Subgroups — C₃₁×#60570 #21517329

Order 7936.

2152 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₃₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3122	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3106	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3105	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3102	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3100	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3041	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
28	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×#542	—	2	1	no	—
31	C₃₁×#542	C₂²	1	2	yes	complemented
32	C₃₁×#540	—	2	1	no	—
33	C₃₁×#540	C₂²	1	2	yes	complemented
34	C₃₁×#538	—	2	2	no	—
35	C₃₁×#537	C₂²	1	1	yes	characteristic
36	C₃₁×#535	C₂²	1	1	yes	characteristic
37	C₃₁×#535	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#532	—	2	1	no	—
39	C₃₁×#532	C₂²	1	2	yes	complemented
40	C₃₁×#529	—	2	1	no	—
41	C₃₁×#529	C₂²	1	2	yes	complemented
42	C₃₁×#525	—	2	2	no	—
43	C₃₁×#520	—	2	1	no	—
44	C₃₁×#520	C₂²	1	1	yes	characteristic
45	C₃₁×#520	C₂²	1	1	yes	characteristic
46	C₃₁×#520	C₂²	1	2	yes	complemented
47	C₃₁×#518	—	2	2	no	—
48	C₃₁×#518	—	2	1	no	—
49	C₃₁×#518	C₂²	1	1	yes	characteristic
50	C₃₁×#518	C₂²	1	2	yes	complemented
51	C₄×#41×C₃₁	—	2	1	no	—
52	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
53	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
54	C₄×#41×C₃₁	C₂²	1	2	yes	complemented
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₃₁	—	2	1	no	—
57	C₂×C₄×D₄×C₃₁	—	2	2	no	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
60	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#485	C₂²	1	2	yes	complemented
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	complemented
64	C₃₁×#482	C₂²	1	2	yes	complemented
65	C₃₁×#482	C₂²	1	2	yes	complemented
66	C₃₁×#481	C₂²	1	2	yes	complemented
67	C₃₁×#480	C₂²	1	2	yes	complemented
68	C₃₁×#480	C₂²	1	2	yes	complemented
69	C₃₁×#479	C₂²	1	2	yes	complemented
70	C₃₁×#478	C₂²	1	2	yes	complemented
71	C₃₁×#478	C₂²	1	2	yes	complemented
72	C₃₁×#478	C₂²	1	2	yes	complemented
73	C₃₁×#477	C₂²	1	2	yes	complemented
74	C₃₁×#476	C₂²	1	2	yes	complemented
75	C₃₁×#474	C₂²	1	2	yes	complemented
76	C₃₁×#474	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#463	C₂²	1	2	yes	complemented
79	C₃₁×#463	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	complemented
81	C₃₁×#460	C₂²	1	2	yes	complemented
82	C₃₁×#459	C₂²	1	2	yes	complemented
83	C₃₁×#459	C₂²	1	2	yes	complemented
84	C₃₁×#459	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#450	C₂²	1	2	yes	complemented
87	C₃₁×#449	C₂²	1	2	yes	—
88	C₃₁×#449	C₂²	1	2	yes	—
89	C₃₁×#449	C₂²	1	2	yes	complemented
90	C₃₁×#447	C₂²	1	2	yes	—
91	C₃₁×#447	C₂²	1	2	yes	—
92	C₃₁×#447	C₂²	1	2	yes	complemented
93	C₃₁×#442	C₂²	1	2	yes	complemented
94	C₃₁×#442	C₂²	1	2	yes	complemented
95	C₃₁×#440	C₂²	1	2	yes	complemented
96	C₃₁×#440	C₂²	1	2	yes	complemented
97	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
98	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
104	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
