Subgroups — C₃₁×#61659 #21518418

Order 7936.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
11	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3278	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3275	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3204	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
22	C₃₁×#3010	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	complemented
25	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
27	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
29	C₃₁×#560	—	2	2	no	—
30	C₃₁×#556	C₂²	1	1	yes	characteristic
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#550	—	2	1	no	—
33	C₃₁×#550	—	2	1	no	—
34	C₃₁×#550	C₂²	1	1	yes	characteristic
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
37	D₄×Q₈×C₃₁	—	2	1	no	—
38	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#548	—	2	2	no	—
41	C₃₁×#548	C₂²	1	2	yes	complemented
42	C₃₁×#548	C₂²	1	2	yes	complemented
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#546	—	2	1	no	—
45	C₃₁×#546	C₂²	1	2	yes	—
46	D₄²×C₃₁	C₂²	1	1	yes	characteristic
47	C₃₁×#542	—	2	1	no	—
48	C₃₁×#538	—	2	2	no	—
49	C₃₁×#537	—	2	2	no	—
50	C₃₁×#537	C₂²	1	2	yes	—
51	C₃₁×#537	C₂²	1	2	yes	complemented
52	C₃₁×#535	—	2	1	no	—
53	C₃₁×#535	C₂²	1	2	yes	—
54	C₃₁×#532	—	2	1	no	—
55	C₃₁×#532	—	2	1	no	—
56	C₃₁×#532	C₂²	1	1	yes	characteristic
57	C₃₁×#532	C₂²	1	1	yes	characteristic
58	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#495	C₂²	1	2	yes	—
62	C₃₁×#493	C₂²	1	1	yes	characteristic
63	C₃₁×#492	C₂²	1	1	yes	characteristic
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#483	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	1	yes	characteristic
74	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
75	C₃₁×#479	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#470	C₂²	1	2	yes	complemented
79	C₃₁×#469	C₂²	1	2	yes	—
80	C₃₁×#469	C₂²	1	2	yes	—
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#466	C₂²	1	2	yes	complemented
83	C₃₁×#465	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	complemented
86	C₃₁×#464	C₂²	1	1	yes	characteristic
87	C₃₁×#464	C₂²	1	1	yes	characteristic
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#461	C₂²	1	1	yes	characteristic
92	C₃₁×#460	C₂²	1	1	yes	characteristic
93	C₃₁×#460	C₂²	1	1	yes	characteristic
94	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#459	C₂²	1	1	yes	characteristic
96	C₃₁×#452	C₂²	1	2	yes	complemented
97	C₃₁×#452	C₂²	1	2	yes	complemented
98	C₃₁×#452	C₂²	1	2	yes	complemented
99	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#451	C₂²	1	2	yes	complemented
101	C₃₁×#450	C₂²	1	2	yes	—
102	C₃₁×#449	C₂²	1	2	yes	—
103	C₃₁×#449	C₂²	1	2	yes	—
104	C₃₁×#449	C₂²	1	2	yes	—
105	C₃₁×#449	C₂²	1	2	yes	complemented
106	C₃₁×#449	C₂²	1	2	yes	complemented
107	C₃₁×#449	C₂²	1	2	yes	complemented
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#448	C₂²	1	1	yes	characteristic
110	C₃₁×#448	C₂²	1	2	yes	—
111	C₃₁×#448	C₂²	1	2	yes	—
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	2	yes	complemented
114	C₃₁×#447	C₂²	1	2	yes	—
115	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic
122	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#436	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
126	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#419	C₂²	1	2	yes	complemented
130	C₃₁×#417	C₂²	1	2	yes	complemented
131	C₃₁×#416	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
133	C₃₁×#408	C₂²	1	2	yes	complemented
134	C₃₁×#408	C₂²	1	2	yes	complemented
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	—	2	1	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
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	C₂×#41×C₃₁	C₂³	1	2	yes	—
146	C₂×#41×C₃₁	C₂³	1	2	yes	—
147	C₂²×Q₈×C₃₁	—	2	2	no	—
148	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
150	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×D₄×C₃₁	—	2	1	no	—
152	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
153	C₃₁×#137	—	4	4	no	—
154	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
155	C₃₁×#135	—	4	4	no	—
156	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
158	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	—	4	4	no	—
160	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
168	C₂×D₈×C₃₁	C₂³	1	2	yes	—
169	C₂×D₈×C₃₁	C₂³	1	2	yes	—
170	C₂×D₈×C₃₁	C₂³	1	2	yes	—
