Subgroups — C₃₁×#60935 #21517694

Order 7936.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3263	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3260	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3258	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3248	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3247	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3246	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3082	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3043	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3042	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#555	—	2	1	no	—
32	C₃₁×#554	—	2	1	no	—
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	—	2	1	no	—
35	C₃₁×#552	—	2	2	no	—
36	C₃₁×#552	—	2	1	no	—
37	C₃₁×#552	—	2	1	no	—
38	C₃₁×#551	—	2	2	no	—
39	C₃₁×#551	—	2	2	no	—
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	C₃₁×#544	C₂²	1	1	yes	characteristic
43	C₃₁×#544	C₂²	1	1	yes	characteristic
44	C₃₁×#542	C₂²	1	2	yes	—
45	C₃₁×#542	C₂²	1	2	yes	complemented
46	C₃₁×#541	C₂²	1	2	yes	complemented
47	C₃₁×#540	C₂²	1	2	yes	—
48	C₃₁×#536	C₂²	1	1	yes	characteristic
49	C₃₁×#535	C₂²	1	1	yes	characteristic
50	C₃₁×#533	C₂²	1	2	yes	complemented
51	C₃₁×#532	C₂²	1	2	yes	—
52	C₃₁×#529	C₂²	1	2	yes	—
53	C₃₁×#529	C₂²	1	2	yes	complemented
54	C₃₁×#525	C₂²	1	1	yes	characteristic
55	C₃₁×#525	C₂²	1	1	yes	characteristic
56	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
58	C₃₁×#520	C₂²	1	1	yes	characteristic
59	C₃₁×#520	C₂²	1	1	yes	characteristic
60	C₃₁×#519	C₂²	1	1	yes	characteristic
61	C₃₁×#518	C₂²	1	1	yes	characteristic
62	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
63	C₃₁×#479	C₂²	1	2	yes	complemented
64	C₃₁×#479	C₂²	1	2	yes	complemented
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#478	C₂²	1	2	yes	complemented
68	C₃₁×#478	C₂²	1	2	yes	complemented
69	C₃₁×#478	C₂²	1	2	yes	complemented
70	C₃₁×#478	C₂²	1	2	yes	complemented
71	C₃₁×#477	C₂²	1	2	yes	complemented
72	C₃₁×#476	C₂²	1	2	yes	complemented
73	C₃₁×#476	C₂²	1	2	yes	complemented
74	C₃₁×#476	C₂²	1	2	yes	complemented
75	C₃₁×#475	C₂²	1	2	yes	complemented
76	C₃₁×#475	C₂²	1	2	yes	complemented
77	C₃₁×#475	C₂²	1	2	yes	complemented
78	C₃₁×#474	C₂²	1	2	yes	complemented
79	C₃₁×#470	C₂²	1	2	yes	complemented
80	C₃₁×#469	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
84	C₃₁×#467	C₂²	1	2	yes	complemented
85	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#466	C₂²	1	2	yes	—
87	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
88	C₃₁×#466	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#465	C₂²	1	2	yes	—
90	C₃₁×#465	C₂²	1	2	yes	—
91	C₃₁×#465	C₂²	1	2	yes	—
92	C₃₁×#465	C₂²	1	2	yes	—
93	C₃₁×#465	C₂²	1	2	yes	—
94	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#465	C₂²	1	2	yes	complemented
96	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#464	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	complemented
101	C₃₁×#464	C₂²	1	2	yes	complemented
102	C₃₁×#464	C₂²	1	2	yes	complemented
103	C₃₁×#463	C₂²	1	2	yes	complemented
104	C₃₁×#463	C₂²	1	2	yes	complemented
105	C₃₁×#463	C₂²	1	2	yes	complemented
106	C₃₁×#463	C₂²	1	2	yes	complemented
107	C₃₁×#462	C₂²	1	2	yes	complemented
108	C₃₁×#461	C₂²	1	2	yes	complemented
109	C₃₁×#461	C₂²	1	2	yes	complemented
110	C₃₁×#461	C₂²	1	2	yes	complemented
111	C₃₁×#460	C₂²	1	2	yes	complemented
112	C₃₁×#460	C₂²	1	2	yes	complemented
113	C₃₁×#460	C₂²	1	2	yes	complemented
114	C₃₁×#459	C₂²	1	2	yes	complemented
115	C₃₁×#428	C₂²	1	1	yes	characteristic
116	C₃₁×#428	C₂²	1	1	yes	characteristic
117	C₃₁×#427	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
119	C₃₁×#424	C₂²	1	1	yes	characteristic
120	C₃₁×#424	C₂²	1	1	yes	characteristic
121	C₃₁×#424	C₂²	1	1	yes	characteristic
122	C₃₁×#424	C₂²	1	1	yes	characteristic
123	C₃₁×#424	C₂²	1	2	yes	complemented
124	C₃₁×#424	C₂²	1	2	yes	complemented
125	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
