Subgroups — C₃₁×#61070 #21517829

Order 7936.

2830 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#575	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3287	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3284	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3274	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3271	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3268	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3055	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3006	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3005	C₂	1	2	yes	maximal, complemented
16	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	2	yes	—
19	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
20	C₃₁×#575	—	2	16	no	—
21	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
27	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
28	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
29	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
31	C₃₁×#550	—	2	1	no	—
32	C₃₁×#550	—	2	1	no	—
33	C₃₁×#550	—	2	2	no	—
34	C₃₁×#550	C₂²	1	2	yes	—
35	C₃₁×#550	C₂²	1	4	yes	complemented
36	C₃₁×#550	C₂²	1	2	yes	complemented
37	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#548	C₂²	1	2	yes	complemented
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#546	—	2	2	no	—
43	C₃₁×#546	C₂²	1	2	yes	complemented
44	D₄²×C₃₁	—	2	1	no	—
45	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#532	—	2	1	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#127	—	2	1	no	—
49	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#525	—	2	2	no	—
51	C₃₁×#525	C₂²	1	2	yes	—
52	C₂×C₃₁×#121	—	2	2	no	—
53	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₃₁	—	2	1	no	—
57	C₂×C₄×D₄×C₃₁	—	2	1	no	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#496	C₂²	1	4	yes	complemented
60	C₃₁×#493	C₂²	1	2	yes	complemented
61	C₃₁×#492	C₂²	1	2	yes	complemented
62	C₃₁×#469	C₂²	1	4	yes	complemented
63	C₃₁×#468	C₂²	1	4	yes	complemented
64	C₃₁×#466	C₂²	1	4	yes	complemented
65	C₃₁×#465	C₂²	1	4	yes	complemented
66	C₃₁×#464	C₂²	1	4	yes	complemented
67	C₃₁×#462	C₂²	1	2	yes	complemented
68	C₃₁×#460	C₂²	1	2	yes	complemented
69	C₃₁×#460	C₂²	1	2	yes	complemented
70	C₃₁×#460	C₂²	1	2	yes	complemented
71	C₃₁×#459	C₂²	1	2	yes	complemented
72	C₃₁×#459	C₂²	1	2	yes	complemented
73	C₃₁×#452	C₂²	1	4	yes	complemented
74	C₃₁×#452	C₂²	1	4	yes	complemented
75	C₃₁×#449	C₂²	1	4	yes	complemented
76	C₃₁×#449	C₂²	1	4	yes	complemented
77	C₃₁×#449	C₂²	1	4	yes	complemented
78	C₃₁×#449	C₂²	1	4	yes	complemented
79	C₃₁×#448	C₂²	1	4	yes	complemented
80	C₃₁×#447	C₂²	1	4	yes	complemented
81	C₃₁×#441	C₂²	1	2	yes	complemented
82	C₃₁×#440	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₃₁×#436	C₂²	1	2	yes	complemented
86	C₃₁×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
88	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#418	C₂²	1	2	yes	complemented
92	C₃₁×#417	C₂²	1	1	yes	characteristic
93	C₃₁×#417	C₂²	1	2	yes	complemented
94	C₃₁×#407	C₂²	1	2	yes	complemented
95	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	—	2	2	no	—
99	C₂×#41×C₃₁	—	2	2	no	—
100	C₂×#41×C₃₁	—	2	8	no	—
101	C₂×#41×C₃₁	—	2	8	no	—
102	C₂×#41×C₃₁	—	4	4	no	—
103	C₂×#41×C₃₁	—	4	4	no	—
104	C₂×#41×C₃₁	C₂³	1	2	yes	—
105	C₂×#41×C₃₁	C₂³	1	2	yes	—
106	C₂×#41×C₃₁	C₂³	1	2	yes	—
107	C₂×#41×C₃₁	C₂³	1	4	yes	—
108	C₂×#41×C₃₁	C₂³	1	4	yes	—
109	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
111	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₃₁	—	2	2	no	—
113	C₂²×D₄×C₃₁	—	2	2	no	—
114	C₂²×D₄×C₃₁	—	2	2	no	—
115	C₂²×D₄×C₃₁	—	2	1	no	—
116	C₂²×D₄×C₃₁	—	2	1	no	—
117	C₂²×D₄×C₃₁	—	2	1	no	—
118	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
119	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
120	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
121	C₂³×C₄×C₃₁	—	2	2	no	—
122	C₂³×C₄×C₃₁	—	2	2	no	—
123	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
124	C₃₁×#137	—	2	8	no	—
125	C₃₁×#137	—	2	16	no	—
126	C₃₁×#137	D₄	1	8	yes	complemented
127	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
128	C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
129	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
130	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
