Subgroups — C₃₁×#61496 #21518255

Order 7936.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3264	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3179	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3167	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×#3110	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×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#555	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	1	yes	characteristic, complemented
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#552	—	2	1	no	—
33	C₃₁×#551	—	2	2	no	—
34	C₃₁×#550	C₂²	1	1	yes	characteristic, complemented
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#546	—	2	1	no	—
40	C₃₁×#546	—	2	2	no	—
41	C₃₁×#546	C₂²	1	2	yes	complemented
42	D₄²×C₃₁	C₂²	1	2	yes	—
43	D₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#542	C₂²	1	2	yes	complemented
45	C₃₁×#540	C₂²	1	2	yes	complemented
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₃₁×#529	C₂²	1	1	yes	characteristic
51	C₃₁×#525	—	2	1	no	—
52	C₃₁×#525	—	2	1	no	—
53	C₂×C₃₁×C₂²⋊Q₈	—	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	complemented
57	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#501	C₂²	1	2	yes	complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#496	C₂²	1	2	yes	complemented
62	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#487	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×#484	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#481	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×#476	C₂²	1	1	yes	characteristic, complemented
76	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
77	C₃₁×#476	C₂²	1	2	yes	complemented
78	C₃₁×#474	C₂²	1	2	yes	complemented
79	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
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×#465	C₂²	1	2	yes	complemented
85	C₃₁×#465	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×#461	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#460	C₂²	1	2	yes	complemented
92	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#459	C₂²	1	2	yes	complemented
94	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#450	C₂²	1	2	yes	—
96	C₃₁×#450	C₂²	1	2	yes	complemented
97	C₃₁×#449	C₂²	1	2	yes	complemented
98	C₃₁×#449	C₂²	1	2	yes	complemented
99	C₃₁×#447	C₂²	1	2	yes	—
100	C₃₁×#447	C₂²	1	2	yes	complemented
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	complemented
107	C₃₁×#440	C₂²	1	2	yes	complemented
108	C₃₁×#440	C₂²	1	2	yes	complemented
109	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
112	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
113	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
114	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
115	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
117	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
119	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
125	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×#107	C₂²	1	1	yes	characteristic, complemented
129	C₃₁×#416	C₂²	1	2	yes	complemented
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
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	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	2	no	—
141	C₂²×D₄×C₃₁	—	2	1	no	—
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₃₁	—	2	1	no	—
146	C₂³×C₄×C₃₁	—	2	1	no	—
147	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×D₈×C₃₁	—	2	4	no	—
153	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₃₁	C₂³	1	2	yes	—
157	C₂×D₈×C₃₁	C₂³	1	2	yes	—
158	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×#127	C₂³	1	1	yes	characteristic
168	C₃₁×#127	C₂³	1	2	yes	—
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#126	D₄	1	2	yes	—
173	C₃₁×#125	—	2	2	no	—
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	2	no	—
178	C₃₁×#124	—	2	2	no	—
179	C₃₁×#124	—	2	1	no	—
180	C₃₁×#124	D₄	1	1	yes	characteristic
181	C₃₁×#124	C₂³	1	2	yes	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
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	D₄	1	2	yes	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	no	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	1	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
