Subgroups — C₃₁×#61488 #21518247

Order 7936.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3524	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3371	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3341	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×#3326	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3285	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×#3126	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3125	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×#2950	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×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#559	—	2	2	no	—
28	C₃₁×#559	C₂²	1	2	yes	—
29	C₃₁×#557	C₂²	1	2	yes	—
30	C₃₁×#555	—	2	2	no	—
31	C₃₁×#555	C₂²	1	2	yes	—
32	C₃₁×#553	—	2	2	no	—
33	C₃₁×#553	C₂²	1	2	yes	—
34	C₃₁×#552	—	2	2	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#550	C₂²	1	2	yes	—
37	C₃₁×#548	C₂²	1	2	yes	—
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#542	—	2	2	no	—
40	C₃₁×#542	C₂²	1	2	yes	—
41	C₃₁×#540	—	2	2	no	—
42	C₃₁×#540	C₂²	1	2	yes	—
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#529	—	2	2	no	—
45	C₃₁×#529	C₂²	1	2	yes	—
46	C₃₁×#529	C₂²	1	1	yes	characteristic
47	C₃₁×#520	C₂²	1	2	yes	—
48	C₃₁×#519	C₂²	1	2	yes	—
49	C₄×#41×C₃₁	C₂²	1	2	yes	—
50	C₃₁×#500	C₂²	1	1	yes	characteristic
51	C₃₁×#499	C₂²	1	1	yes	characteristic
52	C₃₁×#499	C₂²	1	1	yes	characteristic
53	C₃₁×#495	C₂²	1	1	yes	characteristic
54	C₃₁×#495	C₂²	1	1	yes	characteristic
55	C₃₁×#493	C₂²	1	1	yes	characteristic
56	C₃₁×#490	C₂²	1	2	yes	—
57	C₃₁×#489	C₂²	1	2	yes	—
58	C₃₁×#488	C₂²	1	2	yes	—
59	C₃₁×#485	C₂²	1	2	yes	—
60	C₃₁×#483	C₂²	1	2	yes	—
61	C₃₁×#482	C₂²	1	2	yes	—
62	C₃₁×#482	C₂²	1	2	yes	—
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#481	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	2	yes	—
67	C₃₁×#479	C₂²	1	2	yes	—
68	C₃₁×#478	C₂²	1	2	yes	—
69	C₃₁×#476	C₂²	1	2	yes	—
70	C₃₁×#475	C₂²	1	2	yes	—
71	C₃₁×#469	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	2	yes	—
73	C₃₁×#467	C₂²	1	1	yes	characteristic
74	C₃₁×#467	C₂²	1	1	yes	characteristic
75	C₃₁×#466	C₂²	1	1	yes	characteristic
76	C₃₁×#466	C₂²	1	1	yes	characteristic
77	C₃₁×#466	C₂²	1	1	yes	characteristic
78	C₃₁×#466	C₂²	1	1	yes	characteristic
79	C₃₁×#465	C₂²	1	2	yes	—
80	C₃₁×#464	C₂²	1	2	yes	—
81	C₃₁×#464	C₂²	1	2	yes	—
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#460	C₂²	1	2	yes	—
85	C₃₁×#460	C₂²	1	2	yes	—
86	C₃₁×#452	C₂²	1	2	yes	—
87	C₃₁×#452	C₂²	1	2	yes	—
88	C₃₁×#449	C₂²	1	2	yes	—
89	C₃₁×#449	C₂²	1	2	yes	—
90	C₃₁×#448	C₂²	1	2	yes	—
91	C₃₁×#448	C₂²	1	2	yes	—
92	C₃₁×#446	C₂²	1	1	yes	characteristic
93	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
94	C₃₁×#442	C₂²	1	2	yes	—
95	C₃₁×#441	C₂²	1	2	yes	—
96	C₃₁×#441	C₂²	1	2	yes	—
97	C₃₁×#440	C₂²	1	2	yes	—
98	C₃₁×#440	C₂²	1	2	yes	—
99	C₃₁×#440	C₂²	1	2	yes	—
100	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
101	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
102	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
103	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
104	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
105	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
106	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
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
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
119	C₃₁×#433	C₂²	1	1	yes	characteristic
120	C₃₁×#433	C₂²	1	1	yes	characteristic
121	C₃₁×#432	C₂²	1	1	yes	characteristic
122	C₃₁×#427	C₂²	1	1	yes	characteristic
