Subgroups — C₃₁×#60586 #21517345

Order 7936.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3127	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3123	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3121	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3116	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3107	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3093	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#485	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3084	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3046	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3007	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3002	C₂	1	1	yes	maximal, characteristic
19	C₃₁×#2952	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2947	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2924	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
29	C₃₁×#556	—	2	1	no	—
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#552	—	2	2	no	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#541	C₂²	1	2	yes	—
38	C₃₁×#536	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#533	C₂²	1	2	yes	complemented
40	C₃₁×#529	C₂²	1	2	yes	complemented
41	C₃₁×#525	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₃₁×#520	—	2	1	no	—
44	C₃₁×#520	—	2	1	no	—
45	C₃₁×#520	C₂²	1	1	yes	characteristic
46	C₃₁×#520	C₂²	1	1	yes	characteristic
47	C₃₁×#520	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic
49	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#519	C₂²	1	2	yes	—
51	C₃₁×#519	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#518	—	2	2	no	—
53	C₃₁×#518	C₂²	1	2	yes	—
54	C₄×#41×C₃₁	—	2	2	no	—
55	C₄×#41×C₃₁	C₂²	1	2	yes	—
56	C₄×#41×C₃₁	C₂²	1	2	yes	—
57	C₂×C₃₁×#117	—	2	1	no	—
58	C₂×C₃₁×#117	—	2	1	no	—
59	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
60	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
61	C₃₁×#485	C₂²	1	2	yes	—
62	C₃₁×#485	C₂²	1	2	yes	—
63	C₃₁×#485	C₂²	1	2	yes	—
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#482	C₂²	1	2	yes	—
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#479	C₂²	1	2	yes	complemented
70	C₃₁×#479	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#477	C₂²	1	2	yes	complemented
74	C₃₁×#476	C₂²	1	2	yes	complemented
75	C₃₁×#475	C₂²	1	2	yes	complemented
76	C₃₁×#474	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×#462	C₂²	1	2	yes	complemented
83	C₃₁×#461	C₂²	1	2	yes	complemented
84	C₃₁×#461	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	—
86	C₃₁×#452	C₂²	1	1	yes	characteristic
87	C₃₁×#452	C₂²	1	2	yes	—
88	C₃₁×#452	C₂²	1	1	yes	characteristic
89	C₃₁×#451	C₂²	1	2	yes	—
90	C₃₁×#451	C₂²	1	1	yes	characteristic
91	C₃₁×#450	C₂²	1	2	yes	—
92	C₃₁×#450	C₂²	1	1	yes	characteristic
93	C₃₁×#449	C₂²	1	1	yes	characteristic
94	C₃₁×#449	C₂²	1	1	yes	characteristic
95	C₃₁×#448	C₂²	1	1	yes	characteristic
96	C₃₁×#447	C₂²	1	1	yes	characteristic
97	C₃₁×#442	C₂²	1	2	yes	complemented
98	C₃₁×#441	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	2	yes	complemented
100	C₃₁×#441	C₂²	1	2	yes	complemented
101	C₃₁×#440	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
108	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
113	C₃₁×#433	C₂²	1	2	yes	—
114	C₃₁×#433	C₂²	1	2	yes	—
115	C₃₁×#432	C₂²	1	2	yes	complemented
116	C₃₁×#431	C₂²	1	2	yes	complemented
117	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#417	C₂²	1	1	yes	characteristic
124	C₃₁×#417	C₂²	1	1	yes	characteristic
125	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic
129	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#407	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
133	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	4	no	—
136	C₂×#41×C₃₁	—	2	4	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₃₁	—	2	1	no	—
149	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
150	C₃₁×#137	—	2	4	no	—
151	C₃₁×#137	—	2	4	no	—
152	C₃₁×#135	—	2	4	no	—
153	C₃₁×#135	—	2	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×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
164	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
167	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
