Subgroups — C₃₁×#61487 #21518246

Order 7936.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3521	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3376	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3307	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3280	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3177	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3125	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#556	C₂²	1	2	yes	—
28	C₃₁×#556	C₂²	1	2	yes	complemented
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	—	2	2	no	—
31	C₃₁×#553	C₂²	1	2	yes	complemented
32	C₃₁×#552	—	2	2	no	—
33	C₃₁×#552	C₂²	1	2	yes	—
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#551	—	2	2	no	—
36	C₃₁×#547	C₂²	1	2	yes	complemented
37	C₃₁×#546	C₂²	1	2	yes	—
38	C₃₁×#546	C₂²	1	2	yes	—
39	C₃₁×#542	C₂²	1	2	yes	complemented
40	C₃₁×#541	C₂²	1	2	yes	—
41	C₃₁×#539	—	2	2	no	—
42	C₃₁×#538	—	2	2	no	—
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#529	C₂²	1	1	yes	characteristic
45	C₃₁×#529	C₂²	1	2	yes	complemented
46	C₂×C₃₁×#126	—	2	2	no	—
47	C₃₁×#520	C₂²	1	2	yes	complemented
48	C₃₁×#518	C₂²	1	2	yes	—
49	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
50	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#495	C₂²	1	1	yes	characteristic
54	C₃₁×#495	C₂²	1	1	yes	characteristic
55	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#491	C₂²	1	2	yes	complemented
57	C₃₁×#489	C₂²	1	2	yes	complemented
58	C₃₁×#488	C₂²	1	2	yes	complemented
59	C₃₁×#485	C₂²	1	2	yes	—
60	C₃₁×#485	C₂²	1	2	yes	—
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	complemented
64	C₃₁×#481	C₂²	1	2	yes	complemented
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#478	C₂²	1	2	yes	complemented
67	C₃₁×#478	C₂²	1	2	yes	complemented
68	C₃₁×#478	C₂²	1	2	yes	complemented
69	C₃₁×#476	C₂²	1	2	yes	complemented
70	C₃₁×#475	C₂²	1	2	yes	complemented
71	C₃₁×#470	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#467	C₂²	1	1	yes	characteristic
74	C₃₁×#467	C₂²	1	1	yes	characteristic
75	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#466	C₂²	1	1	yes	characteristic
78	C₃₁×#466	C₂²	1	1	yes	characteristic
79	C₃₁×#465	C₂²	1	2	yes	complemented
80	C₃₁×#464	C₂²	1	2	yes	complemented
81	C₃₁×#464	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#461	C₂²	1	2	yes	complemented
85	C₃₁×#461	C₂²	1	2	yes	complemented
86	C₃₁×#452	C₂²	1	2	yes	complemented
87	C₃₁×#452	C₂²	1	2	yes	complemented
88	C₃₁×#450	C₂²	1	2	yes	—
89	C₃₁×#450	C₂²	1	2	yes	—
90	C₃₁×#449	C₂²	1	2	yes	—
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
93	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#442	C₂²	1	2	yes	—
95	C₃₁×#442	C₂²	1	2	yes	—
96	C₃₁×#441	C₂²	1	2	yes	complemented
97	C₃₁×#440	C₂²	1	2	yes	complemented
98	C₃₁×#440	C₂²	1	2	yes	complemented
99	C₃₁×#440	C₂²	1	2	yes	complemented
100	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
105	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
108	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
109	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
113	C₃₁×#436	C₂²	1	1	yes	characteristic
114	C₃₁×#435	C₂²	1	1	yes	characteristic
115	C₃₁×#435	C₂²	1	1	yes	characteristic, complemented
116	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#433	C₂²	1	1	yes	characteristic
120	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#427	C₂²	1	1	yes	characteristic
123	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#418	C₂²	1	2	yes	—
