Subgroups — C₃₁×#61993 #21518752

Order 7936.

1870 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3317	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3315	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3268	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3267	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3250	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3219	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3111	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3035	C₂	1	2	yes	maximal, complemented
23	C₃₁×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₃₁×#135	C₂²	1	2	yes	—
26	C₂×C₃₁×#135	C₂²	1	2	yes	—
27	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#556	C₂²	1	1	yes	characteristic
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	C₂²	1	1	yes	characteristic
31	C₃₁×#553	—	2	1	no	—
32	C₃₁×#553	—	2	2	no	—
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#552	—	2	1	no	—
35	C₃₁×#552	C₂²	1	2	yes	—
36	C₃₁×#551	—	2	2	no	—
37	C₃₁×#550	—	2	1	no	—
38	C₃₁×#550	C₂²	1	2	yes	—
39	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#547	C₂²	1	2	yes	—
43	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#546	C₂²	1	2	yes	—
45	C₃₁×#540	—	2	1	no	—
46	C₃₁×#540	—	2	2	no	—
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#532	C₂²	1	1	yes	characteristic
49	C₃₁×#532	C₂²	1	2	yes	complemented
50	C₃₁×#529	—	2	2	no	—
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	2	yes	—
53	C₃₁×#529	C₂²	1	2	yes	complemented
54	C₃₁×#525	—	2	1	no	—
55	C₃₁×#520	—	2	1	no	—
56	C₄×#41×C₃₁	C₂²	1	2	yes	—
57	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₂×C₃₁×#117	—	2	1	no	—
60	C₃₁×#497	C₂²	1	2	yes	—
61	C₃₁×#496	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
64	C₃₁×#491	C₂²	1	2	yes	complemented
65	C₃₁×#490	C₂²	1	2	yes	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×#484	C₂²	1	1	yes	characteristic
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	1	yes	characteristic
72	C₃₁×#479	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	1	yes	characteristic
75	C₃₁×#478	C₂²	1	1	yes	characteristic
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
78	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
79	C₃₁×#470	C₂²	1	2	yes	—
80	C₃₁×#468	C₂²	1	2	yes	—
81	C₃₁×#467	C₂²	1	2	yes	complemented
82	C₃₁×#466	C₂²	1	2	yes	—
83	C₃₁×#465	C₂²	1	2	yes	—
84	C₃₁×#465	C₂²	1	2	yes	complemented
85	C₃₁×#464	C₂²	1	2	yes	—
86	C₃₁×#464	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#464	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	1	yes	characteristic
90	C₃₁×#463	C₂²	1	1	yes	characteristic
91	C₃₁×#463	C₂²	1	2	yes	—
92	C₃₁×#463	C₂²	1	2	yes	—
93	C₃₁×#463	C₂²	1	2	yes	—
94	C₃₁×#462	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#462	C₂²	1	2	yes	complemented
96	C₃₁×#461	C₂²	1	2	yes	—
97	C₃₁×#461	C₂²	1	1	yes	characteristic
98	C₃₁×#461	C₂²	1	1	yes	characteristic
99	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
100	C₃₁×#460	C₂²	1	2	yes	complemented
101	C₃₁×#459	C₂²	1	2	yes	—
102	C₃₁×#459	C₂²	1	1	yes	characteristic
103	C₃₁×#459	C₂²	1	1	yes	characteristic
104	C₃₁×#452	C₂²	1	2	yes	—
105	C₃₁×#452	C₂²	1	2	yes	—
106	C₃₁×#452	C₂²	1	2	yes	—
107	C₃₁×#452	C₂²	1	2	yes	complemented
108	C₃₁×#452	C₂²	1	2	yes	complemented
109	C₃₁×#450	C₂²	1	1	yes	characteristic
110	C₃₁×#449	C₂²	1	2	yes	—
111	C₃₁×#449	C₂²	1	2	yes	—