170	C₃₁×C₄⋊Q₈	—	2	1	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×#126	—	2	2	no	—
175	C₃₁×#126	—	2	2	no	—
176	C₃₁×#126	—	2	2	no	—
177	C₃₁×#125	—	2	2	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#123	—	2	1	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
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	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₃₁×#121	C₂³	1	1	yes	characteristic
200	C₃₁×#121	C₂³	1	1	yes	characteristic
201	C₃₁×#120	—	2	1	no	—
202	C₄×Q₈×C₃₁	—	2	2	no	—
203	C₄×Q₈×C₃₁	—	2	2	no	—
204	C₄×Q₈×C₃₁	—	2	1	no	—
205	C₄×Q₈×C₃₁	—	2	1	no	—
206	C₄×Q₈×C₃₁	—	2	2	no	—
207	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
210	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
211	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
212	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
213	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	2	no	—
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	1	no	—
220	C₄×D₄×C₃₁	—	2	2	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₃₁×#117	—	2	1	no	—
234	C₃₁×#117	—	2	1	no	—
235	C₃₁×#117	—	2	2	no	—
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	1	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	1	no	—
241	C₃₁×#117	—	2	2	no	—
242	C₃₁×#117	—	2	2	no	—
243	C₃₁×#117	—	2	2	no	—
244	C₃₁×#117	—	2	2	no	—
245	C₃₁×#117	—	2	2	no	—
246	C₃₁×#117	—	2	2	no	—
247	C₃₁×#117	D₄	1	1	yes	characteristic
248	C₃₁×#117	D₄	1	1	yes	characteristic
249	C₃₁×#117	D₄	1	2	yes	—
250	C₃₁×#117	C₂³	1	1	yes	characteristic
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
257	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
272	C₂×C₄²×C₃₁	—	2	1	no	—
273	C₂×C₄²×C₃₁	—	2	2	no	—
274	C₂×C₄²×C₃₁	—	2	2	no	—
275	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#107	C₂³	1	2	yes	—
278	C₃₁×#107	C₂³	1	2	yes	—
279	C₃₁×#107	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
310	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
311	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
312	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
313	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₃₁×#97	C₂³	1	2	yes	—
315	C₃₁×#97	C₂³	1	2	yes	—
316	C₄×C₈×C₃₁	C₂³	1	2	yes	—
317	C₄×C₈×C₃₁	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	1	no	—
319	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
320	#41×C₃₁	—	2	8	no	—
321	#41×C₃₁	—	2	8	no	—
322	#41×C₃₁	—	2	2	no	—
323	#41×C₃₁	—	2	2	no	—
324	#41×C₃₁	—	2	2	no	—
325	#41×C₃₁	—	2	2	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	#41	1	4	yes	—
331	#41×C₃₁	#41	1	4	yes	—
332	C₂×Q₈×C₃₁	—	2	2	no	—
333	C₂×Q₈×C₃₁	—	2	2	no	—
334	C₂×Q₈×C₃₁	—	2	1	no	—
335	C₂×Q₈×C₃₁	—	2	1	no	—
336	C₂×Q₈×C₃₁	—	2	2	no	—
337	C₂×Q₈×C₃₁	—	2	2	no	—
338	C₂×Q₈×C₃₁	—	2	2	no	—
339	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
340	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₃₁	—	2	8	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	1	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	2	2	no	—
349	C₂×D₄×C₃₁	—	2	2	no	—
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	2	1	no	—
352	C₂×D₄×C₃₁	—	2	1	no	—
353	C₂×D₄×C₃₁	—	2	1	no	—
354	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	—	2	8	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	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	2	no	—
364	C₂²×C₄×C₃₁	—	2	2	no	—
365	C₂²×C₄×C₃₁	—	2	1	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	1	no	—
370	C₂²×C₄×C₃₁	—	2	2	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	2	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
380	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	Q₁₆×C₃₁	—	2	2	no	—
384	Q₁₆×C₃₁	—	2	2	no	—
385	Q₁₆×C₃₁	—	2	4	no	—
386	Q₁₆×C₃₁	—	2	4	no	—
387	SD₁₆×C₃₁	—	2	2	no	—
388	SD₁₆×C₃₁	—	2	2	no	—
389	SD₁₆×C₃₁	—	2	2	no	—
390	SD₁₆×C₃₁	—	2	2	no	—
391	SD₁₆×C₃₁	—	2	4	no	—
392	SD₁₆×C₃₁	—	2	4	no	—
393	D₈×C₃₁	—	2	2	no	—
394	D₈×C₃₁	—	2	2	no	—
395	M₁₆×C₃₁	—	2	2	no	—
396	M₁₆×C₃₁	—	2	2	no	—
397	C₂×C₈×C₃₁	—	2	2	no	—
398	C₂×C₈×C₃₁	—	2	2	no	—
399	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
