Subgroups — C₃₁×#61471 #21518230

Order 7936.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3513	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3310	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3306	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3280	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3280	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3176	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×#3119	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3114	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	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#559	C₂²	1	2	yes	complemented
28	C₃₁×#554	C₂²	1	2	yes	complemented
29	C₃₁×#553	—	2	2	no	—
30	C₃₁×#553	C₂²	1	2	yes	complemented
31	C₃₁×#552	C₂²	1	2	yes	—
32	C₃₁×#551	—	2	2	no	—
33	C₃₁×#551	—	2	2	no	—
34	C₃₁×#547	C₂²	1	2	yes	complemented
35	C₃₁×#546	—	2	2	no	—
36	C₃₁×#546	C₂²	1	2	yes	complemented
37	C₃₁×#546	C₂²	1	2	yes	complemented
38	D₄²×C₃₁	C₂²	1	2	yes	—
39	C₃₁×#542	C₂²	1	2	yes	complemented
40	C₃₁×#540	C₂²	1	2	yes	complemented
41	C₃₁×#539	—	2	2	no	—
42	C₃₁×#538	—	2	2	no	—
43	C₃₁×#529	C₂²	1	1	yes	characteristic
44	C₃₁×#529	C₂²	1	2	yes	complemented
45	C₃₁×#525	—	2	2	no	—
46	C₂×C₃₁×#123	—	2	2	no	—
47	C₃₁×#520	C₂²	1	2	yes	complemented
48	C₃₁×#518	C₂²	1	2	yes	complemented
49	C₂×C₄×D₄×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, complemented
54	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#493	C₂²	1	1	yes	characteristic
56	C₃₁×#490	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	complemented
60	C₃₁×#483	C₂²	1	2	yes	complemented
61	C₃₁×#482	C₂²	1	2	yes	complemented
62	C₃₁×#481	C₂²	1	2	yes	complemented
63	C₃₁×#480	C₂²	1	2	yes	complemented
64	C₃₁×#480	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×#474	C₂²	1	2	yes	complemented
71	C₃₁×#469	C₂²	1	2	yes	complemented
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#466	C₂²	1	1	yes	characteristic
76	C₃₁×#466	C₂²	1	1	yes	characteristic
77	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#465	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#463	C₂²	1	2	yes	complemented
82	C₃₁×#463	C₂²	1	2	yes	complemented
83	C₃₁×#463	C₂²	1	2	yes	complemented
84	C₃₁×#460	C₂²	1	2	yes	complemented
85	C₃₁×#459	C₂²	1	2	yes	—
86	C₃₁×#450	C₂²	1	2	yes	complemented
87	C₃₁×#450	C₂²	1	2	yes	complemented
88	C₃₁×#449	C₂²	1	2	yes	complemented
89	C₃₁×#449	C₂²	1	2	yes	complemented
90	C₃₁×#447	C₂²	1	2	yes	—
91	C₃₁×#447	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	complemented
95	C₃₁×#442	C₂²	1	2	yes	complemented
96	C₃₁×#442	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×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
107	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
110	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
111	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
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, complemented
118	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#433	C₂²	1	1	yes	characteristic, complemented
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, complemented
123	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#418	C₂²	1	2	yes	complemented
126	C₃₁×#417	C₂²	1	2	yes	complemented
127	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
128	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
131	C₂×#41×C₃₁	—	2	2	no	—
132	C₂×#41×C₃₁	C₂³	1	2	yes	—
133	C₂²×D₄×C₃₁	—	2	2	no	—
134	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
135	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
136	C₂³×C₄×C₃₁	—	2	2	no	—
137	C₃₁×#135	—	2	4	no	—
138	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×D₈×C₃₁	—	2	4	no	—
