Subgroups — C₃₁×#62202 #21518961

Order 7936.

1744 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#556	C₂²	1	1	yes	characteristic
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#552	—	2	1	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	C₂²	1	2	yes	—
34	C₃₁×#551	—	2	2	no	—
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	—	2	1	no	—
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	2	yes	—
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#544	—	2	1	no	—
43	C₃₁×#544	C₂²	1	2	yes	complemented
44	C₃₁×#542	—	2	1	no	—
45	C₃₁×#542	C₂²	1	2	yes	—
46	C₃₁×#542	C₂²	1	2	yes	complemented
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#536	—	2	2	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#498	C₂²	1	2	yes	complemented
59	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#489	C₂²	1	2	yes	—
62	C₃₁×#488	C₂²	1	2	yes	—
63	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	1	yes	characteristic
67	C₃₁×#483	C₂²	1	2	yes	—
68	C₃₁×#483	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#483	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	1	yes	characteristic
73	C₃₁×#481	C₂²	1	2	yes	—
74	C₃₁×#481	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	1	yes	characteristic
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	1	yes	characteristic
80	C₃₁×#476	C₂²	1	1	yes	characteristic
81	C₃₁×#476	C₂²	1	1	yes	characteristic
82	C₃₁×#476	C₂²	1	2	yes	—
83	C₃₁×#476	C₂²	1	2	yes	—
84	C₃₁×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	1	yes	characteristic
86	C₃₁×#476	C₂²	1	2	yes	—
87	C₃₁×#476	C₂²	1	2	yes	complemented
88	C₃₁×#475	C₂²	1	2	yes	complemented
89	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#475	C₂²	1	2	yes	complemented
91	C₃₁×#475	C₂²	1	2	yes	complemented
92	C₃₁×#475	C₂²	1	2	yes	complemented
93	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#470	C₂²	1	2	yes	complemented
95	C₃₁×#469	C₂²	1	2	yes	—
96	C₃₁×#467	C₂²	1	2	yes	—
97	C₃₁×#465	C₂²	1	2	yes	—
98	C₃₁×#465	C₂²	1	2	yes	—
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#463	C₂²	1	2	yes	—
103	C₃₁×#463	C₂²	1	1	yes	characteristic
104	C₃₁×#463	C₂²	1	1	yes	characteristic
105	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#450	C₂²	1	1	yes	characteristic
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#447	C₂²	1	1	yes	characteristic
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#441	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	2	yes	—
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#106	C₂²	1	2	yes	—
129	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	2	no	—
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
150	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	—	2	2	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	—	2	1	no	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	1	no	—
156	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	1	no	—
168	C₃₁×#126	D₄	1	2	yes	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	—	2	1	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	D₄	1	1	yes	characteristic
175	C₃₁×#125	C₂³	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	D₄	1	1	yes	characteristic
181	C₃₁×#124	C₂³	1	1	yes	characteristic
182	C₃₁×#124	C₂³	1	2	yes	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	1	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	D₄	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
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	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	D₄	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	2	yes	—
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₃₁×#117	—	2	1	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	C₂³	1	2	yes	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
253	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	1	yes	characteristic
