Subgroups — C₃₁×#61660 #21518419

Order 7936.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3333	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3329	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3276	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3104	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3011	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2979	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	—
25	C₂×C₃₁×#137	C₂²	1	2	yes	—
26	C₂×C₃₁×#137	C₂²	1	2	yes	—
27	C₂×C₃₁×#135	C₂²	1	2	yes	—
28	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#562	—	2	2	no	—
30	C₃₁×#555	—	2	1	no	—
31	C₃₁×#555	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#552	C₂²	1	2	yes	—
35	C₃₁×#550	—	2	1	no	—
36	C₃₁×#550	C₂²	1	1	yes	characteristic
37	C₃₁×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₃₁	—	2	1	no	—
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#548	—	2	2	no	—
43	C₃₁×#548	C₂²	1	2	yes	—
44	C₃₁×#548	C₂²	1	2	yes	—
45	C₃₁×#548	C₂²	1	2	yes	—
46	C₃₁×#547	C₂²	1	1	yes	characteristic
47	C₃₁×#544	—	2	1	no	—
48	C₃₁×#542	—	2	2	no	—
49	C₃₁×#540	—	2	1	no	—
50	C₃₁×#537	—	2	2	no	—
51	C₃₁×#537	C₂²	1	2	yes	—
52	C₃₁×#537	C₂²	1	2	yes	—
53	C₃₁×#536	C₂²	1	2	yes	—
54	C₃₁×#533	C₂²	1	1	yes	characteristic
55	C₃₁×#532	—	2	1	no	—
56	C₃₁×#532	—	2	1	no	—
57	C₃₁×#532	C₂²	1	1	yes	characteristic
58	C₃₁×#532	C₂²	1	1	yes	characteristic
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#488	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	1	yes	characteristic
66	C₃₁×#486	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#484	C₂²	1	2	yes	—
70	C₃₁×#483	C₂²	1	1	yes	characteristic
71	C₃₁×#482	C₂²	1	2	yes	—
72	C₃₁×#480	C₂²	1	2	yes	—
73	C₃₁×#480	C₂²	1	1	yes	characteristic
74	C₃₁×#479	C₂²	1	1	yes	characteristic
75	C₃₁×#479	C₂²	1	1	yes	characteristic
76	C₃₁×#477	C₂²	1	1	yes	characteristic
77	C₃₁×#477	C₂²	1	1	yes	characteristic
78	C₃₁×#470	C₂²	1	2	yes	—
79	C₃₁×#468	C₂²	1	2	yes	—
80	C₃₁×#468	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	—
82	C₃₁×#467	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#466	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	1	yes	characteristic
87	C₃₁×#464	C₂²	1	1	yes	characteristic
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#464	C₂²	1	2	yes	—
90	C₃₁×#462	C₂²	1	1	yes	characteristic
91	C₃₁×#462	C₂²	1	1	yes	characteristic
92	C₃₁×#462	C₂²	1	1	yes	characteristic
93	C₃₁×#461	C₂²	1	1	yes	characteristic
94	C₃₁×#460	C₂²	1	1	yes	characteristic
95	C₃₁×#459	C₂²	1	1	yes	characteristic
96	C₃₁×#452	C₂²	1	2	yes	—
97	C₃₁×#452	C₂²	1	2	yes	—
98	C₃₁×#452	C₂²	1	2	yes	—
99	C₃₁×#452	C₂²	1	2	yes	—
100	C₃₁×#452	C₂²	1	2	yes	—
101	C₃₁×#452	C₂²	1	2	yes	—
102	C₃₁×#452	C₂²	1	2	yes	—
103	C₃₁×#451	C₂²	1	2	yes	—
104	C₃₁×#451	C₂²	1	1	yes	characteristic
105	C₃₁×#451	C₂²	1	2	yes	—
106	C₃₁×#451	C₂²	1	2	yes	—
107	C₃₁×#451	C₂²	1	2	yes	—
108	C₃₁×#451	C₂²	1	2	yes	—
109	C₃₁×#449	C₂²	1	2	yes	—
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#449	C₂²	1	2	yes	—
112	C₃₁×#448	C₂²	1	1	yes	characteristic
113	C₃₁×#448	C₂²	1	2	yes	—
114	C₃₁×#448	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	2	yes	—
123	C₃₁×#436	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₃₁	C₂²	1	2	yes	—
126	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
127	C₃₁×#431	C₂²	1	1	yes	characteristic
128	C₃₁×#431	C₂²	1	1	yes	characteristic
129	C₃₁×#419	C₂²	1	2	yes	—
130	C₃₁×#417	C₂²	1	2	yes	—
131	C₃₁×#416	C₂²	1	2	yes	—
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₃₁×#408	C₂²	1	2	yes	—
134	C₃₁×#408	C₂²	1	2	yes	—
135	C₃₁×2₋¹⁺⁴	—	4	4	no	—
136	C₃₁×2₋¹⁺⁴	—	4	4	no	—
137	C₂×#41×C₃₁	—	2	2	no	—
138	C₂×#41×C₃₁	—	2	2	no	—
139	C₂×#41×C₃₁	—	2	2	no	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	2	yes	—
142	C₂×#41×C₃₁	C₂³	1	2	yes	—
143	C₂×#41×C₃₁	C₂³	1	2	yes	—
144	C₂×#41×C₃₁	C₂³	1	2	yes	—
145	C₂²×Q₈×C₃₁	—	2	2	no	—
