	1	4	yes	—
405	#417	C₂²×C₃₁	1	2	yes	—
406	#417	C₂²×C₃₁	1	4	yes	—
407	#416	C₂²×C₃₁	1	4	yes	—
408	C₂×#103	C₂²×C₃₁	1	2	yes	—
409	C₂×#102	C₂²×C₃₁	1	2	yes	—
410	C₂×C₃₁	—	2	2	no	—
411	C₂×C₃₁	—	2	2	no	—
412	C₂×C₃₁	—	2	2	no	—
413	C₂×C₃₁	—	4	4	no	—
414	C₂×C₃₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
415	C₂×C₃₁	#3585	1	1	yes	characteristic
416	C₂×C₃₁	#3586	1	1	yes	characteristic
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	4	no	—
420	C₂×#41	Q₈×C₃₁	1	8	yes	complemented
421	C₂×#41	C₂³×C₃₁	1	2	yes	—
422	C₂×#41	C₂³×C₃₁	1	2	yes	—
423	C₂²×Q₈	—	2	2	no	—
424	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
425	C₂²×D₄	—	2	1	no	—
426	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
430	C₂×M₁₆	—	2	4	no	—
431	C₂×M₁₆	—	2	4	no	—
432	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
433	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
434	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
435	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
436	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
437	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
438	C₄⋊Q₈	—	2	4	no	—
439	C₄⋊Q₈	—	2	4	no	—
440	C₄⋊Q₈	—	2	4	no	—
441	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
442	#125	—	2	4	no	—
443	#125	—	2	4	no	—
444	#125	—	2	4	no	—
445	#125	C₂³×C₃₁	1	8	yes	—
446	C₂²⋊Q₈	—	2	8	no	—
447	C₂²⋊Q₈	—	2	8	no	—
448	C₄×Q₈	—	2	2	no	—
449	C₄×Q₈	—	2	2	no	—
450	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
451	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
452	C₄×D₄	—	2	4	no	—
453	C₄×D₄	—	2	4	no	—
454	C₄×D₄	—	2	2	no	—
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	4	no	—
457	C₄×D₄	—	2	4	no	—
458	C₄×D₄	C₂³×C₃₁	1	4	yes	—
459	C₄×D₄	C₂³×C₃₁	1	4	yes	—
460	#117	—	2	1	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	#117	—	2	1	no	—
464	#117	—	2	2	no	—
465	#117	—	2	2	no	—
466	#117	—	2	4	no	—
467	#117	—	2	4	no	—
468	#117	D₄×C₃₁	1	2	yes	—
469	#117	D₄×C₃₁	1	2	yes	—
470	#117	C₂³×C₃₁	1	2	yes	—
471	#117	C₂³×C₃₁	1	2	yes	—
472	#117	C₂³×C₃₁	1	2	yes	—
473	#117	C₂³×C₃₁	1	2	yes	—
474	#117	C₂³×C₃₁	1	2	yes	—
475	#117	C₂³×C₃₁	1	2	yes	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	2	no	—
480	C₂×C₄⋊C₄	—	2	2	no	—
481	C₂×C₄⋊C₄	—	2	2	no	—
482	C₂×C₄⋊C₄	—	2	2	no	—
483	C₂×C₄⋊C₄	—	2	2	no	—
484	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
485	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	4	no	—
496	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
497	C₂×C₄²	—	2	1	no	—
498	C₂×C₄²	—	2	1	no	—
499	C₂×C₄²	—	2	4	no	—
500	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
501	#107	C₂³×C₃₁	1	8	yes	—
502	#107	C₂³×C₃₁	1	4	yes	—
503	#107	C₂³×C₃₁	1	4	yes	—
504	#106	C₂³×C₃₁	1	8	yes	—
505	#106	C₂³×C₃₁	1	4	yes	—
506	#106	C₂³×C₃₁	1	4	yes	—
507	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
508	C₄⋊C₈	C₂³×C₃₁	1	8	yes	—
509	#103	C₂³×C₃₁	1	8	yes	—
510	#103	C₂³×C₃₁	1	4	yes	—
511	#103	C₂³×C₃₁	1	4	yes	—
512	#102	C₂³×C₃₁	1	8	yes	—
513	#102	C₂³×C₃₁	1	4	yes	—
514	#102	C₂³×C₃₁	1	4	yes	—
515	C₃₁	#60493	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	1	no	—
517	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
518	#41	—	2	8	no	—
519	#41	—	2	8	no	—
520	#41	—	2	4	no	—
521	#41	—	2	4	no	—
522	#41	C₂×Q₈×C₃₁	1	8	yes	—
523	#41	C₂×Q₈×C₃₁	1	8	yes	complemented
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	8	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	8	4	no	—
528	C₂×Q₈	C₂×Q₈×C₃₁	1	4	yes	complemented
