Subgroups — C₃₁×#61956 #21518715

Order 7936.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3211	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3108	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₃₁×#464	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
25	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic
28	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#555	—	2	1	no	—
33	C₃₁×#552	—	2	2	no	—
34	C₃₁×#552	C₂²	1	2	yes	complemented
35	C₃₁×#551	—	2	2	no	—
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#548	C₂²	1	2	yes	complemented
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#546	—	2	1	no	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	D₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#538	—	2	2	no	—
47	C₃₁×#533	—	2	1	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	2	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	2	yes	—
53	C₃₁×#529	C₂²	1	2	yes	complemented
54	C₂×C₃₁×#124	C₂²	1	2	yes	—
55	C₃₁×#518	—	2	1	no	—
56	C₄×#41×C₃₁	—	2	1	no	—
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
60	C₃₁×#495	C₂²	1	2	yes	—
61	C₃₁×#495	C₂²	1	2	yes	complemented
62	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#488	C₂²	1	2	yes	complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#486	C₂²	1	1	yes	characteristic
68	C₃₁×#485	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	1	yes	characteristic
71	C₃₁×#480	C₂²	1	2	yes	—
72	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#474	C₂²	1	1	yes	characteristic
79	C₃₁×#467	C₂²	1	2	yes	complemented
80	C₃₁×#467	C₂²	1	2	yes	complemented
81	C₃₁×#466	C₂²	1	2	yes	—
82	C₃₁×#465	C₂²	1	2	yes	—
83	C₃₁×#465	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	1	yes	characteristic
86	C₃₁×#464	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#464	C₂²	1	2	yes	complemented
92	C₃₁×#464	C₂²	1	2	yes	complemented
93	C₃₁×#464	C₂²	1	2	yes	complemented
94	C₃₁×#464	C₂²	1	2	yes	complemented
95	C₃₁×#463	C₂²	1	1	yes	characteristic
96	C₃₁×#463	C₂²	1	2	yes	complemented
97	C₃₁×#463	C₂²	1	2	yes	complemented
98	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic
101	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#460	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#452	C₂²	1	2	yes	complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#451	C₂²	1	2	yes	complemented
108	C₃₁×#451	C₂²	1	2	yes	complemented
109	C₃₁×#450	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	1	yes	characteristic
111	C₃₁×#448	C₂²	1	2	yes	—
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#447	C₂²	1	2	yes	—
114	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
122	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
123	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
126	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
127	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
128	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#431	C₂²	1	2	yes	complemented
130	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₃₁×#416	C₂²	1	2	yes	complemented
133	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
143	C₃₁×#135	—	4	4	no	—
144	C₂×Q₁₆×C₃₁	—	4	4	no	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	—	4	4	no	—
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	—	2	1	no	—
164	C₃₁×C₄⋊Q₈	—	2	1	no	—
165	C₃₁×C₄⋊Q₈	—	2	1	no	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	C₂³	1	1	yes	characteristic
180	C₃₁×#125	C₂³	1	2	yes	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	2	no	—
185	C₃₁×#124	—	2	2	no	—
186	C₃₁×#124	C₂³	1	1	yes	characteristic
187	C₃₁×#124	C₂³	1	2	yes	—
188	C₃₁×#124	C₂³	1	2	yes	—
189	C₃₁×#124	C₂³	1	2	yes	—
190	C₃₁×#124	C₂³	1	2	yes	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×#123	—	2	2	no	—