126	C₃₁×#417	C₂²	1	2	yes	complemented
127	C₃₁×#416	C₂²	1	2	yes	complemented
128	C₃₁×#405	C₂²	1	1	yes	characteristic
129	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₃₁	C₂³	1	2	yes	—
132	C₂×#41×C₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
134	C₃₁×#135	—	2	4	no	—
135	C₃₁×#135	—	2	4	no	—
136	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	—	2	4	no	—
144	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₃₁	C₂³	1	2	yes	—
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	—	2	2	no	—
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	D₄	1	1	yes	characteristic
166	C₃₁×#126	D₄	1	1	yes	characteristic
167	C₃₁×#125	—	2	2	no	—
168	C₃₁×#125	—	2	2	no	—
169	C₃₁×#125	—	2	2	no	—
170	C₃₁×#125	D₄	1	1	yes	characteristic
171	C₃₁×#125	C₂³	1	2	yes	—
172	C₃₁×#125	C₂³	1	2	yes	—
173	C₃₁×#124	—	2	2	no	—
174	C₃₁×#124	—	2	2	no	—
175	C₃₁×#124	D₄	1	1	yes	characteristic
176	C₃₁×#124	C₂³	1	2	yes	—
177	C₃₁×#124	C₂³	1	2	yes	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
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	D₄	1	1	yes	characteristic
187	C₃₁×#123	D₄	1	1	yes	characteristic
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	D₄	1	1	yes	characteristic
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#120	—	2	2	no	—
206	C₃₁×#120	—	2	2	no	—
207	C₄×Q₈×C₃₁	—	2	2	no	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	2	no	—
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	2	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	2	yes	—
225	C₄×D₄×C₃₁	C₂³	1	2	yes	—
226	C₄×D₄×C₃₁	C₂³	1	2	yes	—
227	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₃₁×#117	—	2	2	no	—
231	C₃₁×#117	—	2	2	no	—
232	C₃₁×#117	—	2	2	no	—
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	C₂³	1	2	yes	—
236	C₃₁×#117	C₂³	1	2	yes	—
237	C₃₁×#117	C₂³	1	1	yes	characteristic
238	C₃₁×#117	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
240	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
241	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
242	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
243	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
244	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
245	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
246	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
247	C₂×C₄²×C₃₁	—	2	2	no	—
248	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
249	C₃₁×#107	C₂³	1	1	yes	characteristic
250	C₃₁×#107	C₂³	1	1	yes	characteristic
251	C₃₁×#107	C₂³	1	2	yes	—
252	C₃₁×#107	C₂³	1	1	yes	characteristic
253	C₃₁×#107	C₂³	1	1	yes	characteristic
254	C₃₁×#107	C₂³	1	2	yes	—
255	C₃₁×#106	C₂³	1	2	yes	—
256	C₃₁×#106	C₂³	1	2	yes	—
257	C₃₁×#106	C₂³	1	2	yes	—
258	C₃₁×#106	C₂³	1	2	yes	—
259	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#103	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×#102	C₂³	1	2	yes	—
279	C₃₁×#102	C₂³	1	2	yes	—
280	C₃₁×#102	C₂³	1	2	yes	—
281	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#97	C₂³	1	1	yes	characteristic
288	C₃₁×#97	C₂³	1	1	yes	characteristic
289	C₃₁×#97	C₂³	1	1	yes	characteristic
290	C₃₁×#97	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
297	C₂⁴×C₃₁	—	2	2	no	—
298	#41×C₃₁	—	2	4	no	—
299	#41×C₃₁	—	2	4	no	—
300	#41×C₃₁	—	4	2	no	—
301	#41×C₃₁	—	4	2	no	—
302	C₂×Q₈×C₃₁	—	2	2	no	—
303	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
304	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
