Subgroups — C₃₁×#62189 #21518948

Order 7936.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#3386	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×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3353	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3344	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×#3323	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3302	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3120	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3084	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#557	—	2	1	no	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	—	2	1	no	—
29	C₃₁×#556	C₂²	1	1	yes	characteristic
30	C₃₁×#556	C₂²	1	2	yes	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#554	C₂²	1	2	yes	—
33	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#551	—	2	2	no	—
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	—	2	1	no	—
39	C₃₁×#547	C₂²	1	1	yes	characteristic
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	—	2	1	no	—
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#541	—	2	2	no	—
46	C₃₁×#541	—	2	1	no	—
47	C₃₁×#541	C₂²	1	2	yes	complemented
48	C₃₁×#539	—	2	2	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	1	yes	characteristic
51	C₃₁×#533	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×#500	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#498	C₂²	1	2	yes	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	—
66	C₃₁×#485	C₂²	1	2	yes	—
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#483	C₂²	1	1	yes	characteristic
70	C₃₁×#483	C₂²	1	1	yes	characteristic
71	C₃₁×#483	C₂²	1	2	yes	complemented
72	C₃₁×#483	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	—
74	C₃₁×#481	C₂²	1	2	yes	—
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	—
79	C₃₁×#478	C₂²	1	2	yes	—
80	C₃₁×#478	C₂²	1	2	yes	—
81	C₃₁×#477	C₂²	1	2	yes	complemented
82	C₃₁×#476	C₂²	1	1	yes	characteristic
83	C₃₁×#476	C₂²	1	1	yes	characteristic
84	C₃₁×#476	C₂²	1	1	yes	characteristic
85	C₃₁×#476	C₂²	1	2	yes	—
86	C₃₁×#476	C₂²	1	1	yes	characteristic
87	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#475	C₂²	1	2	yes	complemented
89	C₃₁×#475	C₂²	1	2	yes	complemented
90	C₃₁×#475	C₂²	1	2	yes	complemented
91	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	1	yes	characteristic
93	C₃₁×#474	C₂²	1	1	yes	characteristic
94	C₃₁×#470	C₂²	1	2	yes	—
95	C₃₁×#470	C₂²	1	2	yes	—
96	C₃₁×#470	C₂²	1	2	yes	complemented
97	C₃₁×#468	C₂²	1	2	yes	—
98	C₃₁×#467	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	—
100	C₃₁×#464	C₂²	1	2	yes	—
101	C₃₁×#464	C₂²	1	2	yes	—
102	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#462	C₂²	1	2	yes	complemented
105	C₃₁×#461	C₂²	1	1	yes	characteristic
106	C₃₁×#461	C₂²	1	1	yes	characteristic
107	C₃₁×#452	C₂²	1	2	yes	—
108	C₃₁×#452	C₂²	1	2	yes	—
109	C₃₁×#450	C₂²	1	1	yes	characteristic
110	C₃₁×#450	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×#441	C₂²	1	2	yes	complemented
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
121	C₃₁×#436	C₂²	1	2	yes	—
122	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#435	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	—
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₃₁×#423	C₂²	1	1	yes	characteristic
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₃₁×#417	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	—	2	1	no	—
138	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₃₁	—	2	1	no	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	—	2	2	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	—	2	2	no	—
