Subgroups — C₃₁×#61619 #21518378

Order 7936.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3330	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3277	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3193	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3189	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
28	C₃₁×#562	—	2	2	no	—
29	C₃₁×#554	C₂²	1	2	yes	—
30	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
31	C₃₁×#548	C₂²	1	2	yes	complemented
32	C₃₁×#548	C₂²	1	2	yes	complemented
33	C₃₁×#547	—	2	2	no	—
34	C₃₁×#547	C₂²	1	2	yes	complemented
35	C₃₁×#547	C₂²	1	2	yes	complemented
36	C₃₁×#546	—	2	2	no	—
37	C₃₁×#546	—	2	2	no	—
38	C₃₁×#546	C₂²	1	2	yes	—
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	C₂²	1	2	yes	complemented
42	C₃₁×#539	—	2	1	no	—
43	C₃₁×#538	—	2	1	no	—
44	C₃₁×#537	—	2	1	no	—
45	C₃₁×#537	—	2	1	no	—
46	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#537	C₂²	1	2	yes	complemented
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#525	—	2	1	no	—
51	C₃₁×#525	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
53	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
54	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
55	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
56	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#497	C₂²	1	2	yes	complemented
58	C₃₁×#495	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#487	C₂²	1	2	yes	complemented
61	C₃₁×#484	C₂²	1	2	yes	—
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#484	C₂²	1	2	yes	complemented
64	C₃₁×#484	C₂²	1	2	yes	complemented
65	C₃₁×#480	C₂²	1	2	yes	complemented
66	C₃₁×#480	C₂²	1	2	yes	complemented
67	C₃₁×#477	C₂²	1	2	yes	complemented
68	C₃₁×#474	C₂²	1	2	yes	complemented
69	C₃₁×#468	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	complemented
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#467	C₂²	1	2	yes	—
74	C₃₁×#467	C₂²	1	2	yes	—
75	C₃₁×#467	C₂²	1	2	yes	complemented
76	C₃₁×#466	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#462	C₂²	1	2	yes	complemented
82	C₃₁×#461	C₂²	1	2	yes	complemented
83	C₃₁×#452	C₂²	1	2	yes	complemented
84	C₃₁×#452	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#452	C₂²	1	2	yes	complemented
87	C₃₁×#451	C₂²	1	2	yes	—
88	C₃₁×#451	C₂²	1	2	yes	complemented
89	C₃₁×#451	C₂²	1	2	yes	complemented
90	C₃₁×#451	C₂²	1	2	yes	complemented
91	C₃₁×#450	C₂²	1	2	yes	—
92	C₃₁×#450	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	—
97	C₃₁×#449	C₂²	1	2	yes	complemented
98	C₃₁×#449	C₂²	1	2	yes	complemented
99	C₃₁×#448	C₂²	1	2	yes	complemented
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
104	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
105	C₃₁×#436	C₂²	1	2	yes	complemented
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₃₁×#435	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	—
109	C₃₁×#433	C₂²	1	2	yes	complemented
110	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#417	C₂²	1	2	yes	complemented
113	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
114	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
115	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₃₁×#407	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
119	C₃₁×2₋¹⁺⁴	—	4	2	no	—
120	C₃₁×2₋¹⁺⁴	—	4	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	2	no	—
123	C₂×#41×C₃₁	—	2	2	no	—
124	C₂×#41×C₃₁	—	2	1	no	—
125	C₂×#41×C₃₁	—	2	1	no	—
126	C₂×#41×C₃₁	—	4	2	no	—
127	C₂×#41×C₃₁	—	4	2	no	—
128	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×#41×C₃₁	C₂³	1	2	yes	—
132	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
133	C₂×#41×C₃₁	C₂³	1	2	yes	—
134	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
135	C₂²×Q₈×C₃₁	—	2	1	no	—
136	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
138	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₃₁	—	2	1	no	—
145	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₃₁×#137	—	4	2	no	—