402	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	1	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	2	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	2	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	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	2	no	—
422	C₄⋊C₄×C₃₁	—	2	1	no	—
423	C₄⋊C₄×C₃₁	—	2	2	no	—
424	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
426	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
427	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
428	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
429	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
431	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	1	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
455	C₄²×C₃₁	—	2	2	no	—
456	C₄²×C₃₁	—	2	2	no	—
457	C₄²×C₃₁	—	2	2	no	—
458	C₄²×C₃₁	—	2	2	no	—
459	C₄²×C₃₁	—	2	2	no	—
460	C₄²×C₃₁	—	2	2	no	—
461	C₄²×C₃₁	—	2	2	no	—
462	C₄²×C₃₁	—	2	2	no	—
463	C₄²×C₃₁	—	2	2	no	—
464	C₄²×C₃₁	—	2	1	no	—
465	C₄²×C₃₁	C₂×D₄	1	2	yes	—
466	C₄²×C₃₁	C₂×D₄	1	2	yes	—
467	C₄²×C₃₁	C₂⁴	1	2	yes	—
468	C₄²×C₃₁	C₂⁴	1	2	yes	—
469	#60586	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
470	C₂³×C₃₁	—	2	4	no	—
471	C₂³×C₃₁	—	2	1	no	—
472	C₂³×C₃₁	—	2	1	no	—
473	C₂³×C₃₁	—	2	2	no	—
474	C₂³×C₃₁	—	2	1	no	—
475	C₂³×C₃₁	—	4	1	no	—
476	C₂³×C₃₁	—	4	1	no	—
477	C₂³×C₃₁	—	8	1	no	—
478	C₂³×C₃₁	—	8	1	no	—
479	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
480	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
481	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
482	Q₈×C₃₁	—	2	4	no	—
483	Q₈×C₃₁	—	2	1	no	—
484	Q₈×C₃₁	—	2	1	no	—
485	Q₈×C₃₁	—	2	2	no	—
486	Q₈×C₃₁	—	2	2	no	—
487	Q₈×C₃₁	—	2	1	no	—
488	Q₈×C₃₁	—	2	1	no	—
489	Q₈×C₃₁	—	4	2	no	—
490	Q₈×C₃₁	—	8	2	no	—
491	Q₈×C₃₁	C₂×#41	1	2	yes	—
492	Q₈×C₃₁	C₂×#41	1	2	yes	—
493	D₄×C₃₁	—	2	4	no	—
494	D₄×C₃₁	—	2	4	no	—
495	D₄×C₃₁	—	2	4	no	—
496	D₄×C₃₁	—	2	4	no	—
497	D₄×C₃₁	—	2	4	no	—
498	D₄×C₃₁	—	2	1	no	—
499	D₄×C₃₁	—	2	1	no	—
500	D₄×C₃₁	—	2	1	no	—
501	D₄×C₃₁	—	2	1	no	—
502	D₄×C₃₁	—	4	2	no	—
503	D₄×C₃₁	—	4	2	no	—
504	D₄×C₃₁	—	8	1	no	—
505	D₄×C₃₁	C₂×#41	1	2	yes	—
506	D₄×C₃₁	C₂×#41	1	2	yes	—
507	C₂×C₄×C₃₁	—	2	4	no	—
508	C₂×C₄×C₃₁	—	2	4	no	—
509	C₂×C₄×C₃₁	—	2	4	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	4	no	—
515	C₂×C₄×C₃₁	—	2	4	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	1	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	2	1	no	—
521	C₂×C₄×C₃₁	—	2	2	no	—
522	C₂×C₄×C₃₁	—	2	2	no	—
523	C₂×C₄×C₃₁	—	2	1	no	—
524	C₂×C₄×C₃₁	—	2	1	no	—
525	C₂×C₄×C₃₁	—	2	2	no	—
526	C₂×C₄×C₃₁	—	2	1	no	—
527	C₂×C₄×C₃₁	—	2	2	no	—
528	C₂×C₄×C₃₁	—	4	2	no	—
529	C₂×C₄×C₃₁	—	4	2	no	—
530	C₂×C₄×C₃₁	—	4	2	no	—
531	C₂×C₄×C₃₁	—	4	2	no	—
532	C₂×C₄×C₃₁	—	8	2	no	—
533	C₂×C₄×C₃₁	—	8	2	no	—
534	C₂×C₄×C₃₁	—	8	2	no	—
535	C₂×C₄×C₃₁	—	8	2	no	—
536	C₂×C₄×C₃₁	—	8	2	no	—
537	C₂×C₄×C₃₁	—	8	1	no	—
538	C₂×C₄×C₃₁	—	8	1	no	—
539	C₂×C₄×C₃₁	—	8	1	no	—
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	2	yes	—
543	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
548	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
549	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
550	C₈×C₃₁	—	2	1	no	—
551	C₈×C₃₁	—	2	1	no	—
552	C₈×C₃₁	—	2	1	no	—
553	C₈×C₃₁	—	2	1	no	—
554	C₈×C₃₁	—	2	2	no	—
555	C₈×C₃₁	—	2	2	no	—
556	#3495	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3428	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3127	C₂×C₃₁	1	2	yes	complemented
559	#3123	C₂×C₃₁	1	2	yes	complemented
560	#3121	C₂×C₃₁	1	2	yes	complemented
561	#3118	C₂×C₃₁	1	2	yes	complemented
562	#3116	C₂×C₃₁	1	2	yes	complemented
563	#3111	C₂×C₃₁	1	2	yes	complemented
564	#3107	C₂×C₃₁	1	2	yes	complemented
565	#3102	C₂×C₃₁	1	2	yes	complemented
566	#3093	C₂×C₃₁	1	1	yes	characteristic, complemented
567	C₂×#485	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3084	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
571	#3046	C₂×C₃₁	1	1	yes	characteristic, complemented
572	#3007	C₂×C₃₁	1	1	yes	characteristic, complemented
573	#3002	C₂×C₃₁	1	1	yes	characteristic
574	#2952	C₂×C₃₁	1	1	yes	characteristic, complemented
575	#2951	C₂×C₃₁	1	1	yes	characteristic, complemented
576	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
577	#2947	C₂×C₃₁	1	1	yes	characteristic, complemented
