Subgroups — C₃₁×#61463 #21518222

Order 7936.

1844 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3364	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×#3352	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3183	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2971	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	2	yes	maximal, complemented
23	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#556	—	2	1	no	—
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#555	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	—	2	2	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#552	C₂²	1	2	yes	—
37	C₃₁×#551	—	2	2	no	—
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#548	C₂²	1	2	yes	—
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#546	C₂²	1	2	yes	—
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	C₂²	1	1	yes	characteristic
46	C₃₁×#533	C₂²	1	1	yes	characteristic
47	C₃₁×#529	—	2	2	no	—
48	C₃₁×#529	—	2	2	no	—
49	C₃₁×#529	C₂²	1	2	yes	—
50	C₃₁×#529	C₂²	1	2	yes	complemented
51	C₃₁×#525	—	2	1	no	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	C₂²	1	2	yes	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×#117	—	2	1	no	—
59	C₃₁×#499	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	—
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#484	C₂²	1	2	yes	—
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	—
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic
80	C₃₁×#474	C₂²	1	1	yes	characteristic
81	C₃₁×#470	C₂²	1	2	yes	—
82	C₃₁×#470	C₂²	1	2	yes	—
83	C₃₁×#470	C₂²	1	2	yes	complemented
84	C₃₁×#469	C₂²	1	2	yes	—
85	C₃₁×#468	C₂²	1	2	yes	—
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	—
91	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#461	C₂²	1	1	yes	characteristic
93	C₃₁×#461	C₂²	1	1	yes	characteristic
94	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#451	C₂²	1	2	yes	complemented
98	C₃₁×#450	C₂²	1	2	yes	—
99	C₃₁×#449	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	—
101	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	1	yes	characteristic
104	C₃₁×#442	C₂²	1	1	yes	characteristic
105	C₃₁×#441	C₂²	1	2	yes	complemented
106	C₃₁×#441	C₂²	1	2	yes	complemented
107	C₃₁×#441	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	—
109	C₃₁×#440	C₂²	1	2	yes	—
110	C₃₁×#440	C₂²	1	1	yes	characteristic
111	C₃₁×#440	C₂²	1	1	yes	characteristic
112	C₃₁×#440	C₂²	1	2	yes	complemented
113	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
114	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	2	yes	—
122	C₃₁×#436	C₂²	1	2	yes	—
123	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#432	C₂²	1	1	yes	characteristic
126	C₃₁×#432	C₂²	1	2	yes	complemented
127	C₃₁×#428	C₂²	1	1	yes	characteristic
128	C₃₁×#428	C₂²	1	2	yes	complemented
129	C₃₁×#419	C₂²	1	2	yes	complemented
130	C₃₁×#418	C₂²	1	1	yes	characteristic
131	C₃₁×#417	C₂²	1	1	yes	characteristic
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₃₁	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	—	2	1	no	—
142	C₃₁×#137	—	2	8	no	—
143	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	1	no	—
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
170	C₃₁×#125	—	2	2	no	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	1	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	C₂³	1	2	yes	—
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	C₂³	1	2	yes	—
180	C₃₁×#124	C₂³	1	2	yes	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×#121	—	2	1	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₃₁×#120	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	2	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	1	no	—
213	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₃₁	—	2	1	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
233	C₄×D₄×C₃₁	D₄	1	2	yes	—
234	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₃₁	C₂³	1	2	yes	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₃₁×#117	—	2	1	no	—