153	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
161	C₃₁×#126	—	2	2	no	—
162	C₃₁×#126	—	2	2	no	—
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	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	D₄	1	2	yes	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	D₄	1	1	yes	characteristic
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	D₄	1	1	yes	characteristic
186	C₃₁×#124	C₂³	1	2	yes	—
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	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	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	D₄	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	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×C₂²⋊Q₈	C₂³	1	2	yes	—
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	2	yes	—
218	C₃₁×#120	—	2	2	no	—
219	C₄×Q₈×C₃₁	—	2	1	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	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
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	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	1	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₃₁×#117	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
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	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×#106	C₂³	1	1	yes	characteristic
268	C₃₁×#106	C₂³	1	2	yes	—
269	C₃₁×#106	C₂³	1	2	yes	—
270	C₃₁×#106	C₂³	1	2	yes	—
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	1	yes	characteristic
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
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	2	no	—
316	C₂×Q₈×C₃₁	—	2	1	no	—
317	C₂×Q₈×C₃₁	—	2	1	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	2	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₃₁	—	2	2	no	—
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	—	4	1	no	—
332	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	—	2	1	no	—
337	C₂²×C₄×C₃₁	—	2	2	no	—
338	C₂²×C₄×C₃₁	—	2	2	no	—
339	C₂²×C₄×C₃₁	—	2	2	no	—
340	C₂²×C₄×C₃₁	—	2	1	no	—
341	C₂²×C₄×C₃₁	—	2	1	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	8	2	no	—
346	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
350	Q₁₆×C₃₁	—	4	2	no	—
351	Q₁₆×C₃₁	—	4	2	no	—
352	SD₁₆×C₃₁	—	2	2	no	—
353	SD₁₆×C₃₁	—	2	2	no	—
354	SD₁₆×C₃₁	—	4	1	no	—
355	SD₁₆×C₃₁	—	4	1	no	—
356	M₁₆×C₃₁	—	4	2	no	—
357	M₁₆×C₃₁	—	4	2	no	—
358	C₂×C₈×C₃₁	—	4	2	no	—
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	1	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	1	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	1	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	1	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	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	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	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	1	no	—
409	C₂²⋊C₄×C₃₁	—	2	1	no	—
410	C₂²⋊C₄×C₃₁	—	2	2	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	2	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	1	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	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
426	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
427	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
428	C₄²×C₃₁	—	2	2	no	—
429	C₄²×C₃₁	—	2	2	no	—
430	C₄²×C₃₁	—	2	2	no	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	2	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄²×C₃₁	C₂⁴	1	2	yes	—
440	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
441	#62189	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂³×C₃₁	—	2	1	no	—
443	C₂³×C₃₁	—	2	1	no	—
444	C₂³×C₃₁	—	4	2	no	—
445	C₂³×C₃₁	—	4	2	no	—
446	C₂³×C₃₁	—	8	1	no	—