131	C₃₁×#135	—	2	16	no	—
132	C₃₁×#135	—	2	16	no	—
133	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
134	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
135	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×D₈×C₃₁	C₂³	1	4	yes	—
141	C₂×D₈×C₃₁	C₂³	1	4	yes	—
142	C₂×D₈×C₃₁	C₂³	1	4	yes	—
143	C₂×M₁₆×C₃₁	—	2	8	no	—
144	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
147	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₃₁×#127	—	2	2	no	—
152	C₃₁×#127	—	2	2	no	—
153	C₃₁×#127	—	2	4	no	—
154	C₃₁×#127	—	2	1	no	—
155	C₃₁×#127	—	2	1	no	—
156	C₃₁×#127	—	2	1	no	—
157	C₃₁×#127	C₂³	1	2	yes	—
158	C₃₁×#127	C₂³	1	2	yes	—
159	C₃₁×#127	C₂³	1	1	yes	characteristic
160	C₃₁×#124	—	2	2	no	—
161	C₃₁×#124	C₂³	1	2	yes	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₃₁×#121	—	2	2	no	—
170	C₃₁×#121	—	2	1	no	—
171	C₃₁×#121	—	2	2	no	—
172	C₃₁×#121	—	2	2	no	—
173	C₃₁×#121	—	2	1	no	—
174	C₃₁×#121	—	2	1	no	—
175	C₃₁×#121	—	2	1	no	—
176	C₃₁×#121	—	2	4	no	—
177	C₃₁×#121	—	2	4	no	—
178	C₃₁×#121	—	2	4	no	—
179	C₃₁×#121	—	2	4	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	—	2	2	no	—
182	C₃₁×#121	C₂³	1	4	yes	—
183	C₃₁×#121	C₂³	1	4	yes	—
184	C₃₁×#121	C₂³	1	2	yes	—
185	C₃₁×#121	C₂³	1	2	yes	—
186	C₃₁×#120	—	2	2	no	—
187	C₃₁×#120	—	2	2	no	—
188	C₃₁×#120	—	2	2	no	—
189	C₄×Q₈×C₃₁	—	2	1	no	—
190	C₄×Q₈×C₃₁	—	2	1	no	—
191	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
192	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
193	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
194	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×D₄×C₃₁	—	2	1	no	—
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	1	no	—
198	C₄×D₄×C₃₁	—	2	1	no	—
199	C₄×D₄×C₃₁	—	2	2	no	—
200	C₄×D₄×C₃₁	—	2	1	no	—
201	C₄×D₄×C₃₁	—	2	2	no	—
202	C₄×D₄×C₃₁	—	2	2	no	—
203	C₄×D₄×C₃₁	—	2	4	no	—
204	C₄×D₄×C₃₁	—	2	2	no	—
205	C₄×D₄×C₃₁	—	2	1	no	—
206	C₄×D₄×C₃₁	—	2	1	no	—
207	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
208	C₄×D₄×C₃₁	D₄	1	2	yes	—
209	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
210	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
211	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
215	C₃₁×#117	—	2	1	no	—
216	C₃₁×#117	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
218	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
219	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
224	C₂×C₄²×C₃₁	—	2	1	no	—
225	C₂×C₄²×C₃₁	—	2	1	no	—
226	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	2	yes	—
228	C₃₁×#106	C₂³	1	2	yes	—
229	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
230	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
231	C₃₁×#103	C₂³	1	2	yes	—
232	C₃₁×#103	C₂³	1	4	yes	—
233	C₃₁×#103	C₂³	1	2	yes	—
234	C₃₁×#103	C₂³	1	2	yes	—
235	C₃₁×#102	C₂³	1	2	yes	—
236	C₃₁×#102	C₂³	1	4	yes	—
237	C₃₁×#102	C₂³	1	4	yes	—
238	C₃₁×#102	C₂³	1	4	yes	—
239	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
240	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
241	C₃₁×#97	C₂³	1	2	yes	—
242	C₄×C₈×C₃₁	C₂³	1	2	yes	—
243	C₂⁴×C₃₁	—	2	2	no	—
244	C₂⁴×C₃₁	—	2	2	no	—
245	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
246	#41×C₃₁	—	2	2	no	—
247	#41×C₃₁	—	2	4	no	—
248	#41×C₃₁	—	2	8	no	—
249	#41×C₃₁	—	2	8	no	—
250	#41×C₃₁	—	2	4	no	—
251	#41×C₃₁	—	2	4	no	—
252	#41×C₃₁	—	2	4	no	—
253	#41×C₃₁	—	4	8	no	—
254	#41×C₃₁	—	4	4	no	—
255	#41×C₃₁	—	4	2	no	—
256	#41×C₃₁	—	4	4	no	—
257	#41×C₃₁	—	4	2	no	—
258	#41×C₃₁	—	4	8	no	—
259	#41×C₃₁	—	4	8	no	—
260	#41×C₃₁	—	4	8	no	—
261	#41×C₃₁	C₂×D₄	1	4	yes	—
262	C₂×Q₈×C₃₁	—	2	1	no	—
263	C₂×Q₈×C₃₁	—	2	2	no	—
264	C₂×Q₈×C₃₁	—	2	2	no	—
265	C₂×Q₈×C₃₁	—	2	4	no	—
266	C₂×Q₈×C₃₁	—	4	2	no	—
267	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	complemented
268	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
269	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
271	C₂×D₄×C₃₁	—	2	1	no	—
272	C₂×D₄×C₃₁	—	2	4	no	—
273	C₂×D₄×C₃₁	—	2	2	no	—
274	C₂×D₄×C₃₁	—	2	2	no	—
275	C₂×D₄×C₃₁	—	2	2	no	—
276	C₂×D₄×C₃₁	—	2	2	no	—
277	C₂×D₄×C₃₁	—	2	4	no	—
278	C₂×D₄×C₃₁	—	2	4	no	—
279	C₂×D₄×C₃₁	—	2	2	no	—
280	C₂×D₄×C₃₁	—	2	4	no	—
281	C₂×D₄×C₃₁	—	2	4	no	—
282	C₂×D₄×C₃₁	—	2	4	no	—
283	C₂×D₄×C₃₁	—	2	1	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	—	2	2	no	—
286	C₂×D₄×C₃₁	—	2	2	no	—
