Subgroups — C₃₁×#62250 #21519009

Order 7936.

1950 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3337	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3304	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3282	C₂	1	2	yes	maximal, complemented
14	D₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3248	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3190	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3188	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3168	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3050	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#465	C₂	1	2	yes	maximal, complemented
23	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
25	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
26	C₂³×C₈×C₃₁	C₂²	1	2	yes	complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#555	C₂²	1	1	yes	characteristic
29	C₃₁×#554	—	2	1	no	—
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#553	C₂²	1	2	yes	—
33	C₃₁×#552	C₂²	1	2	yes	complemented
34	C₃₁×#551	—	2	2	no	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#548	C₂²	1	2	yes	complemented
38	C₃₁×#547	C₂²	1	1	yes	characteristic
39	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	D₄²×C₃₁	—	2	1	no	—
44	D₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₃₁×#542	—	2	1	no	—
46	C₃₁×#540	—	2	1	no	—
47	C₃₁×#539	—	2	2	no	—
48	C₃₁×#538	—	2	2	no	—
49	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#532	C₂²	1	1	yes	characteristic
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#525	C₂²	1	2	yes	—
54	C₃₁×#525	C₂²	1	2	yes	complemented
55	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#121	C₂²	1	2	yes	—
57	C₃₁×#520	—	2	1	no	—
58	C₃₁×#518	—	2	1	no	—
59	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
60	C₃₁×#499	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#495	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#487	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#485	C₂²	1	2	yes	complemented
69	C₃₁×#485	C₂²	1	2	yes	complemented
70	C₃₁×#484	C₂²	1	2	yes	complemented
71	C₃₁×#483	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#481	C₂²	1	2	yes	complemented
75	C₃₁×#480	C₂²	1	2	yes	complemented
76	C₃₁×#479	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#475	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#467	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#467	C₂²	1	2	yes	complemented
84	C₃₁×#467	C₂²	1	2	yes	complemented
85	C₃₁×#466	C₂²	1	1	yes	characteristic
86	C₃₁×#466	C₂²	1	2	yes	complemented
87	C₃₁×#466	C₂²	1	2	yes	complemented
88	C₃₁×#465	C₂²	1	1	yes	characteristic
89	C₃₁×#465	C₂²	1	2	yes	—
90	C₃₁×#465	C₂²	1	2	yes	complemented
91	C₃₁×#465	C₂²	1	2	yes	complemented
92	C₃₁×#465	C₂²	1	2	yes	complemented
93	C₃₁×#465	C₂²	1	2	yes	complemented
94	C₃₁×#465	C₂²	1	2	yes	complemented
95	C₃₁×#465	C₂²	1	2	yes	complemented
96	C₃₁×#465	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#465	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#464	C₂²	1	2	yes	complemented
101	C₃₁×#463	C₂²	1	2	yes	complemented
102	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#452	C₂²	1	2	yes	complemented
107	C₃₁×#452	C₂²	1	2	yes	complemented
108	C₃₁×#451	C₂²	1	2	yes	complemented
109	C₃₁×#450	C₂²	1	2	yes	complemented
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#449	C₂²	1	2	yes	complemented
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#447	C₂²	1	2	yes	complemented
114	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
121	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
125	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
126	C₃₁×#427	C₂²	1	2	yes	complemented
127	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
128	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₃₁×#416	C₂²	1	2	yes	complemented
131	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
133	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×D₄×C₃₁	—	2	2	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
