Subgroups — C₃₁×#62036 #21518795

Order 7936.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3328	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3313	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3044	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂×C₃₁×#137	C₂²	1	2	yes	—
26	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#563	—	2	2	no	—
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#556	—	2	2	no	—
31	C₃₁×#556	—	2	1	no	—
32	C₃₁×#556	C₂²	1	1	yes	characteristic
33	C₃₁×#556	C₂²	1	1	yes	characteristic
34	C₃₁×#556	C₂²	1	2	yes	—
35	C₃₁×#555	—	2	1	no	—
36	C₃₁×#555	C₂²	1	1	yes	characteristic
37	C₃₁×#554	—	2	1	no	—
38	C₃₁×#553	—	2	1	no	—
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
41	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#548	C₂²	1	2	yes	—
43	C₃₁×#548	C₂²	1	2	yes	—
44	C₃₁×#547	C₂²	1	1	yes	characteristic
45	C₃₁×#544	—	2	1	no	—
46	C₃₁×#542	—	2	1	no	—
47	C₃₁×#542	—	2	2	no	—
48	C₃₁×#542	C₂²	1	2	yes	—
49	C₃₁×#541	C₂²	1	2	yes	—
50	C₃₁×#539	—	2	2	no	—
51	C₃₁×#536	C₂²	1	2	yes	—
52	C₃₁×#533	—	2	1	no	—
53	C₃₁×#533	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₃₁×#529	—	2	1	no	—
56	C₃₁×#529	C₂²	1	1	yes	characteristic
57	C₃₁×#529	C₂²	1	1	yes	characteristic
58	C₃₁×#519	C₂²	1	2	yes	—
59	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#497	C₂²	1	2	yes	—
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic
63	C₃₁×#494	C₂²	1	1	yes	characteristic
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	1	yes	characteristic
66	C₃₁×#487	C₂²	1	2	yes	—
67	C₃₁×#487	C₂²	1	1	yes	characteristic
68	C₃₁×#485	C₂²	1	1	yes	characteristic
69	C₃₁×#485	C₂²	1	2	yes	—
70	C₃₁×#485	C₂²	1	2	yes	—
71	C₃₁×#482	C₂²	1	1	yes	characteristic
72	C₃₁×#479	C₂²	1	1	yes	characteristic
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#478	C₂²	1	1	yes	characteristic
75	C₃₁×#477	C₂²	1	1	yes	characteristic
76	C₃₁×#477	C₂²	1	2	yes	—
77	C₃₁×#476	C₂²	1	1	yes	characteristic
78	C₃₁×#475	C₂²	1	2	yes	—
79	C₃₁×#470	C₂²	1	2	yes	—
80	C₃₁×#470	C₂²	1	2	yes	—
81	C₃₁×#468	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×#464	C₂²	1	1	yes	characteristic
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#464	C₂²	1	2	yes	—
91	C₃₁×#463	C₂²	1	1	yes	characteristic
92	C₃₁×#462	C₂²	1	2	yes	—
93	C₃₁×#462	C₂²	1	1	yes	characteristic
94	C₃₁×#462	C₂²	1	1	yes	characteristic
95	C₃₁×#462	C₂²	1	2	yes	—
96	C₃₁×#462	C₂²	1	2	yes	—
97	C₃₁×#462	C₂²	1	1	yes	characteristic
98	C₃₁×#462	C₂²	1	2	yes	—
99	C₃₁×#462	C₂²	1	2	yes	—
100	C₃₁×#461	C₂²	1	1	yes	characteristic
101	C₃₁×#461	C₂²	1	1	yes	characteristic
102	C₃₁×#461	C₂²	1	1	yes	characteristic
103	C₃₁×#461	C₂²	1	2	yes	—
104	C₃₁×#452	C₂²	1	1	yes	characteristic
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#451	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	2	yes	—
108	C₃₁×#451	C₂²	1	2	yes	—
109	C₃₁×#451	C₂²	1	2	yes	—
110	C₃₁×#451	C₂²	1	2	yes	—
111	C₃₁×#449	C₂²	1	1	yes	characteristic
112	C₃₁×#449	C₂²	1	2	yes	—
113	C₃₁×#448	C₂²	1	2	yes	—
114	C₃₁×#446	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
116	C₃₁×#441	C₂²	1	2	yes	—
117	C₃₁×#441	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
120	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
124	C₃₁×#436	C₂²	1	1	yes	characteristic
125	C₃₁×#436	C₂²	1	2	yes	—
126	C₃₁×#435	C₂²	1	2	yes	—
127	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
128	C₃₁×#433	C₂²	1	2	yes	—
129	C₃₁×#431	C₂²	1	1	yes	characteristic
130	C₃₁×#424	C₂²	1	2	yes	—
131	C₃₁×#423	C₂²	1	1	yes	characteristic
132	C₃₁×#419	C₂²	1	2	yes	—
133	C₃₁×#419	C₂²	1	2	yes	—
134	C₃₁×#416	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
136	C₂×#41×C₃₁	C₂³	1	2	yes	—
137	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₃₁×#137	—	4	4	no	—
141	C₃₁×#137	—	4	4	no	—
142	C₂×Q₁₆×C₃₁	—	4	4	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	—	2	2	no	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	—	2	2	no	—
165	C₃₁×C₄⋊Q₈	—	2	1	no	—
166	C₃₁×C₄⋊Q₈	—	2	1	no	—
167	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#126	—	2	2	no	—