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	1	yes	characteristic
266	C₃₁×#106	C₂³	1	2	yes	—
267	C₃₁×#106	C₂³	1	2	yes	—
268	C₃₁×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	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	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	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	2	yes	—
312	C₂⁴×C₃₁	—	2	1	no	—
313	#41×C₃₁	—	2	4	no	—
314	#41×C₃₁	—	4	2	no	—
315	#41×C₃₁	—	8	4	no	—
316	#41×C₃₁	—	8	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	—	8	2	no	—
325	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	1	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	4	1	no	—
335	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	—	2	2	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	8	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	—	4	2	no	—
358	SD₁₆×C₃₁	—	2	2	no	—
359	SD₁₆×C₃₁	—	4	2	no	—
360	SD₁₆×C₃₁	—	4	1	no	—
361	D₈×C₃₁	—	2	2	no	—
362	D₈×C₃₁	—	4	1	no	—
363	M₁₆×C₃₁	—	4	2	no	—
364	C₂×C₈×C₃₁	—	4	2	no	—
365	C₂×C₈×C₃₁	—	4	2	no	—
366	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	1	no	—
392	C₄⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
410	C₂²⋊C₄×C₃₁	—	2	1	no	—
411	C₂²⋊C₄×C₃₁	—	2	2	no	—
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	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	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	C₄²×C₃₁	C₂⁴	1	2	yes	—
442	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
443	#62202	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₃₁	—	2	1	no	—
445	C₂³×C₃₁	—	2	1	no	—
446	C₂³×C₃₁	—	2	1	no	—
447	C₂³×C₃₁	—	4	2	no	—
448	C₂³×C₃₁	—	4	2	no	—
449	C₂³×C₃₁	—	8	1	no	—
450	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
451	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	2	no	—
455	Q₈×C₃₁	—	2	1	no	—
456	Q₈×C₃₁	—	2	2	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	8	1	no	—
459	Q₈×C₃₁	—	8	2	no	—
460	Q₈×C₃₁	—	8	1	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	Q₈×C₃₁	—	8	2	no	—
463	D₄×C₃₁	—	2	4	no	—
464	D₄×C₃₁	—	2	2	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	2	1	no	—
467	D₄×C₃₁	—	2	1	no	—
468	D₄×C₃₁	—	2	1	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	4	2	no	—
471	D₄×C₃₁	—	4	4	no	—
472	D₄×C₃₁	—	4	2	no	—
473	D₄×C₃₁	—	8	2	no	—
474	D₄×C₃₁	—	8	2	no	—
475	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
476	C₂×C₄×C₃₁	—	2	2	no	—
477	C₂×C₄×C₃₁	—	2	2	no	—
478	C₂×C₄×C₃₁	—	2	1	no	—
479	C₂×C₄×C₃₁	—	2	2	no	—
480	C₂×C₄×C₃₁	—	2	1	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	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	2	no	—
491	C₂×C₄×C₃₁	—	4	4	no	—
492	C₂×C₄×C₃₁	—	4	4	no	—
493	C₂×C₄×C₃₁	—	4	2	no	—
494	C₂×C₄×C₃₁	—	4	2	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	8	1	no	—
497	C₂×C₄×C₃₁	—	8	1	no	—
498	C₂×C₄×C₃₁	—	8	2	no	—
499	C₂×C₄×C₃₁	—	8	2	no	—
500	C₂×C₄×C₃₁	—	8	1	no	—
501	C₂×C₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	8	2	no	—
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
512	C₈×C₃₁	—	2	1	no	—
513	C₈×C₃₁	—	2	1	no	—
514	C₈×C₃₁	—	2	1	no	—
515	C₈×C₃₁	—	2	2	no	—
516	C₈×C₃₁	—	2	2	no	—
517	C₈×C₃₁	—	2	1	no	—
518	#3544	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
520	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
521	Q₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3344	C₂×C₃₁	1	2	yes	complemented
526	#3335	C₂×C₃₁	1	2	yes	complemented
527	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3306	C₂×C₃₁	1	2	yes	complemented
530	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3296	C₂×C₃₁	1	2	yes	complemented
532	#3263	C₂×C₃₁	1	2	yes	complemented
533	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3244	C₂×C₃₁	1	2	yes	complemented
535	#3229	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3125	C₂×C₃₁	1	2	yes	complemented