197	C₃₁×#123	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	1	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	no	—
205	C₃₁×C₂²⋊Q₈	—	2	2	no	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	1	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	1	yes	characteristic
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	2	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
233	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	2	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
247	C₄×D₄×C₃₁	D₄	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	—	2	2	no	—
262	C₃₁×#117	D₄	1	2	yes	—
263	C₃₁×#117	D₄	1	1	yes	characteristic
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₄²×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	—	2	1	no	—
272	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#103	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₄×C₈×C₃₁	C₂³	1	2	yes	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	2	2	no	—
318	#41×C₃₁	—	4	1	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	4	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	4	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	—	4	2	no	—
328	C₂×Q₈×C₃₁	—	4	2	no	—
329	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	1	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	4	2	no	—
343	C₂×D₄×C₃₁	—	4	2	no	—
344	C₂×D₄×C₃₁	—	4	4	no	—
345	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
346	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	2	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	Q₁₆×C₃₁	—	2	2	no	—
366	Q₁₆×C₃₁	—	2	4	no	—
367	Q₁₆×C₃₁	—	4	2	no	—
368	Q₁₆×C₃₁	—	4	2	no	—
369	Q₁₆×C₃₁	—	4	2	no	—
370	SD₁₆×C₃₁	—	2	2	no	—
371	SD₁₆×C₃₁	—	2	4	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	2	no	—
374	SD₁₆×C₃₁	—	4	1	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	SD₁₆×C₃₁	—	4	2	no	—
377	D₈×C₃₁	—	4	1	no	—
378	D₈×C₃₁	—	4	2	no	—
379	C₂×C₈×C₃₁	—	4	2	no	—
380	C₂×C₈×C₃₁	—	4	2	no	—
381	C₂×C₈×C₃₁	—	4	2	no	—
382	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
386	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₃₁	—	2	1	no	—
389	C₄⋊C₄×C₃₁	—	2	2	no	—
390	C₄⋊C₄×C₃₁	—	2	2	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	no	—
421	C₂²⋊C₄×C₃₁	—	2	1	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	—	2	1	no	—
445	C₄²×C₃₁	—	2	2	no	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₃₁	C₂×D₄	1	2	yes	—
454	C₄²×C₃₁	C₂×D₄	1	2	yes	—
455	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₃₁	C₂⁴	1	2	yes	—
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	#61956	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₃₁	—	2	1	no	—
460	C₂³×C₃₁	—	2	1	no	—
461	C₂³×C₃₁	—	2	2	no	—
462	C₂³×C₃₁	—	4	4	no	—
463	C₂³×C₃₁	—	8	2	no	—
464	C₂³×C₃₁	—	8	2	no	—
465	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
466	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
467	Q₈×C₃₁	—	2	2	no	—
468	Q₈×C₃₁	—	2	1	no	—
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	2	2	no	—
473	Q₈×C₃₁	—	2	1	no	—
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	4	4	no	—
476	Q₈×C₃₁	—	4	2	no	—
477	Q₈×C₃₁	—	8	2	no	—
478	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
479	D₄×C₃₁	—	2	4	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	2	1	no	—
484	D₄×C₃₁	—	2	1	no	—
485	D₄×C₃₁	—	2	2	no	—
486	D₄×C₃₁	—	4	2	no	—
487	D₄×C₃₁	—	4	4	no	—
488	D₄×C₃₁	—	4	4	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	1	no	—
493	D₄×C₃₁	—	8	2	no	—
494	D₄×C₃₁	#135	1	4	yes	complemented
495	C₂×C₄×C₃₁	—	2	4	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	1	no	—
500	C₂×C₄×C₃₁	—	2	2	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	1	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	4	2	no	—
511	C₂×C₄×C₃₁	—	4	1	no	—
512	C₂×C₄×C₃₁	—	4	2	no	—