287	C₂×D₄×C₃₁	—	2	2	no	—
288	C₂×D₄×C₃₁	—	2	1	no	—
289	C₂×D₄×C₃₁	—	2	2	no	—
290	C₂×D₄×C₃₁	—	2	2	no	—
291	C₂×D₄×C₃₁	—	2	4	no	—
292	C₂×D₄×C₃₁	—	4	2	no	—
293	C₂×D₄×C₃₁	—	4	2	no	—
294	C₂×D₄×C₃₁	—	4	8	no	—
295	C₂×D₄×C₃₁	—	4	4	no	—
296	C₂×D₄×C₃₁	—	4	8	no	—
297	C₂×D₄×C₃₁	—	4	4	no	—
298	C₂×D₄×C₃₁	—	8	2	no	—
299	C₂×D₄×C₃₁	—	8	4	no	—
300	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
303	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
304	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
305	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₃₁	—	2	1	no	—
307	C₂²×C₄×C₃₁	—	2	1	no	—
308	C₂²×C₄×C₃₁	—	2	4	no	—
309	C₂²×C₄×C₃₁	—	2	4	no	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
311	C₂²×C₄×C₃₁	—	2	2	no	—
312	C₂²×C₄×C₃₁	—	2	1	no	—
313	C₂²×C₄×C₃₁	—	2	2	no	—
314	C₂²×C₄×C₃₁	—	2	2	no	—
315	C₂²×C₄×C₃₁	—	2	4	no	—
316	C₂²×C₄×C₃₁	—	2	4	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	4	8	no	—
320	C₂²×C₄×C₃₁	—	4	8	no	—
321	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
323	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
324	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
325	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
329	Q₁₆×C₃₁	—	2	8	no	—
330	Q₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
331	SD₁₆×C₃₁	—	2	8	no	—
332	SD₁₆×C₃₁	—	2	8	no	—
333	SD₁₆×C₃₁	—	2	8	no	—
334	SD₁₆×C₃₁	—	4	4	no	—
335	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
336	D₈×C₃₁	—	2	8	no	—
337	D₈×C₃₁	—	2	8	no	—
338	D₈×C₃₁	—	4	4	no	—
339	M₁₆×C₃₁	—	2	4	no	—
340	M₁₆×C₃₁	—	2	2	no	—
341	M₁₆×C₃₁	—	2	8	no	—
342	M₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
343	C₂×C₈×C₃₁	—	2	8	no	—
344	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
345	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
346	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₃₁	—	2	1	no	—
348	C₄⋊C₄×C₃₁	—	2	2	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	2	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	1	no	—
353	C₄⋊C₄×C₃₁	—	2	1	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
362	C₂²⋊C₄×C₃₁	—	2	2	no	—
363	C₂²⋊C₄×C₃₁	—	2	1	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	—	2	4	no	—
366	C₂²⋊C₄×C₃₁	—	2	4	no	—
367	C₂²⋊C₄×C₃₁	—	2	2	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	1	no	—
370	C₂²⋊C₄×C₃₁	—	2	1	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
377	C₄²×C₃₁	—	2	1	no	—
378	C₄²×C₃₁	—	2	1	no	—
379	C₄²×C₃₁	—	2	1	no	—
380	C₄²×C₃₁	—	2	2	no	—
381	C₄²×C₃₁	—	2	2	no	—
382	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
386	#61070	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂³×C₃₁	—	2	1	no	—
388	C₂³×C₃₁	—	2	4	no	—
389	C₂³×C₃₁	—	2	2	no	—
390	C₂³×C₃₁	—	2	4	no	—
391	C₂³×C₃₁	—	4	2	no	—
392	C₂³×C₃₁	—	4	2	no	—
393	C₂³×C₃₁	—	4	4	no	—
394	C₂³×C₃₁	—	4	4	no	—
395	C₂³×C₃₁	—	4	4	no	—
396	C₂³×C₃₁	—	4	4	no	—
397	C₂³×C₃₁	—	4	4	no	—
398	C₂³×C₃₁	—	8	2	no	—
399	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
400	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
401	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
402	Q₈×C₃₁	—	2	4	no	—
403	Q₈×C₃₁	—	2	2	no	—
404	Q₈×C₃₁	—	2	1	no	—
405	Q₈×C₃₁	—	2	2	no	—
406	Q₈×C₃₁	—	2	2	no	—
407	Q₈×C₃₁	—	4	4	no	—
408	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
409	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
410	D₄×C₃₁	—	2	4	no	—
411	D₄×C₃₁	—	2	2	no	—
412	D₄×C₃₁	—	2	2	no	—
413	D₄×C₃₁	—	2	4	no	—
414	D₄×C₃₁	—	2	2	no	—
415	D₄×C₃₁	—	2	1	no	—
416	D₄×C₃₁	—	2	2	no	—
417	D₄×C₃₁	—	2	4	no	—
418	D₄×C₃₁	—	4	2	no	—
419	D₄×C₃₁	—	4	4	no	—
420	D₄×C₃₁	—	4	4	no	—
421	D₄×C₃₁	—	4	8	no	—
422	D₄×C₃₁	—	4	8	no	—
423	D₄×C₃₁	—	4	4	no	—
424	D₄×C₃₁	—	4	4	no	—
425	D₄×C₃₁	—	4	4	no	—
426	D₄×C₃₁	—	4	4	no	—
427	D₄×C₃₁	—	4	4	no	—
428	D₄×C₃₁	—	4	2	no	—
429	D₄×C₃₁	—	4	4	no	—
430	D₄×C₃₁	—	8	1	no	—
431	D₄×C₃₁	—	8	2	no	—
432	D₄×C₃₁	—	8	2	no	—
433	D₄×C₃₁	—	8	2	no	—
434	D₄×C₃₁	—	8	4	no	—
435	D₄×C₃₁	—	8	4	no	—
436	D₄×C₃₁	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₃₁	—	2	4	no	—
438	C₂×C₄×C₃₁	—	2	4	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	1	no	—
441	C₂×C₄×C₃₁	—	2	4	no	—
442	C₂×C₄×C₃₁	—	2	4	no	—
443	C₂×C₄×C₃₁	—	2	4	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	1	no	—
450	C₂×C₄×C₃₁	—	2	1	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	4	1	no	—