112	C₃₁×#449	C₂²	1	2	yes	—
113	C₃₁×#447	C₂²	1	1	yes	characteristic
114	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#442	C₂²	1	2	yes	—
117	C₃₁×#441	C₂²	1	2	yes	complemented
118	C₃₁×#440	C₂²	1	2	yes	—
119	C₃₁×#440	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
124	C₃₁×#435	C₂²	1	2	yes	—
125	C₃₁×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
128	C₃₁×#432	C₂²	1	2	yes	complemented
129	C₃₁×#431	C₂²	1	1	yes	characteristic
130	C₃₁×#423	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₃₁×#417	C₂²	1	2	yes	—
133	C₃₁×#416	C₂²	1	2	yes	complemented
134	C₃₁×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	2	yes	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₃₁	—	2	1	no	—
143	C₃₁×AGL(1,ℤ/8)	—	4	4	no	—
144	C₃₁×#135	—	4	4	no	—
145	C₃₁×#135	—	4	4	no	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
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×SD₁₆×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₃₁	C₂³	1	2	yes	—
160	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	—	2	2	no	—
168	C₃₁×#127	—	2	1	no	—
169	C₃₁×#127	C₂³	1	1	yes	characteristic
170	C₃₁×#127	C₂³	1	2	yes	—
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	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	2	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	C₂³	1	1	yes	characteristic
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	C₂³	1	1	yes	characteristic
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#124	C₂³	1	2	yes	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	1	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	—	2	2	no	—
192	C₃₁×#123	—	2	2	no	—
193	C₃₁×#123	—	2	2	no	—
194	C₃₁×#123	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	1	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×#121	—	2	1	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	1	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	—	2	2	no	—
216	C₃₁×#121	—	2	2	no	—
217	C₃₁×#121	C₂³	1	1	yes	characteristic
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#120	—	2	2	no	—
221	C₄×Q₈×C₃₁	—	2	1	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	2	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	1	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	1	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	D₄	1	2	yes	—
243	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₃₁	C₂³	1	2	yes	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	—	2	2	no	—
257	C₃₁×#117	—	2	2	no	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	—	2	1	no	—
260	C₃₁×#117	—	2	2	no	—
261	C₃₁×#117	D₄	1	1	yes	characteristic
262	C₃₁×#117	D₄	1	2	yes	—
263	C₃₁×#117	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
265	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	—	2	2	no	—
272	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
273	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	1	yes	characteristic
275	C₃₁×#107	C₂³	1	1	yes	characteristic
276	C₃₁×#107	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	1	yes	characteristic
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₃₁×#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	2	yes	—
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	1	yes	characteristic
297	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
303	C₃₁×#102	C₂³	1	1	yes	characteristic