126	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
127	C₃₁×#419	C₂²	1	1	yes	characteristic
128	C₃₁×#418	C₂²	1	1	yes	characteristic
129	C₃₁×#417	C₂²	1	1	yes	characteristic
130	C₃₁×#417	C₂²	1	1	yes	characteristic
131	C₃₁×#416	C₂²	1	1	yes	characteristic
132	C₃₁×#416	C₂²	1	1	yes	characteristic
133	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
135	C₂×#41×C₃₁	—	2	2	no	—
136	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₃₁×#137	—	4	2	no	—
143	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
144	C₃₁×#135	—	4	2	no	—
145	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	—	4	2	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×M₁₆×C₃₁	—	4	2	no	—
157	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₃₁	—	4	2	no	—
161	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
166	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₃₁×C₄⋊Q₈	—	2	1	no	—
169	C₃₁×C₄⋊Q₈	—	2	1	no	—
170	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×#127	C₂³	1	2	yes	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#126	—	2	2	no	—
178	C₃₁×#126	—	2	2	no	—
179	C₃₁×#126	—	2	2	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	—	2	2	no	—
182	C₃₁×#125	—	2	1	no	—
183	C₃₁×#125	—	2	1	no	—
184	C₃₁×#125	—	2	2	no	—
185	C₃₁×#125	C₂³	1	2	yes	—
186	C₃₁×#125	C₂³	1	2	yes	—
187	C₃₁×#124	—	2	2	no	—
188	C₃₁×#124	—	2	2	no	—
189	C₃₁×#124	—	2	2	no	—
190	C₃₁×#124	C₂³	1	2	yes	—
191	C₃₁×#124	C₂³	1	2	yes	—
192	C₃₁×#123	—	2	1	no	—
193	C₃₁×#123	—	2	1	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×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	1	no	—
202	C₃₁×C₂²⋊Q₈	—	2	1	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	1	no	—
205	C₃₁×C₂²⋊Q₈	—	2	1	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	2	no	—
208	C₃₁×C₂²⋊Q₈	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	1	no	—
220	C₃₁×#121	—	2	1	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	2	yes	—
225	C₃₁×#121	C₂³	1	1	yes	characteristic
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	1	yes	characteristic
228	C₃₁×#121	C₂³	1	1	yes	characteristic
229	C₃₁×#120	—	2	1	no	—
230	C₃₁×#120	—	2	1	no	—
231	C₃₁×#120	—	2	2	no	—
232	C₄×Q₈×C₃₁	—	2	1	no	—
233	C₄×Q₈×C₃₁	—	2	1	no	—
234	C₄×Q₈×C₃₁	—	2	2	no	—
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
237	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
238	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	2	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	2	no	—
248	C₄×D₄×C₃₁	—	2	2	no	—
249	C₄×D₄×C₃₁	—	2	2	no	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	2	yes	—
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	D₄	1	2	yes	—
261	C₃₁×#117	D₄	1	1	yes	characteristic
262	C₃₁×#117	D₄	1	1	yes	characteristic
263	C₃₁×#117	C₂³	1	1	yes	characteristic
264	C₃₁×#117	C₂³	1	1	yes	characteristic
265	C₃₁×#117	C₂³	1	1	yes	characteristic
266	C₃₁×#117	C₂³	1	1	yes	characteristic
267	C₃₁×#117	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
269	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
271	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
276	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
277	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
278	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
279	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
280	C₃₁×#107	C₂³	1	1	yes	characteristic
281	C₃₁×#107	C₂³	1	1	yes	characteristic
282	C₃₁×#107	C₂³	1	2	yes	—
283	C₃₁×#107	C₂³	1	2	yes	—
284	C₃₁×#106	C₂³	1	2	yes	—
285	C₃₁×#106	C₂³	1	2	yes	—
286	C₃₁×#106	C₂³	1	1	yes	characteristic
287	C₃₁×#106	C₂³	1	1	yes	characteristic
288	C₃₁×#106	C₂³	1	2	yes	—
289	C₃₁×#106	C₂³	1	2	yes	—
290	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
291	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
292	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
293	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
294	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