143	C₂×D₈×C₃₁	—	2	4	no	—
144	C₂×D₈×C₃₁	C₂³	1	2	yes	—
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×D₈×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₃₁×#127	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
163	C₃₁×#126	D₄	1	1	yes	characteristic
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	D₄	1	1	yes	characteristic
166	C₃₁×#125	C₂³	1	2	yes	—
167	C₃₁×#125	C₂³	1	2	yes	—
168	C₃₁×#124	—	2	2	no	—
169	C₃₁×#124	—	2	2	no	—
170	C₃₁×#124	D₄	1	1	yes	characteristic
171	C₃₁×#124	C₂³	1	2	yes	—
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#123	—	2	2	no	—
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
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	D₄	1	1	yes	characteristic
186	C₃₁×#123	D₄	1	1	yes	characteristic
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
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	D₄	1	1	yes	characteristic
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	—	2	2	no	—
197	C₃₁×#121	—	2	2	no	—
198	C₃₁×#121	—	2	2	no	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	D₄	1	1	yes	characteristic
202	C₃₁×#121	C₂³	1	2	yes	—
203	C₃₁×#121	C₂³	1	2	yes	—
204	C₃₁×#121	C₂³	1	2	yes	—
205	C₃₁×#121	C₂³	1	2	yes	—
206	C₃₁×#120	—	2	2	no	—
207	C₃₁×#120	—	2	2	no	—
208	C₃₁×#120	—	2	2	no	—
209	C₃₁×#120	—	2	2	no	—
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	—	2	2	no	—
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	2	yes	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	—	2	2	no	—
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	C₂³	1	2	yes	—
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×C₂²⋊C₄×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	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#107	C₂³	1	1	yes	characteristic
255	C₃₁×#107	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×#102	C₂³	1	2	yes	—
270	C₃₁×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	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	C₂⁴×C₃₁	—	2	2	no	—
299	#41×C₃₁	—	2	4	no	—
300	#41×C₃₁	—	4	2	no	—
301	#41×C₃₁	—	8	4	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×D₄×C₃₁	—	2	4	no	—
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	—	2	2	no	—
313	C₂×D₄×C₃₁	—	2	2	no	—
314	C₂×D₄×C₃₁	—	2	2	no	—
315	C₂×D₄×C₃₁	—	2	2	no	—
316	C₂×D₄×C₃₁	—	4	2	no	—
317	C₂×D₄×C₃₁	—	4	2	no	—
318	C₂×D₄×C₃₁	—	8	4	no	—
319	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
320	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
321	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
323	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
324	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	2	2	no	—
332	C₂²×C₄×C₃₁	—	2	2	no	—
333	C₂²×C₄×C₃₁	—	2	2	no	—
334	C₂²×C₄×C₃₁	—	2	2	no	—
335	C₂²×C₄×C₃₁	—	2	2	no	—
336	C₂²×C₄×C₃₁	—	8	4	no	—
337	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
342	Q₁₆×C₃₁	—	2	2	no	—
343	SD₁₆×C₃₁	—	2	4	no	—
344	SD₁₆×C₃₁	—	4	2	no	—
345	SD₁₆×C₃₁	—	4	2	no	—
346	D₈×C₃₁	—	2	4	no	—
347	D₈×C₃₁	—	2	4	no	—
348	D₈×C₃₁	—	2	2	no	—
349	D₈×C₃₁	—	2	2	no	—
350	D₈×C₃₁	—	4	2	no	—
351	D₈×C₃₁	#41	1	4	yes	complemented
352	M₁₆×C₃₁	—	4	1	no	—
353	M₁₆×C₃₁	—	4	1	no	—
354	C₂×C₈×C₃₁	—	2	2	no	—
355	C₂×C₈×C₃₁	—	2	2	no	—
356	C₂×C₈×C₃₁	—	2	2	no	—
357	C₂×C₈×C₃₁	—	4	1	no	—
358	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	2	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
383	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
385	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
386	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
389	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	—	2	2	no	—
407	C₂²⋊C₄×C₃₁	—	2	2	no	—