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	1	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	—	2	2	no	—
214	C₃₁×#121	D₄	1	1	yes	characteristic
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	C₃₁×#120	—	2	2	no	—
223	C₄×Q₈×C₃₁	—	2	1	no	—
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
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	2	no	—
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	1	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	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	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	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	2	yes	—
249	C₄×D₄×C₃₁	C₂³	1	2	yes	—
250	C₄×D₄×C₃₁	C₂³	1	2	yes	—
251	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#117	—	2	1	no	—
253	C₃₁×#117	—	2	2	no	—
254	C₃₁×#117	—	2	1	no	—
255	C₃₁×#117	—	2	1	no	—
256	C₃₁×#117	C₂³	1	2	yes	—
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
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×C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	1	yes	characteristic
273	C₃₁×#107	C₂³	1	1	yes	characteristic
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	2	yes	—
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	2	yes	—
285	C₃₁×#103	C₂³	1	2	yes	—
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#102	C₂³	1	1	yes	characteristic
289	C₃₁×#102	C₂³	1	1	yes	characteristic
290	C₃₁×#102	C₂³	1	1	yes	characteristic
291	C₃₁×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	no	—
316	C₂⁴×C₃₁	—	2	2	no	—
317	#41×C₃₁	—	2	4	no	—
318	#41×C₃₁	—	4	2	no	—
319	#41×C₃₁	—	8	2	no	—
320	#41×C₃₁	—	8	2	no	—
321	#41×C₃₁	—	8	2	no	—
322	C₂×Q₈×C₃₁	—	2	1	no	—
323	C₂×Q₈×C₃₁	—	2	2	no	—
324	C₂×Q₈×C₃₁	—	2	1	no	—
325	C₂×Q₈×C₃₁	—	8	2	no	—
326	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
328	C₂×D₄×C₃₁	—	2	2	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	4	no	—
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	2	no	—
335	C₂×D₄×C₃₁	—	2	2	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	1	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	—	4	1	no	—
344	C₂×D₄×C₃₁	—	4	1	no	—
345	C₂×D₄×C₃₁	—	4	2	no	—
346	C₂×D₄×C₃₁	—	8	2	no	—
347	C₂×D₄×C₃₁	—	8	4	no	—
348	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
353	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
354	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	1	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	1	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	1	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	2	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	1	no	—
369	C₂²×C₄×C₃₁	—	2	1	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	8	2	no	—
372	C₂²×C₄×C₃₁	—	8	2	no	—
373	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
377	SD₁₆×C₃₁	—	2	4	no	—
378	SD₁₆×C₃₁	—	2	4	no	—
379	SD₁₆×C₃₁	—	4	2	no	—
380	SD₁₆×C₃₁	—	4	2	no	—
381	D₈×C₃₁	—	2	2	no	—
382	D₈×C₃₁	—	2	2	no	—
383	D₈×C₃₁	—	2	4	no	—
384	D₈×C₃₁	—	2	2	no	—
385	D₈×C₃₁	—	4	2	no	—
386	D₈×C₃₁	#41	1	4	yes	complemented
387	M₁₆×C₃₁	—	2	4	no	—
388	C₂×C₈×C₃₁	—	2	2	no	—
389	C₂×C₈×C₃₁	—	4	2	no	—
390	C₂×C₈×C₃₁	—	4	1	no	—
391	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
395	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
396	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	1	no	—
400	C₄⋊C₄×C₃₁	—	2	2	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
408	C₄⋊C₄×C₃₁	—	2	2	no	—
409	C₄⋊C₄×C₃₁	—	2	2	no	—
410	C₄⋊C₄×C₃₁	—	2	2	no	—
411	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
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	2	yes	—
421	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	2	no	—
425	C₂²⋊C₄×C₃₁	—	2	2	no	—
426	C₂²⋊C₄×C₃₁	—	2	1	no	—
427	C₂²⋊C₄×C₃₁	—	2	1	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	—	2	2	no	—
433	C₂²⋊C₄×C₃₁	—	2	1	no	—
434	C₂²⋊C₄×C₃₁	—	2	1	no	—
435	C₂²⋊C₄×C₃₁	—	2	1	no	—
436	C₂²⋊C₄×C₃₁	—	2	1	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	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	2	no	—
442	C₂²⋊C₄×C₃₁	—	2	2	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
448	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₄²×C₃₁	—	2	2	no	—
450	C₄²×C₃₁	—	2	2	no	—
451	C₄²×C₃₁	—	2	2	no	—
