Subgroups — C₃₁×#61968 #21518727

Order 7936.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3401	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3319	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3273	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3254	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3217	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3216	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3212	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3106	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
27	C₃₁×#559	—	2	1	no	—
28	C₃₁×#559	C₂²	1	2	yes	complemented
29	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#555	C₂²	1	1	yes	characteristic
31	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#553	—	2	1	no	—
33	C₃₁×#552	—	2	1	no	—
34	C₃₁×#552	C₂²	1	1	yes	characteristic
35	C₃₁×#552	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#551	—	2	1	no	—
37	C₃₁×#551	—	2	1	no	—
38	C₃₁×#550	—	2	1	no	—
39	C₃₁×#550	C₂²	1	2	yes	—
40	C₃₁×#547	C₂²	1	1	yes	characteristic
41	C₃₁×#546	—	2	1	no	—
42	C₃₁×#546	—	2	1	no	—
43	C₃₁×#546	C₂²	1	1	yes	characteristic
44	C₃₁×#546	C₂²	1	2	yes	—
45	C₃₁×#546	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#546	C₂²	1	2	yes	complemented
47	C₃₁×#540	—	2	1	no	—
48	C₃₁×#540	—	2	1	no	—
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#532	C₂²	1	1	yes	characteristic
54	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#529	—	2	1	no	—
58	C₃₁×#529	—	2	1	no	—
59	C₃₁×#529	C₂²	1	1	yes	characteristic
60	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#525	—	2	1	no	—
62	C₃₁×#518	—	2	1	no	—
63	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
64	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
65	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₃₁×#117	—	2	1	no	—
68	C₃₁×#497	C₂²	1	2	yes	complemented
69	C₃₁×#496	C₂²	1	2	yes	—
70	C₃₁×#495	C₂²	1	2	yes	complemented
71	C₃₁×#490	C₂²	1	2	yes	complemented
72	C₃₁×#489	C₂²	1	2	yes	complemented
73	C₃₁×#488	C₂²	1	2	yes	complemented
74	C₃₁×#485	C₂²	1	2	yes	complemented
75	C₃₁×#482	C₂²	1	2	yes	complemented
76	C₃₁×#481	C₂²	1	2	yes	complemented
77	C₃₁×#479	C₂²	1	2	yes	complemented
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
81	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#474	C₂²	1	2	yes	complemented
84	C₃₁×#470	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	—
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#468	C₂²	1	2	yes	complemented
88	C₃₁×#466	C₂²	1	2	yes	complemented
89	C₃₁×#465	C₂²	1	2	yes	complemented
90	C₃₁×#464	C₂²	1	2	yes	complemented
91	C₃₁×#464	C₂²	1	2	yes	complemented
92	C₃₁×#463	C₂²	1	2	yes	complemented
93	C₃₁×#463	C₂²	1	2	yes	complemented
94	C₃₁×#463	C₂²	1	2	yes	complemented
95	C₃₁×#463	C₂²	1	2	yes	complemented
96	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
97	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#461	C₂²	1	2	yes	complemented
100	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
101	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#460	C₂²	1	2	yes	complemented
103	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
105	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#459	C₂²	1	1	yes	characteristic
107	C₃₁×#459	C₂²	1	1	yes	characteristic
108	C₃₁×#459	C₂²	1	1	yes	characteristic
109	C₃₁×#459	C₂²	1	2	yes	—
110	C₃₁×#459	C₂²	1	1	yes	characteristic
111	C₃₁×#452	C₂²	1	2	yes	—
112	C₃₁×#452	C₂²	1	2	yes	complemented
113	C₃₁×#452	C₂²	1	2	yes	complemented
114	C₃₁×#452	C₂²	1	2	yes	complemented
115	C₃₁×#450	C₂²	1	2	yes	complemented
116	C₃₁×#449	C₂²	1	2	yes	complemented
117	C₃₁×#449	C₂²	1	2	yes	complemented
118	C₃₁×#447	C₂²	1	2	yes	—
119	C₃₁×#447	C₂²	1	2	yes	complemented
120	C₃₁×#446	C₂²	1	2	yes	complemented
121	C₃₁×#442	C₂²	1	2	yes	complemented
122	C₃₁×#442	C₂²	1	2	yes	complemented
123	C₃₁×#441	C₂²	1	2	yes	complemented
124	C₃₁×#440	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
126	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
127	C₃₁×#436	C₂²	1	2	yes	—
128	C₃₁×#435	C₂²	1	2	yes	complemented
129	C₃₁×#435	C₂²	1	2	yes	complemented
130	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
133	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
134	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
136	C₃₁×#418	C₂²	1	2	yes	complemented
137	C₃₁×#417	C₂²	1	2	yes	complemented
138	C₃₁×#416	C₂²	1	2	yes	complemented
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×#41×C₃₁	C₂³	1	2	yes	—
145	C₂×#41×C₃₁	C₂³	1	2	yes	—
146	C₂²×D₄×C₃₁	—	2	1	no	—
147	C₂²×D₄×C₃₁	—	2	1	no	—
148	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
150	C₂³×C₄×C₃₁	—	2	1	no	—
151	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
152	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
153	C₃₁×#135	—	4	4	no	—
154	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	2	yes	—
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×D₈×C₃₁	C₂³	1	2	yes	—
166	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
167	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
168	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
169	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
172	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
173	C₃₁×#127	—	2	2	no	—
174	C₃₁×#127	—	2	1	no	—
175	C₃₁×#127	—	2	1	no	—
176	C₃₁×#127	C₂³	1	1	yes	characteristic
177	C₃₁×#127	C₂³	1	1	yes	characteristic
178	C₃₁×#127	C₂³	1	2	yes	—
179	C₃₁×#126	—	2	1	no	—
180	C₃₁×#126	—	2	1	no	—
181	C₃₁×#126	—	2	1	no	—
182	C₃₁×#126	—	2	1	no	—
183	C₃₁×#126	—	2	1	no	—
184	C₃₁×#126	—	2	1	no	—
185	C₃₁×#125	—	2	1	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	—	2	1	no	—
189	C₃₁×#125	C₂³	1	1	yes	characteristic
190	C₃₁×#125	C₂³	1	1	yes	characteristic
191	C₃₁×#124	—	2	2	no	—
192	C₃₁×#124	—	2	1	no	—
193	C₃₁×#124	—	2	1	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	C₂³	1	2	yes	—
