Subgroups — C₃₁×#61498 #21518257

Order 7936.

1936 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×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3295	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3294	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3274	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3265	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
19	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2946	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#559	—	2	1	no	—
27	C₃₁×#559	C₂²	1	1	yes	characteristic, complemented
28	Q₈²×C₃₁	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#555	C₂²	1	1	yes	characteristic
30	C₃₁×#554	—	2	1	no	—
31	C₃₁×#554	C₂²	1	1	yes	characteristic
32	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#553	—	2	1	no	—
34	C₃₁×#553	C₂²	1	2	yes	—
35	C₃₁×#550	C₂²	1	1	yes	characteristic
36	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#548	C₂²	1	2	yes	complemented
38	C₃₁×#547	—	2	2	no	—
39	C₃₁×#547	C₂²	1	2	yes	complemented
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	D₄²×C₃₁	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#542	—	2	2	no	—
45	C₃₁×#542	C₂²	1	2	yes	complemented
46	C₃₁×#540	C₂²	1	2	yes	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#532	—	2	1	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#532	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#529	—	2	1	no	—
52	C₃₁×#529	C₂²	1	1	yes	characteristic
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×#121	—	2	1	no	—
55	C₃₁×#520	C₂²	1	2	yes	complemented
56	C₃₁×#518	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#493	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
66	C₃₁×#486	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#481	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#480	C₂²	1	2	yes	complemented
72	C₃₁×#480	C₂²	1	2	yes	complemented
73	C₃₁×#479	C₂²	1	2	yes	complemented
74	C₃₁×#478	C₂²	1	2	yes	complemented
75	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#476	C₂²	1	1	yes	characteristic
78	C₃₁×#476	C₂²	1	2	yes	complemented
79	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	2	yes	—
81	C₃₁×#469	C₂²	1	2	yes	complemented
82	C₃₁×#468	C₂²	1	2	yes	complemented
83	C₃₁×#466	C₂²	1	2	yes	complemented
84	C₃₁×#466	C₂²	1	2	yes	complemented
85	C₃₁×#466	C₂²	1	2	yes	complemented
86	C₃₁×#465	C₂²	1	2	yes	complemented
87	C₃₁×#463	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#460	C₂²	1	2	yes	complemented
91	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#459	C₂²	1	1	yes	characteristic
93	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#459	C₂²	1	2	yes	complemented
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	complemented
97	C₃₁×#449	C₂²	1	2	yes	complemented
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₃₁×#442	C₂²	1	2	yes	—
104	C₃₁×#442	C₂²	1	2	yes	complemented
105	C₃₁×#442	C₂²	1	2	yes	complemented
106	C₃₁×#440	C₂²	1	2	yes	—
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
111	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
112	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
116	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₃₁	C₂²	1	2	yes	—
119	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#432	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
132	C₂×C₃₁×#102	C₂²	1	2	yes	—
133	C₃₁×#405	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	2	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	1	no	—
139	C₂×#41×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	—	2	2	no	—
143	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
145	C₂³×C₄×C₃₁	—	2	1	no	—
146	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
147	C₂×SD₁₆×C₃₁	—	2	4	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	2	yes	—
155	C₂×D₈×C₃₁	C₂³	1	2	yes	—
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	—	2	1	no	—
163	C₃₁×C₄⋊Q₈	—	2	2	no	—
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	1	no	—
168	C₃₁×#127	C₂³	1	1	yes	characteristic