145	C₃₁×#135	—	4	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	—	4	4	no	—
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂²×C₈×C₃₁	—	4	4	no	—
158	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
164	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	—	2	1	no	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×#127	—	2	1	no	—
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	1	no	—
175	C₃₁×#126	—	2	1	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	C₂³	1	1	yes	characteristic
180	C₃₁×#125	C₂³	1	1	yes	characteristic
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	—	2	2	no	—
184	C₃₁×#124	—	2	1	no	—
185	C₃₁×#124	C₂³	1	1	yes	characteristic
186	C₃₁×#124	C₂³	1	1	yes	characteristic
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	1	no	—
191	C₃₁×#123	—	2	1	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×#123	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	1	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	1	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	—	2	2	no	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	1	no	—
213	C₃₁×#121	—	2	1	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	1	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#121	C₂³	1	2	yes	—
222	C₃₁×#121	C₂³	1	2	yes	—
223	C₃₁×#121	C₂³	1	2	yes	—
224	C₃₁×#121	C₂³	1	1	yes	characteristic
225	C₃₁×#121	C₂³	1	2	yes	—
226	C₃₁×#121	C₂³	1	1	yes	characteristic
227	C₃₁×#120	—	2	2	no	—
228	C₃₁×#120	—	2	2	no	—
229	C₃₁×#120	—	2	2	no	—
230	C₃₁×#120	—	2	2	no	—
231	C₄×Q₈×C₃₁	—	2	1	no	—
232	C₄×Q₈×C₃₁	—	2	1	no	—
233	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
234	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
235	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	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	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	2	no	—
246	C₄×D₄×C₃₁	—	2	2	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
249	C₄×D₄×C₃₁	D₄	1	2	yes	—
250	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	2	yes	—
256	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₃₁×#117	—	2	1	no	—
258	C₃₁×#117	—	2	1	no	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	—	2	1	no	—
262	C₃₁×#117	C₂³	1	2	yes	—
263	C₃₁×#117	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
265	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
272	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	2	yes	—
281	C₃₁×#106	C₂³	1	2	yes	—
282	C₃₁×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
287	C₃₁×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	2	yes	—
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	1	yes	characteristic
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₃₁	—	2	2	no	—
316	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	4	2	no	—
320	#41×C₃₁	—	4	2	no	—
321	#41×C₃₁	—	4	4	no	—
322	#41×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	2	no	—
325	C₂×Q₈×C₃₁	—	2	1	no	—
326	C₂×Q₈×C₃₁	—	4	2	no	—
327	C₂×Q₈×C₃₁	—	4	2	no	—
328	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×D₄×C₃₁	—	2	4	no	—
332	C₂×D₄×C₃₁	—	2	1	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	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	1	no	—
342	C₂×D₄×C₃₁	—	2	1	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	4	2	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	4	4	no	—
347	C₂×D₄×C₃₁	—	8	4	no	—
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₃₁	—	2	2	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	2	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	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	4	2	no	—
363	C₂²×C₄×C₃₁	—	4	2	no	—
364	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	Q₁₆×C₃₁	—	4	1	no	—
373	Q₁₆×C₃₁	—	4	2	no	—
374	SD₁₆×C₃₁	—	2	2	no	—
375	SD₁₆×C₃₁	—	2	4	no	—
376	SD₁₆×C₃₁	—	2	2	no	—
377	SD₁₆×C₃₁	—	4	2	no	—
378	SD₁₆×C₃₁	—	4	2	no	—
379	SD₁₆×C₃₁	—	4	2	no	—
380	D₈×C₃₁	—	4	1	no	—
381	D₈×C₃₁	—	4	2	no	—
382	C₂×C₈×C₃₁	—	2	2	no	—
383	C₂×C₈×C₃₁	—	2	4	no	—
384	C₂×C₈×C₃₁	—	2	4	no	—
385	C₂×C₈×C₃₁	—	4	2	no	—
386	C₂×C₈×C₃₁	—	4	2	no	—