447	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
449	Q₈×C₃₁	—	2	2	no	—
450	Q₈×C₃₁	—	2	1	no	—
451	Q₈×C₃₁	—	2	1	no	—
452	Q₈×C₃₁	—	2	2	no	—
453	Q₈×C₃₁	—	2	1	no	—
454	Q₈×C₃₁	—	2	1	no	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	4	2	no	—
457	Q₈×C₃₁	—	4	2	no	—
458	Q₈×C₃₁	—	8	1	no	—
459	Q₈×C₃₁	—	8	1	no	—
460	Q₈×C₃₁	—	8	2	no	—
461	Q₈×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	2	2	no	—
463	D₄×C₃₁	—	2	1	no	—
464	D₄×C₃₁	—	2	1	no	—
465	D₄×C₃₁	—	2	1	no	—
466	D₄×C₃₁	—	4	2	no	—
467	D₄×C₃₁	—	4	2	no	—
468	D₄×C₃₁	—	4	4	no	—
469	D₄×C₃₁	—	8	2	no	—
470	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	1	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	1	no	—
476	C₂×C₄×C₃₁	—	2	1	no	—
477	C₂×C₄×C₃₁	—	2	1	no	—
478	C₂×C₄×C₃₁	—	2	2	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	2	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	1	no	—
483	C₂×C₄×C₃₁	—	2	2	no	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	4	1	no	—
487	C₂×C₄×C₃₁	—	4	4	no	—
488	C₂×C₄×C₃₁	—	4	2	no	—
489	C₂×C₄×C₃₁	—	4	2	no	—
490	C₂×C₄×C₃₁	—	8	1	no	—
491	C₂×C₄×C₃₁	—	8	1	no	—
492	C₂×C₄×C₃₁	—	8	2	no	—
493	C₂×C₄×C₃₁	—	8	2	no	—
494	C₂×C₄×C₃₁	—	8	1	no	—
495	C₂×C₄×C₃₁	—	8	2	no	—
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
505	C₈×C₃₁	—	2	1	no	—
506	C₈×C₃₁	—	2	1	no	—
507	C₈×C₃₁	—	2	1	no	—
508	C₈×C₃₁	—	2	2	no	—
509	C₈×C₃₁	—	2	1	no	—
510	C₈×C₃₁	—	2	2	no	—
511	#3555	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3520	C₂×C₃₁	1	1	yes	characteristic
513	#3386	C₂×C₃₁	1	1	yes	characteristic, complemented
514	Q₈×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#3356	C₂×C₃₁	1	2	yes	complemented
518	#3353	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3344	C₂×C₃₁	1	2	yes	complemented
520	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3331	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3323	C₂×C₃₁	1	2	yes	complemented
523	#3311	C₂×C₃₁	1	2	yes	complemented
524	#3302	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3258	C₂×C₃₁	1	2	yes	complemented
526	#3255	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3244	C₂×C₃₁	1	2	yes	complemented
528	#3231	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3120	C₂×C₃₁	1	2	yes	complemented
530	#3101	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3084	C₂×C₃₁	1	2	yes	complemented
532	#3077	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
534	C₂²×C₃₁	—	2	1	no	—
535	C₂²×C₃₁	—	2	2	no	—
536	C₂²×C₃₁	—	2	2	no	—
537	C₂²×C₃₁	—	2	1	no	—
538	C₂²×C₃₁	—	2	2	no	—
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	2	2	no	—
541	C₂²×C₃₁	—	4	1	no	—
542	C₂²×C₃₁	—	4	1	no	—
543	C₂²×C₃₁	—	4	1	no	—
544	C₂²×C₃₁	—	4	1	no	—
545	C₂²×C₃₁	—	4	1	no	—
546	C₂²×C₃₁	—	8	4	no	—
547	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₃₁	—	2	1	no	—
549	C₄×C₃₁	—	2	1	no	—
550	C₄×C₃₁	—	2	2	no	—
551	C₄×C₃₁	—	2	2	no	—
552	C₄×C₃₁	—	2	1	no	—
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	2	no	—
555	C₄×C₃₁	—	4	1	no	—
556	C₄×C₃₁	—	4	2	no	—
557	C₄×C₃₁	—	4	1	no	—
558	C₄×C₃₁	—	4	2	no	—
559	C₄×C₃₁	—	4	1	no	—
560	C₄×C₃₁	—	4	1	no	—
561	C₄×C₃₁	—	4	1	no	—
562	C₄×C₃₁	—	4	1	no	—
563	C₄×C₃₁	—	4	2	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	#577	1	2	yes	—
566	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
567	C₄×C₃₁	#585	1	1	yes	characteristic
568	#563	—	2	2	no	—
569	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
570	#557	—	2	1	no	—
571	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
572	#556	—	2	1	no	—
573	#556	C₂²×C₃₁	1	1	yes	characteristic
574	#556	C₂²×C₃₁	1	2	yes	—
575	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