295	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
296	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
297	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	1	yes	characteristic
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	1	yes	characteristic
303	C₃₁×#103	C₂³	1	1	yes	characteristic
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	C₂³	1	2	yes	—
306	C₃₁×#103	C₂³	1	2	yes	—
307	C₃₁×#103	C₂³	1	2	yes	—
308	C₃₁×#102	C₂³	1	2	yes	—
309	C₃₁×#102	C₂³	1	2	yes	—
310	C₃₁×#102	C₂³	1	1	yes	characteristic
311	C₃₁×#102	C₂³	1	1	yes	characteristic
312	C₃₁×#102	C₂³	1	1	yes	characteristic
313	C₃₁×#102	C₂³	1	1	yes	characteristic
314	C₃₁×#102	C₂³	1	2	yes	—
315	C₃₁×#102	C₂³	1	2	yes	—
316	C₃₁×#102	C₂³	1	2	yes	—
317	C₃₁×#102	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	1	no	—
319	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
320	#41×C₃₁	—	2	2	no	—
321	#41×C₃₁	—	2	2	no	—
322	#41×C₃₁	—	2	2	no	—
323	#41×C₃₁	—	2	2	no	—
324	#41×C₃₁	—	8	4	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	2	2	no	—
328	C₂×Q₈×C₃₁	—	2	2	no	—
329	C₂×Q₈×C₃₁	—	2	2	no	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×D₄×C₃₁	—	2	1	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	8	2	no	—
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	1	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	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	Q₁₆×C₃₁	—	4	1	no	—
370	Q₁₆×C₃₁	—	4	2	no	—
371	SD₁₆×C₃₁	—	4	2	no	—
372	SD₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	4	1	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	M₁₆×C₃₁	—	2	2	no	—
380	M₁₆×C₃₁	—	2	2	no	—
381	M₁₆×C₃₁	—	4	2	no	—
382	C₂×C₈×C₃₁	—	2	2	no	—
383	C₂×C₈×C₃₁	—	2	2	no	—
384	C₂×C₈×C₃₁	—	4	1	no	—
385	C₂×C₈×C₃₁	—	4	1	no	—
386	C₂×C₈×C₃₁	—	4	1	no	—
387	C₂×C₈×C₃₁	—	4	1	no	—
388	C₂×C₈×C₃₁	—	4	2	no	—
389	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	1	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	2	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	1	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	—	2	1	no	—
447	C₂²⋊C₄×C₃₁	—	2	1	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	2	no	—
455	C₄²×C₃₁	—	2	2	no	—
456	C₄²×C₃₁	—	2	2	no	—
457	C₄²×C₃₁	—	2	1	no	—
458	C₄²×C₃₁	—	2	1	no	—
459	C₄²×C₃₁	C₂×D₄	1	2	yes	—
460	C₄²×C₃₁	C₂×D₄	1	2	yes	—
461	C₄²×C₃₁	C₂⁴	1	2	yes	—
462	C₄²×C₃₁	C₂⁴	1	2	yes	—
463	#60935	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂³×C₃₁	—	2	2	no	—
465	C₂³×C₃₁	—	2	2	no	—
466	C₂³×C₃₁	—	2	1	no	—
467	C₂³×C₃₁	—	2	2	no	—
468	C₂³×C₃₁	—	2	1	no	—
469	C₂³×C₃₁	—	4	1	no	—
470	C₂³×C₃₁	—	4	2	no	—
471	C₂³×C₃₁	—	8	1	no	—
472	C₂³×C₃₁	—	8	1	no	—
473	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
475	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
476	Q₈×C₃₁	—	2	2	no	—
477	Q₈×C₃₁	—	2	1	no	—
478	Q₈×C₃₁	—	2	1	no	—
479	Q₈×C₃₁	—	2	2	no	—
480	Q₈×C₃₁	—	2	1	no	—
481	Q₈×C₃₁	—	2	1	no	—
482	Q₈×C₃₁	—	4	2	no	—
483	Q₈×C₃₁	—	8	2	no	—
484	Q₈×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	2	1	no	—
486	D₄×C₃₁	—	2	2	no	—
487	D₄×C₃₁	—	2	1	no	—
488	D₄×C₃₁	—	2	2	no	—
489	D₄×C₃₁	—	2	1	no	—
490	D₄×C₃₁	—	2	1	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	4	2	no	—
493	D₄×C₃₁	—	4	2	no	—
494	D₄×C₃₁	—	4	4	no	—
495	D₄×C₃₁	—	4	2	no	—
496	D₄×C₃₁	—	4	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	D₄×C₃₁	—	8	2	no	—
499	D₄×C₃₁	—	8	1	no	—
500	D₄×C₃₁	—	8	1	no	—
501	D₄×C₃₁	—	8	2	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	4	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	1	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	1	no	—
512	C₂×C₄×C₃₁	—	2	1	no	—
513	C₂×C₄×C₃₁	—	2	2	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	2	1	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	2	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	2	no	—
522	C₂×C₄×C₃₁	—	4	2	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	—	8	2	no	—
525	C₂×C₄×C₃₁	—	8	2	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	1	no	—