180	C₃₁×#126	—	2	2	no	—
181	C₃₁×#126	—	2	1	no	—
182	C₃₁×#126	D₄	1	2	yes	—
183	C₃₁×#125	—	2	2	no	—
184	C₃₁×#125	—	2	2	no	—
185	C₃₁×#125	—	2	2	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	D₄	1	1	yes	characteristic
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	—	2	2	no	—
194	C₃₁×#124	—	2	2	no	—
195	C₃₁×#124	D₄	1	1	yes	characteristic
196	C₃₁×#124	C₂³	1	1	yes	characteristic
197	C₃₁×#124	C₂³	1	2	yes	—
198	C₃₁×#124	C₂³	1	2	yes	—
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	D₄	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	1	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	—	2	2	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	—	2	2	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
223	C₃₁×#121	—	2	1	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	2	no	—
227	C₃₁×#121	D₄	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₃₁	—	2	1	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	2	no	—
233	C₄×Q₈×C₃₁	—	2	2	no	—
234	C₄×Q₈×C₃₁	—	2	2	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
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	2	yes	—
241	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
242	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
244	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	1	no	—
249	C₄×D₄×C₃₁	—	2	1	no	—
250	C₄×D₄×C₃₁	—	2	1	no	—
251	C₄×D₄×C₃₁	—	2	2	no	—
252	C₄×D₄×C₃₁	—	2	2	no	—
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₃₁	C₂³	1	2	yes	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	—	2	1	no	—
262	C₃₁×#117	—	2	2	no	—
263	C₃₁×#117	—	2	2	no	—
264	C₃₁×#117	—	2	1	no	—
265	C₃₁×#117	—	2	1	no	—
266	C₃₁×#117	C₂³	1	2	yes	—
267	C₃₁×#117	C₂³	1	1	yes	characteristic
268	C₃₁×#117	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	4	1	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	4	no	—
325	C₂×Q₈×C₃₁	—	4	2	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	—	4	2	no	—
328	C₂×Q₈×C₃₁	—	4	2	no	—
329	C₂×Q₈×C₃₁	—	4	2	no	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
342	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	2	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	1	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
356	Q₁₆×C₃₁	—	2	2	no	—
357	Q₁₆×C₃₁	—	2	4	no	—
358	Q₁₆×C₃₁	—	2	4	no	—
359	Q₁₆×C₃₁	—	4	2	no	—
360	Q₁₆×C₃₁	—	4	2	no	—
361	Q₁₆×C₃₁	—	4	2	no	—
362	Q₁₆×C₃₁	—	4	2	no	—
363	Q₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	2	2	no	—
365	SD₁₆×C₃₁	—	4	1	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	D₈×C₃₁	—	4	1	no	—
370	M₁₆×C₃₁	—	4	2	no	—
371	M₁₆×C₃₁	—	4	2	no	—
372	C₂×C₈×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
378	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
379	C₄⋊C₄×C₃₁	—	2	1	no	—
380	C₄⋊C₄×C₃₁	—	2	1	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	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	1	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	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	—	2	1	no	—
406	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	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	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	1	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
438	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
440	C₄²×C₃₁	—	2	1	no	—
441	C₄²×C₃₁	—	2	1	no	—
442	C₄²×C₃₁	—	2	1	no	—
443	C₄²×C₃₁	—	2	2	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	2	yes	—
454	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
455	#62036	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂³×C₃₁	—	2	1	no	—
457	C₂³×C₃₁	—	2	1	no	—
458	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
459	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	2	1	no	—
466	Q₈×C₃₁	—	2	1	no	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	2	no	—
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	4	4	no	—
471	Q₈×C₃₁	—	8	1	no	—
472	Q₈×C₃₁	—	8	2	no	—
473	Q₈×C₃₁	—	8	2	no	—
474	Q₈×C₃₁	—	8	2	no	—