197	C₃₁×#124	C₂³	1	1	yes	characteristic
198	C₃₁×#124	C₂³	1	2	yes	—
199	C₃₁×#124	C₂³	1	1	yes	characteristic
200	C₃₁×#123	—	2	1	no	—
201	C₃₁×#123	—	2	1	no	—
202	C₃₁×#123	—	2	1	no	—
203	C₃₁×#123	—	2	1	no	—
204	C₃₁×#123	—	2	1	no	—
205	C₃₁×#123	—	2	1	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	2	no	—
208	C₃₁×#123	—	2	2	no	—
209	C₃₁×#123	—	2	2	no	—
210	C₃₁×#123	—	2	1	no	—
211	C₃₁×#123	—	2	1	no	—
212	C₃₁×C₂²⋊Q₈	—	2	1	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	1	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	1	no	—
217	C₃₁×C₂²⋊Q₈	—	2	1	no	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
228	C₃₁×#121	—	2	1	no	—
229	C₃₁×#121	—	2	1	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	1	no	—
232	C₃₁×#121	—	2	1	no	—
233	C₃₁×#121	—	2	2	no	—
234	C₃₁×#121	—	2	2	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	—	2	2	no	—
237	C₃₁×#121	C₂³	1	1	yes	characteristic
238	C₃₁×#121	C₂³	1	2	yes	—
239	C₃₁×#121	C₂³	1	1	yes	characteristic
240	C₃₁×#121	C₂³	1	2	yes	—
241	C₃₁×#120	—	2	1	no	—
242	C₃₁×#120	—	2	1	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	D₄	1	1	yes	characteristic
248	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
249	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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×Q₈×C₃₁	C₂³	1	1	yes	characteristic
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	1	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	—	2	1	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	1	no	—
268	C₄×D₄×C₃₁	—	2	1	no	—
269	C₄×D₄×C₃₁	—	2	1	no	—
270	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
271	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
272	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
273	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
274	C₄×D₄×C₃₁	C₂³	1	2	yes	—
275	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₃₁	C₂³	1	2	yes	—
277	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
278	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
284	C₃₁×#117	—	2	1	no	—
285	C₃₁×#117	—	2	1	no	—
286	C₃₁×#117	—	2	1	no	—
287	C₃₁×#117	—	2	1	no	—
288	C₃₁×#117	—	2	1	no	—
289	C₃₁×#117	—	2	1	no	—
290	C₃₁×#117	—	2	1	no	—
291	C₃₁×#117	—	2	1	no	—
292	C₃₁×#117	—	2	1	no	—
293	C₃₁×#117	—	2	1	no	—
294	C₃₁×#117	D₄	1	1	yes	characteristic
295	C₃₁×#117	D₄	1	1	yes	characteristic
296	C₃₁×#117	D₄	1	1	yes	characteristic
297	C₃₁×#117	C₂³	1	1	yes	characteristic
298	C₃₁×#117	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
300	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
301	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
303	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
304	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
305	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
306	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
307	C₂×C₄²×C₃₁	—	2	1	no	—
308	C₂×C₄²×C₃₁	—	2	1	no	—
309	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
312	C₃₁×#107	C₂³	1	2	yes	—
313	C₃₁×#107	C₂³	1	2	yes	—
314	C₃₁×#106	C₂³	1	2	yes	—
315	C₃₁×#106	C₂³	1	2	yes	—
316	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
318	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
320	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
321	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
322	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
323	C₃₁×#103	C₂³	1	2	yes	—
324	C₃₁×#103	C₂³	1	2	yes	—
325	C₃₁×#103	C₂³	1	2	yes	—
326	C₃₁×#103	C₂³	1	2	yes	—
327	C₃₁×#103	C₂³	1	2	yes	—
328	C₃₁×#103	C₂³	1	2	yes	—
329	C₃₁×#102	C₂³	1	2	yes	—
330	C₃₁×#102	C₂³	1	2	yes	—
331	C₃₁×#102	C₂³	1	2	yes	—
332	C₃₁×#102	C₂³	1	2	yes	—
333	C₃₁×#102	C₂³	1	2	yes	—
334	C₃₁×#102	C₂³	1	2	yes	—
335	C₃₁×#102	C₂³	1	2	yes	—
336	C₃₁×#102	C₂³	1	2	yes	—
337	C₃₁×#102	C₂³	1	2	yes	—
338	C₃₁×#102	C₂³	1	2	yes	—
339	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
340	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₃₁×#97	C₂³	1	2	yes	—
343	C₃₁×#97	C₂³	1	2	yes	—
344	C₄×C₈×C₃₁	C₂³	1	2	yes	—
345	C₂⁴×C₃₁	—	2	1	no	—
346	C₂⁴×C₃₁	—	2	2	no	—
347	#41×C₃₁	—	2	2	no	—
348	#41×C₃₁	—	2	2	no	—
349	#41×C₃₁	—	4	2	no	—
350	#41×C₃₁	—	4	1	no	—
351	#41×C₃₁	—	4	1	no	—
352	#41×C₃₁	—	4	2	no	—
353	#41×C₃₁	—	4	2	no	—
354	#41×C₃₁	—	4	2	no	—
355	#41×C₃₁	—	4	2	no	—
356	#41×C₃₁	—	8	2	no	—
357	#41×C₃₁	—	8	2	no	—
358	C₂×Q₈×C₃₁	—	2	1	no	—
359	C₂×Q₈×C₃₁	—	2	1	no	—
360	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
362	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
363	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
364	C₂×D₄×C₃₁	—	2	2	no	—
365	C₂×D₄×C₃₁	—	2	1	no	—
366	C₂×D₄×C₃₁	—	2	1	no	—
367	C₂×D₄×C₃₁	—	2	1	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	2	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	2	2	no	—
373	C₂×D₄×C₃₁	—	2	1	no	—
374	C₂×D₄×C₃₁	—	2	1	no	—
375	C₂×D₄×C₃₁	—	2	1	no	—
376	C₂×D₄×C₃₁	—	2	2	no	—
377	C₂×D₄×C₃₁	—	2	1	no	—
378	C₂×D₄×C₃₁	—	2	1	no	—
379	C₂×D₄×C₃₁	—	2	2	no	—
380	C₂×D₄×C₃₁	—	2	2	no	—
381	C₂×D₄×C₃₁	—	4	1	no	—
382	C₂×D₄×C₃₁	—	4	2	no	—
383	C₂×D₄×C₃₁	—	4	2	no	—
384	C₂×D₄×C₃₁	—	4	4	no	—
385	C₂×D₄×C₃₁	—	8	2	no	—
386	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
387	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
388	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
389	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
390	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
391	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₃₁	—	2	1	no	—
394	C₂²×C₄×C₃₁	—	2	1	no	—
395	C₂²×C₄×C₃₁	—	2	1	no	—
396	C₂²×C₄×C₃₁	—	2	1	no	—
397	C₂²×C₄×C₃₁	—	2	1	no	—
398	C₂²×C₄×C₃₁	—	2	1	no	—
399	C₂²×C₄×C₃₁	—	2	1	no	—
400	C₂²×C₄×C₃₁	—	2	1	no	—
401	C₂²×C₄×C₃₁	—	2	1	no	—
402	C₂²×C₄×C₃₁	—	2	2	no	—
403	C₂²×C₄×C₃₁	—	2	2	no	—
404	C₂²×C₄×C₃₁	—	2	2	no	—
405	C₂²×C₄×C₃₁	—	2	2	no	—
406	C₂²×C₄×C₃₁	—	4	4	no	—
407	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