452	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
455	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
456	C₄²×C₃₁	C₂⁴	1	2	yes	—
457	#61496	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂³×C₃₁	—	2	1	no	—
459	C₂³×C₃₁	—	2	1	no	—
460	C₂³×C₃₁	—	2	1	no	—
461	C₂³×C₃₁	—	2	1	no	—
462	C₂³×C₃₁	—	2	2	no	—
463	C₂³×C₃₁	—	4	2	no	—
464	C₂³×C₃₁	—	4	2	no	—
465	C₂³×C₃₁	—	4	4	no	—
466	C₂³×C₃₁	—	4	2	no	—
467	C₂³×C₃₁	—	4	2	no	—
468	C₂³×C₃₁	—	8	1	no	—
469	C₂³×C₃₁	—	8	1	no	—
470	C₂³×C₃₁	—	8	2	no	—
471	C₂³×C₃₁	—	8	2	no	—
472	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
473	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
474	Q₈×C₃₁	—	2	2	no	—
475	Q₈×C₃₁	—	2	2	no	—
476	Q₈×C₃₁	—	2	2	no	—
477	Q₈×C₃₁	—	4	2	no	—
478	Q₈×C₃₁	—	8	2	no	—
479	Q₈×C₃₁	—	8	1	no	—
480	D₄×C₃₁	—	2	4	no	—
481	D₄×C₃₁	—	2	2	no	—
482	D₄×C₃₁	—	2	1	no	—
483	D₄×C₃₁	—	2	1	no	—
484	D₄×C₃₁	—	2	2	no	—
485	D₄×C₃₁	—	2	1	no	—
486	D₄×C₃₁	—	2	1	no	—
487	D₄×C₃₁	—	2	1	no	—
488	D₄×C₃₁	—	2	2	no	—
489	D₄×C₃₁	—	2	1	no	—
490	D₄×C₃₁	—	4	4	no	—
491	D₄×C₃₁	—	4	2	no	—
492	D₄×C₃₁	—	4	2	no	—
493	D₄×C₃₁	—	4	4	no	—
494	D₄×C₃₁	—	4	4	no	—
495	D₄×C₃₁	—	4	2	no	—
496	D₄×C₃₁	—	8	2	no	—
497	D₄×C₃₁	—	8	2	no	—
498	D₄×C₃₁	—	8	1	no	—
499	D₄×C₃₁	—	8	2	no	—
500	D₄×C₃₁	—	8	2	no	—
501	D₄×C₃₁	—	8	2	no	—
502	D₄×C₃₁	C₂×#41	1	2	yes	—
503	D₄×C₃₁	C₂×#41	1	2	yes	—
504	C₂×C₄×C₃₁	—	2	2	no	—
505	C₂×C₄×C₃₁	—	2	2	no	—
506	C₂×C₄×C₃₁	—	2	1	no	—
507	C₂×C₄×C₃₁	—	2	2	no	—
508	C₂×C₄×C₃₁	—	2	1	no	—
509	C₂×C₄×C₃₁	—	2	2	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	2	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	—	2	1	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	1	no	—
523	C₂×C₄×C₃₁	—	8	1	no	—
524	C₂×C₄×C₃₁	—	8	1	no	—
525	C₂×C₄×C₃₁	—	8	1	no	—
526	C₂×C₄×C₃₁	—	8	2	no	—
527	C₂×C₄×C₃₁	—	8	2	no	—
528	C₂×C₄×C₃₁	—	8	2	no	—
529	C₂×C₄×C₃₁	—	8	2	no	—
530	C₂×C₄×C₃₁	—	8	1	no	—
531	C₂×C₄×C₃₁	—	8	1	no	—
532	C₂×C₄×C₃₁	—	8	2	no	—
533	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
542	C₈×C₃₁	—	2	1	no	—
543	C₈×C₃₁	—	2	2	no	—
544	C₈×C₃₁	—	2	1	no	—
545	C₈×C₃₁	—	2	2	no	—
546	C₈×C₃₁	—	2	1	no	—
547	C₈×C₃₁	C₂×#41	1	2	yes	—
548	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
550	#3397	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
552	#3360	C₂×C₃₁	1	1	yes	characteristic, complemented
553	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
554	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
555	#3346	C₂×C₃₁	1	2	yes	complemented
556	#3303	C₂×C₃₁	1	1	yes	characteristic, complemented
557	#3297	C₂×C₃₁	1	2	yes	complemented
558	#3295	C₂×C₃₁	1	2	yes	complemented
559	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
560	#3272	C₂×C₃₁	1	1	yes	characteristic, complemented
561	#3264	C₂×C₃₁	1	2	yes	complemented
562	#3179	C₂×C₃₁	1	2	yes	complemented
563	#3167	C₂×C₃₁	1	1	yes	characteristic, complemented
564	#3119	C₂×C₃₁	1	2	yes	complemented
565	#3118	C₂×C₃₁	1	2	yes	complemented
566	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#3109	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#2966	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#2946	C₂×C₃₁	1	2	yes	complemented
570	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
571	C₂²×C₃₁	—	2	1	no	—
572	C₂²×C₃₁	—	2	1	no	—
573	C₂²×C₃₁	—	2	2	no	—
574	C₂²×C₃₁	—	2	2	no	—
575	C₂²×C₃₁	—	2	2	no	—
576	C₂²×C₃₁	—	2	2	no	—
577	C₂²×C₃₁	—	2	2	no	—
578	C₂²×C₃₁	—	4	1	no	—
579	C₂²×C₃₁	—	4	1	no	—
580	C₂²×C₃₁	—	4	1	no	—
581	C₂²×C₃₁	—	4	1	no	—
582	C₂²×C₃₁	—	4	1	no	—
583	C₂²×C₃₁	—	4	1	no	—
584	C₂²×C₃₁	—	4	2	no	—
585	C₂²×C₃₁	—	4	1	no	—
586	C₂²×C₃₁	—	4	1	no	—
587	C₂²×C₃₁	—	4	2	no	—
588	C₂²×C₃₁	—	4	2	no	—
589	C₂²×C₃₁	—	4	1	no	—
590	C₂²×C₃₁	—	4	1	no	—
591	C₂²×C₃₁	—	8	4	no	—
592	C₂²×C₃₁	—	8	4	no	—
593	C₂²×C₃₁	—	16	4	no	—
594	C₂²×C₃₁	#577	1	2	yes	—
595	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
596	C₄×C₃₁	—	2	2	no	—
597	C₄×C₃₁	—	2	1	no	—
598	C₄×C₃₁	—	2	1	no	—
599	C₄×C₃₁	—	2	2	no	—
600	C₄×C₃₁	—	2	1	no	—
601	C₄×C₃₁	—	2	1	no	—
602	C₄×C₃₁	—	2	2	no	—
603	C₄×C₃₁	—	4	2	no	—
604	C₄×C₃₁	—	4	1	no	—
605	C₄×C₃₁	—	4	1	no	—
606	C₄×C₃₁	—	4	1	no	—
607	C₄×C₃₁	—	4	1	no	—
608	C₄×C₃₁	—	4	2	no	—
609	C₄×C₃₁	—	4	2	no	—
610	C₄×C₃₁	#576	1	2	yes	—
611	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