304	C₃₁×#102	C₂³	1	1	yes	characteristic
305	C₃₁×#102	C₂³	1	1	yes	characteristic
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	2	yes	—
312	C₃₁×#97	C₂³	1	2	yes	—
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
315	C₂⁴×C₃₁	—	2	1	no	—
316	#41×C₃₁	—	2	4	no	—
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	2	no	—
322	#41×C₃₁	—	4	2	no	—
323	#41×C₃₁	—	4	2	no	—
324	#41×C₃₁	—	4	2	no	—
325	#41×C₃₁	—	4	4	no	—
326	C₂×Q₈×C₃₁	—	2	1	no	—
327	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	2	1	no	—
340	C₂×D₄×C₃₁	—	2	2	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	1	no	—
344	C₂×D₄×C₃₁	—	4	1	no	—
345	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₃₁	—	2	1	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	2	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	2	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	2	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	4	4	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	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
370	Q₁₆×C₃₁	—	4	2	no	—
371	Q₁₆×C₃₁	—	4	2	no	—
372	Q₁₆×C₃₁	—	4	2	no	—
373	SD₁₆×C₃₁	—	2	2	no	—
374	SD₁₆×C₃₁	—	2	4	no	—
375	SD₁₆×C₃₁	—	4	2	no	—
376	SD₁₆×C₃₁	—	4	1	no	—
377	SD₁₆×C₃₁	—	4	2	no	—
378	SD₁₆×C₃₁	—	4	2	no	—
379	SD₁₆×C₃₁	—	4	2	no	—
380	D₈×C₃₁	—	2	2	no	—
381	D₈×C₃₁	—	2	4	no	—
382	D₈×C₃₁	—	4	1	no	—
383	D₈×C₃₁	—	4	2	no	—
384	M₁₆×C₃₁	—	4	2	no	—
385	C₂×C₈×C₃₁	—	4	2	no	—
386	C₂×C₈×C₃₁	—	4	2	no	—
387	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
392	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
393	C₄⋊C₄×C₃₁	—	2	2	no	—
394	C₄⋊C₄×C₃₁	—	2	1	no	—
395	C₄⋊C₄×C₃₁	—	2	1	no	—
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	2	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	1	no	—
402	C₄⋊C₄×C₃₁	—	2	1	no	—
403	C₄⋊C₄×C₃₁	—	2	2	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	—	2	1	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	2	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	C₂²⋊C₄×C₃₁	—	2	2	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
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	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	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	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	1	no	—
443	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₄²×C₃₁	—	2	2	no	—
447	C₄²×C₃₁	—	2	2	no	—
448	C₄²×C₃₁	—	2	2	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	1	no	—
451	C₄²×C₃₁	C₂×D₄	1	2	yes	—
452	C₄²×C₃₁	C₂×D₄	1	2	yes	—
453	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₃₁	C₂⁴	1	2	yes	—
457	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
458	#61993	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₃₁	—	2	1	no	—
460	C₂³×C₃₁	—	2	1	no	—
461	C₂³×C₃₁	—	2	2	no	—
462	C₂³×C₃₁	—	2	1	no	—
463	C₂³×C₃₁	—	4	2	no	—
464	C₂³×C₃₁	—	4	2	no	—
465	C₂³×C₃₁	—	8	1	no	—
466	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
468	Q₈×C₃₁	—	2	2	no	—
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	2	1	no	—
471	Q₈×C₃₁	—	2	2	no	—
472	Q₈×C₃₁	—	2	2	no	—
473	Q₈×C₃₁	—	2	1	no	—
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	8	1	no	—
476	D₄×C₃₁	—	2	2	no	—
477	D₄×C₃₁	—	2	2	no	—
478	D₄×C₃₁	—	2	1	no	—
479	D₄×C₃₁	—	2	1	no	—
480	D₄×C₃₁	—	2	1	no	—
481	D₄×C₃₁	—	2	1	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	2	2	no	—
484	D₄×C₃₁	—	4	2	no	—