528	C₂×C₄×C₃₁	—	8	1	no	—
529	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
538	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
539	C₈×C₃₁	—	2	1	no	—
540	C₈×C₃₁	—	2	1	no	—
541	C₈×C₃₁	—	2	1	no	—
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	2	no	—
544	C₈×C₃₁	—	2	2	no	—
545	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3494	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3263	C₂×C₃₁	1	2	yes	complemented
548	#3260	C₂×C₃₁	1	2	yes	complemented
549	#3258	C₂×C₃₁	1	2	yes	complemented
550	#3257	C₂×C₃₁	1	2	yes	complemented
551	#3250	C₂×C₃₁	1	2	yes	complemented
552	#3248	C₂×C₃₁	1	2	yes	complemented
553	#3247	C₂×C₃₁	1	2	yes	complemented
554	#3246	C₂×C₃₁	1	2	yes	complemented
555	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3082	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3056	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3055	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
562	C₂×#465	C₂×C₃₁	1	1	yes	characteristic, complemented
563	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3043	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#3042	C₂×C₃₁	1	1	yes	characteristic, complemented
567	C₂×#424	C₂×C₃₁	1	1	yes	characteristic, complemented
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	1	no	—
570	C₂²×C₃₁	—	2	1	no	—
571	C₂²×C₃₁	—	2	1	no	—
572	C₂²×C₃₁	—	2	1	no	—
573	C₂²×C₃₁	—	2	1	no	—
574	C₂²×C₃₁	—	2	1	no	—
575	C₂²×C₃₁	—	4	4	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	1	no	—
581	C₂²×C₃₁	—	4	2	no	—
582	C₂²×C₃₁	—	4	1	no	—
583	C₂²×C₃₁	—	4	2	no	—
584	C₂²×C₃₁	—	4	1	no	—
585	C₂²×C₃₁	—	16	2	no	—
586	C₂²×C₃₁	#537	1	2	yes	—
587	C₂²×C₃₁	#577	1	2	yes	—
588	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₃₁	—	2	2	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	2	1	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	2	no	—
594	C₄×C₃₁	—	2	2	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	2	no	—
597	C₄×C₃₁	—	4	1	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	—	4	1	no	—
600	C₄×C₃₁	—	4	2	no	—
601	C₄×C₃₁	—	4	2	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	1	no	—
604	C₄×C₃₁	#537	1	2	yes	—
605	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
607	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
608	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
609	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
610	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
611	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
612	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
613	#556	—	2	1	no	—
614	#555	—	2	1	no	—
615	#554	—	2	1	no	—
616	#553	—	2	1	no	—
617	#553	—	2	1	no	—
618	#552	—	2	2	no	—
619	#552	—	2	1	no	—
620	#552	—	2	1	no	—
621	#551	—	2	2	no	—
622	#551	—	2	2	no	—
623	#547	—	2	1	no	—
624	#546	—	2	2	no	—
625	#544	C₂²×C₃₁	1	1	yes	characteristic
626	#544	C₂²×C₃₁	1	1	yes	characteristic
627	#542	C₂²×C₃₁	1	2	yes	—
628	#542	C₂²×C₃₁	1	2	yes	complemented
629	#541	C₂²×C₃₁	1	2	yes	complemented
630	#540	C₂²×C₃₁	1	2	yes	—
631	#536	C₂²×C₃₁	1	1	yes	characteristic
632	#535	C₂²×C₃₁	1	1	yes	characteristic
633	#533	C₂²×C₃₁	1	2	yes	complemented
634	#532	C₂²×C₃₁	1	2	yes	—
635	#529	C₂²×C₃₁	1	2	yes	—
636	#529	C₂²×C₃₁	1	2	yes	complemented
637	#525	C₂²×C₃₁	1	1	yes	characteristic
638	#525	C₂²×C₃₁	1	1	yes	characteristic
639	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
640	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
641	#520	C₂²×C₃₁	1	1	yes	characteristic
642	#520	C₂²×C₃₁	1	1	yes	characteristic
643	#519	C₂²×C₃₁	1	1	yes	characteristic
644	#518	C₂²×C₃₁	1	1	yes	characteristic
645	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
646	#479	C₂²×C₃₁	1	2	yes	complemented
647	#479	C₂²×C₃₁	1	2	yes	complemented
648	#479	C₂²×C₃₁	1	2	yes	complemented
649	#479	C₂²×C₃₁	1	2	yes	complemented
650	#478	C₂²×C₃₁	1	2	yes	complemented
651	#478	C₂²×C₃₁	1	2	yes	complemented
652	#478	C₂²×C₃₁	1	2	yes	complemented