123	C₃₁×#427	C₂²	1	1	yes	characteristic
124	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
125	C₃₁×#419	C₂²	1	2	yes	—
126	C₃₁×#417	C₂²	1	2	yes	—
127	C₃₁×#416	C₂²	1	2	yes	—
128	C₃₁×#405	C₂²	1	1	yes	characteristic
129	C₃₁×#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
131	C₂×#41×C₃₁	C₂³	1	2	yes	—
132	C₂×#41×C₃₁	C₂³	1	2	yes	—
133	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₃₁×#135	—	2	4	no	—
135	C₃₁×#135	—	2	4	no	—
136	C₂×Q₁₆×C₃₁	—	2	4	no	—
137	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₃₁	C₂³	1	2	yes	—
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	—	2	2	no	—
154	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₃₁×#127	—	2	2	no	—
156	C₃₁×#127	C₂³	1	2	yes	—
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	D₄	1	1	yes	characteristic
162	C₃₁×#126	D₄	1	1	yes	characteristic
163	C₃₁×#125	—	2	2	no	—
164	C₃₁×#125	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	D₄	1	1	yes	characteristic
167	C₃₁×#125	C₂³	1	2	yes	—
168	C₃₁×#125	C₂³	1	2	yes	—
169	C₃₁×#124	—	2	2	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	—	2	2	no	—
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	D₄	1	1	yes	characteristic
192	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×#121	—	2	2	no	—
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	—	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×#121	C₂³	1	2	yes	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	—	2	2	no	—
208	C₄×Q₈×C₃₁	—	2	2	no	—
209	C₄×Q₈×C₃₁	—	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	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
215	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
216	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
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	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	—	2	2	no	—
236	C₃₁×#117	—	2	2	no	—
237	C₃₁×#117	—	2	2	no	—
238	C₃₁×#117	—	2	2	no	—
239	C₃₁×#117	—	2	2	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₃₁×#117	C₂³	1	2	yes	—
243	C₃₁×#117	C₂³	1	1	yes	characteristic
244	C₃₁×#117	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
246	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
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	#41×C₃₁	—	2	4	no	—
298	#41×C₃₁	—	2	4	no	—
299	#41×C₃₁	—	4	2	no	—
300	#41×C₃₁	—	4	2	no	—
301	C₂×Q₈×C₃₁	—	2	2	no	—
302	C₂×Q₈×C₃₁	—	2	2	no	—
303	C₂×Q₈×C₃₁	—	2	4	no	—
304	C₂×Q₈×C₃₁	—	4	2	no	—
305	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
306	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
307	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
320	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
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	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
334	Q₁₆×C₃₁	—	2	4	no	—
335	Q₁₆×C₃₁	—	2	2	no	—
336	Q₁₆×C₃₁	#41	1	4	yes	—
337	SD₁₆×C₃₁	—	2	4	no	—
338	SD₁₆×C₃₁	—	2	4	no	—
339	SD₁₆×C₃₁	—	4	2	no	—
340	SD₁₆×C₃₁	—	4	2	no	—
341	D₈×C₃₁	—	2	2	no	—
342	D₈×C₃₁	—	2	2	no	—
343	D₈×C₃₁	—	4	2	no	—
344	M₁₆×C₃₁	—	4	1	no	—
345	M₁₆×C₃₁	—	4	1	no	—
346	C₂×C₈×C₃₁	—	2	2	no	—
347	C₂×C₈×C₃₁	—	2	2	no	—
348	C₂×C₈×C₃₁	—	2	2	no	—
349	C₂×C₈×C₃₁	—	4	1	no	—
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	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₃₁	—	2	2	no	—
413	C₄²×C₃₁	—	2	2	no	—
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	#61488	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	C₂²×D₄	1	1	yes	characteristic
430	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