306	C₂×D₄×C₃₁	—	2	4	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	2	2	no	—
312	C₂×D₄×C₃₁	—	4	2	no	—
313	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
314	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
317	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₃₁	—	2	2	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	2	no	—
322	C₂²×C₄×C₃₁	—	2	2	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	Q₁₆×C₃₁	—	2	2	no	—
333	Q₁₆×C₃₁	—	2	2	no	—
334	Q₁₆×C₃₁	—	4	2	no	—
335	SD₁₆×C₃₁	—	2	4	no	—
336	SD₁₆×C₃₁	—	2	4	no	—
337	SD₁₆×C₃₁	—	4	2	no	—
338	SD₁₆×C₃₁	—	4	2	no	—
339	D₈×C₃₁	—	2	4	no	—
340	D₈×C₃₁	—	2	2	no	—
341	D₈×C₃₁	#41	1	4	yes	—
342	M₁₆×C₃₁	—	4	1	no	—
343	M₁₆×C₃₁	—	4	1	no	—
344	C₂×C₈×C₃₁	—	2	2	no	—
345	C₂×C₈×C₃₁	—	2	2	no	—
346	C₂×C₈×C₃₁	—	2	2	no	—
347	C₂×C₈×C₃₁	—	4	1	no	—
348	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	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	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	—	2	2	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
400	C₂²⋊C₄×C₃₁	—	2	2	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₃₁	—	2	2	no	—
415	C₄²×C₃₁	—	2	2	no	—
416	C₄²×C₃₁	—	2	2	no	—
417	C₄²×C₃₁	—	2	2	no	—
418	C₄²×C₃₁	—	2	2	no	—
419	C₄²×C₃₁	—	2	2	no	—
420	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
425	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
426	#61487	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂³×C₃₁	—	2	2	no	—
428	C₂³×C₃₁	—	2	2	no	—
429	C₂³×C₃₁	—	4	4	no	—
430	C₂³×C₃₁	—	8	2	no	—
431	C₂³×C₃₁	—	8	2	no	—
432	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
433	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
434	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
435	Q₈×C₃₁	—	2	2	no	—
436	Q₈×C₃₁	—	2	2	no	—
437	Q₈×C₃₁	—	2	2	no	—
438	Q₈×C₃₁	—	2	2	no	—
439	Q₈×C₃₁	—	4	1	no	—
440	Q₈×C₃₁	—	8	2	no	—
441	D₄×C₃₁	—	2	2	no	—
442	D₄×C₃₁	—	2	2	no	—
443	D₄×C₃₁	—	2	2	no	—
444	D₄×C₃₁	—	4	1	no	—
445	D₄×C₃₁	—	4	1	no	—
446	D₄×C₃₁	—	4	1	no	—
447	D₄×C₃₁	—	4	4	no	—
448	D₄×C₃₁	—	4	4	no	—
449	D₄×C₃₁	—	4	4	no	—
450	D₄×C₃₁	—	8	2	no	—
451	D₄×C₃₁	—	8	2	no	—
452	D₄×C₃₁	C₂×#41	1	4	yes	—
453	C₂×C₄×C₃₁	—	2	1	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	1	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	2	1	no	—
458	C₂×C₄×C₃₁	—	2	1	no	—
459	C₂×C₄×C₃₁	—	2	2	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	2	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	4	1	no	—
466	C₂×C₄×C₃₁	—	4	1	no	—
467	C₂×C₄×C₃₁	—	4	4	no	—
468	C₂×C₄×C₃₁	—	4	4	no	—
469	C₂×C₄×C₃₁	—	8	2	no	—
470	C₂×C₄×C₃₁	—	8	2	no	—
471	C₂×C₄×C₃₁	—	8	2	no	—
472	C₂×C₄×C₃₁	—	8	2	no	—
473	C₂×C₄×C₃₁	—	8	2	no	—
474	C₂×C₄×C₃₁	—	8	2	no	—
475	C₂×C₄×C₃₁	—	8	2	no	—
476	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
488	C₈×C₃₁	—	2	1	no	—
489	C₈×C₃₁	—	2	1	no	—
490	C₈×C₃₁	—	2	1	no	—
491	C₈×C₃₁	—	2	1	no	—
492	C₈×C₃₁	—	2	1	no	—
493	C₈×C₃₁	—	2	1	no	—
494	C₈×C₃₁	—	2	1	no	—
495	C₈×C₃₁	C₂×#41	1	2	yes	—
496	#3521	C₂×C₃₁	1	2	yes	complemented
497	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3376	C₂×C₃₁	1	2	yes	complemented
500	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
501	#3339	C₂×C₃₁	1	1	yes	characteristic, complemented
502	#3336	C₂×C₃₁	1	1	yes	characteristic, complemented
503	#3323	C₂×C₃₁	1	2	yes	complemented
504	#3311	C₂×C₃₁	1	2	yes	complemented
505	#3307	C₂×C₃₁	1	2	yes	complemented