653	#478	C₂²×C₃₁	1	2	yes	complemented
654	#477	C₂²×C₃₁	1	2	yes	complemented
655	#476	C₂²×C₃₁	1	2	yes	complemented
656	#476	C₂²×C₃₁	1	2	yes	complemented
657	#476	C₂²×C₃₁	1	2	yes	complemented
658	#475	C₂²×C₃₁	1	2	yes	complemented
659	#475	C₂²×C₃₁	1	2	yes	complemented
660	#475	C₂²×C₃₁	1	2	yes	complemented
661	#474	C₂²×C₃₁	1	2	yes	complemented
662	#470	C₂²×C₃₁	1	2	yes	complemented
663	#469	C₂²×C₃₁	1	2	yes	—
664	#468	C₂²×C₃₁	1	2	yes	—
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
667	#467	C₂²×C₃₁	1	2	yes	complemented
668	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#466	C₂²×C₃₁	1	2	yes	—
670	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#466	C₂²×C₃₁	1	1	yes	characteristic, complemented
672	#465	C₂²×C₃₁	1	2	yes	—
673	#465	C₂²×C₃₁	1	2	yes	—
674	#465	C₂²×C₃₁	1	2	yes	—
675	#465	C₂²×C₃₁	1	2	yes	—
676	#465	C₂²×C₃₁	1	2	yes	—
677	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#465	C₂²×C₃₁	1	2	yes	complemented
679	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#464	C₂²×C₃₁	1	2	yes	complemented
683	#464	C₂²×C₃₁	1	2	yes	complemented
684	#464	C₂²×C₃₁	1	2	yes	complemented
685	#464	C₂²×C₃₁	1	2	yes	complemented
686	#463	C₂²×C₃₁	1	2	yes	complemented
687	#463	C₂²×C₃₁	1	2	yes	complemented
688	#463	C₂²×C₃₁	1	2	yes	complemented
689	#463	C₂²×C₃₁	1	2	yes	complemented
690	#462	C₂²×C₃₁	1	2	yes	complemented
691	#461	C₂²×C₃₁	1	2	yes	complemented
692	#461	C₂²×C₃₁	1	2	yes	complemented
693	#461	C₂²×C₃₁	1	2	yes	complemented
694	#460	C₂²×C₃₁	1	2	yes	complemented
695	#460	C₂²×C₃₁	1	2	yes	complemented
696	#460	C₂²×C₃₁	1	2	yes	complemented
697	#459	C₂²×C₃₁	1	2	yes	complemented
698	#428	C₂²×C₃₁	1	1	yes	characteristic
699	#428	C₂²×C₃₁	1	1	yes	characteristic
700	#427	C₂²×C₃₁	1	1	yes	characteristic
701	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
702	#424	C₂²×C₃₁	1	1	yes	characteristic
703	#424	C₂²×C₃₁	1	1	yes	characteristic
704	#424	C₂²×C₃₁	1	1	yes	characteristic
705	#424	C₂²×C₃₁	1	1	yes	characteristic
706	#424	C₂²×C₃₁	1	2	yes	complemented
707	#424	C₂²×C₃₁	1	2	yes	complemented
708	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
709	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
710	#419	C₂²×C₃₁	1	1	yes	characteristic
711	#418	C₂²×C₃₁	1	1	yes	characteristic
712	#417	C₂²×C₃₁	1	1	yes	characteristic
713	#417	C₂²×C₃₁	1	1	yes	characteristic
714	#416	C₂²×C₃₁	1	1	yes	characteristic
715	#416	C₂²×C₃₁	1	1	yes	characteristic
716	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
717	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
718	C₂×C₃₁	—	2	2	no	—
719	C₂×C₃₁	—	2	2	no	—
720	C₂×C₃₁	—	4	1	no	—
721	C₂×C₃₁	—	8	1	no	—
722	C₂×C₃₁	—	8	1	no	—
723	C₂×C₃₁	—	8	2	no	—
724	C₂×C₃₁	C₂×#537	1	1	yes	characteristic
725	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
726	C₂×C₃₁	#3584	1	1	yes	characteristic
727	C₂×#41	—	2	2	no	—
728	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
730	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
731	C₂²×D₄	—	2	1	no	—
732	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
733	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
734	#137	—	4	2	no	—
735	AGL(1,ℤ/8)	—	4	2	no	—
736	#135	—	4	2	no	—
737	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
738	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
739	C₂×SD₁₆	—	4	2	no	—
740	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
742	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
746	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×D₈	C₂³×C₃₁	1	2	yes	—
748	C₂×M₁₆	—	4	2	no	—
749	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
750	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
751	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
752	C₂²×C₈	—	4	2	no	—
753	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	—	2	1	no	—
762	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
763	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