147	C₃₁×#137	—	4	4	no	—
148	C₃₁×#137	—	4	2	no	—
149	C₃₁×#135	—	4	4	no	—
150	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	—	4	2	no	—
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	—	4	2	no	—
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
170	C₃₁×C₄⋊Q₈	—	2	2	no	—
171	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#125	—	2	2	no	—
175	C₃₁×#124	—	2	2	no	—
176	C₃₁×#124	—	2	2	no	—
177	C₃₁×#124	—	2	2	no	—
178	C₃₁×#124	C₂³	1	2	yes	—
179	C₃₁×#124	C₂³	1	2	yes	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	D₄	1	2	yes	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
206	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	1	no	—
222	C₃₁×#121	—	2	1	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	D₄	1	1	yes	characteristic
226	C₃₁×#121	D₄	1	1	yes	characteristic
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	2	yes	—
230	C₃₁×#121	C₂³	1	2	yes	—
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	D₄	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
235	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	2	no	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₃₁×#117	—	2	1	no	—
246	C₃₁×#117	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
250	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
260	C₃₁×#107	C₂³	1	2	yes	—
261	C₃₁×#107	C₂³	1	2	yes	—
262	C₃₁×#107	C₂³	1	2	yes	—
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
265	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#103	C₂³	1	2	yes	—
273	C₃₁×#103	C₂³	1	2	yes	—
274	C₃₁×#103	C₂³	1	2	yes	—
275	C₃₁×#103	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×#102	C₂³	1	2	yes	—
279	C₃₁×#102	C₂³	1	2	yes	—
280	C₃₁×#102	C₂³	1	2	yes	—
281	C₃₁×#102	C₂³	1	2	yes	—
282	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#97	C₂³	1	2	yes	—
289	C₄×C₈×C₃₁	C₂³	1	2	yes	—
290	C₂⁴×C₃₁	—	2	1	no	—
291	C₂⁴×C₃₁	—	2	1	no	—
292	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
293	#41×C₃₁	—	2	2	no	—
294	#41×C₃₁	—	2	2	no	—
295	#41×C₃₁	—	2	2	no	—
296	#41×C₃₁	—	2	4	no	—
297	#41×C₃₁	—	2	2	no	—
298	#41×C₃₁	—	4	1	no	—
299	#41×C₃₁	—	4	1	no	—
300	#41×C₃₁	—	4	1	no	—
301	#41×C₃₁	—	4	1	no	—
302	#41×C₃₁	—	4	1	no	—
303	#41×C₃₁	—	4	1	no	—
304	#41×C₃₁	—	4	2	no	—
305	#41×C₃₁	—	4	4	no	—
306	#41×C₃₁	—	4	4	no	—
307	#41×C₃₁	—	4	2	no	—
308	#41×C₃₁	—	4	2	no	—
309	#41×C₃₁	—	4	4	no	—
310	#41×C₃₁	—	4	8	no	—
311	#41×C₃₁	—	8	4	no	—
312	C₂×Q₈×C₃₁	—	2	1	no	—
313	C₂×Q₈×C₃₁	—	2	2	no	—
314	C₂×Q₈×C₃₁	—	2	1	no	—
315	C₂×Q₈×C₃₁	—	2	1	no	—
316	C₂×Q₈×C₃₁	—	2	2	no	—
317	C₂×Q₈×C₃₁	—	2	2	no	—
318	C₂×Q₈×C₃₁	—	2	4	no	—
319	C₂×Q₈×C₃₁	—	4	1	no	—
320	C₂×Q₈×C₃₁	—	4	2	no	—
321	C₂×Q₈×C₃₁	—	4	1	no	—
322	C₂×Q₈×C₃₁	—	4	1	no	—
323	C₂×Q₈×C₃₁	—	4	4	no	—
324	C₂×Q₈×C₃₁	—	4	1	no	—
325	C₂×Q₈×C₃₁	—	4	1	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	1	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	2	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	2	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	4	1	no	—
345	C₂×D₄×C₃₁	—	4	1	no	—
346	C₂×D₄×C₃₁	—	4	1	no	—
347	C₂×D₄×C₃₁	—	4	4	no	—
348	C₂×D₄×C₃₁	—	8	2	no	—
349	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
350	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	1	no	—
367	C₂²×C₄×C₃₁	—	2	1	no	—
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	2	2	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	4	1	no	—
373	C₂²×C₄×C₃₁	—	4	1	no	—
374	C₂²×C₄×C₃₁	—	4	4	no	—
375	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
380	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	Q₁₆×C₃₁	—	2	4	no	—
383	Q₁₆×C₃₁	—	4	2	no	—
384	Q₁₆×C₃₁	—	4	2	no	—
385	Q₁₆×C₃₁	—	4	2	no	—
386	SD₁₆×C₃₁	—	2	4	no	—
387	SD₁₆×C₃₁	—	2	4	no	—
388	SD₁₆×C₃₁	—	4	2	no	—
389	SD₁₆×C₃₁	—	4	2	no	—
390	SD₁₆×C₃₁	—	4	2	no	—
391	SD₁₆×C₃₁	—	4	2	no	—
392	D₈×C₃₁	—	2	4	no	—
393	D₈×C₃₁	—	4	2	no	—
394	M₁₆×C₃₁	—	4	1	no	—
395	M₁₆×C₃₁	—	4	2	no	—
396	M₁₆×C₃₁	—	4	1	no	—
397	C₂×C₈×C₃₁	—	4	1	no	—
398	C₂×C₈×C₃₁	—	4	1	no	—
399	C₂×C₈×C₃₁	—	4	2	no	—
