Subgroups — C₃₁×#61380 #21518139

Order 7936.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3390	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3389	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3388	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3387	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3386	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3384	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#501	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3079	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic
22	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic
23	C₃₁×#2943	C₂	1	1	yes	maximal, characteristic
24	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
25	Q₈²×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#557	C₂²	1	2	yes	—
27	C₃₁×#557	C₂²	1	2	yes	—
28	C₃₁×#557	C₂²	1	2	yes	—
29	C₃₁×#554	—	2	2	no	—
30	C₃₁×#554	—	2	2	no	—
31	C₃₁×#554	—	2	2	no	—
32	C₃₁×#554	C₂²	1	2	yes	—
33	C₃₁×#554	C₂²	1	2	yes	—
34	C₃₁×#554	C₂²	1	2	yes	—
35	D₄×Q₈×C₃₁	—	2	2	no	—
36	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
37	C₃₁×#544	—	2	1	no	—
38	C₃₁×#544	—	2	1	no	—
39	C₃₁×#544	—	2	1	no	—
40	C₃₁×#544	—	2	1	no	—
41	C₃₁×#544	C₂²	1	1	yes	characteristic
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#544	C₂²	1	1	yes	characteristic
44	C₃₁×#544	C₂²	1	1	yes	characteristic
45	C₃₁×#533	—	2	1	no	—
46	C₃₁×#533	—	2	1	no	—
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
49	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#125	—	2	1	no	—
51	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
52	C₃₁×#520	C₂²	1	1	yes	characteristic
53	C₃₁×#520	C₂²	1	1	yes	characteristic
54	C₃₁×#520	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	1	yes	characteristic
56	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₃₁×#501	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#501	C₂²	1	2	yes	—
61	C₃₁×#501	C₂²	1	2	yes	—
62	C₃₁×#501	C₂²	1	2	yes	—
63	C₃₁×#501	C₂²	1	2	yes	—
64	C₃₁×#501	C₂²	1	2	yes	—
65	C₃₁×#501	C₂²	1	2	yes	—
66	C₃₁×#500	C₂²	1	2	yes	—
67	C₃₁×#499	C₂²	1	2	yes	—
68	C₃₁×#499	C₂²	1	2	yes	—
69	C₃₁×#498	C₂²	1	2	yes	—
70	C₃₁×#479	C₂²	1	2	yes	—
71	C₃₁×#479	C₂²	1	2	yes	—
72	C₃₁×#479	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#479	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	—
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	—
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#478	C₂²	1	2	yes	—
82	C₃₁×#477	C₂²	1	2	yes	—
83	C₃₁×#477	C₂²	1	2	yes	—
84	C₃₁×#477	C₂²	1	2	yes	—
85	C₃₁×#476	C₂²	1	2	yes	—
86	C₃₁×#476	C₂²	1	2	yes	—
87	C₃₁×#476	C₂²	1	2	yes	—
88	C₃₁×#475	C₂²	1	2	yes	—
89	C₃₁×#475	C₂²	1	2	yes	—
90	C₃₁×#475	C₂²	1	2	yes	—
91	C₃₁×#474	C₂²	1	2	yes	—
92	C₃₁×#474	C₂²	1	2	yes	—
93	C₃₁×#474	C₂²	1	2	yes	—
94	C₃₁×#446	C₂²	1	2	yes	—
95	C₃₁×#446	C₂²	1	2	yes	—
96	C₃₁×#446	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	—
98	C₃₁×#442	C₂²	1	1	yes	characteristic
99	C₃₁×#442	C₂²	1	2	yes	—
100	C₃₁×#442	C₂²	1	1	yes	characteristic