171	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
172	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
174	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
175	C₃₁×C₄⋊Q₈	—	2	1	no	—
176	C₃₁×C₄⋊Q₈	—	2	1	no	—
177	C₃₁×C₄⋊Q₈	D₄	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	—	2	1	no	—
183	C₃₁×#127	—	2	2	no	—
184	C₃₁×#127	D₄	1	1	yes	characteristic
185	C₃₁×#127	C₂³	1	1	yes	characteristic
186	C₃₁×#127	C₂³	1	1	yes	characteristic
187	C₃₁×#126	—	2	2	no	—
188	C₃₁×#126	—	2	2	no	—
189	C₃₁×#126	—	2	1	no	—
190	C₃₁×#125	C₂³	1	1	yes	characteristic
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	2	no	—
194	C₃₁×#124	—	2	2	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	D₄	1	2	yes	—
197	C₃₁×#124	C₂³	1	2	yes	—
198	C₃₁×#124	C₂³	1	1	yes	characteristic
199	C₃₁×#123	—	2	1	no	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	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	2	no	—
206	C₃₁×C₂²⋊Q₈	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	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	2	yes	—
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	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	1	no	—
224	C₃₁×#121	—	2	1	no	—
225	C₃₁×#121	—	2	1	no	—
226	C₃₁×#121	—	2	1	no	—
227	C₃₁×#121	—	2	2	no	—
228	C₃₁×#121	—	2	2	no	—
229	C₃₁×#121	—	2	2	no	—
230	C₃₁×#121	—	2	2	no	—
231	C₃₁×#121	D₄	1	1	yes	characteristic
232	C₃₁×#121	D₄	1	1	yes	characteristic
233	C₃₁×#121	D₄	1	2	yes	—
234	C₃₁×#121	C₂³	1	2	yes	—
235	C₃₁×#121	C₂³	1	1	yes	characteristic
236	C₃₁×#121	C₂³	1	2	yes	—
237	C₃₁×#121	C₂³	1	2	yes	—
238	C₃₁×#121	C₂³	1	2	yes	—
239	C₃₁×#121	C₂³	1	2	yes	—
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#120	—	2	2	no	—
242	C₃₁×#120	—	2	2	no	—
243	C₃₁×#120	—	2	2	no	—
244	C₃₁×#120	—	2	2	no	—
245	C₄×Q₈×C₃₁	—	2	1	no	—
246	C₄×Q₈×C₃₁	—	2	1	no	—
247	C₄×Q₈×C₃₁	—	2	1	no	—
248	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	no	—
259	C₄×D₄×C₃₁	—	2	2	no	—
260	C₄×D₄×C₃₁	—	2	2	no	—
261	C₄×D₄×C₃₁	—	2	2	no	—
262	C₄×D₄×C₃₁	—	2	1	no	—
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₃₁	C₂³	1	2	yes	—
267	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
268	C₄×D₄×C₃₁	C₂³	1	2	yes	—
269	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂×C₄²×C₃₁	—	2	1	no	—
277	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
278	C₃₁×#107	C₂³	1	1	yes	characteristic
279	C₃₁×#107	C₂³	1	1	yes	characteristic
280	C₃₁×#106	C₂³	1	1	yes	characteristic
281	C₃₁×#106	C₂³	1	1	yes	characteristic
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
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	C₂⁴×C₃₁	—	2	2	no	—
319	#41×C₃₁	—	2	4	no	—
320	#41×C₃₁	—	2	4	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	2	no	—
327	#41×C₃₁	—	4	8	no	—
328	#41×C₃₁	—	4	8	no	—
329	#41×C₃₁	—	4	2	no	—
330	#41×C₃₁	—	4	2	no	—
331	#41×C₃₁	—	4	8	no	—
332	#41×C₃₁	—	8	2	no	—
333	#41×C₃₁	—	8	2	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	1	no	—
338	C₂×Q₈×C₃₁	—	2	2	no	—
339	C₂×Q₈×C₃₁	—	2	2	no	—
340	C₂×Q₈×C₃₁	—	2	4	no	—
341	C₂×Q₈×C₃₁	—	2	4	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	1	yes	characteristic
349	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	—	2	2	no	—
351	C₂×D₄×C₃₁	—	2	2	no	—
352	C₂×D₄×C₃₁	—	2	2	no	—
353	C₂×D₄×C₃₁	—	2	1	no	—
354	C₂×D₄×C₃₁	—	2	2	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	2	no	—
360	C₂×D₄×C₃₁	—	2	2	no	—
361	C₂×D₄×C₃₁	—	2	1	no	—
362	C₂×D₄×C₃₁	—	2	1	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	2	1	no	—
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	4	2	no	—
367	C₂×D₄×C₃₁	—	4	2	no	—
368	C₂×D₄×C₃₁	—	8	2	no	—
369	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
371	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
373	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
376	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	2	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	1	no	—
382	C₂²×C₄×C₃₁	—	2	2	no	—
383	C₂²×C₄×C₃₁	—	2	1	no	—
384	C₂²×C₄×C₃₁	—	2	2	no	—
385	C₂²×C₄×C₃₁	—	2	2	no	—
386	C₂²×C₄×C₃₁	—	2	2	no	—
387	C₂²×C₄×C₃₁	—	2	2	no	—
388	C₂²×C₄×C₃₁	—	2	2	no	—
389	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
394	Q₁₆×C₃₁	—	2	2	no	—
395	Q₁₆×C₃₁	—	2	2	no	—
396	Q₁₆×C₃₁	—	4	2	no	—
397	SD₁₆×C₃₁	—	2	2	no	—
398	SD₁₆×C₃₁	—	2	4	no	—
399	SD₁₆×C₃₁	—	2	2	no	—
400	SD₁₆×C₃₁	—	2	4	no	—
401	SD₁₆×C₃₁	—	4	2	no	—
402	SD₁₆×C₃₁	—	4	2	no	—