244	C₃₁×#117	—	2	1	no	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	—	2	1	no	—
247	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	2	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	2	no	—
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	D₄	1	1	yes	characteristic
255	C₃₁×#117	D₄	1	2	yes	—
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	2	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	2	yes	—
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	1	yes	characteristic
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
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	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	1	yes	characteristic
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	1	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	1	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	4	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	4	no	—
325	C₂×Q₈×C₃₁	—	4	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	4	1	no	—
337	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	2	no	—
344	C₂²×C₄×C₃₁	—	2	1	no	—
345	C₂²×C₄×C₃₁	—	2	1	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	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	4	4	no	—
355	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
359	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
361	Q₁₆×C₃₁	—	2	4	no	—
362	Q₁₆×C₃₁	—	2	4	no	—
363	Q₁₆×C₃₁	—	4	2	no	—
364	SD₁₆×C₃₁	—	2	2	no	—
365	SD₁₆×C₃₁	—	2	4	no	—
366	SD₁₆×C₃₁	—	4	2	no	—
367	SD₁₆×C₃₁	—	4	2	no	—
368	SD₁₆×C₃₁	#41	1	4	yes	complemented
369	D₈×C₃₁	—	2	2	no	—
370	D₈×C₃₁	—	2	2	no	—
371	M₁₆×C₃₁	—	2	2	no	—
372	M₁₆×C₃₁	—	2	4	no	—
373	M₁₆×C₃₁	—	4	2	no	—
374	M₁₆×C₃₁	—	4	1	no	—
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	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²⋊C₄×C₃₁	—	2	2	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	2	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	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	1	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	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₄²×C₃₁	—	2	1	no	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	—	2	2	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	2	no	—
445	C₄²×C₃₁	C₂×D₄	1	2	yes	—
446	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	2	yes	—
451	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
452	#61463	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₃₁	—	2	1	no	—
454	C₂³×C₃₁	—	2	1	no	—
455	C₂³×C₃₁	—	2	1	no	—
456	C₂³×C₃₁	—	4	2	no	—
457	C₂³×C₃₁	—	4	2	no	—
458	C₂³×C₃₁	—	8	1	no	—
459	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	1	no	—
463	Q₈×C₃₁	—	2	2	no	—
464	Q₈×C₃₁	—	2	2	no	—
465	Q₈×C₃₁	—	2	2	no	—
466	Q₈×C₃₁	—	2	2	no	—
467	Q₈×C₃₁	—	4	4	no	—
468	Q₈×C₃₁	—	4	2	no	—
469	Q₈×C₃₁	—	8	1	no	—
470	Q₈×C₃₁	C₂×#41	1	2	yes	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	1	no	—
476	D₄×C₃₁	—	2	1	no	—
477	D₄×C₃₁	—	4	2	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	2	no	—
480	D₄×C₃₁	—	4	4	no	—
481	D₄×C₃₁	—	4	4	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	C₂×#41	1	2	yes	—
484	C₂×C₄×C₃₁	—	2	1	no	—
485	C₂×C₄×C₃₁	—	2	2	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	2	no	—
488	C₂×C₄×C₃₁	—	2	1	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	1	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	2	no	—
495	C₂×C₄×C₃₁	—	2	2	no	—
496	C₂×C₄×C₃₁	—	2	2	no	—
497	C₂×C₄×C₃₁	—	2	1	no	—
498	C₂×C₄×C₃₁	—	4	2	no	—
499	C₂×C₄×C₃₁	—	4	1	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	4	4	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	—	4	2	no	—
507	C₂×C₄×C₃₁	—	4	2	no	—
508	C₂×C₄×C₃₁	—	4	4	no	—
509	C₂×C₄×C₃₁	—	4	2	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
522	C₈×C₃₁	—	2	1	no	—
523	C₈×C₃₁	—	2	2	no	—
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	—	2	2	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	C₂×#41	1	2	yes	—
528	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3352	C₂×C₃₁	1	2	yes	complemented