513	C₂×C₄×C₃₁	—	4	4	no	—
514	C₂×C₄×C₃₁	—	4	2	no	—
515	C₂×C₄×C₃₁	—	4	4	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	2	no	—
518	C₂×C₄×C₃₁	—	8	2	no	—
519	C₂×C₄×C₃₁	—	8	2	no	—
520	C₂×C₄×C₃₁	—	8	2	no	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
530	C₈×C₃₁	—	2	2	no	—
531	C₈×C₃₁	—	2	1	no	—
532	C₈×C₃₁	—	2	2	no	—
533	C₈×C₃₁	—	2	1	no	—
534	C₈×C₃₁	—	2	1	no	—
535	C₈×C₃₁	—	2	1	no	—
536	#3514	C₂×C₃₁	1	1	yes	characteristic, complemented
537	#3482	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3394	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3393	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3365	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#3364	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3300	C₂×C₃₁	1	2	yes	complemented
543	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3296	C₂×C₃₁	1	2	yes	complemented
545	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
546	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3285	C₂×C₃₁	1	2	yes	complemented
548	#3282	C₂×C₃₁	1	2	yes	complemented
549	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3250	C₂×C₃₁	1	2	yes	complemented
551	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3211	C₂×C₃₁	1	2	yes	complemented
553	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3108	C₂×C₃₁	1	2	yes	complemented
555	#3102	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
557	C₂×#464	C₂×C₃₁	1	2	yes	complemented
558	#2988	C₂×C₃₁	1	1	yes	characteristic, complemented
559	C₂²×C₃₁	—	2	2	no	—
560	C₂²×C₃₁	—	2	2	no	—
561	C₂²×C₃₁	—	2	1	no	—
562	C₂²×C₃₁	—	2	1	no	—
563	C₂²×C₃₁	—	2	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	4	1	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	2	no	—
569	C₂²×C₃₁	—	4	1	no	—
570	C₂²×C₃₁	—	4	1	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	2	no	—
573	C₂²×C₃₁	—	16	4	no	—
574	C₂²×C₃₁	C₂×#135	1	4	yes	—
575	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₃₁	—	2	1	no	—
577	C₄×C₃₁	—	2	2	no	—
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	1	no	—
580	C₄×C₃₁	—	2	2	no	—
581	C₄×C₃₁	—	2	2	no	—
582	C₄×C₃₁	—	2	1	no	—
583	C₄×C₃₁	—	2	2	no	—
584	C₄×C₃₁	—	4	1	no	—
585	C₄×C₃₁	—	4	1	no	—
586	C₄×C₃₁	—	4	2	no	—
587	C₄×C₃₁	—	4	2	no	—
588	C₄×C₃₁	—	4	1	no	—
589	C₄×C₃₁	—	4	1	no	—
590	C₄×C₃₁	—	4	1	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	C₂×#135	1	2	yes	—
593	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
594	C₄×C₃₁	#585	1	1	yes	characteristic
595	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
596	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
597	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
598	#559	C₂²×C₃₁	1	1	yes	characteristic
599	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
600	#556	—	2	1	no	—
601	#556	C₂²×C₃₁	1	1	yes	characteristic
602	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#555	—	2	1	no	—
604	#552	—	2	2	no	—
605	#552	C₂²×C₃₁	1	2	yes	complemented
606	#551	—	2	2	no	—
607	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
608	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
609	#548	C₂²×C₃₁	1	2	yes	—
610	#548	C₂²×C₃₁	1	2	yes	complemented
611	#547	—	2	1	no	—
612	#547	C₂²×C₃₁	1	1	yes	characteristic
613	#546	—	2	1	no	—
614	#546	C₂²×C₃₁	1	2	yes	—
615	D₄²	C₂²×C₃₁	1	1	yes	characteristic
616	#542	—	2	1	no	—
617	#538	—	2	2	no	—
618	#533	—	2	1	no	—
619	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#532	C₂²×C₃₁	1	1	yes	characteristic
621	#529	—	2	2	no	—
622	#529	C₂²×C₃₁	1	1	yes	characteristic
623	#529	C₂²×C₃₁	1	2	yes	—
624	#529	C₂²×C₃₁	1	2	yes	complemented
625	C₂×#124	C₂²×C₃₁	1	2	yes	—
626	#518	—	2	1	no	—
627	C₄×#41	—	2	1	no	—
628	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
629	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