485	D₄×C₃₁	—	4	2	no	—
486	D₄×C₃₁	—	4	4	no	—
487	D₄×C₃₁	—	4	4	no	—
488	D₄×C₃₁	—	4	2	no	—
489	D₄×C₃₁	—	8	2	no	—
490	D₄×C₃₁	—	8	1	no	—
491	D₄×C₃₁	—	8	2	no	—
492	D₄×C₃₁	—	8	2	no	—
493	D₄×C₃₁	—	8	1	no	—
494	D₄×C₃₁	—	8	2	no	—
495	D₄×C₃₁	—	8	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	no	—
504	C₂×C₄×C₃₁	—	2	1	no	—
505	C₂×C₄×C₃₁	—	2	2	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	1	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	4	2	no	—
512	C₂×C₄×C₃₁	—	4	1	no	—
513	C₂×C₄×C₃₁	—	4	2	no	—
514	C₂×C₄×C₃₁	—	4	4	no	—
515	C₂×C₄×C₃₁	—	4	2	no	—
516	C₂×C₄×C₃₁	—	4	2	no	—
517	C₂×C₄×C₃₁	—	4	4	no	—
518	C₂×C₄×C₃₁	—	4	2	no	—
519	C₂×C₄×C₃₁	—	4	2	no	—
520	C₂×C₄×C₃₁	—	4	2	no	—
521	C₂×C₄×C₃₁	—	4	2	no	—
522	C₂×C₄×C₃₁	—	8	2	no	—
523	C₂×C₄×C₃₁	—	8	2	no	—
524	C₂×C₄×C₃₁	—	8	2	no	—
525	C₂×C₄×C₃₁	—	8	2	no	—
526	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
535	C₈×C₃₁	—	2	1	no	—
536	C₈×C₃₁	—	2	1	no	—
537	C₈×C₃₁	—	2	2	no	—
538	C₈×C₃₁	—	2	2	no	—
539	C₈×C₃₁	—	2	1	no	—
540	C₈×C₃₁	—	2	1	no	—
541	#3517	C₂×C₃₁	1	1	yes	characteristic, complemented
542	#3475	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
544	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3372	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3366	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3317	C₂×C₃₁	1	2	yes	complemented
548	#3315	C₂×C₃₁	1	2	yes	complemented
549	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3284	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3283	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3268	C₂×C₃₁	1	2	yes	complemented
554	#3267	C₂×C₃₁	1	2	yes	complemented
555	#3252	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3250	C₂×C₃₁	1	2	yes	complemented
557	#3219	C₂×C₃₁	1	2	yes	complemented
558	#3210	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3111	C₂×C₃₁	1	2	yes	complemented
560	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3036	C₂×C₃₁	1	1	yes	characteristic, complemented
562	#3035	C₂×C₃₁	1	2	yes	complemented
563	#2990	C₂×C₃₁	1	1	yes	characteristic, complemented
564	C₂²×C₃₁	—	2	2	no	—
565	C₂²×C₃₁	—	2	1	no	—
566	C₂²×C₃₁	—	2	2	no	—
567	C₂²×C₃₁	—	2	1	no	—
568	C₂²×C₃₁	—	2	2	no	—
569	C₂²×C₃₁	—	2	1	no	—
570	C₂²×C₃₁	—	2	2	no	—
571	C₂²×C₃₁	—	4	1	no	—
572	C₂²×C₃₁	—	4	1	no	—
573	C₂²×C₃₁	—	4	1	no	—
574	C₂²×C₃₁	—	4	2	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	4	1	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	2	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	8	4	no	—
583	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₃₁	—	2	1	no	—
585	C₄×C₃₁	—	2	2	no	—
586	C₄×C₃₁	—	2	1	no	—
587	C₄×C₃₁	—	2	2	no	—
588	C₄×C₃₁	—	2	1	no	—
589	C₄×C₃₁	—	2	1	no	—
590	C₄×C₃₁	—	2	2	no	—
591	C₄×C₃₁	—	4	2	no	—
592	C₄×C₃₁	—	4	1	no	—
593	C₄×C₃₁	—	4	2	no	—
594	C₄×C₃₁	—	4	2	no	—
595	C₄×C₃₁	—	4	1	no	—
596	C₄×C₃₁	—	4	1	no	—
597	C₄×C₃₁	—	4	1	no	—
598	C₄×C₃₁	—	4	1	no	—
599	C₄×C₃₁	#575	1	2	yes	—
600	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₄×C₃₁	#585	1	1	yes	characteristic
602	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
603	C₂×#135	C₂²×C₃₁	1	2	yes	—
604	C₂×#135	C₂²×C₃₁	1	2	yes	—
605	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
606	#556	C₂²×C₃₁	1	1	yes	characteristic
607	#555	C₂²×C₃₁	1	1	yes	characteristic
608	#554	C₂²×C₃₁	1	1	yes	characteristic
609	#553	—	2	1	no	—
610	#553	—	2	2	no	—