475	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	1	no	—
478	D₄×C₃₁	—	2	1	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	4	2	no	—
482	D₄×C₃₁	—	4	2	no	—
483	D₄×C₃₁	—	4	2	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	1	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	2	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	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	2	1	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	4	1	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	4	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	4	2	no	—
506	C₂×C₄×C₃₁	—	8	1	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	—	2	2	no	—
521	C₈×C₃₁	—	2	1	no	—
522	C₈×C₃₁	—	2	2	no	—
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	1	no	—
525	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3518	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3363	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3328	C₂×C₃₁	1	2	yes	complemented
533	#3313	C₂×C₃₁	1	2	yes	complemented
534	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
535	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3277	C₂×C₃₁	1	2	yes	complemented
537	#3276	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3270	C₂×C₃₁	1	2	yes	complemented
539	#3258	C₂×C₃₁	1	2	yes	complemented
540	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3225	C₂×C₃₁	1	2	yes	complemented
542	#3209	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3127	C₂×C₃₁	1	2	yes	complemented
544	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3044	C₂×C₃₁	1	2	yes	complemented
546	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#2993	C₂×C₃₁	1	1	yes	characteristic, complemented
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	2	2	no	—
550	C₂²×C₃₁	—	2	2	no	—
551	C₂²×C₃₁	—	2	1	no	—
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	4	1	no	—
555	C₂²×C₃₁	—	4	1	no	—
556	C₂²×C₃₁	—	4	1	no	—
557	C₂²×C₃₁	—	4	1	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	2	2	no	—
564	C₄×C₃₁	—	2	1	no	—
565	C₄×C₃₁	—	2	2	no	—
566	C₄×C₃₁	—	2	2	no	—
567	C₄×C₃₁	—	2	1	no	—
568	C₄×C₃₁	—	2	2	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	—	4	2	no	—
574	C₄×C₃₁	—	4	2	no	—
575	C₄×C₃₁	—	4	1	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	1	no	—
578	C₄×C₃₁	#578	1	2	yes	—
579	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
580	C₄×C₃₁	#585	1	1	yes	characteristic
581	C₂×#137	C₂²×C₃₁	1	2	yes	—
582	C₂×#137	C₂²×C₃₁	1	2	yes	—
583	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
584	#563	—	2	2	no	—
585	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
586	#557	C₂²×C₃₁	1	1	yes	characteristic
587	#556	—	2	2	no	—
588	#556	—	2	1	no	—
589	#556	C₂²×C₃₁	1	1	yes	characteristic
590	#556	C₂²×C₃₁	1	1	yes	characteristic
591	#556	C₂²×C₃₁	1	2	yes	—
592	#555	—	2	1	no	—
593	#555	C₂²×C₃₁	1	1	yes	characteristic
594	#554	—	2	1	no	—
595	#553	—	2	1	no	—
596	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
597	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
598	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
599	#548	C₂²×C₃₁	1	2	yes	—
600	#548	C₂²×C₃₁	1	2	yes	—
601	#547	C₂²×C₃₁	1	1	yes	characteristic
602	#544	—	2	1	no	—
603	#542	—	2	1	no	—
604	#542	—	2	2	no	—
605	#542	C₂²×C₃₁	1	2	yes	—
606	#541	C₂²×C₃₁	1	2	yes	—
607	#539	—	2	2	no	—
608	#536	C₂²×C₃₁	1	2	yes	—
609	#533	—	2	1	no	—
610	#533	C₂²×C₃₁	1	1	yes	characteristic
611	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
612	#529	—	2	1	no	—
613	#529	C₂²×C₃₁	1	1	yes	characteristic
614	#529	C₂²×C₃₁	1	1	yes	characteristic
615	#519	C₂²×C₃₁	1	2	yes	—
616	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
617	#497	C₂²×C₃₁	1	2	yes	—
618	#495	C₂²×C₃₁	1	2	yes	—
619	#494	C₂²×C₃₁	1	1	yes	characteristic
620	#494	C₂²×C₃₁	1	1	yes	characteristic
621	#489	C₂²×C₃₁	1	2	yes	—
622	#487	C₂²×C₃₁	1	2	yes	—
623	#487	C₂²×C₃₁	1	1	yes	characteristic
624	#487	C₂²×C₃₁	1	1	yes	characteristic
625	#485	C₂²×C₃₁	1	1	yes	characteristic
626	#485	C₂²×C₃₁	1	2	yes	—