578	#2924	C₂×C₃₁	1	1	yes	characteristic, complemented
579	C₂²×C₃₁	—	2	1	no	—
580	C₂²×C₃₁	—	2	1	no	—
581	C₂²×C₃₁	—	2	1	no	—
582	C₂²×C₃₁	—	2	1	no	—
583	C₂²×C₃₁	—	2	1	no	—
584	C₂²×C₃₁	—	2	1	no	—
585	C₂²×C₃₁	—	2	1	no	—
586	C₂²×C₃₁	—	2	1	no	—
587	C₂²×C₃₁	—	2	2	no	—
588	C₂²×C₃₁	—	2	2	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	4	1	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	1	no	—
593	C₂²×C₃₁	—	4	1	no	—
594	C₂²×C₃₁	—	4	1	no	—
595	C₂²×C₃₁	—	4	1	no	—
596	C₂²×C₃₁	—	8	2	no	—
597	C₂²×C₃₁	—	8	4	no	—
598	C₂²×C₃₁	#525	1	2	yes	—
599	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
600	C₄×C₃₁	—	2	2	no	—
601	C₄×C₃₁	—	2	2	no	—
602	C₄×C₃₁	—	2	2	no	—
603	C₄×C₃₁	—	2	2	no	—
604	C₄×C₃₁	—	2	1	no	—
605	C₄×C₃₁	—	2	2	no	—
606	C₄×C₃₁	—	2	2	no	—
607	C₄×C₃₁	—	2	1	no	—
608	C₄×C₃₁	—	4	2	no	—
609	C₄×C₃₁	—	4	2	no	—
610	C₄×C₃₁	—	4	1	no	—
611	C₄×C₃₁	—	4	2	no	—
612	C₄×C₃₁	—	4	1	no	—
613	C₄×C₃₁	—	4	1	no	—
614	C₄×C₃₁	—	4	2	no	—
615	C₄×C₃₁	#525	1	2	yes	—
616	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
617	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
618	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
620	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
621	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
622	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
623	#556	—	2	1	no	—
624	#554	—	2	1	no	—
625	#552	—	2	2	no	—
626	#552	—	2	1	no	—
627	#552	—	2	1	no	—
628	#551	—	2	2	no	—
629	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#542	C₂²×C₃₁	1	2	yes	—
631	#541	C₂²×C₃₁	1	2	yes	—
632	#536	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#533	C₂²×C₃₁	1	2	yes	complemented
634	#529	C₂²×C₃₁	1	2	yes	complemented
635	#525	C₂²×C₃₁	1	1	yes	characteristic
636	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
637	#520	—	2	1	no	—
638	#520	—	2	1	no	—
639	#520	C₂²×C₃₁	1	1	yes	characteristic
640	#520	C₂²×C₃₁	1	1	yes	characteristic
641	#520	C₂²×C₃₁	1	1	yes	characteristic
642	#520	C₂²×C₃₁	1	1	yes	characteristic
643	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#519	C₂²×C₃₁	1	2	yes	—
645	#519	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#518	—	2	2	no	—
647	#518	C₂²×C₃₁	1	2	yes	—
648	C₄×#41	—	2	2	no	—
649	C₄×#41	C₂²×C₃₁	1	2	yes	—
650	C₄×#41	C₂²×C₃₁	1	2	yes	—
651	C₂×#117	—	2	1	no	—
652	C₂×#117	—	2	1	no	—
653	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
654	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
655	#485	C₂²×C₃₁	1	2	yes	—
656	#485	C₂²×C₃₁	1	2	yes	—
657	#485	C₂²×C₃₁	1	2	yes	—
658	#485	C₂²×C₃₁	1	2	yes	complemented
659	#485	C₂²×C₃₁	1	2	yes	complemented
660	#485	C₂²×C₃₁	1	2	yes	complemented
661	#482	C₂²×C₃₁	1	2	yes	—
662	#482	C₂²×C₃₁	1	2	yes	complemented
663	#479	C₂²×C₃₁	1	2	yes	complemented
664	#479	C₂²×C₃₁	1	2	yes	complemented
665	#478	C₂²×C₃₁	1	2	yes	complemented
666	#478	C₂²×C₃₁	1	2	yes	complemented
667	#477	C₂²×C₃₁	1	2	yes	complemented
668	#476	C₂²×C₃₁	1	2	yes	complemented
669	#475	C₂²×C₃₁	1	2	yes	complemented
670	#474	C₂²×C₃₁	1	2	yes	complemented
671	#464	C₂²×C₃₁	1	2	yes	complemented
672	#464	C₂²×C₃₁	1	2	yes	complemented
673	#463	C₂²×C₃₁	1	2	yes	complemented
674	#463	C₂²×C₃₁	1	2	yes	complemented
675	#462	C₂²×C₃₁	1	2	yes	complemented
676	#462	C₂²×C₃₁	1	2	yes	complemented
677	#461	C₂²×C₃₁	1	2	yes	complemented
678	#461	C₂²×C₃₁	1	2	yes	complemented
679	#452	C₂²×C₃₁	1	2	yes	—
680	#452	C₂²×C₃₁	1	1	yes	characteristic
681	#452	C₂²×C₃₁	1	2	yes	—
682	#452	C₂²×C₃₁	1	1	yes	characteristic
683	#451	C₂²×C₃₁	1	2	yes	—
684	#451	C₂²×C₃₁	1	1	yes	characteristic
685	#450	C₂²×C₃₁	1	2	yes	—
686	#450	C₂²×C₃₁	1	1	yes	characteristic
687	#449	C₂²×C₃₁	1	1	yes	characteristic
688	#449	C₂²×C₃₁	1	1	yes	characteristic
689	#448	C₂²×C₃₁	1	1	yes	characteristic
690	#447	C₂²×C₃₁	1	1	yes	characteristic
691	#442	C₂²×C₃₁	1	2	yes	complemented
692	#441	C₂²×C₃₁	1	2	yes	complemented
693	#441	C₂²×C₃₁	1	2	yes	complemented
694	#441	C₂²×C₃₁	1	2	yes	complemented
695	#440	C₂²×C₃₁	1	2	yes	complemented
696	#440	C₂²×C₃₁	1	2	yes	complemented
697	#440	C₂²×C₃₁	1	2	yes	complemented
698	#440	C₂²×C₃₁	1	2	yes	complemented
699	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
700	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