611	#553	—	2	1	no	—
612	#552	—	2	1	no	—
613	#552	C₂²×C₃₁	1	2	yes	—
614	#551	—	2	2	no	—
615	#550	—	2	1	no	—
616	#550	C₂²×C₃₁	1	2	yes	—
617	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
619	#547	C₂²×C₃₁	1	1	yes	characteristic
620	#547	C₂²×C₃₁	1	2	yes	—
621	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
622	#546	C₂²×C₃₁	1	2	yes	—
623	#540	—	2	1	no	—
624	#540	—	2	2	no	—
625	#533	C₂²×C₃₁	1	1	yes	characteristic
626	#532	C₂²×C₃₁	1	1	yes	characteristic
627	#532	C₂²×C₃₁	1	2	yes	complemented
628	#529	—	2	2	no	—
629	#529	C₂²×C₃₁	1	1	yes	characteristic
630	#529	C₂²×C₃₁	1	2	yes	—
631	#529	C₂²×C₃₁	1	2	yes	complemented
632	#525	—	2	1	no	—
633	#520	—	2	1	no	—
634	C₄×#41	C₂²×C₃₁	1	2	yes	—
635	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
637	C₂×#117	—	2	1	no	—
638	#497	C₂²×C₃₁	1	2	yes	—
639	#496	C₂²×C₃₁	1	2	yes	—
640	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
642	#491	C₂²×C₃₁	1	2	yes	complemented
643	#490	C₂²×C₃₁	1	2	yes	complemented
644	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
645	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#485	C₂²×C₃₁	1	2	yes	complemented
647	#484	C₂²×C₃₁	1	1	yes	characteristic
648	#482	C₂²×C₃₁	1	2	yes	complemented
649	#481	C₂²×C₃₁	1	1	yes	characteristic
650	#479	C₂²×C₃₁	1	2	yes	complemented
651	#479	C₂²×C₃₁	1	2	yes	complemented
652	#478	C₂²×C₃₁	1	1	yes	characteristic
653	#478	C₂²×C₃₁	1	1	yes	characteristic
654	#478	C₂²×C₃₁	1	2	yes	complemented
655	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
656	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#470	C₂²×C₃₁	1	2	yes	—
658	#468	C₂²×C₃₁	1	2	yes	—
659	#467	C₂²×C₃₁	1	2	yes	complemented
660	#466	C₂²×C₃₁	1	2	yes	—
661	#465	C₂²×C₃₁	1	2	yes	—
662	#465	C₂²×C₃₁	1	2	yes	complemented
663	#464	C₂²×C₃₁	1	2	yes	—
664	#464	C₂²×C₃₁	1	2	yes	complemented
665	#464	C₂²×C₃₁	1	2	yes	complemented
666	#464	C₂²×C₃₁	1	2	yes	complemented
667	#463	C₂²×C₃₁	1	1	yes	characteristic
668	#463	C₂²×C₃₁	1	1	yes	characteristic
669	#463	C₂²×C₃₁	1	2	yes	—
670	#463	C₂²×C₃₁	1	2	yes	—
671	#463	C₂²×C₃₁	1	2	yes	—
672	#462	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#462	C₂²×C₃₁	1	2	yes	complemented
674	#461	C₂²×C₃₁	1	2	yes	—
675	#461	C₂²×C₃₁	1	1	yes	characteristic
676	#461	C₂²×C₃₁	1	1	yes	characteristic
677	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	#460	C₂²×C₃₁	1	2	yes	complemented
679	#459	C₂²×C₃₁	1	2	yes	—
680	#459	C₂²×C₃₁	1	1	yes	characteristic
681	#459	C₂²×C₃₁	1	1	yes	characteristic
682	#452	C₂²×C₃₁	1	2	yes	—
683	#452	C₂²×C₃₁	1	2	yes	—
684	#452	C₂²×C₃₁	1	2	yes	—
685	#452	C₂²×C₃₁	1	2	yes	complemented
686	#452	C₂²×C₃₁	1	2	yes	complemented
687	#450	C₂²×C₃₁	1	1	yes	characteristic
688	#449	C₂²×C₃₁	1	2	yes	—
689	#449	C₂²×C₃₁	1	2	yes	—
690	#449	C₂²×C₃₁	1	2	yes	—
691	#447	C₂²×C₃₁	1	1	yes	characteristic
692	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
693	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#442	C₂²×C₃₁	1	2	yes	—
695	#441	C₂²×C₃₁	1	2	yes	complemented
696	#440	C₂²×C₃₁	1	2	yes	—
697	#440	C₂²×C₃₁	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
700	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
701	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
702	#435	C₂²×C₃₁	1	2	yes	—
703	#435	C₂²×C₃₁	1	2	yes	—
704	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	#432	C₂²×C₃₁	1	2	yes	complemented