400	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
401	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
402	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
403	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
424	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
426	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	C₂⁴	1	2	yes	—
450	#61619	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
451	C₂³×C₃₁	—	2	1	no	—
452	C₂³×C₃₁	—	2	2	no	—
453	C₂³×C₃₁	—	2	2	no	—
454	C₂³×C₃₁	—	2	1	no	—
455	C₂³×C₃₁	—	4	1	no	—
456	C₂³×C₃₁	—	4	1	no	—
457	C₂³×C₃₁	—	4	2	no	—
458	C₂³×C₃₁	—	4	2	no	—
459	C₂³×C₃₁	—	4	2	no	—
460	C₂³×C₃₁	—	8	1	no	—
461	C₂³×C₃₁	—	8	1	no	—
462	C₂³×C₃₁	—	8	1	no	—
463	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	Q₈×C₃₁	—	2	1	no	—
468	Q₈×C₃₁	—	2	2	no	—
469	Q₈×C₃₁	—	2	1	no	—
470	Q₈×C₃₁	—	2	2	no	—
471	Q₈×C₃₁	—	2	2	no	—
472	Q₈×C₃₁	—	2	2	no	—
473	Q₈×C₃₁	—	2	1	no	—
474	Q₈×C₃₁	—	4	1	no	—
475	Q₈×C₃₁	—	4	4	no	—
476	Q₈×C₃₁	—	4	2	no	—
477	Q₈×C₃₁	—	4	2	no	—
478	Q₈×C₃₁	—	8	1	no	—
479	Q₈×C₃₁	—	8	2	no	—
480	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
481	D₄×C₃₁	—	2	4	no	—
482	D₄×C₃₁	—	2	4	no	—
483	D₄×C₃₁	—	2	1	no	—
484	D₄×C₃₁	—	2	2	no	—
485	D₄×C₃₁	—	2	1	no	—
486	D₄×C₃₁	—	2	2	no	—
487	D₄×C₃₁	—	2	1	no	—
488	D₄×C₃₁	—	4	1	no	—
489	D₄×C₃₁	—	4	2	no	—
490	D₄×C₃₁	—	4	2	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	4	no	—
497	D₄×C₃₁	—	8	1	no	—
498	D₄×C₃₁	—	8	2	no	—
499	D₄×C₃₁	—	8	2	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	—	8	2	no	—
502	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
503	C₂×C₄×C₃₁	—	2	4	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	2	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	2	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	4	1	no	—
520	C₂×C₄×C₃₁	—	4	1	no	—
521	C₂×C₄×C₃₁	—	4	1	no	—
522	C₂×C₄×C₃₁	—	4	2	no	—
523	C₂×C₄×C₃₁	—	4	2	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	4	4	no	—
526	C₂×C₄×C₃₁	—	4	4	no	—
527	C₂×C₄×C₃₁	—	4	2	no	—
528	C₂×C₄×C₃₁	—	4	2	no	—
529	C₂×C₄×C₃₁	—	4	2	no	—
530	C₂×C₄×C₃₁	—	8	2	no	—
531	C₂×C₄×C₃₁	—	8	2	no	—
532	C₂×C₄×C₃₁	—	8	2	no	—
533	C₂×C₄×C₃₁	—	8	1	no	—
534	C₂×C₄×C₃₁	—	8	1	no	—
535	C₂×C₄×C₃₁	—	8	1	no	—
536	C₂×C₄×C₃₁	—	8	2	no	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
538	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
539	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
544	C₈×C₃₁	—	2	2	no	—
545	C₈×C₃₁	—	2	2	no	—
546	C₈×C₃₁	—	2	2	no	—
547	C₈×C₃₁	—	2	2	no	—
548	#3536	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3489	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3330	C₂×C₃₁	1	2	yes	complemented
551	#3314	C₂×C₃₁	1	2	yes	complemented
552	#3308	C₂×C₃₁	1	2	yes	complemented
553	#3299	C₂×C₃₁	1	2	yes	complemented
554	#3280	C₂×C₃₁	1	2	yes	complemented
555	#3277	C₂×C₃₁	1	2	yes	complemented
556	#3269	C₂×C₃₁	1	2	yes	complemented
557	#3266	C₂×C₃₁	1	2	yes	complemented
558	#3225	C₂×C₃₁	1	2	yes	complemented
559	#3203	C₂×C₃₁	1	2	yes	complemented
560	#3193	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3189	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3124	C₂×C₃₁	1	2	yes	complemented
563	#3013	C₂×C₃₁	1	2	yes	complemented
564	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
565	C₂×#449	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#2976	C₂×C₃₁	1	1	yes	characteristic, complemented
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	1	no	—
570	C₂²×C₃₁	—	2	2	no	—
571	C₂²×C₃₁	—	2	1	no	—
572	C₂²×C₃₁	—	2	1	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	2	no	—
575	C₂²×C₃₁	—	2	1	no	—
576	C₂²×C₃₁	—	2	2	no	—
577	C₂²×C₃₁	—	2	1	no	—
578	C₂²×C₃₁	—	2	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	1	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	4	1	no	—
586	C₂²×C₃₁	—	4	2	no	—
587	C₂²×C₃₁	—	8	2	no	—
588	C₂²×C₃₁	—	8	4	no	—
589	C₂²×C₃₁	—	16	2	no	—
590	C₂²×C₃₁	#578	1	2	yes	—
591	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