169	C₃₁×#127	C₂³	1	2	yes	—
170	C₃₁×#127	C₂³	1	1	yes	characteristic
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	—	2	2	no	—
173	C₃₁×#126	D₄	1	2	yes	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	D₄	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#124	—	2	1	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	—	2	1	no	—
183	C₃₁×#124	D₄	1	1	yes	characteristic
184	C₃₁×#124	C₂³	1	2	yes	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	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	D₄	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	—	2	1	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
200	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	1	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	1	no	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	1	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	—	2	2	no	—
210	C₃₁×#121	—	2	2	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	D₄	1	1	yes	characteristic
214	C₃₁×#121	C₂³	1	2	yes	—
215	C₃₁×#121	C₂³	1	2	yes	—
216	C₃₁×#121	C₂³	1	2	yes	—
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#120	—	2	2	no	—
220	C₃₁×#120	—	2	2	no	—
221	C₃₁×#120	—	2	2	no	—
222	C₄×Q₈×C₃₁	—	2	1	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₃₁	—	2	1	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	1	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	2	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	2	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	1	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	1	no	—
244	C₄×D₄×C₃₁	C₂³	1	2	yes	—
245	C₄×D₄×C₃₁	C₂³	1	2	yes	—
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₄×D₄×C₃₁	C₂³	1	2	yes	—
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₃₁×#117	—	2	2	no	—
256	C₃₁×#117	—	2	1	no	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₃₁×#117	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
266	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
268	C₂×C₄²×C₃₁	—	2	1	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	2	yes	—
271	C₃₁×#107	C₂³	1	2	yes	—
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#107	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	1	yes	characteristic
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	1	yes	characteristic
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	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×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	1	yes	characteristic
293	C₃₁×#102	C₂³	1	1	yes	characteristic
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
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	2	yes	—
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	2	yes	—
314	C₂⁴×C₃₁	—	2	1	no	—
315	C₂⁴×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	2	4	no	—
317	#41×C₃₁	—	4	2	no	—
318	#41×C₃₁	—	8	2	no	—
319	#41×C₃₁	—	8	2	no	—
320	#41×C₃₁	—	8	4	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	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	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	4	1	no	—
328	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	4	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	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	1	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	1	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	4	1	no	—
348	C₂×D₄×C₃₁	—	4	2	no	—
349	C₂×D₄×C₃₁	—	8	2	no	—
350	C₂×D₄×C₃₁	—	8	4	no	—
351	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
354	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₃₁	—	2	1	no	—
358	C₂²×C₄×C₃₁	—	2	1	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	2	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	2	no	—
366	C₂²×C₄×C₃₁	—	2	2	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	2	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	8	2	no	—
372	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
376	SD₁₆×C₃₁	—	2	2	no	—
377	SD₁₆×C₃₁	—	2	4	no	—
378	SD₁₆×C₃₁	—	2	2	no	—
379	SD₁₆×C₃₁	—	2	2	no	—
380	SD₁₆×C₃₁	—	4	2	no	—