108	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
109	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
110	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
111	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
113	C₃₁×#433	C₂²	1	2	yes	complemented
114	C₃₁×#433	C₂²	1	2	yes	complemented
115	C₃₁×#431	C₂²	1	2	yes	complemented
116	C₃₁×#431	C₂²	1	2	yes	complemented
117	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
118	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#424	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#418	C₂²	1	1	yes	characteristic
124	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#417	C₂²	1	1	yes	characteristic
126	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#416	C₂²	1	1	yes	characteristic
128	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#408	C₂²	1	1	yes	characteristic
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×H(5,𝔽₂)	—	2	4	no	—
136	C₃₁×H(5,𝔽₂)	—	2	4	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂×#41×C₃₁	—	2	2	no	—
139	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
140	C₂×#41×C₃₁	C₂³	1	2	yes	—
141	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	—	2	2	no	—
144	C₂²×D₄×C₃₁	—	2	1	no	—
145	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
147	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
148	C₂³×C₄×C₃₁	—	2	1	no	—
149	C₂³×C₄×C₃₁	—	2	2	no	—
150	C₂³×C₄×C₃₁	—	2	1	no	—
151	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
152	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
153	C₃₁×#135	—	2	4	no	—
154	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
159	C₂×D₈×C₃₁	—	2	4	no	—
160	C₂×D₈×C₃₁	C₂³	1	2	yes	—
161	C₂×D₈×C₃₁	C₂³	1	2	yes	—
162	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
163	C₂×D₈×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	2	yes	—
165	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
166	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
167	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
168	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
169	C₃₁×C₄⋊Q₈	—	2	1	no	—
170	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
171	C₃₁×#127	—	2	1	no	—
172	C₃₁×#127	C₂³	1	2	yes	—
173	C₃₁×#126	—	2	2	no	—
174	C₃₁×#126	—	2	2	no	—
175	C₃₁×#125	—	2	1	no	—
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	C₂³	1	2	yes	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	—	2	2	no	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	1	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	—	2	1	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	1	no	—
193	C₃₁×#121	—	2	1	no	—
194	C₃₁×#121	—	2	2	no	—
195	C₃₁×#121	—	2	2	no	—
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₃₁×#121	C₂³	1	2	yes	—
198	C₃₁×#121	C₂³	1	2	yes	—
199	C₃₁×#120	—	2	2	no	—
200	C₃₁×#120	—	2	2	no	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
203	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
209	C₄×D₄×C₃₁	—	2	2	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	1	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	1	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	1	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	2	no	—