707	#431	C₂²×C₃₁	1	1	yes	characteristic
708	#423	C₂²×C₃₁	1	1	yes	characteristic
709	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	complemented
710	#417	C₂²×C₃₁	1	2	yes	—
711	#416	C₂²×C₃₁	1	2	yes	complemented
712	#416	C₂²×C₃₁	1	2	yes	complemented
713	C₂×C₃₁	—	4	2	no	—
714	C₂×C₃₁	—	4	1	no	—
715	C₂×C₃₁	—	4	2	no	—
716	C₂×C₃₁	—	8	2	no	—
717	C₂×C₃₁	—	8	1	no	—
718	C₂×C₃₁	—	8	1	no	—
719	C₂×C₃₁	#3488	1	1	yes	characteristic
720	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
721	C₂×C₃₁	#3584	1	1	yes	characteristic
722	C₂×#41	—	2	1	no	—
723	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
724	C₂×#41	C₂³×C₃₁	1	2	yes	—
725	C₂×#41	C₂³×C₃₁	1	2	yes	—
726	C₂×#41	C₂³×C₃₁	1	2	yes	—
727	C₂×#41	C₂³×C₃₁	1	2	yes	—
728	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
729	C₂³×C₄	—	2	1	no	—
730	AGL(1,ℤ/8)	—	4	4	no	—
731	#135	—	4	4	no	—
732	#135	—	4	4	no	—
733	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
743	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×D₈	C₂³×C₃₁	1	2	yes	—
745	C₂×D₈	C₂³×C₃₁	1	2	yes	—
746	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
748	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
749	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
752	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
754	#127	—	2	2	no	—
755	#127	—	2	1	no	—
756	#127	C₂³×C₃₁	1	1	yes	characteristic
757	#127	C₂³×C₃₁	1	2	yes	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	1	no	—
762	#126	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	—	2	2	no	—
766	#125	—	2	1	no	—
767	#125	C₂³×C₃₁	1	1	yes	characteristic
768	#125	C₂³×C₃₁	1	2	yes	—
769	#124	—	2	2	no	—
770	#124	C₂³×C₃₁	1	1	yes	characteristic
771	#124	C₂³×C₃₁	1	2	yes	—
772	#124	C₂³×C₃₁	1	2	yes	—
773	#123	—	2	2	no	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	C₂³×C₃₁	1	2	yes	—
805	#121	C₂³×C₃₁	1	1	yes	characteristic
806	#121	C₂³×C₃₁	1	2	yes	—
807	#120	—	2	2	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
813	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
815	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	D₄×C₃₁	1	2	yes	—
830	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₃₁	1	2	yes	—
836	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₃₁	1	2	yes	—
838	C₄×D₄	C₂³×C₃₁	1	2	yes	—
839	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	1	no	—
847	#117	—	2	2	no	—
848	#117	D₄×C₃₁	1	1	yes	characteristic
849	#117	D₄×C₃₁	1	2	yes	—
850	#117	C₂³×C₃₁	1	2	yes	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	2	no	—
854	C₂×C₄⋊C₄	—	2	1	no	—
855	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
856	C₂×C₂²⋊C₄	—	2	1	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₄²	—	2	2	no	—
859	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
860	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
861	#107	C₂³×C₃₁	1	1	yes	characteristic
862	#107	C₂³×C₃₁	1	1	yes	characteristic
863	#107	C₂³×C₃₁	1	2	yes	—
864	#106	C₂³×C₃₁	1	1	yes	characteristic
865	#106	C₂³×C₃₁	1	1	yes	characteristic
866	#106	C₂³×C₃₁	1	2	yes	—
867	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
869	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
870	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
871	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
874	#103	C₂³×C₃₁	1	1	yes	characteristic
875	#103	C₂³×C₃₁	1	2	yes	—
876	#103	C₂³×C₃₁	1	2	yes	—