146	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₃₁×#137	—	4	4	no	—
151	C₃₁×#137	—	4	4	no	—
152	C₃₁×#135	—	4	4	no	—
153	C₂×Q₁₆×C₃₁	—	4	4	no	—
154	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂×D₈×C₃₁	C₂³	1	2	yes	—
168	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
169	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
170	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
171	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
172	C₃₁×C₄⋊Q₈	—	2	2	no	—
173	C₃₁×C₄⋊Q₈	—	2	1	no	—
174	C₃₁×C₄⋊Q₈	—	2	1	no	—
175	C₃₁×C₄⋊Q₈	—	2	1	no	—
176	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
177	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
178	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
179	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
180	C₃₁×#127	—	2	1	no	—
181	C₃₁×#127	—	2	1	no	—
182	C₃₁×#127	D₄	1	1	yes	characteristic
183	C₃₁×#127	C₂³	1	1	yes	characteristic
184	C₃₁×#126	—	2	2	no	—
185	C₃₁×#126	—	2	1	no	—
186	C₃₁×#125	—	2	2	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	—	2	1	no	—
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#124	—	2	2	no	—
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	—	2	2	no	—
194	C₃₁×#124	—	2	2	no	—
195	C₃₁×#124	D₄	1	2	yes	—
196	C₃₁×#124	C₂³	1	2	yes	—
197	C₃₁×#124	C₂³	1	1	yes	characteristic
198	C₃₁×#123	—	2	2	no	—
199	C₃₁×#123	—	2	2	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	—	2	2	no	—
204	C₃₁×C₂²⋊Q₈	—	2	2	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	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	2	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
214	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	—	2	2	no	—
226	C₃₁×#121	—	2	2	no	—
227	C₃₁×#121	—	2	2	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	—	2	2	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	2	no	—
234	C₃₁×#121	—	2	2	no	—
235	C₃₁×#121	D₄	1	1	yes	characteristic
236	C₃₁×#121	D₄	1	1	yes	characteristic
237	C₃₁×#121	D₄	1	2	yes	—
238	C₃₁×#121	C₂³	1	1	yes	characteristic
239	C₃₁×#121	C₂³	1	2	yes	—
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#121	C₂³	1	2	yes	—
242	C₄×Q₈×C₃₁	—	2	1	no	—
243	C₄×Q₈×C₃₁	—	2	1	no	—
244	C₄×Q₈×C₃₁	—	2	1	no	—
245	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
249	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	—	2	1	no	—
252	C₄×D₄×C₃₁	—	2	1	no	—
253	C₄×D₄×C₃₁	—	2	1	no	—
254	C₄×D₄×C₃₁	—	2	1	no	—
255	C₄×D₄×C₃₁	—	2	1	no	—
256	C₄×D₄×C₃₁	—	2	1	no	—
257	C₄×D₄×C₃₁	—	2	1	no	—
258	C₄×D₄×C₃₁	—	2	2	no	—
259	C₄×D₄×C₃₁	—	2	2	no	—
260	C₄×D₄×C₃₁	—	2	2	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₃₁	C₂³	1	2	yes	—
266	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₃₁×#117	—	2	1	no	—
268	C₃₁×#117	—	2	1	no	—
269	C₃₁×#117	—	2	2	no	—
270	C₃₁×#117	—	2	1	no	—
271	C₃₁×#117	C₂³	1	2	yes	—
272	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
273	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₃₁	—	2	1	no	—
277	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
278	C₃₁×#107	C₂³	1	2	yes	—
279	C₃₁×#107	C₂³	1	1	yes	characteristic
280	C₃₁×#107	C₂³	1	2	yes	—
281	C₃₁×#107	C₂³	1	1	yes	characteristic
282	C₃₁×#106	C₂³	1	1	yes	characteristic
283	C₃₁×#106	C₂³	1	1	yes	characteristic
284	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₃₁×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×#102	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₃₁	C₂³	1	2	yes	—
318	#41×C₃₁	—	2	4	no	—
319	#41×C₃₁	—	2	4	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	2	no	—
322	#41×C₃₁	—	4	2	no	—
323	#41×C₃₁	—	4	2	no	—
324	#41×C₃₁	—	4	2	no	—
325	#41×C₃₁	—	4	2	no	—
326	#41×C₃₁	—	4	8	no	—
327	#41×C₃₁	—	4	8	no	—
328	#41×C₃₁	—	4	2	no	—
329	#41×C₃₁	—	4	2	no	—
330	#41×C₃₁	—	4	8	no	—
331	C₂×Q₈×C₃₁	—	2	2	no	—
332	C₂×Q₈×C₃₁	—	2	2	no	—
333	C₂×Q₈×C₃₁	—	2	1	no	—
334	C₂×Q₈×C₃₁	—	2	2	no	—
335	C₂×Q₈×C₃₁	—	2	2	no	—
336	C₂×Q₈×C₃₁	—	2	1	no	—