764	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
765	#127	C₂³×C₃₁	1	2	yes	—
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#125	—	2	2	no	—
773	#125	—	2	2	no	—
774	#125	—	2	1	no	—
775	#125	—	2	1	no	—
776	#125	—	2	2	no	—
777	#125	C₂³×C₃₁	1	2	yes	—
778	#125	C₂³×C₃₁	1	2	yes	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	—	2	2	no	—
782	#124	C₂³×C₃₁	1	2	yes	—
783	#124	C₂³×C₃₁	1	2	yes	—
784	#123	—	2	1	no	—
785	#123	—	2	1	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
804	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	C₂³×C₃₁	1	2	yes	—
816	#121	C₂³×C₃₁	1	2	yes	—
817	#121	C₂³×C₃₁	1	1	yes	characteristic
818	#121	C₂³×C₃₁	1	1	yes	characteristic
819	#121	C₂³×C₃₁	1	1	yes	characteristic
820	#121	C₂³×C₃₁	1	1	yes	characteristic
821	#120	—	2	1	no	—
822	#120	—	2	1	no	—
823	#120	—	2	2	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	—	2	1	no	—
826	C₄×Q₈	—	2	2	no	—
827	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
828	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
829	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
830	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	C₂³×C₃₁	1	2	yes	—
843	C₄×D₄	C₂³×C₃₁	1	2	yes	—
844	C₄×D₄	C₂³×C₃₁	1	2	yes	—
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	#117	—	2	2	no	—
847	#117	—	2	1	no	—
848	#117	—	2	1	no	—
849	#117	—	2	2	no	—
850	#117	—	2	2	no	—
851	#117	—	2	2	no	—
852	#117	D₄×C₃₁	1	2	yes	—
853	#117	D₄×C₃₁	1	1	yes	characteristic
854	#117	D₄×C₃₁	1	1	yes	characteristic
855	#117	C₂³×C₃₁	1	1	yes	characteristic
856	#117	C₂³×C₃₁	1	1	yes	characteristic
857	#117	C₂³×C₃₁	1	1	yes	characteristic
858	#117	C₂³×C₃₁	1	1	yes	characteristic
859	#117	C₂³×C₃₁	1	2	yes	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
864	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
865	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
867	C₂×C₂²⋊C₄	—	2	1	no	—
868	C₂×C₂²⋊C₄	—	2	1	no	—
869	C₂×C₂²⋊C₄	—	2	2	no	—
870	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
871	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
872	#107	C₂³×C₃₁	1	1	yes	characteristic
873	#107	C₂³×C₃₁	1	1	yes	characteristic
874	#107	C₂³×C₃₁	1	2	yes	—
875	#107	C₂³×C₃₁	1	2	yes	—
876	#106	C₂³×C₃₁	1	2	yes	—
877	#106	C₂³×C₃₁	1	2	yes	—
878	#106	C₂³×C₃₁	1	1	yes	characteristic
879	#106	C₂³×C₃₁	1	1	yes	characteristic
880	#106	C₂³×C₃₁	1	2	yes	—
881	#106	C₂³×C₃₁	1	2	yes	—
882	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
883	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
884	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
885	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
886	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
887	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
888	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
889	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
890	#103	C₂³×C₃₁	1	2	yes	—
891	#103	C₂³×C₃₁	1	2	yes	—
892	#103	C₂³×C₃₁	1	1	yes	characteristic
893	#103	C₂³×C₃₁	1	1	yes	characteristic
894	#103	C₂³×C₃₁	1	1	yes	characteristic
895	#103	C₂³×C₃₁	1	1	yes	characteristic
896	#103	C₂³×C₃₁	1	2	yes	—
897	#103	C₂³×C₃₁	1	2	yes	—
898	#103	C₂³×C₃₁	1	2	yes	—
899	#103	C₂³×C₃₁	1	2	yes	—
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	1	yes	characteristic
903	#102	C₂³×C₃₁	1	1	yes	characteristic
904	#102	C₂³×C₃₁	1	1	yes	characteristic
905	#102	C₂³×C₃₁	1	1	yes	characteristic
906	#102	C₂³×C₃₁	1	2	yes	—
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	2	yes	—
909	#102	C₂³×C₃₁	1	2	yes	—
910	C₃₁	#60935	1	1	yes	characteristic, direct product factor, Sylow
911	C₂⁴	—	2	1	no	—
912	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	8	4	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	—	2	2	no	—
920	C₂×Q₈	—	2	2	no	—
921	C₂×Q₈	—	2	2	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
925	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	8	2	no	—
940	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