409	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
410	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
416	Q₁₆×C₃₁	—	4	2	no	—
417	Q₁₆×C₃₁	—	4	2	no	—
418	SD₁₆×C₃₁	—	2	4	no	—
419	SD₁₆×C₃₁	—	4	2	no	—
420	SD₁₆×C₃₁	—	4	2	no	—
421	SD₁₆×C₃₁	—	4	2	no	—
422	SD₁₆×C₃₁	—	4	2	no	—
423	SD₁₆×C₃₁	—	4	2	no	—
424	D₈×C₃₁	—	2	4	no	—
425	D₈×C₃₁	—	2	4	no	—
426	D₈×C₃₁	—	4	2	no	—
427	D₈×C₃₁	—	4	2	no	—
428	M₁₆×C₃₁	—	4	2	no	—
429	M₁₆×C₃₁	—	4	2	no	—
430	C₂×C₈×C₃₁	—	4	2	no	—
431	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
432	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
433	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
434	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
435	C₄⋊C₄×C₃₁	—	2	1	no	—
436	C₄⋊C₄×C₃₁	—	2	1	no	—
437	C₄⋊C₄×C₃₁	—	2	1	no	—
438	C₄⋊C₄×C₃₁	—	2	1	no	—
439	C₄⋊C₄×C₃₁	—	2	1	no	—
440	C₄⋊C₄×C₃₁	—	2	1	no	—
441	C₄⋊C₄×C₃₁	—	2	1	no	—
442	C₄⋊C₄×C₃₁	—	2	1	no	—
443	C₄⋊C₄×C₃₁	—	2	1	no	—
444	C₄⋊C₄×C₃₁	—	2	1	no	—
445	C₄⋊C₄×C₃₁	—	2	1	no	—
446	C₄⋊C₄×C₃₁	—	2	1	no	—
447	C₄⋊C₄×C₃₁	—	2	1	no	—
448	C₄⋊C₄×C₃₁	—	2	1	no	—
449	C₄⋊C₄×C₃₁	—	2	1	no	—
450	C₄⋊C₄×C₃₁	—	2	1	no	—
451	C₄⋊C₄×C₃₁	—	2	2	no	—
452	C₄⋊C₄×C₃₁	—	2	1	no	—
453	C₄⋊C₄×C₃₁	—	2	1	no	—
454	C₄⋊C₄×C₃₁	—	2	1	no	—
455	C₄⋊C₄×C₃₁	—	2	2	no	—
456	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
457	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
458	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
465	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
467	C₂²⋊C₄×C₃₁	—	2	2	no	—
468	C₂²⋊C₄×C₃₁	—	2	1	no	—
469	C₂²⋊C₄×C₃₁	—	2	1	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	1	no	—
472	C₂²⋊C₄×C₃₁	—	2	1	no	—
473	C₂²⋊C₄×C₃₁	—	2	1	no	—
474	C₂²⋊C₄×C₃₁	—	2	1	no	—
475	C₂²⋊C₄×C₃₁	—	2	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	1	no	—
477	C₂²⋊C₄×C₃₁	—	2	1	no	—
478	C₂²⋊C₄×C₃₁	—	2	1	no	—
479	C₂²⋊C₄×C₃₁	—	2	2	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	2	no	—
482	C₂²⋊C₄×C₃₁	—	2	2	no	—
483	C₂²⋊C₄×C₃₁	—	2	1	no	—
484	C₂²⋊C₄×C₃₁	—	2	1	no	—
485	C₂²⋊C₄×C₃₁	—	2	1	no	—
486	C₂²⋊C₄×C₃₁	—	2	1	no	—
487	C₂²⋊C₄×C₃₁	—	2	1	no	—
488	C₂²⋊C₄×C₃₁	—	2	2	no	—
489	C₂²⋊C₄×C₃₁	—	2	2	no	—
490	C₂²⋊C₄×C₃₁	—	2	1	no	—
491	C₂²⋊C₄×C₃₁	—	2	1	no	—
492	C₂²⋊C₄×C₃₁	—	2	2	no	—
493	C₂²⋊C₄×C₃₁	—	2	2	no	—
494	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
495	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
496	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
497	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
498	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
499	C₂²⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₃₁	—	2	1	no	—
501	C₄²×C₃₁	—	2	1	no	—
502	C₄²×C₃₁	—	2	1	no	—
503	C₄²×C₃₁	—	2	1	no	—
504	C₄²×C₃₁	—	2	1	no	—
505	C₄²×C₃₁	—	2	1	no	—
506	C₄²×C₃₁	—	2	2	no	—
507	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
508	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
509	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
510	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
511	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
512	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
513	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
514	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
515	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
516	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
517	#61968	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
518	C₂³×C₃₁	—	2	1	no	—
519	C₂³×C₃₁	—	2	1	no	—
520	C₂³×C₃₁	—	2	2	no	—
521	C₂³×C₃₁	—	2	2	no	—
522	C₂³×C₃₁	—	4	2	no	—
523	C₂³×C₃₁	—	4	2	no	—
524	C₂³×C₃₁	—	4	4	no	—
525	C₂³×C₃₁	—	8	1	no	—
526	C₂³×C₃₁	—	8	2	no	—
527	C₂³×C₃₁	—	8	2	no	—
528	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
529	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
530	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	Q₈×C₃₁	—	2	2	no	—
532	Q₈×C₃₁	—	2	1	no	—
533	Q₈×C₃₁	—	2	1	no	—
534	Q₈×C₃₁	—	2	1	no	—
535	Q₈×C₃₁	—	2	1	no	—
536	Q₈×C₃₁	—	2	2	no	—
537	Q₈×C₃₁	—	4	1	no	—
538	Q₈×C₃₁	—	4	2	no	—
539	Q₈×C₃₁	—	8	1	no	—
540	D₄×C₃₁	—	2	2	no	—
541	D₄×C₃₁	—	2	2	no	—
542	D₄×C₃₁	—	2	1	no	—
543	D₄×C₃₁	—	2	1	no	—
544	D₄×C₃₁	—	2	1	no	—
545	D₄×C₃₁	—	2	2	no	—
546	D₄×C₃₁	—	2	2	no	—
547	D₄×C₃₁	—	4	1	no	—
548	D₄×C₃₁	—	4	1	no	—
549	D₄×C₃₁	—	4	1	no	—
550	D₄×C₃₁	—	4	2	no	—
551	D₄×C₃₁	—	4	4	no	—
552	D₄×C₃₁	—	4	2	no	—
553	D₄×C₃₁	—	4	2	no	—
554	D₄×C₃₁	—	4	2	no	—
555	D₄×C₃₁	—	4	2	no	—
556	D₄×C₃₁	—	4	2	no	—
557	D₄×C₃₁	—	4	2	no	—
558	D₄×C₃₁	—	8	2	no	—
559	D₄×C₃₁	—	8	2	no	—
560	D₄×C₃₁	—	8	1	no	—
561	D₄×C₃₁	—	8	1	no	—
562	D₄×C₃₁	—	8	2	no	—
563	D₄×C₃₁	—	8	2	no	—
564	D₄×C₃₁	—	8	2	no	—
565	D₄×C₃₁	—	8	2	no	—
566	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
567	C₂×C₄×C₃₁	—	2	2	no	—
568	C₂×C₄×C₃₁	—	2	2	no	—
569	C₂×C₄×C₃₁	—	2	2	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	1	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	2	1	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	1	no	—
577	C₂×C₄×C₃₁	—	2	1	no	—
578	C₂×C₄×C₃₁	—	2	1	no	—
579	C₂×C₄×C₃₁	—	2	1	no	—
580	C₂×C₄×C₃₁	—	2	1	no	—
581	C₂×C₄×C₃₁	—	2	2	no	—
582	C₂×C₄×C₃₁	—	2	2	no	—
583	C₂×C₄×C₃₁	—	2	1	no	—
584	C₂×C₄×C₃₁	—	4	1	no	—
585	C₂×C₄×C₃₁	—	4	1	no	—
586	C₂×C₄×C₃₁	—	4	1	no	—
587	C₂×C₄×C₃₁	—	4	2	no	—
588	C₂×C₄×C₃₁	—	4	2	no	—
589	C₂×C₄×C₃₁	—	4	2	no	—
590	C₂×C₄×C₃₁	—	4	2	no	—
591	C₂×C₄×C₃₁	—	4	2	no	—
592	C₂×C₄×C₃₁	—	4	2	no	—
593	C₂×C₄×C₃₁	—	4	2	no	—
594	C₂×C₄×C₃₁	—	8	1	no	—
595	C₂×C₄×C₃₁	—	8	1	no	—
596	C₂×C₄×C₃₁	—	8	2	no	—
597	C₂×C₄×C₃₁	—	8	2	no	—
598	C₂×C₄×C₃₁	—	8	2	no	—
599	C₂×C₄×C₃₁	—	8	2	no	—
600	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
608	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
612	C₈×C₃₁	—	2	2	no	—
613	C₈×C₃₁	—	2	2	no	—
614	C₈×C₃₁	—	2	2	no	—
615	C₈×C₃₁	—	2	2	no	—
616	#3508	C₂×C₃₁	1	1	yes	characteristic, complemented
617	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
618	#3401	C₂×C₃₁	1	2	yes	complemented