403	SD₁₆×C₃₁	—	4	2	no	—
404	SD₁₆×C₃₁	—	4	2	no	—
405	D₈×C₃₁	—	4	2	no	—
406	D₈×C₃₁	—	4	2	no	—
407	D₈×C₃₁	—	4	2	no	—
408	M₁₆×C₃₁	—	4	2	no	—
409	M₁₆×C₃₁	—	4	2	no	—
410	C₂×C₈×C₃₁	—	4	2	no	—
411	C₂×C₈×C₃₁	—	4	2	no	—
412	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
415	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
416	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₃₁	—	2	1	no	—
419	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
424	C₄⋊C₄×C₃₁	—	2	1	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	—	2	1	no	—
427	C₄⋊C₄×C₃₁	—	2	1	no	—
428	C₄⋊C₄×C₃₁	—	2	1	no	—
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	2	no	—
431	C₄⋊C₄×C₃₁	—	2	1	no	—
432	C₄⋊C₄×C₃₁	—	2	2	no	—
433	C₄⋊C₄×C₃₁	—	2	1	no	—
434	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
435	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
441	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	1	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	1	no	—
450	C₂²⋊C₄×C₃₁	—	2	1	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
456	C₂²⋊C₄×C₃₁	—	2	2	no	—
457	C₂²⋊C₄×C₃₁	—	2	2	no	—
458	C₂²⋊C₄×C₃₁	—	2	1	no	—
459	C₂²⋊C₄×C₃₁	—	2	2	no	—
460	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
464	C₄²×C₃₁	—	2	1	no	—
465	C₄²×C₃₁	—	2	1	no	—
466	C₄²×C₃₁	—	2	1	no	—
467	C₄²×C₃₁	—	2	1	no	—
468	C₄²×C₃₁	—	2	1	no	—
469	C₄²×C₃₁	—	2	2	no	—
470	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
473	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
474	#61659	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂³×C₃₁	—	2	1	no	—
476	C₂³×C₃₁	—	2	2	no	—
477	C₂³×C₃₁	—	2	2	no	—
478	C₂³×C₃₁	—	8	2	no	—
479	C₂³×C₃₁	—	8	2	no	—
480	C₂³×C₃₁	—	8	2	no	—
481	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
482	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
483	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	Q₈×C₃₁	—	2	4	no	—
485	Q₈×C₃₁	—	2	1	no	—
486	Q₈×C₃₁	—	2	1	no	—
487	Q₈×C₃₁	—	2	1	no	—
488	Q₈×C₃₁	—	2	2	no	—
489	Q₈×C₃₁	—	2	2	no	—
490	Q₈×C₃₁	—	2	1	no	—
491	Q₈×C₃₁	—	4	2	no	—
492	Q₈×C₃₁	—	4	4	no	—
493	Q₈×C₃₁	—	4	4	no	—
494	Q₈×C₃₁	—	4	2	no	—
495	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
496	Q₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
497	D₄×C₃₁	—	2	2	no	—
498	D₄×C₃₁	—	2	2	no	—
499	D₄×C₃₁	—	2	1	no	—
500	D₄×C₃₁	—	2	2	no	—
501	D₄×C₃₁	—	2	2	no	—
502	D₄×C₃₁	—	2	2	no	—
503	D₄×C₃₁	—	2	2	no	—
504	D₄×C₃₁	—	2	1	no	—
505	D₄×C₃₁	—	4	2	no	—
506	D₄×C₃₁	—	4	2	no	—
507	D₄×C₃₁	—	4	2	no	—
508	D₄×C₃₁	—	4	2	no	—
509	D₄×C₃₁	—	4	4	no	—
510	D₄×C₃₁	—	4	4	no	—
511	D₄×C₃₁	—	4	4	no	—
512	D₄×C₃₁	—	4	2	no	—
513	D₄×C₃₁	—	4	2	no	—
514	D₄×C₃₁	—	8	1	no	—
515	D₄×C₃₁	—	8	1	no	—
516	D₄×C₃₁	—	8	2	no	—
517	D₄×C₃₁	—	8	2	no	—
518	D₄×C₃₁	—	8	2	no	—
519	D₄×C₃₁	—	8	1	no	—
520	D₄×C₃₁	—	8	2	no	—
521	D₄×C₃₁	—	8	2	no	—
522	D₄×C₃₁	—	8	2	no	—
523	D₄×C₃₁	—	8	2	no	—
524	D₄×C₃₁	—	8	2	no	—
525	C₂×C₄×C₃₁	—	2	4	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	2	no	—
529	C₂×C₄×C₃₁	—	2	2	no	—
530	C₂×C₄×C₃₁	—	2	2	no	—
531	C₂×C₄×C₃₁	—	2	2	no	—
532	C₂×C₄×C₃₁	—	2	2	no	—
533	C₂×C₄×C₃₁	—	2	1	no	—
534	C₂×C₄×C₃₁	—	2	1	no	—
535	C₂×C₄×C₃₁	—	2	1	no	—
536	C₂×C₄×C₃₁	—	2	1	no	—
537	C₂×C₄×C₃₁	—	2	1	no	—
538	C₂×C₄×C₃₁	—	2	1	no	—
539	C₂×C₄×C₃₁	—	2	2	no	—
540	C₂×C₄×C₃₁	—	2	1	no	—
541	C₂×C₄×C₃₁	—	2	2	no	—
542	C₂×C₄×C₃₁	—	4	1	no	—
543	C₂×C₄×C₃₁	—	4	4	no	—
544	C₂×C₄×C₃₁	—	4	4	no	—
545	C₂×C₄×C₃₁	—	4	4	no	—
546	C₂×C₄×C₃₁	—	4	4	no	—
547	C₂×C₄×C₃₁	—	4	4	no	—
548	C₂×C₄×C₃₁	—	4	2	no	—
549	C₂×C₄×C₃₁	—	8	2	no	—
550	C₂×C₄×C₃₁	—	8	2	no	—
551	C₂×C₄×C₃₁	—	8	1	no	—
552	C₂×C₄×C₃₁	—	8	2	no	—
553	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
555	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
559	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
560	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
561	C₈×C₃₁	—	2	1	no	—
562	C₈×C₃₁	—	2	1	no	—
563	C₈×C₃₁	—	2	2	no	—
564	C₈×C₃₁	—	2	1	no	—
565	C₈×C₃₁	—	2	2	no	—
566	C₈×C₃₁	—	2	1	no	—
567	#3546	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3497	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3332	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#3328	C₂×C₃₁	1	1	yes	characteristic, complemented
571	#3326	C₂×C₃₁	1	2	yes	complemented
572	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
573	#3301	C₂×C₃₁	1	2	yes	complemented
574	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#3287	C₂×C₃₁	1	1	yes	characteristic, complemented