537	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3084	C₂×C₃₁	1	2	yes	complemented
539	C₂×#476	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
541	C₂²×C₃₁	—	2	1	no	—
542	C₂²×C₃₁	—	2	1	no	—
543	C₂²×C₃₁	—	2	2	no	—
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	2	no	—
547	C₂²×C₃₁	—	4	1	no	—
548	C₂²×C₃₁	—	4	1	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	—	4	1	no	—
553	C₂²×C₃₁	—	4	1	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	8	4	no	—
556	C₂²×C₃₁	#577	1	2	yes	—
557	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	2	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	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	—	4	1	no	—
573	C₄×C₃₁	—	4	2	no	—
574	C₄×C₃₁	#577	1	2	yes	—
575	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
576	C₄×C₃₁	#585	1	1	yes	characteristic
577	#563	—	2	2	no	—
578	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
579	#556	C₂²×C₃₁	1	1	yes	characteristic
580	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
581	#554	C₂²×C₃₁	1	2	yes	—
582	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#552	—	2	1	no	—
585	#552	—	2	1	no	—
586	#552	C₂²×C₃₁	1	2	yes	—
587	#551	—	2	2	no	—
588	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
589	#548	—	2	1	no	—
590	#547	—	2	1	no	—
591	#547	C₂²×C₃₁	1	1	yes	characteristic
592	#547	C₂²×C₃₁	1	1	yes	characteristic
593	#547	C₂²×C₃₁	1	2	yes	—
594	#546	C₂²×C₃₁	1	2	yes	—
595	#544	—	2	1	no	—
596	#544	C₂²×C₃₁	1	2	yes	complemented
597	#542	—	2	1	no	—
598	#542	C₂²×C₃₁	1	2	yes	—
599	#542	C₂²×C₃₁	1	2	yes	complemented
600	#539	—	2	2	no	—
601	#536	—	2	2	no	—
602	#533	C₂²×C₃₁	1	1	yes	characteristic
603	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
604	#529	C₂²×C₃₁	1	1	yes	characteristic
605	#529	C₂²×C₃₁	1	1	yes	characteristic
606	#525	—	2	1	no	—
607	C₂×C₂²⋊Q₈	—	2	1	no	—
608	#520	C₂²×C₃₁	1	2	yes	—
609	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
610	#501	C₂²×C₃₁	1	2	yes	complemented
611	#498	C₂²×C₃₁	1	2	yes	complemented
612	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
613	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
614	#489	C₂²×C₃₁	1	2	yes	—
615	#488	C₂²×C₃₁	1	2	yes	—
616	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#485	C₂²×C₃₁	1	2	yes	complemented
619	#484	C₂²×C₃₁	1	1	yes	characteristic
620	#483	C₂²×C₃₁	1	2	yes	—
621	#483	C₂²×C₃₁	1	2	yes	—
622	#483	C₂²×C₃₁	1	2	yes	complemented
623	#483	C₂²×C₃₁	1	2	yes	complemented
624	#482	C₂²×C₃₁	1	2	yes	—
625	#481	C₂²×C₃₁	1	1	yes	characteristic
626	#481	C₂²×C₃₁	1	2	yes	—
627	#481	C₂²×C₃₁	1	2	yes	complemented
628	#479	C₂²×C₃₁	1	2	yes	complemented
629	#479	C₂²×C₃₁	1	2	yes	complemented
630	#478	C₂²×C₃₁	1	1	yes	characteristic
631	#478	C₂²×C₃₁	1	2	yes	—
632	#478	C₂²×C₃₁	1	1	yes	characteristic
633	#476	C₂²×C₃₁	1	1	yes	characteristic
634	#476	C₂²×C₃₁	1	1	yes	characteristic
635	#476	C₂²×C₃₁	1	2	yes	—
636	#476	C₂²×C₃₁	1	2	yes	—
637	#476	C₂²×C₃₁	1	1	yes	characteristic
638	#476	C₂²×C₃₁	1	1	yes	characteristic
639	#476	C₂²×C₃₁	1	2	yes	—
640	#476	C₂²×C₃₁	1	2	yes	complemented
641	#475	C₂²×C₃₁	1	2	yes	complemented
642	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
643	#475	C₂²×C₃₁	1	2	yes	complemented
644	#475	C₂²×C₃₁	1	2	yes	complemented
645	#475	C₂²×C₃₁	1	2	yes	complemented
646	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#470	C₂²×C₃₁	1	2	yes	complemented
648	#469	C₂²×C₃₁	1	2	yes	—
649	#467	C₂²×C₃₁	1	2	yes	—
650	#465	C₂²×C₃₁	1	2	yes	—
651	#465	C₂²×C₃₁	1	2	yes	—
652	#465	C₂²×C₃₁	1	2	yes	complemented
653	#464	C₂²×C₃₁	1	2	yes	—
654	#464	C₂²×C₃₁	1	2	yes	complemented
655	#463	C₂²×C₃₁	1	2	yes	—
656	#463	C₂²×C₃₁	1	1	yes	characteristic
657	#463	C₂²×C₃₁	1	1	yes	characteristic
658	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#452	C₂²×C₃₁	1	2	yes	—
661	#450	C₂²×C₃₁	1	1	yes	characteristic
662	#449	C₂²×C₃₁	1	2	yes	—