387	C₂×C₈×C₃₁	—	4	2	no	—
388	C₂×C₈×C₃₁	—	4	1	no	—
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
393	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
394	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	1	no	—
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	1	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	2	no	—
414	C₄⋊C₄×C₃₁	—	2	1	no	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	2	no	—
436	C₂²⋊C₄×C₃₁	—	2	2	no	—
437	C₂²⋊C₄×C₃₁	—	2	2	no	—
438	C₂²⋊C₄×C₃₁	—	2	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	1	no	—
440	C₂²⋊C₄×C₃₁	—	2	1	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	1	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	1	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	—	2	1	no	—
447	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₄²×C₃₁	—	2	2	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	—	2	1	no	—
456	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
459	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
460	#62250	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂³×C₃₁	—	2	4	no	—
462	C₂³×C₃₁	—	2	4	no	—
463	C₂³×C₃₁	—	2	1	no	—
464	C₂³×C₃₁	—	2	1	no	—
465	C₂³×C₃₁	—	2	2	no	—
466	C₂³×C₃₁	—	4	2	no	—
467	C₂³×C₃₁	—	4	4	no	—
468	C₂³×C₃₁	—	8	2	no	—
469	C₂³×C₃₁	—	8	2	no	—
470	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
471	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
472	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
473	Q₈×C₃₁	—	2	1	no	—
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	2	1	no	—
476	Q₈×C₃₁	—	2	2	no	—
477	Q₈×C₃₁	—	2	1	no	—
478	Q₈×C₃₁	—	2	1	no	—
479	Q₈×C₃₁	—	4	2	no	—
480	Q₈×C₃₁	—	8	2	no	—
481	Q₈×C₃₁	—	8	1	no	—
482	D₄×C₃₁	—	2	4	no	—
483	D₄×C₃₁	—	2	2	no	—
484	D₄×C₃₁	—	2	1	no	—
485	D₄×C₃₁	—	2	2	no	—
486	D₄×C₃₁	—	2	1	no	—
487	D₄×C₃₁	—	2	1	no	—
488	D₄×C₃₁	—	2	1	no	—
489	D₄×C₃₁	—	2	2	no	—
490	D₄×C₃₁	—	4	4	no	—
491	D₄×C₃₁	—	4	4	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	—	8	2	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	#135	1	4	yes	complemented
503	C₂×C₄×C₃₁	—	2	2	no	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	1	no	—
506	C₂×C₄×C₃₁	—	2	2	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	2	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	1	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	2	2	no	—
517	C₂×C₄×C₃₁	—	2	2	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	2	no	—
522	C₂×C₄×C₃₁	—	4	2	no	—
523	C₂×C₄×C₃₁	—	4	4	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	4	2	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	2	no	—
528	C₂×C₄×C₃₁	—	8	2	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	—	8	2	no	—
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
539	C₈×C₃₁	—	2	1	no	—
540	C₈×C₃₁	—	2	2	no	—
541	C₈×C₃₁	—	2	2	no	—
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	1	no	—
544	C₈×C₃₁	H(5,𝔽₂)	1	2	yes	—
545	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3337	C₂×C₃₁	1	2	yes	complemented
549	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3304	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3301	C₂×C₃₁	1	2	yes	complemented
553	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3296	C₂×C₃₁	1	2	yes	complemented
555	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3282	C₂×C₃₁	1	2	yes	complemented
558	D₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3248	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3190	C₂×C₃₁	1	2	yes	complemented
562	#3188	C₂×C₃₁	1	2	yes	complemented
563	#3168	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#3050	C₂×C₃₁	1	2	yes	complemented
566	C₂×#465	C₂×C₃₁	1	2	yes	complemented
567	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	2	no	—
570	C₂²×C₃₁	—	2	1	no	—
571	C₂²×C₃₁	—	2	2	no	—
572	C₂²×C₃₁	—	2	2	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	2	no	—
575	C₂²×C₃₁	—	4	8	no	—
576	C₂²×C₃₁	—	4	1	no	—
577	C₂²×C₃₁	—	4	2	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	1	no	—
581	C₂²×C₃₁	—	4	2	no	—
582	C₂²×C₃₁	—	4	2	no	—