576	#3282	C₂×C₃₁	1	2	yes	complemented
577	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
578	#3278	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#3275	C₂×C₃₁	1	2	yes	complemented
580	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
581	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
582	#3207	C₂×C₃₁	1	1	yes	characteristic, complemented
583	#3204	C₂×C₃₁	1	2	yes	complemented
584	#3198	C₂×C₃₁	1	2	yes	complemented
585	#3108	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#3103	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#3013	C₂×C₃₁	1	2	yes	complemented
588	#3010	C₂×C₃₁	1	2	yes	complemented
589	#2979	C₂×C₃₁	1	1	yes	characteristic, complemented
590	C₂²×C₃₁	—	2	1	no	—
591	C₂²×C₃₁	—	2	2	no	—
592	C₂²×C₃₁	—	2	2	no	—
593	C₂²×C₃₁	—	2	1	no	—
594	C₂²×C₃₁	—	2	2	no	—
595	C₂²×C₃₁	—	2	2	no	—
596	C₂²×C₃₁	—	2	1	no	—
597	C₂²×C₃₁	—	2	2	no	—
598	C₂²×C₃₁	—	2	2	no	—
599	C₂²×C₃₁	—	4	2	no	—
600	C₂²×C₃₁	—	4	2	no	—
601	C₂²×C₃₁	—	4	1	no	—
602	C₂²×C₃₁	—	4	2	no	—
603	C₂²×C₃₁	—	4	2	no	—
604	C₂²×C₃₁	—	4	1	no	—
605	C₂²×C₃₁	—	4	1	no	—
606	C₂²×C₃₁	—	4	2	no	—
607	C₂²×C₃₁	—	4	2	no	—
608	C₂²×C₃₁	—	16	4	no	—
609	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
610	C₄×C₃₁	—	2	1	no	—
611	C₄×C₃₁	—	2	1	no	—
612	C₄×C₃₁	—	2	2	no	—
613	C₄×C₃₁	—	2	2	no	—
614	C₄×C₃₁	—	2	1	no	—
615	C₄×C₃₁	—	2	2	no	—
616	C₄×C₃₁	—	2	2	no	—
617	C₄×C₃₁	—	2	1	no	—
618	C₄×C₃₁	—	4	1	no	—
619	C₄×C₃₁	—	4	1	no	—
620	C₄×C₃₁	—	4	1	no	—
621	C₄×C₃₁	—	4	2	no	—
622	C₄×C₃₁	—	4	1	no	—
623	C₄×C₃₁	—	4	1	no	—
624	C₄×C₃₁	—	4	2	no	—
625	C₄×C₃₁	#577	1	2	yes	—
626	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
627	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	complemented
629	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
630	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
631	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
632	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
633	#560	—	2	2	no	—
634	#556	C₂²×C₃₁	1	1	yes	characteristic
635	#553	C₂²×C₃₁	1	2	yes	—
636	#550	—	2	1	no	—
637	#550	—	2	1	no	—
638	#550	C₂²×C₃₁	1	1	yes	characteristic
639	#550	C₂²×C₃₁	1	1	yes	characteristic
640	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	D₄×Q₈	—	2	1	no	—
642	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
643	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#548	—	2	2	no	—
645	#548	C₂²×C₃₁	1	2	yes	complemented
646	#548	C₂²×C₃₁	1	2	yes	complemented
647	#547	C₂²×C₃₁	1	1	yes	characteristic
648	#546	—	2	1	no	—
649	#546	C₂²×C₃₁	1	2	yes	—
650	D₄²	C₂²×C₃₁	1	1	yes	characteristic
651	#542	—	2	1	no	—
652	#538	—	2	2	no	—
653	#537	—	2	2	no	—
654	#537	C₂²×C₃₁	1	2	yes	—
655	#537	C₂²×C₃₁	1	2	yes	complemented
656	#535	—	2	1	no	—
657	#535	C₂²×C₃₁	1	2	yes	—
658	#532	—	2	1	no	—
659	#532	—	2	1	no	—
660	#532	C₂²×C₃₁	1	1	yes	characteristic
661	#532	C₂²×C₃₁	1	1	yes	characteristic
662	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#529	C₂²×C₃₁	1	1	yes	characteristic
664	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#495	C₂²×C₃₁	1	2	yes	—
666	#493	C₂²×C₃₁	1	1	yes	characteristic
667	#492	C₂²×C₃₁	1	1	yes	characteristic
668	#488	C₂²×C₃₁	1	2	yes	complemented
669	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#485	C₂²×C₃₁	1	2	yes	complemented
672	#483	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#483	C₂²×C₃₁	1	2	yes	complemented
674	#482	C₂²×C₃₁	1	2	yes	complemented
675	#481	C₂²×C₃₁	1	2	yes	complemented
676	#481	C₂²×C₃₁	1	2	yes	complemented
677	#480	C₂²×C₃₁	1	1	yes	characteristic
678	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#479	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#470	C₂²×C₃₁	1	2	yes	complemented
683	#469	C₂²×C₃₁	1	2	yes	—
684	#469	C₂²×C₃₁	1	2	yes	—
685	#468	C₂²×C₃₁	1	2	yes	complemented
686	#466	C₂²×C₃₁	1	2	yes	complemented
687	#465	C₂²×C₃₁	1	2	yes	—
688	#465	C₂²×C₃₁	1	2	yes	—
689	#465	C₂²×C₃₁	1	2	yes	complemented
690	#464	C₂²×C₃₁	1	1	yes	characteristic
691	#464	C₂²×C₃₁	1	1	yes	characteristic
692	#463	C₂²×C₃₁	1	2	yes	complemented
693	#463	C₂²×C₃₁	1	2	yes	complemented
694	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	#461	C₂²×C₃₁	1	1	yes	characteristic
696	#460	C₂²×C₃₁	1	1	yes	characteristic
697	#460	C₂²×C₃₁	1	1	yes	characteristic
698	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#459	C₂²×C₃₁	1	1	yes	characteristic
700	#452	C₂²×C₃₁	1	2	yes	complemented