529	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
530	C₂×D₄	—	2	8	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	C₂×Q₈×C₃₁	1	4	yes	complemented
536	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	2	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	8	2	no	—
551	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
552	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
553	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
556	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
557	C₂²×C₄	#41×C₃₁	1	4	yes	—
558	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
560	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
561	M₁₆	—	2	4	no	—
562	M₁₆	—	2	4	no	—
563	M₁₆	—	2	4	no	—
564	M₁₆	—	2	4	no	—
565	C₂×C₈	—	2	4	no	—
566	C₂×C₈	—	2	4	no	—
567	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
568	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	8	no	—
577	C₄⋊C₄	—	2	8	no	—
578	C₄⋊C₄	—	2	8	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
582	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
583	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
584	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
585	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
586	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
587	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
588	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
589	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	—	2	2	no	—
594	C₂²⋊C₄	—	2	4	no	—
595	C₂²⋊C₄	—	2	4	no	—
596	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
597	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
598	C₄²	—	2	2	no	—
599	C₄²	—	2	4	no	—
600	C₄²	—	2	4	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	C₂×D₄×C₃₁	1	4	yes	—
605	C₄²	C₂⁴×C₃₁	1	4	yes	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	4	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	8	1	no	—
611	C₂³	—	8	1	no	—
612	C₂³	C₃₁×C₂²⋊Q₈	1	4	yes	—
613	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
614	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
615	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
616	Q₈	—	2	4	no	—
617	Q₈	—	2	2	no	—
618	Q₈	—	8	8	no	—
619	Q₈	C₂²×Q₈×C₃₁	1	4	yes	—
620	D₄	—	2	8	no	—
621	D₄	—	2	8	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	2	no	—
624	D₄	C₂²×Q₈×C₃₁	1	4	yes	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	2	8	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	2	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	2	no	—
639	C₂×C₄	—	8	4	no	—
640	C₂×C₄	—	8	4	no	—
641	C₂×C₄	—	8	1	no	—
642	C₂×C₄	—	8	1	no	—
643	C₂×C₄	—	8	2	no	—
644	C₂×C₄	—	8	2	no	—
645	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
646	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
647	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
649	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
650	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
652	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
653	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
654	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
655	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
656	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
657	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
658	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
659	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
660	C₈	—	2	4	no	—