536	#3330	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3327	C₂×C₃₁	1	2	yes	complemented
539	#3323	C₂×C₃₁	1	2	yes	complemented
540	#3276	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3275	C₂×C₃₁	1	2	yes	complemented
542	#3185	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3183	C₂×C₃₁	1	2	yes	complemented
544	#3117	C₂×C₃₁	1	2	yes	complemented
545	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3111	C₂×C₃₁	1	2	yes	complemented
547	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#2971	C₂×C₃₁	1	1	yes	characteristic, complemented
549	C₄×#137	C₂×C₃₁	1	2	yes	complemented
550	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
551	C₂²×C₃₁	—	2	2	no	—
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	2	no	—
554	C₂²×C₃₁	—	2	1	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	1	no	—
557	C₂²×C₃₁	—	2	2	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	1	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	1	no	—
566	C₂²×C₃₁	—	8	4	no	—
567	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₃₁	—	2	1	no	—
569	C₄×C₃₁	—	2	2	no	—
570	C₄×C₃₁	—	2	1	no	—
571	C₄×C₃₁	—	2	1	no	—
572	C₄×C₃₁	—	2	2	no	—
573	C₄×C₃₁	—	2	2	no	—
574	C₄×C₃₁	—	2	1	no	—
575	C₄×C₃₁	—	2	2	no	—
576	C₄×C₃₁	—	4	1	no	—
577	C₄×C₃₁	—	4	2	no	—
578	C₄×C₃₁	—	4	2	no	—
579	C₄×C₃₁	—	4	2	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	2	no	—
584	C₄×C₃₁	#575	1	2	yes	—
585	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
586	C₄×C₃₁	#585	1	1	yes	characteristic
587	C₂×#137	C₂²×C₃₁	1	2	yes	—
588	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
589	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
590	#556	—	2	1	no	—
591	#556	C₂²×C₃₁	1	1	yes	characteristic
592	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#555	C₂²×C₃₁	1	1	yes	characteristic
594	#554	C₂²×C₃₁	1	1	yes	characteristic
595	#553	—	2	1	no	—
596	#552	—	2	1	no	—
597	#552	—	2	2	no	—
598	#552	C₂²×C₃₁	1	2	yes	—
599	#552	C₂²×C₃₁	1	2	yes	—
600	#551	—	2	2	no	—
601	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
602	#548	C₂²×C₃₁	1	2	yes	—
603	#547	—	2	1	no	—
604	#547	C₂²×C₃₁	1	1	yes	characteristic
605	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#546	C₂²×C₃₁	1	2	yes	—
607	#533	—	2	1	no	—
608	#533	C₂²×C₃₁	1	1	yes	characteristic
609	#533	C₂²×C₃₁	1	1	yes	characteristic
610	#529	—	2	2	no	—
611	#529	—	2	2	no	—
612	#529	C₂²×C₃₁	1	2	yes	—
613	#529	C₂²×C₃₁	1	2	yes	complemented
614	#525	—	2	1	no	—
615	C₄×#41	—	2	1	no	—
616	C₄×#41	C₂²×C₃₁	1	2	yes	—
617	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
618	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
620	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
621	C₂×#117	—	2	1	no	—
622	#499	C₂²×C₃₁	1	2	yes	complemented
623	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#495	C₂²×C₃₁	1	2	yes	—
625	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#488	C₂²×C₃₁	1	2	yes	—
627	#488	C₂²×C₃₁	1	2	yes	complemented
628	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
629	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#485	C₂²×C₃₁	1	2	yes	—
631	#485	C₂²×C₃₁	1	2	yes	complemented
632	#484	C₂²×C₃₁	1	2	yes	—
633	#484	C₂²×C₃₁	1	2	yes	complemented
634	#482	C₂²×C₃₁	1	2	yes	complemented
635	#481	C₂²×C₃₁	1	2	yes	—
636	#479	C₂²×C₃₁	1	2	yes	complemented
637	#479	C₂²×C₃₁	1	2	yes	complemented
638	#479	C₂²×C₃₁	1	2	yes	complemented
639	#478	C₂²×C₃₁	1	2	yes	—
640	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#474	C₂²×C₃₁	1	1	yes	characteristic
643	#474	C₂²×C₃₁	1	1	yes	characteristic
644	#470	C₂²×C₃₁	1	2	yes	—
645	#470	C₂²×C₃₁	1	2	yes	—
646	#470	C₂²×C₃₁	1	2	yes	complemented
647	#469	C₂²×C₃₁	1	2	yes	—
648	#468	C₂²×C₃₁	1	2	yes	—
649	#468	C₂²×C₃₁	1	2	yes	complemented
650	#464	C₂²×C₃₁	1	2	yes	—
651	#464	C₂²×C₃₁	1	2	yes	—
652	#464	C₂²×C₃₁	1	2	yes	complemented
653	#463	C₂²×C₃₁	1	2	yes	—
654	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#461	C₂²×C₃₁	1	1	yes	characteristic
656	#461	C₂²×C₃₁	1	1	yes	characteristic
657	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	#452	C₂²×C₃₁	1	2	yes	—