583	C₂²×C₃₁	—	4	1	no	—
584	C₂²×C₃₁	—	4	1	no	—
585	C₂²×C₃₁	—	16	4	no	—
586	C₂²×C₃₁	C₂×#135	1	4	yes	—
587	C₂²×C₃₁	#577	1	2	yes	—
588	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	2	2	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	1	no	—
594	C₄×C₃₁	—	2	1	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	2	no	—
597	C₄×C₃₁	—	4	1	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	—	4	1	no	—
600	C₄×C₃₁	—	4	2	no	—
601	C₄×C₃₁	—	4	1	no	—
602	C₄×C₃₁	—	4	2	no	—
603	C₄×C₃₁	—	4	1	no	—
604	C₄×C₃₁	C₂×#135	1	2	yes	—
605	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
606	C₄×C₃₁	#585	1	1	yes	characteristic
607	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
608	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
609	C₂³×C₈	C₂²×C₃₁	1	2	yes	complemented
610	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	#555	C₂²×C₃₁	1	1	yes	characteristic
612	#554	—	2	1	no	—
613	#554	C₂²×C₃₁	1	1	yes	characteristic
614	#553	—	2	1	no	—
615	#553	C₂²×C₃₁	1	2	yes	—
616	#552	C₂²×C₃₁	1	2	yes	complemented
617	#551	—	2	2	no	—
618	#550	C₂²×C₃₁	1	1	yes	characteristic
619	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
620	#548	C₂²×C₃₁	1	2	yes	complemented
621	#547	C₂²×C₃₁	1	1	yes	characteristic
622	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
623	#546	—	2	1	no	—
624	#546	—	2	2	no	—
625	#546	C₂²×C₃₁	1	2	yes	—
626	D₄²	—	2	1	no	—
627	D₄²	C₂²×C₃₁	1	1	yes	characteristic
628	#542	—	2	1	no	—
629	#540	—	2	1	no	—
630	#539	—	2	2	no	—
631	#538	—	2	2	no	—
632	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#532	C₂²×C₃₁	1	1	yes	characteristic
634	#529	C₂²×C₃₁	1	1	yes	characteristic
635	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
636	#525	C₂²×C₃₁	1	2	yes	—
637	#525	C₂²×C₃₁	1	2	yes	complemented
638	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
639	C₂×#121	C₂²×C₃₁	1	2	yes	—
640	#520	—	2	1	no	—
641	#518	—	2	1	no	—
642	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
643	#499	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#495	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
647	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#485	C₂²×C₃₁	1	2	yes	complemented
652	#485	C₂²×C₃₁	1	2	yes	complemented
653	#484	C₂²×C₃₁	1	2	yes	complemented
654	#483	C₂²×C₃₁	1	2	yes	complemented
655	#482	C₂²×C₃₁	1	2	yes	complemented
656	#482	C₂²×C₃₁	1	2	yes	complemented
657	#481	C₂²×C₃₁	1	2	yes	complemented
658	#480	C₂²×C₃₁	1	2	yes	complemented
659	#479	C₂²×C₃₁	1	2	yes	complemented
660	#478	C₂²×C₃₁	1	2	yes	complemented
661	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
662	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#475	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#467	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#467	C₂²×C₃₁	1	2	yes	complemented
667	#467	C₂²×C₃₁	1	2	yes	complemented
668	#466	C₂²×C₃₁	1	1	yes	characteristic
669	#466	C₂²×C₃₁	1	2	yes	complemented
670	#466	C₂²×C₃₁	1	2	yes	complemented
671	#465	C₂²×C₃₁	1	1	yes	characteristic
672	#465	C₂²×C₃₁	1	2	yes	—
673	#465	C₂²×C₃₁	1	2	yes	complemented
674	#465	C₂²×C₃₁	1	2	yes	complemented
675	#465	C₂²×C₃₁	1	2	yes	complemented
676	#465	C₂²×C₃₁	1	2	yes	complemented
677	#465	C₂²×C₃₁	1	2	yes	complemented
678	#465	C₂²×C₃₁	1	2	yes	complemented
679	#465	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#465	C₂²×C₃₁	1	2	yes	complemented
681	#465	C₂²×C₃₁	1	2	yes	complemented
682	#465	C₂²×C₃₁	1	2	yes	complemented
683	#464	C₂²×C₃₁	1	2	yes	complemented
684	#463	C₂²×C₃₁	1	2	yes	complemented
685	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
687	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#452	C₂²×C₃₁	1	2	yes	complemented
690	#452	C₂²×C₃₁	1	2	yes	complemented
691	#451	C₂²×C₃₁	1	2	yes	complemented
692	#450	C₂²×C₃₁	1	2	yes	complemented
693	#449	C₂²×C₃₁	1	2	yes	complemented
694	#449	C₂²×C₃₁	1	2	yes	complemented
695	#448	C₂²×C₃₁	1	2	yes	complemented
696	#447	C₂²×C₃₁	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
702	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