592	C₄×C₃₁	—	2	2	no	—
593	C₄×C₃₁	—	2	1	no	—
594	C₄×C₃₁	—	2	2	no	—
595	C₄×C₃₁	—	2	1	no	—
596	C₄×C₃₁	—	2	2	no	—
597	C₄×C₃₁	—	2	1	no	—
598	C₄×C₃₁	—	2	2	no	—
599	C₄×C₃₁	—	4	2	no	—
600	C₄×C₃₁	—	4	2	no	—
601	C₄×C₃₁	—	4	2	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	2	no	—
604	C₄×C₃₁	—	4	2	no	—
605	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
608	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
609	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
610	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
612	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
613	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
614	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
615	#562	—	2	2	no	—
616	#554	C₂²×C₃₁	1	2	yes	—
617	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
618	#548	C₂²×C₃₁	1	2	yes	complemented
619	#548	C₂²×C₃₁	1	2	yes	complemented
620	#547	—	2	2	no	—
621	#547	C₂²×C₃₁	1	2	yes	complemented
622	#547	C₂²×C₃₁	1	2	yes	complemented
623	#546	—	2	2	no	—
624	#546	—	2	2	no	—
625	#546	C₂²×C₃₁	1	2	yes	—
626	#546	C₂²×C₃₁	1	2	yes	—
627	#543	—	2	1	no	—
628	#542	C₂²×C₃₁	1	2	yes	complemented
629	#539	—	2	1	no	—
630	#538	—	2	1	no	—
631	#537	—	2	1	no	—
632	#537	—	2	1	no	—
633	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#537	C₂²×C₃₁	1	2	yes	complemented
635	#536	—	2	1	no	—
636	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
637	#525	—	2	1	no	—
638	#525	C₂²×C₃₁	1	1	yes	characteristic
639	C₂×C₂²⋊Q₈	—	2	1	no	—
640	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
641	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
642	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
643	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#497	C₂²×C₃₁	1	2	yes	complemented
645	#495	C₂²×C₃₁	1	2	yes	complemented
646	#489	C₂²×C₃₁	1	2	yes	complemented
647	#487	C₂²×C₃₁	1	2	yes	complemented
648	#484	C₂²×C₃₁	1	2	yes	—
649	#484	C₂²×C₃₁	1	2	yes	complemented
650	#484	C₂²×C₃₁	1	2	yes	complemented
651	#484	C₂²×C₃₁	1	2	yes	complemented
652	#480	C₂²×C₃₁	1	2	yes	complemented
653	#480	C₂²×C₃₁	1	2	yes	complemented
654	#477	C₂²×C₃₁	1	2	yes	complemented
655	#474	C₂²×C₃₁	1	2	yes	complemented
656	#468	C₂²×C₃₁	1	2	yes	complemented
657	#468	C₂²×C₃₁	1	2	yes	complemented
658	#468	C₂²×C₃₁	1	2	yes	complemented
659	#468	C₂²×C₃₁	1	2	yes	complemented
660	#467	C₂²×C₃₁	1	2	yes	—
661	#467	C₂²×C₃₁	1	2	yes	—
662	#467	C₂²×C₃₁	1	2	yes	complemented
663	#466	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	2	yes	complemented
667	#463	C₂²×C₃₁	1	2	yes	complemented
668	#462	C₂²×C₃₁	1	2	yes	complemented
669	#461	C₂²×C₃₁	1	2	yes	complemented
670	#452	C₂²×C₃₁	1	2	yes	complemented
671	#452	C₂²×C₃₁	1	2	yes	complemented
672	#452	C₂²×C₃₁	1	2	yes	complemented
673	#452	C₂²×C₃₁	1	2	yes	complemented
674	#451	C₂²×C₃₁	1	2	yes	—
675	#451	C₂²×C₃₁	1	2	yes	complemented
676	#451	C₂²×C₃₁	1	2	yes	complemented
677	#451	C₂²×C₃₁	1	2	yes	complemented
678	#450	C₂²×C₃₁	1	2	yes	—
679	#450	C₂²×C₃₁	1	2	yes	—
680	#449	C₂²×C₃₁	1	2	yes	—
681	#449	C₂²×C₃₁	1	2	yes	—
682	#449	C₂²×C₃₁	1	2	yes	—
683	#449	C₂²×C₃₁	1	2	yes	—
684	#449	C₂²×C₃₁	1	2	yes	complemented
685	#449	C₂²×C₃₁	1	2	yes	complemented
686	#448	C₂²×C₃₁	1	2	yes	complemented
687	#448	C₂²×C₃₁	1	2	yes	complemented
688	#440	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	2	yes	complemented
690	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
691	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
692	#436	C₂²×C₃₁	1	2	yes	complemented
693	#435	C₂²×C₃₁	1	2	yes	—
694	#435	C₂²×C₃₁	1	2	yes	complemented
695	C₈×D₄	C₂²×C₃₁	1	2	yes	—
696	#433	C₂²×C₃₁	1	2	yes	complemented
697	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	#417	C₂²×C₃₁	1	2	yes	complemented
699	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
701	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
702	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
703	#408	C₂²×C₃₁	1	2	yes	complemented