619	#3370	C₂×C₃₁	1	2	yes	complemented
620	#3323	C₂×C₃₁	1	2	yes	complemented
621	#3319	C₂×C₃₁	1	2	yes	complemented
622	#3317	C₂×C₃₁	1	2	yes	complemented
623	#3273	C₂×C₃₁	1	2	yes	complemented
624	#3268	C₂×C₃₁	1	2	yes	complemented
625	#3267	C₂×C₃₁	1	2	yes	complemented
626	#3254	C₂×C₃₁	1	1	yes	characteristic, complemented
627	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
628	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
629	#3217	C₂×C₃₁	1	1	yes	characteristic, complemented
630	#3216	C₂×C₃₁	1	1	yes	characteristic, complemented
631	#3212	C₂×C₃₁	1	1	yes	characteristic, complemented
632	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
633	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
634	#3106	C₂×C₃₁	1	1	yes	characteristic, complemented
635	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
636	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
637	#3035	C₂×C₃₁	1	1	yes	characteristic, complemented
638	#2989	C₂×C₃₁	1	1	yes	characteristic, complemented
639	C₂²×C₃₁	—	2	1	no	—
640	C₂²×C₃₁	—	2	1	no	—
641	C₂²×C₃₁	—	2	1	no	—
642	C₂²×C₃₁	—	2	1	no	—
643	C₂²×C₃₁	—	2	1	no	—
644	C₂²×C₃₁	—	2	1	no	—
645	C₂²×C₃₁	—	2	2	no	—
646	C₂²×C₃₁	—	2	1	no	—
647	C₂²×C₃₁	—	2	1	no	—
648	C₂²×C₃₁	—	2	1	no	—
649	C₂²×C₃₁	—	4	1	no	—
650	C₂²×C₃₁	—	4	1	no	—
651	C₂²×C₃₁	—	4	2	no	—
652	C₂²×C₃₁	—	4	2	no	—
653	C₂²×C₃₁	—	4	1	no	—
654	C₂²×C₃₁	—	4	2	no	—
655	C₂²×C₃₁	—	4	2	no	—
656	C₂²×C₃₁	—	4	1	no	—
657	C₂²×C₃₁	—	4	1	no	—
658	C₂²×C₃₁	—	4	2	no	—
659	C₂²×C₃₁	—	4	2	no	—
660	C₂²×C₃₁	—	8	4	no	—
661	C₂²×C₃₁	—	16	4	no	—
662	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
663	C₄×C₃₁	—	2	1	no	—
664	C₄×C₃₁	—	2	1	no	—
665	C₄×C₃₁	—	2	1	no	—
666	C₄×C₃₁	—	2	1	no	—
667	C₄×C₃₁	—	2	1	no	—
668	C₄×C₃₁	—	2	1	no	—
669	C₄×C₃₁	—	2	1	no	—
670	C₄×C₃₁	—	2	1	no	—
671	C₄×C₃₁	—	2	1	no	—
672	C₄×C₃₁	—	2	1	no	—
673	C₄×C₃₁	—	4	2	no	—
674	C₄×C₃₁	—	4	1	no	—
675	C₄×C₃₁	—	4	1	no	—
676	C₄×C₃₁	—	4	1	no	—
677	C₄×C₃₁	—	4	1	no	—
678	C₄×C₃₁	—	4	2	no	—
679	C₄×C₃₁	—	4	1	no	—
680	C₄×C₃₁	—	4	1	no	—
681	C₄×C₃₁	#575	1	2	yes	—
682	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
683	C₄×C₃₁	#585	1	1	yes	characteristic
684	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
685	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
686	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
687	#559	—	2	1	no	—
688	#559	C₂²×C₃₁	1	2	yes	complemented
689	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
690	#555	C₂²×C₃₁	1	1	yes	characteristic
691	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#553	—	2	1	no	—
693	#552	—	2	1	no	—
694	#552	C₂²×C₃₁	1	1	yes	characteristic
695	#552	C₂²×C₃₁	1	1	yes	characteristic, complemented
696	#551	—	2	1	no	—
697	#551	—	2	1	no	—
698	#550	—	2	1	no	—
699	#550	C₂²×C₃₁	1	2	yes	—
700	#547	C₂²×C₃₁	1	1	yes	characteristic
701	#546	—	2	1	no	—
702	#546	—	2	1	no	—
703	#546	C₂²×C₃₁	1	1	yes	characteristic
704	#546	C₂²×C₃₁	1	2	yes	—
705	#546	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#546	C₂²×C₃₁	1	2	yes	complemented
707	#540	—	2	1	no	—
708	#540	—	2	1	no	—
709	#535	—	2	1	no	—
710	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#532	C₂²×C₃₁	1	1	yes	characteristic
713	#532	C₂²×C₃₁	1	1	yes	characteristic
714	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#529	—	2	1	no	—
718	#529	—	2	1	no	—
719	#529	C₂²×C₃₁	1	1	yes	characteristic
720	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	#525	—	2	1	no	—
722	#518	—	2	1	no	—
723	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
724	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
725	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
726	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	C₂×#117	—	2	1	no	—
728	#497	C₂²×C₃₁	1	2	yes	complemented
729	#496	C₂²×C₃₁	1	2	yes	—
730	#495	C₂²×C₃₁	1	2	yes	complemented
731	#490	C₂²×C₃₁	1	2	yes	complemented
732	#489	C₂²×C₃₁	1	2	yes	complemented
733	#488	C₂²×C₃₁	1	2	yes	complemented
734	#485	C₂²×C₃₁	1	2	yes	complemented
735	#482	C₂²×C₃₁	1	2	yes	complemented
736	#481	C₂²×C₃₁	1	2	yes	complemented
737	#479	C₂²×C₃₁	1	2	yes	complemented
738	#478	C₂²×C₃₁	1	2	yes	complemented
739	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
740	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
741	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
743	#474	C₂²×C₃₁	1	2	yes	complemented
744	#470	C₂²×C₃₁	1	2	yes	complemented
745	#468	C₂²×C₃₁	1	2	yes	—
746	#468	C₂²×C₃₁	1	2	yes	complemented
747	#468	C₂²×C₃₁	1	2	yes	complemented
748	#466	C₂²×C₃₁	1	2	yes	complemented
749	#465	C₂²×C₃₁	1	2	yes	complemented
750	#464	C₂²×C₃₁	1	2	yes	complemented
751	#464	C₂²×C₃₁	1	2	yes	complemented
752	#463	C₂²×C₃₁	1	2	yes	complemented
753	#463	C₂²×C₃₁	1	2	yes	complemented
754	#463	C₂²×C₃₁	1	2	yes	complemented
755	#463	C₂²×C₃₁	1	2	yes	complemented
756	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
757	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
758	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
759	#461	C₂²×C₃₁	1	2	yes	complemented
760	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
761	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
762	#460	C₂²×C₃₁	1	2	yes	complemented
763	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
764	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#459	C₂²×C₃₁	1	1	yes	characteristic
767	#459	C₂²×C₃₁	1	1	yes	characteristic
768	#459	C₂²×C₃₁	1	1	yes	characteristic
769	#459	C₂²×C₃₁	1	2	yes	—
770	#459	C₂²×C₃₁	1	1	yes	characteristic
771	#452	C₂²×C₃₁	1	2	yes	—
772	#452	C₂²×C₃₁	1	2	yes	complemented
773	#452	C₂²×C₃₁	1	2	yes	complemented
774	#452	C₂²×C₃₁	1	2	yes	complemented
775	#450	C₂²×C₃₁	1	2	yes	complemented
776	#449	C₂²×C₃₁	1	2	yes	complemented
777	#449	C₂²×C₃₁	1	2	yes	complemented
778	#447	C₂²×C₃₁	1	2	yes	—
779	#447	C₂²×C₃₁	1	2	yes	complemented
780	#446	C₂²×C₃₁	1	2	yes	complemented
781	#442	C₂²×C₃₁	1	2	yes	complemented