337	C₂×Q₈×C₃₁	—	2	2	no	—
338	C₂×Q₈×C₃₁	—	2	4	no	—
339	C₂×Q₈×C₃₁	—	2	4	no	—
340	C₂×Q₈×C₃₁	—	4	2	no	—
341	C₂×Q₈×C₃₁	—	4	2	no	—
342	C₂×Q₈×C₃₁	—	4	2	no	—
343	C₂×Q₈×C₃₁	—	4	2	no	—
344	C₂×Q₈×C₃₁	—	4	8	no	—
345	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
346	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
347	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
349	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	—	2	2	no	—
352	C₂×D₄×C₃₁	—	2	2	no	—
353	C₂×D₄×C₃₁	—	2	2	no	—
354	C₂×D₄×C₃₁	—	2	1	no	—
355	C₂×D₄×C₃₁	—	2	2	no	—
356	C₂×D₄×C₃₁	—	2	2	no	—
357	C₂×D₄×C₃₁	—	2	2	no	—
358	C₂×D₄×C₃₁	—	2	2	no	—
359	C₂×D₄×C₃₁	—	2	1	no	—
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
366	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
368	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	2	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	—	2	2	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
384	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
385	Q₁₆×C₃₁	—	2	2	no	—
386	Q₁₆×C₃₁	—	2	4	no	—
387	Q₁₆×C₃₁	—	2	2	no	—
388	Q₁₆×C₃₁	—	2	4	no	—
389	Q₁₆×C₃₁	—	4	2	no	—
390	Q₁₆×C₃₁	—	4	2	no	—
391	Q₁₆×C₃₁	—	4	2	no	—
392	SD₁₆×C₃₁	—	2	2	no	—
393	SD₁₆×C₃₁	—	2	2	no	—
394	SD₁₆×C₃₁	—	4	2	no	—
395	SD₁₆×C₃₁	—	4	2	no	—
396	SD₁₆×C₃₁	—	4	2	no	—
397	SD₁₆×C₃₁	—	4	2	no	—
398	D₈×C₃₁	—	4	2	no	—
399	M₁₆×C₃₁	—	4	2	no	—
400	M₁₆×C₃₁	—	4	2	no	—
401	C₂×C₈×C₃₁	—	4	2	no	—
402	C₂×C₈×C₃₁	—	4	2	no	—
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
406	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
408	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	—	2	1	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	1	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	1	no	—
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	—	2	1	no	—
424	C₄⋊C₄×C₃₁	—	2	2	no	—
425	C₄⋊C₄×C₃₁	—	2	2	no	—
426	C₄⋊C₄×C₃₁	—	2	2	no	—
427	C₄⋊C₄×C₃₁	—	2	2	no	—
428	C₄⋊C₄×C₃₁	—	2	1	no	—
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	1	no	—
431	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
433	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
437	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₂²⋊C₄×C₃₁	—	2	2	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	2	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	1	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	—	2	1	no	—
452	C₂²⋊C₄×C₃₁	—	2	2	no	—
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	2	no	—
455	C₂²⋊C₄×C₃₁	—	2	1	no	—
456	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
457	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
458	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
459	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
460	C₄²×C₃₁	—	2	1	no	—
461	C₄²×C₃₁	—	2	1	no	—
462	C₄²×C₃₁	—	2	1	no	—
463	C₄²×C₃₁	—	2	1	no	—
464	C₄²×C₃₁	—	2	2	no	—
465	C₄²×C₃₁	—	2	2	no	—
466	C₄²×C₃₁	—	2	1	no	—
467	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
468	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
470	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
471	#61660	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
472	C₂³×C₃₁	—	2	1	no	—
473	C₂³×C₃₁	—	2	2	no	—
474	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
475	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
476	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
477	Q₈×C₃₁	—	2	4	no	—
478	Q₈×C₃₁	—	2	1	no	—
479	Q₈×C₃₁	—	2	1	no	—
480	Q₈×C₃₁	—	2	1	no	—
481	Q₈×C₃₁	—	2	2	no	—
482	Q₈×C₃₁	—	2	2	no	—
483	Q₈×C₃₁	—	2	2	no	—
484	Q₈×C₃₁	—	2	1	no	—
485	Q₈×C₃₁	—	2	2	no	—
486	Q₈×C₃₁	—	4	2	no	—
487	Q₈×C₃₁	—	4	4	no	—
488	Q₈×C₃₁	—	4	4	no	—
489	Q₈×C₃₁	—	8	1	no	—
490	Q₈×C₃₁	—	8	2	no	—
491	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
492	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
493	D₄×C₃₁	—	2	2	no	—
494	D₄×C₃₁	—	2	2	no	—
495	D₄×C₃₁	—	2	1	no	—
496	D₄×C₃₁	—	2	2	no	—