101	C₃₁×#441	C₂²	1	1	yes	characteristic
102	C₃₁×#441	C₂²	1	2	yes	—
103	C₃₁×#441	C₂²	1	1	yes	characteristic
104	C₃₁×#440	C₂²	1	1	yes	characteristic
105	C₃₁×#440	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	1	yes	characteristic
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	1	yes	characteristic
109	C₃₁×#440	C₂²	1	1	yes	characteristic
110	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
113	C₄×D₈×C₃₁	C₂²	1	2	yes	—
114	C₃₁×#428	C₂²	1	1	yes	characteristic
115	C₃₁×#428	C₂²	1	1	yes	characteristic
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#428	C₂²	1	1	yes	characteristic
118	C₃₁×#427	C₂²	1	1	yes	characteristic
119	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
120	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
121	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
122	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
123	C₃₁×#424	C₂²	1	1	yes	characteristic
124	C₃₁×#424	C₂²	1	1	yes	characteristic
125	C₃₁×#423	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic
127	C₃₁×#417	C₂²	1	1	yes	characteristic
128	C₃₁×#417	C₂²	1	1	yes	characteristic
129	C₃₁×#417	C₂²	1	1	yes	characteristic
130	C₃₁×#416	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₃₁×#405	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	—	2	2	no	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₃₁×#135	Q₈	1	8	yes	complemented
140	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	—	2	2	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	1	no	—
153	C₃₁×C₄⋊Q₈	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	—	2	2	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×#125	—	2	1	no	—
169	C₃₁×#125	—	2	1	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	1	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	D₄	1	1	yes	characteristic
181	C₃₁×#125	D₄	1	1	yes	characteristic
182	C₃₁×#125	C₂³	1	2	yes	—
183	C₃₁×#125	C₂³	1	2	yes	—
184	C₃₁×#125	C₂³	1	2	yes	—
185	C₃₁×#125	C₂³	1	2	yes	—
186	C₃₁×#125	C₂³	1	2	yes	—
187	C₃₁×#125	C₂³	1	2	yes	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
206	C₄×Q₈×C₃₁	—	2	2	no	—
207	C₄×Q₈×C₃₁	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	1	no	—
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	—	2	1	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	1	no	—
241	C₃₁×#117	—	2	1	no	—
242	C₃₁×#117	C₂³	1	1	yes	characteristic
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₃₁×#117	C₂³	1	1	yes	characteristic
245	C₃₁×#117	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
247	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
251	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
260	C₂×C₄²×C₃₁	—	2	1	no	—
261	C₂×C₄²×C₃₁	—	2	1	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	1	yes	characteristic
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#97	C₂³	1	1	yes	characteristic
306	C₃₁×#97	C₂³	1	1	yes	characteristic
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
313	#41×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	2	2	no	—