782	#442	C₂²×C₃₁	1	2	yes	complemented
783	#441	C₂²×C₃₁	1	2	yes	complemented
784	#440	C₂²×C₃₁	1	2	yes	complemented
785	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
786	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
787	#436	C₂²×C₃₁	1	2	yes	—
788	#435	C₂²×C₃₁	1	2	yes	complemented
789	#435	C₂²×C₃₁	1	2	yes	complemented
790	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
791	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
792	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
793	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
794	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
795	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
796	#418	C₂²×C₃₁	1	2	yes	complemented
797	#417	C₂²×C₃₁	1	2	yes	complemented
798	#416	C₂²×C₃₁	1	2	yes	complemented
799	C₂×C₃₁	—	4	1	no	—
800	C₂×C₃₁	—	4	1	no	—
801	C₂×C₃₁	—	4	1	no	—
802	C₂×C₃₁	—	4	2	no	—
803	C₂×C₃₁	—	8	1	no	—
804	C₂×C₃₁	—	8	2	no	—
805	C₂×C₃₁	—	8	2	no	—
806	C₂×C₃₁	#3488	1	1	yes	characteristic
807	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
808	C₂×C₃₁	#3585	1	1	yes	characteristic
809	C₂×#41	—	2	1	no	—
810	C₂×#41	—	2	1	no	—
811	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
812	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
814	C₂×#41	C₂³×C₃₁	1	2	yes	—
815	C₂×#41	C₂³×C₃₁	1	2	yes	—
816	C₂²×D₄	—	2	1	no	—
817	C₂²×D₄	—	2	1	no	—
818	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
819	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
820	C₂³×C₄	—	2	1	no	—
821	AGL(1,ℤ/8)	—	4	4	no	—
822	AGL(1,ℤ/8)	—	4	4	no	—
823	#135	—	4	4	no	—
824	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
825	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
826	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
827	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
828	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
829	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
830	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
831	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
832	C₂×D₈	C₂³×C₃₁	1	2	yes	—
833	C₂×D₈	C₂³×C₃₁	1	2	yes	—
834	C₂×D₈	C₂³×C₃₁	1	2	yes	—
835	C₂×D₈	C₂³×C₃₁	1	2	yes	—
836	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
837	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
838	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
839	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
840	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
842	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
843	#127	—	2	2	no	—
844	#127	—	2	1	no	—
845	#127	—	2	1	no	—
846	#127	C₂³×C₃₁	1	1	yes	characteristic
847	#127	C₂³×C₃₁	1	1	yes	characteristic
848	#127	C₂³×C₃₁	1	2	yes	—
849	#126	—	2	1	no	—
850	#126	—	2	1	no	—
851	#126	—	2	1	no	—
852	#126	—	2	1	no	—
853	#126	—	2	1	no	—
854	#126	—	2	1	no	—
855	#125	—	2	1	no	—
856	#125	—	2	1	no	—
857	#125	—	2	1	no	—
858	#125	—	2	1	no	—
859	#125	C₂³×C₃₁	1	1	yes	characteristic
860	#125	C₂³×C₃₁	1	1	yes	characteristic
861	#124	—	2	2	no	—
862	#124	—	2	1	no	—
863	#124	—	2	1	no	—
864	#124	—	2	1	no	—
865	#124	—	2	1	no	—
866	#124	C₂³×C₃₁	1	1	yes	characteristic
867	#124	C₂³×C₃₁	1	1	yes	characteristic
868	#124	C₂³×C₃₁	1	2	yes	—
869	#124	C₂³×C₃₁	1	2	yes	—
870	#123	—	2	1	no	—
871	#123	—	2	1	no	—
872	#123	—	2	1	no	—
873	#123	—	2	1	no	—
874	#123	—	2	1	no	—
875	#123	—	2	1	no	—
876	#123	—	2	2	no	—
877	#123	—	2	2	no	—
878	#123	—	2	2	no	—
879	#123	—	2	2	no	—
880	#123	—	2	1	no	—
881	#123	—	2	1	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	1	no	—
884	C₂²⋊Q₈	—	2	1	no	—
885	C₂²⋊Q₈	—	2	1	no	—
886	C₂²⋊Q₈	—	2	1	no	—
887	C₂²⋊Q₈	—	2	1	no	—
888	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
889	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
890	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
891	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
892	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
893	#121	—	2	1	no	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	—	2	1	no	—
901	#121	—	2	1	no	—
902	#121	—	2	1	no	—
903	#121	—	2	2	no	—
904	#121	—	2	2	no	—
905	#121	—	2	2	no	—
906	#121	—	2	2	no	—
907	#121	C₂³×C₃₁	1	1	yes	characteristic
908	#121	C₂³×C₃₁	1	1	yes	characteristic
909	#121	C₂³×C₃₁	1	2	yes	—
910	#121	C₂³×C₃₁	1	2	yes	—
911	#120	—	2	1	no	—
912	#120	—	2	1	no	—
913	#120	—	2	2	no	—
914	#120	—	2	2	no	—
915	C₄×Q₈	—	2	1	no	—
916	C₄×Q₈	—	2	1	no	—
917	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
918	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
919	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
920	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
921	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
922	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
923	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	1	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	1	no	—
928	C₄×D₄	—	2	1	no	—
929	C₄×D₄	—	2	1	no	—
930	C₄×D₄	—	2	2	no	—
931	C₄×D₄	—	2	2	no	—
932	C₄×D₄	—	2	1	no	—
933	C₄×D₄	—	2	1	no	—
934	C₄×D₄	—	2	1	no	—
935	C₄×D₄	—	2	1	no	—
936	C₄×D₄	—	2	1	no	—
937	C₄×D₄	—	2	1	no	—
938	C₄×D₄	—	2	1	no	—
939	C₄×D₄	—	2	1	no	—
940	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
941	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
942	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
943	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
944	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
945	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
946	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
947	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
948	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
949	C₄×D₄	C₂³×C₃₁	1	2	yes	—
950	C₄×D₄	C₂³×C₃₁	1	2	yes	—
951	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
952	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
953	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