701	#452	C₂²×C₃₁	1	2	yes	complemented
702	#452	C₂²×C₃₁	1	2	yes	complemented
703	#451	C₂²×C₃₁	1	2	yes	complemented
704	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#450	C₂²×C₃₁	1	2	yes	—
706	#449	C₂²×C₃₁	1	2	yes	—
707	#449	C₂²×C₃₁	1	2	yes	—
708	#449	C₂²×C₃₁	1	2	yes	—
709	#449	C₂²×C₃₁	1	2	yes	complemented
710	#449	C₂²×C₃₁	1	2	yes	complemented
711	#449	C₂²×C₃₁	1	2	yes	complemented
712	#449	C₂²×C₃₁	1	2	yes	complemented
713	#448	C₂²×C₃₁	1	1	yes	characteristic
714	#448	C₂²×C₃₁	1	2	yes	—
715	#448	C₂²×C₃₁	1	2	yes	—
716	#448	C₂²×C₃₁	1	2	yes	complemented
717	#448	C₂²×C₃₁	1	2	yes	complemented
718	#447	C₂²×C₃₁	1	2	yes	—
719	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
722	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
723	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
724	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
725	#436	C₂²×C₃₁	1	1	yes	characteristic
726	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#436	C₂²×C₃₁	1	2	yes	complemented
728	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
729	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
730	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
733	#419	C₂²×C₃₁	1	2	yes	complemented
734	#417	C₂²×C₃₁	1	2	yes	complemented
735	#416	C₂²×C₃₁	1	2	yes	complemented
736	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
737	#408	C₂²×C₃₁	1	2	yes	complemented
738	#408	C₂²×C₃₁	1	2	yes	complemented
739	C₂×C₃₁	—	4	1	no	—
740	C₂×C₃₁	—	4	2	no	—
741	C₂×C₃₁	—	4	2	no	—
742	C₂×C₃₁	—	8	2	no	—
743	C₂×C₃₁	—	8	2	no	—
744	C₂×C₃₁	—	8	1	no	—
745	C₂×C₃₁	#3484	1	1	yes	characteristic
746	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
747	C₂×C₃₁	#3584	1	1	yes	characteristic
748	2₋¹⁺⁴	—	4	4	no	—
749	2₋¹⁺⁴	—	4	4	no	—
750	C₂×#41	—	2	2	no	—
751	C₂×#41	—	2	2	no	—
752	C₂×#41	—	2	2	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	C₂³×C₃₁	1	2	yes	—
756	C₂×#41	C₂³×C₃₁	1	2	yes	—
757	C₂×#41	C₂³×C₃₁	1	2	yes	—
758	C₂×#41	C₂³×C₃₁	1	2	yes	—
759	C₂×#41	C₂³×C₃₁	1	2	yes	—
760	C₂²×Q₈	—	2	2	no	—
761	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
762	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
763	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
766	#137	—	4	4	no	—
767	AGL(1,ℤ/8)	—	4	4	no	—
768	#135	—	4	4	no	—
769	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
770	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
772	C₂×SD₁₆	—	4	4	no	—
773	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
775	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
778	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
779	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
780	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
781	C₂×D₈	C₂³×C₃₁	1	2	yes	—
782	C₂×D₈	C₂³×C₃₁	1	2	yes	—
783	C₂×D₈	C₂³×C₃₁	1	2	yes	—
784	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
785	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
786	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
787	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
788	C₄⋊Q₈	—	2	1	no	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
791	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
792	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
793	#127	—	2	1	no	—
794	#127	—	2	1	no	—
795	#127	—	2	1	no	—
796	#127	—	2	2	no	—
797	#127	D₄×C₃₁	1	1	yes	characteristic
798	#127	C₂³×C₃₁	1	1	yes	characteristic
799	#127	C₂³×C₃₁	1	1	yes	characteristic
800	#126	—	2	2	no	—
801	#126	—	2	2	no	—
802	#126	—	2	1	no	—
803	#125	C₂³×C₃₁	1	1	yes	characteristic
804	#124	—	2	2	no	—
805	#124	—	2	1	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	1	no	—
809	#124	D₄×C₃₁	1	2	yes	—
810	#124	C₂³×C₃₁	1	1	yes	characteristic
811	#124	C₂³×C₃₁	1	2	yes	—
812	#123	—	2	1	no	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	2	no	—
819	C₂²⋊Q₈	—	2	2	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	2	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
824	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	1	no	—
837	#121	—	2	1	no	—
838	#121	—	2	1	no	—
839	#121	—	2	1	no	—
840	#121	—	2	2	no	—
841	#121	—	2	2	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#121	D₄×C₃₁	1	1	yes	characteristic
845	#121	D₄×C₃₁	1	1	yes	characteristic
846	#121	D₄×C₃₁	1	2	yes	—
847	#121	C₂³×C₃₁	1	1	yes	characteristic
848	#121	C₂³×C₃₁	1	2	yes	—
849	#121	C₂³×C₃₁	1	2	yes	—