631	#495	C₂²×C₃₁	1	2	yes	—
632	#495	C₂²×C₃₁	1	2	yes	complemented
633	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#492	C₂²×C₃₁	1	1	yes	characteristic
635	#488	C₂²×C₃₁	1	2	yes	—
636	#488	C₂²×C₃₁	1	2	yes	complemented
637	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#486	C₂²×C₃₁	1	1	yes	characteristic
639	#485	C₂²×C₃₁	1	1	yes	characteristic, complemented
640	#483	C₂²×C₃₁	1	2	yes	complemented
641	#482	C₂²×C₃₁	1	1	yes	characteristic
642	#480	C₂²×C₃₁	1	2	yes	—
643	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#479	C₂²×C₃₁	1	2	yes	complemented
645	#479	C₂²×C₃₁	1	2	yes	complemented
646	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#478	C₂²×C₃₁	1	2	yes	complemented
648	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#474	C₂²×C₃₁	1	1	yes	characteristic
650	#467	C₂²×C₃₁	1	2	yes	complemented
651	#467	C₂²×C₃₁	1	2	yes	complemented
652	#466	C₂²×C₃₁	1	2	yes	—
653	#465	C₂²×C₃₁	1	2	yes	—
654	#465	C₂²×C₃₁	1	2	yes	—
655	#465	C₂²×C₃₁	1	2	yes	complemented
656	#464	C₂²×C₃₁	1	1	yes	characteristic
657	#464	C₂²×C₃₁	1	2	yes	—
658	#464	C₂²×C₃₁	1	2	yes	—
659	#464	C₂²×C₃₁	1	2	yes	—
660	#464	C₂²×C₃₁	1	2	yes	complemented
661	#464	C₂²×C₃₁	1	2	yes	complemented
662	#464	C₂²×C₃₁	1	2	yes	complemented
663	#464	C₂²×C₃₁	1	2	yes	complemented
664	#464	C₂²×C₃₁	1	2	yes	complemented
665	#464	C₂²×C₃₁	1	2	yes	complemented
666	#463	C₂²×C₃₁	1	1	yes	characteristic
667	#463	C₂²×C₃₁	1	2	yes	complemented
668	#463	C₂²×C₃₁	1	2	yes	complemented
669	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#461	C₂²×C₃₁	1	1	yes	characteristic
672	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#460	C₂²×C₃₁	1	1	yes	characteristic
674	#459	C₂²×C₃₁	1	1	yes	characteristic
675	#452	C₂²×C₃₁	1	1	yes	characteristic, complemented
676	#452	C₂²×C₃₁	1	2	yes	complemented
677	#452	C₂²×C₃₁	1	2	yes	complemented
678	#451	C₂²×C₃₁	1	2	yes	complemented
679	#451	C₂²×C₃₁	1	2	yes	complemented
680	#450	C₂²×C₃₁	1	2	yes	—
681	#449	C₂²×C₃₁	1	1	yes	characteristic
682	#448	C₂²×C₃₁	1	2	yes	—
683	#448	C₂²×C₃₁	1	2	yes	complemented
684	#447	C₂²×C₃₁	1	2	yes	—
685	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
689	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
690	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
691	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
693	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
694	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
695	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
696	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
697	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
698	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
699	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	#431	C₂²×C₃₁	1	2	yes	complemented
701	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
702	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
703	#416	C₂²×C₃₁	1	2	yes	complemented
704	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
705	C₂×#102	C₂²×C₃₁	1	2	yes	—
706	C₂×C₃₁	—	2	4	no	—
707	C₂×C₃₁	—	4	1	no	—
708	C₂×C₃₁	—	8	1	no	—
709	C₂×C₃₁	—	8	2	no	—
710	C₂×C₃₁	—	8	1	no	—
711	C₂×C₃₁	#3488	1	1	yes	characteristic
712	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
713	C₂×C₃₁	#3586	1	1	yes	characteristic
714	C₂×#41	—	2	1	no	—
715	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
716	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×#41	C₂³×C₃₁	1	2	yes	—
718	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
719	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
720	C₂²×D₄	—	2	1	no	—
721	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
722	#135	—	4	4	no	—
723	C₂×Q₁₆	—	4	4	no	—
724	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
729	C₂×SD₁₆	—	4	4	no	—