701	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
703	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
704	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
705	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
706	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
707	#433	C₂²×C₃₁	1	2	yes	—
708	#433	C₂²×C₃₁	1	2	yes	—
709	#432	C₂²×C₃₁	1	2	yes	complemented
710	#431	C₂²×C₃₁	1	2	yes	complemented
711	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#417	C₂²×C₃₁	1	1	yes	characteristic
718	#417	C₂²×C₃₁	1	1	yes	characteristic
719	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
720	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	#416	C₂²×C₃₁	1	1	yes	characteristic
722	#416	C₂²×C₃₁	1	1	yes	characteristic
723	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	#407	C₂²×C₃₁	1	1	yes	characteristic
726	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
727	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
728	#405	C₂²×C₃₁	1	1	yes	characteristic, complemented
729	C₂×C₃₁	—	2	2	no	—
730	C₂×C₃₁	—	4	1	no	—
731	C₂×C₃₁	—	4	1	no	—
732	C₂×C₃₁	—	4	2	no	—
733	C₂×C₃₁	—	4	2	no	—
734	C₂×C₃₁	—	8	1	no	—
735	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
736	C₂×C₃₁	#3584	1	1	yes	characteristic
737	C₂×C₃₁	#3586	1	1	yes	characteristic
738	C₂×#41	—	2	4	no	—
739	C₂×#41	—	2	4	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
747	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
748	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
749	C₂²×D₄	—	2	1	no	—
750	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
751	C₂³×C₄	—	2	1	no	—
752	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
753	#137	—	2	4	no	—
754	#137	—	2	4	no	—
755	#135	—	2	4	no	—
756	#135	—	2	4	no	—
757	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
760	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
763	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
764	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
765	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
766	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
767	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
769	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
770	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
771	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
773	C₄⋊Q₈	—	2	1	no	—
774	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
775	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	#126	—	2	2	no	—
777	#126	—	2	2	no	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#125	—	2	2	no	—
781	#125	—	2	2	no	—
782	#125	—	2	1	no	—
783	#125	—	2	2	no	—
784	#125	C₂³×C₃₁	1	2	yes	—
785	#124	—	2	2	no	—
786	#124	C₂³×C₃₁	1	2	yes	—
787	#123	—	2	1	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	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	1	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
801	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
802	#121	C₂³×C₃₁	1	1	yes	characteristic
803	#121	C₂³×C₃₁	1	1	yes	characteristic
804	#120	—	2	1	no	—
805	C₄×Q₈	—	2	2	no	—
806	C₄×Q₈	—	2	2	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	2	no	—
810	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
811	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
814	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
816	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	C₂³×C₃₁	1	2	yes	—
832	C₄×D₄	C₂³×C₃₁	1	2	yes	—
833	C₄×D₄	C₂³×C₃₁	1	2	yes	—
834	C₄×D₄	C₂³×C₃₁	1	2	yes	—
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	#117	—	2	1	no	—
837	#117	—	2	1	no	—
838	#117	—	2	2	no	—
839	#117	—	2	1	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	1	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	—	2	2	no	—
848	#117	—	2	2	no	—
849	#117	—	2	2	no	—
850	#117	D₄×C₃₁	1	1	yes	characteristic
851	#117	D₄×C₃₁	1	1	yes	characteristic
852	#117	D₄×C₃₁	1	2	yes	—
853	#117	C₂³×C₃₁	1	2	yes	—
854	#117	C₂³×C₃₁	1	2	yes	—
855	#117	C₂³×C₃₁	1	1	yes	characteristic
856	#117	C₂³×C₃₁	1	2	yes	—
857	#117	C₂³×C₃₁	1	1	yes	characteristic
858	#117	C₂³×C₃₁	1	1	yes	characteristic
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