704	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
705	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
706	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
708	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	#427	C₂²×C₃₁	1	2	yes	complemented
710	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
711	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#416	C₂²×C₃₁	1	2	yes	complemented
713	#416	C₂²×C₃₁	1	2	yes	complemented
714	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
715	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
716	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
717	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	C₂×C₃₁	—	2	2	no	—
719	C₂×C₃₁	—	2	4	no	—
720	C₂×C₃₁	—	4	2	no	—
721	C₂×C₃₁	—	8	1	no	—
722	C₂×C₃₁	—	8	2	no	—
723	C₂×C₃₁	—	8	1	no	—
724	C₂×C₃₁	#3496	1	1	yes	characteristic
725	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
726	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
727	C₂×#41	—	2	1	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	C₂³×C₃₁	1	2	yes	—
730	C₂×#41	C₂³×C₃₁	1	2	yes	—
731	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
732	C₂²×D₄	—	2	2	no	—
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
736	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
737	#135	—	4	4	no	—
738	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
739	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
740	C₂×SD₁₆	—	4	4	no	—
741	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
747	C₂×D₈	C₂³×C₃₁	1	2	yes	—
748	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
749	C₂²×C₈	—	4	4	no	—
750	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
752	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
753	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
754	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
755	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
756	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
761	#127	—	2	1	no	—
762	#127	C₂³×C₃₁	1	1	yes	characteristic
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	1	no	—
767	#126	—	2	1	no	—
768	#125	—	2	2	no	—
769	#125	—	2	1	no	—
770	#125	—	2	1	no	—
771	#125	C₂³×C₃₁	1	1	yes	characteristic
772	#125	C₂³×C₃₁	1	1	yes	characteristic
773	#124	—	2	1	no	—
774	#124	—	2	2	no	—
775	#124	—	2	2	no	—
776	#124	—	2	1	no	—
777	#124	C₂³×C₃₁	1	1	yes	characteristic
778	#124	C₂³×C₃₁	1	1	yes	characteristic
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	1	no	—
783	#123	—	2	1	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
797	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
798	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	C₂³×C₃₁	1	1	yes	characteristic
813	#121	C₂³×C₃₁	1	2	yes	—
814	#121	C₂³×C₃₁	1	2	yes	—
815	#121	C₂³×C₃₁	1	2	yes	—
816	#121	C₂³×C₃₁	1	2	yes	—
817	#121	C₂³×C₃₁	1	1	yes	characteristic
818	#121	C₂³×C₃₁	1	2	yes	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	—	2	1	no	—
825	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
841	C₄×D₄	D₄×C₃₁	1	2	yes	—
842	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₃₁	1	2	yes	—
848	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
849	#117	—	2	1	no	—
850	#117	—	2	1	no	—
851	#117	—	2	2	no	—
852	#117	—	2	1	no	—
853	#117	—	2	1	no	—
854	#117	C₂³×C₃₁	1	2	yes	—
855	#117	C₂³×C₃₁	1	2	yes	—
856	C₂×C₄⋊C₄	—	2	2	no	—
857	C₂×C₄⋊C₄	—	2	1	no	—
858	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
859	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
860	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
861	C₂×C₂²⋊C₄	—	2	2	no	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
865	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
866	#107	C₂³×C₃₁	1	2	yes	—
867	#107	C₂³×C₃₁	1	2	yes	—
868	#107	C₂³×C₃₁	1	1	yes	characteristic
869	#107	C₂³×C₃₁	1	1	yes	characteristic
870	#106	C₂³×C₃₁	1	1	yes	characteristic
871	#106	C₂³×C₃₁	1	2	yes	—
872	#106	C₂³×C₃₁	1	2	yes	—
873	#106	C₂³×C₃₁	1	2	yes	—
874	#106	C₂³×C₃₁	1	1	yes	characteristic
875	#106	C₂³×C₃₁	1	2	yes	—