218	C₄×D₄×C₃₁	—	2	1	no	—
219	C₄×D₄×C₃₁	—	2	2	no	—
220	C₄×D₄×C₃₁	—	2	1	no	—
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	1	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	1	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	D₄	1	2	yes	—
233	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
234	C₄×D₄×C₃₁	D₄	1	2	yes	—
235	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
236	C₄×D₄×C₃₁	C₂³	1	2	yes	—
237	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₃₁	C₂³	1	2	yes	—
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	2	yes	—
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
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	C₃₁×#117	—	2	1	no	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	2	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	C₂³	1	1	yes	characteristic
254	C₃₁×#117	C₂³	1	1	yes	characteristic
255	C₃₁×#117	C₂³	1	2	yes	—
256	C₃₁×#117	C₂³	1	1	yes	characteristic
257	C₃₁×#117	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₃₁	—	2	2	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	—	2	1	no	—
270	C₂×C₄²×C₃₁	—	2	2	no	—
271	C₂×C₄²×C₃₁	—	2	1	no	—
272	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
274	C₃₁×#107	C₂³	1	2	yes	—
275	C₃₁×#107	C₂³	1	2	yes	—
276	C₃₁×#107	C₂³	1	1	yes	characteristic
277	C₃₁×#107	C₂³	1	1	yes	characteristic
278	C₃₁×#107	C₂³	1	2	yes	—
279	C₃₁×#107	C₂³	1	2	yes	—
280	C₃₁×#106	C₂³	1	1	yes	characteristic
281	C₃₁×#106	C₂³	1	1	yes	characteristic
282	C₃₁×#106	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	2	yes	—
284	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
285	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
286	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	1	yes	characteristic
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	1	yes	characteristic
291	C₃₁×#103	C₂³	1	1	yes	characteristic
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	2	yes	—
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	1	yes	characteristic
299	C₃₁×#102	C₂³	1	1	yes	characteristic
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×#102	C₂³	1	2	yes	—
305	C₃₁×#102	C₂³	1	2	yes	—
306	C₃₁×#102	C₂³	1	2	yes	—
307	C₃₁×#102	C₂³	1	2	yes	—
308	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₃₁×C₂²⋊C₈	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	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₃₁	C₂³	1	2	yes	—
318	C₂⁴×C₃₁	—	2	2	no	—
319	C₂⁴×C₃₁	—	2	1	no	—
320	C₂⁴×C₃₁	—	2	1	no	—
321	#41×C₃₁	—	2	8	no	—
322	#41×C₃₁	—	2	4	no	—
323	#41×C₃₁	—	2	4	no	—
324	#41×C₃₁	—	2	2	no	—
325	#41×C₃₁	—	2	2	no	—
326	#41×C₃₁	—	2	2	no	—
327	#41×C₃₁	—	2	2	no	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	8	4	no	—
330	#41×C₃₁	#41	1	4	yes	complemented
331	C₂×Q₈×C₃₁	—	2	2	no	—
332	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₃₁	—	2	16	no	—
336	C₂×D₄×C₃₁	—	2	8	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	—	2	1	no	—
339	C₂×D₄×C₃₁	—	2	4	no	—
340	C₂×D₄×C₃₁	—	2	4	no	—
341	C₂×D₄×C₃₁	—	2	1	no	—