381	SD₁₆×C₃₁	#41	1	4	yes	complemented
382	D₈×C₃₁	—	2	4	no	—
383	D₈×C₃₁	—	2	4	no	—
384	D₈×C₃₁	—	4	2	no	—
385	D₈×C₃₁	—	4	2	no	—
386	M₁₆×C₃₁	—	2	4	no	—
387	C₂×C₈×C₃₁	—	2	2	no	—
388	C₂×C₈×C₃₁	—	4	1	no	—
389	C₂×C₈×C₃₁	—	4	2	no	—
390	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
394	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
395	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₃₁	—	2	1	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	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	1	no	—
405	C₄⋊C₄×C₃₁	—	2	1	no	—
406	C₄⋊C₄×C₃₁	—	2	1	no	—
407	C₄⋊C₄×C₃₁	—	2	2	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	1	no	—
429	C₂²⋊C₄×C₃₁	—	2	2	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	2	no	—
434	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
441	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₄²×C₃₁	—	2	1	no	—
446	C₄²×C₃₁	—	2	1	no	—
447	C₄²×C₃₁	—	2	1	no	—
448	C₄²×C₃₁	—	2	1	no	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	2	no	—
451	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
454	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	2	yes	—
456	#61498	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂³×C₃₁	—	2	1	no	—
458	C₂³×C₃₁	—	2	2	no	—
459	C₂³×C₃₁	—	2	2	no	—
460	C₂³×C₃₁	—	2	1	no	—
461	C₂³×C₃₁	—	4	2	no	—
462	C₂³×C₃₁	—	4	4	no	—
463	C₂³×C₃₁	—	4	2	no	—
464	C₂³×C₃₁	—	8	1	no	—
465	C₂³×C₃₁	—	8	2	no	—
466	C₂³×C₃₁	—	8	2	no	—
467	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
468	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
469	Q₈×C₃₁	—	2	2	no	—
470	Q₈×C₃₁	—	2	1	no	—
471	Q₈×C₃₁	—	2	1	no	—
472	Q₈×C₃₁	—	2	1	no	—
473	Q₈×C₃₁	—	4	2	no	—
474	Q₈×C₃₁	—	8	1	no	—
475	Q₈×C₃₁	—	8	1	no	—
476	Q₈×C₃₁	—	8	2	no	—
477	Q₈×C₃₁	C₂×#41	1	2	yes	—
478	D₄×C₃₁	—	2	4	no	—
479	D₄×C₃₁	—	2	2	no	—
480	D₄×C₃₁	—	2	2	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	2	1	no	—
484	D₄×C₃₁	—	2	1	no	—
485	D₄×C₃₁	—	2	2	no	—
486	D₄×C₃₁	—	2	2	no	—
487	D₄×C₃₁	—	4	4	no	—
488	D₄×C₃₁	—	4	2	no	—
489	D₄×C₃₁	—	4	4	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	—	8	2	no	—
495	D₄×C₃₁	—	8	1	no	—
496	D₄×C₃₁	—	8	1	no	—
497	D₄×C₃₁	—	8	2	no	—
498	D₄×C₃₁	—	8	2	no	—
499	D₄×C₃₁	—	8	2	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	C₂×#41	1	2	yes	—
502	C₂×C₄×C₃₁	—	2	2	no	—
503	C₂×C₄×C₃₁	—	2	1	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	1	no	—
508	C₂×C₄×C₃₁	—	2	2	no	—
509	C₂×C₄×C₃₁	—	2	1	no	—
510	C₂×C₄×C₃₁	—	2	1	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	2	no	—
515	C₂×C₄×C₃₁	—	2	1	no	—
516	C₂×C₄×C₃₁	—	4	4	no	—
517	C₂×C₄×C₃₁	—	4	2	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	—	8	1	no	—
522	C₂×C₄×C₃₁	—	8	1	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	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	2	no	—
528	C₂×C₄×C₃₁	—	8	1	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
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	1	no	—
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	2	no	—
544	C₈×C₃₁	C₂×#41	1	2	yes	—
545	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
546	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3399	C₂×C₃₁	1	1	yes	characteristic, complemented
548	#3385	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3362	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3361	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3357	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3345	C₂×C₃₁	1	2	yes	complemented
553	#3305	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3301	C₂×C₃₁	1	2	yes	complemented
555	#3295	C₂×C₃₁	1	1	yes	characteristic, complemented
556	#3294	C₂×C₃₁	1	2	yes	complemented
557	#3274	C₂×C₃₁	1	1	yes	characteristic, complemented
558	#3265	C₂×C₃₁	1	2	yes	complemented
559	#3179	C₂×C₃₁	1	2	yes	complemented
560	#3169	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3119	C₂×C₃₁	1	2	yes	complemented
562	#3118	C₂×C₃₁	1	2	yes	complemented
563	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
565	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