315	#41×C₃₁	C₂×Q₈	1	4	yes	—
316	#41×C₃₁	C₂×Q₈	1	4	yes	complemented
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	8	4	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₃₁	—	2	1	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	—	2	1	no	—
334	C₂²×C₄×C₃₁	—	2	1	no	—
335	C₂²×C₄×C₃₁	—	2	1	no	—
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	1	no	—
338	C₂²×C₄×C₃₁	—	2	1	no	—
339	C₂²×C₄×C₃₁	—	2	1	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	1	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	Q₁₆×C₃₁	C₂×Q₈	1	4	yes	complemented
351	SD₁₆×C₃₁	C₂×Q₈	1	4	yes	complemented
352	SD₁₆×C₃₁	C₂×Q₈	1	4	yes	complemented
353	D₈×C₃₁	C₂×Q₈	1	4	yes	complemented
354	M₁₆×C₃₁	—	2	2	no	—
355	M₁₆×C₃₁	—	2	2	no	—
356	C₂×C₈×C₃₁	—	2	2	no	—
357	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	complemented
358	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
359	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	1	no	—
369	C₄⋊C₄×C₃₁	—	2	1	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
377	C₄⋊C₄×C₃₁	—	2	2	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	1	no	—
413	C₂²⋊C₄×C₃₁	—	2	1	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	1	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	1	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
424	C₄²×C₃₁	—	2	1	no	—
425	C₄²×C₃₁	—	2	1	no	—
426	C₄²×C₃₁	—	2	1	no	—
427	C₄²×C₃₁	—	2	1	no	—
428	C₄²×C₃₁	—	2	1	no	—
429	C₄²×C₃₁	—	2	1	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	2	no	—
432	C₄²×C₃₁	—	2	2	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₃₁	C₂⁴	1	2	yes	—
437	C₄²×C₃₁	C₂⁴	1	2	yes	—
438	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
440	#61380	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂³×C₃₁	—	2	1	no	—
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
444	Q₈×C₃₁	—	2	1	no	—
445	Q₈×C₃₁	—	2	1	no	—
446	Q₈×C₃₁	—	4	2	no	—
447	Q₈×C₃₁	—	4	2	no	—
448	Q₈×C₃₁	—	4	4	no	—
449	Q₈×C₃₁	—	8	2	no	—
450	Q₈×C₃₁	—	8	2	no	—
451	Q₈×C₃₁	—	8	2	no	—
452	Q₈×C₃₁	—	8	2	no	—
453	Q₈×C₃₁	—	8	2	no	—
454	Q₈×C₃₁	C₂²×Q₈	1	2	yes	—
455	Q₈×C₃₁	C₂²×Q₈	1	2	yes	—
456	D₄×C₃₁	—	2	4	no	—
457	D₄×C₃₁	—	2	4	no	—
458	D₄×C₃₁	—	2	1	no	—
459	D₄×C₃₁	—	2	1	no	—
460	D₄×C₃₁	C₂²×Q₈	1	2	yes	—
461	D₄×C₃₁	C₂²×Q₈	1	2	yes	—
462	C₂×C₄×C₃₁	—	2	1	no	—
463	C₂×C₄×C₃₁	—	2	1	no	—
464	C₂×C₄×C₃₁	—	2	4	no	—
465	C₂×C₄×C₃₁	—	2	4	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	2	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	4	1	no	—
475	C₂×C₄×C₃₁	—	4	1	no	—
476	C₂×C₄×C₃₁	—	4	2	no	—
477	C₂×C₄×C₃₁	—	4	2	no	—
478	C₂×C₄×C₃₁	—	8	1	no	—
479	C₂×C₄×C₃₁	—	8	2	no	—
480	C₂×C₄×C₃₁	—	8	1	no	—
481	C₂×C₄×C₃₁	—	8	2	no	—
482	C₂×C₄×C₃₁	—	8	2	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	—	8	1	no	—
485	C₂×C₄×C₃₁	—	8	1	no	—
486	C₂×C₄×C₃₁	—	8	1	no	—
487	C₂×C₄×C₃₁	—	8	1	no	—
488	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
498	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
499	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
500	C₈×C₃₁	—	2	1	no	—
501	C₈×C₃₁	—	2	1	no	—