431	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
432	Q₈×C₃₁	—	2	2	no	—
433	Q₈×C₃₁	—	2	2	no	—
434	Q₈×C₃₁	—	2	2	no	—
435	Q₈×C₃₁	—	4	1	no	—
436	Q₈×C₃₁	—	4	4	no	—
437	Q₈×C₃₁	—	8	2	no	—
438	Q₈×C₃₁	C₂×#41	1	4	yes	—
439	D₄×C₃₁	—	2	2	no	—
440	D₄×C₃₁	—	2	2	no	—
441	D₄×C₃₁	—	2	2	no	—
442	D₄×C₃₁	—	2	2	no	—
443	D₄×C₃₁	—	4	1	no	—
444	D₄×C₃₁	—	4	1	no	—
445	D₄×C₃₁	—	4	1	no	—
446	D₄×C₃₁	—	4	4	no	—
447	D₄×C₃₁	—	4	4	no	—
448	D₄×C₃₁	—	8	2	no	—
449	D₄×C₃₁	—	8	2	no	—
450	D₄×C₃₁	—	8	2	no	—
451	D₄×C₃₁	—	8	2	no	—
452	D₄×C₃₁	—	8	2	no	—
453	D₄×C₃₁	—	8	2	no	—
454	C₂×C₄×C₃₁	—	2	2	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	1	no	—
460	C₂×C₄×C₃₁	—	2	1	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	—	2	2	no	—
466	C₂×C₄×C₃₁	—	4	1	no	—
467	C₂×C₄×C₃₁	—	4	1	no	—
468	C₂×C₄×C₃₁	—	4	4	no	—
469	C₂×C₄×C₃₁	—	4	4	no	—
470	C₂×C₄×C₃₁	—	4	4	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	#3524	C₂×C₃₁	1	2	yes	complemented
497	#3396	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3383	C₂×C₃₁	1	1	yes	characteristic, complemented
499	#3371	C₂×C₃₁	1	2	yes	complemented
500	#3341	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	#3326	C₂×C₃₁	1	2	yes	complemented
504	#3321	C₂×C₃₁	1	2	yes	complemented
505	#3317	C₂×C₃₁	1	2	yes	complemented
506	#3287	C₂×C₃₁	1	1	yes	characteristic, complemented
507	#3285	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3285	C₂×C₃₁	1	1	yes	characteristic, complemented
509	#3176	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	#3126	C₂×C₃₁	1	2	yes	complemented
513	#3125	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	#2950	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	—	4	2	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	C₂³×D₄	1	1	yes	characteristic
535	C₄×C₃₁	—	2	1	no	—
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	4	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	C₂²×#41	1	1	yes	characteristic
553	C₄×C₃₁	#585	1	1	yes	characteristic
554	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
555	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
556	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
557	#559	—	2	2	no	—
558	#559	C₂²×C₃₁	1	2	yes	—
559	#557	C₂²×C₃₁	1	2	yes	—
560	#555	—	2	2	no	—
561	#555	C₂²×C₃₁	1	2	yes	—
562	#553	—	2	2	no	—
563	#553	C₂²×C₃₁	1	2	yes	—
564	#552	—	2	2	no	—
565	#552	C₂²×C₃₁	1	2	yes	—
566	#550	C₂²×C₃₁	1	2	yes	—
567	#548	C₂²×C₃₁	1	2	yes	—
568	#548	C₂²×C₃₁	1	2	yes	—
569	#542	—	2	2	no	—
570	#542	C₂²×C₃₁	1	2	yes	—
571	#540	—	2	2	no	—
572	#540	C₂²×C₃₁	1	2	yes	—
573	#529	—	2	2	no	—
574	#529	—	2	2	no	—
575	#529	C₂²×C₃₁	1	2	yes	—
576	#529	C₂²×C₃₁	1	1	yes	characteristic
577	#520	C₂²×C₃₁	1	2	yes	—
578	#519	C₂²×C₃₁	1	2	yes	—
579	C₄×#41	C₂²×C₃₁	1	2	yes	—
580	#500	C₂²×C₃₁	1	1	yes	characteristic
581	#499	C₂²×C₃₁	1	1	yes	characteristic
582	#499	C₂²×C₃₁	1	1	yes	characteristic
583	#495	C₂²×C₃₁	1	1	yes	characteristic
584	#495	C₂²×C₃₁	1	1	yes	characteristic
585	#493	C₂²×C₃₁	1	1	yes	characteristic
586	#490	C₂²×C₃₁	1	2	yes	—
587	#489	C₂²×C₃₁	1	2	yes	—
588	#488	C₂²×C₃₁	1	2	yes	—
589	#485	C₂²×C₃₁	1	2	yes	—
590	#483	C₂²×C₃₁	1	2	yes	—
591	#482	C₂²×C₃₁	1	2	yes	—
592	#482	C₂²×C₃₁	1	2	yes	—
593	#482	C₂²×C₃₁	1	2	yes	—
594	#481	C₂²×C₃₁	1	2	yes	—
595	#479	C₂²×C₃₁	1	2	yes	—
596	#479	C₂²×C₃₁	1	2	yes	—
597	#479	C₂²×C₃₁	1	2	yes	—
598	#478	C₂²×C₃₁	1	2	yes	—
599	#476	C₂²×C₃₁	1	2	yes	—
600	#475	C₂²×C₃₁	1	2	yes	—
601	#469	C₂²×C₃₁	1	2	yes	—
602	#468	C₂²×C₃₁	1	2	yes	—
603	#467	C₂²×C₃₁	1	1	yes	characteristic
604	#467	C₂²×C₃₁	1	1	yes	characteristic
605	#466	C₂²×C₃₁	1	1	yes	characteristic