497	D₄×C₃₁	—	2	1	no	—
498	D₄×C₃₁	—	2	2	no	—
499	D₄×C₃₁	—	4	2	no	—
500	D₄×C₃₁	—	4	2	no	—
501	D₄×C₃₁	—	4	2	no	—
502	D₄×C₃₁	—	4	2	no	—
503	D₄×C₃₁	—	4	4	no	—
504	D₄×C₃₁	—	4	4	no	—
505	D₄×C₃₁	—	4	4	no	—
506	D₄×C₃₁	—	4	2	no	—
507	D₄×C₃₁	—	8	1	no	—
508	D₄×C₃₁	—	8	1	no	—
509	D₄×C₃₁	—	8	2	no	—
510	D₄×C₃₁	—	8	2	no	—
511	D₄×C₃₁	—	8	2	no	—
512	D₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	—	2	4	no	—
514	C₂×C₄×C₃₁	—	2	1	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	2	no	—
519	C₂×C₄×C₃₁	—	2	2	no	—
520	C₂×C₄×C₃₁	—	2	2	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	1	no	—
523	C₂×C₄×C₃₁	—	2	1	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	1	no	—
526	C₂×C₄×C₃₁	—	2	2	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	2	no	—
530	C₂×C₄×C₃₁	—	2	2	no	—
531	C₂×C₄×C₃₁	—	4	1	no	—
532	C₂×C₄×C₃₁	—	4	4	no	—
533	C₂×C₄×C₃₁	—	4	4	no	—
534	C₂×C₄×C₃₁	—	4	4	no	—
535	C₂×C₄×C₃₁	—	4	4	no	—
536	C₂×C₄×C₃₁	—	4	4	no	—
537	C₂×C₄×C₃₁	—	4	2	no	—
538	C₂×C₄×C₃₁	—	8	2	no	—
539	C₂×C₄×C₃₁	—	8	2	no	—
540	C₂×C₄×C₃₁	—	8	1	no	—
541	C₂×C₄×C₃₁	—	8	2	no	—
542	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
550	C₈×C₃₁	—	2	2	no	—
551	C₈×C₃₁	—	2	1	no	—
552	C₈×C₃₁	—	2	1	no	—
553	C₈×C₃₁	—	2	1	no	—
554	C₈×C₃₁	—	2	1	no	—
555	C₈×C₃₁	—	2	2	no	—
556	#3547	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3497	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3333	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3329	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3327	C₂×C₃₁	1	2	yes	complemented
561	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3300	C₂×C₃₁	1	2	yes	complemented
563	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
564	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3285	C₂×C₃₁	1	2	yes	complemented
566	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#3278	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3277	C₂×C₃₁	1	2	yes	complemented
569	#3276	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
571	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
572	#3203	C₂×C₃₁	1	2	yes	complemented
573	#3201	C₂×C₃₁	1	2	yes	complemented
574	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#3104	C₂×C₃₁	1	1	yes	characteristic, complemented
576	#3013	C₂×C₃₁	1	2	yes	complemented
577	#3011	C₂×C₃₁	1	2	yes	complemented
578	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
579	C₂²×C₃₁	—	2	1	no	—
580	C₂²×C₃₁	—	2	2	no	—
581	C₂²×C₃₁	—	2	2	no	—
582	C₂²×C₃₁	—	2	1	no	—
583	C₂²×C₃₁	—	2	2	no	—
584	C₂²×C₃₁	—	2	2	no	—
585	C₂²×C₃₁	—	2	1	no	—
586	C₂²×C₃₁	—	2	2	no	—
587	C₂²×C₃₁	—	2	2	no	—
588	C₂²×C₃₁	—	4	2	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	4	2	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	1	no	—
593	C₂²×C₃₁	—	4	2	no	—
594	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
595	C₄×C₃₁	—	2	1	no	—
596	C₄×C₃₁	—	2	1	no	—
597	C₄×C₃₁	—	2	2	no	—
598	C₄×C₃₁	—	2	2	no	—
599	C₄×C₃₁	—	2	1	no	—
600	C₄×C₃₁	—	2	2	no	—
601	C₄×C₃₁	—	2	2	no	—
602	C₄×C₃₁	—	2	1	no	—
603	C₄×C₃₁	—	4	1	no	—
604	C₄×C₃₁	—	4	1	no	—
605	C₄×C₃₁	—	4	1	no	—
606	C₄×C₃₁	—	4	2	no	—
607	C₄×C₃₁	—	4	2	no	—
608	C₄×C₃₁	—	4	2	no	—
609	C₄×C₃₁	—	4	1	no	—
610	C₄×C₃₁	—	4	1	no	—
611	C₄×C₃₁	#578	1	2	yes	—
612	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	—
615	C₂×#137	C₂²×C₃₁	1	2	yes	—
616	C₂×#137	C₂²×C₃₁	1	2	yes	—
617	C₂×#135	C₂²×C₃₁	1	2	yes	—
618	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
619	#562	—	2	2	no	—
620	#555	—	2	1	no	—
621	#555	C₂²×C₃₁	1	1	yes	characteristic
622	#554	C₂²×C₃₁	1	1	yes	characteristic
623	#553	—	2	1	no	—
624	#552	C₂²×C₃₁	1	2	yes	—
625	#550	—	2	1	no	—
626	#550	C₂²×C₃₁	1	1	yes	characteristic
627	#550	C₂²×C₃₁	1	1	yes	characteristic
628	D₄×Q₈	—	2	1	no	—
629	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
630	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
631	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