454	C₂×C₄×C₃₁	—	4	4	no	—
455	C₂×C₄×C₃₁	—	4	8	no	—
456	C₂×C₄×C₃₁	—	4	8	no	—
457	C₂×C₄×C₃₁	—	4	4	no	—
458	C₂×C₄×C₃₁	—	4	4	no	—
459	C₂×C₄×C₃₁	—	4	2	no	—
460	C₂×C₄×C₃₁	—	4	4	no	—
461	C₂×C₄×C₃₁	—	4	2	no	—
462	C₂×C₄×C₃₁	—	8	1	no	—
463	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
472	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
473	C₈×C₃₁	—	2	4	no	—
474	C₈×C₃₁	—	2	2	no	—
475	C₈×C₃₁	C₂²×D₄	1	4	yes	—
476	C₂×#575	C₂×C₃₁	1	2	yes	complemented
477	D₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
478	C₂×#550	C₂×C₃₁	1	1	yes	characteristic, complemented
479	#3287	C₂×C₃₁	1	2	yes	complemented
480	#3284	C₂×C₃₁	1	2	yes	complemented
481	#3278	C₂×C₃₁	1	2	yes	complemented
482	#3274	C₂×C₃₁	1	2	yes	complemented
483	#3271	C₂×C₃₁	1	4	yes	complemented
484	#3268	C₂×C₃₁	1	4	yes	complemented
485	#3151	C₂×C₃₁	1	1	yes	characteristic, complemented
486	#3055	C₂×C₃₁	1	2	yes	complemented
487	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
488	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#3006	C₂×C₃₁	1	2	yes	complemented
490	#3005	C₂×C₃₁	1	2	yes	complemented
491	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
492	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
493	C₂²×C₃₁	—	2	1	no	—
494	C₂²×C₃₁	—	2	1	no	—
495	C₂²×C₃₁	—	2	2	no	—
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	2	no	—
498	C₂²×C₃₁	—	2	2	no	—
499	C₂²×C₃₁	—	2	2	no	—
500	C₂²×C₃₁	—	2	2	no	—
501	C₂²×C₃₁	—	2	2	no	—
502	C₂²×C₃₁	—	4	1	no	—
503	C₂²×C₃₁	—	4	1	no	—
504	C₂²×C₃₁	—	4	4	no	—
505	C₂²×C₃₁	—	4	2	no	—
506	C₂²×C₃₁	—	4	4	no	—
507	C₂²×C₃₁	—	4	2	no	—
508	C₂²×C₃₁	—	4	4	no	—
509	C₂²×C₃₁	—	4	2	no	—
510	C₂²×C₃₁	—	8	4	no	—
511	C₂²×C₃₁	—	8	8	no	—
512	C₂²×C₃₁	—	8	8	no	—
513	C₂²×C₃₁	D₄²	1	2	yes	—
514	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₃₁	—	2	1	no	—
516	C₄×C₃₁	—	2	1	no	—
517	C₄×C₃₁	—	2	2	no	—
518	C₄×C₃₁	—	2	2	no	—
519	C₄×C₃₁	—	2	2	no	—
520	C₄×C₃₁	—	2	4	no	—
521	C₄×C₃₁	—	2	1	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	—	4	1	no	—
524	C₄×C₃₁	—	4	2	no	—
525	C₄×C₃₁	—	4	1	no	—
526	C₄×C₃₁	D₄²	1	2	yes	—
527	C₄×C₃₁	#575	1	2	yes	complemented
528	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
529	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂²×#41	C₂²×C₃₁	1	2	yes	—
531	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
532	#575	—	2	16	no	—
533	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
534	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
535	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
536	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
537	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
538	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
539	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
540	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
541	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
542	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
543	#550	—	2	1	no	—
544	#550	—	2	1	no	—
545	#550	—	2	2	no	—
546	#550	C₂²×C₃₁	1	2	yes	—
547	#550	C₂²×C₃₁	1	4	yes	complemented
548	#550	C₂²×C₃₁	1	2	yes	complemented
549	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
550	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
551	#548	C₂²×C₃₁	1	2	yes	complemented
552	#547	—	2	1	no	—
553	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#546	—	2	2	no	—
555	#546	C₂²×C₃₁	1	2	yes	complemented
556	D₄²	—	2	1	no	—
557	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
558	#532	—	2	1	no	—
559	#532	C₂²×C₃₁	1	1	yes	characteristic
560	C₂×#127	—	2	1	no	—
561	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	#525	—	2	2	no	—
563	#525	C₂²×C₃₁	1	2	yes	—
564	C₂×#121	—	2	2	no	—
565	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
566	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
567	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	C₂×C₄×D₄	—	2	1	no	—
569	C₂×C₄×D₄	—	2	1	no	—
570	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
571	#496	C₂²×C₃₁	1	4	yes	complemented
572	#493	C₂²×C₃₁	1	2	yes	complemented
573	#492	C₂²×C₃₁	1	2	yes	complemented
574	#469	C₂²×C₃₁	1	4	yes	complemented
575	#468	C₂²×C₃₁	1	4	yes	complemented
576	#466	C₂²×C₃₁	1	4	yes	complemented
577	#465	C₂²×C₃₁	1	4	yes	complemented
578	#464	C₂²×C₃₁	1	4	yes	complemented