576	#554	C₂²×C₃₁	1	2	yes	—
577	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
578	#552	—	2	1	no	—
579	#552	C₂²×C₃₁	1	2	yes	—
580	#551	—	2	2	no	—
581	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
582	#548	—	2	1	no	—
583	#547	C₂²×C₃₁	1	1	yes	characteristic
584	#547	C₂²×C₃₁	1	1	yes	characteristic
585	#546	C₂²×C₃₁	1	2	yes	—
586	#544	C₂²×C₃₁	1	2	yes	complemented
587	#542	—	2	1	no	—
588	#542	C₂²×C₃₁	1	2	yes	—
589	#541	—	2	2	no	—
590	#541	—	2	1	no	—
591	#541	C₂²×C₃₁	1	2	yes	complemented
592	#539	—	2	2	no	—
593	#533	C₂²×C₃₁	1	1	yes	characteristic
594	#533	C₂²×C₃₁	1	1	yes	characteristic
595	#533	C₂²×C₃₁	1	1	yes	characteristic
596	#529	C₂²×C₃₁	1	1	yes	characteristic
597	#525	—	2	1	no	—
598	C₂×C₂²⋊Q₈	—	2	1	no	—
599	#520	C₂²×C₃₁	1	2	yes	—
600	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
601	#501	C₂²×C₃₁	1	2	yes	complemented
602	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
604	#498	C₂²×C₃₁	1	2	yes	complemented
605	#489	C₂²×C₃₁	1	2	yes	—
606	#488	C₂²×C₃₁	1	2	yes	—
607	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#485	C₂²×C₃₁	1	2	yes	—
610	#485	C₂²×C₃₁	1	2	yes	—
611	#485	C₂²×C₃₁	1	2	yes	complemented
612	#484	C₂²×C₃₁	1	2	yes	complemented
613	#483	C₂²×C₃₁	1	1	yes	characteristic
614	#483	C₂²×C₃₁	1	1	yes	characteristic
615	#483	C₂²×C₃₁	1	2	yes	complemented
616	#483	C₂²×C₃₁	1	2	yes	complemented
617	#482	C₂²×C₃₁	1	2	yes	—
618	#481	C₂²×C₃₁	1	2	yes	—
619	#479	C₂²×C₃₁	1	2	yes	complemented
620	#479	C₂²×C₃₁	1	2	yes	complemented
621	#479	C₂²×C₃₁	1	2	yes	complemented
622	#478	C₂²×C₃₁	1	2	yes	—
623	#478	C₂²×C₃₁	1	2	yes	—
624	#478	C₂²×C₃₁	1	2	yes	—
625	#477	C₂²×C₃₁	1	2	yes	complemented
626	#476	C₂²×C₃₁	1	1	yes	characteristic
627	#476	C₂²×C₃₁	1	1	yes	characteristic
628	#476	C₂²×C₃₁	1	1	yes	characteristic
629	#476	C₂²×C₃₁	1	2	yes	—
630	#476	C₂²×C₃₁	1	1	yes	characteristic
631	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#475	C₂²×C₃₁	1	2	yes	complemented
633	#475	C₂²×C₃₁	1	2	yes	complemented
634	#475	C₂²×C₃₁	1	2	yes	complemented
635	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#474	C₂²×C₃₁	1	1	yes	characteristic
637	#474	C₂²×C₃₁	1	1	yes	characteristic
638	#470	C₂²×C₃₁	1	2	yes	—
639	#470	C₂²×C₃₁	1	2	yes	—
640	#470	C₂²×C₃₁	1	2	yes	complemented
641	#468	C₂²×C₃₁	1	2	yes	—
642	#467	C₂²×C₃₁	1	2	yes	complemented
643	#465	C₂²×C₃₁	1	2	yes	—
644	#464	C₂²×C₃₁	1	2	yes	—
645	#464	C₂²×C₃₁	1	2	yes	—
646	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#462	C₂²×C₃₁	1	2	yes	complemented
649	#461	C₂²×C₃₁	1	1	yes	characteristic
650	#461	C₂²×C₃₁	1	1	yes	characteristic
651	#452	C₂²×C₃₁	1	2	yes	—
652	#452	C₂²×C₃₁	1	2	yes	—
653	#450	C₂²×C₃₁	1	1	yes	characteristic
654	#450	C₂²×C₃₁	1	1	yes	characteristic
655	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#441	C₂²×C₃₁	1	2	yes	complemented
658	#440	C₂²×C₃₁	1	2	yes	—
659	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
660	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
661	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
665	#436	C₂²×C₃₁	1	2	yes	—
666	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#435	C₂²×C₃₁	1	2	yes	—
668	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#433	C₂²×C₃₁	1	2	yes	complemented
670	#431	C₂²×C₃₁	1	1	yes	characteristic
671	#428	C₂²×C₃₁	1	2	yes	—
672	#428	C₂²×C₃₁	1	2	yes	complemented
673	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
674	#424	C₂²×C₃₁	1	2	yes	complemented
675	#423	C₂²×C₃₁	1	1	yes	characteristic
676	#418	C₂²×C₃₁	1	2	yes	—
677	#417	C₂²×C₃₁	1	2	yes	—
678	#416	C₂²×C₃₁	1	2	yes	—
679	C₂×C₃₁	—	4	2	no	—
680	C₂×C₃₁	—	4	1	no	—
681	C₂×C₃₁	—	4	2	no	—
682	C₂×C₃₁	—	8	1	no	—