612	C₄×C₃₁	#585	1	1	yes	characteristic
613	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	—
614	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
615	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
616	#555	C₂²×C₃₁	1	1	yes	characteristic, complemented
617	#554	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#554	C₂²×C₃₁	1	2	yes	complemented
619	#553	—	2	1	no	—
620	#553	C₂²×C₃₁	1	2	yes	—
621	#552	—	2	1	no	—
622	#551	—	2	2	no	—
623	#550	C₂²×C₃₁	1	1	yes	characteristic, complemented
624	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
625	#548	—	2	1	no	—
626	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#546	—	2	1	no	—
629	#546	—	2	2	no	—
630	#546	C₂²×C₃₁	1	2	yes	complemented
631	D₄²	C₂²×C₃₁	1	2	yes	—
632	D₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
633	#542	C₂²×C₃₁	1	2	yes	complemented
634	#540	C₂²×C₃₁	1	2	yes	complemented
635	#539	—	2	2	no	—
636	#538	—	2	2	no	—
637	#533	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#532	C₂²×C₃₁	1	1	yes	characteristic
639	#529	C₂²×C₃₁	1	1	yes	characteristic
640	#525	—	2	1	no	—
641	#525	—	2	1	no	—
642	C₂×C₂²⋊Q₈	—	2	1	no	—
643	C₂×#121	—	2	1	no	—
644	#520	C₂²×C₃₁	1	2	yes	complemented
645	#518	C₂²×C₃₁	1	2	yes	complemented
646	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
647	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
648	#501	C₂²×C₃₁	1	2	yes	complemented
649	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#496	C₂²×C₃₁	1	2	yes	complemented
651	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	#488	C₂²×C₃₁	1	2	yes	complemented
653	#487	C₂²×C₃₁	1	1	yes	characteristic, complemented
654	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
655	#486	C₂²×C₃₁	1	2	yes	complemented
656	#485	C₂²×C₃₁	1	2	yes	complemented
657	#484	C₂²×C₃₁	1	2	yes	complemented
658	#482	C₂²×C₃₁	1	2	yes	complemented
659	#481	C₂²×C₃₁	1	2	yes	complemented
660	#481	C₂²×C₃₁	1	2	yes	complemented
661	#480	C₂²×C₃₁	1	2	yes	complemented
662	#479	C₂²×C₃₁	1	2	yes	complemented
663	#478	C₂²×C₃₁	1	2	yes	complemented
664	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
665	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#476	C₂²×C₃₁	1	2	yes	complemented
667	#474	C₂²×C₃₁	1	2	yes	complemented
668	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
670	#469	C₂²×C₃₁	1	2	yes	complemented
671	#468	C₂²×C₃₁	1	2	yes	complemented
672	#466	C₂²×C₃₁	1	2	yes	complemented
673	#465	C₂²×C₃₁	1	2	yes	complemented
674	#465	C₂²×C₃₁	1	2	yes	complemented
675	#465	C₂²×C₃₁	1	2	yes	complemented
676	#463	C₂²×C₃₁	1	2	yes	—
677	#463	C₂²×C₃₁	1	2	yes	complemented
678	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#460	C₂²×C₃₁	1	2	yes	complemented
681	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#459	C₂²×C₃₁	1	2	yes	complemented
683	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
684	#450	C₂²×C₃₁	1	2	yes	—
685	#450	C₂²×C₃₁	1	2	yes	complemented
686	#449	C₂²×C₃₁	1	2	yes	complemented
687	#449	C₂²×C₃₁	1	2	yes	complemented
688	#447	C₂²×C₃₁	1	2	yes	—
689	#447	C₂²×C₃₁	1	2	yes	complemented
690	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
691	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#442	C₂²×C₃₁	1	2	yes	—
693	#442	C₂²×C₃₁	1	2	yes	complemented
694	#442	C₂²×C₃₁	1	2	yes	complemented
695	#440	C₂²×C₃₁	1	2	yes	complemented
696	#440	C₂²×C₃₁	1	2	yes	complemented
697	#440	C₂²×C₃₁	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
700	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
701	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
702	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
703	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
704	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
705	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
708	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
709	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
710	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
711	#435	C₂²×C₃₁	1	2	yes	complemented
712	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
713	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
714	#433	C₂²×C₃₁	1	2	yes	complemented
715	#432	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#428	C₂²×C₃₁	1	2	yes	complemented