342	C₂×D₄×C₃₁	—	2	2	no	—
343	C₂×D₄×C₃₁	—	2	2	no	—
344	C₂×D₄×C₃₁	—	2	2	no	—
345	C₂×D₄×C₃₁	—	2	2	no	—
346	C₂×D₄×C₃₁	—	2	1	no	—
347	C₂×D₄×C₃₁	—	2	1	no	—
348	C₂×D₄×C₃₁	—	2	2	no	—
349	C₂×D₄×C₃₁	—	2	2	no	—
350	C₂×D₄×C₃₁	—	2	2	no	—
351	C₂×D₄×C₃₁	—	2	2	no	—
352	C₂×D₄×C₃₁	—	2	2	no	—
353	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
354	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₂×D₄×C₃₁	#41	1	4	yes	complemented
356	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
357	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	2	1	no	—
362	C₂²×C₄×C₃₁	—	2	2	no	—
363	C₂²×C₄×C₃₁	—	2	1	no	—
364	C₂²×C₄×C₃₁	—	2	1	no	—
365	C₂²×C₄×C₃₁	—	2	1	no	—
366	C₂²×C₄×C₃₁	—	2	1	no	—
367	C₂²×C₄×C₃₁	—	2	2	no	—
368	C₂²×C₄×C₃₁	—	2	1	no	—
369	C₂²×C₄×C₃₁	—	2	2	no	—
370	C₂²×C₄×C₃₁	—	2	1	no	—
371	C₂²×C₄×C₃₁	—	2	2	no	—
372	C₂²×C₄×C₃₁	—	2	1	no	—
373	C₂²×C₄×C₃₁	—	2	2	no	—
374	C₂²×C₄×C₃₁	—	2	2	no	—
375	C₂²×C₄×C₃₁	—	2	2	no	—
376	C₂²×C₄×C₃₁	—	2	2	no	—
377	C₂²×C₄×C₃₁	—	8	2	no	—
378	C₂²×C₄×C₃₁	—	8	2	no	—
379	C₂²×C₄×C₃₁	—	8	4	no	—
380	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
384	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
386	Q₁₆×C₃₁	—	2	2	no	—
387	SD₁₆×C₃₁	—	2	2	no	—
388	SD₁₆×C₃₁	—	2	4	no	—
389	SD₁₆×C₃₁	—	2	2	no	—
390	SD₁₆×C₃₁	—	2	4	no	—
391	D₈×C₃₁	—	2	4	no	—
392	D₈×C₃₁	—	2	4	no	—
393	D₈×C₃₁	—	2	2	no	—
394	D₈×C₃₁	—	2	4	no	—
395	D₈×C₃₁	—	2	4	no	—
396	M₁₆×C₃₁	—	2	2	no	—
397	M₁₆×C₃₁	—	2	2	no	—
398	C₂×C₈×C₃₁	—	2	2	no	—
399	C₂×C₈×C₃₁	—	2	2	no	—
400	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
405	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
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	1	no	—
410	C₄⋊C₄×C₃₁	—	2	1	no	—
411	C₄⋊C₄×C₃₁	—	2	1	no	—
412	C₄⋊C₄×C₃₁	—	2	1	no	—
413	C₄⋊C₄×C₃₁	—	2	1	no	—
414	C₄⋊C₄×C₃₁	—	2	2	no	—
415	C₄⋊C₄×C₃₁	—	2	2	no	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	1	no	—
431	C₂²⋊C₄×C₃₁	—	2	2	no	—
432	C₂²⋊C₄×C₃₁	—	2	1	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	1	no	—
439	C₂²⋊C₄×C₃₁	—	2	2	no	—
440	C₂²⋊C₄×C₃₁	—	2	2	no	—
441	C₂²⋊C₄×C₃₁	—	2	1	no	—
442	C₂²⋊C₄×C₃₁	—	2	1	no	—
443	C₂²⋊C₄×C₃₁	—	2	2	no	—
444	C₂²⋊C₄×C₃₁	—	2	2	no	—
445	C₂²⋊C₄×C₃₁	—	2	2	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	2	no	—
448	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
451	C₄²×C₃₁	—	2	1	no	—
452	C₄²×C₃₁	—	2	2	no	—
453	C₄²×C₃₁	—	2	2	no	—
454	C₄²×C₃₁	—	2	1	no	—
455	C₄²×C₃₁	—	2	1	no	—
456	C₄²×C₃₁	—	2	1	no	—
457	C₄²×C₃₁	—	2	1	no	—
458	C₄²×C₃₁	—	2	1	no	—
459	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₃₁	C₂×D₄	1	2	yes	—
461	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
462	C₄²×C₃₁	C₂×D₄	1	2	yes	—
463	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
464	C₄²×C₃₁	C₂⁴	1	2	yes	—
465	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
466	#60570	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂³×C₃₁	—	2	8	no	—
468	C₂³×C₃₁	—	2	2	no	—
469	C₂³×C₃₁	—	2	1	no	—
470	C₂³×C₃₁	—	2	4	no	—
471	C₂³×C₃₁	—	2	2	no	—
472	C₂³×C₃₁	—	2	1	no	—
473	C₂³×C₃₁	—	4	2	no	—
474	C₂³×C₃₁	—	8	1	no	—
475	C₂³×C₃₁	—	8	1	no	—
476	C₂³×C₃₁	—	8	2	no	—