661	C₈	—	2	4	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	8	4	no	—
673	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
674	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
675	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
676	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
677	C₄	—	2	4	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	4	no	—
680	C₄	—	4	4	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	2	no	—
684	C₄	—	4	2	no	—
685	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
686	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
687	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
688	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
689	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
690	C₂	—	2	2	no	—
691	C₂	—	2	2	no	—
692	C₂	—	2	2	no	—
693	C₂	—	4	4	no	—
694	C₂	C₂²×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
695	C₂	C₃₁×#3585	1	1	yes	characteristic
696	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×#41×C₃₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#544	C₂	semidirect
3. C₃₁×#3084	C₂	semidirect
4. C₃₁×#3083	C₂	semidirect
5. C₃₁×#3082	C₂	semidirect
6. C₃₁×#3081	C₂	semidirect
7. C₃₁×#3080	C₂	semidirect
8. C₃₁×#3079	C₂	semidirect
9. C₃₁×#2911	C₂	semidirect
10. C₂×C₃₁×#428	C₂	semidirect
11. C₃₁×#2905	C₂	semidirect
20. C₃₁×#544	C₂²	semidirect
22. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₃₁×#125	C₂²	semidirect
40. C₃₁×#479	C₂²	semidirect
41. C₃₁×#479	C₂²	semidirect
42. C₃₁×#478	C₂²	semidirect
43. C₃₁×#478	C₂²	semidirect
44. C₃₁×#477	C₂²	semidirect
45. C₃₁×#476	C₂²	semidirect
46. C₃₁×#475	C₂²	semidirect
47. C₃₁×#474	C₂²	semidirect
49. C₃₁×#428	C₂²	semidirect
50. C₃₁×#428	C₂²	semidirect
51. C₃₁×#428	C₂²	semidirect
52. C₃₁×#428	C₂²	semidirect
53. C₃₁×#428	C₂²	semidirect
55. C₂×C₃₁×#107	C₂²	semidirect
56. C₂×C₃₁×#106	C₂²	semidirect
58. C₃₁×#424	C₂²	semidirect
59. C₃₁×#423	C₂²	semidirect
72. C₂×#41×C₃₁	Q₈	semidirect
174. #41×C₃₁	C₂×Q₈	semidirect
179. C₂×Q₈×C₃₁	C₂×Q₈	semidirect
186. C₂×D₄×C₃₁	C₂×Q₈	semidirect
257. #60493	C₃₁	direct (N × H)
314. C₂×#544	C₂×C₃₁	semidirect
316. #3084	C₂×C₃₁	semidirect
317. #3083	C₂×C₃₁	semidirect
318. #3082	C₂×C₃₁	semidirect
319. #3081	C₂×C₃₁	semidirect
320. #3080	C₂×C₃₁	semidirect
321. #3079	C₂×C₃₁	semidirect
322. #2911	C₂×C₃₁	semidirect
323. C₂×#428	C₂×C₃₁	semidirect
324. #2905	C₂×C₃₁	semidirect
361. #544	C₂²×C₃₁	semidirect
363. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
365. C₂×#125	C₂²×C₃₁	semidirect
381. #479	C₂²×C₃₁	semidirect
382. #479	C₂²×C₃₁	semidirect
383. #478	C₂²×C₃₁	semidirect
384. #478	C₂²×C₃₁	semidirect
385. #477	C₂²×C₃₁	semidirect
386. #476	C₂²×C₃₁	semidirect
387. #475	C₂²×C₃₁	semidirect
388. #474	C₂²×C₃₁	semidirect
390. #428	C₂²×C₃₁	semidirect
391. #428	C₂²×C₃₁	semidirect
392. #428	C₂²×C₃₁	semidirect
393. #428	C₂²×C₃₁	semidirect
394. #428	C₂²×C₃₁	semidirect
396. C₂×#107	C₂²×C₃₁	semidirect
397. C₂×#106	C₂²×C₃₁	semidirect
399. #424	C₂²×C₃₁	semidirect
400. #423	C₂²×C₃₁	semidirect
420. C₂×#41	Q₈×C₃₁	semidirect
515. C₃₁	#60493	direct (N × H)
523. #41	C₂×Q₈×C₃₁	semidirect
528. C₂×Q₈	C₂×Q₈×C₃₁	semidirect
535. C₂×D₄	C₂×Q₈×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×#544	2
C₃₁×#3428	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3080	2
C₃₁×#3079	2
C₃₁×#2911	2
C₂×C₃₁×#428	2
C₃₁×#2905	2
C₃₁×#2896	2
C₂×C₃₁×#417	2
#60493	31

Subgroups — C31×#60493 #21517252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60493 #21517252