632	#548	—	2	2	no	—
633	#548	C₂²×C₃₁	1	2	yes	—
634	#548	C₂²×C₃₁	1	2	yes	—
635	#548	C₂²×C₃₁	1	2	yes	—
636	#547	C₂²×C₃₁	1	1	yes	characteristic
637	#544	—	2	1	no	—
638	#542	—	2	2	no	—
639	#540	—	2	1	no	—
640	#537	—	2	2	no	—
641	#537	C₂²×C₃₁	1	2	yes	—
642	#537	C₂²×C₃₁	1	2	yes	—
643	#536	C₂²×C₃₁	1	2	yes	—
644	#533	C₂²×C₃₁	1	1	yes	characteristic
645	#532	—	2	1	no	—
646	#532	—	2	1	no	—
647	#532	C₂²×C₃₁	1	1	yes	characteristic
648	#532	C₂²×C₃₁	1	1	yes	characteristic
649	#529	C₂²×C₃₁	1	1	yes	characteristic
650	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
651	#495	C₂²×C₃₁	1	2	yes	—
652	#494	C₂²×C₃₁	1	1	yes	characteristic
653	#492	C₂²×C₃₁	1	1	yes	characteristic
654	#488	C₂²×C₃₁	1	2	yes	—
655	#487	C₂²×C₃₁	1	1	yes	characteristic
656	#486	C₂²×C₃₁	1	1	yes	characteristic
657	#485	C₂²×C₃₁	1	2	yes	—
658	#484	C₂²×C₃₁	1	2	yes	—
659	#484	C₂²×C₃₁	1	2	yes	—
660	#483	C₂²×C₃₁	1	1	yes	characteristic
661	#482	C₂²×C₃₁	1	2	yes	—
662	#480	C₂²×C₃₁	1	2	yes	—
663	#480	C₂²×C₃₁	1	1	yes	characteristic
664	#479	C₂²×C₃₁	1	1	yes	characteristic
665	#479	C₂²×C₃₁	1	1	yes	characteristic
666	#477	C₂²×C₃₁	1	1	yes	characteristic
667	#477	C₂²×C₃₁	1	1	yes	characteristic
668	#470	C₂²×C₃₁	1	2	yes	—
669	#468	C₂²×C₃₁	1	2	yes	—
670	#468	C₂²×C₃₁	1	2	yes	—
671	#468	C₂²×C₃₁	1	2	yes	—
672	#467	C₂²×C₃₁	1	2	yes	—
673	#467	C₂²×C₃₁	1	2	yes	—
674	#466	C₂²×C₃₁	1	2	yes	—
675	#465	C₂²×C₃₁	1	2	yes	—
676	#464	C₂²×C₃₁	1	1	yes	characteristic
677	#464	C₂²×C₃₁	1	1	yes	characteristic
678	#464	C₂²×C₃₁	1	2	yes	—
679	#464	C₂²×C₃₁	1	2	yes	—
680	#462	C₂²×C₃₁	1	1	yes	characteristic
681	#462	C₂²×C₃₁	1	1	yes	characteristic
682	#462	C₂²×C₃₁	1	1	yes	characteristic
683	#461	C₂²×C₃₁	1	1	yes	characteristic
684	#460	C₂²×C₃₁	1	1	yes	characteristic
685	#459	C₂²×C₃₁	1	1	yes	characteristic
686	#452	C₂²×C₃₁	1	2	yes	—
687	#452	C₂²×C₃₁	1	2	yes	—
688	#452	C₂²×C₃₁	1	2	yes	—
689	#452	C₂²×C₃₁	1	2	yes	—
690	#452	C₂²×C₃₁	1	2	yes	—
691	#452	C₂²×C₃₁	1	2	yes	—
692	#452	C₂²×C₃₁	1	2	yes	—
693	#451	C₂²×C₃₁	1	2	yes	—
694	#451	C₂²×C₃₁	1	1	yes	characteristic
695	#451	C₂²×C₃₁	1	2	yes	—
696	#451	C₂²×C₃₁	1	2	yes	—
697	#451	C₂²×C₃₁	1	2	yes	—
698	#451	C₂²×C₃₁	1	2	yes	—
699	#449	C₂²×C₃₁	1	2	yes	—
700	#449	C₂²×C₃₁	1	2	yes	—
701	#449	C₂²×C₃₁	1	2	yes	—
702	#448	C₂²×C₃₁	1	2	yes	—
703	#448	C₂²×C₃₁	1	1	yes	characteristic
704	#448	C₂²×C₃₁	1	2	yes	—
705	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
706	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
707	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
708	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
709	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
710	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
711	#436	C₂²×C₃₁	1	1	yes	characteristic
712	#436	C₂²×C₃₁	1	1	yes	characteristic
713	#436	C₂²×C₃₁	1	2	yes	—
714	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
715	C₈×D₄	C₂²×C₃₁	1	2	yes	—
716	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
717	#431	C₂²×C₃₁	1	1	yes	characteristic
718	#431	C₂²×C₃₁	1	1	yes	characteristic
719	#419	C₂²×C₃₁	1	2	yes	—
720	#417	C₂²×C₃₁	1	2	yes	—
721	#416	C₂²×C₃₁	1	2	yes	—
722	C₂×#103	C₂²×C₃₁	1	2	yes	—
723	#408	C₂²×C₃₁	1	2	yes	—
724	#408	C₂²×C₃₁	1	2	yes	—
725	C₂×C₃₁	—	4	1	no	—
726	C₂×C₃₁	—	4	2	no	—
727	C₂×C₃₁	—	4	2	no	—
728	C₂×C₃₁	—	8	2	no	—
729	C₂×C₃₁	—	8	1	no	—
730	C₂×C₃₁	#3484	1	1	yes	characteristic
731	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
732	C₂×C₃₁	#3584	1	1	yes	characteristic
733	2₋¹⁺⁴	—	4	4	no	—
734	2₋¹⁺⁴	—	4	4	no	—
735	C₂×#41	—	2	2	no	—
736	C₂×#41	—	2	2	no	—
737	C₂×#41	—	2	2	no	—
738	C₂×#41	C₂³×C₃₁	1	2	yes	—
739	C₂×#41	C₂³×C₃₁	1	2	yes	—
740	C₂×#41	C₂³×C₃₁	1	2	yes	—
741	C₂×#41	C₂³×C₃₁	1	2	yes	—
742	C₂×#41	C₂³×C₃₁	1	2	yes	—
743	C₂²×Q₈	—	2	2	no	—
744	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
745	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
746	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