954	#117	—	2	1	no	—
955	#117	—	2	1	no	—
956	#117	—	2	1	no	—
957	#117	—	2	1	no	—
958	#117	—	2	1	no	—
959	#117	—	2	1	no	—
960	#117	—	2	1	no	—
961	#117	—	2	1	no	—
962	#117	—	2	1	no	—
963	#117	—	2	1	no	—
964	#117	D₄×C₃₁	1	1	yes	characteristic
965	#117	D₄×C₃₁	1	1	yes	characteristic
966	#117	D₄×C₃₁	1	1	yes	characteristic
967	#117	C₂³×C₃₁	1	1	yes	characteristic
968	#117	C₂³×C₃₁	1	1	yes	characteristic
969	C₂×C₄⋊C₄	—	2	1	no	—
970	C₂×C₄⋊C₄	—	2	1	no	—
971	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
972	C₂×C₂²⋊C₄	—	2	1	no	—
973	C₂×C₂²⋊C₄	—	2	1	no	—
974	C₂×C₂²⋊C₄	—	2	1	no	—
975	C₂×C₂²⋊C₄	—	2	2	no	—
976	C₂×C₂²⋊C₄	—	2	2	no	—
977	C₂×C₄²	—	2	1	no	—
978	C₂×C₄²	—	2	1	no	—
979	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
980	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
981	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
982	#107	C₂³×C₃₁	1	2	yes	—
983	#107	C₂³×C₃₁	1	2	yes	—
984	#106	C₂³×C₃₁	1	2	yes	—
985	#106	C₂³×C₃₁	1	2	yes	—
986	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
987	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
988	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
989	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
990	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
991	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
992	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
993	#103	C₂³×C₃₁	1	2	yes	—
994	#103	C₂³×C₃₁	1	2	yes	—
995	#103	C₂³×C₃₁	1	2	yes	—
996	#103	C₂³×C₃₁	1	2	yes	—
997	#103	C₂³×C₃₁	1	2	yes	—
998	#103	C₂³×C₃₁	1	2	yes	—
999	#102	C₂³×C₃₁	1	2	yes	—
1000	#102	C₂³×C₃₁	1	2	yes	—
1001	#102	C₂³×C₃₁	1	2	yes	—
1002	#102	C₂³×C₃₁	1	2	yes	—
1003	#102	C₂³×C₃₁	1	2	yes	—
1004	#102	C₂³×C₃₁	1	2	yes	—
1005	#102	C₂³×C₃₁	1	2	yes	—
1006	#102	C₂³×C₃₁	1	2	yes	—
1007	#102	C₂³×C₃₁	1	2	yes	—
1008	#102	C₂³×C₃₁	1	2	yes	—
1009	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1010	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1011	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
1012	#97	C₂³×C₃₁	1	2	yes	—
1013	#97	C₂³×C₃₁	1	2	yes	—
1014	C₄×C₈	C₂³×C₃₁	1	2	yes	—
1015	C₃₁	#61968	1	1	yes	characteristic, direct product factor, Sylow
1016	C₂⁴	—	2	1	no	—
1017	C₂⁴	—	2	2	no	—
1018	#41	—	2	2	no	—
1019	#41	—	2	2	no	—
1020	#41	—	4	2	no	—
1021	#41	—	4	1	no	—
1022	#41	—	4	1	no	—
1023	#41	—	4	2	no	—
1024	#41	—	4	2	no	—
1025	#41	—	4	2	no	—
1026	#41	—	4	2	no	—
1027	#41	—	8	2	no	—
1028	#41	—	8	2	no	—
1029	C₂×Q₈	—	2	1	no	—
1030	C₂×Q₈	—	2	1	no	—
1031	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1032	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1033	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	1	no	—
1037	C₂×D₄	—	2	1	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	2	no	—
1041	C₂×D₄	—	2	2	no	—
1042	C₂×D₄	—	2	2	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	2	1	no	—
1046	C₂×D₄	—	2	1	no	—
1047	C₂×D₄	—	2	2	no	—
1048	C₂×D₄	—	2	1	no	—
1049	C₂×D₄	—	2	1	no	—
1050	C₂×D₄	—	2	2	no	—
1051	C₂×D₄	—	2	2	no	—
1052	C₂×D₄	—	4	1	no	—
1053	C₂×D₄	—	4	2	no	—
1054	C₂×D₄	—	4	2	no	—
1055	C₂×D₄	—	4	4	no	—
1056	C₂×D₄	—	8	2	no	—
1057	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1058	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1059	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1060	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1061	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1062	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1063	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1064	C₂²×C₄	—	2	1	no	—
1065	C₂²×C₄	—	2	1	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	1	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	1	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	2	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	2	no	—
1076	C₂²×C₄	—	2	2	no	—
1077	C₂²×C₄	—	4	4	no	—
1078	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1079	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1080	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1081	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1084	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1085	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1086	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1087	Q₁₆	—	4	2	no	—
1088	Q₁₆	—	4	2	no	—
1089	SD₁₆	—	2	4	no	—
1090	SD₁₆	—	4	2	no	—
1091	SD₁₆	—	4	2	no	—
1092	SD₁₆	—	4	2	no	—
1093	SD₁₆	—	4	2	no	—
1094	SD₁₆	—	4	2	no	—
1095	D₈	—	2	4	no	—
1096	D₈	—	2	4	no	—
1097	D₈	—	4	2	no	—
1098	D₈	—	4	2	no	—
1099	M₁₆	—	4	2	no	—
1100	M₁₆	—	4	2	no	—
1101	C₂×C₈	—	4	2	no	—
1102	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1103	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1104	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1105	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	1	no	—
1109	C₄⋊C₄	—	2	1	no	—
1110	C₄⋊C₄	—	2	1	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	1	no	—
1113	C₄⋊C₄	—	2	1	no	—
1114	C₄⋊C₄	—	2	1	no	—
1115	C₄⋊C₄	—	2	1	no	—
1116	C₄⋊C₄	—	2	1	no	—
1117	C₄⋊C₄	—	2	1	no	—
1118	C₄⋊C₄	—	2	1	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	1	no	—
1121	C₄⋊C₄	—	2	1	no	—
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	—	2	1	no	—
1125	C₄⋊C₄	—	2	1	no	—
1126	C₄⋊C₄	—	2	2	no	—
1127	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1128	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1129	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1130	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1131	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1132	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1133	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1134	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1135	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1136	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1137	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	1	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	2	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	—	2	2	no	—