717	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#416	C₂²×C₃₁	1	2	yes	complemented
719	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
720	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
722	#405	C₂²×C₃₁	1	2	yes	complemented
723	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
724	C₂×C₃₁	—	2	2	no	—
725	C₂×C₃₁	—	4	2	no	—
726	C₂×C₃₁	—	4	2	no	—
727	C₂×C₃₁	—	4	2	no	—
728	C₂×C₃₁	—	8	1	no	—
729	C₂×C₃₁	—	8	1	no	—
730	C₂×C₃₁	—	8	2	no	—
731	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
732	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
733	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
734	C₂×#41	—	2	1	no	—
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	C₂³×C₃₁	1	2	yes	—
738	C₂²×Q₈	—	2	1	no	—
739	C₂²×D₄	—	2	2	no	—
740	C₂²×D₄	—	2	1	no	—
741	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
743	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
744	C₂³×C₄	—	2	1	no	—
745	C₂³×C₄	—	2	1	no	—
746	AGL(1,ℤ/8)	—	2	8	no	—
747	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
751	C₂×D₈	—	2	4	no	—
752	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
753	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
755	C₂×D₈	C₂³×C₃₁	1	2	yes	—
756	C₂×D₈	C₂³×C₃₁	1	2	yes	—
757	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
758	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
759	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
760	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
761	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
762	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
766	#127	C₂³×C₃₁	1	1	yes	characteristic
767	#127	C₂³×C₃₁	1	2	yes	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	D₄×C₃₁	1	2	yes	—
772	#125	—	2	2	no	—
773	#125	—	2	1	no	—
774	#125	D₄×C₃₁	1	1	yes	characteristic
775	#125	C₂³×C₃₁	1	2	yes	—
776	#124	—	2	2	no	—
777	#124	—	2	2	no	—
778	#124	—	2	1	no	—
779	#124	D₄×C₃₁	1	1	yes	characteristic
780	#124	C₂³×C₃₁	1	2	yes	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	D₄×C₃₁	1	2	yes	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	1	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	D₄×C₃₁	1	1	yes	characteristic
814	#121	C₂³×C₃₁	1	2	yes	—
815	#121	C₂³×C₃₁	1	2	yes	—
816	#121	C₂³×C₃₁	1	2	yes	—
817	#121	C₂³×C₃₁	1	2	yes	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
824	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
825	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	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	—	2	1	no	—
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	1	yes	characteristic
841	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
845	C₄×D₄	C₂³×C₃₁	1	2	yes	—
846	C₄×D₄	C₂³×C₃₁	1	2	yes	—
847	C₄×D₄	C₂³×C₃₁	1	2	yes	—
848	C₄×D₄	C₂³×C₃₁	1	2	yes	—
849	C₄×D₄	C₂³×C₃₁	1	2	yes	—
850	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
851	#117	—	2	1	no	—
852	#117	—	2	2	no	—
853	#117	—	2	1	no	—
854	#117	—	2	1	no	—
855	#117	C₂³×C₃₁	1	2	yes	—
856	#117	C₂³×C₃₁	1	2	yes	—
857	C₂×C₄⋊C₄	—	2	2	no	—
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
863	C₂×C₂²⋊C₄	—	2	1	no	—
864	C₂×C₂²⋊C₄	—	2	1	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₂²⋊C₄	—	2	2	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
869	#107	C₂³×C₃₁	1	1	yes	characteristic
870	#107	C₂³×C₃₁	1	1	yes	characteristic
871	#107	C₂³×C₃₁	1	1	yes	characteristic
872	#107	C₂³×C₃₁	1	1	yes	characteristic
873	#107	C₂³×C₃₁	1	2	yes	—
874	#107	C₂³×C₃₁	1	2	yes	—
875	#106	C₂³×C₃₁	1	2	yes	—
876	#106	C₂³×C₃₁	1	2	yes	—
877	#106	C₂³×C₃₁	1	2	yes	—
878	#106	C₂³×C₃₁	1	2	yes	—
879	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
880	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
882	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
883	#103	C₂³×C₃₁	1	2	yes	—
884	#103	C₂³×C₃₁	1	2	yes	—
885	#103	C₂³×C₃₁	1	2	yes	—
886	#103	C₂³×C₃₁	1	2	yes	—
887	#102	C₂³×C₃₁	1	1	yes	characteristic
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	1	yes	characteristic
894	#102	C₂³×C₃₁	1	1	yes	characteristic
895	#102	C₂³×C₃₁	1	2	yes	—
896	#102	C₂³×C₃₁	1	2	yes	—
897	#102	C₂³×C₃₁	1	2	yes	—
898	#102	C₂³×C₃₁	1	2	yes	—
899	#102	C₂³×C₃₁	1	2	yes	—
900	#102	C₂³×C₃₁	1	2	yes	—
901	#102	C₂³×C₃₁	1	2	yes	—