408	C₂²⋊C₄×C₃₁	—	2	2	no	—
409	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
415	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
420	C₄²×C₃₁	—	2	2	no	—
421	C₄²×C₃₁	—	2	2	no	—
422	C₄²×C₃₁	—	2	2	no	—
423	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
425	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
429	#61471	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
430	C₂³×C₃₁	—	2	2	no	—
431	C₂³×C₃₁	—	2	2	no	—
432	C₂³×C₃₁	—	2	2	no	—
433	C₂³×C₃₁	—	4	4	no	—
434	C₂³×C₃₁	—	4	4	no	—
435	C₂³×C₃₁	—	4	4	no	—
436	C₂³×C₃₁	—	8	2	no	—
437	C₂³×C₃₁	—	8	2	no	—
438	C₂³×C₃₁	—	8	2	no	—
439	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
440	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₃₁	—	2	2	no	—
443	Q₈×C₃₁	—	2	2	no	—
444	Q₈×C₃₁	—	4	1	no	—
445	Q₈×C₃₁	—	8	2	no	—
446	D₄×C₃₁	—	2	2	no	—
447	D₄×C₃₁	—	2	2	no	—
448	D₄×C₃₁	—	2	2	no	—
449	D₄×C₃₁	—	2	2	no	—
450	D₄×C₃₁	—	2	2	no	—
451	D₄×C₃₁	—	2	2	no	—
452	D₄×C₃₁	—	2	2	no	—
453	D₄×C₃₁	—	4	1	no	—
454	D₄×C₃₁	—	4	4	no	—
455	D₄×C₃₁	—	4	4	no	—
456	D₄×C₃₁	—	4	4	no	—
457	D₄×C₃₁	—	4	4	no	—
458	D₄×C₃₁	—	8	2	no	—
459	D₄×C₃₁	—	8	2	no	—
460	D₄×C₃₁	—	8	2	no	—
461	D₄×C₃₁	—	8	2	no	—
462	D₄×C₃₁	—	8	2	no	—
463	D₄×C₃₁	C₂×#41	1	4	yes	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	1	no	—
467	C₂×C₄×C₃₁	—	2	1	no	—
468	C₂×C₄×C₃₁	—	2	1	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	2	1	no	—
471	C₂×C₄×C₃₁	—	2	2	no	—
472	C₂×C₄×C₃₁	—	2	2	no	—
473	C₂×C₄×C₃₁	—	2	2	no	—
474	C₂×C₄×C₃₁	—	2	2	no	—
475	C₂×C₄×C₃₁	—	2	2	no	—
476	C₂×C₄×C₃₁	—	4	1	no	—
477	C₂×C₄×C₃₁	—	4	4	no	—
478	C₂×C₄×C₃₁	—	4	4	no	—
479	C₂×C₄×C₃₁	—	8	2	no	—
480	C₂×C₄×C₃₁	—	8	2	no	—
481	C₂×C₄×C₃₁	—	8	2	no	—
482	C₂×C₄×C₃₁	—	8	2	no	—
483	C₂×C₄×C₃₁	—	8	2	no	—
484	C₂×C₄×C₃₁	—	8	2	no	—
485	C₂×C₄×C₃₁	—	8	2	no	—
486	C₂×C₄×C₃₁	—	8	2	no	—
487	C₂×C₄×C₃₁	—	8	2	no	—
488	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
500	C₈×C₃₁	—	2	1	no	—
501	C₈×C₃₁	—	2	1	no	—
502	C₈×C₃₁	—	2	1	no	—
503	C₈×C₃₁	—	2	1	no	—
504	C₈×C₃₁	—	2	1	no	—
505	C₈×C₃₁	—	2	1	no	—
506	C₈×C₃₁	—	2	1	no	—
507	C₈×C₃₁	C₂×#41	1	2	yes	—
508	#3513	C₂×C₃₁	1	2	yes	complemented
509	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3380	C₂×C₃₁	1	1	yes	characteristic, complemented
511	#3370	C₂×C₃₁	1	2	yes	complemented
512	#3339	C₂×C₃₁	1	1	yes	characteristic, complemented
513	#3336	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
515	#3322	C₂×C₃₁	1	2	yes	complemented
516	#3310	C₂×C₃₁	1	2	yes	complemented
517	#3306	C₂×C₃₁	1	2	yes	complemented
518	#3280	C₂×C₃₁	1	1	yes	characteristic, complemented
519	#3280	C₂×C₃₁	1	1	yes	characteristic, complemented
520	D₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
521	#3176	C₂×C₃₁	1	1	yes	characteristic, complemented
522	#3175	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3119	C₂×C₃₁	1	2	yes	complemented
525	#3118	C₂×C₃₁	1	2	yes	complemented
526	#3114	C₂×C₃₁	1	2	yes	complemented
527	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
528	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#2948	C₂×C₃₁	1	1	yes	characteristic, complemented
530	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
531	C₂²×C₃₁	—	2	1	no	—
532	C₂²×C₃₁	—	2	1	no	—
533	C₂²×C₃₁	—	2	1	no	—
534	C₂²×C₃₁	—	2	1	no	—
535	C₂²×C₃₁	—	2	1	no	—
536	C₂²×C₃₁	—	2	1	no	—
537	C₂²×C₃₁	—	2	4	no	—
538	C₂²×C₃₁	—	2	1	no	—
539	C₂²×C₃₁	—	2	1	no	—
540	C₂²×C₃₁	—	4	2	no	—
541	C₂²×C₃₁	—	4	2	no	—
542	C₂²×C₃₁	—	4	2	no	—
543	C₂²×C₃₁	—	4	2	no	—
544	C₂²×C₃₁	—	4	2	no	—
545	C₂²×C₃₁	—	4	2	no	—
546	C₂²×C₃₁	—	4	2	no	—
547	C₂²×C₃₁	—	4	2	no	—
548	C₂²×C₃₁	—	8	8	no	—
549	C₂²×C₃₁	—	16	4	no	—
550	C₂²×C₃₁	#576	1	2	yes	—
551	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