1154	C₂²⋊C₄	—	2	1	no	—
1155	C₂²⋊C₄	—	2	1	no	—
1156	C₂²⋊C₄	—	2	1	no	—
1157	C₂²⋊C₄	—	2	1	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	—	2	2	no	—
1160	C₂²⋊C₄	—	2	2	no	—
1161	C₂²⋊C₄	—	2	1	no	—
1162	C₂²⋊C₄	—	2	1	no	—
1163	C₂²⋊C₄	—	2	2	no	—
1164	C₂²⋊C₄	—	2	2	no	—
1165	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1166	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1167	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1168	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1169	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1170	C₂²⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1171	C₄²	—	2	1	no	—
1172	C₄²	—	2	1	no	—
1173	C₄²	—	2	1	no	—
1174	C₄²	—	2	1	no	—
1175	C₄²	—	2	1	no	—
1176	C₄²	—	2	1	no	—
1177	C₄²	—	2	2	no	—
1178	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1179	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1180	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1181	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1182	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1183	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1184	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1185	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1186	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1187	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1188	C₂³	—	2	1	no	—
1189	C₂³	—	2	1	no	—
1190	C₂³	—	2	2	no	—
1191	C₂³	—	2	2	no	—
1192	C₂³	—	4	2	no	—
1193	C₂³	—	4	2	no	—
1194	C₂³	—	4	4	no	—
1195	C₂³	—	8	1	no	—
1196	C₂³	—	8	2	no	—
1197	C₂³	—	8	2	no	—
1198	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1199	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1200	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1201	Q₈	—	2	2	no	—
1202	Q₈	—	2	1	no	—
1203	Q₈	—	2	1	no	—
1204	Q₈	—	2	1	no	—
1205	Q₈	—	2	1	no	—
1206	Q₈	—	2	2	no	—
1207	Q₈	—	4	1	no	—
1208	Q₈	—	4	2	no	—
1209	Q₈	—	8	1	no	—
1210	D₄	—	2	2	no	—
1211	D₄	—	2	2	no	—
1212	D₄	—	2	1	no	—
1213	D₄	—	2	1	no	—
1214	D₄	—	2	1	no	—
1215	D₄	—	2	2	no	—
1216	D₄	—	2	2	no	—
1217	D₄	—	4	1	no	—
1218	D₄	—	4	1	no	—
1219	D₄	—	4	1	no	—
1220	D₄	—	4	2	no	—
1221	D₄	—	4	4	no	—
1222	D₄	—	4	2	no	—
1223	D₄	—	4	2	no	—
1224	D₄	—	4	2	no	—
1225	D₄	—	4	2	no	—
1226	D₄	—	4	2	no	—
1227	D₄	—	4	2	no	—
1228	D₄	—	8	2	no	—
1229	D₄	—	8	2	no	—
1230	D₄	—	8	1	no	—
1231	D₄	—	8	1	no	—
1232	D₄	—	8	2	no	—
1233	D₄	—	8	2	no	—
1234	D₄	—	8	2	no	—
1235	D₄	—	8	2	no	—
1236	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1237	C₂×C₄	—	2	2	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	2	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	2	no	—
1252	C₂×C₄	—	2	2	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	4	1	no	—
1255	C₂×C₄	—	4	1	no	—
1256	C₂×C₄	—	4	1	no	—
1257	C₂×C₄	—	4	2	no	—
1258	C₂×C₄	—	4	2	no	—
1259	C₂×C₄	—	4	2	no	—
1260	C₂×C₄	—	4	2	no	—
1261	C₂×C₄	—	4	2	no	—
1262	C₂×C₄	—	4	2	no	—
1263	C₂×C₄	—	4	2	no	—
1264	C₂×C₄	—	8	1	no	—
1265	C₂×C₄	—	8	1	no	—
1266	C₂×C₄	—	8	2	no	—
1267	C₂×C₄	—	8	2	no	—
1268	C₂×C₄	—	8	2	no	—
1269	C₂×C₄	—	8	2	no	—
1270	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1271	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1272	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1273	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1274	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1275	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1276	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1277	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1278	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1279	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1280	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1281	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1282	C₈	—	2	2	no	—
1283	C₈	—	2	2	no	—
1284	C₈	—	2	2	no	—
1285	C₈	—	2	2	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	1	no	—
1288	C₂²	—	2	1	no	—
1289	C₂²	—	2	2	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	1	no	—
1292	C₂²	—	2	1	no	—
1293	C₂²	—	2	1	no	—
1294	C₂²	—	2	1	no	—
1295	C₂²	—	2	1	no	—
1296	C₂²	—	4	1	no	—
1297	C₂²	—	4	1	no	—
1298	C₂²	—	4	2	no	—
1299	C₂²	—	4	2	no	—
1300	C₂²	—	4	1	no	—
1301	C₂²	—	4	1	no	—
1302	C₂²	—	4	2	no	—
1303	C₂²	—	4	2	no	—
1304	C₂²	—	4	2	no	—
1305	C₂²	—	4	2	no	—
1306	C₂²	—	4	1	no	—
1307	C₂²	—	8	4	no	—
1308	C₂²	—	16	4	no	—
1309	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1310	C₄	—	2	1	no	—
1311	C₄	—	2	1	no	—
1312	C₄	—	2	1	no	—
1313	C₄	—	2	1	no	—
1314	C₄	—	2	1	no	—
1315	C₄	—	2	1	no	—
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	4	1	no	—
1321	C₄	—	4	1	no	—
1322	C₄	—	4	2	no	—
1323	C₄	—	4	1	no	—
1324	C₄	—	4	1	no	—
1325	C₄	—	4	2	no	—
1326	C₄	—	4	1	no	—
1327	C₄	—	4	1	no	—
1328	C₄	C₃₁×#575	1	2	yes	—
1329	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1330	C₄	C₃₁×#585	1	1	yes	characteristic
1331	C₂	—	4	1	no	—
1332	C₂	—	4	1	no	—
1333	C₂	—	4	1	no	—
1334	C₂	—	4	2	no	—
1335	C₂	—	8	1	no	—
1336	C₂	—	8	2	no	—
1337	C₂	—	8	2	no	—
1338	C₂	C₃₁×#3488	1	1	yes	characteristic
1339	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1340	C₂	C₃₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3508	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3401	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3323	C₂	semidirect
6. C₃₁×#3319	C₂	semidirect
7. C₃₁×#3317	C₂	semidirect
8. C₃₁×#3273	C₂	semidirect
9. C₃₁×#3268	C₂	semidirect
10. C₃₁×#3267	C₂	semidirect
11. C₃₁×#3254	C₂	semidirect
12. C₃₁×#3252	C₂	semidirect
13. C₃₁×#3247	C₂	semidirect
14. C₃₁×#3217	C₂	semidirect
15. C₃₁×#3216	C₂	semidirect
16. C₃₁×#3212	C₂	semidirect
17. C₃₁×#3116	C₂	semidirect
18. C₃₁×#3109	C₂	semidirect
19. C₃₁×#3106	C₂	semidirect
20. C₃₁×#3038	C₂	semidirect
21. C₃₁×#3036	C₂	semidirect