663	#447	C₂²×C₃₁	1	1	yes	characteristic
664	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#442	C₂²×C₃₁	1	2	yes	—
667	#441	C₂²×C₃₁	1	2	yes	complemented
668	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
671	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
672	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
673	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
674	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#435	C₂²×C₃₁	1	2	yes	—
676	C₈×D₄	C₂²×C₃₁	1	2	yes	—
677	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#433	C₂²×C₃₁	1	2	yes	complemented
679	#431	C₂²×C₃₁	1	1	yes	characteristic
680	#428	C₂²×C₃₁	1	2	yes	complemented
681	C₂×#106	C₂²×C₃₁	1	2	yes	—
682	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
683	#424	C₂²×C₃₁	1	2	yes	complemented
684	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
685	#417	C₂²×C₃₁	1	2	yes	—
686	#416	C₂²×C₃₁	1	2	yes	—
687	C₂×#102	C₂²×C₃₁	1	2	yes	—
688	C₂×C₃₁	—	2	2	no	—
689	C₂×C₃₁	—	4	2	no	—
690	C₂×C₃₁	—	4	2	no	—
691	C₂×C₃₁	—	8	1	no	—
692	C₂×C₃₁	—	8	1	no	—
693	C₂×C₃₁	#3489	1	1	yes	characteristic
694	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
695	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
696	C₂×#41	—	2	1	no	—
697	C₂×#41	—	2	2	no	—
698	C₂×#41	C₂³×C₃₁	1	2	yes	—
699	C₂²×Q₈	—	2	1	no	—
700	C₂²×Q₈	—	2	1	no	—
701	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
702	C₂³×C₄	—	2	1	no	—
703	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
707	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
711	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
712	C₄⋊Q₈	—	2	2	no	—
713	C₄⋊Q₈	—	2	2	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	1	no	—
717	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	1	no	—
729	#126	D₄×C₃₁	1	2	yes	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	1	no	—
735	#125	D₄×C₃₁	1	1	yes	characteristic
736	#125	C₂³×C₃₁	1	1	yes	characteristic
737	#125	C₂³×C₃₁	1	2	yes	—
738	#124	—	2	2	no	—
739	#124	—	2	2	no	—
740	#124	—	2	2	no	—
741	#124	D₄×C₃₁	1	1	yes	characteristic
742	#124	C₂³×C₃₁	1	1	yes	characteristic
743	#124	C₂³×C₃₁	1	2	yes	—
744	#123	—	2	2	no	—
745	#123	—	2	1	no	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	D₄×C₃₁	1	2	yes	—
754	C₂²⋊Q₈	—	2	1	no	—
755	C₂²⋊Q₈	—	2	1	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
770	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
771	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	D₄×C₃₁	1	1	yes	characteristic
778	#121	C₂³×C₃₁	1	1	yes	characteristic
779	#121	C₂³×C₃₁	1	2	yes	—
780	#121	C₂³×C₃₁	1	2	yes	—
781	#120	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
798	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
799	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
800	C₄×D₄	C₂³×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	2	yes	—
803	C₄×D₄	C₂³×C₃₁	1	2	yes	—
804	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
805	#117	—	2	1	no	—
806	#117	—	2	2	no	—
807	#117	—	2	1	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	C₂³×C₃₁	1	2	yes	—
812	#117	C₂³×C₃₁	1	2	yes	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	—	2	1	no	—
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
821	C₂×C₂²⋊C₄	—	2	1	no	—
822	C₂×C₂²⋊C₄	—	2	2	no	—
823	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
824	#107	C₂³×C₃₁	1	1	yes	characteristic
825	#107	C₂³×C₃₁	1	2	yes	—
826	#107	C₂³×C₃₁	1	1	yes	characteristic
827	#106	C₂³×C₃₁	1	2	yes	—
828	#106	C₂³×C₃₁	1	2	yes	—
829	#106	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	2	yes	—
831	#106	C₂³×C₃₁	1	1	yes	characteristic
832	#106	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	2	yes	—
834	#106	C₂³×C₃₁	1	2	yes	—
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	1	yes	characteristic
837	#106	C₂³×C₃₁	1	2	yes	—
838	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