566	#2946	C₂×C₃₁	1	2	yes	complemented
567	C₂×C₄×SD₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
568	C₂²×C₃₁	—	2	1	no	—
569	C₂²×C₃₁	—	2	1	no	—
570	C₂²×C₃₁	—	2	2	no	—
571	C₂²×C₃₁	—	2	2	no	—
572	C₂²×C₃₁	—	2	2	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	4	1	no	—
575	C₂²×C₃₁	—	4	1	no	—
576	C₂²×C₃₁	—	4	2	no	—
577	C₂²×C₃₁	—	4	1	no	—
578	C₂²×C₃₁	—	4	2	no	—
579	C₂²×C₃₁	—	4	2	no	—
580	C₂²×C₃₁	—	4	2	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	1	no	—
583	C₂²×C₃₁	—	4	2	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	8	4	no	—
586	C₂²×C₃₁	—	16	4	no	—
587	C₂²×C₃₁	#576	1	2	yes	—
588	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₃₁	—	2	2	no	—
590	C₄×C₃₁	—	2	1	no	—
591	C₄×C₃₁	—	2	2	no	—
592	C₄×C₃₁	—	2	1	no	—
593	C₄×C₃₁	—	2	1	no	—
594	C₄×C₃₁	—	2	2	no	—
595	C₄×C₃₁	—	2	1	no	—
596	C₄×C₃₁	—	2	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	2	no	—
602	C₄×C₃₁	—	4	1	no	—
603	C₄×C₃₁	—	4	1	no	—
604	C₄×C₃₁	#577	1	2	yes	—
605	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
606	C₄×C₃₁	#585	1	1	yes	characteristic
607	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
608	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
609	#559	—	2	1	no	—
610	#559	C₂²×C₃₁	1	1	yes	characteristic, complemented
611	Q₈²	C₂²×C₃₁	1	1	yes	characteristic, complemented
612	#555	C₂²×C₃₁	1	1	yes	characteristic
613	#554	—	2	1	no	—
614	#554	C₂²×C₃₁	1	1	yes	characteristic
615	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#553	—	2	1	no	—
617	#553	C₂²×C₃₁	1	2	yes	—
618	#550	C₂²×C₃₁	1	1	yes	characteristic
619	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#548	C₂²×C₃₁	1	2	yes	complemented
621	#547	—	2	2	no	—
622	#547	C₂²×C₃₁	1	2	yes	complemented
623	#546	—	2	1	no	—
624	#546	—	2	2	no	—
625	D₄²	C₂²×C₃₁	1	2	yes	—
626	D₄²	C₂²×C₃₁	1	1	yes	characteristic
627	#542	—	2	2	no	—
628	#542	C₂²×C₃₁	1	2	yes	complemented
629	#540	C₂²×C₃₁	1	2	yes	—
630	#538	—	2	2	no	—
631	#532	—	2	1	no	—
632	#532	C₂²×C₃₁	1	1	yes	characteristic
633	#532	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#529	—	2	1	no	—
635	#529	C₂²×C₃₁	1	1	yes	characteristic
636	#525	—	2	1	no	—
637	C₂×#121	—	2	1	no	—
638	#520	C₂²×C₃₁	1	2	yes	complemented
639	#518	C₂²×C₃₁	1	2	yes	—
640	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
641	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
642	#501	C₂²×C₃₁	1	2	yes	complemented
643	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
644	#496	C₂²×C₃₁	1	2	yes	complemented
645	#493	C₂²×C₃₁	1	1	yes	characteristic, complemented
646	#488	C₂²×C₃₁	1	2	yes	complemented
647	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#486	C₂²×C₃₁	1	2	yes	complemented
650	#485	C₂²×C₃₁	1	2	yes	complemented
651	#482	C₂²×C₃₁	1	2	yes	complemented
652	#481	C₂²×C₃₁	1	2	yes	complemented
653	#481	C₂²×C₃₁	1	2	yes	complemented
654	#480	C₂²×C₃₁	1	2	yes	complemented
655	#480	C₂²×C₃₁	1	2	yes	complemented
656	#479	C₂²×C₃₁	1	2	yes	complemented
657	#478	C₂²×C₃₁	1	2	yes	complemented
658	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#476	C₂²×C₃₁	1	1	yes	characteristic
661	#476	C₂²×C₃₁	1	2	yes	complemented
662	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
663	#474	C₂²×C₃₁	1	2	yes	—
664	#469	C₂²×C₃₁	1	2	yes	complemented
665	#468	C₂²×C₃₁	1	2	yes	complemented
666	#466	C₂²×C₃₁	1	2	yes	complemented
667	#466	C₂²×C₃₁	1	2	yes	complemented
668	#466	C₂²×C₃₁	1	2	yes	complemented
669	#465	C₂²×C₃₁	1	2	yes	complemented
670	#463	C₂²×C₃₁	1	2	yes	—
671	#463	C₂²×C₃₁	1	2	yes	complemented
672	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#460	C₂²×C₃₁	1	2	yes	complemented
674	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
675	#459	C₂²×C₃₁	1	1	yes	characteristic
676	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	#459	C₂²×C₃₁	1	2	yes	complemented
678	#450	C₂²×C₃₁	1	2	yes	—
679	#449	C₂²×C₃₁	1	2	yes	complemented
680	#449	C₂²×C₃₁	1	2	yes	complemented
681	#448	C₂²×C₃₁	1	2	yes	complemented
682	#447	C₂²×C₃₁	1	2	yes	—
683	#447	C₂²×C₃₁	1	2	yes	—
684	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