552	C₄×C₃₁	—	2	1	no	—
553	C₄×C₃₁	—	2	1	no	—
554	C₄×C₃₁	—	2	1	no	—
555	C₄×C₃₁	—	2	1	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	1	no	—
559	C₄×C₃₁	—	2	1	no	—
560	C₄×C₃₁	—	2	1	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	1	no	—
563	C₄×C₃₁	—	4	2	no	—
564	C₄×C₃₁	—	4	2	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	2	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
569	C₄×C₃₁	#585	1	1	yes	characteristic
570	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
571	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
572	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
573	#559	C₂²×C₃₁	1	2	yes	complemented
574	#554	C₂²×C₃₁	1	2	yes	complemented
575	#553	—	2	2	no	—
576	#553	C₂²×C₃₁	1	2	yes	complemented
577	#552	C₂²×C₃₁	1	2	yes	—
578	#551	—	2	2	no	—
579	#551	—	2	2	no	—
580	#547	C₂²×C₃₁	1	2	yes	complemented
581	#546	—	2	2	no	—
582	#546	C₂²×C₃₁	1	2	yes	complemented
583	#546	C₂²×C₃₁	1	2	yes	complemented
584	D₄²	C₂²×C₃₁	1	2	yes	—
585	#542	C₂²×C₃₁	1	2	yes	complemented
586	#540	C₂²×C₃₁	1	2	yes	complemented
587	#539	—	2	2	no	—
588	#538	—	2	2	no	—
589	#529	C₂²×C₃₁	1	1	yes	characteristic
590	#529	C₂²×C₃₁	1	2	yes	complemented
591	#525	—	2	2	no	—
592	C₂×#123	—	2	2	no	—
593	#520	C₂²×C₃₁	1	2	yes	complemented
594	#518	C₂²×C₃₁	1	2	yes	complemented
595	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
596	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
597	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
601	#493	C₂²×C₃₁	1	1	yes	characteristic
602	#490	C₂²×C₃₁	1	2	yes	complemented
603	#489	C₂²×C₃₁	1	2	yes	complemented
604	#488	C₂²×C₃₁	1	2	yes	complemented
605	#485	C₂²×C₃₁	1	2	yes	complemented
606	#483	C₂²×C₃₁	1	2	yes	complemented
607	#482	C₂²×C₃₁	1	2	yes	complemented
608	#481	C₂²×C₃₁	1	2	yes	complemented
609	#480	C₂²×C₃₁	1	2	yes	complemented
610	#480	C₂²×C₃₁	1	2	yes	complemented
611	#479	C₂²×C₃₁	1	2	yes	complemented
612	#478	C₂²×C₃₁	1	2	yes	complemented
613	#478	C₂²×C₃₁	1	2	yes	complemented
614	#478	C₂²×C₃₁	1	2	yes	complemented
615	#476	C₂²×C₃₁	1	2	yes	complemented
616	#474	C₂²×C₃₁	1	2	yes	complemented
617	#469	C₂²×C₃₁	1	2	yes	complemented
618	#468	C₂²×C₃₁	1	2	yes	complemented
619	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#466	C₂²×C₃₁	1	1	yes	characteristic
622	#466	C₂²×C₃₁	1	1	yes	characteristic
623	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#465	C₂²×C₃₁	1	2	yes	complemented
626	#463	C₂²×C₃₁	1	2	yes	complemented
627	#463	C₂²×C₃₁	1	2	yes	complemented
628	#463	C₂²×C₃₁	1	2	yes	complemented
629	#463	C₂²×C₃₁	1	2	yes	complemented
630	#460	C₂²×C₃₁	1	2	yes	complemented
631	#459	C₂²×C₃₁	1	2	yes	—
632	#450	C₂²×C₃₁	1	2	yes	complemented
633	#450	C₂²×C₃₁	1	2	yes	complemented
634	#449	C₂²×C₃₁	1	2	yes	complemented
635	#449	C₂²×C₃₁	1	2	yes	complemented
636	#447	C₂²×C₃₁	1	2	yes	—
637	#447	C₂²×C₃₁	1	2	yes	—
638	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
639	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#442	C₂²×C₃₁	1	2	yes	complemented
641	#442	C₂²×C₃₁	1	2	yes	complemented
642	#442	C₂²×C₃₁	1	2	yes	complemented
643	#440	C₂²×C₃₁	1	2	yes	complemented
644	#440	C₂²×C₃₁	1	2	yes	complemented
645	#440	C₂²×C₃₁	1	2	yes	complemented
646	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
649	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
650	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
651	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
652	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
653	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
656	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
657	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