22. C₃₁×#3035	C₂	semidirect
23. C₃₁×#2989	C₂	semidirect
25. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₃₁×#135	C₂²	semidirect
28. C₃₁×#559	C₂²	semidirect
29. C₃₁×#556	C₂²	semidirect
31. C₃₁×#554	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
45. C₃₁×#546	C₂²	semidirect
46. C₃₁×#546	C₂²	semidirect
50. C₃₁×#533	C₂²	semidirect
51. C₃₁×#533	C₂²	semidirect
54. C₃₁×#532	C₂²	semidirect
55. C₃₁×#532	C₂²	semidirect
56. C₂×C₃₁×#127	C₂²	semidirect
60. C₃₁×#529	C₂²	semidirect
65. C₄×#41×C₃₁	C₂²	semidirect
66. C₂×C₄×D₄×C₃₁	C₂²	semidirect
68. C₃₁×#497	C₂²	semidirect
70. C₃₁×#495	C₂²	semidirect
71. C₃₁×#490	C₂²	semidirect
72. C₃₁×#489	C₂²	semidirect
73. C₃₁×#488	C₂²	semidirect
74. C₃₁×#485	C₂²	semidirect
75. C₃₁×#482	C₂²	semidirect
76. C₃₁×#481	C₂²	semidirect
77. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#477	C₂²	semidirect
80. C₃₁×#477	C₂²	semidirect
81. C₃₁×#476	C₂²	semidirect
82. C₃₁×#476	C₂²	semidirect
83. C₃₁×#474	C₂²	semidirect
84. C₃₁×#470	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#468	C₂²	semidirect
88. C₃₁×#466	C₂²	semidirect
89. C₃₁×#465	C₂²	semidirect
90. C₃₁×#464	C₂²	semidirect
91. C₃₁×#464	C₂²	semidirect
92. C₃₁×#463	C₂²	semidirect
93. C₃₁×#463	C₂²	semidirect
94. C₃₁×#463	C₂²	semidirect
95. C₃₁×#463	C₂²	semidirect
96. C₃₁×#462	C₂²	semidirect
97. C₃₁×#462	C₂²	semidirect
98. C₃₁×#461	C₂²	semidirect
99. C₃₁×#461	C₂²	semidirect
100. C₃₁×#461	C₂²	semidirect
101. C₃₁×#460	C₂²	semidirect
102. C₃₁×#460	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#460	C₂²	semidirect
112. C₃₁×#452	C₂²	semidirect
113. C₃₁×#452	C₂²	semidirect
114. C₃₁×#452	C₂²	semidirect
115. C₃₁×#450	C₂²	semidirect
116. C₃₁×#449	C₂²	semidirect
117. C₃₁×#449	C₂²	semidirect
119. C₃₁×#447	C₂²	semidirect
120. C₃₁×#446	C₂²	semidirect
121. C₃₁×#442	C₂²	semidirect
122. C₃₁×#442	C₂²	semidirect
123. C₃₁×#441	C₂²	semidirect
124. C₃₁×#440	C₂²	semidirect
125. C₄×SD₁₆×C₃₁	C₂²	semidirect
126. C₄×D₈×C₃₁	C₂²	semidirect
128. C₃₁×#435	C₂²	semidirect
129. C₃₁×#435	C₂²	semidirect
130. C₃₁×#432	C₂²	semidirect
131. C₃₁×#432	C₂²	semidirect
132. C₃₁×#431	C₂²	semidirect
133. C₃₁×#423	C₂²	semidirect
134. C₃₁×#423	C₂²	semidirect
135. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
136. C₃₁×#418	C₂²	semidirect
137. C₃₁×#417	C₂²	semidirect
138. C₃₁×#416	C₂²	semidirect
517. #61968	C₃₁	direct (N × H)
616. #3508	C₂×C₃₁	semidirect
617. #3475	C₂×C₃₁	semidirect
618. #3401	C₂×C₃₁	semidirect
619. #3370	C₂×C₃₁	semidirect
620. #3323	C₂×C₃₁	semidirect
621. #3319	C₂×C₃₁	semidirect
622. #3317	C₂×C₃₁	semidirect
623. #3273	C₂×C₃₁	semidirect
624. #3268	C₂×C₃₁	semidirect
625. #3267	C₂×C₃₁	semidirect
626. #3254	C₂×C₃₁	semidirect
627. #3252	C₂×C₃₁	semidirect
628. #3247	C₂×C₃₁	semidirect
629. #3217	C₂×C₃₁	semidirect
630. #3216	C₂×C₃₁	semidirect
631. #3212	C₂×C₃₁	semidirect
632. #3116	C₂×C₃₁	semidirect
633. #3109	C₂×C₃₁	semidirect
634. #3106	C₂×C₃₁	semidirect
635. #3038	C₂×C₃₁	semidirect
636. #3036	C₂×C₃₁	semidirect
637. #3035	C₂×C₃₁	semidirect
638. #2989	C₂×C₃₁	semidirect
685. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
686. C₂×#135	C₂²×C₃₁	semidirect
688. #559	C₂²×C₃₁	semidirect
689. #556	C₂²×C₃₁	semidirect
691. #554	C₂²×C₃₁	semidirect
695. #552	C₂²×C₃₁	semidirect
705. #546	C₂²×C₃₁	semidirect
706. #546	C₂²×C₃₁	semidirect
710. #533	C₂²×C₃₁	semidirect
711. #533	C₂²×C₃₁	semidirect
714. #532	C₂²×C₃₁	semidirect
715. #532	C₂²×C₃₁	semidirect
716. C₂×#127	C₂²×C₃₁	semidirect
720. #529	C₂²×C₃₁	semidirect
725. C₄×#41	C₂²×C₃₁	semidirect
726. C₂×C₄×D₄	C₂²×C₃₁	semidirect
728. #497	C₂²×C₃₁	semidirect
730. #495	C₂²×C₃₁	semidirect
731. #490	C₂²×C₃₁	semidirect
732. #489	C₂²×C₃₁	semidirect
733. #488	C₂²×C₃₁	semidirect
734. #485	C₂²×C₃₁	semidirect
735. #482	C₂²×C₃₁	semidirect
736. #481	C₂²×C₃₁	semidirect
737. #479	C₂²×C₃₁	semidirect
738. #478	C₂²×C₃₁	semidirect
739. #477	C₂²×C₃₁	semidirect
740. #477	C₂²×C₃₁	semidirect
741. #476	C₂²×C₃₁	semidirect
742. #476	C₂²×C₃₁	semidirect
743. #474	C₂²×C₃₁	semidirect
744. #470	C₂²×C₃₁	semidirect
746. #468	C₂²×C₃₁	semidirect
747. #468	C₂²×C₃₁	semidirect
748. #466	C₂²×C₃₁	semidirect
749. #465	C₂²×C₃₁	semidirect
750. #464	C₂²×C₃₁	semidirect
751. #464	C₂²×C₃₁	semidirect
752. #463	C₂²×C₃₁	semidirect
753. #463	C₂²×C₃₁	semidirect
754. #463	C₂²×C₃₁	semidirect
755. #463	C₂²×C₃₁	semidirect
756. #462	C₂²×C₃₁	semidirect
757. #462	C₂²×C₃₁	semidirect
758. #461	C₂²×C₃₁	semidirect
759. #461	C₂²×C₃₁	semidirect
760. #461	C₂²×C₃₁	semidirect
761. #460	C₂²×C₃₁	semidirect
762. #460	C₂²×C₃₁	semidirect
763. #460	C₂²×C₃₁	semidirect
764. #460	C₂²×C₃₁	semidirect
765. #460	C₂²×C₃₁	semidirect
772. #452	C₂²×C₃₁	semidirect
773. #452	C₂²×C₃₁	semidirect
774. #452	C₂²×C₃₁	semidirect
775. #450	C₂²×C₃₁	semidirect
776. #449	C₂²×C₃₁	semidirect
777. #449	C₂²×C₃₁	semidirect
779. #447	C₂²×C₃₁	semidirect
780. #446	C₂²×C₃₁	semidirect
781. #442	C₂²×C₃₁	semidirect
782. #442	C₂²×C₃₁	semidirect
783. #441	C₂²×C₃₁	semidirect
784. #440	C₂²×C₃₁	semidirect
785. C₄×SD₁₆	C₂²×C₃₁	semidirect
786. C₄×D₈	C₂²×C₃₁	semidirect
788. #435	C₂²×C₃₁	semidirect
789. #435	C₂²×C₃₁	semidirect
790. #432	C₂²×C₃₁	semidirect
791. #432	C₂²×C₃₁	semidirect
792. #431	C₂²×C₃₁	semidirect
793. #423	C₂²×C₃₁	semidirect
794. #423	C₂²×C₃₁	semidirect
795. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
796. #418	C₂²×C₃₁	semidirect
797. #417	C₂²×C₃₁	semidirect
798. #416	C₂²×C₃₁	semidirect
1015. C₃₁	#61968	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×#3508	2
C₃₁×#3475	2
C₃₁×#3401	2
C₃₁×#3370	2
C₃₁×#3323	2
C₃₁×#3319	2
C₃₁×#3317	2
C₃₁×#3273	2
C₃₁×#3268	2
C₃₁×#3267	2
C₃₁×#3254	2
C₃₁×#3252	2
C₃₁×#3247	2
C₃₁×#3217	2
C₃₁×#3216	2
C₃₁×#3212	2
C₃₁×#3116	2
C₃₁×#3109	2
C₃₁×#3106	2
C₃₁×#3038	2
C₃₁×#3036	2
C₃₁×#3035	2
C₃₁×#2989	2
#61968	31

Subgroups — C31×#61968 #21518727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61968 #21518727