747	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
748	#137	—	4	4	no	—
749	#137	—	4	4	no	—
750	#135	—	4	4	no	—
751	C₂×Q₁₆	—	4	4	no	—
752	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
753	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
754	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
755	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
756	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
757	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
758	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
759	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
765	C₂×D₈	C₂³×C₃₁	1	2	yes	—
766	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
767	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
768	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
769	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
770	C₄⋊Q₈	—	2	2	no	—
771	C₄⋊Q₈	—	2	1	no	—
772	C₄⋊Q₈	—	2	1	no	—
773	C₄⋊Q₈	—	2	1	no	—
774	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
775	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
776	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
777	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	#127	—	2	1	no	—
779	#127	—	2	1	no	—
780	#127	D₄×C₃₁	1	1	yes	characteristic
781	#127	C₂³×C₃₁	1	1	yes	characteristic
782	#126	—	2	2	no	—
783	#126	—	2	1	no	—
784	#125	—	2	2	no	—
785	#125	—	2	1	no	—
786	#125	—	2	1	no	—
787	#125	C₂³×C₃₁	1	1	yes	characteristic
788	#124	—	2	2	no	—
789	#124	—	2	2	no	—
790	#124	—	2	2	no	—
791	#124	—	2	2	no	—
792	#124	—	2	2	no	—
793	#124	D₄×C₃₁	1	2	yes	—
794	#124	C₂³×C₃₁	1	1	yes	characteristic
795	#124	C₂³×C₃₁	1	2	yes	—
796	#123	—	2	2	no	—
797	#123	—	2	2	no	—
798	#123	—	2	2	no	—
799	#123	—	2	1	no	—
800	#123	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	—	2	1	no	—
804	C₂²⋊Q₈	—	2	2	no	—
805	C₂²⋊Q₈	—	2	2	no	—
806	C₂²⋊Q₈	—	2	2	no	—
807	C₂²⋊Q₈	—	2	2	no	—
808	C₂²⋊Q₈	—	2	2	no	—
809	C₂²⋊Q₈	—	2	2	no	—
810	C₂²⋊Q₈	—	2	2	no	—
811	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
812	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
813	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
814	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
815	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
816	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
817	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	1	no	—
827	#121	—	2	2	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	D₄×C₃₁	1	1	yes	characteristic
834	#121	D₄×C₃₁	1	1	yes	characteristic
835	#121	D₄×C₃₁	1	2	yes	—
836	#121	C₂³×C₃₁	1	1	yes	characteristic
837	#121	C₂³×C₃₁	1	2	yes	—
838	#121	C₂³×C₃₁	1	2	yes	—
839	#121	C₂³×C₃₁	1	2	yes	—
840	C₄×Q₈	—	2	1	no	—
841	C₄×Q₈	—	2	1	no	—
842	C₄×Q₈	—	2	1	no	—
843	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
844	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
845	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
846	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
847	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
863	C₄×D₄	C₂³×C₃₁	1	2	yes	—
864	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
865	#117	—	2	1	no	—
866	#117	—	2	1	no	—
867	#117	—	2	2	no	—
868	#117	—	2	1	no	—
869	#117	C₂³×C₃₁	1	2	yes	—
870	C₂×C₄⋊C₄	—	2	1	no	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
874	C₂×C₄²	—	2	1	no	—
875	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
876	#107	C₂³×C₃₁	1	2	yes	—
877	#107	C₂³×C₃₁	1	1	yes	characteristic
878	#107	C₂³×C₃₁	1	2	yes	—
879	#107	C₂³×C₃₁	1	1	yes	characteristic
880	#106	C₂³×C₃₁	1	1	yes	characteristic
881	#106	C₂³×C₃₁	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
884	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
886	#103	C₂³×C₃₁	1	1	yes	characteristic
887	#103	C₂³×C₃₁	1	2	yes	—
888	#103	C₂³×C₃₁	1	2	yes	—
889	#103	C₂³×C₃₁	1	2	yes	—