683	C₂×C₃₁	#3489	1	1	yes	characteristic
684	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
685	C₂×C₃₁	#3586	1	1	yes	characteristic
686	C₂×#41	—	2	1	no	—
687	C₂×#41	C₂³×C₃₁	1	2	yes	—
688	C₂²×Q₈	—	2	1	no	—
689	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
690	C₂³×C₄	—	2	1	no	—
691	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
692	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
697	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
698	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
699	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	2	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	—	2	2	no	—
704	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
711	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	2	no	—
719	#126	—	2	2	no	—
720	#126	D₄×C₃₁	1	2	yes	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	1	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	D₄×C₃₁	1	1	yes	characteristic
731	#125	C₂³×C₃₁	1	2	yes	—
732	#125	C₂³×C₃₁	1	2	yes	—
733	#124	—	2	1	no	—
734	#124	—	2	2	no	—
735	#124	—	2	2	no	—
736	#124	D₄×C₃₁	1	1	yes	characteristic
737	#124	C₂³×C₃₁	1	2	yes	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	D₄×C₃₁	1	2	yes	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
761	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
765	#121	—	2	1	no	—
766	#121	—	2	2	no	—
767	#121	D₄×C₃₁	1	1	yes	characteristic
768	#121	C₂³×C₃₁	1	2	yes	—
769	#120	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
779	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
784	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	2	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
795	C₄×D₄	C₂³×C₃₁	1	2	yes	—
796	C₄×D₄	C₂³×C₃₁	1	2	yes	—
797	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
798	#117	—	2	1	no	—
799	#117	—	2	1	no	—
800	#117	—	2	2	no	—
801	#117	—	2	1	no	—
802	#117	—	2	2	no	—
803	#117	C₂³×C₃₁	1	2	yes	—
804	#117	C₂³×C₃₁	1	2	yes	—
805	#117	C₂³×C₃₁	1	2	yes	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
811	C₂×C₂²⋊C₄	—	2	1	no	—
812	C₂×C₂²⋊C₄	—	2	2	no	—
813	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
814	#107	C₂³×C₃₁	1	2	yes	—
815	#107	C₂³×C₃₁	1	2	yes	—
816	#107	C₂³×C₃₁	1	2	yes	—
817	#107	C₂³×C₃₁	1	2	yes	—
818	#106	C₂³×C₃₁	1	1	yes	characteristic
819	#106	C₂³×C₃₁	1	2	yes	—
820	#106	C₂³×C₃₁	1	2	yes	—
821	#106	C₂³×C₃₁	1	2	yes	—
822	#106	C₂³×C₃₁	1	2	yes	—
823	#106	C₂³×C₃₁	1	1	yes	characteristic
824	#106	C₂³×C₃₁	1	2	yes	—
825	#106	C₂³×C₃₁	1	1	yes	characteristic
826	#106	C₂³×C₃₁	1	1	yes	characteristic
827	#106	C₂³×C₃₁	1	2	yes	—
828	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
829	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
833	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
834	C₄⋊C₈	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	#103	C₂³×C₃₁	1	1	yes	characteristic
840	#103	C₂³×C₃₁	1	1	yes	characteristic
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	1	yes	characteristic
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#102	C₂³×C₃₁	1	1	yes	characteristic
848	#102	C₂³×C₃₁	1	2	yes	—
849	#102	C₂³×C₃₁	1	1	yes	characteristic
850	#102	C₂³×C₃₁	1	2	yes	—
851	#102	C₂³×C₃₁	1	2	yes	—
852	#102	C₂³×C₃₁	1	2	yes	—
853	#102	C₂³×C₃₁	1	1	yes	characteristic
854	#102	C₂³×C₃₁	1	1	yes	characteristic
855	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
859	#97	C₂³×C₃₁	1	2	yes	—
860	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×C₈	C₂³×C₃₁	1	2	yes	—
863	C₃₁	#62189	1	1	yes	characteristic, direct product factor, Sylow
864	C₂⁴	—	2	1	no	—
865	#41	—	2	4	no	—
866	#41	—	4	2	no	—