942	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	2	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	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	C₂×D₄×C₃₁	1	2	yes	—
955	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
956	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
957	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
959	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
962	Q₁₆	—	4	1	no	—
963	Q₁₆	—	4	2	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	1	no	—
967	SD₁₆	—	4	1	no	—
968	SD₁₆	—	4	2	no	—
969	SD₁₆	—	4	2	no	—
970	D₈	—	4	1	no	—
971	D₈	—	4	2	no	—
972	M₁₆	—	2	2	no	—
973	M₁₆	—	2	2	no	—
974	M₁₆	—	4	2	no	—
975	C₂×C₈	—	2	2	no	—
976	C₂×C₈	—	2	2	no	—
977	C₂×C₈	—	4	1	no	—
978	C₂×C₈	—	4	1	no	—
979	C₂×C₈	—	4	1	no	—
980	C₂×C₈	—	4	1	no	—
981	C₂×C₈	—	4	2	no	—
982	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
983	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1011	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1013	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1015	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1043	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	2	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	1	no	—
1051	C₄²	—	2	1	no	—
1052	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1053	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1054	C₄²	C₂⁴×C₃₁	1	2	yes	—
1055	C₄²	C₂⁴×C₃₁	1	2	yes	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	4	1	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	1	no	—
1065	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1066	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1067	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	4	2	no	—
1075	Q₈	—	8	2	no	—
1076	Q₈	—	8	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	1	no	—
1092	D₄	—	8	1	no	—
1093	D₄	—	8	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	4	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	1	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1122	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1123	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1124	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1128	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1129	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1130	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	2	no	—
1136	C₈	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	4	4	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	16	2	no	—
1155	C₂²	C₃₁×#537	1	2	yes	—
1156	C₂²	C₃₁×#577	1	2	yes	—
1157	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₃₁×#537	1	2	yes	—
1174	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1175	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	2	2	no	—
1178	C₂	—	4	1	no	—
1179	C₂	—	8	2	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₂×C₃₁×#537	1	1	yes	characteristic
1183	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1184	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 ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3494	C₂	semidirect
3. C₃₁×#3263	C₂	semidirect
4. C₃₁×#3260	C₂	semidirect
5. C₃₁×#3258	C₂	semidirect
6. C₃₁×#3257	C₂	semidirect
7. C₃₁×#3250	C₂	semidirect
8. C₃₁×#3248	C₂	semidirect
9. C₃₁×#3247	C₂	semidirect
10. C₃₁×#3246	C₂	semidirect
11. C₃₁×#3084	C₂	semidirect
12. C₃₁×#3084	C₂	semidirect
13. C₃₁×#3082	C₂	semidirect
14. C₃₁×#3081	C₂	semidirect
15. C₃₁×#3056	C₂	semidirect
16. C₃₁×#3055	C₂	semidirect
17. C₃₁×#3050	C₂	semidirect
18. C₂×C₃₁×#465	C₂	semidirect
19. C₃₁×#3046	C₂	semidirect
20. C₃₁×#3045	C₂	semidirect
21. C₃₁×#3043	C₂	semidirect
22. C₃₁×#3042	C₂	semidirect
23. C₂×C₃₁×#424	C₂	semidirect
45. C₃₁×#542	C₂²	semidirect
46. C₃₁×#541	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
63. C₃₁×#479	C₂²	semidirect
64. C₃₁×#479	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
67. C₃₁×#478	C₂²	semidirect
68. C₃₁×#478	C₂²	semidirect