902	#102	C₂³×C₃₁	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
906	#97	C₂³×C₃₁	1	2	yes	—
907	#97	C₂³×C₃₁	1	2	yes	—
908	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
909	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
910	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
911	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
912	C₄×C₈	C₂³×C₃₁	1	2	yes	—
913	C₃₁	#61496	1	1	yes	characteristic, direct product factor, Sylow
914	C₂⁴	—	2	1	no	—
915	C₂⁴	—	2	1	no	—
916	C₂⁴	—	2	2	no	—
917	#41	—	2	4	no	—
918	#41	—	4	2	no	—
919	#41	—	8	2	no	—
920	#41	—	8	2	no	—
921	#41	—	8	2	no	—
922	C₂×Q₈	—	2	1	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	8	2	no	—
926	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
927	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	4	1	no	—
944	C₂×D₄	—	4	1	no	—
945	C₂×D₄	—	4	2	no	—
946	C₂×D₄	—	8	2	no	—
947	C₂×D₄	—	8	4	no	—
948	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
950	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
951	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
952	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
953	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	1	no	—
960	C₂²×C₄	—	2	1	no	—
961	C₂²×C₄	—	2	1	no	—
962	C₂²×C₄	—	2	1	no	—
963	C₂²×C₄	—	2	1	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	2	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	8	2	no	—
972	C₂²×C₄	—	8	2	no	—
973	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
974	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
975	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
976	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
977	SD₁₆	—	2	4	no	—
978	SD₁₆	—	2	4	no	—
979	SD₁₆	—	4	2	no	—
980	SD₁₆	—	4	2	no	—
981	D₈	—	2	2	no	—
982	D₈	—	2	2	no	—
983	D₈	—	2	4	no	—
984	D₈	—	2	2	no	—
985	D₈	—	4	2	no	—
986	D₈	#41×C₃₁	1	4	yes	complemented
987	M₁₆	—	2	4	no	—
988	C₂×C₈	—	2	2	no	—
989	C₂×C₈	—	4	2	no	—
990	C₂×C₈	—	4	1	no	—
991	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
995	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
996	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
997	C₄⋊C₄	—	2	2	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	—	2	2	no	—
1004	C₄⋊C₄	—	2	1	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1012	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1013	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1015	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1016	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1017	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1018	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1020	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1021	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	1	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1047	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1048	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1049	C₄²	—	2	2	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1053	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₃₁	1	2	yes	—
1057	C₂³	—	2	1	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	1	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	2	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	2	no	—
1066	C₂³	—	4	2	no	—
1067	C₂³	—	8	1	no	—
1068	C₂³	—	8	1	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	—	8	2	no	—
1071	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1072	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1073	Q₈	—	2	2	no	—
1074	Q₈	—	2	2	no	—
1075	Q₈	—	2	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	—	8	2	no	—
1078	Q₈	—	8	1	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	2	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	2	1	no	—
1087	D₄	—	2	2	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	4	no	—
1090	D₄	—	4	2	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	4	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	2	no	—
1095	D₄	—	8	2	no	—
1096	D₄	—	8	2	no	—
1097	D₄	—	8	1	no	—
1098	D₄	—	8	2	no	—
1099	D₄	—	8	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	C₂×#41×C₃₁	1	2	yes	—
1102	D₄	C₂×#41×C₃₁	1	2	yes	—
1103	C₂×C₄	—	2	2	no	—