686	#442	C₂²×C₃₁	1	2	yes	—
687	#442	C₂²×C₃₁	1	2	yes	complemented
688	#442	C₂²×C₃₁	1	2	yes	complemented
689	#440	C₂²×C₃₁	1	2	yes	—
690	#440	C₂²×C₃₁	1	2	yes	complemented
691	#440	C₂²×C₃₁	1	2	yes	complemented
692	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
693	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
694	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
695	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
696	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
697	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
701	C₄×D₈	C₂²×C₃₁	1	2	yes	—
702	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
703	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
704	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	#435	C₂²×C₃₁	1	2	yes	complemented
706	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
707	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	#433	C₂²×C₃₁	1	2	yes	complemented
709	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	#428	C₂²×C₃₁	1	2	yes	complemented
711	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#416	C₂²×C₃₁	1	2	yes	complemented
713	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
715	C₂×#102	C₂²×C₃₁	1	2	yes	—
716	#405	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	—	4	2	no	—
720	C₂×C₃₁	—	4	2	no	—
721	C₂×C₃₁	—	8	2	no	—
722	C₂×C₃₁	—	8	1	no	—
723	C₂×C₃₁	—	8	2	no	—
724	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
725	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
726	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
727	C₂×#41	—	2	1	no	—
728	C₂×#41	—	2	2	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	2	1	no	—
731	C₂×#41	C₂³×C₃₁	1	2	yes	—
732	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
733	C₂²×D₄	—	2	1	no	—
734	C₂²×D₄	—	2	2	no	—
735	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
736	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
737	C₂³×C₄	—	2	1	no	—
738	AGL(1,ℤ/8)	—	2	8	no	—
739	C₂×SD₁₆	—	2	4	no	—
740	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
741	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×D₈	C₂³×C₃₁	1	2	yes	—
747	C₂×D₈	C₂³×C₃₁	1	2	yes	—
748	C₂×D₈	C₂³×C₃₁	1	2	yes	—
749	C₂×D₈	C₂³×C₃₁	1	2	yes	—
750	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
751	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	—	2	2	no	—
756	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
757	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
759	#127	—	2	1	no	—
760	#127	C₂³×C₃₁	1	1	yes	characteristic
761	#127	C₂³×C₃₁	1	1	yes	characteristic
762	#127	C₂³×C₃₁	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	D₄×C₃₁	1	2	yes	—
766	#125	—	2	1	no	—
767	#125	D₄×C₃₁	1	1	yes	characteristic
768	#125	C₂³×C₃₁	1	2	yes	—
769	#124	—	2	1	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	1	no	—
774	#124	—	2	1	no	—
775	#124	D₄×C₃₁	1	1	yes	characteristic
776	#124	C₂³×C₃₁	1	2	yes	—
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	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	D₄×C₃₁	1	2	yes	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	2	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
792	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
793	#121	—	2	2	no	—
794	#121	—	2	1	no	—
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	1	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	D₄×C₃₁	1	1	yes	characteristic
806	#121	C₂³×C₃₁	1	2	yes	—
807	#121	C₂³×C₃₁	1	2	yes	—
808	#121	C₂³×C₃₁	1	2	yes	—
809	#121	C₂³×C₃₁	1	2	yes	—
810	#121	C₂³×C₃₁	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	#120	—	2	2	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
822	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	2	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₃₁	1	2	yes	—
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	C₄×D₄	C₂³×C₃₁	1	2	yes	—
843	C₄×D₄	C₂³×C₃₁	1	2	yes	—
844	C₄×D₄	C₂³×C₃₁	1	2	yes	—
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
847	#117	—	2	2	no	—