867	#41	—	8	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	8	2	no	—
875	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
877	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	4	1	no	—
884	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
885	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
886	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	8	2	no	—
898	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
900	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
902	Q₁₆	—	4	2	no	—
903	Q₁₆	—	4	2	no	—
904	SD₁₆	—	2	2	no	—
905	SD₁₆	—	2	2	no	—
906	SD₁₆	—	4	1	no	—
907	SD₁₆	—	4	1	no	—
908	M₁₆	—	4	2	no	—
909	M₁₆	—	4	2	no	—
910	C₂×C₈	—	4	2	no	—
911	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
914	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	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	1	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	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
950	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
951	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
956	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	1	no	—
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	2	no	—
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
978	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	2	2	no	—
983	C₄²	—	2	1	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	2	2	no	—
986	C₄²	—	2	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
989	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₄²	C₂⁴×C₃₁	1	2	yes	—
992	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	4	2	no	—
996	C₂³	—	4	2	no	—
997	C₂³	—	8	1	no	—
998	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
999	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1000	Q₈	—	2	2	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	2	2	no	—
1004	Q₈	—	2	1	no	—
1005	Q₈	—	2	1	no	—
1006	Q₈	—	2	2	no	—
1007	Q₈	—	4	2	no	—
1008	Q₈	—	4	2	no	—
1009	Q₈	—	8	1	no	—
1010	Q₈	—	8	1	no	—
1011	Q₈	—	8	2	no	—
1012	Q₈	—	8	2	no	—
1013	D₄	—	2	2	no	—
1014	D₄	—	2	1	no	—
1015	D₄	—	2	1	no	—
1016	D₄	—	2	1	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	4	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	8	2	no	—
1021	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	2	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	4	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	1	no	—
1046	C₂×C₄	—	8	2	no	—
1047	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1054	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1055	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	2	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	4	1	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	1	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	8	4	no	—
1075	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	1	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	C₃₁×#577	1	2	yes	—
1094	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1095	C₄	C₃₁×#585	1	1	yes	characteristic
1096	C₂	—	4	1	no	—
1097	C₂	—	4	2	no	—
1098	C₂	—	4	2	no	—
1099	C₂	—	8	1	no	—
1100	C₂	C₃₁×#3489	1	1	yes	characteristic
1101	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1102	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	C₃₁×#3520	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×#3555	C₂	semidirect
3. C₃₁×#3386	C₂	semidirect
4. Q₈×SD₁₆×C₃₁	C₂	semidirect
5. C₃₁×#3369	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3356	C₂	semidirect
8. C₃₁×#3353	C₂	semidirect
9. C₃₁×#3344	C₂	semidirect
10. C₃₁×#3335	C₂	semidirect
11. C₃₁×#3331	C₂	semidirect