658	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#435	C₂²×C₃₁	1	1	yes	characteristic
661	#435	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
663	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#433	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
668	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#418	C₂²×C₃₁	1	2	yes	complemented
672	#417	C₂²×C₃₁	1	2	yes	complemented
673	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
674	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	C₂×C₃₁	—	2	2	no	—
678	C₂×C₃₁	—	4	1	no	—
679	C₂×C₃₁	—	4	1	no	—
680	C₂×C₃₁	—	4	4	no	—
681	C₂×C₃₁	—	8	2	no	—
682	C₂×C₃₁	—	8	2	no	—
683	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
684	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
685	C₂×C₃₁	#3584	1	1	yes	characteristic
686	C₂×#41	—	2	2	no	—
687	C₂×#41	C₂³×C₃₁	1	2	yes	—
688	C₂²×D₄	—	2	2	no	—
689	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
690	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
691	C₂³×C₄	—	2	2	no	—
692	#135	—	2	4	no	—
693	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
695	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
696	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
697	C₂×D₈	—	2	4	no	—
698	C₂×D₈	—	2	4	no	—
699	C₂×D₈	C₂³×C₃₁	1	2	yes	—
700	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
701	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
702	C₂×D₈	C₂³×C₃₁	1	2	yes	—
703	C₂×D₈	C₂³×C₃₁	1	2	yes	—
704	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
705	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
706	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
708	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
709	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	#127	C₂³×C₃₁	1	2	yes	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	D₄×C₃₁	1	1	yes	characteristic
718	#126	D₄×C₃₁	1	1	yes	characteristic
719	#125	—	2	2	no	—
720	#125	D₄×C₃₁	1	1	yes	characteristic
721	#125	C₂³×C₃₁	1	2	yes	—
722	#125	C₂³×C₃₁	1	2	yes	—
723	#124	—	2	2	no	—
724	#124	—	2	2	no	—
725	#124	D₄×C₃₁	1	1	yes	characteristic
726	#124	C₂³×C₃₁	1	2	yes	—
727	#124	C₂³×C₃₁	1	2	yes	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	#123	D₄×C₃₁	1	1	yes	characteristic
741	#123	D₄×C₃₁	1	1	yes	characteristic
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
748	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
749	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
750	#121	—	2	2	no	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	—	2	2	no	—
754	#121	—	2	2	no	—
755	#121	—	2	2	no	—
756	#121	D₄×C₃₁	1	1	yes	characteristic
757	#121	C₂³×C₃₁	1	2	yes	—
758	#121	C₂³×C₃₁	1	2	yes	—
759	#121	C₂³×C₃₁	1	2	yes	—
760	#121	C₂³×C₃₁	1	2	yes	—
761	#120	—	2	2	no	—
762	#120	—	2	2	no	—
763	#120	—	2	2	no	—
764	#120	—	2	2	no	—
765	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
766	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
767	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	2	no	—
773	C₄×D₄	—	2	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	C₂³×C₃₁	1	2	yes	—
778	C₄×D₄	C₂³×C₃₁	1	2	yes	—
779	C₄×D₄	C₂³×C₃₁	1	2	yes	—
780	C₄×D₄	C₂³×C₃₁	1	2	yes	—
781	C₄×D₄	C₂³×C₃₁	1	2	yes	—
782	C₄×D₄	C₂³×C₃₁	1	2	yes	—
783	C₄×D₄	C₂³×C₃₁	1	2	yes	—
784	C₄×D₄	C₂³×C₃₁	1	2	yes	—
785	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
786	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
788	#117	—	2	2	no	—
789	#117	—	2	2	no	—
790	#117	—	2	2	no	—
791	#117	C₂³×C₃₁	1	2	yes	—
792	#117	C₂³×C₃₁	1	1	yes	characteristic
793	#117	C₂³×C₃₁	1	1	yes	characteristic
794	C₂×C₄⋊C₄	—	2	2	no	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
