Subgroups — C₃₁×#61499 #21518258

Order 7936.

1806 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3298	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3178	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2947	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#559	—	2	1	no	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#557	—	2	1	no	—
30	C₃₁×#557	C₂²	1	1	yes	characteristic
31	C₃₁×#557	C₂²	1	1	yes	characteristic
32	C₃₁×#556	—	2	1	no	—
33	C₃₁×#556	C₂²	1	1	yes	characteristic
34	C₃₁×#554	—	2	1	no	—
35	C₃₁×#554	C₂²	1	1	yes	characteristic
36	C₃₁×#552	—	2	2	no	—
37	C₃₁×#552	C₂²	1	2	yes	—
38	C₃₁×#550	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#548	C₂²	1	2	yes	—
42	C₃₁×#547	—	2	2	no	—
43	C₃₁×#547	C₂²	1	2	yes	—
44	C₃₁×#542	—	2	2	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#541	—	2	2	no	—
47	C₃₁×#541	C₂²	1	2	yes	—
48	C₃₁×#533	—	2	1	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#532	—	2	1	no	—
51	C₃₁×#532	C₂²	1	1	yes	characteristic
52	C₃₁×#529	—	2	1	no	—
53	C₃₁×#529	—	2	1	no	—
54	C₃₁×#529	C₂²	1	1	yes	characteristic
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₃₁×#519	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#497	C₂²	1	2	yes	—
62	C₃₁×#492	C₂²	1	1	yes	characteristic
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#487	C₂²	1	1	yes	characteristic
65	C₃₁×#487	C₂²	1	2	yes	—
66	C₃₁×#486	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	2	yes	—
70	C₃₁×#483	C₂²	1	2	yes	—
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#480	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	2	yes	—
76	C₃₁×#477	C₂²	1	1	yes	characteristic
77	C₃₁×#477	C₂²	1	1	yes	characteristic
78	C₃₁×#475	C₂²	1	1	yes	characteristic
79	C₃₁×#475	C₂²	1	1	yes	characteristic
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#470	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	1	yes	characteristic
90	C₃₁×#462	C₂²	1	2	yes	—
91	C₃₁×#462	C₂²	1	1	yes	characteristic
92	C₃₁×#461	C₂²	1	2	yes	—
93	C₃₁×#460	C₂²	1	1	yes	characteristic
94	C₃₁×#460	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#451	C₂²	1	2	yes	—
98	C₃₁×#451	C₂²	1	2	yes	—
99	C₃₁×#448	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
103	C₃₁×#441	C₂²	1	2	yes	—
104	C₃₁×#441	C₂²	1	2	yes	—
105	C₃₁×#441	C₂²	1	2	yes	—
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	—
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
112	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#433	C₂²	1	2	yes	—
126	C₃₁×#432	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	—
128	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
129	C₃₁×#416	C₂²	1	2	yes	—
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₃₁×#405	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₃₁×#137	—	2	8	no	—
142	C₂×Q₁₆×C₃₁	—	2	4	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	—	2	2	no	—
161	C₃₁×C₄⋊Q₈	—	2	2	no	—
162	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	1	no	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	D₄	1	2	yes	—
175	C₃₁×#125	—	2	1	no	—
176	C₃₁×#125	—	2	1	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	D₄	1	1	yes	characteristic
184	C₃₁×#125	C₂³	1	2	yes	—
185	C₃₁×#124	—	2	1	no	—
186	C₃₁×#124	—	2	1	no	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	—	2	1	no	—
190	C₃₁×#124	D₄	1	1	yes	characteristic
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	D₄	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	1	no	—
219	C₄×Q₈×C₃₁	—	2	2	no	—
220	C₄×Q₈×C₃₁	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	—	2	1	no	—
227	C₄×Q₈×C₃₁	—	2	1	no	—
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
240	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	—	2	2	no	—
249	C₄×D₄×C₃₁	—	2	1	no	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	C₂³	1	2	yes	—
260	C₃₁×#117	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
263	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	#41×C₃₁	—	2	4	no	—
315	#41×C₃₁	—	4	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	#41×C₃₁	—	8	4	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	2	no	—