1104	C₂×C₄	—	2	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	1	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	2	no	—
1113	C₂×C₄	—	2	2	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	4	4	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	4	2	no	—
1121	C₂×C₄	—	8	1	no	—
1122	C₂×C₄	—	8	1	no	—
1123	C₂×C₄	—	8	1	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	2	no	—
1127	C₂×C₄	—	8	2	no	—
1128	C₂×C₄	—	8	2	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	8	2	no	—
1132	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1133	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1134	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1137	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1139	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1140	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1141	C₈	—	2	1	no	—
1142	C₈	—	2	2	no	—
1143	C₈	—	2	1	no	—
1144	C₈	—	2	2	no	—
1145	C₈	—	2	1	no	—
1146	C₈	C₂×#41×C₃₁	1	2	yes	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	2	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	1	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	2	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	8	4	no	—
1168	C₂²	—	8	4	no	—
1169	C₂²	—	16	4	no	—
1170	C₂²	C₃₁×#577	1	2	yes	—
1171	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1172	C₄	—	2	2	no	—
1173	C₄	—	2	1	no	—
1174	C₄	—	2	1	no	—
1175	C₄	—	2	2	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	4	2	no	—
1180	C₄	—	4	1	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	2	no	—
1186	C₄	C₃₁×#576	1	2	yes	—
1187	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1188	C₄	C₃₁×#585	1	1	yes	characteristic
1189	C₂	—	2	2	no	—
1190	C₂	—	4	2	no	—
1191	C₂	—	4	2	no	—
1192	C₂	—	4	2	no	—
1193	C₂	—	8	1	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	2	no	—
1196	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1197	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1198	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×#3520	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3397	C₂	semidirect
4. C₃₁×#3384	C₂	semidirect
5. C₃₁×#3360	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3354	C₂	semidirect
8. C₃₁×#3346	C₂	semidirect
9. C₃₁×#3303	C₂	semidirect
10. C₃₁×#3297	C₂	semidirect
11. C₃₁×#3295	C₂	semidirect
12. C₃₁×#3294	C₂	semidirect
13. C₃₁×#3272	C₂	semidirect
14. C₃₁×#3264	C₂	semidirect
15. C₃₁×#3179	C₂	semidirect
16. C₃₁×#3167	C₂	semidirect
17. C₃₁×#3119	C₂	semidirect
18. C₃₁×#3118	C₂	semidirect
19. C₃₁×#3110	C₂	semidirect
20. C₃₁×#3109	C₂	semidirect
21. C₃₁×#2966	C₂	semidirect
22. C₃₁×#2946	C₂	semidirect
23. C₂×C₄×D₈×C₃₁	C₂	semidirect
26. C₃₁×#556	C₂²	semidirect
27. C₃₁×#555	C₂²	semidirect
28. C₃₁×#554	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
34. C₃₁×#550	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
38. C₃₁×#547	C₂²	semidirect
41. C₃₁×#546	C₂²	semidirect
43. D₄²×C₃₁	C₂²	semidirect
44. C₃₁×#542	C₂²	semidirect
45. C₃₁×#540	C₂²	semidirect
48. C₃₁×#533	C₂²	semidirect
55. C₃₁×#520	C₂²	semidirect
56. C₃₁×#518	C₂²	semidirect
58. C₂×C₄×D₄×C₃₁	C₂²	semidirect
59. C₃₁×#501	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#496	C₂²	semidirect
62. C₃₁×#492	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#487	C₂²	semidirect
65. C₃₁×#486	C₂²	semidirect
66. C₃₁×#486	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#480	C₂²	semidirect
73. C₃₁×#479	C₂²	semidirect
74. C₃₁×#478	C₂²	semidirect
75. C₃₁×#476	C₂²	semidirect
76. C₃₁×#476	C₂²	semidirect
77. C₃₁×#476	C₂²	semidirect
78. C₃₁×#474	C₂²	semidirect
79. C₃₁×#474	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
81. C₃₁×#469	C₂²	semidirect
82. C₃₁×#468	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#465	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#461	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#460	C₂²	semidirect
92. C₃₁×#459	C₂²	semidirect
93. C₃₁×#459	C₂²	semidirect
94. C₃₁×#459	C₂²	semidirect
96. C₃₁×#450	C₂²	semidirect
97. C₃₁×#449	C₂²	semidirect
98. C₃₁×#449	C₂²	semidirect
100. C₃₁×#447	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₈×Q₈×C₃₁	C₂²	semidirect
104. C₃₁×#442	C₂²	semidirect
105. C₃₁×#442	C₂²	semidirect
106. C₃₁×#440	C₂²	semidirect