890	#103	C₂³×C₃₁	1	1	yes	characteristic
891	#103	C₂³×C₃₁	1	1	yes	characteristic
892	#103	C₂³×C₃₁	1	2	yes	—
893	#103	C₂³×C₃₁	1	1	yes	characteristic
894	#103	C₂³×C₃₁	1	2	yes	—
895	#103	C₂³×C₃₁	1	2	yes	—
896	#103	C₂³×C₃₁	1	1	yes	characteristic
897	#103	C₂³×C₃₁	1	2	yes	—
898	#103	C₂³×C₃₁	1	2	yes	—
899	#103	C₂³×C₃₁	1	1	yes	characteristic
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	2	yes	—
903	#102	C₂³×C₃₁	1	2	yes	—
904	#102	C₂³×C₃₁	1	1	yes	characteristic
905	#102	C₂³×C₃₁	1	1	yes	characteristic
906	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
907	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
913	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
914	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
915	C₄×C₈	C₂³×C₃₁	1	2	yes	—
916	C₃₁	#61660	1	1	yes	characteristic, direct product factor, Sylow
917	#41	—	2	4	no	—
918	#41	—	2	4	no	—
919	#41	—	4	2	no	—
920	#41	—	4	2	no	—
921	#41	—	4	2	no	—
922	#41	—	4	2	no	—
923	#41	—	4	2	no	—
924	#41	—	4	2	no	—
925	#41	—	4	8	no	—
926	#41	—	4	8	no	—
927	#41	—	4	2	no	—
928	#41	—	4	2	no	—
929	#41	—	4	8	no	—
930	C₂×Q₈	—	2	2	no	—
931	C₂×Q₈	—	2	2	no	—
932	C₂×Q₈	—	2	1	no	—
933	C₂×Q₈	—	2	2	no	—
934	C₂×Q₈	—	2	2	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	4	no	—
938	C₂×Q₈	—	2	4	no	—
939	C₂×Q₈	—	4	2	no	—
940	C₂×Q₈	—	4	2	no	—
941	C₂×Q₈	—	4	2	no	—
942	C₂×Q₈	—	4	2	no	—
943	C₂×Q₈	—	4	8	no	—
944	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
945	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
946	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
948	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
962	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
963	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
964	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
965	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
966	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
967	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	2	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	2	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	2	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
980	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
982	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
983	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
984	Q₁₆	—	2	2	no	—
985	Q₁₆	—	2	4	no	—
986	Q₁₆	—	2	2	no	—
987	Q₁₆	—	2	4	no	—
988	Q₁₆	—	4	2	no	—
989	Q₁₆	—	4	2	no	—
990	Q₁₆	—	4	2	no	—
991	SD₁₆	—	2	2	no	—
992	SD₁₆	—	2	2	no	—
993	SD₁₆	—	4	2	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	2	no	—
997	D₈	—	4	2	no	—
998	M₁₆	—	4	2	no	—
999	M₁₆	—	4	2	no	—
1000	C₂×C₈	—	4	2	no	—
1001	C₂×C₈	—	4	2	no	—
1002	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1003	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1005	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1007	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1033	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1035	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1036	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	2	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1059	C₄²	—	2	1	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1067	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1070	C₂³	—	2	1	no	—
1071	C₂³	—	2	2	no	—
1072	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1073	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1074	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1075	Q₈	—	2	4	no	—
1076	Q₈	—	2	1	no	—
1077	Q₈	—	2	1	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	2	no	—
1080	Q₈	—	2	2	no	—
1081	Q₈	—	2	2	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	2	no	—
1084	Q₈	—	4	2	no	—
1085	Q₈	—	4	4	no	—
1086	Q₈	—	4	4	no	—
1087	Q₈	—	8	1	no	—
1088	Q₈	—	8	2	no	—