477	C₂³×C₃₁	—	8	1	no	—
478	C₂³×C₃₁	—	8	1	no	—
479	C₂³×C₃₁	—	8	2	no	—
480	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
481	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
482	Q₈×C₃₁	—	2	2	no	—
483	Q₈×C₃₁	—	2	1	no	—
484	Q₈×C₃₁	—	2	1	no	—
485	Q₈×C₃₁	—	2	1	no	—
486	Q₈×C₃₁	—	8	2	no	—
487	Q₈×C₃₁	C₂×#41	1	2	yes	—
488	D₄×C₃₁	—	2	8	no	—
489	D₄×C₃₁	—	2	8	no	—
490	D₄×C₃₁	—	2	4	no	—
491	D₄×C₃₁	—	2	4	no	—
492	D₄×C₃₁	—	2	2	no	—
493	D₄×C₃₁	—	2	4	no	—
494	D₄×C₃₁	—	2	2	no	—
495	D₄×C₃₁	—	2	1	no	—
496	D₄×C₃₁	—	2	2	no	—
497	D₄×C₃₁	—	2	1	no	—
498	D₄×C₃₁	—	2	2	no	—
499	D₄×C₃₁	—	2	1	no	—
500	D₄×C₃₁	—	4	2	no	—
501	D₄×C₃₁	—	4	2	no	—
502	D₄×C₃₁	—	8	2	no	—
503	D₄×C₃₁	—	8	2	no	—
504	D₄×C₃₁	—	8	2	no	—
505	D₄×C₃₁	—	8	2	no	—
506	D₄×C₃₁	—	8	2	no	—
507	D₄×C₃₁	C₂×#41	1	2	yes	—
508	D₄×C₃₁	C₂×#41	1	4	yes	—
509	C₂×C₄×C₃₁	—	2	8	no	—
510	C₂×C₄×C₃₁	—	2	1	no	—
511	C₂×C₄×C₃₁	—	2	4	no	—
512	C₂×C₄×C₃₁	—	2	2	no	—
513	C₂×C₄×C₃₁	—	2	4	no	—
514	C₂×C₄×C₃₁	—	2	2	no	—
515	C₂×C₄×C₃₁	—	2	2	no	—
516	C₂×C₄×C₃₁	—	2	1	no	—
517	C₂×C₄×C₃₁	—	2	1	no	—
518	C₂×C₄×C₃₁	—	2	1	no	—
519	C₂×C₄×C₃₁	—	2	1	no	—
520	C₂×C₄×C₃₁	—	2	2	no	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	2	no	—
523	C₂×C₄×C₃₁	—	4	1	no	—
524	C₂×C₄×C₃₁	—	4	2	no	—
525	C₂×C₄×C₃₁	—	4	2	no	—
526	C₂×C₄×C₃₁	—	4	2	no	—
527	C₂×C₄×C₃₁	—	4	4	no	—
528	C₂×C₄×C₃₁	—	4	4	no	—
529	C₂×C₄×C₃₁	—	4	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	—	8	2	no	—
534	C₂×C₄×C₃₁	—	8	2	no	—
535	C₂×C₄×C₃₁	—	8	2	no	—
536	C₂×C₄×C₃₁	—	8	2	no	—
537	C₂×C₄×C₃₁	—	8	1	no	—
538	C₂×C₄×C₃₁	—	8	2	no	—
539	C₂×C₄×C₃₁	—	8	1	no	—
540	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
542	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
549	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
550	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
551	C₈×C₃₁	—	2	1	no	—
552	C₈×C₃₁	—	2	1	no	—
553	C₈×C₃₁	—	2	1	no	—
554	C₈×C₃₁	—	2	1	no	—
555	C₈×C₃₁	—	2	2	no	—
556	C₈×C₃₁	—	2	2	no	—
557	#3460	C₂×C₃₁	1	1	yes	characteristic, complemented
558	C₄×H(5,𝔽₂)	C₂×C₃₁	1	1	yes	characteristic, complemented
559	#3124	C₂×C₃₁	1	2	yes	complemented
560	#3122	C₂×C₃₁	1	2	yes	complemented
561	#3119	C₂×C₃₁	1	2	yes	complemented
562	#3118	C₂×C₃₁	1	2	yes	complemented
563	#3106	C₂×C₃₁	1	2	yes	complemented
564	#3105	C₂×C₃₁	1	2	yes	complemented
565	#3102	C₂×C₃₁	1	2	yes	complemented
566	#3100	C₂×C₃₁	1	2	yes	complemented
567	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
569	#3083	C₂×C₃₁	1	1	yes	characteristic, complemented
570	#3081	C₂×C₃₁	1	1	yes	characteristic, complemented
571	#3045	C₂×C₃₁	1	1	yes	characteristic, complemented
572	#3041	C₂×C₃₁	1	1	yes	characteristic, complemented
573	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
574	#3008	C₂×C₃₁	1	1	yes	characteristic, complemented
575	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
576	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
577	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
578	C₂×C₄×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#2922	C₂×C₃₁	1	1	yes	characteristic, complemented
580	C₂²×C₃₁	—	2	1	no	—
581	C₂²×C₃₁	—	2	1	no	—