502	C₈×C₃₁	—	2	2	no	—
503	C₈×C₃₁	—	2	2	no	—
504	C₈×C₃₁	C₂²×Q₈	1	2	yes	—
505	C₈×C₃₁	C₂²×Q₈	1	2	yes	—
506	#3504	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3503	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3390	C₂×C₃₁	1	2	yes	complemented
509	#3389	C₂×C₃₁	1	2	yes	complemented
510	#3388	C₂×C₃₁	1	2	yes	complemented
511	#3388	C₂×C₃₁	1	2	yes	complemented
512	#3387	C₂×C₃₁	1	2	yes	complemented
513	#3386	C₂×C₃₁	1	2	yes	complemented
514	#3385	C₂×C₃₁	1	2	yes	complemented
515	#3384	C₂×C₃₁	1	2	yes	complemented
516	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3163	C₂×C₃₁	1	1	yes	characteristic, complemented
518	C₂×#501	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3079	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#2961	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#2952	C₂×C₃₁	1	1	yes	characteristic
527	#2951	C₂×C₃₁	1	1	yes	characteristic
528	#2943	C₂×C₃₁	1	1	yes	characteristic
529	C₂²×C₃₁	—	2	1	no	—
530	C₂²×C₃₁	—	2	1	no	—
531	C₂²×C₃₁	—	2	2	no	—
532	C₂²×C₃₁	—	2	2	no	—
533	C₂²×C₃₁	—	4	1	no	—
534	C₂²×C₃₁	—	4	1	no	—
535	C₂²×C₃₁	—	4	1	no	—
536	C₂²×C₃₁	—	4	1	no	—
537	C₂²×C₃₁	D₄×Q₈	1	2	yes	—
538	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
539	C₄×C₃₁	—	2	1	no	—
540	C₄×C₃₁	—	2	1	no	—
541	C₄×C₃₁	—	2	2	no	—
542	C₄×C₃₁	—	2	2	no	—
543	C₄×C₃₁	—	2	1	no	—
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	2	2	no	—
546	C₄×C₃₁	—	2	2	no	—
547	C₄×C₃₁	—	2	2	no	—
548	C₄×C₃₁	—	2	2	no	—
549	C₄×C₃₁	—	4	1	no	—
550	C₄×C₃₁	—	4	2	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	2	no	—
553	C₄×C₃₁	—	4	1	no	—
554	C₄×C₃₁	—	4	1	no	—
555	C₄×C₃₁	—	4	2	no	—
556	C₄×C₃₁	—	4	1	no	—
557	C₄×C₃₁	D₄×Q₈	1	2	yes	—
558	C₄×C₃₁	C₂³×Q₈	1	1	yes	characteristic
559	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
560	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
561	Q₈²	C₂²×C₃₁	1	2	yes	—
562	#557	C₂²×C₃₁	1	2	yes	—
563	#557	C₂²×C₃₁	1	2	yes	—
564	#557	C₂²×C₃₁	1	2	yes	—
565	#554	—	2	2	no	—
566	#554	—	2	2	no	—
567	#554	—	2	2	no	—
568	#554	C₂²×C₃₁	1	2	yes	—
569	#554	C₂²×C₃₁	1	2	yes	—
570	#554	C₂²×C₃₁	1	2	yes	—
571	D₄×Q₈	—	2	2	no	—
572	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
573	#544	—	2	1	no	—
574	#544	—	2	1	no	—
575	#544	—	2	1	no	—
576	#544	—	2	1	no	—
577	#544	C₂²×C₃₁	1	1	yes	characteristic
578	#544	C₂²×C₃₁	1	1	yes	characteristic
579	#544	C₂²×C₃₁	1	1	yes	characteristic
580	#544	C₂²×C₃₁	1	1	yes	characteristic
581	#533	—	2	1	no	—
582	#533	—	2	1	no	—
583	#533	C₂²×C₃₁	1	1	yes	characteristic
584	C₂×C₄⋊Q₈	—	2	1	no	—
585	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
586	C₂×#125	—	2	1	no	—
587	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
588	#520	C₂²×C₃₁	1	1	yes	characteristic
589	#520	C₂²×C₃₁	1	1	yes	characteristic
590	#520	C₂²×C₃₁	1	1	yes	characteristic
591	#520	C₂²×C₃₁	1	1	yes	characteristic
592	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
593	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
594	#501	C₂²×C₃₁	1	2	yes	—
595	#501	C₂²×C₃₁	1	2	yes	—
596	#501	C₂²×C₃₁	1	2	yes	—