1089	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1090	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1091	D₄	—	2	2	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	2	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	4	4	no	—
1102	D₄	—	4	4	no	—
1103	D₄	—	4	4	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	8	1	no	—
1106	D₄	—	8	1	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	2	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	4	1	no	—
1130	C₂×C₄	—	4	4	no	—
1131	C₂×C₄	—	4	4	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	4	no	—
1135	C₂×C₄	—	4	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	1	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1141	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1142	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1143	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1144	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1145	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1146	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1147	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1148	C₈	—	2	2	no	—
1149	C₈	—	2	1	no	—
1150	C₈	—	2	1	no	—
1151	C₈	—	2	1	no	—
1152	C₈	—	2	1	no	—
1153	C₈	—	2	2	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	2	1	no	—
1158	C₂²	—	2	2	no	—
1159	C₂²	—	2	2	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	2	no	—
1162	C₂²	—	2	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	2	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1170	C₄	—	2	2	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	2	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	1	no	—
1185	C₄	—	4	2	no	—
1186	C₄	C₃₁×#578	1	2	yes	—
1187	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1188	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1189	C₂	—	4	1	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	8	2	no	—
1193	C₂	—	8	1	no	—
1194	C₂	C₃₁×#3484	1	1	yes	characteristic
1195	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1196	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3547	C₂	semidirect
2. C₃₁×#3497	C₂	semidirect
3. C₃₁×#3333	C₂	semidirect
4. C₃₁×#3329	C₂	semidirect
5. C₃₁×#3327	C₂	semidirect
6. C₃₁×#3305	C₂	semidirect
7. C₃₁×#3300	C₂	semidirect
8. C₃₁×#3299	C₂	semidirect
9. D₄×Q₁₆×C₃₁	C₂	semidirect
10. C₃₁×#3285	C₂	semidirect
11. C₃₁×#3284	C₂	semidirect
12. C₃₁×#3278	C₂	semidirect
13. C₃₁×#3277	C₂	semidirect
14. C₃₁×#3276	C₂	semidirect
15. C₃₁×#3212	C₂	semidirect
16. C₃₁×#3210	C₂	semidirect
17. C₃₁×#3203	C₂	semidirect
18. C₃₁×#3201	C₂	semidirect
19. C₃₁×#3108	C₂	semidirect
20. C₃₁×#3104	C₂	semidirect
21. C₃₁×#3013	C₂	semidirect
22. C₃₁×#3011	C₂	semidirect
23. C₃₁×#2979	C₂	semidirect
471. #61660	C₃₁	direct (N × H)
556. #3547	C₂×C₃₁	semidirect
557. #3497	C₂×C₃₁	semidirect
558. #3333	C₂×C₃₁	semidirect
559. #3329	C₂×C₃₁	semidirect
560. #3327	C₂×C₃₁	semidirect
561. #3305	C₂×C₃₁	semidirect
562. #3300	C₂×C₃₁	semidirect
563. #3299	C₂×C₃₁	semidirect
564. D₄×Q₁₆	C₂×C₃₁	semidirect
565. #3285	C₂×C₃₁	semidirect
566. #3284	C₂×C₃₁	semidirect
567. #3278	C₂×C₃₁	semidirect
568. #3277	C₂×C₃₁	semidirect
569. #3276	C₂×C₃₁	semidirect
570. #3212	C₂×C₃₁	semidirect
571. #3210	C₂×C₃₁	semidirect
572. #3203	C₂×C₃₁	semidirect
573. #3201	C₂×C₃₁	semidirect
574. #3108	C₂×C₃₁	semidirect
575. #3104	C₂×C₃₁	semidirect
576. #3013	C₂×C₃₁	semidirect
577. #3011	C₂×C₃₁	semidirect
578. #2979	C₂×C₃₁	semidirect
916. C₃₁	#61660	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×#3547	2
C₃₁×#3497	2
C₃₁×#3333	2
C₃₁×#3329	2
C₃₁×#3327	2
C₃₁×#3305	2
C₃₁×#3300	2
C₃₁×#3299	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3285	2
C₃₁×#3284	2
C₃₁×#3278	2
C₃₁×#3277	2
C₃₁×#3276	2
C₃₁×#3212	2
C₃₁×#3210	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3108	2
C₃₁×#3104	2
C₃₁×#3013	2
C₃₁×#3011	2
C₃₁×#2979	2
#61660	31

Subgroups — C31×#61660 #21518419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61660 #21518419