579	#462	C₂²×C₃₁	1	2	yes	complemented
580	#460	C₂²×C₃₁	1	2	yes	complemented
581	#460	C₂²×C₃₁	1	2	yes	complemented
582	#460	C₂²×C₃₁	1	2	yes	complemented
583	#459	C₂²×C₃₁	1	2	yes	complemented
584	#459	C₂²×C₃₁	1	2	yes	complemented
585	#452	C₂²×C₃₁	1	4	yes	complemented
586	#452	C₂²×C₃₁	1	4	yes	complemented
587	#449	C₂²×C₃₁	1	4	yes	complemented
588	#449	C₂²×C₃₁	1	4	yes	complemented
589	#449	C₂²×C₃₁	1	4	yes	complemented
590	#449	C₂²×C₃₁	1	4	yes	complemented
591	#448	C₂²×C₃₁	1	4	yes	complemented
592	#447	C₂²×C₃₁	1	4	yes	complemented
593	#441	C₂²×C₃₁	1	2	yes	complemented
594	#440	C₂²×C₃₁	1	2	yes	complemented
595	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
596	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
597	#436	C₂²×C₃₁	1	2	yes	complemented
598	#435	C₂²×C₃₁	1	4	yes	complemented
599	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
600	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#418	C₂²×C₃₁	1	2	yes	complemented
604	#417	C₂²×C₃₁	1	1	yes	characteristic
605	#417	C₂²×C₃₁	1	2	yes	complemented
606	#407	C₂²×C₃₁	1	2	yes	complemented
607	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	C₂×C₃₁	—	2	2	no	—
609	C₂×C₃₁	—	4	2	no	—
610	C₂×C₃₁	—	4	2	no	—
611	C₂×C₃₁	—	4	2	no	—
612	C₂×C₃₁	—	8	4	no	—
613	C₂×C₃₁	—	8	2	no	—
614	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
615	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
616	C₂×C₃₁	#3585	1	1	yes	characteristic
617	C₂×#41	—	2	2	no	—
618	C₂×#41	—	2	2	no	—
619	C₂×#41	—	2	2	no	—
620	C₂×#41	—	2	2	no	—
621	C₂×#41	—	2	8	no	—
622	C₂×#41	—	2	8	no	—
623	C₂×#41	—	4	4	no	—
624	C₂×#41	—	4	4	no	—
625	C₂×#41	C₂³×C₃₁	1	2	yes	—
626	C₂×#41	C₂³×C₃₁	1	2	yes	—
627	C₂×#41	C₂³×C₃₁	1	2	yes	—
628	C₂×#41	C₂³×C₃₁	1	4	yes	—
629	C₂×#41	C₂³×C₃₁	1	4	yes	—
630	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
632	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₂²×D₄	—	2	2	no	—
634	C₂²×D₄	—	2	2	no	—
635	C₂²×D₄	—	2	2	no	—
636	C₂²×D₄	—	2	1	no	—
637	C₂²×D₄	—	2	1	no	—
638	C₂²×D₄	—	2	1	no	—
639	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
640	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
641	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
642	C₂³×C₄	—	2	2	no	—
643	C₂³×C₄	—	2	2	no	—
644	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
645	#137	—	2	8	no	—
646	#137	—	2	16	no	—
647	#137	D₄×C₃₁	1	8	yes	complemented
648	AGL(1,ℤ/8)	—	2	8	no	—
649	AGL(1,ℤ/8)	—	2	16	no	—
650	AGL(1,ℤ/8)	—	2	8	no	—
651	AGL(1,ℤ/8)	—	4	4	no	—
652	#135	—	2	16	no	—
653	#135	—	2	16	no	—
654	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
655	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
656	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
657	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
658	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
659	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
660	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
661	C₂×D₈	C₂³×C₃₁	1	4	yes	—
662	C₂×D₈	C₂³×C₃₁	1	4	yes	—
663	C₂×D₈	C₂³×C₃₁	1	4	yes	—
664	C₂×M₁₆	—	2	8	no	—
665	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
667	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
668	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
669	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
670	C₄⋊Q₈	—	2	1	no	—
671	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
672	#127	—	2	2	no	—
673	#127	—	2	2	no	—
674	#127	—	2	4	no	—
675	#127	—	2	1	no	—
676	#127	—	2	1	no	—
677	#127	—	2	1	no	—
678	#127	C₂³×C₃₁	1	2	yes	—
679	#127	C₂³×C₃₁	1	2	yes	—
680	#127	C₂³×C₃₁	1	1	yes	characteristic
681	#124	—	2	2	no	—
682	#124	C₂³×C₃₁	1	2	yes	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
690	#121	—	2	2	no	—
691	#121	—	2	1	no	—
692	#121	—	2	2	no	—
693	#121	—	2	2	no	—
694	#121	—	2	1	no	—
695	#121	—	2	1	no	—
696	#121	—	2	1	no	—
697	#121	—	2	4	no	—
698	#121	—	2	4	no	—
699	#121	—	2	4	no	—
700	#121	—	2	4	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	C₂³×C₃₁	1	4	yes	—
704	#121	C₂³×C₃₁	1	4	yes	—
705	#121	C₂³×C₃₁	1	2	yes	—
706	#121	C₂³×C₃₁	1	2	yes	—
707	#120	—	2	2	no	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
713	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
714	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