597	#501	C₂²×C₃₁	1	2	yes	—
598	#501	C₂²×C₃₁	1	2	yes	—
599	#501	C₂²×C₃₁	1	2	yes	—
600	#501	C₂²×C₃₁	1	2	yes	—
601	#501	C₂²×C₃₁	1	2	yes	—
602	#500	C₂²×C₃₁	1	2	yes	—
603	#499	C₂²×C₃₁	1	2	yes	—
604	#499	C₂²×C₃₁	1	2	yes	—
605	#498	C₂²×C₃₁	1	2	yes	—
606	#479	C₂²×C₃₁	1	2	yes	—
607	#479	C₂²×C₃₁	1	2	yes	—
608	#479	C₂²×C₃₁	1	2	yes	—
609	#479	C₂²×C₃₁	1	2	yes	—
610	#479	C₂²×C₃₁	1	2	yes	—
611	#479	C₂²×C₃₁	1	2	yes	—
612	#478	C₂²×C₃₁	1	2	yes	—
613	#478	C₂²×C₃₁	1	2	yes	—
614	#478	C₂²×C₃₁	1	2	yes	—
615	#478	C₂²×C₃₁	1	2	yes	—
616	#478	C₂²×C₃₁	1	2	yes	—
617	#478	C₂²×C₃₁	1	2	yes	—
618	#477	C₂²×C₃₁	1	2	yes	—
619	#477	C₂²×C₃₁	1	2	yes	—
620	#477	C₂²×C₃₁	1	2	yes	—
621	#476	C₂²×C₃₁	1	2	yes	—
622	#476	C₂²×C₃₁	1	2	yes	—
623	#476	C₂²×C₃₁	1	2	yes	—
624	#475	C₂²×C₃₁	1	2	yes	—
625	#475	C₂²×C₃₁	1	2	yes	—
626	#475	C₂²×C₃₁	1	2	yes	—
627	#474	C₂²×C₃₁	1	2	yes	—
628	#474	C₂²×C₃₁	1	2	yes	—
629	#474	C₂²×C₃₁	1	2	yes	—
630	#446	C₂²×C₃₁	1	2	yes	—
631	#446	C₂²×C₃₁	1	2	yes	—
632	#446	C₂²×C₃₁	1	2	yes	—
633	#446	C₂²×C₃₁	1	2	yes	—
634	#442	C₂²×C₃₁	1	1	yes	characteristic
635	#442	C₂²×C₃₁	1	2	yes	—
636	#442	C₂²×C₃₁	1	1	yes	characteristic
637	#441	C₂²×C₃₁	1	1	yes	characteristic
638	#441	C₂²×C₃₁	1	2	yes	—
639	#441	C₂²×C₃₁	1	1	yes	characteristic
640	#440	C₂²×C₃₁	1	1	yes	characteristic
641	#440	C₂²×C₃₁	1	2	yes	—
642	#440	C₂²×C₃₁	1	1	yes	characteristic
643	#440	C₂²×C₃₁	1	2	yes	—
644	#440	C₂²×C₃₁	1	1	yes	characteristic
645	#440	C₂²×C₃₁	1	1	yes	characteristic
646	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
647	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
648	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
649	C₄×D₈	C₂²×C₃₁	1	2	yes	—
650	#428	C₂²×C₃₁	1	1	yes	characteristic
651	#428	C₂²×C₃₁	1	1	yes	characteristic
652	#428	C₂²×C₃₁	1	1	yes	characteristic
653	#428	C₂²×C₃₁	1	1	yes	characteristic
654	#427	C₂²×C₃₁	1	1	yes	characteristic
655	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
656	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
657	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
658	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
659	#424	C₂²×C₃₁	1	1	yes	characteristic
660	#424	C₂²×C₃₁	1	1	yes	characteristic
661	#423	C₂²×C₃₁	1	1	yes	characteristic
662	#417	C₂²×C₃₁	1	1	yes	characteristic
663	#417	C₂²×C₃₁	1	1	yes	characteristic
664	#417	C₂²×C₃₁	1	1	yes	characteristic
665	#417	C₂²×C₃₁	1	1	yes	characteristic
666	#416	C₂²×C₃₁	1	1	yes	characteristic
667	#416	C₂²×C₃₁	1	1	yes	characteristic
668	#405	C₂²×C₃₁	1	1	yes	characteristic
669	#405	C₂²×C₃₁	1	1	yes	characteristic
670	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
671	C₂×C₃₁	—	2	2	no	—
672	C₂×C₃₁	—	4	2	no	—
673	C₂×C₃₁	—	4	2	no	—
674	C₂×C₃₁	C₂×D₄×Q₈	1	1	yes	characteristic
675	C₂×C₃₁	#3585	1	1	yes	characteristic
676	C₂×C₃₁	#3586	1	1	yes	characteristic
677	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
678	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
679	C₂²×Q₈	—	2	2	no	—
680	C₂²×Q₈	—	2	1	no	—
681	#135	Q₈×C₃₁	1	8	yes	complemented