843	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
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	#102	C₂³×C₃₁	1	2	yes	—
855	#102	C₂³×C₃₁	1	2	yes	—
856	#102	C₂³×C₃₁	1	2	yes	—
857	#102	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	1	yes	characteristic
861	#102	C₂³×C₃₁	1	1	yes	characteristic
862	#102	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
867	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
869	#97	C₂³×C₃₁	1	2	yes	—
870	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄×C₈	C₂³×C₃₁	1	2	yes	—
873	C₃₁	#62202	1	1	yes	characteristic, direct product factor, Sylow
874	C₂⁴	—	2	1	no	—
875	#41	—	2	4	no	—
876	#41	—	4	2	no	—
877	#41	—	8	4	no	—
878	#41	—	8	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	2	no	—
884	C₂×Q₈	—	2	1	no	—
885	C₂×Q₈	—	8	2	no	—
886	C₂×Q₈	—	8	2	no	—
887	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
889	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×D₄	—	2	2	no	—
891	C₂×D₄	—	2	2	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	4	1	no	—
897	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
900	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	8	2	no	—
915	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
919	Q₁₆	—	4	2	no	—
920	SD₁₆	—	2	2	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	1	no	—
923	D₈	—	2	2	no	—
924	D₈	—	4	1	no	—
925	M₁₆	—	4	2	no	—
926	C₂×C₈	—	4	2	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
932	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	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	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
965	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	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	1	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
992	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
994	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1001	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1002	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₃₁	1	2	yes	—
1004	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂³	—	2	1	no	—
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	4	2	no	—
1009	C₂³	—	4	2	no	—
1010	C₂³	—	8	1	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	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	4	2	no	—
1019	Q₈	—	8	1	no	—
1020	Q₈	—	8	2	no	—
1021	Q₈	—	8	1	no	—
1022	Q₈	—	8	2	no	—
1023	Q₈	—	8	2	no	—
1024	D₄	—	2	4	no	—
1025	D₄	—	2	2	no	—
1026	D₄	—	2	1	no	—
1027	D₄	—	2	1	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	4	2	no	—
1032	D₄	—	4	4	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	8	2	no	—
1035	D₄	—	8	2	no	—
1036	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	2	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	4	4	no	—
1053	C₂×C₄	—	4	4	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	8	2	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	—	8	2	no	—
1063	C₂×C₄	—	8	2	no	—
1064	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1068	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1072	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	2	no	—
1077	C₈	—	2	2	no	—
1078	C₈	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	8	4	no	—
1094	C₂²	C₃₁×#577	1	2	yes	—
1095	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1096	C₄	—	2	2	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	2	no	—
1112	C₄	C₃₁×#577	1	2	yes	—
1113	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1114	C₄	C₃₁×#585	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	4	2	no	—
1118	C₂	—	8	1	no	—
1119	C₂	—	8	1	no	—
1120	C₂	C₃₁×#3489	1	1	yes	characteristic
1121	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1122	C₂	C₂×C₃₁×#577	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3544	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. Q₈×SD₁₆×C₃₁	C₂	semidirect