715	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	1	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	4	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
729	C₄×D₄	D₄×C₃₁	1	2	yes	—
730	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
733	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
734	C₄×D₄	C₂³×C₃₁	1	2	yes	—
735	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
736	#117	—	2	1	no	—
737	#117	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	—	2	1	no	—
740	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
741	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	—	2	2	no	—
743	C₂×C₂²⋊C₄	—	2	2	no	—
744	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
745	C₂×C₄²	—	2	1	no	—
746	C₂×C₄²	—	2	1	no	—
747	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
748	#107	C₂³×C₃₁	1	2	yes	—
749	#106	C₂³×C₃₁	1	2	yes	—
750	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
751	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
752	#103	C₂³×C₃₁	1	2	yes	—
753	#103	C₂³×C₃₁	1	4	yes	—
754	#103	C₂³×C₃₁	1	2	yes	—
755	#103	C₂³×C₃₁	1	2	yes	—
756	#102	C₂³×C₃₁	1	2	yes	—
757	#102	C₂³×C₃₁	1	4	yes	—
758	#102	C₂³×C₃₁	1	4	yes	—
759	#102	C₂³×C₃₁	1	4	yes	—
760	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
761	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
762	#97	C₂³×C₃₁	1	2	yes	—
763	C₄×C₈	C₂³×C₃₁	1	2	yes	—
764	C₃₁	#61070	1	1	yes	characteristic, direct product factor, Sylow
765	C₂⁴	—	2	2	no	—
766	C₂⁴	—	2	2	no	—
767	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
768	#41	—	2	2	no	—
769	#41	—	2	4	no	—
770	#41	—	2	8	no	—
771	#41	—	2	8	no	—
772	#41	—	2	4	no	—
773	#41	—	2	4	no	—
774	#41	—	2	4	no	—
775	#41	—	4	8	no	—
776	#41	—	4	4	no	—
777	#41	—	4	2	no	—
778	#41	—	4	4	no	—
779	#41	—	4	2	no	—
780	#41	—	4	8	no	—
781	#41	—	4	8	no	—
782	#41	—	4	8	no	—
783	#41	C₂×D₄×C₃₁	1	4	yes	—
784	C₂×Q₈	—	2	1	no	—
785	C₂×Q₈	—	2	2	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	4	no	—
788	C₂×Q₈	—	4	2	no	—
789	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	complemented
790	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
791	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	4	no	—
800	C₂×D₄	—	2	4	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	4	no	—
803	C₂×D₄	—	2	4	no	—
804	C₂×D₄	—	2	4	no	—
805	C₂×D₄	—	2	1	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	1	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	4	2	no	—
815	C₂×D₄	—	4	2	no	—
816	C₂×D₄	—	4	8	no	—
817	C₂×D₄	—	4	4	no	—
818	C₂×D₄	—	4	8	no	—
819	C₂×D₄	—	4	4	no	—
820	C₂×D₄	—	8	2	no	—
821	C₂×D₄	—	8	4	no	—
822	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
823	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
825	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
826	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
827	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	4	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	4	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	1	no	—
841	C₂²×C₄	—	4	8	no	—
842	C₂²×C₄	—	4	8	no	—
843	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
844	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
845	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
846	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
847	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
851	Q₁₆	—	2	8	no	—
852	Q₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
853	SD₁₆	—	2	8	no	—
854	SD₁₆	—	2	8	no	—
855	SD₁₆	—	2	8	no	—
856	SD₁₆	—	4	4	no	—
857	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
858	D₈	—	2	8	no	—
859	D₈	—	2	8	no	—
860	D₈	—	4	4	no	—
861	M₁₆	—	2	4	no	—
862	M₁₆	—	2	2	no	—
863	M₁₆	—	2	8	no	—
864	M₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
865	C₂×C₈	—	2	8	no	—
866	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
867	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
868	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
879	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
880	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
882	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
883	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	1	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