606	#466	C₂²×C₃₁	1	1	yes	characteristic
607	#466	C₂²×C₃₁	1	1	yes	characteristic
608	#466	C₂²×C₃₁	1	1	yes	characteristic
609	#465	C₂²×C₃₁	1	2	yes	—
610	#464	C₂²×C₃₁	1	2	yes	—
611	#464	C₂²×C₃₁	1	2	yes	—
612	#463	C₂²×C₃₁	1	2	yes	—
613	#463	C₂²×C₃₁	1	2	yes	—
614	#460	C₂²×C₃₁	1	2	yes	—
615	#460	C₂²×C₃₁	1	2	yes	—
616	#452	C₂²×C₃₁	1	2	yes	—
617	#452	C₂²×C₃₁	1	2	yes	—
618	#449	C₂²×C₃₁	1	2	yes	—
619	#449	C₂²×C₃₁	1	2	yes	—
620	#448	C₂²×C₃₁	1	2	yes	—
621	#448	C₂²×C₃₁	1	2	yes	—
622	#446	C₂²×C₃₁	1	1	yes	characteristic
623	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
624	#442	C₂²×C₃₁	1	2	yes	—
625	#441	C₂²×C₃₁	1	2	yes	—
626	#441	C₂²×C₃₁	1	2	yes	—
627	#440	C₂²×C₃₁	1	2	yes	—
628	#440	C₂²×C₃₁	1	2	yes	—
629	#440	C₂²×C₃₁	1	2	yes	—
630	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
631	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
632	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
633	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
634	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
635	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
636	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
637	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
638	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
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	#436	C₂²×C₃₁	1	1	yes	characteristic
644	#435	C₂²×C₃₁	1	1	yes	characteristic
645	#435	C₂²×C₃₁	1	1	yes	characteristic
646	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
647	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
648	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
649	#433	C₂²×C₃₁	1	1	yes	characteristic
650	#433	C₂²×C₃₁	1	1	yes	characteristic
651	#432	C₂²×C₃₁	1	1	yes	characteristic
652	#427	C₂²×C₃₁	1	1	yes	characteristic
653	#427	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
655	#419	C₂²×C₃₁	1	2	yes	—
656	#417	C₂²×C₃₁	1	2	yes	—
657	#416	C₂²×C₃₁	1	2	yes	—
658	#405	C₂²×C₃₁	1	1	yes	characteristic
659	#405	C₂²×C₃₁	1	1	yes	characteristic
660	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
661	C₂×C₃₁	—	4	1	no	—
662	C₂×C₃₁	—	4	1	no	—
663	C₂×C₃₁	—	4	1	no	—
664	C₂×C₃₁	—	8	2	no	—
665	C₂×C₃₁	—	8	2	no	—
666	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
667	C₂×C₃₁	#3584	1	1	yes	characteristic
668	C₂×C₃₁	#3584	1	1	yes	characteristic
669	C₂×#41	C₂³×C₃₁	1	2	yes	—
670	C₂×#41	C₂³×C₃₁	1	2	yes	—
671	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
672	#135	—	2	4	no	—
673	#135	—	2	4	no	—
674	C₂×Q₁₆	—	2	4	no	—
675	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
676	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
677	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
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	C₂³×C₃₁	1	1	yes	characteristic
683	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×D₈	C₂³×C₃₁	1	2	yes	—
685	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
687	C₂²×C₈	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	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	#127	—	2	2	no	—
694	#127	C₂³×C₃₁	1	2	yes	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	D₄×C₃₁	1	1	yes	characteristic
700	#126	D₄×C₃₁	1	1	yes	characteristic
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	D₄×C₃₁	1	1	yes	characteristic
705	#125	C₂³×C₃₁	1	2	yes	—
706	#125	C₂³×C₃₁	1	2	yes	—
707	#124	—	2	2	no	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	—	2	2	no	—
711	#124	—	2	2	no	—
712	#124	—	2	2	no	—
713	#124	D₄×C₃₁	1	1	yes	characteristic
714	#124	C₂³×C₃₁	1	2	yes	—