704	#407	C₂²×C₃₁	1	1	yes	characteristic
705	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
706	C₂×C₃₁	—	2	2	no	—
707	C₂×C₃₁	—	4	2	no	—
708	C₂×C₃₁	—	4	1	no	—
709	C₂×C₃₁	—	4	1	no	—
710	C₂×C₃₁	—	4	2	no	—
711	C₂×C₃₁	—	8	1	no	—
712	C₂×C₃₁	—	8	2	no	—
713	C₂×C₃₁	#3484	1	1	yes	characteristic
714	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
715	C₂×C₃₁	#3585	1	1	yes	characteristic
716	2₋¹⁺⁴	—	4	2	no	—
717	2₋¹⁺⁴	—	4	2	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	2	no	—
720	C₂×#41	—	2	2	no	—
721	C₂×#41	—	2	1	no	—
722	C₂×#41	—	2	1	no	—
723	C₂×#41	—	4	2	no	—
724	C₂×#41	—	4	2	no	—
725	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
726	C₂×#41	C₂³×C₃₁	1	2	yes	—
727	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
728	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
729	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
730	C₂×#41	C₂³×C₃₁	1	2	yes	—
731	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
732	C₂²×Q₈	—	2	1	no	—
733	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
734	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
735	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₂²×D₄	—	2	1	no	—
738	C₂²×D₄	—	2	1	no	—
739	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
740	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
741	C₂³×C₄	—	2	1	no	—
742	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
743	#137	—	4	2	no	—
744	#137	—	4	4	no	—
745	#137	—	4	2	no	—
746	#135	—	4	4	no	—
747	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
748	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
749	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
750	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
751	C₂×SD₁₆	—	4	2	no	—
752	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
758	C₂×D₈	—	4	2	no	—
759	C₂×D₈	C₂³×C₃₁	1	2	yes	—
760	C₂×D₈	C₂³×C₃₁	1	2	yes	—
761	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
764	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
766	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
767	C₄⋊Q₈	—	2	2	no	—
768	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
769	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
770	#126	—	2	2	no	—
771	#125	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	2	no	—
774	#124	—	2	2	no	—
775	#124	C₂³×C₃₁	1	2	yes	—
776	#124	C₂³×C₃₁	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	D₄×C₃₁	1	2	yes	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	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	D₄×C₃₁	1	1	yes	characteristic
803	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
805	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
806	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
807	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
809	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
810	#121	—	2	1	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	—	2	2	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	D₄×C₃₁	1	1	yes	characteristic
823	#121	D₄×C₃₁	1	1	yes	characteristic
824	#121	C₂³×C₃₁	1	2	yes	—
825	#121	C₂³×C₃₁	1	2	yes	—
826	#121	C₂³×C₃₁	1	2	yes	—
827	#121	C₂³×C₃₁	1	2	yes	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	D₄×C₃₁	1	2	yes	—
831	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
832	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	C₂³×C₃₁	1	2	yes	—
839	C₄×D₄	C₂³×C₃₁	1	2	yes	—
840	C₄×D₄	C₂³×C₃₁	1	2	yes	—
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	#117	—	2	1	no	—
843	#117	C₂³×C₃₁	1	1	yes	characteristic
844	C₂×C₄⋊C₄	—	2	1	no	—
845	C₂×C₄⋊C₄	—	2	1	no	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	2	no	—
848	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
849	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
850	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
851	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