682	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
685	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	2	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
703	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
708	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
709	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
710	#125	—	2	1	no	—
711	#125	—	2	1	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	1	no	—
715	#125	—	2	1	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	2	no	—
719	#125	—	2	2	no	—
720	#125	—	2	1	no	—
721	#125	—	2	1	no	—
722	#125	D₄×C₃₁	1	1	yes	characteristic
723	#125	D₄×C₃₁	1	1	yes	characteristic
724	#125	C₂³×C₃₁	1	2	yes	—
725	#125	C₂³×C₃₁	1	2	yes	—
726	#125	C₂³×C₃₁	1	2	yes	—
727	#125	C₂³×C₃₁	1	2	yes	—
728	#125	C₂³×C₃₁	1	2	yes	—
729	#125	C₂³×C₃₁	1	2	yes	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
747	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	—	2	2	no	—
750	C₄×Q₈	—	2	2	no	—
751	C₄×Q₈	—	2	2	no	—
752	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
759	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
760	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
761	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
774	C₄×D₄	C₂³×C₃₁	1	2	yes	—
775	C₄×D₄	C₂³×C₃₁	1	2	yes	—
776	C₄×D₄	C₂³×C₃₁	1	2	yes	—
777	C₄×D₄	C₂³×C₃₁	1	2	yes	—
778	#117	—	2	1	no	—
779	#117	—	2	1	no	—
780	#117	—	2	1	no	—
781	#117	—	2	1	no	—
782	#117	—	2	1	no	—
783	#117	—	2	1	no	—
784	#117	C₂³×C₃₁	1	1	yes	characteristic
785	#117	C₂³×C₃₁	1	1	yes	characteristic
786	#117	C₂³×C₃₁	1	1	yes	characteristic
787	#117	C₂³×C₃₁	1	1	yes	characteristic
788	C₂×C₄⋊C₄	—	2	1	no	—
789	C₂×C₄⋊C₄	—	2	1	no	—
790	C₂×C₄⋊C₄	—	2	1	no	—
791	C₂×C₄⋊C₄	—	2	1	no	—
792	C₂×C₄⋊C₄	—	2	1	no	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	—	2	1	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	—	2	2	no	—
798	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
801	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₂×C₄²	—	2	1	no	—
803	C₂×C₄²	—	2	1	no	—
804	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
805	#107	C₂³×C₃₁	1	2	yes	—
806	#107	C₂³×C₃₁	1	2	yes	—
807	#107	C₂³×C₃₁	1	2	yes	—
808	#107	C₂³×C₃₁	1	2	yes	—
809	#107	C₂³×C₃₁	1	1	yes	characteristic
810	#107	C₂³×C₃₁	1	1	yes	characteristic
811	#107	C₂³×C₃₁	1	2	yes	—
812	#107	C₂³×C₃₁	1	2	yes	—
813	#107	C₂³×C₃₁	1	2	yes	—
814	#107	C₂³×C₃₁	1	2	yes	—
815	#106	C₂³×C₃₁	1	2	yes	—
816	#106	C₂³×C₃₁	1	2	yes	—
817	#106	C₂³×C₃₁	1	2	yes	—
818	#106	C₂³×C₃₁	1	2	yes	—
819	#106	C₂³×C₃₁	1	1	yes	characteristic
820	#106	C₂³×C₃₁	1	1	yes	characteristic
821	#106	C₂³×C₃₁	1	2	yes	—
822	#106	C₂³×C₃₁	1	2	yes	—
823	#106	C₂³×C₃₁	1	2	yes	—
824	#106	C₂³×C₃₁	1	2	yes	—
825	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
826	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
827	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
828	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
829	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
830	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