866	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
875	C₂×C₄²	—	2	1	no	—
876	C₂×C₄²	—	2	2	no	—
877	C₂×C₄²	—	2	2	no	—
878	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
879	#107	C₂³×C₃₁	1	2	yes	—
880	#107	C₂³×C₃₁	1	2	yes	—
881	#107	C₂³×C₃₁	1	2	yes	—
882	#107	C₂³×C₃₁	1	2	yes	—
883	#106	C₂³×C₃₁	1	2	yes	—
884	#106	C₂³×C₃₁	1	2	yes	—
885	#106	C₂³×C₃₁	1	2	yes	—
886	#106	C₂³×C₃₁	1	2	yes	—
887	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
888	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
889	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
890	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
891	#103	C₂³×C₃₁	1	2	yes	—
892	#103	C₂³×C₃₁	1	2	yes	—
893	#103	C₂³×C₃₁	1	2	yes	—
894	#103	C₂³×C₃₁	1	2	yes	—
895	#103	C₂³×C₃₁	1	1	yes	characteristic
896	#103	C₂³×C₃₁	1	1	yes	characteristic
897	#103	C₂³×C₃₁	1	1	yes	characteristic
898	#103	C₂³×C₃₁	1	1	yes	characteristic
899	#103	C₂³×C₃₁	1	2	yes	—
900	#103	C₂³×C₃₁	1	2	yes	—
901	#103	C₂³×C₃₁	1	2	yes	—
902	#103	C₂³×C₃₁	1	2	yes	—
903	#102	C₂³×C₃₁	1	1	yes	characteristic
904	#102	C₂³×C₃₁	1	1	yes	characteristic
905	#102	C₂³×C₃₁	1	1	yes	characteristic
906	#102	C₂³×C₃₁	1	1	yes	characteristic
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	2	yes	—
909	#102	C₂³×C₃₁	1	2	yes	—
910	#102	C₂³×C₃₁	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
912	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
913	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
914	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
915	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
917	#97	C₂³×C₃₁	1	2	yes	—
918	#97	C₂³×C₃₁	1	2	yes	—
919	C₄×C₈	C₂³×C₃₁	1	2	yes	—
920	C₄×C₈	C₂³×C₃₁	1	2	yes	—
921	C₃₁	#60586	1	1	yes	characteristic, direct product factor, Sylow
922	C₂⁴	—	2	1	no	—
923	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
924	#41	—	2	8	no	—
925	#41	—	2	8	no	—
926	#41	—	2	2	no	—
927	#41	—	2	2	no	—
928	#41	—	2	2	no	—
929	#41	—	2	2	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	#41×C₃₁	1	4	yes	—
935	#41	#41×C₃₁	1	4	yes	—
936	C₂×Q₈	—	2	2	no	—
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	—	2	1	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	—	2	2	no	—
943	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
944	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
947	C₂×D₄	—	2	8	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	1	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	1	no	—
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
961	C₂²×C₄	—	2	8	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	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	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	2	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	C₂×D₄×C₃₁	1	1	yes	characteristic
982	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
983	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
984	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
987	Q₁₆	—	2	2	no	—
988	Q₁₆	—	2	2	no	—
989	Q₁₆	—	2	4	no	—
990	Q₁₆	—	2	4	no	—
991	SD₁₆	—	2	2	no	—
992	SD₁₆	—	2	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	2	no	—
995	SD₁₆	—	2	4	no	—
996	SD₁₆	—	2	4	no	—
997	D₈	—	2	2	no	—
998	D₈	—	2	2	no	—
999	M₁₆	—	2	2	no	—
1000	M₁₆	—	2	2	no	—
1001	C₂×C₈	—	2	2	no	—
1002	C₂×C₈	—	2	2	no	—
1003	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1004	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1005	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1006	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1007	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	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	—	2	2	no	—
1018	C₄⋊C₄	—	2	2	no	—
1019	C₄⋊C₄	—	2	2	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1029	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
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	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1035	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1037	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1038	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