730	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
731	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×D₈	C₂³×C₃₁	1	2	yes	—
738	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
739	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
740	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
741	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	1	no	—
745	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
746	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	#127	C₂³×C₃₁	1	1	yes	characteristic
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	2	1	no	—
754	#126	—	2	2	no	—
755	#125	—	2	2	no	—
756	#125	—	2	2	no	—
757	#125	—	2	1	no	—
758	#125	C₂³×C₃₁	1	1	yes	characteristic
759	#125	C₂³×C₃₁	1	2	yes	—
760	#124	—	2	1	no	—
761	#124	—	2	2	no	—
762	#124	—	2	2	no	—
763	#124	—	2	2	no	—
764	#124	—	2	2	no	—
765	#124	C₂³×C₃₁	1	1	yes	characteristic
766	#124	C₂³×C₃₁	1	2	yes	—
767	#124	C₂³×C₃₁	1	2	yes	—
768	#124	C₂³×C₃₁	1	2	yes	—
769	#124	C₂³×C₃₁	1	2	yes	—
770	#123	—	2	2	no	—
771	#123	—	2	1	no	—
772	#123	—	2	2	no	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	C₂²⋊Q₈	—	2	1	no	—
778	C₂²⋊Q₈	—	2	1	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	2	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	—	2	1	no	—
792	#121	—	2	1	no	—
793	#121	—	2	1	no	—
794	#121	—	2	2	no	—
795	#121	C₂³×C₃₁	1	2	yes	—
796	#121	C₂³×C₃₁	1	1	yes	characteristic
797	#121	C₂³×C₃₁	1	2	yes	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
805	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
807	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
808	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
811	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	2	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
826	C₄×D₄	D₄×C₃₁	1	2	yes	—
827	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
830	C₄×D₄	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	2	yes	—
833	#117	—	2	1	no	—
834	#117	—	2	1	no	—
835	#117	—	2	1	no	—
836	#117	—	2	2	no	—
837	#117	—	2	1	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	2	no	—
841	#117	D₄×C₃₁	1	2	yes	—
842	#117	D₄×C₃₁	1	1	yes	characteristic
843	#117	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	—	2	2	no	—
845	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
846	C₂×C₂²⋊C₄	—	2	2	no	—
847	C₂×C₂²⋊C₄	—	2	2	no	—
848	C₂×C₂²⋊C₄	—	2	2	no	—
849	C₂×C₄²	—	2	2	no	—
850	C₂×C₄²	—	2	1	no	—
851	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
852	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
853	#107	C₂³×C₃₁	1	1	yes	characteristic
854	#107	C₂³×C₃₁	1	2	yes	—
855	#107	C₂³×C₃₁	1	1	yes	characteristic
856	#106	C₂³×C₃₁	1	1	yes	characteristic
857	#106	C₂³×C₃₁	1	1	yes	characteristic
858	#106	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
860	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
864	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
865	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
866	#103	C₂³×C₃₁	1	1	yes	characteristic
867	#103	C₂³×C₃₁	1	2	yes	—
868	#103	C₂³×C₃₁	1	2	yes	—
869	#103	C₂³×C₃₁	1	2	yes	—
870	#103	C₂³×C₃₁	1	2	yes	—
871	#103	C₂³×C₃₁	1	1	yes	characteristic
872	#103	C₂³×C₃₁	1	1	yes	characteristic
873	#103	C₂³×C₃₁	1	2	yes	—
874	#103	C₂³×C₃₁	1	2	yes	—
875	#103	C₂³×C₃₁	1	2	yes	—
876	#103	C₂³×C₃₁	1	1	yes	characteristic
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	#102	C₂³×C₃₁	1	2	yes	—
881	#102	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	1	yes	characteristic
886	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₃₁	1	2	yes	—
893	C₄×C₈	C₂³×C₃₁	1	2	yes	—
894	C₃₁	#61956	1	1	yes	characteristic, direct product factor, Sylow
895	C₂⁴	—	2	2	no	—
896	#41	—	2	4	no	—
897	#41	—	2	2	no	—