627	#485	C₂²×C₃₁	1	2	yes	—
628	#482	C₂²×C₃₁	1	1	yes	characteristic
629	#479	C₂²×C₃₁	1	1	yes	characteristic
630	#479	C₂²×C₃₁	1	2	yes	—
631	#478	C₂²×C₃₁	1	1	yes	characteristic
632	#477	C₂²×C₃₁	1	1	yes	characteristic
633	#477	C₂²×C₃₁	1	2	yes	—
634	#476	C₂²×C₃₁	1	1	yes	characteristic
635	#475	C₂²×C₃₁	1	2	yes	—
636	#470	C₂²×C₃₁	1	2	yes	—
637	#470	C₂²×C₃₁	1	2	yes	—
638	#468	C₂²×C₃₁	1	2	yes	—
639	#468	C₂²×C₃₁	1	2	yes	—
640	#467	C₂²×C₃₁	1	2	yes	—
641	#465	C₂²×C₃₁	1	2	yes	—
642	#464	C₂²×C₃₁	1	1	yes	characteristic
643	#464	C₂²×C₃₁	1	2	yes	—
644	#464	C₂²×C₃₁	1	2	yes	—
645	#464	C₂²×C₃₁	1	2	yes	—
646	#464	C₂²×C₃₁	1	2	yes	—
647	#464	C₂²×C₃₁	1	2	yes	—
648	#463	C₂²×C₃₁	1	1	yes	characteristic
649	#462	C₂²×C₃₁	1	2	yes	—
650	#462	C₂²×C₃₁	1	2	yes	—
651	#462	C₂²×C₃₁	1	1	yes	characteristic
652	#462	C₂²×C₃₁	1	1	yes	characteristic
653	#462	C₂²×C₃₁	1	2	yes	—
654	#462	C₂²×C₃₁	1	2	yes	—
655	#462	C₂²×C₃₁	1	1	yes	characteristic
656	#462	C₂²×C₃₁	1	2	yes	—
657	#461	C₂²×C₃₁	1	1	yes	characteristic
658	#461	C₂²×C₃₁	1	1	yes	characteristic
659	#461	C₂²×C₃₁	1	1	yes	characteristic
660	#461	C₂²×C₃₁	1	2	yes	—
661	#452	C₂²×C₃₁	1	1	yes	characteristic
662	#452	C₂²×C₃₁	1	2	yes	—
663	#451	C₂²×C₃₁	1	2	yes	—
664	#451	C₂²×C₃₁	1	2	yes	—
665	#451	C₂²×C₃₁	1	2	yes	—
666	#451	C₂²×C₃₁	1	2	yes	—
667	#451	C₂²×C₃₁	1	2	yes	—
668	#449	C₂²×C₃₁	1	1	yes	characteristic
669	#449	C₂²×C₃₁	1	2	yes	—
670	#448	C₂²×C₃₁	1	2	yes	—
671	#446	C₂²×C₃₁	1	1	yes	characteristic
672	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
673	#441	C₂²×C₃₁	1	2	yes	—
674	#441	C₂²×C₃₁	1	2	yes	—
675	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
676	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
677	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
680	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
681	#436	C₂²×C₃₁	1	2	yes	—
682	#436	C₂²×C₃₁	1	1	yes	characteristic
683	#435	C₂²×C₃₁	1	2	yes	—
684	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
685	#433	C₂²×C₃₁	1	2	yes	—
686	#431	C₂²×C₃₁	1	1	yes	characteristic
687	#424	C₂²×C₃₁	1	2	yes	—
688	#423	C₂²×C₃₁	1	1	yes	characteristic
689	#419	C₂²×C₃₁	1	2	yes	—
690	#419	C₂²×C₃₁	1	2	yes	—
691	#416	C₂²×C₃₁	1	2	yes	—
692	C₂×C₃₁	—	4	1	no	—
693	C₂×C₃₁	—	4	2	no	—
694	C₂×C₃₁	—	8	1	no	—
695	C₂×C₃₁	—	8	1	no	—
696	C₂×C₃₁	#3488	1	1	yes	characteristic
697	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
698	C₂×C₃₁	#3586	1	1	yes	characteristic
699	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
700	C₂×#41	C₂³×C₃₁	1	2	yes	—
701	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
702	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
703	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
704	#137	—	4	4	no	—
705	#137	—	4	4	no	—
706	C₂×Q₁₆	—	4	4	no	—
707	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
711	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
712	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
713	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
714	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
719	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
723	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	—	2	2	no	—
729	C₄⋊Q₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
732	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
736	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	1	no	—
746	#126	D₄×C₃₁	1	2	yes	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	—	2	1	no	—
752	#125	D₄×C₃₁	1	1	yes	characteristic
753	#125	C₂³×C₃₁	1	1	yes	characteristic
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	—	2	2	no	—
759	#124	D₄×C₃₁	1	1	yes	characteristic
760	#124	C₂³×C₃₁	1	1	yes	characteristic
761	#124	C₂³×C₃₁	1	2	yes	—
762	#124	C₂³×C₃₁	1	2	yes	—
763	#123	—	2	1	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	D₄×C₃₁	1	2	yes	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	2	2	no	—
779	C₂²⋊Q₈	—	2	2	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
784	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