876	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
879	#103	C₂³×C₃₁	1	1	yes	characteristic
880	#103	C₂³×C₃₁	1	2	yes	—
881	#103	C₂³×C₃₁	1	2	yes	—
882	#103	C₂³×C₃₁	1	2	yes	—
883	#103	C₂³×C₃₁	1	1	yes	characteristic
884	#103	C₂³×C₃₁	1	2	yes	—
885	#103	C₂³×C₃₁	1	2	yes	—
886	#103	C₂³×C₃₁	1	1	yes	characteristic
887	#103	C₂³×C₃₁	1	2	yes	—
888	#103	C₂³×C₃₁	1	1	yes	characteristic
889	#102	C₂³×C₃₁	1	1	yes	characteristic
890	#102	C₂³×C₃₁	1	2	yes	—
891	#102	C₂³×C₃₁	1	2	yes	—
892	#102	C₂³×C₃₁	1	2	yes	—
893	#102	C₂³×C₃₁	1	1	yes	characteristic
894	#102	C₂³×C₃₁	1	2	yes	—
895	#102	C₂³×C₃₁	1	2	yes	—
896	#102	C₂³×C₃₁	1	2	yes	—
897	#102	C₂³×C₃₁	1	1	yes	characteristic
898	#102	C₂³×C₃₁	1	1	yes	characteristic
899	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
903	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
904	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
905	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
906	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
907	C₃₁	#62250	1	1	yes	characteristic, direct product factor, Sylow
908	C₂⁴	—	2	2	no	—
909	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	4	no	—
915	#41	—	8	2	no	—
916	C₂×Q₈	—	2	1	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	—	4	2	no	—
920	C₂×Q₈	—	4	2	no	—
921	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
924	C₂×D₄	—	2	4	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
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	2	no	—
934	C₂×D₄	—	2	1	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	4	2	no	—
938	C₂×D₄	—	4	2	no	—
939	C₂×D₄	—	4	4	no	—
940	C₂×D₄	—	8	4	no	—
941	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
942	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
943	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	2	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	4	2	no	—
956	C₂²×C₄	—	4	2	no	—
957	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
958	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
959	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
961	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
962	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
963	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
964	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	Q₁₆	—	4	1	no	—
966	Q₁₆	—	4	2	no	—
967	SD₁₆	—	2	2	no	—
968	SD₁₆	—	2	4	no	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	4	2	no	—
971	SD₁₆	—	4	2	no	—
972	SD₁₆	—	4	2	no	—
973	D₈	—	4	1	no	—
974	D₈	—	4	2	no	—
975	C₂×C₈	—	2	2	no	—
976	C₂×C₈	—	2	4	no	—
977	C₂×C₈	—	2	4	no	—
978	C₂×C₈	—	4	2	no	—
979	C₂×C₈	—	4	2	no	—
980	C₂×C₈	—	4	2	no	—
981	C₂×C₈	—	4	1	no	—
982	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
986	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
987	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	1	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1013	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	1	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	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	C₄²	—	2	2	no	—
1045	C₄²	—	2	2	no	—
1046	C₄²	—	2	2	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	1	no	—
1049	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1052	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₂³	—	2	4	no	—
1054	C₂³	—	2	4	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	1	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	4	2	no	—
1059	C₂³	—	4	4	no	—
1060	C₂³	—	8	2	no	—
1061	C₂³	—	8	2	no	—
1062	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1063	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1064	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	2	no	—
1067	Q₈	—	2	1	no	—
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	1	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	4	2	no	—
1072	Q₈	—	8	2	no	—
1073	Q₈	—	8	1	no	—
1074	D₄	—	2	4	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	1	no	—
1079	D₄	—	2	1	no	—
1080	D₄	—	2	1	no	—
1081	D₄	—	2	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	4	4	no	—