898	#41	—	4	1	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	4	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	2	4	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
912	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	2	no	—
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	1	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	2	no	—
924	C₂×D₄	—	4	4	no	—
925	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
929	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂²×C₄	—	2	2	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
940	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
941	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
942	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
945	Q₁₆	—	2	2	no	—
946	Q₁₆	—	2	4	no	—
947	Q₁₆	—	4	2	no	—
948	Q₁₆	—	4	2	no	—
949	Q₁₆	—	4	2	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	2	4	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	1	no	—
955	SD₁₆	—	4	2	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	4	1	no	—
958	D₈	—	4	2	no	—
959	C₂×C₈	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
966	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
992	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1032	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1035	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₃₁	1	2	yes	—
1037	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1045	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	4	4	no	—
1055	Q₈	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	1	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	C₃₁×#135	1	4	yes	complemented
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1104	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	1	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₂×C₃₁×#135	1	4	yes	—
1131	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₂×C₃₁×#135	1	2	yes	—
1149	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1150	C₄	C₃₁×#585	1	1	yes	characteristic
1151	C₂	—	2	4	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₃₁×#3488	1	1	yes	characteristic
1157	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
1158	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3514	C₂	semidirect
2. C₃₁×#3482	C₂	semidirect
3. C₃₁×#3394	C₂	semidirect
4. C₃₁×#3393	C₂	semidirect
5. C₃₁×#3365	C₂	semidirect
6. C₃₁×#3364	C₂	semidirect
7. C₃₁×#3300	C₂	semidirect
8. C₃₁×#3298	C₂	semidirect
9. C₃₁×#3296	C₂	semidirect
10. C₃₁×#3294	C₂	semidirect
11. D₄×Q₁₆×C₃₁	C₂	semidirect
12. C₃₁×#3285	C₂	semidirect
13. C₃₁×#3282	C₂	semidirect
14. D₄×SD₁₆×C₃₁	C₂	semidirect
15. C₃₁×#3250	C₂	semidirect
16. C₃₁×#3248	C₂	semidirect
17. C₃₁×#3211	C₂	semidirect
18. C₃₁×#3210	C₂	semidirect
19. C₃₁×#3108	C₂	semidirect
20. C₃₁×#3102	C₂	semidirect
21. C₃₁×#3035	C₂	semidirect
22. C₂×C₃₁×#464	C₂	semidirect
23. C₃₁×#2988	C₂	semidirect
24. C₂×C₃₁×#135	C₂²	semidirect
25. C₂²×Q₁₆×C₃₁	C₂²	semidirect
28. C₃₁×#557	C₂²	semidirect
31. C₃₁×#556	C₂²	semidirect
34. C₃₁×#552	C₂²	semidirect
39. C₃₁×#548	C₂²	semidirect
48. C₃₁×#533	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
58. C₄×#41×C₃₁	C₂²	semidirect
59. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
61. C₃₁×#495	C₂²	semidirect
62. C₃₁×#494	C₂²	semidirect
65. C₃₁×#488	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#478	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
79. C₃₁×#467	C₂²	semidirect
80. C₃₁×#467	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
89. C₃₁×#464	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#464	C₂²	semidirect
92. C₃₁×#464	C₂²	semidirect
93. C₃₁×#464	C₂²	semidirect
94. C₃₁×#464	C₂²	semidirect
96. C₃₁×#463	C₂²	semidirect
97. C₃₁×#463	C₂²	semidirect
98. C₃₁×#462	C₂²	semidirect
99. C₃₁×#462	C₂²	semidirect
101. C₃₁×#461	C₂²	semidirect