848	#117	—	2	1	no	—
849	#117	C₂³×C₃₁	1	2	yes	—
850	#117	C₂³×C₃₁	1	2	yes	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	2	no	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
856	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
857	C₂×C₂²⋊C₄	—	2	1	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
862	#107	C₂³×C₃₁	1	2	yes	—
863	#107	C₂³×C₃₁	1	2	yes	—
864	#107	C₂³×C₃₁	1	2	yes	—
865	#107	C₂³×C₃₁	1	2	yes	—
866	#106	C₂³×C₃₁	1	1	yes	characteristic
867	#106	C₂³×C₃₁	1	1	yes	characteristic
868	#106	C₂³×C₃₁	1	1	yes	characteristic
869	#106	C₂³×C₃₁	1	1	yes	characteristic
870	#106	C₂³×C₃₁	1	2	yes	—
871	#106	C₂³×C₃₁	1	2	yes	—
872	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
874	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
875	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
876	#103	C₂³×C₃₁	1	1	yes	characteristic
877	#103	C₂³×C₃₁	1	1	yes	characteristic
878	#103	C₂³×C₃₁	1	1	yes	characteristic
879	#103	C₂³×C₃₁	1	1	yes	characteristic
880	#103	C₂³×C₃₁	1	2	yes	—
881	#103	C₂³×C₃₁	1	2	yes	—
882	#102	C₂³×C₃₁	1	1	yes	characteristic
883	#102	C₂³×C₃₁	1	2	yes	—
884	#102	C₂³×C₃₁	1	1	yes	characteristic
885	#102	C₂³×C₃₁	1	1	yes	characteristic
886	#102	C₂³×C₃₁	1	1	yes	characteristic
887	#102	C₂³×C₃₁	1	2	yes	—
888	#102	C₂³×C₃₁	1	2	yes	—
889	#102	C₂³×C₃₁	1	2	yes	—
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	2	yes	—
894	#102	C₂³×C₃₁	1	2	yes	—
895	#102	C₂³×C₃₁	1	2	yes	—
896	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
898	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
899	#97	C₂³×C₃₁	1	2	yes	—
900	#97	C₂³×C₃₁	1	2	yes	—
901	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
902	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
903	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
904	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
905	C₄×C₈	C₂³×C₃₁	1	2	yes	—
906	C₃₁	#61498	1	1	yes	characteristic, direct product factor, Sylow
907	C₂⁴	—	2	1	no	—
908	C₂⁴	—	2	2	no	—
909	#41	—	2	4	no	—
910	#41	—	4	2	no	—
911	#41	—	8	2	no	—
912	#41	—	8	2	no	—
913	#41	—	8	4	no	—
914	#41	—	8	2	no	—
915	C₂×Q₈	—	2	1	no	—
916	C₂×Q₈	—	2	1	no	—
917	C₂×Q₈	—	2	2	no	—
918	C₂×Q₈	—	2	1	no	—
919	C₂×Q₈	—	2	2	no	—
920	C₂×Q₈	—	4	1	no	—
921	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	4	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	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	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	4	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	8	2	no	—
943	C₂×D₄	—	8	4	no	—
944	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
945	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
947	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
948	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
949	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	2	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	2	2	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	8	2	no	—
965	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
967	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
968	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
969	SD₁₆	—	2	2	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	2	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	#41×C₃₁	1	4	yes	complemented
975	D₈	—	2	4	no	—
976	D₈	—	2	4	no	—
977	D₈	—	4	2	no	—
978	D₈	—	4	2	no	—
979	M₁₆	—	2	4	no	—
980	C₂×C₈	—	2	2	no	—
981	C₂×C₈	—	4	1	no	—
982	C₂×C₈	—	4	2	no	—
983	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
984	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
985	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
987	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
988	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1006	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1008	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1009	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1011	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1014	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1034	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1035	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1036	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	2	no	—