797	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
798	C₂×C₂²⋊C₄	—	2	2	no	—
799	C₂×C₂²⋊C₄	—	2	2	no	—
800	C₂×C₂²⋊C₄	—	2	2	no	—
801	C₂×C₂²⋊C₄	—	2	2	no	—
802	C₂×C₂²⋊C₄	—	2	2	no	—
803	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
804	#107	C₂³×C₃₁	1	1	yes	characteristic
805	#107	C₂³×C₃₁	1	1	yes	characteristic
806	#107	C₂³×C₃₁	1	1	yes	characteristic
807	#107	C₂³×C₃₁	1	2	yes	—
808	#107	C₂³×C₃₁	1	2	yes	—
809	#107	C₂³×C₃₁	1	1	yes	characteristic
810	#107	C₂³×C₃₁	1	2	yes	—
811	#106	C₂³×C₃₁	1	2	yes	—
812	#106	C₂³×C₃₁	1	2	yes	—
813	#106	C₂³×C₃₁	1	2	yes	—
814	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
820	#103	C₂³×C₃₁	1	2	yes	—
821	#103	C₂³×C₃₁	1	2	yes	—
822	#103	C₂³×C₃₁	1	2	yes	—
823	#103	C₂³×C₃₁	1	2	yes	—
824	#102	C₂³×C₃₁	1	2	yes	—
825	#102	C₂³×C₃₁	1	2	yes	—
826	#102	C₂³×C₃₁	1	2	yes	—
827	#102	C₂³×C₃₁	1	2	yes	—
828	#102	C₂³×C₃₁	1	2	yes	—
829	#102	C₂³×C₃₁	1	2	yes	—
830	#102	C₂³×C₃₁	1	2	yes	—
831	#102	C₂³×C₃₁	1	2	yes	—
832	#102	C₂³×C₃₁	1	2	yes	—
833	#102	C₂³×C₃₁	1	2	yes	—
834	#102	C₂³×C₃₁	1	2	yes	—
835	#102	C₂³×C₃₁	1	2	yes	—
836	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
837	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
838	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
842	#97	C₂³×C₃₁	1	1	yes	characteristic
843	#97	C₂³×C₃₁	1	1	yes	characteristic
844	#97	C₂³×C₃₁	1	1	yes	characteristic
845	#97	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	1	yes	characteristic
849	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₃₁	#61471	1	1	yes	characteristic, direct product factor, Sylow
853	C₂⁴	—	2	2	no	—
854	C₂⁴	—	2	2	no	—
855	#41	—	2	4	no	—
856	#41	—	4	2	no	—
857	#41	—	8	4	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
860	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
861	C₂×D₄	—	2	4	no	—
862	C₂×D₄	—	2	4	no	—
863	C₂×D₄	—	2	2	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	2	no	—
872	C₂×D₄	—	4	2	no	—
873	C₂×D₄	—	4	2	no	—
874	C₂×D₄	—	8	4	no	—
875	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
876	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
878	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
879	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
880	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	8	4	no	—
893	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
898	Q₁₆	—	2	2	no	—
899	SD₁₆	—	2	4	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	4	2	no	—
902	D₈	—	2	4	no	—
903	D₈	—	2	4	no	—
904	D₈	—	2	2	no	—
905	D₈	—	2	2	no	—
906	D₈	—	4	2	no	—
907	D₈	#41×C₃₁	1	4	yes	complemented
908	M₁₆	—	4	1	no	—
909	M₁₆	—	4	1	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	—	4	1	no	—
914	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
938	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
968	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
970	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
971	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
972	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
973	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
974	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
980	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	2	2	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	4	4	no	—
991	C₂³	—	8	2	no	—
992	C₂³	—	8	2	no	—
993	C₂³	—	8	2	no	—
994	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
995	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
996	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	4	1	no	—
1000	Q₈	—	8	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	4	1	no	—
1009	D₄	—	4	4	no	—