852	C₂×C₂²⋊C₄	—	2	1	no	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	1	no	—
855	C₂×C₂²⋊C₄	—	2	2	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	#107	C₂³×C₃₁	1	2	yes	—
858	#107	C₂³×C₃₁	1	2	yes	—
859	#107	C₂³×C₃₁	1	2	yes	—
860	#107	C₂³×C₃₁	1	2	yes	—
861	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
863	#103	C₂³×C₃₁	1	2	yes	—
864	#103	C₂³×C₃₁	1	2	yes	—
865	#103	C₂³×C₃₁	1	2	yes	—
866	#103	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
872	#103	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	2	yes	—
874	#102	C₂³×C₃₁	1	2	yes	—
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	2	yes	—
877	#102	C₂³×C₃₁	1	2	yes	—
878	#102	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
885	#97	C₂³×C₃₁	1	2	yes	—
886	C₄×C₈	C₂³×C₃₁	1	2	yes	—
887	C₃₁	#61619	1	1	yes	characteristic, direct product factor, Sylow
888	C₂⁴	—	2	1	no	—
889	C₂⁴	—	2	1	no	—
890	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
891	#41	—	2	2	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	2	4	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	4	1	no	—
898	#41	—	4	1	no	—
899	#41	—	4	1	no	—
900	#41	—	4	1	no	—
901	#41	—	4	1	no	—
902	#41	—	4	2	no	—
903	#41	—	4	4	no	—
904	#41	—	4	4	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	4	no	—
908	#41	—	4	8	no	—
909	#41	—	8	4	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	1	no	—
913	C₂×Q₈	—	2	1	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	—	2	2	no	—
916	C₂×Q₈	—	2	4	no	—
917	C₂×Q₈	—	4	1	no	—
918	C₂×Q₈	—	4	2	no	—
919	C₂×Q₈	—	4	1	no	—
920	C₂×Q₈	—	4	1	no	—
921	C₂×Q₈	—	4	4	no	—
922	C₂×Q₈	—	4	1	no	—
923	C₂×Q₈	—	4	1	no	—
924	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
925	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
926	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
927	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
928	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	1	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	4	1	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	1	no	—
945	C₂×D₄	—	4	4	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
948	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
951	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
953	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	1	no	—
965	C₂²×C₄	—	2	1	no	—
966	C₂²×C₄	—	2	1	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	4	1	no	—
971	C₂²×C₄	—	4	1	no	—
972	C₂²×C₄	—	4	4	no	—
973	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
978	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
980	Q₁₆	—	2	4	no	—
981	Q₁₆	—	4	2	no	—
982	Q₁₆	—	4	2	no	—
983	Q₁₆	—	4	2	no	—
984	SD₁₆	—	2	4	no	—
985	SD₁₆	—	2	4	no	—
986	SD₁₆	—	4	2	no	—
987	SD₁₆	—	4	2	no	—
988	SD₁₆	—	4	2	no	—
989	SD₁₆	—	4	2	no	—
990	D₈	—	2	4	no	—
991	D₈	—	4	2	no	—
992	M₁₆	—	4	1	no	—
993	M₁₆	—	4	2	no	—
994	M₁₆	—	4	1	no	—
995	C₂×C₈	—	4	1	no	—
996	C₂×C₈	—	4	1	no	—
997	C₂×C₈	—	4	2	no	—
998	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
999	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1000	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1001	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	2	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1019	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1020	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1022	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1023	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	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	2	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	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1041	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
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	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	C₂⁴×C₃₁	1	2	yes	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	2	1	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	4	1	no	—
1054	C₂³	—	4	2	no	—