905	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂³	—	2	1	no	—
909	C₂³	—	2	4	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	4	no	—
912	C₂³	—	4	2	no	—
913	C₂³	—	4	2	no	—
914	C₂³	—	4	4	no	—
915	C₂³	—	4	4	no	—
916	C₂³	—	4	4	no	—
917	C₂³	—	4	4	no	—
918	C₂³	—	4	4	no	—
919	C₂³	—	8	2	no	—
920	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
921	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
922	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
923	Q₈	—	2	4	no	—
924	Q₈	—	2	2	no	—
925	Q₈	—	2	1	no	—
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	4	no	—
929	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
930	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
931	D₄	—	2	4	no	—
932	D₄	—	2	2	no	—
933	D₄	—	2	2	no	—
934	D₄	—	2	4	no	—
935	D₄	—	2	2	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	2	no	—
938	D₄	—	2	4	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	4	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	8	no	—
943	D₄	—	4	8	no	—
944	D₄	—	4	4	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	4	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	2	no	—
950	D₄	—	4	4	no	—
951	D₄	—	8	1	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	2	no	—
955	D₄	—	8	4	no	—
956	D₄	—	8	4	no	—
957	D₄	C₂²×D₄×C₃₁	1	2	yes	—
958	C₂×C₄	—	2	4	no	—
959	C₂×C₄	—	2	4	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	4	no	—
963	C₂×C₄	—	2	4	no	—
964	C₂×C₄	—	2	4	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	4	1	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	8	no	—
977	C₂×C₄	—	4	8	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	2	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	2	no	—
983	C₂×C₄	—	8	1	no	—
984	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
985	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
986	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
988	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
989	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
991	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
992	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
993	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
994	C₈	—	2	4	no	—
995	C₈	—	2	2	no	—
996	C₈	C₂²×D₄×C₃₁	1	4	yes	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	4	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	4	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	4	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	8	4	no	—
1015	C₂²	—	8	8	no	—
1016	C₂²	—	8	8	no	—
1017	C₂²	D₄²×C₃₁	1	2	yes	—
1018	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1019	C₄	—	2	2	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	4	no	—
1023	C₄	—	2	1	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	2	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	1	no	—
1030	C₄	D₄²×C₃₁	1	2	yes	—
1031	C₄	C₃₁×#575	1	2	yes	complemented
1032	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1033	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1034	C₂	—	2	2	no	—
1035	C₂	—	4	2	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	2	no	—
1038	C₂	—	8	4	no	—
1039	C₂	—	8	2	no	—
1040	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1041	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1042	C₂	C₃₁×#3585	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. C₂×C₃₁×#575	C₂	semidirect
2. D₄×#41×C₃₁	C₂	semidirect
3. C₂×C₃₁×#550	C₂	semidirect
4. C₃₁×#3287	C₂	semidirect
5. C₃₁×#3284	C₂	semidirect
6. C₃₁×#3278	C₂	semidirect
7. C₃₁×#3274	C₂	semidirect
8. C₃₁×#3271	C₂	semidirect
9. C₃₁×#3268	C₂	semidirect
10. C₃₁×#3151	C₂	semidirect
11. C₃₁×#3055	C₂	semidirect
12. C₃₁×#3038	C₂	semidirect
13. C₃₁×#3037	C₂	semidirect
14. C₃₁×#3006	C₂	semidirect
15. C₃₁×#3005	C₂	semidirect
16. C₄×C₃₁×#137	C₂	semidirect
17. D₄×M₁₆×C₃₁	C₂	semidirect
19. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
27. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₃₁×#135	C₂²	semidirect
29. C₂×C₃₁×#135	C₂²	semidirect
30. C₂²×M₁₆×C₃₁	C₂²	semidirect
35. C₃₁×#550	C₂²	semidirect
36. C₃₁×#550	C₂²	semidirect
37. C₃₁×#550	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
39. C₃₁×#548	C₂²	semidirect
41. C₃₁×#547	C₂²	semidirect
43. C₃₁×#546	C₂²	semidirect
45. D₄²×C₃₁	C₂²	semidirect