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	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	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	1	no	—
1054	C₂²⋊C₄	—	2	2	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	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	2	no	—
1063	C₄²	—	2	2	no	—
1064	C₄²	—	2	2	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	—	2	2	no	—
1067	C₄²	—	2	2	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1070	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1071	C₄²	C₂⁴×C₃₁	1	2	yes	—
1072	C₄²	C₂⁴×C₃₁	1	2	yes	—
1073	C₂³	—	2	4	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	1	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	4	1	no	—
1079	C₂³	—	4	1	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	1	no	—
1082	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1083	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1084	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1085	Q₈	—	2	4	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	2	2	no	—
1089	Q₈	—	2	2	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	2	1	no	—
1092	Q₈	—	4	2	no	—
1093	Q₈	—	8	2	no	—
1094	Q₈	C₂×#41×C₃₁	1	2	yes	—
1095	Q₈	C₂×#41×C₃₁	1	2	yes	—
1096	D₄	—	2	4	no	—
1097	D₄	—	2	4	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	4	no	—
1100	D₄	—	2	4	no	—
1101	D₄	—	2	1	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	8	1	no	—
1108	D₄	C₂×#41×C₃₁	1	2	yes	—
1109	D₄	C₂×#41×C₃₁	1	2	yes	—
1110	C₂×C₄	—	2	4	no	—
1111	C₂×C₄	—	2	4	no	—
1112	C₂×C₄	—	2	4	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	4	no	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	2	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	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	1	no	—
1128	C₂×C₄	—	2	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	2	no	—
1133	C₂×C₄	—	4	2	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	8	2	no	—
1136	C₂×C₄	—	8	2	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	—	8	1	no	—
1141	C₂×C₄	—	8	1	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	C₂²×D₄×C₃₁	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1149	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1150	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1151	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1152	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1153	C₈	—	2	1	no	—
1154	C₈	—	2	1	no	—
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	2	no	—
1158	C₈	—	2	2	no	—
1159	C₂²	—	2	1	no	—
1160	C₂²	—	2	1	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	1	no	—
1167	C₂²	—	2	1	no	—
1168	C₂²	—	2	1	no	—
1169	C₂²	—	4	1	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	1	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	8	2	no	—
1177	C₂²	—	8	4	no	—
1178	C₂²	C₃₁×#525	1	2	yes	—
1179	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1180	C₄	—	2	1	no	—
1181	C₄	—	2	2	no	—
1182	C₄	—	2	2	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	2	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	2	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	2	no	—
1190	C₄	—	4	2	no	—
1191	C₄	—	4	2	no	—
1192	C₄	—	4	1	no	—
1193	C₄	—	4	2	no	—
1194	C₄	—	4	1	no	—
1195	C₄	C₃₁×#525	1	2	yes	—
1196	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1197	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1198	C₂	—	2	2	no	—
1199	C₂	—	4	1	no	—
1200	C₂	—	4	1	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	4	2	no	—
1203	C₂	—	8	1	no	—
1204	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1205	C₂	C₃₁×#3584	1	1	yes	characteristic
1206	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3495	C₂	semidirect
2. C₃₁×#3428	C₂	semidirect
3. C₃₁×#3127	C₂	semidirect
4. C₃₁×#3123	C₂	semidirect
5. C₃₁×#3121	C₂	semidirect
6. C₃₁×#3118	C₂	semidirect
7. C₃₁×#3116	C₂	semidirect
8. C₃₁×#3111	C₂	semidirect
9. C₃₁×#3107	C₂	semidirect
10. C₃₁×#3102	C₂	semidirect
11. C₃₁×#3093	C₂	semidirect
12. C₂×C₃₁×#485	C₂	semidirect
13. C₃₁×#3084	C₂	semidirect
14. C₃₁×#3083	C₂	semidirect
15. C₃₁×#3046	C₂	semidirect
16. C₃₁×#3046	C₂	semidirect
17. C₃₁×#3007	C₂	semidirect
19. C₃₁×#2952	C₂	semidirect
20. C₃₁×#2951	C₂	semidirect
21. C₃₁×#2947	C₂	semidirect