877	#103	C₂³×C₃₁	1	2	yes	—
878	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
884	#102	C₂³×C₃₁	1	2	yes	—
885	#102	C₂³×C₃₁	1	2	yes	—
886	#102	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	1	yes	characteristic
889	#102	C₂³×C₃₁	1	1	yes	characteristic
890	#102	C₂³×C₃₁	1	1	yes	characteristic
891	#102	C₂³×C₃₁	1	1	yes	characteristic
892	#102	C₂³×C₃₁	1	1	yes	characteristic
893	#102	C₂³×C₃₁	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
898	#97	C₂³×C₃₁	1	2	yes	—
899	#97	C₂³×C₃₁	1	2	yes	—
900	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
902	C₃₁	#61993	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	—	2	1	no	—
904	#41	—	2	4	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	4	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
917	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	4	1	no	—
933	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
934	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
935	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
936	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	4	4	no	—
952	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
955	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	2	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	—	4	1	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	2	no	—
968	D₈	—	2	2	no	—
969	D₈	—	2	4	no	—
970	D₈	—	4	1	no	—
971	D₈	—	4	2	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
980	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1003	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1008	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1040	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1041	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₃₁	1	2	yes	—
1045	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1054	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	8	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	1	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	2	no	—
1084	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	4	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1116	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1121	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	8	4	no	—
1147	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	C₃₁×#575	1	2	yes	—
1164	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₃₁×#585	1	1	yes	characteristic
1166	C₂	—	4	1	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₃₁×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₃₁×#575	1	1	yes	characteristic
1174	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3517	C₂	semidirect
2. C₃₁×#3475	C₂	semidirect
3. C₃₁×#3398	C₂	semidirect
4. C₃₁×#3397	C₂	semidirect
5. C₃₁×#3372	C₂	semidirect
6. C₃₁×#3366	C₂	semidirect
7. C₃₁×#3317	C₂	semidirect
8. C₃₁×#3315	C₂	semidirect
9. C₃₁×#3305	C₂	semidirect
10. C₃₁×#3303	C₂	semidirect
11. C₃₁×#3284	C₂	semidirect
12. C₃₁×#3283	C₂	semidirect
13. C₃₁×#3268	C₂	semidirect
14. C₃₁×#3267	C₂	semidirect
15. C₃₁×#3252	C₂	semidirect
16. C₃₁×#3250	C₂	semidirect
17. C₃₁×#3219	C₂	semidirect
18. C₃₁×#3210	C₂	semidirect
19. C₃₁×#3111	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3036	C₂	semidirect
22. C₃₁×#3035	C₂	semidirect
23. C₃₁×#2990	C₂	semidirect
27. C₃₁×#557	C₂²	semidirect
39. C₃₁×#550	C₂²	semidirect
40. C₃₁×#550	C₂²	semidirect