1087	D₄	—	4	2	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	C₃₁×#135	1	4	yes	complemented
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	2	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	2	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	1	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	2	no	—
1114	C₂×C₄	—	4	2	no	—
1115	C₂×C₄	—	4	4	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1126	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1130	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	C₃₁×H(5,𝔽₂)	1	2	yes	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	4	8	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	2	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	2	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	16	4	no	—
1155	C₂²	C₂×C₃₁×#135	1	4	yes	—
1156	C₂²	C₃₁×#577	1	2	yes	—
1157	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₂×C₃₁×#135	1	2	yes	—
1174	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1175	C₄	C₃₁×#585	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	2	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	1	no	—
1182	C₂	C₃₁×#3496	1	1	yes	characteristic
1183	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
1184	C₂	C₂×C₃₁×#577	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3520	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3340	C₂	semidirect
4. C₃₁×#3337	C₂	semidirect
5. C₃₁×#3335	C₂	semidirect
6. C₃₁×#3304	C₂	semidirect
7. C₃₁×#3303	C₂	semidirect
8. C₃₁×#3301	C₂	semidirect
9. C₃₁×#3299	C₂	semidirect
10. C₃₁×#3296	C₂	semidirect
11. C₃₁×#3294	C₂	semidirect
12. C₃₁×#3284	C₂	semidirect
13. C₃₁×#3282	C₂	semidirect
14. D₄×SD₁₆×C₃₁	C₂	semidirect
15. C₃₁×#3248	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3190	C₂	semidirect
18. C₃₁×#3188	C₂	semidirect
19. C₃₁×#3168	C₂	semidirect
20. C₃₁×#3167	C₂	semidirect
21. C₃₁×#3050	C₂	semidirect
22. C₂×C₃₁×#465	C₂	semidirect
23. C₂×C₈×D₄×C₃₁	C₂	semidirect
24. C₂×C₃₁×#135	C₂²	semidirect
25. C₂²×SD₁₆×C₃₁	C₂²	semidirect
26. C₂³×C₈×C₃₁	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
33. C₃₁×#552	C₂²	semidirect
37. C₃₁×#548	C₂²	semidirect
39. C₃₁×#547	C₂²	semidirect
49. C₃₁×#533	C₂²	semidirect
52. C₃₁×#529	C₂²	semidirect
54. C₃₁×#525	C₂²	semidirect
55. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
60. C₃₁×#499	C₂²	semidirect
61. C₃₁×#498	C₂²	semidirect
62. C₃₁×#495	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#488	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
69. C₃₁×#485	C₂²	semidirect
70. C₃₁×#484	C₂²	semidirect
71. C₃₁×#483	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
74. C₃₁×#481	C₂²	semidirect
75. C₃₁×#480	C₂²	semidirect
76. C₃₁×#479	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#477	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
80. C₃₁×#475	C₂²	semidirect
81. C₃₁×#474	C₂²	semidirect
82. C₃₁×#467	C₂²	semidirect
83. C₃₁×#467	C₂²	semidirect
84. C₃₁×#467	C₂²	semidirect
86. C₃₁×#466	C₂²	semidirect
87. C₃₁×#466	C₂²	semidirect
90. C₃₁×#465	C₂²	semidirect
91. C₃₁×#465	C₂²	semidirect
92. C₃₁×#465	C₂²	semidirect
93. C₃₁×#465	C₂²	semidirect
94. C₃₁×#465	C₂²	semidirect
95. C₃₁×#465	C₂²	semidirect
96. C₃₁×#465	C₂²	semidirect
97. C₃₁×#465	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
100. C₃₁×#464	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#462	C₂²	semidirect
103. C₃₁×#461	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#459	C₂²	semidirect
106. C₃₁×#452	C₂²	semidirect
107. C₃₁×#452	C₂²	semidirect
108. C₃₁×#451	C₂²	semidirect
109. C₃₁×#450	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
111. C₃₁×#449	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
113. C₃₁×#447	C₂²	semidirect
114. C₄×Q₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
118. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
122. C₈×D₄×C₃₁	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₈×D₄×C₃₁	C₂²	semidirect
126. C₃₁×#427	C₂²	semidirect