326	C₂×Q₈×C₃₁	—	2	4	no	—
327	C₂×Q₈×C₃₁	—	4	1	no	—
328	C₂×Q₈×C₃₁	—	4	1	no	—
329	C₂×Q₈×C₃₁	—	4	2	no	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
342	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	1	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	2	no	—
349	C₂²×C₄×C₃₁	—	2	2	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
357	Q₁₆×C₃₁	—	2	2	no	—
358	Q₁₆×C₃₁	—	2	2	no	—
359	Q₁₆×C₃₁	—	2	4	no	—
360	Q₁₆×C₃₁	—	2	2	no	—
361	Q₁₆×C₃₁	—	4	2	no	—
362	Q₁₆×C₃₁	#41	1	4	yes	complemented
363	SD₁₆×C₃₁	—	2	4	no	—
364	SD₁₆×C₃₁	—	2	4	no	—
365	SD₁₆×C₃₁	—	4	2	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	M₁₆×C₃₁	—	2	4	no	—
368	C₂×C₈×C₃₁	—	2	2	no	—
369	C₂×C₈×C₃₁	—	4	1	no	—
370	C₂×C₈×C₃₁	—	4	2	no	—
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	2	no	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	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	1	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	1	no	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	1	no	—
435	C₄²×C₃₁	—	2	1	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	1	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	1	no	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	2	yes	—
451	#61499	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
454	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	2	no	—
459	Q₈×C₃₁	—	2	1	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	4	4	no	—
465	Q₈×C₃₁	—	4	2	no	—
466	Q₈×C₃₁	—	4	2	no	—
467	Q₈×C₃₁	—	4	2	no	—
468	Q₈×C₃₁	—	8	1	no	—
469	Q₈×C₃₁	—	8	2	no	—
470	Q₈×C₃₁	C₂×#41	1	2	yes	—
471	Q₈×C₃₁	C₂×#41	1	2	yes	—
472	D₄×C₃₁	—	2	4	no	—
473	D₄×C₃₁	—	2	2	no	—
474	D₄×C₃₁	—	2	2	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	4	4	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	8	1	no	—
480	D₄×C₃₁	—	8	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	2	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	1	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	4	4	no	—
499	C₂×C₄×C₃₁	—	4	2	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	4	4	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	2	no	—
506	C₂×C₄×C₃₁	—	8	2	no	—
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	2	no	—
518	C₈×C₃₁	—	2	1	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	C₂×#41	1	2	yes	—
522	#3523	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3522	C₂×C₃₁	1	1	yes	characteristic
524	#3400	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3363	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3356	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3343	C₂×C₃₁	1	2	yes	complemented
530	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3300	C₂×C₃₁	1	2	yes	complemented
532	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3298	C₂×C₃₁	1	2	yes	complemented
534	#3278	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3270	C₂×C₃₁	1	2	yes	complemented
536	#3178	C₂×C₃₁	1	2	yes	complemented
537	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3121	C₂×C₃₁	1	2	yes	complemented
539	#3120	C₂×C₃₁	1	2	yes	complemented
540	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#2947	C₂×C₃₁	1	2	yes	complemented
544	C₂×C₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
545	C₂²×C₃₁	—	2	1	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	2	no	—
548	C₂²×C₃₁	—	2	2	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	4	2	no	—
551	C₂²×C₃₁	—	4	2	no	—
552	C₂²×C₃₁	—	4	2	no	—
553	C₂²×C₃₁	#577	1	2	yes	—
554	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	2	no	—
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	2	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	1	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	1	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	2	no	—
573	C₄×C₃₁	#578	1	2	yes	—
574	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
575	C₄×C₃₁	#585	1	1	yes	characteristic
576	C₂×#137	C₂²×C₃₁	1	2	yes	—
577	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
578	#559	—	2	1	no	—
579	#559	C₂²×C₃₁	1	1	yes	characteristic