5. C₃₁×#3369	C₂	semidirect
6. C₃₁×#3360	C₂	semidirect
7. C₃₁×#3354	C₂	semidirect
8. C₃₁×#3344	C₂	semidirect
9. C₃₁×#3335	C₂	semidirect
10. C₃₁×#3335	C₂	semidirect
11. C₃₁×#3331	C₂	semidirect
12. C₃₁×#3306	C₂	semidirect
13. C₃₁×#3303	C₂	semidirect
14. C₃₁×#3296	C₂	semidirect
15. C₃₁×#3263	C₂	semidirect
16. C₃₁×#3248	C₂	semidirect
17. C₃₁×#3244	C₂	semidirect
18. C₃₁×#3229	C₂	semidirect
19. C₃₁×#3125	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3084	C₂	semidirect
22. C₂×C₃₁×#476	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
25. Q₈²×C₃₁	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
30. C₃₁×#554	C₂²	semidirect
43. C₃₁×#544	C₂²	semidirect
46. C₃₁×#542	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#498	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#483	C₂²	semidirect
74. C₃₁×#481	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
87. C₃₁×#476	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#475	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#475	C₂²	semidirect
92. C₃₁×#475	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#470	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
105. C₃₁×#462	C₂²	semidirect
106. C₃₁×#461	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#441	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
129. C₂×C₃₁×#106	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
443. #62202	C₃₁	direct (N × H)
518. #3544	C₂×C₃₁	semidirect
519. #3520	C₂×C₃₁	semidirect
520. #3384	C₂×C₃₁	semidirect
521. Q₈×SD₁₆	C₂×C₃₁	semidirect
522. #3369	C₂×C₃₁	semidirect
523. #3360	C₂×C₃₁	semidirect
524. #3354	C₂×C₃₁	semidirect
525. #3344	C₂×C₃₁	semidirect
526. #3335	C₂×C₃₁	semidirect
527. #3335	C₂×C₃₁	semidirect
528. #3331	C₂×C₃₁	semidirect
529. #3306	C₂×C₃₁	semidirect
530. #3303	C₂×C₃₁	semidirect
531. #3296	C₂×C₃₁	semidirect
532. #3263	C₂×C₃₁	semidirect
533. #3248	C₂×C₃₁	semidirect
534. #3244	C₂×C₃₁	semidirect
535. #3229	C₂×C₃₁	semidirect
536. #3125	C₂×C₃₁	semidirect
537. #3105	C₂×C₃₁	semidirect
538. #3084	C₂×C₃₁	semidirect
539. C₂×#476	C₂×C₃₁	semidirect
540. #2994	C₂×C₃₁	semidirect
578. Q₈²	C₂²×C₃₁	semidirect
580. #555	C₂²×C₃₁	semidirect
582. #554	C₂²×C₃₁	semidirect
583. #554	C₂²×C₃₁	semidirect
596. #544	C₂²×C₃₁	semidirect
599. #542	C₂²×C₃₁	semidirect
610. #501	C₂²×C₃₁	semidirect
611. #498	C₂²×C₃₁	semidirect
612. #498	C₂²×C₃₁	semidirect
613. #498	C₂²×C₃₁	semidirect
616. #487	C₂²×C₃₁	semidirect
617. #487	C₂²×C₃₁	semidirect
618. #485	C₂²×C₃₁	semidirect
622. #483	C₂²×C₃₁	semidirect
623. #483	C₂²×C₃₁	semidirect
627. #481	C₂²×C₃₁	semidirect
628. #479	C₂²×C₃₁	semidirect
629. #479	C₂²×C₃₁	semidirect
640. #476	C₂²×C₃₁	semidirect
641. #475	C₂²×C₃₁	semidirect
642. #475	C₂²×C₃₁	semidirect
643. #475	C₂²×C₃₁	semidirect
644. #475	C₂²×C₃₁	semidirect
645. #475	C₂²×C₃₁	semidirect
646. #474	C₂²×C₃₁	semidirect
647. #470	C₂²×C₃₁	semidirect
652. #465	C₂²×C₃₁	semidirect
654. #464	C₂²×C₃₁	semidirect
658. #462	C₂²×C₃₁	semidirect
659. #461	C₂²×C₃₁	semidirect
664. #446	C₂²×C₃₁	semidirect
665. C₈×Q₈	C₂²×C₃₁	semidirect
667. #441	C₂²×C₃₁	semidirect
671. C₄×SD₁₆	C₂²×C₃₁	semidirect
674. #436	C₂²×C₃₁	semidirect
677. C₈×D₄	C₂²×C₃₁	semidirect
678. #433	C₂²×C₃₁	semidirect
680. #428	C₂²×C₃₁	semidirect
682. C₂×#106	C₂²×C₃₁	semidirect
683. #424	C₂²×C₃₁	semidirect
873. C₃₁	#62202	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3544	2
C₃₁×#3520	2
C₃₁×#3384	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3369	2
C₃₁×#3360	2
C₃₁×#3354	2
C₃₁×#3344	2
C₃₁×#3335	2
C₃₁×#3331	2
C₃₁×#3306	2
C₃₁×#3303	2
C₃₁×#3296	2
C₃₁×#3263	2
C₃₁×#3248	2
C₃₁×#3244	2
C₃₁×#3229	2
C₃₁×#3125	2
C₃₁×#3105	2
C₃₁×#3084	2
C₂×C₃₁×#476	2
C₃₁×#2994	2
#62202	31

Subgroups — C31×#62202 #21518961

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62202 #21518961