850	#121	C₂³×C₃₁	1	2	yes	—
851	#121	C₂³×C₃₁	1	2	yes	—
852	#121	C₂³×C₃₁	1	2	yes	—
853	#121	C₂³×C₃₁	1	2	yes	—
854	#120	—	2	2	no	—
855	#120	—	2	2	no	—
856	#120	—	2	2	no	—
857	#120	—	2	2	no	—
858	C₄×Q₈	—	2	1	no	—
859	C₄×Q₈	—	2	1	no	—
860	C₄×Q₈	—	2	1	no	—
861	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
862	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
863	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
864	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
865	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
871	C₄×D₄	—	2	1	no	—
872	C₄×D₄	—	2	2	no	—
873	C₄×D₄	—	2	2	no	—
874	C₄×D₄	—	2	2	no	—
875	C₄×D₄	—	2	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
879	C₄×D₄	C₂³×C₃₁	1	2	yes	—
880	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
881	C₄×D₄	C₂³×C₃₁	1	2	yes	—
882	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
883	#117	—	2	1	no	—
884	#117	C₂³×C₃₁	1	2	yes	—
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₄²	—	2	1	no	—
890	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
891	#107	C₂³×C₃₁	1	1	yes	characteristic
892	#107	C₂³×C₃₁	1	1	yes	characteristic
893	#106	C₂³×C₃₁	1	1	yes	characteristic
894	#106	C₂³×C₃₁	1	1	yes	characteristic
895	#106	C₂³×C₃₁	1	2	yes	—
896	#106	C₂³×C₃₁	1	2	yes	—
897	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
898	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
899	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
901	#103	C₂³×C₃₁	1	1	yes	characteristic
902	#103	C₂³×C₃₁	1	2	yes	—
903	#103	C₂³×C₃₁	1	2	yes	—
904	#103	C₂³×C₃₁	1	2	yes	—
905	#103	C₂³×C₃₁	1	1	yes	characteristic
906	#103	C₂³×C₃₁	1	1	yes	characteristic
907	#103	C₂³×C₃₁	1	2	yes	—
908	#103	C₂³×C₃₁	1	1	yes	characteristic
909	#103	C₂³×C₃₁	1	2	yes	—
910	#103	C₂³×C₃₁	1	2	yes	—
911	#103	C₂³×C₃₁	1	1	yes	characteristic
912	#103	C₂³×C₃₁	1	1	yes	characteristic
913	#102	C₂³×C₃₁	1	2	yes	—
914	#102	C₂³×C₃₁	1	2	yes	—
915	#102	C₂³×C₃₁	1	2	yes	—
916	#102	C₂³×C₃₁	1	2	yes	—
917	#102	C₂³×C₃₁	1	1	yes	characteristic
918	#102	C₂³×C₃₁	1	1	yes	characteristic
919	#102	C₂³×C₃₁	1	2	yes	—
920	#102	C₂³×C₃₁	1	2	yes	—
921	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
922	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
925	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
928	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
929	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
930	C₄×C₈	C₂³×C₃₁	1	2	yes	—
931	C₃₁	#61659	1	1	yes	characteristic, direct product factor, Sylow
932	C₂⁴	—	2	2	no	—
933	#41	—	2	4	no	—
934	#41	—	2	4	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	4	2	no	—
939	#41	—	4	2	no	—
940	#41	—	4	2	no	—
941	#41	—	4	8	no	—
942	#41	—	4	8	no	—
943	#41	—	4	2	no	—
944	#41	—	4	2	no	—
945	#41	—	4	8	no	—
946	#41	—	8	2	no	—
947	#41	—	8	2	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	2	1	no	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	2	no	—
954	C₂×Q₈	—	2	4	no	—
955	C₂×Q₈	—	2	4	no	—
956	C₂×Q₈	—	4	2	no	—
957	C₂×Q₈	—	4	2	no	—
958	C₂×Q₈	—	4	8	no	—
959	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
960	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
961	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
962	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	—	2	2	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	1	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	2	no	—
975	C₂×D₄	—	2	1	no	—
976	C₂×D₄	—	2	1	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	2	no	—
980	C₂×D₄	—	4	2	no	—
981	C₂×D₄	—	4	2	no	—
982	C₂×D₄	—	8	2	no	—
983	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
985	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
990	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
991	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	2	no	—
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	2	no	—
1000	C₂²×C₄	—	2	2	no	—
1001	C₂²×C₄	—	2	2	no	—
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	2	2	no	—
1010	Q₁₆	—	4	2	no	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	2	4	no	—
1013	SD₁₆	—	2	2	no	—
1014	SD₁₆	—	2	4	no	—
1015	SD₁₆	—	4	2	no	—
1016	SD₁₆	—	4	2	no	—
1017	SD₁₆	—	4	2	no	—
1018	SD₁₆	—	4	2	no	—
1019	D₈	—	4	2	no	—
1020	D₈	—	4	2	no	—
1021	D₈	—	4	2	no	—
1022	M₁₆	—	4	2	no	—
1023	M₁₆	—	4	2	no	—
1024	C₂×C₈	—	4	2	no	—
1025	C₂×C₈	—	4	2	no	—