582	C₂²×C₃₁	—	2	2	no	—
583	C₂²×C₃₁	—	2	2	no	—
584	C₂²×C₃₁	—	2	4	no	—
585	C₂²×C₃₁	—	2	2	no	—
586	C₂²×C₃₁	—	2	2	no	—
587	C₂²×C₃₁	—	4	2	no	—
588	C₂²×C₃₁	—	4	1	no	—
589	C₂²×C₃₁	—	4	2	no	—
590	C₂²×C₃₁	—	4	1	no	—
591	C₂²×C₃₁	—	4	1	no	—
592	C₂²×C₃₁	—	4	2	no	—
593	C₂²×C₃₁	—	4	1	no	—
594	C₂²×C₃₁	—	4	2	no	—
595	C₂²×C₃₁	—	4	2	no	—
596	C₂²×C₃₁	—	4	1	no	—
597	C₂²×C₃₁	—	8	4	no	—
598	C₂²×C₃₁	—	8	4	no	—
599	C₂²×C₃₁	—	8	8	no	—
600	C₂²×C₃₁	#525	1	2	yes	—
601	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
602	C₄×C₃₁	—	2	1	no	—
603	C₄×C₃₁	—	2	1	no	—
604	C₄×C₃₁	—	2	2	no	—
605	C₄×C₃₁	—	2	2	no	—
606	C₄×C₃₁	—	2	2	no	—
607	C₄×C₃₁	—	2	1	no	—
608	C₄×C₃₁	—	2	2	no	—
609	C₄×C₃₁	—	4	1	no	—
610	C₄×C₃₁	—	4	1	no	—
611	C₄×C₃₁	—	4	1	no	—
612	C₄×C₃₁	—	4	2	no	—
613	C₄×C₃₁	—	4	1	no	—
614	C₄×C₃₁	—	4	2	no	—
615	C₄×C₃₁	—	4	1	no	—
616	C₄×C₃₁	#525	1	2	yes	—
617	C₄×C₃₁	#576	1	2	yes	—
618	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
619	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
620	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
621	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
622	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
623	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
624	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
625	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
626	#542	—	2	1	no	—
627	#542	C₂²×C₃₁	1	2	yes	complemented
628	#540	—	2	1	no	—
629	#540	C₂²×C₃₁	1	2	yes	complemented
630	#538	—	2	2	no	—
631	#537	C₂²×C₃₁	1	1	yes	characteristic
632	#535	C₂²×C₃₁	1	1	yes	characteristic
633	#535	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#532	—	2	1	no	—
635	#532	C₂²×C₃₁	1	2	yes	complemented
636	#529	—	2	1	no	—
637	#529	C₂²×C₃₁	1	2	yes	complemented
638	#525	—	2	2	no	—
639	#520	—	2	1	no	—
640	#520	C₂²×C₃₁	1	1	yes	characteristic
641	#520	C₂²×C₃₁	1	1	yes	characteristic
642	#520	C₂²×C₃₁	1	2	yes	complemented
643	#518	—	2	2	no	—
644	#518	—	2	1	no	—
645	#518	C₂²×C₃₁	1	1	yes	characteristic
646	#518	C₂²×C₃₁	1	2	yes	complemented
647	C₄×#41	—	2	1	no	—
648	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
649	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
650	C₄×#41	C₂²×C₃₁	1	2	yes	complemented
651	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
652	C₂×C₄×D₄	—	2	1	no	—
653	C₂×C₄×D₄	—	2	2	no	—
654	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
655	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
656	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
657	#485	C₂²×C₃₁	1	2	yes	complemented
658	#484	C₂²×C₃₁	1	2	yes	complemented
659	#482	C₂²×C₃₁	1	2	yes	complemented
660	#482	C₂²×C₃₁	1	2	yes	complemented
661	#482	C₂²×C₃₁	1	2	yes	complemented
662	#481	C₂²×C₃₁	1	2	yes	complemented
663	#480	C₂²×C₃₁	1	2	yes	complemented
664	#480	C₂²×C₃₁	1	2	yes	complemented
665	#479	C₂²×C₃₁	1	2	yes	complemented
666	#478	C₂²×C₃₁	1	2	yes	complemented
667	#478	C₂²×C₃₁	1	2	yes	complemented
668	#478	C₂²×C₃₁	1	2	yes	complemented
669	#477	C₂²×C₃₁	1	2	yes	complemented
670	#476	C₂²×C₃₁	1	2	yes	complemented
671	#474	C₂²×C₃₁	1	2	yes	complemented