49. C₂×C₃₁×#127	C₂²	semidirect
53. C₂×C₃₁×#121	C₂²	semidirect
55. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#496	C₂²	semidirect
60. C₃₁×#493	C₂²	semidirect
61. C₃₁×#492	C₂²	semidirect
62. C₃₁×#469	C₂²	semidirect
63. C₃₁×#468	C₂²	semidirect
64. C₃₁×#466	C₂²	semidirect
65. C₃₁×#465	C₂²	semidirect
66. C₃₁×#464	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#460	C₂²	semidirect
69. C₃₁×#460	C₂²	semidirect
70. C₃₁×#460	C₂²	semidirect
71. C₃₁×#459	C₂²	semidirect
72. C₃₁×#459	C₂²	semidirect
73. C₃₁×#452	C₂²	semidirect
74. C₃₁×#452	C₂²	semidirect
75. C₃₁×#449	C₂²	semidirect
76. C₃₁×#449	C₂²	semidirect
77. C₃₁×#449	C₂²	semidirect
78. C₃₁×#449	C₂²	semidirect
79. C₃₁×#448	C₂²	semidirect
80. C₃₁×#447	C₂²	semidirect
81. C₃₁×#441	C₂²	semidirect
82. C₃₁×#440	C₂²	semidirect
83. C₄×Q₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₃₁×#436	C₂²	semidirect
86. C₃₁×#435	C₂²	semidirect
87. C₈×D₄×C₃₁	C₂²	semidirect
88. C₃₁×#428	C₂²	semidirect
89. C₃₁×#423	C₂²	semidirect
90. C₃₁×#419	C₂²	semidirect
91. C₃₁×#418	C₂²	semidirect
93. C₃₁×#417	C₂²	semidirect
94. C₃₁×#407	C₂²	semidirect
95. C₄×M₁₆×C₃₁	C₂²	semidirect
126. C₃₁×#137	D₄	semidirect
267. C₂×Q₈×C₃₁	C₂×D₄	semidirect
330. Q₁₆×C₃₁	C₂×D₄	semidirect
335. SD₁₆×C₃₁	C₂×D₄	semidirect
342. M₁₆×C₃₁	C₂×D₄	semidirect
386. #61070	C₃₁	direct (N × H)
476. C₂×#575	C₂×C₃₁	semidirect
477. D₄×#41	C₂×C₃₁	semidirect
478. C₂×#550	C₂×C₃₁	semidirect
479. #3287	C₂×C₃₁	semidirect
480. #3284	C₂×C₃₁	semidirect
481. #3278	C₂×C₃₁	semidirect
482. #3274	C₂×C₃₁	semidirect
483. #3271	C₂×C₃₁	semidirect
484. #3268	C₂×C₃₁	semidirect
485. #3151	C₂×C₃₁	semidirect
486. #3055	C₂×C₃₁	semidirect
487. #3038	C₂×C₃₁	semidirect
488. #3037	C₂×C₃₁	semidirect
489. #3006	C₂×C₃₁	semidirect
490. #3005	C₂×C₃₁	semidirect
491. C₄×#137	C₂×C₃₁	semidirect
492. D₄×M₁₆	C₂×C₃₁	semidirect
527. C₄×C₃₁	#575	semidirect
531. C₂²×#41	C₂²×C₃₁	semidirect
534. C₂×#137	C₂²×C₃₁	semidirect
535. C₂×#137	C₂²×C₃₁	semidirect
537. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
538. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
539. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
540. C₂×#135	C₂²×C₃₁	semidirect
541. C₂×#135	C₂²×C₃₁	semidirect
542. C₂²×M₁₆	C₂²×C₃₁	semidirect
547. #550	C₂²×C₃₁	semidirect
548. #550	C₂²×C₃₁	semidirect
549. #550	C₂²×C₃₁	semidirect
550. D₄×Q₈	C₂²×C₃₁	semidirect
551. #548	C₂²×C₃₁	semidirect
553. #547	C₂²×C₃₁	semidirect
555. #546	C₂²×C₃₁	semidirect
557. D₄²	C₂²×C₃₁	semidirect
561. C₂×#127	C₂²×C₃₁	semidirect
565. C₂×#121	C₂²×C₃₁	semidirect
567. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
571. #496	C₂²×C₃₁	semidirect
572. #493	C₂²×C₃₁	semidirect
573. #492	C₂²×C₃₁	semidirect
574. #469	C₂²×C₃₁	semidirect
575. #468	C₂²×C₃₁	semidirect
576. #466	C₂²×C₃₁	semidirect
577. #465	C₂²×C₃₁	semidirect
578. #464	C₂²×C₃₁	semidirect
579. #462	C₂²×C₃₁	semidirect
580. #460	C₂²×C₃₁	semidirect
581. #460	C₂²×C₃₁	semidirect
582. #460	C₂²×C₃₁	semidirect
583. #459	C₂²×C₃₁	semidirect
584. #459	C₂²×C₃₁	semidirect
585. #452	C₂²×C₃₁	semidirect
586. #452	C₂²×C₃₁	semidirect
587. #449	C₂²×C₃₁	semidirect
588. #449	C₂²×C₃₁	semidirect
589. #449	C₂²×C₃₁	semidirect
590. #449	C₂²×C₃₁	semidirect
591. #448	C₂²×C₃₁	semidirect
592. #447	C₂²×C₃₁	semidirect
593. #441	C₂²×C₃₁	semidirect
594. #440	C₂²×C₃₁	semidirect
595. C₄×Q₁₆	C₂²×C₃₁	semidirect
596. C₄×SD₁₆	C₂²×C₃₁	semidirect
597. #436	C₂²×C₃₁	semidirect
598. #435	C₂²×C₃₁	semidirect
599. C₈×D₄	C₂²×C₃₁	semidirect
600. #428	C₂²×C₃₁	semidirect
601. #423	C₂²×C₃₁	semidirect
602. #419	C₂²×C₃₁	semidirect
603. #418	C₂²×C₃₁	semidirect
605. #417	C₂²×C₃₁	semidirect
606. #407	C₂²×C₃₁	semidirect
607. C₄×M₁₆	C₂²×C₃₁	semidirect
647. #137	D₄×C₃₁	semidirect
764. C₃₁	#61070	direct (N × H)
789. C₂×Q₈	C₂×D₄×C₃₁	semidirect
852. Q₁₆	C₂×D₄×C₃₁	semidirect
857. SD₁₆	C₂×D₄×C₃₁	semidirect
864. M₁₆	C₂×D₄×C₃₁	semidirect
1031. C₄	C₃₁×#575	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#575	2
D₄×#41×C₃₁	2
C₂×C₃₁×#550	2
C₃₁×#3287	2
C₃₁×#3284	2
C₃₁×#3278	2
C₃₁×#3274	2
C₃₁×#3271	2
C₃₁×#3268	2
C₃₁×#3151	2
C₃₁×#3055	2
C₃₁×#3038	2
C₃₁×#3037	2
C₃₁×#3006	2
C₃₁×#3005	2
C₄×C₃₁×#137	2
D₄×M₁₆×C₃₁	2
#61070	31

Subgroups — C31×#61070 #21517829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61070 #21517829