506	#3283	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3280	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3280	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3177	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3175	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3125	C₂×C₃₁	1	2	yes	complemented
513	#3123	C₂×C₃₁	1	2	yes	complemented
514	#3111	C₂×C₃₁	1	2	yes	complemented
515	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
516	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
517	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
518	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
519	C₂²×C₃₁	—	2	1	no	—
520	C₂²×C₃₁	—	2	1	no	—
521	C₂²×C₃₁	—	2	1	no	—
522	C₂²×C₃₁	—	2	1	no	—
523	C₂²×C₃₁	—	2	1	no	—
524	C₂²×C₃₁	—	2	1	no	—
525	C₂²×C₃₁	—	2	1	no	—
526	C₂²×C₃₁	—	2	1	no	—
527	C₂²×C₃₁	—	2	1	no	—
528	C₂²×C₃₁	—	2	4	no	—
529	C₂²×C₃₁	—	4	2	no	—
530	C₂²×C₃₁	—	4	2	no	—
531	C₂²×C₃₁	—	4	2	no	—
532	C₂²×C₃₁	—	4	2	no	—
533	C₂²×C₃₁	—	4	2	no	—
534	C₂²×C₃₁	—	16	4	no	—
535	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
536	C₄×C₃₁	—	2	1	no	—
537	C₄×C₃₁	—	2	1	no	—
538	C₄×C₃₁	—	2	1	no	—
539	C₄×C₃₁	—	2	1	no	—
540	C₄×C₃₁	—	2	1	no	—
541	C₄×C₃₁	—	2	1	no	—
542	C₄×C₃₁	—	2	1	no	—
543	C₄×C₃₁	—	2	1	no	—
544	C₄×C₃₁	—	2	1	no	—
545	C₄×C₃₁	—	2	1	no	—
546	C₄×C₃₁	—	2	1	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	—	4	2	no	—
549	C₄×C₃₁	—	4	2	no	—
550	C₄×C₃₁	—	4	2	no	—
551	C₄×C₃₁	—	4	2	no	—
552	C₄×C₃₁	—	4	2	no	—
553	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
554	C₄×C₃₁	#585	1	1	yes	characteristic
555	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
556	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
557	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
558	#556	C₂²×C₃₁	1	2	yes	—
559	#556	C₂²×C₃₁	1	2	yes	complemented
560	#554	C₂²×C₃₁	1	2	yes	complemented
561	#553	—	2	2	no	—
562	#553	C₂²×C₃₁	1	2	yes	complemented
563	#552	—	2	2	no	—
564	#552	C₂²×C₃₁	1	2	yes	—
565	#551	—	2	2	no	—
566	#551	—	2	2	no	—
567	#547	C₂²×C₃₁	1	2	yes	complemented
568	#546	C₂²×C₃₁	1	2	yes	—
569	#546	C₂²×C₃₁	1	2	yes	—
570	#542	C₂²×C₃₁	1	2	yes	complemented
571	#541	C₂²×C₃₁	1	2	yes	—
572	#539	—	2	2	no	—
573	#538	—	2	2	no	—
574	#529	—	2	2	no	—
575	#529	C₂²×C₃₁	1	1	yes	characteristic
576	#529	C₂²×C₃₁	1	2	yes	complemented
577	C₂×#126	—	2	2	no	—
578	#520	C₂²×C₃₁	1	2	yes	complemented
579	#518	C₂²×C₃₁	1	2	yes	—
580	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
581	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
582	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
584	#495	C₂²×C₃₁	1	1	yes	characteristic
585	#495	C₂²×C₃₁	1	1	yes	characteristic
586	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#491	C₂²×C₃₁	1	2	yes	complemented
588	#489	C₂²×C₃₁	1	2	yes	complemented
589	#488	C₂²×C₃₁	1	2	yes	complemented
590	#485	C₂²×C₃₁	1	2	yes	—
591	#485	C₂²×C₃₁	1	2	yes	—
592	#485	C₂²×C₃₁	1	2	yes	complemented
593	#483	C₂²×C₃₁	1	2	yes	complemented
594	#482	C₂²×C₃₁	1	2	yes	complemented
595	#481	C₂²×C₃₁	1	2	yes	complemented
596	#479	C₂²×C₃₁	1	2	yes	complemented
597	#478	C₂²×C₃₁	1	2	yes	complemented
598	#478	C₂²×C₃₁	1	2	yes	complemented
599	#478	C₂²×C₃₁	1	2	yes	complemented
600	#476	C₂²×C₃₁	1	2	yes	complemented
601	#475	C₂²×C₃₁	1	2	yes	complemented
602	#470	C₂²×C₃₁	1	2	yes	—
603	#468	C₂²×C₃₁	1	2	yes	complemented
604	#467	C₂²×C₃₁	1	1	yes	characteristic
605	#467	C₂²×C₃₁	1	1	yes	characteristic
606	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
607	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	#466	C₂²×C₃₁	1	1	yes	characteristic