1055	C₂³	—	4	2	no	—
1056	C₂³	—	4	2	no	—
1057	C₂³	—	8	1	no	—
1058	C₂³	—	8	1	no	—
1059	C₂³	—	8	1	no	—
1060	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1061	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1062	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1063	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	Q₈	—	2	1	no	—
1065	Q₈	—	2	2	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	4	1	no	—
1072	Q₈	—	4	4	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	4	2	no	—
1075	Q₈	—	8	1	no	—
1076	Q₈	—	8	2	no	—
1077	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	4	1	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	4	2	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	4	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	8	1	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	2	no	—
1098	D₄	—	8	2	no	—
1099	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1100	C₂×C₄	—	2	4	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	1	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	2	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	2	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	1	no	—
1117	C₂×C₄	—	4	1	no	—
1118	C₂×C₄	—	4	1	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	4	no	—
1123	C₂×C₄	—	4	4	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	2	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	1	no	—
1132	C₂×C₄	—	8	1	no	—
1133	C₂×C₄	—	8	2	no	—
1134	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1136	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1138	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1141	C₈	—	2	2	no	—
1142	C₈	—	2	2	no	—
1143	C₈	—	2	2	no	—
1144	C₈	—	2	2	no	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	2	2	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	1	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	1	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	1	no	—
1155	C₂²	—	2	2	no	—
1156	C₂²	—	2	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	2	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	8	2	no	—
1166	C₂²	—	8	4	no	—
1167	C₂²	—	16	2	no	—
1168	C₂²	C₃₁×#578	1	2	yes	—
1169	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1170	C₄	—	2	1	no	—
1171	C₄	—	2	2	no	—
1172	C₄	—	2	1	no	—
1173	C₄	—	2	2	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	2	no	—
1177	C₄	—	4	1	no	—
1178	C₄	—	4	2	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	2	no	—
1182	C₄	—	4	2	no	—
1183	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1184	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1185	C₂	—	2	2	no	—
1186	C₂	—	4	1	no	—
1187	C₂	—	4	1	no	—
1188	C₂	—	4	2	no	—
1189	C₂	—	4	2	no	—
1190	C₂	—	8	1	no	—
1191	C₂	—	8	2	no	—
1192	C₂	C₃₁×#3484	1	1	yes	characteristic
1193	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1194	C₂	C₃₁×#3585	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3536	C₂	semidirect
2. C₃₁×#3489	C₂	semidirect
3. C₃₁×#3330	C₂	semidirect
4. C₃₁×#3314	C₂	semidirect
5. C₃₁×#3308	C₂	semidirect
6. C₃₁×#3299	C₂	semidirect
7. C₃₁×#3280	C₂	semidirect
8. C₃₁×#3277	C₂	semidirect
9. C₃₁×#3269	C₂	semidirect
10. C₃₁×#3266	C₂	semidirect
11. C₃₁×#3225	C₂	semidirect
12. C₃₁×#3203	C₂	semidirect
13. C₃₁×#3193	C₂	semidirect
14. C₃₁×#3189	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3013	C₂	semidirect
17. C₃₁×#3007	C₂	semidirect
18. C₂×C₃₁×#449	C₂	semidirect
19. C₃₁×#2976	C₂	semidirect
20. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
23. C₂×C₃₁×#137	C₂²	semidirect
24. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
31. C₃₁×#548	C₂²	semidirect
32. C₃₁×#548	C₂²	semidirect
34. C₃₁×#547	C₂²	semidirect
35. C₃₁×#547	C₂²	semidirect
41. C₃₁×#542	C₂²	semidirect
46. C₃₁×#537	C₂²	semidirect
47. C₃₁×#537	C₂²	semidirect
49. C₃₁×#536	C₂²	semidirect
56. C₃₁×#520	C₂²	semidirect
57. C₃₁×#497	C₂²	semidirect
58. C₃₁×#495	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#487	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