831	#103	C₂³×C₃₁	1	1	yes	characteristic
832	#103	C₂³×C₃₁	1	1	yes	characteristic
833	#103	C₂³×C₃₁	1	1	yes	characteristic
834	#103	C₂³×C₃₁	1	1	yes	characteristic
835	#103	C₂³×C₃₁	1	2	yes	—
836	#103	C₂³×C₃₁	1	2	yes	—
837	#103	C₂³×C₃₁	1	2	yes	—
838	#103	C₂³×C₃₁	1	2	yes	—
839	#102	C₂³×C₃₁	1	1	yes	characteristic
840	#102	C₂³×C₃₁	1	1	yes	characteristic
841	#102	C₂³×C₃₁	1	1	yes	characteristic
842	#102	C₂³×C₃₁	1	1	yes	characteristic
843	#102	C₂³×C₃₁	1	2	yes	—
844	#102	C₂³×C₃₁	1	2	yes	—
845	#102	C₂³×C₃₁	1	2	yes	—
846	#102	C₂³×C₃₁	1	2	yes	—
847	#97	C₂³×C₃₁	1	1	yes	characteristic
848	#97	C₂³×C₃₁	1	1	yes	characteristic
849	#97	C₂³×C₃₁	1	1	yes	characteristic
850	#97	C₂³×C₃₁	1	1	yes	characteristic
851	#97	C₂³×C₃₁	1	2	yes	—
852	#97	C₂³×C₃₁	1	2	yes	—
853	C₄×C₈	C₂³×C₃₁	1	2	yes	—
854	C₄×C₈	C₂³×C₃₁	1	2	yes	—
855	C₃₁	#61380	1	1	yes	characteristic, direct product factor, Sylow
856	#41	—	2	2	no	—
857	#41	—	2	2	no	—
858	#41	C₂×Q₈×C₃₁	1	4	yes	—
859	#41	C₂×Q₈×C₃₁	1	4	yes	complemented
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	2	2	no	—
866	C₂×Q₈	—	8	2	no	—
867	C₂×Q₈	—	8	4	no	—
868	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
869	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
870	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
891	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
893	Q₁₆	C₂×Q₈×C₃₁	1	4	yes	complemented
894	SD₁₆	C₂×Q₈×C₃₁	1	4	yes	complemented
895	SD₁₆	C₂×Q₈×C₃₁	1	4	yes	complemented
896	D₈	C₂×Q₈×C₃₁	1	4	yes	complemented
897	M₁₆	—	2	2	no	—
898	M₁₆	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	complemented
901	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
902	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
903	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
938	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
948	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
978	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
979	C₄²	C₂⁴×C₃₁	1	2	yes	—
980	C₄²	C₂⁴×C₃₁	1	2	yes	—
981	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
986	Q₈	—	2	1	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	4	2	no	—
989	Q₈	—	4	2	no	—
990	Q₈	—	4	4	no	—
991	Q₈	—	8	2	no	—
992	Q₈	—	8	2	no	—
993	Q₈	—	8	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	—	8	2	no	—
996	Q₈	C₂²×Q₈×C₃₁	1	2	yes	—
997	Q₈	C₂²×Q₈×C₃₁	1	2	yes	—
998	D₄	—	2	4	no	—
999	D₄	—	2	4	no	—
1000	D₄	—	2	1	no	—
1001	D₄	—	2	1	no	—
1002	D₄	C₂²×Q₈×C₃₁	1	2	yes	—
1003	D₄	C₂²×Q₈×C₃₁	1	2	yes	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	4	1	no	—
1017	C₂×C₄	—	4	1	no	—
1018	C₂×C₄	—	4	2	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	8	1	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	1	no	—
1023	C₂×C₄	—	8	2	no	—
1024	C₂×C₄	—	8	2	no	—
1025	C₂×C₄	—	8	2	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	8	1	no	—
1028	C₂×C₄	—	8	1	no	—
1029	C₂×C₄	—	8	1	no	—