715	#124	C₂³×C₃₁	1	2	yes	—
716	#123	—	2	2	no	—
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	D₄×C₃₁	1	1	yes	characteristic
725	#123	D₄×C₃₁	1	1	yes	characteristic
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
730	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	D₄×C₃₁	1	1	yes	characteristic
741	#121	C₂³×C₃₁	1	2	yes	—
742	#121	C₂³×C₃₁	1	2	yes	—
743	#121	C₂³×C₃₁	1	2	yes	—
744	#121	C₂³×C₃₁	1	2	yes	—
745	C₄×Q₈	—	2	2	no	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
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	2	yes	—
752	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
753	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
754	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	C₂³×C₃₁	1	2	yes	—
766	C₄×D₄	C₂³×C₃₁	1	2	yes	—
767	C₄×D₄	C₂³×C₃₁	1	2	yes	—
768	C₄×D₄	C₂³×C₃₁	1	2	yes	—
769	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
772	#117	—	2	2	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	—	2	2	no	—
776	#117	—	2	2	no	—
777	#117	—	2	2	no	—
778	#117	—	2	2	no	—
779	#117	C₂³×C₃₁	1	2	yes	—
780	#117	C₂³×C₃₁	1	2	yes	—
781	#117	C₂³×C₃₁	1	1	yes	characteristic
782	#117	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
785	C₂×C₄²	—	2	2	no	—
786	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
787	#107	C₂³×C₃₁	1	1	yes	characteristic
788	#107	C₂³×C₃₁	1	1	yes	characteristic
789	#107	C₂³×C₃₁	1	2	yes	—
790	#107	C₂³×C₃₁	1	1	yes	characteristic
791	#107	C₂³×C₃₁	1	1	yes	characteristic
792	#107	C₂³×C₃₁	1	2	yes	—
793	#106	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	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	#103	C₂³×C₃₁	1	2	yes	—
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	#102	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	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	#97	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	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
830	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
831	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
834	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
835	C₃₁	#61488	1	1	yes	characteristic, direct product factor, Sylow
836	#41	—	2	4	no	—
837	#41	—	2	4	no	—
838	#41	—	4	2	no	—
839	#41	—	4	2	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	2	2	no	—
842	C₂×Q₈	—	2	4	no	—
843	C₂×Q₈	—	4	2	no	—
844	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
845	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
846	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
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	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
857	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
858	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
859	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
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	—	2	2	no	—
868	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
869	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
873	Q₁₆	—	2	4	no	—
874	Q₁₆	—	2	2	no	—
875	Q₁₆	#41×C₃₁	1	4	yes	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	2	4	no	—
878	SD₁₆	—	4	2	no	—
879	SD₁₆	—	4	2	no	—
880	D₈	—	2	2	no	—
881	D₈	—	2	2	no	—
882	D₈	—	4	2	no	—
883	M₁₆	—	4	1	no	—
884	M₁₆	—	4	1	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	2	2	no	—
888	C₂×C₈	—	4	1	no	—
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	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
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	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁴×C₃₁	1	2	yes	—