63. C₃₁×#484	C₂²	semidirect
64. C₃₁×#484	C₂²	semidirect
65. C₃₁×#480	C₂²	semidirect
66. C₃₁×#480	C₂²	semidirect
67. C₃₁×#477	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#468	C₂²	semidirect
70. C₃₁×#468	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
75. C₃₁×#467	C₂²	semidirect
76. C₃₁×#466	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#462	C₂²	semidirect
82. C₃₁×#461	C₂²	semidirect
83. C₃₁×#452	C₂²	semidirect
84. C₃₁×#452	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#452	C₂²	semidirect
88. C₃₁×#451	C₂²	semidirect
89. C₃₁×#451	C₂²	semidirect
90. C₃₁×#451	C₂²	semidirect
97. C₃₁×#449	C₂²	semidirect
98. C₃₁×#449	C₂²	semidirect
99. C₃₁×#448	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₄×Q₁₆×C₃₁	C₂²	semidirect
104. C₄×D₈×C₃₁	C₂²	semidirect
105. C₃₁×#436	C₂²	semidirect
107. C₃₁×#435	C₂²	semidirect
109. C₃₁×#433	C₂²	semidirect
110. C₃₁×#417	C₂²	semidirect
111. C₃₁×#417	C₂²	semidirect
112. C₃₁×#417	C₂²	semidirect
114. C₂×C₃₁×#103	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
450. #61619	C₃₁	direct (N × H)
548. #3536	C₂×C₃₁	semidirect
549. #3489	C₂×C₃₁	semidirect
550. #3330	C₂×C₃₁	semidirect
551. #3314	C₂×C₃₁	semidirect
552. #3308	C₂×C₃₁	semidirect
553. #3299	C₂×C₃₁	semidirect
554. #3280	C₂×C₃₁	semidirect
555. #3277	C₂×C₃₁	semidirect
556. #3269	C₂×C₃₁	semidirect
557. #3266	C₂×C₃₁	semidirect
558. #3225	C₂×C₃₁	semidirect
559. #3203	C₂×C₃₁	semidirect
560. #3193	C₂×C₃₁	semidirect
561. #3189	C₂×C₃₁	semidirect
562. #3124	C₂×C₃₁	semidirect
563. #3013	C₂×C₃₁	semidirect
564. #3007	C₂×C₃₁	semidirect
565. C₂×#449	C₂×C₃₁	semidirect
566. #2976	C₂×C₃₁	semidirect
607. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
609. C₂×#137	C₂²×C₃₁	semidirect
610. C₂×#137	C₂²×C₃₁	semidirect
611. C₂×#137	C₂²×C₃₁	semidirect
612. C₂×#135	C₂²×C₃₁	semidirect
618. #548	C₂²×C₃₁	semidirect
619. #548	C₂²×C₃₁	semidirect
621. #547	C₂²×C₃₁	semidirect
622. #547	C₂²×C₃₁	semidirect
628. #542	C₂²×C₃₁	semidirect
633. #537	C₂²×C₃₁	semidirect
634. #537	C₂²×C₃₁	semidirect
636. #536	C₂²×C₃₁	semidirect
643. #520	C₂²×C₃₁	semidirect
644. #497	C₂²×C₃₁	semidirect
645. #495	C₂²×C₃₁	semidirect
646. #489	C₂²×C₃₁	semidirect
647. #487	C₂²×C₃₁	semidirect
649. #484	C₂²×C₃₁	semidirect
650. #484	C₂²×C₃₁	semidirect
651. #484	C₂²×C₃₁	semidirect
652. #480	C₂²×C₃₁	semidirect
653. #480	C₂²×C₃₁	semidirect
654. #477	C₂²×C₃₁	semidirect
655. #474	C₂²×C₃₁	semidirect
656. #468	C₂²×C₃₁	semidirect
657. #468	C₂²×C₃₁	semidirect
658. #468	C₂²×C₃₁	semidirect
659. #468	C₂²×C₃₁	semidirect
662. #467	C₂²×C₃₁	semidirect
663. #466	C₂²×C₃₁	semidirect
664. #464	C₂²×C₃₁	semidirect
665. #464	C₂²×C₃₁	semidirect
666. #463	C₂²×C₃₁	semidirect
667. #463	C₂²×C₃₁	semidirect
668. #462	C₂²×C₃₁	semidirect
669. #461	C₂²×C₃₁	semidirect
670. #452	C₂²×C₃₁	semidirect
671. #452	C₂²×C₃₁	semidirect
672. #452	C₂²×C₃₁	semidirect
673. #452	C₂²×C₃₁	semidirect
675. #451	C₂²×C₃₁	semidirect
676. #451	C₂²×C₃₁	semidirect
677. #451	C₂²×C₃₁	semidirect
684. #449	C₂²×C₃₁	semidirect
685. #449	C₂²×C₃₁	semidirect
686. #448	C₂²×C₃₁	semidirect
687. #448	C₂²×C₃₁	semidirect
688. #440	C₂²×C₃₁	semidirect
689. #440	C₂²×C₃₁	semidirect
690. C₄×Q₁₆	C₂²×C₃₁	semidirect
691. C₄×D₈	C₂²×C₃₁	semidirect
692. #436	C₂²×C₃₁	semidirect
694. #435	C₂²×C₃₁	semidirect
696. #433	C₂²×C₃₁	semidirect
697. #417	C₂²×C₃₁	semidirect
698. #417	C₂²×C₃₁	semidirect
699. #417	C₂²×C₃₁	semidirect
701. C₂×#103	C₂²×C₃₁	semidirect
703. #408	C₂²×C₃₁	semidirect
887. C₃₁	#61619	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×#3536	2
C₃₁×#3489	2
C₃₁×#3330	2
C₃₁×#3314	2
C₃₁×#3308	2
C₃₁×#3299	2
C₃₁×#3280	2
C₃₁×#3277	2
C₃₁×#3269	2
C₃₁×#3266	2
C₃₁×#3225	2
C₃₁×#3203	2
C₃₁×#3193	2
C₃₁×#3189	2
C₃₁×#3124	2
C₃₁×#3013	2
C₃₁×#3007	2
C₂×C₃₁×#449	2
C₃₁×#2976	2
#61619	31

Subgroups — C31×#61619 #21518378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61619 #21518378