1030	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1031	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1032	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1033	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1034	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1036	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1039	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
1040	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1041	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	2	2	no	—
1045	C₈	—	2	2	no	—
1046	C₈	C₂²×Q₈×C₃₁	1	2	yes	—
1047	C₈	C₂²×Q₈×C₃₁	1	2	yes	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	D₄×Q₈×C₃₁	1	2	yes	—
1057	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	D₄×Q₈×C₃₁	1	2	yes	—
1077	C₄	C₂³×Q₈×C₃₁	1	1	yes	characteristic
1078	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	4	2	no	—
1082	C₂	C₂×D₄×Q₈×C₃₁	1	1	yes	characteristic
1083	C₂	C₃₁×#3585	1	1	yes	characteristic
1084	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	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3504	C₂	semidirect
2. C₃₁×#3503	C₂	semidirect
3. C₃₁×#3390	C₂	semidirect
4. C₃₁×#3389	C₂	semidirect
5. C₃₁×#3388	C₂	semidirect
6. C₃₁×#3388	C₂	semidirect
7. C₃₁×#3387	C₂	semidirect
8. C₃₁×#3386	C₂	semidirect
9. C₃₁×#3385	C₂	semidirect
10. C₃₁×#3384	C₂	semidirect
11. C₃₁×#3164	C₂	semidirect
12. C₃₁×#3163	C₂	semidirect
13. C₂×C₃₁×#501	C₂	semidirect
14. C₃₁×#3084	C₂	semidirect
15. C₃₁×#3084	C₂	semidirect
16. C₃₁×#3083	C₂	semidirect
17. C₃₁×#3083	C₂	semidirect
18. C₃₁×#3080	C₂	semidirect
19. C₃₁×#3079	C₂	semidirect
20. C₃₁×#2961	C₂	semidirect
139. C₃₁×#135	Q₈	semidirect
316. #41×C₃₁	C₂×Q₈	semidirect
350. Q₁₆×C₃₁	C₂×Q₈	semidirect
351. SD₁₆×C₃₁	C₂×Q₈	semidirect
352. SD₁₆×C₃₁	C₂×Q₈	semidirect
353. D₈×C₃₁	C₂×Q₈	semidirect
357. C₂×C₈×C₃₁	C₂×Q₈	semidirect
440. #61380	C₃₁	direct (N × H)
506. #3504	C₂×C₃₁	semidirect
507. #3503	C₂×C₃₁	semidirect
508. #3390	C₂×C₃₁	semidirect
509. #3389	C₂×C₃₁	semidirect
510. #3388	C₂×C₃₁	semidirect
511. #3388	C₂×C₃₁	semidirect
512. #3387	C₂×C₃₁	semidirect
513. #3386	C₂×C₃₁	semidirect
514. #3385	C₂×C₃₁	semidirect
515. #3384	C₂×C₃₁	semidirect
516. #3164	C₂×C₃₁	semidirect
517. #3163	C₂×C₃₁	semidirect
518. C₂×#501	C₂×C₃₁	semidirect
519. #3084	C₂×C₃₁	semidirect
520. #3084	C₂×C₃₁	semidirect
521. #3083	C₂×C₃₁	semidirect
522. #3083	C₂×C₃₁	semidirect
523. #3080	C₂×C₃₁	semidirect
524. #3079	C₂×C₃₁	semidirect
525. #2961	C₂×C₃₁	semidirect
681. #135	Q₈×C₃₁	semidirect
855. C₃₁	#61380	direct (N × H)
859. #41	C₂×Q₈×C₃₁	semidirect
893. Q₁₆	C₂×Q₈×C₃₁	semidirect
894. SD₁₆	C₂×Q₈×C₃₁	semidirect
895. SD₁₆	C₂×Q₈×C₃₁	semidirect
896. D₈	C₂×Q₈×C₃₁	semidirect
900. C₂×C₈	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
C₃₁×#3504	2
C₃₁×#3503	2
C₃₁×#3390	2
C₃₁×#3389	2
C₃₁×#3388	2
C₃₁×#3387	2
C₃₁×#3386	2
C₃₁×#3385	2
C₃₁×#3384	2
C₃₁×#3164	2
C₃₁×#3163	2
C₂×C₃₁×#501	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3080	2
C₃₁×#3079	2
C₃₁×#2961	2
C₃₁×#2952	2
C₃₁×#2951	2
C₃₁×#2943	2
#61380	31

Subgroups — C31×#61380 #21518139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61380 #21518139