43. C₃₁×#547	C₂²	semidirect
49. C₃₁×#532	C₂²	semidirect
53. C₃₁×#529	C₂²	semidirect
62. C₃₁×#494	C₂²	semidirect
63. C₃₁×#492	C₂²	semidirect
64. C₃₁×#491	C₂²	semidirect
65. C₃₁×#490	C₂²	semidirect
66. C₃₁×#487	C₂²	semidirect
67. C₃₁×#486	C₂²	semidirect
68. C₃₁×#485	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
72. C₃₁×#479	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
81. C₃₁×#467	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#464	C₂²	semidirect
94. C₃₁×#462	C₂²	semidirect
95. C₃₁×#462	C₂²	semidirect
99. C₃₁×#461	C₂²	semidirect
100. C₃₁×#460	C₂²	semidirect
107. C₃₁×#452	C₂²	semidirect
108. C₃₁×#452	C₂²	semidirect
114. C₃₁×#446	C₂²	semidirect
115. C₃₁×#446	C₂²	semidirect
117. C₃₁×#441	C₂²	semidirect
119. C₃₁×#440	C₂²	semidirect
126. C₈×D₄×C₃₁	C₂²	semidirect
127. C₈×D₄×C₃₁	C₂²	semidirect
128. C₃₁×#432	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
133. C₃₁×#416	C₂²	semidirect
134. C₃₁×#416	C₂²	semidirect
458. #61993	C₃₁	direct (N × H)
541. #3517	C₂×C₃₁	semidirect
542. #3475	C₂×C₃₁	semidirect
543. #3398	C₂×C₃₁	semidirect
544. #3397	C₂×C₃₁	semidirect
545. #3372	C₂×C₃₁	semidirect
546. #3366	C₂×C₃₁	semidirect
547. #3317	C₂×C₃₁	semidirect
548. #3315	C₂×C₃₁	semidirect
549. #3305	C₂×C₃₁	semidirect
550. #3303	C₂×C₃₁	semidirect
551. #3284	C₂×C₃₁	semidirect
552. #3283	C₂×C₃₁	semidirect
553. #3268	C₂×C₃₁	semidirect
554. #3267	C₂×C₃₁	semidirect
555. #3252	C₂×C₃₁	semidirect
556. #3250	C₂×C₃₁	semidirect
557. #3219	C₂×C₃₁	semidirect
558. #3210	C₂×C₃₁	semidirect
559. #3111	C₂×C₃₁	semidirect
560. #3105	C₂×C₃₁	semidirect
561. #3036	C₂×C₃₁	semidirect
562. #3035	C₂×C₃₁	semidirect
563. #2990	C₂×C₃₁	semidirect
605. #557	C₂²×C₃₁	semidirect
617. #550	C₂²×C₃₁	semidirect
618. #550	C₂²×C₃₁	semidirect
621. #547	C₂²×C₃₁	semidirect
627. #532	C₂²×C₃₁	semidirect
631. #529	C₂²×C₃₁	semidirect
640. #494	C₂²×C₃₁	semidirect
641. #492	C₂²×C₃₁	semidirect
642. #491	C₂²×C₃₁	semidirect
643. #490	C₂²×C₃₁	semidirect
644. #487	C₂²×C₃₁	semidirect
645. #486	C₂²×C₃₁	semidirect
646. #485	C₂²×C₃₁	semidirect
648. #482	C₂²×C₃₁	semidirect
650. #479	C₂²×C₃₁	semidirect
651. #479	C₂²×C₃₁	semidirect
654. #478	C₂²×C₃₁	semidirect
655. #477	C₂²×C₃₁	semidirect
656. #476	C₂²×C₃₁	semidirect
659. #467	C₂²×C₃₁	semidirect
662. #465	C₂²×C₃₁	semidirect
664. #464	C₂²×C₃₁	semidirect
665. #464	C₂²×C₃₁	semidirect
666. #464	C₂²×C₃₁	semidirect
672. #462	C₂²×C₃₁	semidirect
673. #462	C₂²×C₃₁	semidirect
677. #461	C₂²×C₃₁	semidirect
678. #460	C₂²×C₃₁	semidirect
685. #452	C₂²×C₃₁	semidirect
686. #452	C₂²×C₃₁	semidirect
692. #446	C₂²×C₃₁	semidirect
693. #446	C₂²×C₃₁	semidirect
695. #441	C₂²×C₃₁	semidirect
697. #440	C₂²×C₃₁	semidirect
704. C₈×D₄	C₂²×C₃₁	semidirect
705. C₈×D₄	C₂²×C₃₁	semidirect
706. #432	C₂²×C₃₁	semidirect
709. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
711. #416	C₂²×C₃₁	semidirect
712. #416	C₂²×C₃₁	semidirect
902. C₃₁	#61993	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×#3517	2
C₃₁×#3475	2
C₃₁×#3398	2
C₃₁×#3397	2
C₃₁×#3372	2
C₃₁×#3366	2
C₃₁×#3317	2
C₃₁×#3315	2
C₃₁×#3305	2
C₃₁×#3303	2
C₃₁×#3284	2
C₃₁×#3283	2
C₃₁×#3268	2
C₃₁×#3267	2
C₃₁×#3252	2
C₃₁×#3250	2
C₃₁×#3219	2
C₃₁×#3210	2
C₃₁×#3111	2
C₃₁×#3105	2
C₃₁×#3036	2
C₃₁×#3035	2
C₃₁×#2990	2
#61993	31

Subgroups — C31×#61993 #21518752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61993 #21518752