1010	D₄	—	4	4	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	D₄	C₂×#41×C₃₁	1	4	yes	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	4	1	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	2	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	2	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1054	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	1	no	—
1062	C₈	C₂×#41×C₃₁	1	2	yes	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	8	8	no	—
1081	C₂²	—	16	4	no	—
1082	C₂²	C₃₁×#576	1	2	yes	—
1083	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1101	C₄	C₃₁×#585	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	1	no	—
1104	C₂	—	4	1	no	—
1105	C₂	—	4	4	no	—
1106	C₂	—	8	2	no	—
1107	C₂	—	8	2	no	—
1108	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1109	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1110	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×#3513	C₂	semidirect
2. C₃₁×#3396	C₂	semidirect
3. C₃₁×#3380	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3339	C₂	semidirect
6. C₃₁×#3336	C₂	semidirect
7. C₃₁×#3334	C₂	semidirect
8. C₃₁×#3322	C₂	semidirect
9. C₃₁×#3310	C₂	semidirect
10. C₃₁×#3306	C₂	semidirect
11. C₃₁×#3280	C₂	semidirect
12. C₃₁×#3280	C₂	semidirect
13. D₄×D₈×C₃₁	C₂	semidirect
14. C₃₁×#3176	C₂	semidirect
15. C₃₁×#3175	C₂	semidirect
16. C₃₁×#3168	C₂	semidirect
17. C₃₁×#3119	C₂	semidirect
18. C₃₁×#3118	C₂	semidirect
19. C₃₁×#3114	C₂	semidirect
20. C₃₁×#2966	C₂	semidirect
21. C₃₁×#2951	C₂	semidirect
22. C₃₁×#2948	C₂	semidirect
23. C₂×C₄×D₈×C₃₁	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
30. C₃₁×#553	C₂²	semidirect
34. C₃₁×#547	C₂²	semidirect
36. C₃₁×#546	C₂²	semidirect
37. C₃₁×#546	C₂²	semidirect
39. C₃₁×#542	C₂²	semidirect
40. C₃₁×#540	C₂²	semidirect
44. C₃₁×#529	C₂²	semidirect
47. C₃₁×#520	C₂²	semidirect
48. C₃₁×#518	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₃₁×#500	C₂²	semidirect
51. C₃₁×#499	C₂²	semidirect
52. C₃₁×#499	C₂²	semidirect
53. C₃₁×#495	C₂²	semidirect
54. C₃₁×#495	C₂²	semidirect
56. C₃₁×#490	C₂²	semidirect
57. C₃₁×#489	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
59. C₃₁×#485	C₂²	semidirect
60. C₃₁×#483	C₂²	semidirect
61. C₃₁×#482	C₂²	semidirect
62. C₃₁×#481	C₂²	semidirect
63. C₃₁×#480	C₂²	semidirect
64. C₃₁×#480	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×#474	C₂²	semidirect
71. C₃₁×#469	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#467	C₂²	semidirect
74. C₃₁×#467	C₂²	semidirect
77. C₃₁×#466	C₂²	semidirect
78. C₃₁×#466	C₂²	semidirect
79. C₃₁×#465	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#463	C₂²	semidirect
82. C₃₁×#463	C₂²	semidirect
83. C₃₁×#463	C₂²	semidirect
84. C₃₁×#460	C₂²	semidirect
86. C₃₁×#450	C₂²	semidirect
87. C₃₁×#450	C₂²	semidirect
88. C₃₁×#449	C₂²	semidirect
89. C₃₁×#449	C₂²	semidirect
92. C₃₁×#446	C₂²	semidirect
93. C₈×Q₈×C₃₁	C₂²	semidirect
94. C₃₁×#442	C₂²	semidirect
95. C₃₁×#442	C₂²	semidirect
96. C₃₁×#442	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×SD₁₆×C₃₁	C₂²	semidirect
107. C₄×D₈×C₃₁	C₂²	semidirect
108. C₄×D₈×C₃₁	C₂²	semidirect
109. C₄×D₈×C₃₁	C₂²	semidirect
110. C₄×D₈×C₃₁	C₂²	semidirect
111. C₄×D₈×C₃₁	C₂²	semidirect
112. C₄×D₈×C₃₁	C₂²	semidirect
113. C₃₁×#436	C₂²	semidirect
115. C₃₁×#435	C₂²	semidirect
117. C₈×D₄×C₃₁	C₂²	semidirect
118. C₈×D₄×C₃₁	C₂²	semidirect
119. C₃₁×#433	C₂²	semidirect
120. C₃₁×#433	C₂²	semidirect
121. C₃₁×#432	C₂²	semidirect
122. C₃₁×#427	C₂²	semidirect
123. C₂×C₃₁×#107	C₂²	semidirect
124. C₂×C₃₁×#107	C₂²	semidirect
125. C₃₁×#418	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
127. C₂×C₃₁×#102	C₂²	semidirect
128. C₃₁×#405	C₂²	semidirect
129. C₃₁×#405	C₂²	semidirect
130. C₂×C₄×C₈×C₃₁	C₂²	semidirect