787	#121	—	2	1	no	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	—	2	2	no	—
791	#121	D₄×C₃₁	1	1	yes	characteristic
792	#121	C₂³×C₃₁	1	1	yes	characteristic
793	#121	C₂³×C₃₁	1	2	yes	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	2	no	—
797	C₄×Q₈	—	2	2	no	—
798	C₄×Q₈	—	2	2	no	—
799	C₄×Q₈	—	2	1	no	—
800	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
803	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
805	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	—	2	1	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×D₄	C₂³×C₃₁	1	2	yes	—
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	1	no	—
830	#117	C₂³×C₃₁	1	1	yes	characteristic
831	#117	C₂³×C₃₁	1	2	yes	—
832	#117	C₂³×C₃₁	1	2	yes	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄²	—	2	1	no	—
837	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
838	#107	C₂³×C₃₁	1	1	yes	characteristic
839	#107	C₂³×C₃₁	1	1	yes	characteristic
840	#107	C₂³×C₃₁	1	2	yes	—
841	#106	C₂³×C₃₁	1	1	yes	characteristic
842	#106	C₂³×C₃₁	1	1	yes	characteristic
843	#106	C₂³×C₃₁	1	2	yes	—
844	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
845	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
849	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
850	C₄⋊C₈	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	1	yes	characteristic
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	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	1	yes	characteristic
860	#103	C₂³×C₃₁	1	1	yes	characteristic
861	#103	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	1	yes	characteristic
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	1	yes	characteristic
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
875	#97	C₂³×C₃₁	1	2	yes	—
876	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄×C₈	C₂³×C₃₁	1	2	yes	—
879	C₃₁	#62036	1	1	yes	characteristic, direct product factor, Sylow
880	#41	—	2	2	no	—
881	#41	—	4	1	no	—
882	#41	—	4	2	no	—
883	#41	—	4	2	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	4	no	—
890	C₂×Q₈	—	4	2	no	—
891	C₂×Q₈	—	4	2	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	—	4	2	no	—
894	C₂×Q₈	—	4	2	no	—
895	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
896	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
897	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
898	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
899	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
901	C₂×D₄	—	2	1	no	—
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
907	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
908	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	1	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
921	Q₁₆	—	2	2	no	—
922	Q₁₆	—	2	4	no	—
923	Q₁₆	—	2	4	no	—
924	Q₁₆	—	4	2	no	—
925	Q₁₆	—	4	2	no	—
926	Q₁₆	—	4	2	no	—
927	Q₁₆	—	4	2	no	—
928	Q₁₆	—	4	2	no	—
929	SD₁₆	—	2	2	no	—
930	SD₁₆	—	4	1	no	—
931	SD₁₆	—	4	2	no	—
932	SD₁₆	—	4	2	no	—
933	SD₁₆	—	4	2	no	—
934	D₈	—	4	1	no	—
935	M₁₆	—	4	2	no	—
936	M₁₆	—	4	2	no	—
937	C₂×C₈	—	4	2	no	—
938	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
943	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
972	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
975	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
977	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1001	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1002	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1003	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	2	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	2	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1016	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1017	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₃₁	1	2	yes	—
1019	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂³	—	2	1	no	—
1021	C₂³	—	2	1	no	—