1026	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1030	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1031	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1049	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1052	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1055	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	2	no	—
1069	C₂²⋊C₄	—	2	2	no	—
1070	C₂²⋊C₄	—	2	2	no	—
1071	C₂²⋊C₄	—	2	2	no	—
1072	C₂²⋊C₄	—	2	1	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	2	no	—
1084	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1085	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1086	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1087	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1088	C₂³	—	2	1	no	—
1089	C₂³	—	2	2	no	—
1090	C₂³	—	2	2	no	—
1091	C₂³	—	8	2	no	—
1092	C₂³	—	8	2	no	—
1093	C₂³	—	8	2	no	—
1094	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1095	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1096	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1097	Q₈	—	2	4	no	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	1	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	2	no	—
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	1	no	—
1104	Q₈	—	4	2	no	—
1105	Q₈	—	4	4	no	—
1106	Q₈	—	4	4	no	—
1107	Q₈	—	4	2	no	—
1108	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1109	Q₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1110	D₄	—	2	2	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	2	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	4	4	no	—
1123	D₄	—	4	4	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	2	no	—
1126	D₄	—	4	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	1	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	1	no	—
1133	D₄	—	8	2	no	—
1134	D₄	—	8	2	no	—
1135	D₄	—	8	2	no	—
1136	D₄	—	8	2	no	—
1137	D₄	—	8	2	no	—
1138	C₂×C₄	—	2	4	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	2	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	2	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	2	no	—
1155	C₂×C₄	—	4	1	no	—
1156	C₂×C₄	—	4	4	no	—
1157	C₂×C₄	—	4	4	no	—
1158	C₂×C₄	—	4	4	no	—
1159	C₂×C₄	—	4	4	no	—
1160	C₂×C₄	—	4	4	no	—
1161	C₂×C₄	—	4	2	no	—
1162	C₂×C₄	—	8	2	no	—
1163	C₂×C₄	—	8	2	no	—
1164	C₂×C₄	—	8	1	no	—
1165	C₂×C₄	—	8	2	no	—
1166	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1170	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1171	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1172	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1173	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	2	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	2	2	no	—
1179	C₈	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	1	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	1	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	2	2	no	—
1189	C₂²	—	4	2	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	2	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	16	4	no	—
1199	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1200	C₄	—	2	2	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	1	no	—
1208	C₄	—	4	2	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	C₃₁×#577	1	2	yes	—
1216	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1217	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1218	C₂	—	4	2	no	—
1219	C₂	—	4	1	no	—
1220	C₂	—	4	2	no	—
1221	C₂	—	8	1	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	2	no	—
1224	C₂	C₃₁×#3484	1	1	yes	characteristic
1225	C₂	C₂×C₃₁×#577	1	1	yes	characteristic
1226	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×#3546	C₂	semidirect
2. C₃₁×#3497	C₂	semidirect
3. C₃₁×#3332	C₂	semidirect
4. C₃₁×#3328	C₂	semidirect
5. C₃₁×#3326	C₂	semidirect
6. C₃₁×#3304	C₂	semidirect
7. C₃₁×#3301	C₂	semidirect
8. C₃₁×#3298	C₂	semidirect
9. C₃₁×#3287	C₂	semidirect
10. C₃₁×#3282	C₂	semidirect
11. D₄×SD₁₆×C₃₁	C₂	semidirect
12. C₃₁×#3278	C₂	semidirect
13. C₃₁×#3275	C₂	semidirect
14. C₃₁×#3274	C₂	semidirect
15. C₃₁×#3212	C₂	semidirect
16. C₃₁×#3207	C₂	semidirect
17. C₃₁×#3204	C₂	semidirect
18. C₃₁×#3198	C₂	semidirect
19. C₃₁×#3108	C₂	semidirect
20. C₃₁×#3103	C₂	semidirect
21. C₃₁×#3013	C₂	semidirect
22. C₃₁×#3010	C₂	semidirect
23. C₃₁×#2979	C₂	semidirect
24. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
25. C₂×C₃₁×#137	C₂²	semidirect
27. C₂×C₃₁×#135	C₂²	semidirect