609	#466	C₂²×C₃₁	1	1	yes	characteristic
610	#465	C₂²×C₃₁	1	2	yes	complemented
611	#464	C₂²×C₃₁	1	2	yes	complemented
612	#464	C₂²×C₃₁	1	2	yes	complemented
613	#463	C₂²×C₃₁	1	2	yes	—
614	#463	C₂²×C₃₁	1	2	yes	—
615	#461	C₂²×C₃₁	1	2	yes	complemented
616	#461	C₂²×C₃₁	1	2	yes	complemented
617	#452	C₂²×C₃₁	1	2	yes	complemented
618	#452	C₂²×C₃₁	1	2	yes	complemented
619	#450	C₂²×C₃₁	1	2	yes	—
620	#450	C₂²×C₃₁	1	2	yes	—
621	#449	C₂²×C₃₁	1	2	yes	—
622	#449	C₂²×C₃₁	1	2	yes	—
623	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#442	C₂²×C₃₁	1	2	yes	—
626	#442	C₂²×C₃₁	1	2	yes	—
627	#441	C₂²×C₃₁	1	2	yes	complemented
628	#440	C₂²×C₃₁	1	2	yes	complemented
629	#440	C₂²×C₃₁	1	2	yes	complemented
630	#440	C₂²×C₃₁	1	2	yes	complemented
631	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
636	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
637	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
638	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
639	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
640	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
641	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
642	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
643	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
644	#436	C₂²×C₃₁	1	1	yes	characteristic
645	#435	C₂²×C₃₁	1	1	yes	characteristic
646	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
648	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
649	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#433	C₂²×C₃₁	1	1	yes	characteristic
651	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#427	C₂²×C₃₁	1	1	yes	characteristic
654	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#418	C₂²×C₃₁	1	2	yes	—
657	#417	C₂²×C₃₁	1	2	yes	complemented
658	#416	C₂²×C₃₁	1	2	yes	complemented
659	#405	C₂²×C₃₁	1	1	yes	characteristic
660	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
661	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₂×C₃₁	—	4	1	no	—
663	C₂×C₃₁	—	4	1	no	—
664	C₂×C₃₁	—	4	1	no	—
665	C₂×C₃₁	—	4	4	no	—
666	C₂×C₃₁	—	8	2	no	—
667	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
668	C₂×C₃₁	#3584	1	1	yes	characteristic
669	C₂×C₃₁	#3584	1	1	yes	characteristic
670	C₂×#41	C₂³×C₃₁	1	2	yes	—
671	C₂×#41	C₂³×C₃₁	1	2	yes	—
672	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
673	#135	—	2	4	no	—
674	#135	—	2	4	no	—
675	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
682	C₂×D₈	—	2	4	no	—
683	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×D₈	C₂³×C₃₁	1	2	yes	—
685	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#126	D₄×C₃₁	1	1	yes	characteristic
705	#126	D₄×C₃₁	1	1	yes	characteristic
706	#125	—	2	2	no	—
707	#125	—	2	2	no	—
708	#125	—	2	2	no	—
709	#125	D₄×C₃₁	1	1	yes	characteristic
710	#125	C₂³×C₃₁	1	2	yes	—
711	#125	C₂³×C₃₁	1	2	yes	—
712	#124	—	2	2	no	—
713	#124	—	2	2	no	—
714	#124	D₄×C₃₁	1	1	yes	characteristic
715	#124	C₂³×C₃₁	1	2	yes	—
716	#124	C₂³×C₃₁	1	2	yes	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	D₄×C₃₁	1	1	yes	characteristic
726	#123	D₄×C₃₁	1	1	yes	characteristic
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
735	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
736	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	D₄×C₃₁	1	1	yes	characteristic
742	#121	C₂³×C₃₁	1	2	yes	—
743	#121	C₂³×C₃₁	1	2	yes	—
744	#120	—	2	2	no	—
745	#120	—	2	2	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