580	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
581	#557	—	2	1	no	—
582	#557	C₂²×C₃₁	1	1	yes	characteristic
583	#557	C₂²×C₃₁	1	1	yes	characteristic
584	#556	—	2	1	no	—
585	#556	C₂²×C₃₁	1	1	yes	characteristic
586	#554	—	2	1	no	—
587	#554	C₂²×C₃₁	1	1	yes	characteristic
588	#552	—	2	2	no	—
589	#552	C₂²×C₃₁	1	2	yes	—
590	#550	C₂²×C₃₁	1	1	yes	characteristic
591	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
592	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
593	#548	C₂²×C₃₁	1	2	yes	—
594	#547	—	2	2	no	—
595	#547	C₂²×C₃₁	1	2	yes	—
596	#542	—	2	2	no	—
597	#542	C₂²×C₃₁	1	2	yes	—
598	#541	—	2	2	no	—
599	#541	C₂²×C₃₁	1	2	yes	—
600	#533	—	2	1	no	—
601	#533	C₂²×C₃₁	1	1	yes	characteristic
602	#532	—	2	1	no	—
603	#532	C₂²×C₃₁	1	1	yes	characteristic
604	#529	—	2	1	no	—
605	#529	—	2	1	no	—
606	#529	C₂²×C₃₁	1	1	yes	characteristic
607	#520	C₂²×C₃₁	1	2	yes	—
608	#519	C₂²×C₃₁	1	2	yes	—
609	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
610	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
611	#501	C₂²×C₃₁	1	2	yes	—
612	#498	C₂²×C₃₁	1	1	yes	characteristic
613	#497	C₂²×C₃₁	1	2	yes	—
614	#492	C₂²×C₃₁	1	1	yes	characteristic
615	#488	C₂²×C₃₁	1	2	yes	—
616	#487	C₂²×C₃₁	1	1	yes	characteristic
617	#487	C₂²×C₃₁	1	2	yes	—
618	#486	C₂²×C₃₁	1	1	yes	characteristic
619	#485	C₂²×C₃₁	1	2	yes	—
620	#484	C₂²×C₃₁	1	2	yes	—
621	#483	C₂²×C₃₁	1	2	yes	—
622	#483	C₂²×C₃₁	1	2	yes	—
623	#482	C₂²×C₃₁	1	2	yes	—
624	#480	C₂²×C₃₁	1	2	yes	—
625	#479	C₂²×C₃₁	1	2	yes	—
626	#478	C₂²×C₃₁	1	2	yes	—
627	#477	C₂²×C₃₁	1	2	yes	—
628	#477	C₂²×C₃₁	1	1	yes	characteristic
629	#477	C₂²×C₃₁	1	1	yes	characteristic
630	#475	C₂²×C₃₁	1	1	yes	characteristic
631	#475	C₂²×C₃₁	1	1	yes	characteristic
632	#475	C₂²×C₃₁	1	2	yes	—
633	#470	C₂²×C₃₁	1	2	yes	—
634	#468	C₂²×C₃₁	1	2	yes	—
635	#467	C₂²×C₃₁	1	2	yes	—
636	#465	C₂²×C₃₁	1	2	yes	—
637	#465	C₂²×C₃₁	1	2	yes	—
638	#465	C₂²×C₃₁	1	2	yes	—
639	#464	C₂²×C₃₁	1	2	yes	—
640	#464	C₂²×C₃₁	1	2	yes	—
641	#462	C₂²×C₃₁	1	1	yes	characteristic
642	#462	C₂²×C₃₁	1	2	yes	—
643	#462	C₂²×C₃₁	1	1	yes	characteristic
644	#461	C₂²×C₃₁	1	2	yes	—
645	#460	C₂²×C₃₁	1	1	yes	characteristic
646	#460	C₂²×C₃₁	1	1	yes	characteristic
647	#452	C₂²×C₃₁	1	2	yes	—
648	#452	C₂²×C₃₁	1	2	yes	—
649	#451	C₂²×C₃₁	1	2	yes	—
650	#451	C₂²×C₃₁	1	2	yes	—
651	#448	C₂²×C₃₁	1	2	yes	—
652	#448	C₂²×C₃₁	1	2	yes	—
653	#446	C₂²×C₃₁	1	1	yes	characteristic
654	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
655	#441	C₂²×C₃₁	1	2	yes	—
656	#441	C₂²×C₃₁	1	2	yes	—
657	#441	C₂²×C₃₁	1	2	yes	—
658	#440	C₂²×C₃₁	1	2	yes	—
659	#440	C₂²×C₃₁	1	2	yes	—
660	#440	C₂²×C₃₁	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
662	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
663	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
664	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
665	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
666	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
667	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
668	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
669	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
671	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
672	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
673	#436	C₂²×C₃₁	1	1	yes	characteristic
674	#435	C₂²×C₃₁	1	2	yes	—
675	C₈×D₄	C₂²×C₃₁	1	2	yes	—
676	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
677	#433	C₂²×C₃₁	1	2	yes	—
678	#432	C₂²×C₃₁	1	1	yes	characteristic
679	#428	C₂²×C₃₁	1	2	yes	—
680	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
681	#416	C₂²×C₃₁	1	2	yes	—
682	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
683	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
684	C₂×#103	C₂²×C₃₁	1	2	yes	—
685	#405	C₂²×C₃₁	1	2	yes	—
686	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
687	C₂×C₃₁	—	2	2	no	—
688	C₂×C₃₁	—	4	2	no	—
689	C₂×C₃₁	—	8	2	no	—
690	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
691	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
692	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
693	C₂×#41	—	2	2	no	—
694	C₂×#41	—	2	1	no	—