104. C₃₁×#452	C₂²	semidirect
105. C₃₁×#452	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#451	C₂²	semidirect
108. C₃₁×#451	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
114. C₈×Q₈×C₃₁	C₂²	semidirect
115. C₈×Q₈×C₃₁	C₂²	semidirect
116. C₄×Q₁₆×C₃₁	C₂²	semidirect
117. C₄×Q₁₆×C₃₁	C₂²	semidirect
118. C₄×Q₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
121. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₈×D₄×C₃₁	C₂²	semidirect
127. C₈×D₄×C₃₁	C₂²	semidirect
128. C₃₁×#431	C₂²	semidirect
129. C₃₁×#431	C₂²	semidirect
130. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
132. C₃₁×#416	C₂²	semidirect
133. C₂×C₃₁×#103	C₂²	semidirect
458. #61956	C₃₁	direct (N × H)
494. D₄×C₃₁	#135	semidirect
536. #3514	C₂×C₃₁	semidirect
537. #3482	C₂×C₃₁	semidirect
538. #3394	C₂×C₃₁	semidirect
539. #3393	C₂×C₃₁	semidirect
540. #3365	C₂×C₃₁	semidirect
541. #3364	C₂×C₃₁	semidirect
542. #3300	C₂×C₃₁	semidirect
543. #3298	C₂×C₃₁	semidirect
544. #3296	C₂×C₃₁	semidirect
545. #3294	C₂×C₃₁	semidirect
546. D₄×Q₁₆	C₂×C₃₁	semidirect
547. #3285	C₂×C₃₁	semidirect
548. #3282	C₂×C₃₁	semidirect
549. D₄×SD₁₆	C₂×C₃₁	semidirect
550. #3250	C₂×C₃₁	semidirect
551. #3248	C₂×C₃₁	semidirect
552. #3211	C₂×C₃₁	semidirect
553. #3210	C₂×C₃₁	semidirect
554. #3108	C₂×C₃₁	semidirect
555. #3102	C₂×C₃₁	semidirect
556. #3035	C₂×C₃₁	semidirect
557. C₂×#464	C₂×C₃₁	semidirect
558. #2988	C₂×C₃₁	semidirect
595. C₂×#135	C₂²×C₃₁	semidirect
596. C₂²×Q₁₆	C₂²×C₃₁	semidirect
599. #557	C₂²×C₃₁	semidirect
602. #556	C₂²×C₃₁	semidirect
605. #552	C₂²×C₃₁	semidirect
610. #548	C₂²×C₃₁	semidirect
619. #533	C₂²×C₃₁	semidirect
624. #529	C₂²×C₃₁	semidirect
629. C₄×#41	C₂²×C₃₁	semidirect
630. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
632. #495	C₂²×C₃₁	semidirect
633. #494	C₂²×C₃₁	semidirect
636. #488	C₂²×C₃₁	semidirect
637. #487	C₂²×C₃₁	semidirect
639. #485	C₂²×C₃₁	semidirect
640. #483	C₂²×C₃₁	semidirect
643. #479	C₂²×C₃₁	semidirect
644. #479	C₂²×C₃₁	semidirect
645. #479	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #475	C₂²×C₃₁	semidirect
650. #467	C₂²×C₃₁	semidirect
651. #467	C₂²×C₃₁	semidirect
655. #465	C₂²×C₃₁	semidirect
660. #464	C₂²×C₃₁	semidirect
661. #464	C₂²×C₃₁	semidirect
662. #464	C₂²×C₃₁	semidirect
663. #464	C₂²×C₃₁	semidirect
664. #464	C₂²×C₃₁	semidirect
665. #464	C₂²×C₃₁	semidirect
667. #463	C₂²×C₃₁	semidirect
668. #463	C₂²×C₃₁	semidirect
669. #462	C₂²×C₃₁	semidirect
670. #462	C₂²×C₃₁	semidirect
672. #461	C₂²×C₃₁	semidirect
675. #452	C₂²×C₃₁	semidirect
676. #452	C₂²×C₃₁	semidirect
677. #452	C₂²×C₃₁	semidirect
678. #451	C₂²×C₃₁	semidirect
679. #451	C₂²×C₃₁	semidirect
683. #448	C₂²×C₃₁	semidirect
685. C₈×Q₈	C₂²×C₃₁	semidirect
686. C₈×Q₈	C₂²×C₃₁	semidirect
687. C₄×Q₁₆	C₂²×C₃₁	semidirect
688. C₄×Q₁₆	C₂²×C₃₁	semidirect
689. C₄×Q₁₆	C₂²×C₃₁	semidirect
691. C₄×SD₁₆	C₂²×C₃₁	semidirect
692. C₄×SD₁₆	C₂²×C₃₁	semidirect
693. C₄×SD₁₆	C₂²×C₃₁	semidirect
697. C₈×D₄	C₂²×C₃₁	semidirect
698. C₈×D₄	C₂²×C₃₁	semidirect
699. #431	C₂²×C₃₁	semidirect
700. #431	C₂²×C₃₁	semidirect
701. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
702. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
703. #416	C₂²×C₃₁	semidirect
704. C₂×#103	C₂²×C₃₁	semidirect
894. C₃₁	#61956	direct (N × H)
1073. D₄	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3514	2
C₃₁×#3482	2
C₃₁×#3394	2
C₃₁×#3393	2
C₃₁×#3365	2
C₃₁×#3364	2
C₃₁×#3300	2
C₃₁×#3298	2
C₃₁×#3296	2
C₃₁×#3294	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3285	2
C₃₁×#3282	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3250	2
C₃₁×#3248	2
C₃₁×#3211	2
C₃₁×#3210	2
C₃₁×#3108	2
C₃₁×#3102	2
C₃₁×#3035	2
C₂×C₃₁×#464	2
C₃₁×#2988	2
#61956	31

Subgroups — C31×#61956 #21518715

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61956 #21518715