69. C₃₁×#478	C₂²	semidirect
70. C₃₁×#478	C₂²	semidirect
71. C₃₁×#477	C₂²	semidirect
72. C₃₁×#476	C₂²	semidirect
73. C₃₁×#476	C₂²	semidirect
74. C₃₁×#476	C₂²	semidirect
75. C₃₁×#475	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
84. C₃₁×#467	C₂²	semidirect
85. C₃₁×#467	C₂²	semidirect
87. C₃₁×#466	C₂²	semidirect
88. C₃₁×#466	C₂²	semidirect
94. C₃₁×#465	C₂²	semidirect
95. C₃₁×#465	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
97. C₃₁×#465	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#464	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#464	C₂²	semidirect
102. C₃₁×#464	C₂²	semidirect
103. C₃₁×#463	C₂²	semidirect
104. C₃₁×#463	C₂²	semidirect
105. C₃₁×#463	C₂²	semidirect
106. C₃₁×#463	C₂²	semidirect
107. C₃₁×#462	C₂²	semidirect
108. C₃₁×#461	C₂²	semidirect
109. C₃₁×#461	C₂²	semidirect
110. C₃₁×#461	C₂²	semidirect
111. C₃₁×#460	C₂²	semidirect
112. C₃₁×#460	C₂²	semidirect
113. C₃₁×#460	C₂²	semidirect
114. C₃₁×#459	C₂²	semidirect
123. C₃₁×#424	C₂²	semidirect
124. C₃₁×#424	C₂²	semidirect
125. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
126. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
463. #60935	C₃₁	direct (N × H)
545. #3495	C₂×C₃₁	semidirect
546. #3494	C₂×C₃₁	semidirect
547. #3263	C₂×C₃₁	semidirect
548. #3260	C₂×C₃₁	semidirect
549. #3258	C₂×C₃₁	semidirect
550. #3257	C₂×C₃₁	semidirect
551. #3250	C₂×C₃₁	semidirect
552. #3248	C₂×C₃₁	semidirect
553. #3247	C₂×C₃₁	semidirect
554. #3246	C₂×C₃₁	semidirect
555. #3084	C₂×C₃₁	semidirect
556. #3084	C₂×C₃₁	semidirect
557. #3082	C₂×C₃₁	semidirect
558. #3081	C₂×C₃₁	semidirect
559. #3056	C₂×C₃₁	semidirect
560. #3055	C₂×C₃₁	semidirect
561. #3050	C₂×C₃₁	semidirect
562. C₂×#465	C₂×C₃₁	semidirect
563. #3046	C₂×C₃₁	semidirect
564. #3045	C₂×C₃₁	semidirect
565. #3043	C₂×C₃₁	semidirect
566. #3042	C₂×C₃₁	semidirect
567. C₂×#424	C₂×C₃₁	semidirect
628. #542	C₂²×C₃₁	semidirect
629. #541	C₂²×C₃₁	semidirect
633. #533	C₂²×C₃₁	semidirect
636. #529	C₂²×C₃₁	semidirect
646. #479	C₂²×C₃₁	semidirect
647. #479	C₂²×C₃₁	semidirect
648. #479	C₂²×C₃₁	semidirect
649. #479	C₂²×C₃₁	semidirect
650. #478	C₂²×C₃₁	semidirect
651. #478	C₂²×C₃₁	semidirect
652. #478	C₂²×C₃₁	semidirect
653. #478	C₂²×C₃₁	semidirect
654. #477	C₂²×C₃₁	semidirect
655. #476	C₂²×C₃₁	semidirect
656. #476	C₂²×C₃₁	semidirect
657. #476	C₂²×C₃₁	semidirect
658. #475	C₂²×C₃₁	semidirect
659. #475	C₂²×C₃₁	semidirect
660. #475	C₂²×C₃₁	semidirect
661. #474	C₂²×C₃₁	semidirect
662. #470	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
666. #467	C₂²×C₃₁	semidirect
667. #467	C₂²×C₃₁	semidirect
668. #467	C₂²×C₃₁	semidirect
670. #466	C₂²×C₃₁	semidirect
671. #466	C₂²×C₃₁	semidirect
677. #465	C₂²×C₃₁	semidirect
678. #465	C₂²×C₃₁	semidirect
679. #465	C₂²×C₃₁	semidirect
680. #465	C₂²×C₃₁	semidirect
681. #465	C₂²×C₃₁	semidirect
682. #464	C₂²×C₃₁	semidirect
683. #464	C₂²×C₃₁	semidirect
684. #464	C₂²×C₃₁	semidirect
685. #464	C₂²×C₃₁	semidirect
686. #463	C₂²×C₃₁	semidirect
687. #463	C₂²×C₃₁	semidirect
688. #463	C₂²×C₃₁	semidirect
689. #463	C₂²×C₃₁	semidirect
690. #462	C₂²×C₃₁	semidirect
691. #461	C₂²×C₃₁	semidirect
692. #461	C₂²×C₃₁	semidirect
693. #461	C₂²×C₃₁	semidirect
694. #460	C₂²×C₃₁	semidirect
695. #460	C₂²×C₃₁	semidirect
696. #460	C₂²×C₃₁	semidirect
697. #459	C₂²×C₃₁	semidirect
706. #424	C₂²×C₃₁	semidirect
707. #424	C₂²×C₃₁	semidirect
708. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
709. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
910. C₃₁	#60935	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×#3495	2
C₃₁×#3494	2
C₃₁×#3263	2
C₃₁×#3260	2
C₃₁×#3258	2
C₃₁×#3257	2
C₃₁×#3250	2
C₃₁×#3248	2
C₃₁×#3247	2
C₃₁×#3246	2
C₃₁×#3084	2
C₃₁×#3082	2
C₃₁×#3081	2
C₃₁×#3056	2
C₃₁×#3055	2
C₃₁×#3050	2
C₂×C₃₁×#465	2
C₃₁×#3046	2
C₃₁×#3045	2
C₃₁×#3043	2
C₃₁×#3042	2
C₂×C₃₁×#424	2
#60935	31

Subgroups — C31×#60935 #21517694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60935 #21517694