1044	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1045	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1047	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1048	C₄²	C₂⁴×C₃₁	1	2	yes	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	2	2	no	—
1051	C₂³	—	2	2	no	—
1052	C₂³	—	2	1	no	—
1053	C₂³	—	4	2	no	—
1054	C₂³	—	4	4	no	—
1055	C₂³	—	4	2	no	—
1056	C₂³	—	8	1	no	—
1057	C₂³	—	8	2	no	—
1058	C₂³	—	8	2	no	—
1059	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1060	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1061	Q₈	—	2	2	no	—
1062	Q₈	—	2	1	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	1	no	—
1065	Q₈	—	4	2	no	—
1066	Q₈	—	8	1	no	—
1067	Q₈	—	8	1	no	—
1068	Q₈	—	8	2	no	—
1069	Q₈	C₂×#41×C₃₁	1	2	yes	—
1070	D₄	—	2	4	no	—
1071	D₄	—	2	2	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	1	no	—
1076	D₄	—	2	1	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	4	4	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	4	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	4	2	no	—
1086	D₄	—	8	2	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	1	no	—
1089	D₄	—	8	2	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	C₂×#41×C₃₁	1	2	yes	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	2	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	4	4	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	8	1	no	—
1114	C₂×C₄	—	8	1	no	—
1115	C₂×C₄	—	8	2	no	—
1116	C₂×C₄	—	8	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
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	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	2	no	—
1136	C₈	C₂×#41×C₃₁	1	2	yes	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	1	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	8	4	no	—
1155	C₂²	—	16	4	no	—
1156	C₂²	C₃₁×#576	1	2	yes	—
1157	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	2	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	2	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₃₁×#577	1	2	yes	—
1174	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1175	C₄	C₃₁×#585	1	1	yes	characteristic
1176	C₂	—	2	2	no	—
1177	C₂	—	4	2	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	—	8	2	no	—
1181	C₂	—	8	2	no	—
1182	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1183	C₂	C₂×C₃₁×#576	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 ◁ C₃₁×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3522	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3399	C₂	semidirect
4. C₃₁×#3385	C₂	semidirect
5. C₃₁×#3362	C₂	semidirect
6. C₃₁×#3361	C₂	semidirect
7. C₃₁×#3357	C₂	semidirect
8. C₃₁×#3345	C₂	semidirect
9. C₃₁×#3305	C₂	semidirect
10. C₃₁×#3301	C₂	semidirect
11. C₃₁×#3295	C₂	semidirect
12. C₃₁×#3294	C₂	semidirect
13. C₃₁×#3274	C₂	semidirect
14. C₃₁×#3265	C₂	semidirect
15. C₃₁×#3179	C₂	semidirect
16. C₃₁×#3169	C₂	semidirect
17. C₃₁×#3119	C₂	semidirect
18. C₃₁×#3118	C₂	semidirect
19. C₃₁×#3112	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
27. C₃₁×#559	C₂²	semidirect
28. Q₈²×C₃₁	C₂²	semidirect
32. C₃₁×#554	C₂²	semidirect
36. C₃₁×#550	C₂²	semidirect
37. C₃₁×#548	C₂²	semidirect
39. C₃₁×#547	C₂²	semidirect
45. C₃₁×#542	C₂²	semidirect
50. C₃₁×#532	C₂²	semidirect
55. C₃₁×#520	C₂²	semidirect
57. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#500	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
62. C₃₁×#493	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#481	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#480	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#477	C₂²	semidirect
76. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#476	C₂²	semidirect
81. C₃₁×#469	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#466	C₂²	semidirect
85. C₃₁×#466	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#460	C₂²	semidirect