36. C₃₁×#550	C₂²	semidirect
39. D₄×Q₈×C₃₁	C₂²	semidirect
41. C₃₁×#548	C₂²	semidirect
42. C₃₁×#548	C₂²	semidirect
51. C₃₁×#537	C₂²	semidirect
58. C₃₁×#532	C₂²	semidirect
60. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#487	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#483	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#475	C₂²	semidirect
77. C₃₁×#475	C₂²	semidirect
78. C₃₁×#470	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#466	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
90. C₃₁×#462	C₂²	semidirect
94. C₃₁×#460	C₂²	semidirect
96. C₃₁×#452	C₂²	semidirect
97. C₃₁×#452	C₂²	semidirect
98. C₃₁×#452	C₂²	semidirect
99. C₃₁×#451	C₂²	semidirect
100. C₃₁×#451	C₂²	semidirect
105. C₃₁×#449	C₂²	semidirect
106. C₃₁×#449	C₂²	semidirect
107. C₃₁×#449	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
115. C₄×Q₁₆×C₃₁	C₂²	semidirect
116. C₄×Q₁₆×C₃₁	C₂²	semidirect
119. C₄×SD₁₆×C₃₁	C₂²	semidirect
120. C₄×SD₁₆×C₃₁	C₂²	semidirect
122. C₃₁×#436	C₂²	semidirect
123. C₃₁×#436	C₂²	semidirect
125. C₈×D₄×C₃₁	C₂²	semidirect
126. C₈×D₄×C₃₁	C₂²	semidirect
127. C₃₁×#431	C₂²	semidirect
128. C₃₁×#431	C₂²	semidirect
129. C₃₁×#419	C₂²	semidirect
130. C₃₁×#417	C₂²	semidirect
131. C₃₁×#416	C₂²	semidirect
132. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#408	C₂²	semidirect
134. C₃₁×#408	C₂²	semidirect
474. #61659	C₃₁	direct (N × H)
567. #3546	C₂×C₃₁	semidirect
568. #3497	C₂×C₃₁	semidirect
569. #3332	C₂×C₃₁	semidirect
570. #3328	C₂×C₃₁	semidirect
571. #3326	C₂×C₃₁	semidirect
572. #3304	C₂×C₃₁	semidirect
573. #3301	C₂×C₃₁	semidirect
574. #3298	C₂×C₃₁	semidirect
575. #3287	C₂×C₃₁	semidirect
576. #3282	C₂×C₃₁	semidirect
577. D₄×SD₁₆	C₂×C₃₁	semidirect
578. #3278	C₂×C₃₁	semidirect
579. #3275	C₂×C₃₁	semidirect
580. #3274	C₂×C₃₁	semidirect
581. #3212	C₂×C₃₁	semidirect
582. #3207	C₂×C₃₁	semidirect
583. #3204	C₂×C₃₁	semidirect
584. #3198	C₂×C₃₁	semidirect
585. #3108	C₂×C₃₁	semidirect
586. #3103	C₂×C₃₁	semidirect
587. #3013	C₂×C₃₁	semidirect
588. #3010	C₂×C₃₁	semidirect
589. #2979	C₂×C₃₁	semidirect
628. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
629. C₂×#137	C₂²×C₃₁	semidirect
631. C₂×#135	C₂²×C₃₁	semidirect
640. #550	C₂²×C₃₁	semidirect
643. D₄×Q₈	C₂²×C₃₁	semidirect
645. #548	C₂²×C₃₁	semidirect
646. #548	C₂²×C₃₁	semidirect
655. #537	C₂²×C₃₁	semidirect
662. #532	C₂²×C₃₁	semidirect
664. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
668. #488	C₂²×C₃₁	semidirect
669. #487	C₂²×C₃₁	semidirect
670. #486	C₂²×C₃₁	semidirect
671. #485	C₂²×C₃₁	semidirect
672. #483	C₂²×C₃₁	semidirect
673. #483	C₂²×C₃₁	semidirect
674. #482	C₂²×C₃₁	semidirect
675. #481	C₂²×C₃₁	semidirect
676. #481	C₂²×C₃₁	semidirect
678. #479	C₂²×C₃₁	semidirect
679. #479	C₂²×C₃₁	semidirect
680. #475	C₂²×C₃₁	semidirect
681. #475	C₂²×C₃₁	semidirect
682. #470	C₂²×C₃₁	semidirect
685. #468	C₂²×C₃₁	semidirect
686. #466	C₂²×C₃₁	semidirect
689. #465	C₂²×C₃₁	semidirect
692. #463	C₂²×C₃₁	semidirect
693. #463	C₂²×C₃₁	semidirect
694. #462	C₂²×C₃₁	semidirect
698. #460	C₂²×C₃₁	semidirect
700. #452	C₂²×C₃₁	semidirect
701. #452	C₂²×C₃₁	semidirect
702. #452	C₂²×C₃₁	semidirect
703. #451	C₂²×C₃₁	semidirect
704. #451	C₂²×C₃₁	semidirect
709. #449	C₂²×C₃₁	semidirect
710. #449	C₂²×C₃₁	semidirect
711. #449	C₂²×C₃₁	semidirect
712. #449	C₂²×C₃₁	semidirect
716. #448	C₂²×C₃₁	semidirect
717. #448	C₂²×C₃₁	semidirect
719. C₄×Q₁₆	C₂²×C₃₁	semidirect
720. C₄×Q₁₆	C₂²×C₃₁	semidirect
723. C₄×SD₁₆	C₂²×C₃₁	semidirect
724. C₄×SD₁₆	C₂²×C₃₁	semidirect
726. #436	C₂²×C₃₁	semidirect
727. #436	C₂²×C₃₁	semidirect
729. C₈×D₄	C₂²×C₃₁	semidirect
730. C₈×D₄	C₂²×C₃₁	semidirect
731. #431	C₂²×C₃₁	semidirect
732. #431	C₂²×C₃₁	semidirect
733. #419	C₂²×C₃₁	semidirect
734. #417	C₂²×C₃₁	semidirect
735. #416	C₂²×C₃₁	semidirect
736. C₂×#103	C₂²×C₃₁	semidirect
737. #408	C₂²×C₃₁	semidirect
738. #408	C₂²×C₃₁	semidirect
931. C₃₁	#61659	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×#3546	2
C₃₁×#3497	2
C₃₁×#3332	2
C₃₁×#3328	2
C₃₁×#3326	2
C₃₁×#3304	2
C₃₁×#3301	2
C₃₁×#3298	2
C₃₁×#3287	2
C₃₁×#3282	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3278	2
C₃₁×#3275	2
C₃₁×#3274	2
C₃₁×#3212	2
C₃₁×#3207	2
C₃₁×#3204	2
C₃₁×#3198	2
C₃₁×#3108	2
C₃₁×#3103	2
C₃₁×#3013	2
C₃₁×#3010	2
C₃₁×#2979	2
#61659	31

Subgroups — C31×#61659 #21518418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61659 #21518418