695	C₂×#41	C₂³×C₃₁	1	2	yes	—
696	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
699	#137	—	2	8	no	—
700	C₂×Q₁₆	—	2	4	no	—
701	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
703	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
705	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
708	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	2	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
722	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
725	#127	—	2	1	no	—
726	#127	C₂³×C₃₁	1	1	yes	characteristic
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	D₄×C₃₁	1	2	yes	—
733	#125	—	2	1	no	—
734	#125	—	2	1	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	2	no	—
738	#125	—	2	2	no	—
739	#125	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	D₄×C₃₁	1	1	yes	characteristic
742	#125	C₂³×C₃₁	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	1	no	—
745	#124	—	2	2	no	—
746	#124	—	2	2	no	—
747	#124	—	2	1	no	—
748	#124	D₄×C₃₁	1	1	yes	characteristic
749	#124	C₂³×C₃₁	1	2	yes	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	D₄×C₃₁	1	2	yes	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
765	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
768	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	#121	—	2	2	no	—
770	#121	—	2	1	no	—
771	#121	—	2	2	no	—
772	#121	D₄×C₃₁	1	1	yes	characteristic
773	#121	C₂³×C₃₁	1	2	yes	—
774	#121	C₂³×C₃₁	1	2	yes	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	2	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	1	no	—
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
795	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
796	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
797	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
798	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	C₂³×C₃₁	1	2	yes	—
809	C₄×D₄	C₂³×C₃₁	1	2	yes	—
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
812	#117	—	2	1	no	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	—	2	2	no	—
816	#117	—	2	2	no	—
817	#117	C₂³×C₃₁	1	2	yes	—
818	#117	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄⋊C₄	—	2	1	no	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
823	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
825	C₂×C₄²	—	2	1	no	—
826	C₂×C₄²	—	2	1	no	—
827	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
828	#107	C₂³×C₃₁	1	1	yes	characteristic
829	#107	C₂³×C₃₁	1	1	yes	characteristic
830	#107	C₂³×C₃₁	1	1	yes	characteristic
831	#107	C₂³×C₃₁	1	1	yes	characteristic
832	#107	C₂³×C₃₁	1	2	yes	—
833	#107	C₂³×C₃₁	1	2	yes	—
834	#106	C₂³×C₃₁	1	2	yes	—
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	#106	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
841	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
842	#103	C₂³×C₃₁	1	1	yes	characteristic
843	#103	C₂³×C₃₁	1	1	yes	characteristic
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	1	yes	characteristic
846	#103	C₂³×C₃₁	1	1	yes	characteristic
847	#103	C₂³×C₃₁	1	1	yes	characteristic
848	#103	C₂³×C₃₁	1	1	yes	characteristic
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	2	yes	—
852	#103	C₂³×C₃₁	1	2	yes	—
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	2	yes	—
859	#102	C₂³×C₃₁	1	2	yes	—
860	#102	C₂³×C₃₁	1	2	yes	—
861	#102	C₂³×C₃₁	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
865	#97	C₂³×C₃₁	1	2	yes	—
866	#97	C₂³×C₃₁	1	2	yes	—
867	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₃₁	1	2	yes	—
872	C₃₁	#61499	1	1	yes	characteristic, direct product factor, Sylow
873	#41	—	2	4	no	—
874	#41	—	4	2	no	—
875	#41	—	8	2	no	—
876	#41	—	8	4	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	2	no	—
882	C₂×Q₈	—	2	1	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	4	no	—
886	C₂×Q₈	—	4	1	no	—
887	C₂×Q₈	—	4	1	no	—
888	C₂×Q₈	—	4	2	no	—
889	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
890	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	1	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
901	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