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	C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
942	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
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	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₄²	C₂⁴×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	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
968	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
969	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	4	1	no	—
974	Q₈	—	4	4	no	—
975	Q₈	—	8	2	no	—
976	Q₈	C₂×#41×C₃₁	1	4	yes	—
977	D₄	—	2	2	no	—
978	D₄	—	2	2	no	—
979	D₄	—	2	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	1	no	—
983	D₄	—	4	1	no	—
984	D₄	—	4	4	no	—
985	D₄	—	4	4	no	—
986	D₄	—	8	2	no	—
987	D₄	—	8	2	no	—
988	D₄	—	8	2	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	2	no	—
992	C₂×C₄	—	2	2	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	1	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	—	4	4	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	C₂²×D₄×C₃₁	1	1	yes	characteristic
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	C₂⁵×C₃₁	1	1	yes	characteristic
1026	C₈	—	2	1	no	—
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	C₂×#41×C₃₁	1	2	yes	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	4	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	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1068	C₄	C₃₁×#585	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	8	2	no	—
1074	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1075	C₂	C₃₁×#3584	1	1	yes	characteristic
1076	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×#3524	C₂	semidirect
2. C₃₁×#3396	C₂	semidirect
3. C₃₁×#3383	C₂	semidirect
4. C₃₁×#3371	C₂	semidirect
5. C₃₁×#3341	C₂	semidirect
6. C₃₁×#3339	C₂	semidirect
7. C₃₁×#3336	C₂	semidirect
8. C₃₁×#3326	C₂	semidirect
9. C₃₁×#3321	C₂	semidirect
10. C₃₁×#3317	C₂	semidirect
11. C₃₁×#3287	C₂	semidirect
12. C₃₁×#3285	C₂	semidirect
13. C₃₁×#3285	C₂	semidirect
14. C₃₁×#3176	C₂	semidirect
15. C₃₁×#3175	C₂	semidirect
16. C₃₁×#3168	C₂	semidirect
17. C₃₁×#3126	C₂	semidirect
18. C₃₁×#3125	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#2966	C₂	semidirect
21. C₃₁×#2951	C₂	semidirect
22. C₃₁×#2950	C₂	semidirect
23. C₄×C₃₁×#135	C₂	semidirect
426. #61488	C₃₁	direct (N × H)
496. #3524	C₂×C₃₁	semidirect
497. #3396	C₂×C₃₁	semidirect
498. #3383	C₂×C₃₁	semidirect
499. #3371	C₂×C₃₁	semidirect
500. #3341	C₂×C₃₁	semidirect
501. #3339	C₂×C₃₁	semidirect
502. #3336	C₂×C₃₁	semidirect
503. #3326	C₂×C₃₁	semidirect
504. #3321	C₂×C₃₁	semidirect
505. #3317	C₂×C₃₁	semidirect
506. #3287	C₂×C₃₁	semidirect
507. #3285	C₂×C₃₁	semidirect
508. #3285	C₂×C₃₁	semidirect
509. #3176	C₂×C₃₁	semidirect
510. #3175	C₂×C₃₁	semidirect
511. #3168	C₂×C₃₁	semidirect
512. #3126	C₂×C₃₁	semidirect
513. #3125	C₂×C₃₁	semidirect
514. #3111	C₂×C₃₁	semidirect
515. #2966	C₂×C₃₁	semidirect
516. #2951	C₂×C₃₁	semidirect
517. #2950	C₂×C₃₁	semidirect
518. C₄×#135	C₂×C₃₁	semidirect
835. C₃₁	#61488	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×#3524	2
C₃₁×#3396	2
C₃₁×#3383	2
C₃₁×#3371	2
C₃₁×#3341	2
C₃₁×#3339	2
C₃₁×#3336	2
C₃₁×#3326	2
C₃₁×#3321	2
C₃₁×#3317	2
C₃₁×#3287	2
C₃₁×#3285	2
C₃₁×#3176	2
C₃₁×#3175	2
C₃₁×#3168	2
C₃₁×#3126	2
C₃₁×#3125	2
C₃₁×#3111	2
C₃₁×#2966	2
C₃₁×#2951	2
C₃₁×#2950	2
C₄×C₃₁×#135	2
#61488	31

Subgroups — C31×#61488 #21518247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61488 #21518247