22. C₃₁×#2947	C₂	semidirect
23. C₃₁×#2924	C₂	semidirect
35. C₃₁×#544	C₂²	semidirect
38. C₃₁×#536	C₂²	semidirect
39. C₃₁×#533	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
51. C₃₁×#519	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#479	C₂²	semidirect
70. C₃₁×#479	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#477	C₂²	semidirect
74. C₃₁×#476	C₂²	semidirect
75. C₃₁×#475	C₂²	semidirect
76. C₃₁×#474	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×#462	C₂²	semidirect
83. C₃₁×#461	C₂²	semidirect
84. C₃₁×#461	C₂²	semidirect
97. C₃₁×#442	C₂²	semidirect
98. C₃₁×#441	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#441	C₂²	semidirect
101. C₃₁×#440	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₄×Q₁₆×C₃₁	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
107. C₄×Q₁₆×C₃₁	C₂²	semidirect
108. C₄×SD₁₆×C₃₁	C₂²	semidirect
109. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
112. C₄×D₈×C₃₁	C₂²	semidirect
115. C₃₁×#432	C₂²	semidirect
116. C₃₁×#431	C₂²	semidirect
117. C₃₁×#428	C₂²	semidirect
118. C₃₁×#428	C₂²	semidirect
119. C₂×C₃₁×#107	C₂²	semidirect
120. C₂×C₃₁×#106	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
125. C₃₁×#417	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
129. C₂×C₃₁×#103	C₂²	semidirect
130. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₃₁×#405	C₂²	semidirect
469. #60586	C₃₁	direct (N × H)
556. #3495	C₂×C₃₁	semidirect
557. #3428	C₂×C₃₁	semidirect
558. #3127	C₂×C₃₁	semidirect
559. #3123	C₂×C₃₁	semidirect
560. #3121	C₂×C₃₁	semidirect
561. #3118	C₂×C₃₁	semidirect
562. #3116	C₂×C₃₁	semidirect
563. #3111	C₂×C₃₁	semidirect
564. #3107	C₂×C₃₁	semidirect
565. #3102	C₂×C₃₁	semidirect
566. #3093	C₂×C₃₁	semidirect
567. C₂×#485	C₂×C₃₁	semidirect
568. #3084	C₂×C₃₁	semidirect
569. #3083	C₂×C₃₁	semidirect
570. #3046	C₂×C₃₁	semidirect
571. #3046	C₂×C₃₁	semidirect
572. #3007	C₂×C₃₁	semidirect
574. #2952	C₂×C₃₁	semidirect
575. #2951	C₂×C₃₁	semidirect
576. #2947	C₂×C₃₁	semidirect
577. #2947	C₂×C₃₁	semidirect
578. #2924	C₂×C₃₁	semidirect
629. #544	C₂²×C₃₁	semidirect
632. #536	C₂²×C₃₁	semidirect
633. #533	C₂²×C₃₁	semidirect
634. #529	C₂²×C₃₁	semidirect
643. #520	C₂²×C₃₁	semidirect
645. #519	C₂²×C₃₁	semidirect
658. #485	C₂²×C₃₁	semidirect
659. #485	C₂²×C₃₁	semidirect
660. #485	C₂²×C₃₁	semidirect
662. #482	C₂²×C₃₁	semidirect
663. #479	C₂²×C₃₁	semidirect
664. #479	C₂²×C₃₁	semidirect
665. #478	C₂²×C₃₁	semidirect
666. #478	C₂²×C₃₁	semidirect
667. #477	C₂²×C₃₁	semidirect
668. #476	C₂²×C₃₁	semidirect
669. #475	C₂²×C₃₁	semidirect
670. #474	C₂²×C₃₁	semidirect
671. #464	C₂²×C₃₁	semidirect
672. #464	C₂²×C₃₁	semidirect
673. #463	C₂²×C₃₁	semidirect
674. #463	C₂²×C₃₁	semidirect
675. #462	C₂²×C₃₁	semidirect
676. #462	C₂²×C₃₁	semidirect
677. #461	C₂²×C₃₁	semidirect
678. #461	C₂²×C₃₁	semidirect
691. #442	C₂²×C₃₁	semidirect
692. #441	C₂²×C₃₁	semidirect
693. #441	C₂²×C₃₁	semidirect
694. #441	C₂²×C₃₁	semidirect
695. #440	C₂²×C₃₁	semidirect
696. #440	C₂²×C₃₁	semidirect
697. #440	C₂²×C₃₁	semidirect
698. #440	C₂²×C₃₁	semidirect
699. C₄×Q₁₆	C₂²×C₃₁	semidirect
700. C₄×Q₁₆	C₂²×C₃₁	semidirect
701. C₄×Q₁₆	C₂²×C₃₁	semidirect
702. C₄×SD₁₆	C₂²×C₃₁	semidirect
703. C₄×SD₁₆	C₂²×C₃₁	semidirect
704. C₄×SD₁₆	C₂²×C₃₁	semidirect
705. C₄×SD₁₆	C₂²×C₃₁	semidirect
706. C₄×D₈	C₂²×C₃₁	semidirect
709. #432	C₂²×C₃₁	semidirect
710. #431	C₂²×C₃₁	semidirect
711. #428	C₂²×C₃₁	semidirect
712. #428	C₂²×C₃₁	semidirect
713. C₂×#107	C₂²×C₃₁	semidirect
714. C₂×#106	C₂²×C₃₁	semidirect
715. #424	C₂²×C₃₁	semidirect
716. #424	C₂²×C₃₁	semidirect
719. #417	C₂²×C₃₁	semidirect
720. #417	C₂²×C₃₁	semidirect
723. C₂×#103	C₂²×C₃₁	semidirect
724. C₂×#103	C₂²×C₃₁	semidirect
727. #405	C₂²×C₃₁	semidirect
728. #405	C₂²×C₃₁	semidirect
921. C₃₁	#60586	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3495	2
C₃₁×#3428	2
C₃₁×#3127	2
C₃₁×#3123	2
C₃₁×#3121	2
C₃₁×#3118	2
C₃₁×#3116	2
C₃₁×#3111	2
C₃₁×#3107	2
C₃₁×#3102	2
C₃₁×#3093	2
C₂×C₃₁×#485	2
C₃₁×#3084	2
C₃₁×#3083	2
C₃₁×#3046	2
C₃₁×#3007	2
C₃₁×#3002	2
C₃₁×#2952	2
C₃₁×#2951	2
C₃₁×#2947	2
C₃₁×#2924	2
#60586	31

Subgroups — C31×#60586 #21517345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60586 #21517345