659	#452	C₂²×C₃₁	1	2	yes	—
660	#451	C₂²×C₃₁	1	2	yes	complemented
661	#450	C₂²×C₃₁	1	2	yes	—
662	#449	C₂²×C₃₁	1	2	yes	—
663	#448	C₂²×C₃₁	1	2	yes	—
664	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#442	C₂²×C₃₁	1	1	yes	characteristic
667	#442	C₂²×C₃₁	1	1	yes	characteristic
668	#441	C₂²×C₃₁	1	2	yes	complemented
669	#441	C₂²×C₃₁	1	2	yes	complemented
670	#441	C₂²×C₃₁	1	2	yes	complemented
671	#440	C₂²×C₃₁	1	2	yes	—
672	#440	C₂²×C₃₁	1	2	yes	—
673	#440	C₂²×C₃₁	1	1	yes	characteristic
674	#440	C₂²×C₃₁	1	1	yes	characteristic
675	#440	C₂²×C₃₁	1	2	yes	complemented
676	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
677	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
678	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
680	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
681	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
682	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
684	#436	C₂²×C₃₁	1	2	yes	—
685	#436	C₂²×C₃₁	1	2	yes	—
686	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#432	C₂²×C₃₁	1	1	yes	characteristic
689	#432	C₂²×C₃₁	1	2	yes	complemented
690	#428	C₂²×C₃₁	1	1	yes	characteristic
691	#428	C₂²×C₃₁	1	2	yes	complemented
692	#419	C₂²×C₃₁	1	2	yes	complemented
693	#418	C₂²×C₃₁	1	1	yes	characteristic
694	#417	C₂²×C₃₁	1	2	yes	—
695	#417	C₂²×C₃₁	1	1	yes	characteristic
696	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
697	C₄×M₁₆	C₂²×C₃₁	1	2	yes	complemented
698	C₂×C₃₁	—	4	2	no	—
699	C₂×C₃₁	—	4	1	no	—
700	C₂×C₃₁	—	4	2	no	—
701	C₂×C₃₁	—	8	1	no	—
702	C₂×C₃₁	—	8	1	no	—
703	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
704	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
705	C₂×C₃₁	#3586	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
708	C₂×#41	C₂³×C₃₁	1	2	yes	—
709	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
710	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
711	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
712	C₂³×C₄	—	2	1	no	—
713	#137	—	2	8	no	—
714	AGL(1,ℤ/8)	—	2	4	no	—
715	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
716	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
727	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
729	C₄⋊Q₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	#126	—	2	2	no	—
736	#126	—	2	2	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#125	—	2	2	no	—
742	#125	—	2	2	no	—
743	#125	—	2	2	no	—
744	#125	—	2	1	no	—
745	#125	—	2	1	no	—
746	#125	C₂³×C₃₁	1	2	yes	—
747	#125	C₂³×C₃₁	1	2	yes	—
748	#124	—	2	2	no	—
749	#124	—	2	2	no	—
750	#124	C₂³×C₃₁	1	2	yes	—
751	#124	C₂³×C₃₁	1	2	yes	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	#123	—	2	2	no	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	1	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
772	#121	—	2	1	no	—
773	#121	—	2	1	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	C₂³×C₃₁	1	2	yes	—
777	#121	C₂³×C₃₁	1	2	yes	—
778	#120	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	—	2	2	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
789	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
790	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
792	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	2	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
804	C₄×D₄	D₄×C₃₁	1	2	yes	—
805	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
809	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₃₁	1	2	yes	—
811	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₃₁	1	2	yes	—
813	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
814	#117	—	2	1	no	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	—	2	1	no	—
819	#117	—	2	2	no	—
820	#117	—	2	2	no	—
821	#117	—	2	2	no	—
822	#117	—	2	2	no	—
823	#117	—	2	1	no	—
824	#117	—	2	2	no	—
825	#117	D₄×C₃₁	1	1	yes	characteristic
826	#117	D₄×C₃₁	1	2	yes	—
827	#117	C₂³×C₃₁	1	1	yes	characteristic
828	#117	C₂³×C₃₁	1	2	yes	—
829	C₂×C₄⋊C₄	—	2	2	no	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