902	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
916	Q₁₆	—	2	2	no	—
917	Q₁₆	—	2	2	no	—
918	Q₁₆	—	2	4	no	—
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	4	2	no	—
921	Q₁₆	#41×C₃₁	1	4	yes	complemented
922	SD₁₆	—	2	4	no	—
923	SD₁₆	—	2	4	no	—
924	SD₁₆	—	4	2	no	—
925	SD₁₆	—	4	2	no	—
926	M₁₆	—	2	4	no	—
927	C₂×C₈	—	2	2	no	—
928	C₂×C₈	—	4	1	no	—
929	C₂×C₈	—	4	2	no	—
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
934	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
935	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
969	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	2	no	—
1005	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1006	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₃₁	1	2	yes	—
1010	C₂³	—	2	2	no	—
1011	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1012	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1013	Q₈	—	2	2	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	1	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	4	4	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	4	2	no	—
1025	Q₈	—	4	2	no	—
1026	Q₈	—	8	1	no	—
1027	Q₈	—	8	2	no	—
1028	Q₈	C₂×#41×C₃₁	1	2	yes	—
1029	Q₈	C₂×#41×C₃₁	1	2	yes	—
1030	D₄	—	2	4	no	—
1031	D₄	—	2	2	no	—
1032	D₄	—	2	2	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	4	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	8	1	no	—
1038	D₄	—	8	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	2	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1066	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1067	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	2	no	—
1079	C₈	C₂×#41×C₃₁	1	2	yes	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	C₃₁×#577	1	2	yes	—
1089	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	4	1	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	4	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	C₃₁×#578	1	2	yes	—
1109	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1110	C₄	C₃₁×#585	1	1	yes	characteristic
1111	C₂	—	2	2	no	—
1112	C₂	—	4	2	no	—
1113	C₂	—	8	2	no	—
1114	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1115	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1116	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3523	C₂	semidirect
3. C₃₁×#3400	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3365	C₂	semidirect
6. C₃₁×#3363	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3343	C₂	semidirect
9. C₃₁×#3304	C₂	semidirect
10. C₃₁×#3300	C₂	semidirect
11. C₃₁×#3299	C₂	semidirect
12. C₃₁×#3298	C₂	semidirect
13. C₃₁×#3278	C₂	semidirect
14. C₃₁×#3270	C₂	semidirect
15. C₃₁×#3178	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3121	C₂	semidirect
18. C₃₁×#3120	C₂	semidirect
19. C₃₁×#3113	C₂	semidirect
20. C₃₁×#3112	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2947	C₂	semidirect
23. C₂×C₄×Q₁₆×C₃₁	C₂	semidirect
362. Q₁₆×C₃₁	#41	semidirect
451. #61499	C₃₁	direct (N × H)
522. #3523	C₂×C₃₁	semidirect
524. #3400	C₂×C₃₁	semidirect
525. #3387	C₂×C₃₁	semidirect
526. #3365	C₂×C₃₁	semidirect
527. #3363	C₂×C₃₁	semidirect
528. #3356	C₂×C₃₁	semidirect
529. #3343	C₂×C₃₁	semidirect
530. #3304	C₂×C₃₁	semidirect
531. #3300	C₂×C₃₁	semidirect
532. #3299	C₂×C₃₁	semidirect
533. #3298	C₂×C₃₁	semidirect
534. #3278	C₂×C₃₁	semidirect
535. #3270	C₂×C₃₁	semidirect
536. #3178	C₂×C₃₁	semidirect
537. #3167	C₂×C₃₁	semidirect
538. #3121	C₂×C₃₁	semidirect
539. #3120	C₂×C₃₁	semidirect
540. #3113	C₂×C₃₁	semidirect
541. #3112	C₂×C₃₁	semidirect
542. #2966	C₂×C₃₁	semidirect
543. #2947	C₂×C₃₁	semidirect
544. C₂×C₄×Q₁₆	C₂×C₃₁	semidirect
872. C₃₁	#61499	direct (N × H)
921. Q₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3523	2
C₃₁×#3522	2
C₃₁×#3400	2
C₃₁×#3387	2
C₃₁×#3365	2
C₃₁×#3363	2
C₃₁×#3356	2
C₃₁×#3343	2
C₃₁×#3304	2
C₃₁×#3300	2
C₃₁×#3299	2
C₃₁×#3298	2
C₃₁×#3278	2
C₃₁×#3270	2
C₃₁×#3178	2
C₃₁×#3167	2
C₃₁×#3121	2
C₃₁×#3120	2
C₃₁×#3113	2
C₃₁×#3112	2
C₃₁×#2966	2
C₃₁×#2947	2
C₂×C₄×Q₁₆×C₃₁	2
#61499	31

Subgroups — C31×#61499 #21518258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61499 #21518258