107. C₃₁×#440	C₂²	semidirect
108. C₃₁×#440	C₂²	semidirect
109. C₄×SD₁₆×C₃₁	C₂²	semidirect
110. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₄×SD₁₆×C₃₁	C₂²	semidirect
116. C₄×D₈×C₃₁	C₂²	semidirect
117. C₄×D₈×C₃₁	C₂²	semidirect
118. C₄×D₈×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×#107	C₂²	semidirect
129. C₃₁×#416	C₂²	semidirect
131. C₂×C₃₁×#102	C₂²	semidirect
132. C₂×C₃₁×#102	C₂²	semidirect
133. C₃₁×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
386. D₈×C₃₁	#41	semidirect
457. #61496	C₃₁	direct (N × H)
548. #3520	C₂×C₃₁	semidirect
549. #3519	C₂×C₃₁	semidirect
550. #3397	C₂×C₃₁	semidirect
551. #3384	C₂×C₃₁	semidirect
552. #3360	C₂×C₃₁	semidirect
553. #3358	C₂×C₃₁	semidirect
554. #3354	C₂×C₃₁	semidirect
555. #3346	C₂×C₃₁	semidirect
556. #3303	C₂×C₃₁	semidirect
557. #3297	C₂×C₃₁	semidirect
558. #3295	C₂×C₃₁	semidirect
559. #3294	C₂×C₃₁	semidirect
560. #3272	C₂×C₃₁	semidirect
561. #3264	C₂×C₃₁	semidirect
562. #3179	C₂×C₃₁	semidirect
563. #3167	C₂×C₃₁	semidirect
564. #3119	C₂×C₃₁	semidirect
565. #3118	C₂×C₃₁	semidirect
566. #3110	C₂×C₃₁	semidirect
567. #3109	C₂×C₃₁	semidirect
568. #2966	C₂×C₃₁	semidirect
569. #2946	C₂×C₃₁	semidirect
570. C₂×C₄×D₈	C₂×C₃₁	semidirect
615. #556	C₂²×C₃₁	semidirect
616. #555	C₂²×C₃₁	semidirect
617. #554	C₂²×C₃₁	semidirect
618. #554	C₂²×C₃₁	semidirect
623. #550	C₂²×C₃₁	semidirect
624. D₄×Q₈	C₂²×C₃₁	semidirect
626. #547	C₂²×C₃₁	semidirect
627. #547	C₂²×C₃₁	semidirect
630. #546	C₂²×C₃₁	semidirect
632. D₄²	C₂²×C₃₁	semidirect
633. #542	C₂²×C₃₁	semidirect
634. #540	C₂²×C₃₁	semidirect
637. #533	C₂²×C₃₁	semidirect
644. #520	C₂²×C₃₁	semidirect
645. #518	C₂²×C₃₁	semidirect
647. C₂×C₄×D₄	C₂²×C₃₁	semidirect
648. #501	C₂²×C₃₁	semidirect
649. #498	C₂²×C₃₁	semidirect
650. #496	C₂²×C₃₁	semidirect
651. #492	C₂²×C₃₁	semidirect
652. #488	C₂²×C₃₁	semidirect
653. #487	C₂²×C₃₁	semidirect
654. #486	C₂²×C₃₁	semidirect
655. #486	C₂²×C₃₁	semidirect
656. #485	C₂²×C₃₁	semidirect
657. #484	C₂²×C₃₁	semidirect
658. #482	C₂²×C₃₁	semidirect
659. #481	C₂²×C₃₁	semidirect
660. #481	C₂²×C₃₁	semidirect
661. #480	C₂²×C₃₁	semidirect
662. #479	C₂²×C₃₁	semidirect
663. #478	C₂²×C₃₁	semidirect
664. #476	C₂²×C₃₁	semidirect
665. #476	C₂²×C₃₁	semidirect
666. #476	C₂²×C₃₁	semidirect
667. #474	C₂²×C₃₁	semidirect
668. #474	C₂²×C₃₁	semidirect
669. #474	C₂²×C₃₁	semidirect
670. #469	C₂²×C₃₁	semidirect
671. #468	C₂²×C₃₁	semidirect
672. #466	C₂²×C₃₁	semidirect
673. #465	C₂²×C₃₁	semidirect
674. #465	C₂²×C₃₁	semidirect
675. #465	C₂²×C₃₁	semidirect
677. #463	C₂²×C₃₁	semidirect
678. #461	C₂²×C₃₁	semidirect
679. #461	C₂²×C₃₁	semidirect
680. #460	C₂²×C₃₁	semidirect
681. #459	C₂²×C₃₁	semidirect
682. #459	C₂²×C₃₁	semidirect
683. #459	C₂²×C₃₁	semidirect
685. #450	C₂²×C₃₁	semidirect
686. #449	C₂²×C₃₁	semidirect
687. #449	C₂²×C₃₁	semidirect
689. #447	C₂²×C₃₁	semidirect
690. #446	C₂²×C₃₁	semidirect
691. C₈×Q₈	C₂²×C₃₁	semidirect
693. #442	C₂²×C₃₁	semidirect
694. #442	C₂²×C₃₁	semidirect
695. #440	C₂²×C₃₁	semidirect
696. #440	C₂²×C₃₁	semidirect
697. #440	C₂²×C₃₁	semidirect
698. C₄×SD₁₆	C₂²×C₃₁	semidirect
699. C₄×SD₁₆	C₂²×C₃₁	semidirect
700. C₄×SD₁₆	C₂²×C₃₁	semidirect
705. C₄×D₈	C₂²×C₃₁	semidirect
706. C₄×D₈	C₂²×C₃₁	semidirect
707. C₄×D₈	C₂²×C₃₁	semidirect
708. C₄×D₈	C₂²×C₃₁	semidirect
709. C₄×D₈	C₂²×C₃₁	semidirect
710. #436	C₂²×C₃₁	semidirect
711. #435	C₂²×C₃₁	semidirect
712. C₈×D₄	C₂²×C₃₁	semidirect
713. C₈×D₄	C₂²×C₃₁	semidirect
714. #433	C₂²×C₃₁	semidirect
715. #432	C₂²×C₃₁	semidirect
716. #428	C₂²×C₃₁	semidirect
717. C₂×#107	C₂²×C₃₁	semidirect
718. #416	C₂²×C₃₁	semidirect
720. C₂×#102	C₂²×C₃₁	semidirect
721. C₂×#102	C₂²×C₃₁	semidirect
722. #405	C₂²×C₃₁	semidirect
723. C₂×C₄×C₈	C₂²×C₃₁	semidirect
913. C₃₁	#61496	direct (N × H)
986. D₈	#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×#3520	2
C₃₁×#3519	2
C₃₁×#3397	2
C₃₁×#3384	2
C₃₁×#3360	2
C₃₁×#3358	2
C₃₁×#3354	2
C₃₁×#3346	2
C₃₁×#3303	2
C₃₁×#3297	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3272	2
C₃₁×#3264	2
C₃₁×#3179	2
C₃₁×#3167	2
C₃₁×#3119	2
C₃₁×#3118	2
C₃₁×#3110	2
C₃₁×#3109	2
C₃₁×#2966	2
C₃₁×#2946	2
C₂×C₄×D₈×C₃₁	2
#61496	31

Subgroups — C31×#61496 #21518255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61496 #21518255