1022	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1023	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1024	Q₈	—	2	2	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	2	2	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	1	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	2	2	no	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	4	4	no	—
1035	Q₈	—	8	1	no	—
1036	Q₈	—	8	2	no	—
1037	Q₈	—	8	2	no	—
1038	Q₈	—	8	2	no	—
1039	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1040	D₄	—	2	2	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	2	1	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	8	2	no	—
1049	D₄	—	8	2	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	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	—	2	1	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	4	1	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	4	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	8	1	no	—
1071	C₂×C₄	—	8	2	no	—
1072	C₂×C₄	—	8	2	no	—
1073	C₂×C₄	—	8	2	no	—
1074	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1076	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1077	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1078	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1079	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1080	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1081	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1082	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	2	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	2	2	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₂²	—	2	2	no	—
1090	C₂²	—	2	1	no	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	4	1	no	—
1101	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	4	2	no	—
1111	C₄	—	4	2	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	1	no	—
1118	C₄	—	4	2	no	—
1119	C₄	C₃₁×#578	1	2	yes	—
1120	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1121	C₄	C₃₁×#585	1	1	yes	characteristic
1122	C₂	—	4	2	no	—
1123	C₂	—	4	1	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	1	no	—
1126	C₂	C₃₁×#3488	1	1	yes	characteristic
1127	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1128	C₂	C₃₁×#3586	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×#3552	C₂	semidirect
2. C₃₁×#3518	C₂	semidirect
3. C₃₁×#3398	C₂	semidirect
4. C₃₁×#3393	C₂	semidirect
5. C₃₁×#3369	C₂	semidirect
6. C₃₁×#3363	C₂	semidirect
7. C₃₁×#3329	C₂	semidirect
8. C₃₁×#3328	C₂	semidirect
9. C₃₁×#3313	C₂	semidirect
10. C₃₁×#3303	C₂	semidirect
11. D₄×Q₁₆×C₃₁	C₂	semidirect
12. C₃₁×#3277	C₂	semidirect
13. C₃₁×#3276	C₂	semidirect
14. C₃₁×#3270	C₂	semidirect
15. C₃₁×#3258	C₂	semidirect
16. C₃₁×#3252	C₂	semidirect
17. C₃₁×#3225	C₂	semidirect
18. C₃₁×#3209	C₂	semidirect
19. C₃₁×#3127	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3044	C₂	semidirect
22. C₃₁×#3039	C₂	semidirect
23. C₃₁×#2993	C₂	semidirect
455. #62036	C₃₁	direct (N × H)
525. #3552	C₂×C₃₁	semidirect
526. #3518	C₂×C₃₁	semidirect
527. #3398	C₂×C₃₁	semidirect
528. #3393	C₂×C₃₁	semidirect
529. #3369	C₂×C₃₁	semidirect
530. #3363	C₂×C₃₁	semidirect
531. #3329	C₂×C₃₁	semidirect
532. #3328	C₂×C₃₁	semidirect
533. #3313	C₂×C₃₁	semidirect
534. #3303	C₂×C₃₁	semidirect
535. D₄×Q₁₆	C₂×C₃₁	semidirect
536. #3277	C₂×C₃₁	semidirect
537. #3276	C₂×C₃₁	semidirect
538. #3270	C₂×C₃₁	semidirect
539. #3258	C₂×C₃₁	semidirect
540. #3252	C₂×C₃₁	semidirect
541. #3225	C₂×C₃₁	semidirect
542. #3209	C₂×C₃₁	semidirect
543. #3127	C₂×C₃₁	semidirect
544. #3102	C₂×C₃₁	semidirect
545. #3044	C₂×C₃₁	semidirect
546. #3039	C₂×C₃₁	semidirect
547. #2993	C₂×C₃₁	semidirect
879. C₃₁	#62036	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×#3552	2
C₃₁×#3518	2
C₃₁×#3398	2
C₃₁×#3393	2
C₃₁×#3369	2
C₃₁×#3363	2
C₃₁×#3329	2
C₃₁×#3328	2
C₃₁×#3313	2
C₃₁×#3303	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3277	2
C₃₁×#3276	2
C₃₁×#3270	2
C₃₁×#3258	2
C₃₁×#3252	2
C₃₁×#3225	2
C₃₁×#3209	2
C₃₁×#3127	2
C₃₁×#3102	2
C₃₁×#3044	2
C₃₁×#3039	2
C₃₁×#2993	2
#62036	31

Subgroups — C31×#62036 #21518795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62036 #21518795