90. C₃₁×#460	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
93. C₃₁×#459	C₂²	semidirect
94. C₃₁×#459	C₂²	semidirect
96. C₃₁×#449	C₂²	semidirect
97. C₃₁×#449	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
113. C₄×SD₁₆×C₃₁	C₂²	semidirect
114. C₄×SD₁₆×C₃₁	C₂²	semidirect
115. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×SD₁₆×C₃₁	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#432	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₂×C₃₁×#106	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
130. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
381. SD₁₆×C₃₁	#41	semidirect
456. #61498	C₃₁	direct (N × H)
545. #3522	C₂×C₃₁	semidirect
546. #3519	C₂×C₃₁	semidirect
547. #3399	C₂×C₃₁	semidirect
548. #3385	C₂×C₃₁	semidirect
549. #3362	C₂×C₃₁	semidirect
550. #3361	C₂×C₃₁	semidirect
551. #3357	C₂×C₃₁	semidirect
552. #3345	C₂×C₃₁	semidirect
553. #3305	C₂×C₃₁	semidirect
554. #3301	C₂×C₃₁	semidirect
555. #3295	C₂×C₃₁	semidirect
556. #3294	C₂×C₃₁	semidirect
557. #3274	C₂×C₃₁	semidirect
558. #3265	C₂×C₃₁	semidirect
559. #3179	C₂×C₃₁	semidirect
560. #3169	C₂×C₃₁	semidirect
561. #3119	C₂×C₃₁	semidirect
562. #3118	C₂×C₃₁	semidirect
563. #3112	C₂×C₃₁	semidirect
564. #3109	C₂×C₃₁	semidirect
565. #2966	C₂×C₃₁	semidirect
566. #2946	C₂×C₃₁	semidirect
567. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
610. #559	C₂²×C₃₁	semidirect
611. Q₈²	C₂²×C₃₁	semidirect
615. #554	C₂²×C₃₁	semidirect
619. #550	C₂²×C₃₁	semidirect
620. #548	C₂²×C₃₁	semidirect
622. #547	C₂²×C₃₁	semidirect
628. #542	C₂²×C₃₁	semidirect
633. #532	C₂²×C₃₁	semidirect
638. #520	C₂²×C₃₁	semidirect
640. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
642. #501	C₂²×C₃₁	semidirect
643. #500	C₂²×C₃₁	semidirect
644. #496	C₂²×C₃₁	semidirect
645. #493	C₂²×C₃₁	semidirect
646. #488	C₂²×C₃₁	semidirect
647. #486	C₂²×C₃₁	semidirect
648. #486	C₂²×C₃₁	semidirect
649. #486	C₂²×C₃₁	semidirect
650. #485	C₂²×C₃₁	semidirect
651. #482	C₂²×C₃₁	semidirect
652. #481	C₂²×C₃₁	semidirect
653. #481	C₂²×C₃₁	semidirect
654. #480	C₂²×C₃₁	semidirect
655. #480	C₂²×C₃₁	semidirect
656. #479	C₂²×C₃₁	semidirect
657. #478	C₂²×C₃₁	semidirect
658. #477	C₂²×C₃₁	semidirect
659. #477	C₂²×C₃₁	semidirect
661. #476	C₂²×C₃₁	semidirect
662. #476	C₂²×C₃₁	semidirect
664. #469	C₂²×C₃₁	semidirect
665. #468	C₂²×C₃₁	semidirect
666. #466	C₂²×C₃₁	semidirect
667. #466	C₂²×C₃₁	semidirect
668. #466	C₂²×C₃₁	semidirect
669. #465	C₂²×C₃₁	semidirect
671. #463	C₂²×C₃₁	semidirect
672. #460	C₂²×C₃₁	semidirect
673. #460	C₂²×C₃₁	semidirect
674. #460	C₂²×C₃₁	semidirect
676. #459	C₂²×C₃₁	semidirect
677. #459	C₂²×C₃₁	semidirect
679. #449	C₂²×C₃₁	semidirect
680. #449	C₂²×C₃₁	semidirect
681. #448	C₂²×C₃₁	semidirect
684. #446	C₂²×C₃₁	semidirect
685. C₈×Q₈	C₂²×C₃₁	semidirect
687. #442	C₂²×C₃₁	semidirect
688. #442	C₂²×C₃₁	semidirect
690. #440	C₂²×C₃₁	semidirect
691. #440	C₂²×C₃₁	semidirect
696. C₄×SD₁₆	C₂²×C₃₁	semidirect
697. C₄×SD₁₆	C₂²×C₃₁	semidirect
698. C₄×SD₁₆	C₂²×C₃₁	semidirect
699. C₄×SD₁₆	C₂²×C₃₁	semidirect
700. C₄×SD₁₆	C₂²×C₃₁	semidirect
702. C₄×D₈	C₂²×C₃₁	semidirect
703. C₄×D₈	C₂²×C₃₁	semidirect
704. #436	C₂²×C₃₁	semidirect
705. #435	C₂²×C₃₁	semidirect
706. C₈×D₄	C₂²×C₃₁	semidirect
707. C₈×D₄	C₂²×C₃₁	semidirect
708. #433	C₂²×C₃₁	semidirect
709. #432	C₂²×C₃₁	semidirect
710. #428	C₂²×C₃₁	semidirect
711. C₂×#106	C₂²×C₃₁	semidirect
712. #416	C₂²×C₃₁	semidirect
713. C₂×#103	C₂²×C₃₁	semidirect
716. #405	C₂²×C₃₁	semidirect
717. C₂×C₄×C₈	C₂²×C₃₁	semidirect
906. C₃₁	#61498	direct (N × H)
974. SD₁₆	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3522	2
C₃₁×#3519	2
C₃₁×#3399	2
C₃₁×#3385	2
C₃₁×#3362	2
C₃₁×#3361	2
C₃₁×#3357	2
C₃₁×#3345	2
C₃₁×#3305	2
C₃₁×#3301	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3274	2
C₃₁×#3265	2
C₃₁×#3179	2
C₃₁×#3169	2
C₃₁×#3119	2
C₃₁×#3118	2
C₃₁×#3112	2
C₃₁×#3109	2
C₃₁×#2966	2
C₃₁×#2946	2
C₂×C₄×SD₁₆×C₃₁	2
#61498	31

Subgroups — C31×#61498 #21518257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61498 #21518257