748	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
749	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
750	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
751	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
752	C₄×D₄	—	2	2	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	C₂³×C₃₁	1	2	yes	—
761	C₄×D₄	C₂³×C₃₁	1	2	yes	—
762	C₄×D₄	C₂³×C₃₁	1	2	yes	—
763	C₄×D₄	C₂³×C₃₁	1	2	yes	—
764	C₄×D₄	C₂³×C₃₁	1	2	yes	—
765	C₄×D₄	C₂³×C₃₁	1	2	yes	—
766	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
769	#117	—	2	2	no	—
770	#117	—	2	2	no	—
771	#117	—	2	2	no	—
772	#117	—	2	2	no	—
773	#117	—	2	2	no	—
774	#117	C₂³×C₃₁	1	2	yes	—
775	#117	C₂³×C₃₁	1	2	yes	—
776	#117	C₂³×C₃₁	1	1	yes	characteristic
777	#117	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×C₄⋊C₄	—	2	2	no	—
779	C₂×C₄⋊C₄	—	2	2	no	—
780	C₂×C₄⋊C₄	—	2	2	no	—
781	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
782	C₂×C₂²⋊C₄	—	2	2	no	—
783	C₂×C₂²⋊C₄	—	2	2	no	—
784	C₂×C₂²⋊C₄	—	2	2	no	—
785	C₂×C₂²⋊C₄	—	2	2	no	—
786	C₂×C₄²	—	2	2	no	—
787	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
788	#107	C₂³×C₃₁	1	1	yes	characteristic
789	#107	C₂³×C₃₁	1	1	yes	characteristic
790	#107	C₂³×C₃₁	1	2	yes	—
791	#107	C₂³×C₃₁	1	1	yes	characteristic
792	#107	C₂³×C₃₁	1	1	yes	characteristic
793	#107	C₂³×C₃₁	1	2	yes	—
794	#106	C₂³×C₃₁	1	2	yes	—
795	#106	C₂³×C₃₁	1	2	yes	—
796	#106	C₂³×C₃₁	1	2	yes	—
797	#106	C₂³×C₃₁	1	2	yes	—
798	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
799	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
802	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
804	#103	C₂³×C₃₁	1	2	yes	—
805	#103	C₂³×C₃₁	1	2	yes	—
806	#103	C₂³×C₃₁	1	2	yes	—
807	#103	C₂³×C₃₁	1	2	yes	—
808	#103	C₂³×C₃₁	1	2	yes	—
809	#103	C₂³×C₃₁	1	2	yes	—
810	#103	C₂³×C₃₁	1	2	yes	—
811	#103	C₂³×C₃₁	1	2	yes	—
812	#102	C₂³×C₃₁	1	2	yes	—
813	#102	C₂³×C₃₁	1	2	yes	—
814	#102	C₂³×C₃₁	1	2	yes	—
815	#102	C₂³×C₃₁	1	2	yes	—
816	#102	C₂³×C₃₁	1	2	yes	—
817	#102	C₂³×C₃₁	1	2	yes	—
818	#102	C₂³×C₃₁	1	2	yes	—
819	#102	C₂³×C₃₁	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
821	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
822	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
824	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
826	#97	C₂³×C₃₁	1	1	yes	characteristic
827	#97	C₂³×C₃₁	1	1	yes	characteristic
828	#97	C₂³×C₃₁	1	1	yes	characteristic
829	#97	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	1	yes	characteristic
833	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
836	C₃₁	#61487	1	1	yes	characteristic, direct product factor, Sylow
837	C₂⁴	—	2	2	no	—
838	#41	—	2	4	no	—
839	#41	—	2	4	no	—
840	#41	—	4	2	no	—
841	#41	—	4	2	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
844	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
845	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
846	C₂×D₄	—	2	4	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	4	2	no	—
853	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
854	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
855	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
857	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	2	2	no	—
874	Q₁₆	—	4	2	no	—
875	SD₁₆	—	2	4	no	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	4	2	no	—
878	SD₁₆	—	4	2	no	—
879	D₈	—	2	4	no	—
880	D₈	—	2	2	no	—
881	D₈	#41×C₃₁	1	4	yes	—
882	M₁₆	—	4	1	no	—
883	M₁₆	—	4	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	4	1	no	—