834	C₂×C₂²⋊C₄	—	2	1	no	—
835	C₂×C₂²⋊C₄	—	2	2	no	—
836	C₂×C₄²	—	2	2	no	—
837	C₂×C₄²	—	2	2	no	—
838	C₂×C₄²	—	2	1	no	—
839	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
840	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
841	#107	C₂³×C₃₁	1	1	yes	characteristic
842	#107	C₂³×C₃₁	1	1	yes	characteristic
843	#107	C₂³×C₃₁	1	2	yes	—
844	#107	C₂³×C₃₁	1	2	yes	—
845	#107	C₂³×C₃₁	1	2	yes	—
846	#106	C₂³×C₃₁	1	1	yes	characteristic
847	#106	C₂³×C₃₁	1	1	yes	characteristic
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	#106	C₂³×C₃₁	1	2	yes	—
851	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	1	yes	characteristic
856	#103	C₂³×C₃₁	1	1	yes	characteristic
857	#103	C₂³×C₃₁	1	2	yes	—
858	#103	C₂³×C₃₁	1	2	yes	—
859	#103	C₂³×C₃₁	1	2	yes	—
860	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	2	yes	—
862	#103	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
868	#102	C₂³×C₃₁	1	1	yes	characteristic
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	1	yes	characteristic
872	#102	C₂³×C₃₁	1	1	yes	characteristic
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
878	#97	C₂³×C₃₁	1	1	yes	characteristic
879	#97	C₂³×C₃₁	1	1	yes	characteristic
880	#97	C₂³×C₃₁	1	2	yes	—
881	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₃₁	1	2	yes	—
884	C₄×C₈	C₂³×C₃₁	1	2	yes	—
885	C₃₁	#61463	1	1	yes	characteristic, direct product factor, Sylow
886	C₂⁴	—	2	1	no	—
887	#41	—	2	2	no	—
888	#41	—	2	4	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	2	no	—
892	#41	—	4	4	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	4	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
899	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
901	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	4	1	no	—
909	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
911	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
912	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
913	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	4	4	no	—
927	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
928	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
929	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
931	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
932	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
933	Q₁₆	—	2	4	no	—
934	Q₁₆	—	2	4	no	—
935	Q₁₆	—	4	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	#41×C₃₁	1	4	yes	complemented
941	D₈	—	2	2	no	—
942	D₈	—	2	2	no	—
943	M₁₆	—	2	2	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	—	4	2	no	—
946	M₁₆	—	4	1	no	—
947	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
950	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
951	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	2	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1018	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1020	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₃₁	1	2	yes	—
1023	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	4	4	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	1	no	—
1041	Q₈	C₂×#41×C₃₁	1	2	yes	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	4	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	8	2	no	—
1054	D₄	C₂×#41×C₃₁	1	2	yes	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	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	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	1	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	C₂×#41×C₃₁	1	2	yes	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	8	4	no	—
1115	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	C₃₁×#575	1	2	yes	—
1133	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1134	C₄	C₃₁×#585	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1141	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1142	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 ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3482	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3393	C₂	semidirect