351. D₈×C₃₁	#41	semidirect
429. #61471	C₃₁	direct (N × H)
508. #3513	C₂×C₃₁	semidirect
509. #3396	C₂×C₃₁	semidirect
510. #3380	C₂×C₃₁	semidirect
511. #3370	C₂×C₃₁	semidirect
512. #3339	C₂×C₃₁	semidirect
513. #3336	C₂×C₃₁	semidirect
514. #3334	C₂×C₃₁	semidirect
515. #3322	C₂×C₃₁	semidirect
516. #3310	C₂×C₃₁	semidirect
517. #3306	C₂×C₃₁	semidirect
518. #3280	C₂×C₃₁	semidirect
519. #3280	C₂×C₃₁	semidirect
520. D₄×D₈	C₂×C₃₁	semidirect
521. #3176	C₂×C₃₁	semidirect
522. #3175	C₂×C₃₁	semidirect
523. #3168	C₂×C₃₁	semidirect
524. #3119	C₂×C₃₁	semidirect
525. #3118	C₂×C₃₁	semidirect
526. #3114	C₂×C₃₁	semidirect
527. #2966	C₂×C₃₁	semidirect
528. #2951	C₂×C₃₁	semidirect
529. #2948	C₂×C₃₁	semidirect
530. C₂×C₄×D₈	C₂×C₃₁	semidirect
573. #559	C₂²×C₃₁	semidirect
574. #554	C₂²×C₃₁	semidirect
576. #553	C₂²×C₃₁	semidirect
580. #547	C₂²×C₃₁	semidirect
582. #546	C₂²×C₃₁	semidirect
583. #546	C₂²×C₃₁	semidirect
585. #542	C₂²×C₃₁	semidirect
586. #540	C₂²×C₃₁	semidirect
590. #529	C₂²×C₃₁	semidirect
593. #520	C₂²×C₃₁	semidirect
594. #518	C₂²×C₃₁	semidirect
595. C₂×C₄×D₄	C₂²×C₃₁	semidirect
596. #500	C₂²×C₃₁	semidirect
597. #499	C₂²×C₃₁	semidirect
598. #499	C₂²×C₃₁	semidirect
599. #495	C₂²×C₃₁	semidirect
600. #495	C₂²×C₃₁	semidirect
602. #490	C₂²×C₃₁	semidirect
603. #489	C₂²×C₃₁	semidirect
604. #488	C₂²×C₃₁	semidirect
605. #485	C₂²×C₃₁	semidirect
606. #483	C₂²×C₃₁	semidirect
607. #482	C₂²×C₃₁	semidirect
608. #481	C₂²×C₃₁	semidirect
609. #480	C₂²×C₃₁	semidirect
610. #480	C₂²×C₃₁	semidirect
611. #479	C₂²×C₃₁	semidirect
612. #478	C₂²×C₃₁	semidirect
613. #478	C₂²×C₃₁	semidirect
614. #478	C₂²×C₃₁	semidirect
615. #476	C₂²×C₃₁	semidirect
616. #474	C₂²×C₃₁	semidirect
617. #469	C₂²×C₃₁	semidirect
618. #468	C₂²×C₃₁	semidirect
619. #467	C₂²×C₃₁	semidirect
620. #467	C₂²×C₃₁	semidirect
623. #466	C₂²×C₃₁	semidirect
624. #466	C₂²×C₃₁	semidirect
625. #465	C₂²×C₃₁	semidirect
626. #463	C₂²×C₃₁	semidirect
627. #463	C₂²×C₃₁	semidirect
628. #463	C₂²×C₃₁	semidirect
629. #463	C₂²×C₃₁	semidirect
630. #460	C₂²×C₃₁	semidirect
632. #450	C₂²×C₃₁	semidirect
633. #450	C₂²×C₃₁	semidirect
634. #449	C₂²×C₃₁	semidirect
635. #449	C₂²×C₃₁	semidirect
638. #446	C₂²×C₃₁	semidirect
639. C₈×Q₈	C₂²×C₃₁	semidirect
640. #442	C₂²×C₃₁	semidirect
641. #442	C₂²×C₃₁	semidirect
642. #442	C₂²×C₃₁	semidirect
643. #440	C₂²×C₃₁	semidirect
644. #440	C₂²×C₃₁	semidirect
645. #440	C₂²×C₃₁	semidirect
646. C₄×Q₁₆	C₂²×C₃₁	semidirect
647. C₄×Q₁₆	C₂²×C₃₁	semidirect
648. C₄×SD₁₆	C₂²×C₃₁	semidirect
653. C₄×D₈	C₂²×C₃₁	semidirect
654. C₄×D₈	C₂²×C₃₁	semidirect
655. C₄×D₈	C₂²×C₃₁	semidirect
656. C₄×D₈	C₂²×C₃₁	semidirect
657. C₄×D₈	C₂²×C₃₁	semidirect
658. C₄×D₈	C₂²×C₃₁	semidirect
659. #436	C₂²×C₃₁	semidirect
661. #435	C₂²×C₃₁	semidirect
663. C₈×D₄	C₂²×C₃₁	semidirect
664. C₈×D₄	C₂²×C₃₁	semidirect
665. #433	C₂²×C₃₁	semidirect
666. #433	C₂²×C₃₁	semidirect
667. #432	C₂²×C₃₁	semidirect
668. #427	C₂²×C₃₁	semidirect
669. C₂×#107	C₂²×C₃₁	semidirect
670. C₂×#107	C₂²×C₃₁	semidirect
671. #418	C₂²×C₃₁	semidirect
672. #417	C₂²×C₃₁	semidirect
673. C₂×#102	C₂²×C₃₁	semidirect
674. #405	C₂²×C₃₁	semidirect
675. #405	C₂²×C₃₁	semidirect
676. C₂×C₄×C₈	C₂²×C₃₁	semidirect
852. C₃₁	#61471	direct (N × H)
907. D₈	#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×#3513	2
C₃₁×#3396	2
C₃₁×#3380	2
C₃₁×#3370	2
C₃₁×#3339	2
C₃₁×#3336	2
C₃₁×#3334	2
C₃₁×#3322	2
C₃₁×#3310	2
C₃₁×#3306	2
C₃₁×#3280	2
D₄×D₈×C₃₁	2
C₃₁×#3176	2
C₃₁×#3175	2
C₃₁×#3168	2
C₃₁×#3119	2
C₃₁×#3118	2
C₃₁×#3114	2
C₃₁×#2966	2
C₃₁×#2951	2
C₃₁×#2948	2
C₂×C₄×D₈×C₃₁	2
#61471	31

Subgroups — C31×#61471 #21518230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61471 #21518230