888	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
914	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
915	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
951	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
952	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	2	no	—
960	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	4	4	no	—
969	C₂³	—	8	2	no	—
970	C₂³	—	8	2	no	—
971	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
972	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
973	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	2	no	—
977	Q₈	—	2	2	no	—
978	Q₈	—	4	1	no	—
979	Q₈	—	8	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	2	2	no	—
983	D₄	—	4	1	no	—
984	D₄	—	4	1	no	—
985	D₄	—	4	1	no	—
986	D₄	—	4	4	no	—
987	D₄	—	4	4	no	—
988	D₄	—	4	4	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	D₄	C₂×#41×C₃₁	1	4	yes	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	4	4	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	—	8	2	no	—
1015	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1026	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	C₂×#41×C₃₁	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	4	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	—	4	2	no	—
1050	C₂²	—	16	4	no	—
1051	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	2	no	—
1069	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1070	C₄	C₃₁×#585	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	4	4	no	—
1075	C₂	—	8	2	no	—
1076	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1077	C₂	C₃₁×#3584	1	1	yes	characteristic
1078	C₂	C₃₁×#3584	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×#3521	C₂	semidirect
2. C₃₁×#3393	C₂	semidirect
3. C₃₁×#3380	C₂	semidirect
4. C₃₁×#3376	C₂	semidirect
5. C₃₁×#3342	C₂	semidirect
6. C₃₁×#3339	C₂	semidirect
7. C₃₁×#3336	C₂	semidirect
8. C₃₁×#3323	C₂	semidirect
9. C₃₁×#3311	C₂	semidirect
10. C₃₁×#3307	C₂	semidirect
11. C₃₁×#3283	C₂	semidirect
12. C₃₁×#3280	C₂	semidirect
13. C₃₁×#3280	C₂	semidirect
14. C₃₁×#3177	C₂	semidirect
15. C₃₁×#3175	C₂	semidirect
16. C₃₁×#3168	C₂	semidirect
17. C₃₁×#3125	C₂	semidirect
18. C₃₁×#3123	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#2966	C₂	semidirect
21. C₃₁×#2951	C₂	semidirect
22. C₃₁×#2948	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
28. C₃₁×#556	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
31. C₃₁×#553	C₂²	semidirect
36. C₃₁×#547	C₂²	semidirect
39. C₃₁×#542	C₂²	semidirect
45. C₃₁×#529	C₂²	semidirect
47. C₃₁×#520	C₂²	semidirect
49. C₄×#41×C₃₁	C₂²	semidirect
50. C₃₁×#500	C₂²	semidirect
51. C₃₁×#499	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
55. C₃₁×#494	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#483	C₂²	semidirect
63. C₃₁×#482	C₂²	semidirect
64. C₃₁×#481	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#478	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#476	C₂²	semidirect
70. C₃₁×#475	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
75. C₃₁×#467	C₂²	semidirect
76. C₃₁×#467	C₂²	semidirect
79. C₃₁×#465	C₂²	semidirect
80. C₃₁×#464	C₂²	semidirect
81. C₃₁×#464	C₂²	semidirect
84. C₃₁×#461	C₂²	semidirect
85. C₃₁×#461	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
87. C₃₁×#452	C₂²	semidirect
92. C₃₁×#446	C₂²	semidirect
93. C₈×Q₈×C₃₁	C₂²	semidirect
96. C₃₁×#441	C₂²	semidirect
97. C₃₁×#440	C₂²	semidirect
98. C₃₁×#440	C₂²	semidirect
99. C₃₁×#440	C₂²	semidirect