4. C₃₁×#3381	C₂	semidirect
5. C₃₁×#3364	C₂	semidirect
6. C₃₁×#3360	C₂	semidirect
7. C₃₁×#3354	C₂	semidirect
8. C₃₁×#3352	C₂	semidirect
9. C₃₁×#3330	C₂	semidirect
10. C₃₁×#3329	C₂	semidirect
11. C₃₁×#3327	C₂	semidirect
12. C₃₁×#3323	C₂	semidirect
13. C₃₁×#3276	C₂	semidirect
14. C₃₁×#3275	C₂	semidirect
15. C₃₁×#3185	C₂	semidirect
16. C₃₁×#3183	C₂	semidirect
17. C₃₁×#3117	C₂	semidirect
18. C₃₁×#3116	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3110	C₂	semidirect
21. C₃₁×#2971	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
26. C₃₁×#557	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
42. C₃₁×#547	C₂²	semidirect
50. C₃₁×#529	C₂²	semidirect
56. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#499	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
62. C₃₁×#494	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
83. C₃₁×#470	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
89. C₃₁×#464	C₂²	semidirect
91. C₃₁×#462	C₂²	semidirect
94. C₃₁×#461	C₂²	semidirect
97. C₃₁×#451	C₂²	semidirect
101. C₈×Q₈×C₃₁	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
105. C₃₁×#441	C₂²	semidirect
106. C₃₁×#441	C₂²	semidirect
107. C₃₁×#441	C₂²	semidirect
112. C₃₁×#440	C₂²	semidirect
113. C₄×Q₁₆×C₃₁	C₂²	semidirect
114. C₄×Q₁₆×C₃₁	C₂²	semidirect
123. C₃₁×#436	C₂²	semidirect
124. C₃₁×#436	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
128. C₃₁×#428	C₂²	semidirect
129. C₃₁×#419	C₂²	semidirect
134. C₄×M₁₆×C₃₁	C₂²	semidirect
368. SD₁₆×C₃₁	#41	semidirect
452. #61463	C₃₁	direct (N × H)
528. #3482	C₂×C₃₁	semidirect
529. #3475	C₂×C₃₁	semidirect
530. #3393	C₂×C₃₁	semidirect
531. #3381	C₂×C₃₁	semidirect
532. #3364	C₂×C₃₁	semidirect
533. #3360	C₂×C₃₁	semidirect
534. #3354	C₂×C₃₁	semidirect
535. #3352	C₂×C₃₁	semidirect
536. #3330	C₂×C₃₁	semidirect
537. #3329	C₂×C₃₁	semidirect
538. #3327	C₂×C₃₁	semidirect
539. #3323	C₂×C₃₁	semidirect
540. #3276	C₂×C₃₁	semidirect
541. #3275	C₂×C₃₁	semidirect
542. #3185	C₂×C₃₁	semidirect
543. #3183	C₂×C₃₁	semidirect
544. #3117	C₂×C₃₁	semidirect
545. #3116	C₂×C₃₁	semidirect
546. #3111	C₂×C₃₁	semidirect
547. #3110	C₂×C₃₁	semidirect
548. #2971	C₂×C₃₁	semidirect
549. C₄×#137	C₂×C₃₁	semidirect
550. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
589. #557	C₂²×C₃₁	semidirect
592. #556	C₂²×C₃₁	semidirect
601. D₄×Q₈	C₂²×C₃₁	semidirect
605. #547	C₂²×C₃₁	semidirect
613. #529	C₂²×C₃₁	semidirect
619. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
622. #499	C₂²×C₃₁	semidirect
623. #498	C₂²×C₃₁	semidirect
625. #494	C₂²×C₃₁	semidirect
627. #488	C₂²×C₃₁	semidirect
628. #487	C₂²×C₃₁	semidirect
629. #487	C₂²×C₃₁	semidirect
631. #485	C₂²×C₃₁	semidirect
633. #484	C₂²×C₃₁	semidirect
634. #482	C₂²×C₃₁	semidirect
636. #479	C₂²×C₃₁	semidirect
637. #479	C₂²×C₃₁	semidirect
638. #479	C₂²×C₃₁	semidirect
640. #477	C₂²×C₃₁	semidirect
641. #476	C₂²×C₃₁	semidirect
646. #470	C₂²×C₃₁	semidirect
649. #468	C₂²×C₃₁	semidirect
652. #464	C₂²×C₃₁	semidirect
654. #462	C₂²×C₃₁	semidirect
657. #461	C₂²×C₃₁	semidirect
660. #451	C₂²×C₃₁	semidirect
664. C₈×Q₈	C₂²×C₃₁	semidirect
665. C₈×Q₈	C₂²×C₃₁	semidirect
668. #441	C₂²×C₃₁	semidirect
669. #441	C₂²×C₃₁	semidirect
670. #441	C₂²×C₃₁	semidirect
675. #440	C₂²×C₃₁	semidirect
676. C₄×Q₁₆	C₂²×C₃₁	semidirect
677. C₄×Q₁₆	C₂²×C₃₁	semidirect
686. #436	C₂²×C₃₁	semidirect
687. #436	C₂²×C₃₁	semidirect
689. #432	C₂²×C₃₁	semidirect
691. #428	C₂²×C₃₁	semidirect
692. #419	C₂²×C₃₁	semidirect
697. C₄×M₁₆	C₂²×C₃₁	semidirect
885. C₃₁	#61463	direct (N × H)
940. SD₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3482	2
C₃₁×#3475	2
C₃₁×#3393	2
C₃₁×#3381	2
C₃₁×#3364	2
C₃₁×#3360	2
C₃₁×#3354	2
C₃₁×#3352	2
C₃₁×#3330	2
C₃₁×#3329	2
C₃₁×#3327	2
C₃₁×#3323	2
C₃₁×#3276	2
C₃₁×#3275	2
C₃₁×#3185	2
C₃₁×#3183	2
C₃₁×#3117	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3110	2
C₃₁×#2971	2
C₄×C₃₁×#137	2
C₄×C₃₁×AGL(1,ℤ/8)	2
#61463	31

Subgroups — C31×#61463 #21518222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61463 #21518222