12. C₃₁×#3323	C₂	semidirect
13. C₃₁×#3311	C₂	semidirect
14. C₃₁×#3302	C₂	semidirect
15. C₃₁×#3258	C₂	semidirect
16. C₃₁×#3255	C₂	semidirect
17. C₃₁×#3244	C₂	semidirect
18. C₃₁×#3231	C₂	semidirect
19. C₃₁×#3120	C₂	semidirect
20. C₃₁×#3101	C₂	semidirect
21. C₃₁×#3084	C₂	semidirect
22. C₃₁×#3077	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
25. Q₈²×C₃₁	C₂²	semidirect
27. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
33. C₃₁×#554	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
47. C₃₁×#541	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#500	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
63. C₃₁×#487	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
71. C₃₁×#483	C₂²	semidirect
72. C₃₁×#483	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
81. C₃₁×#477	C₂²	semidirect
87. C₃₁×#475	C₂²	semidirect
88. C₃₁×#475	C₂²	semidirect
89. C₃₁×#475	C₂²	semidirect
90. C₃₁×#475	C₂²	semidirect
91. C₃₁×#475	C₂²	semidirect
96. C₃₁×#470	C₂²	semidirect
98. C₃₁×#467	C₂²	semidirect
102. C₃₁×#462	C₂²	semidirect
103. C₃₁×#462	C₂²	semidirect
104. C₃₁×#462	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
113. C₃₁×#441	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₂×C₃₁×#106	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
441. #62189	C₃₁	direct (N × H)
511. #3555	C₂×C₃₁	semidirect
513. #3386	C₂×C₃₁	semidirect
514. Q₈×SD₁₆	C₂×C₃₁	semidirect
515. #3369	C₂×C₃₁	semidirect
516. #3364	C₂×C₃₁	semidirect
517. #3356	C₂×C₃₁	semidirect
518. #3353	C₂×C₃₁	semidirect
519. #3344	C₂×C₃₁	semidirect
520. #3335	C₂×C₃₁	semidirect
521. #3331	C₂×C₃₁	semidirect
522. #3323	C₂×C₃₁	semidirect
523. #3311	C₂×C₃₁	semidirect
524. #3302	C₂×C₃₁	semidirect
525. #3258	C₂×C₃₁	semidirect
526. #3255	C₂×C₃₁	semidirect
527. #3244	C₂×C₃₁	semidirect
528. #3231	C₂×C₃₁	semidirect
529. #3120	C₂×C₃₁	semidirect
530. #3101	C₂×C₃₁	semidirect
531. #3084	C₂×C₃₁	semidirect
532. #3077	C₂×C₃₁	semidirect
533. #2993	C₂×C₃₁	semidirect
569. Q₈²	C₂²×C₃₁	semidirect
571. #557	C₂²×C₃₁	semidirect
575. #556	C₂²×C₃₁	semidirect
577. #554	C₂²×C₃₁	semidirect
586. #544	C₂²×C₃₁	semidirect
591. #541	C₂²×C₃₁	semidirect
601. #501	C₂²×C₃₁	semidirect
602. #500	C₂²×C₃₁	semidirect
603. #498	C₂²×C₃₁	semidirect
604. #498	C₂²×C₃₁	semidirect
607. #487	C₂²×C₃₁	semidirect
608. #487	C₂²×C₃₁	semidirect
611. #485	C₂²×C₃₁	semidirect
612. #484	C₂²×C₃₁	semidirect
615. #483	C₂²×C₃₁	semidirect
616. #483	C₂²×C₃₁	semidirect
619. #479	C₂²×C₃₁	semidirect
620. #479	C₂²×C₃₁	semidirect
621. #479	C₂²×C₃₁	semidirect
625. #477	C₂²×C₃₁	semidirect
631. #475	C₂²×C₃₁	semidirect
632. #475	C₂²×C₃₁	semidirect
633. #475	C₂²×C₃₁	semidirect
634. #475	C₂²×C₃₁	semidirect
635. #475	C₂²×C₃₁	semidirect
640. #470	C₂²×C₃₁	semidirect
642. #467	C₂²×C₃₁	semidirect
646. #462	C₂²×C₃₁	semidirect
647. #462	C₂²×C₃₁	semidirect
648. #462	C₂²×C₃₁	semidirect
655. #446	C₂²×C₃₁	semidirect
656. C₈×Q₈	C₂²×C₃₁	semidirect
657. #441	C₂²×C₃₁	semidirect
659. C₄×Q₁₆	C₂²×C₃₁	semidirect
666. #436	C₂²×C₃₁	semidirect
668. C₈×D₄	C₂²×C₃₁	semidirect
669. #433	C₂²×C₃₁	semidirect
672. #428	C₂²×C₃₁	semidirect
673. C₂×#106	C₂²×C₃₁	semidirect
674. #424	C₂²×C₃₁	semidirect
863. C₃₁	#62189	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×#3555	2
C₃₁×#3520	2
C₃₁×#3386	2
Q₈×SD₁₆×C₃₁	2
C₃₁×#3369	2
C₃₁×#3364	2
C₃₁×#3356	2
C₃₁×#3353	2
C₃₁×#3344	2
C₃₁×#3335	2
C₃₁×#3331	2
C₃₁×#3323	2
C₃₁×#3311	2
C₃₁×#3302	2
C₃₁×#3258	2
C₃₁×#3255	2
C₃₁×#3244	2
C₃₁×#3231	2
C₃₁×#3120	2
C₃₁×#3101	2
C₃₁×#3084	2
C₃₁×#3077	2
C₃₁×#2993	2
#62189	31

Subgroups — C31×#62189 #21518948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62189 #21518948