100. C₄×Q₁₆×C₃₁	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×Q₁₆×C₃₁	C₂²	semidirect
103. C₄×Q₁₆×C₃₁	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₄×SD₁₆×C₃₁	C₂²	semidirect
106. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₃₁×#435	C₂²	semidirect
118. C₈×D₄×C₃₁	C₂²	semidirect
120. C₃₁×#433	C₂²	semidirect
121. C₃₁×#432	C₂²	semidirect
123. C₃₁×#427	C₂²	semidirect
124. C₂×C₃₁×#107	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
127. C₃₁×#416	C₂²	semidirect
129. C₃₁×#405	C₂²	semidirect
130. C₂×C₄×C₈×C₃₁	C₂²	semidirect
426. #61487	C₃₁	direct (N × H)
496. #3521	C₂×C₃₁	semidirect
497. #3393	C₂×C₃₁	semidirect
498. #3380	C₂×C₃₁	semidirect
499. #3376	C₂×C₃₁	semidirect
500. #3342	C₂×C₃₁	semidirect
501. #3339	C₂×C₃₁	semidirect
502. #3336	C₂×C₃₁	semidirect
503. #3323	C₂×C₃₁	semidirect
504. #3311	C₂×C₃₁	semidirect
505. #3307	C₂×C₃₁	semidirect
506. #3283	C₂×C₃₁	semidirect
507. #3280	C₂×C₃₁	semidirect
508. #3280	C₂×C₃₁	semidirect
509. #3177	C₂×C₃₁	semidirect
510. #3175	C₂×C₃₁	semidirect
511. #3168	C₂×C₃₁	semidirect
512. #3125	C₂×C₃₁	semidirect
513. #3123	C₂×C₃₁	semidirect
514. #3111	C₂×C₃₁	semidirect
515. #2966	C₂×C₃₁	semidirect
516. #2951	C₂×C₃₁	semidirect
517. #2948	C₂×C₃₁	semidirect
518. C₄×#135	C₂×C₃₁	semidirect
559. #556	C₂²×C₃₁	semidirect
560. #554	C₂²×C₃₁	semidirect
562. #553	C₂²×C₃₁	semidirect
567. #547	C₂²×C₃₁	semidirect
570. #542	C₂²×C₃₁	semidirect
576. #529	C₂²×C₃₁	semidirect
578. #520	C₂²×C₃₁	semidirect
580. C₄×#41	C₂²×C₃₁	semidirect
581. #500	C₂²×C₃₁	semidirect
582. #499	C₂²×C₃₁	semidirect
583. #499	C₂²×C₃₁	semidirect
586. #494	C₂²×C₃₁	semidirect
587. #491	C₂²×C₃₁	semidirect
588. #489	C₂²×C₃₁	semidirect
589. #488	C₂²×C₃₁	semidirect
592. #485	C₂²×C₃₁	semidirect
593. #483	C₂²×C₃₁	semidirect
594. #482	C₂²×C₃₁	semidirect
595. #481	C₂²×C₃₁	semidirect
596. #479	C₂²×C₃₁	semidirect
597. #478	C₂²×C₃₁	semidirect
598. #478	C₂²×C₃₁	semidirect
599. #478	C₂²×C₃₁	semidirect
600. #476	C₂²×C₃₁	semidirect
601. #475	C₂²×C₃₁	semidirect
603. #468	C₂²×C₃₁	semidirect
606. #467	C₂²×C₃₁	semidirect
607. #467	C₂²×C₃₁	semidirect
610. #465	C₂²×C₃₁	semidirect
611. #464	C₂²×C₃₁	semidirect
612. #464	C₂²×C₃₁	semidirect
615. #461	C₂²×C₃₁	semidirect
616. #461	C₂²×C₃₁	semidirect
617. #452	C₂²×C₃₁	semidirect
618. #452	C₂²×C₃₁	semidirect
623. #446	C₂²×C₃₁	semidirect
624. C₈×Q₈	C₂²×C₃₁	semidirect
627. #441	C₂²×C₃₁	semidirect
628. #440	C₂²×C₃₁	semidirect
629. #440	C₂²×C₃₁	semidirect
630. #440	C₂²×C₃₁	semidirect
631. C₄×Q₁₆	C₂²×C₃₁	semidirect
632. C₄×Q₁₆	C₂²×C₃₁	semidirect
633. C₄×Q₁₆	C₂²×C₃₁	semidirect
634. C₄×Q₁₆	C₂²×C₃₁	semidirect
635. C₄×SD₁₆	C₂²×C₃₁	semidirect
636. C₄×SD₁₆	C₂²×C₃₁	semidirect
637. C₄×SD₁₆	C₂²×C₃₁	semidirect
646. #435	C₂²×C₃₁	semidirect
649. C₈×D₄	C₂²×C₃₁	semidirect
651. #433	C₂²×C₃₁	semidirect
652. #432	C₂²×C₃₁	semidirect
654. #427	C₂²×C₃₁	semidirect
655. C₂×#107	C₂²×C₃₁	semidirect
657. #417	C₂²×C₃₁	semidirect
658. #416	C₂²×C₃₁	semidirect
660. #405	C₂²×C₃₁	semidirect
661. C₂×C₄×C₈	C₂²×C₃₁	semidirect
836. C₃₁	#61487	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×#3521	2
C₃₁×#3393	2
C₃₁×#3380	2
C₃₁×#3376	2
C₃₁×#3342	2
C₃₁×#3339	2
C₃₁×#3336	2
C₃₁×#3323	2
C₃₁×#3311	2
C₃₁×#3307	2
C₃₁×#3283	2
C₃₁×#3280	2
C₃₁×#3177	2
C₃₁×#3175	2
C₃₁×#3168	2
C₃₁×#3125	2
C₃₁×#3123	2
C₃₁×#3111	2
C₃₁×#2966	2
C₃₁×#2951	2
C₃₁×#2948	2
C₄×C₃₁×#135	2
#61487	31

Subgroups — C31×#61487 #21518246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61487 #21518246