127. C₂×C₃₁×#106	C₂²	semidirect
128. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
130. C₃₁×#416	C₂²	semidirect
131. C₂×C₃₁×#103	C₂²	semidirect
132. C₂×C₃₁×#102	C₂²	semidirect
133. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
460. #62250	C₃₁	direct (N × H)
502. D₄×C₃₁	#135	semidirect
545. #3520	C₂×C₃₁	semidirect
546. #3519	C₂×C₃₁	semidirect
547. #3340	C₂×C₃₁	semidirect
548. #3337	C₂×C₃₁	semidirect
549. #3335	C₂×C₃₁	semidirect
550. #3304	C₂×C₃₁	semidirect
551. #3303	C₂×C₃₁	semidirect
552. #3301	C₂×C₃₁	semidirect
553. #3299	C₂×C₃₁	semidirect
554. #3296	C₂×C₃₁	semidirect
555. #3294	C₂×C₃₁	semidirect
556. #3284	C₂×C₃₁	semidirect
557. #3282	C₂×C₃₁	semidirect
558. D₄×SD₁₆	C₂×C₃₁	semidirect
559. #3248	C₂×C₃₁	semidirect
560. #3247	C₂×C₃₁	semidirect
561. #3190	C₂×C₃₁	semidirect
562. #3188	C₂×C₃₁	semidirect
563. #3168	C₂×C₃₁	semidirect
564. #3167	C₂×C₃₁	semidirect
565. #3050	C₂×C₃₁	semidirect
566. C₂×#465	C₂×C₃₁	semidirect
567. C₂×C₈×D₄	C₂×C₃₁	semidirect
607. C₂×#135	C₂²×C₃₁	semidirect
608. C₂²×SD₁₆	C₂²×C₃₁	semidirect
609. C₂³×C₈	C₂²×C₃₁	semidirect
610. #556	C₂²×C₃₁	semidirect
616. #552	C₂²×C₃₁	semidirect
620. #548	C₂²×C₃₁	semidirect
622. #547	C₂²×C₃₁	semidirect
632. #533	C₂²×C₃₁	semidirect
635. #529	C₂²×C₃₁	semidirect
637. #525	C₂²×C₃₁	semidirect
638. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
643. #499	C₂²×C₃₁	semidirect
644. #498	C₂²×C₃₁	semidirect
645. #495	C₂²×C₃₁	semidirect
646. #492	C₂²×C₃₁	semidirect
647. #488	C₂²×C₃₁	semidirect
648. #488	C₂²×C₃₁	semidirect
649. #487	C₂²×C₃₁	semidirect
650. #486	C₂²×C₃₁	semidirect
651. #485	C₂²×C₃₁	semidirect
652. #485	C₂²×C₃₁	semidirect
653. #484	C₂²×C₃₁	semidirect
654. #483	C₂²×C₃₁	semidirect
655. #482	C₂²×C₃₁	semidirect
656. #482	C₂²×C₃₁	semidirect
657. #481	C₂²×C₃₁	semidirect
658. #480	C₂²×C₃₁	semidirect
659. #479	C₂²×C₃₁	semidirect
660. #478	C₂²×C₃₁	semidirect
661. #477	C₂²×C₃₁	semidirect
662. #476	C₂²×C₃₁	semidirect
663. #475	C₂²×C₃₁	semidirect
664. #474	C₂²×C₃₁	semidirect
665. #467	C₂²×C₃₁	semidirect
666. #467	C₂²×C₃₁	semidirect
667. #467	C₂²×C₃₁	semidirect
669. #466	C₂²×C₃₁	semidirect
670. #466	C₂²×C₃₁	semidirect
673. #465	C₂²×C₃₁	semidirect
674. #465	C₂²×C₃₁	semidirect
675. #465	C₂²×C₃₁	semidirect
676. #465	C₂²×C₃₁	semidirect
677. #465	C₂²×C₃₁	semidirect
678. #465	C₂²×C₃₁	semidirect
679. #465	C₂²×C₃₁	semidirect
680. #465	C₂²×C₃₁	semidirect
681. #465	C₂²×C₃₁	semidirect
682. #465	C₂²×C₃₁	semidirect
683. #464	C₂²×C₃₁	semidirect
684. #463	C₂²×C₃₁	semidirect
685. #462	C₂²×C₃₁	semidirect
686. #461	C₂²×C₃₁	semidirect
687. #460	C₂²×C₃₁	semidirect
688. #459	C₂²×C₃₁	semidirect
689. #452	C₂²×C₃₁	semidirect
690. #452	C₂²×C₃₁	semidirect
691. #451	C₂²×C₃₁	semidirect
692. #450	C₂²×C₃₁	semidirect
693. #449	C₂²×C₃₁	semidirect
694. #449	C₂²×C₃₁	semidirect
695. #448	C₂²×C₃₁	semidirect
696. #447	C₂²×C₃₁	semidirect
697. C₄×Q₁₆	C₂²×C₃₁	semidirect
698. C₄×SD₁₆	C₂²×C₃₁	semidirect
699. C₄×SD₁₆	C₂²×C₃₁	semidirect
700. C₄×SD₁₆	C₂²×C₃₁	semidirect
701. C₄×SD₁₆	C₂²×C₃₁	semidirect
702. C₄×D₈	C₂²×C₃₁	semidirect
705. C₈×D₄	C₂²×C₃₁	semidirect
706. C₈×D₄	C₂²×C₃₁	semidirect
707. C₈×D₄	C₂²×C₃₁	semidirect
708. C₈×D₄	C₂²×C₃₁	semidirect
709. #427	C₂²×C₃₁	semidirect
710. C₂×#106	C₂²×C₃₁	semidirect
711. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
712. #416	C₂²×C₃₁	semidirect
713. #416	C₂²×C₃₁	semidirect
714. C₂×#103	C₂²×C₃₁	semidirect
715. C₂×#102	C₂²×C₃₁	semidirect
716. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
717. C₂×C₄×C₈	C₂²×C₃₁	semidirect
907. C₃₁	#62250	direct (N × H)
1094. D₄	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3520	2
C₃₁×#3519	2
C₃₁×#3340	2
C₃₁×#3337	2
C₃₁×#3335	2
C₃₁×#3304	2
C₃₁×#3303	2
C₃₁×#3301	2
C₃₁×#3299	2
C₃₁×#3296	2
C₃₁×#3294	2
C₃₁×#3284	2
C₃₁×#3282	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3248	2
C₃₁×#3247	2
C₃₁×#3190	2
C₃₁×#3188	2
C₃₁×#3168	2
C₃₁×#3167	2
C₃₁×#3050	2
C₂×C₃₁×#465	2
C₂×C₈×D₄×C₃₁	2
#62250	31

Subgroups — C31×#62250 #21519009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62250 #21519009