672	#474	C₂²×C₃₁	1	2	yes	complemented
673	#464	C₂²×C₃₁	1	2	yes	complemented
674	#463	C₂²×C₃₁	1	2	yes	complemented
675	#463	C₂²×C₃₁	1	2	yes	complemented
676	#463	C₂²×C₃₁	1	2	yes	complemented
677	#460	C₂²×C₃₁	1	2	yes	complemented
678	#459	C₂²×C₃₁	1	2	yes	complemented
679	#459	C₂²×C₃₁	1	2	yes	complemented
680	#459	C₂²×C₃₁	1	2	yes	complemented
681	#452	C₂²×C₃₁	1	2	yes	complemented
682	#450	C₂²×C₃₁	1	2	yes	complemented
683	#449	C₂²×C₃₁	1	2	yes	—
684	#449	C₂²×C₃₁	1	2	yes	—
685	#449	C₂²×C₃₁	1	2	yes	complemented
686	#447	C₂²×C₃₁	1	2	yes	—
687	#447	C₂²×C₃₁	1	2	yes	—
688	#447	C₂²×C₃₁	1	2	yes	complemented
689	#442	C₂²×C₃₁	1	2	yes	complemented
690	#442	C₂²×C₃₁	1	2	yes	complemented
691	#440	C₂²×C₃₁	1	2	yes	complemented
692	#440	C₂²×C₃₁	1	2	yes	complemented
693	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
695	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
696	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
697	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
702	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
703	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
704	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
705	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
706	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
707	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
709	#433	C₂²×C₃₁	1	2	yes	complemented
710	#433	C₂²×C₃₁	1	2	yes	complemented
711	#431	C₂²×C₃₁	1	2	yes	complemented
712	#431	C₂²×C₃₁	1	2	yes	complemented
713	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
714	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#424	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#418	C₂²×C₃₁	1	1	yes	characteristic
720	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
721	#417	C₂²×C₃₁	1	1	yes	characteristic
722	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
723	#416	C₂²×C₃₁	1	1	yes	characteristic
724	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
725	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
726	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
727	#408	C₂²×C₃₁	1	1	yes	characteristic
728	#408	C₂²×C₃₁	1	1	yes	characteristic
729	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	C₂×C₃₁	—	2	2	no	—
732	C₂×C₃₁	—	4	2	no	—
733	C₂×C₃₁	—	4	4	no	—
734	C₂×C₃₁	—	4	2	no	—
735	C₂×C₃₁	—	8	1	no	—
736	C₂×C₃₁	—	8	2	no	—
737	C₂×C₃₁	C₂×#525	1	1	yes	characteristic
738	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
739	C₂×C₃₁	#3584	1	1	yes	characteristic
740	H(5,𝔽₂)	—	2	4	no	—
741	H(5,𝔽₂)	—	2	4	no	—
742	C₂×#41	—	2	1	no	—
743	C₂×#41	—	2	2	no	—
744	C₂×#41	C₂³×C₃₁	1	2	yes	—
745	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
746	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
748	C₂²×D₄	—	2	2	no	—
749	C₂²×D₄	—	2	1	no	—
750	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
751	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
752	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
753	C₂³×C₄	—	2	1	no	—
754	C₂³×C₄	—	2	2	no	—
755	C₂³×C₄	—	2	1	no	—
756	AGL(1,ℤ/8)	—	2	4	no	—
757	AGL(1,ℤ/8)	—	2	4	no	—
758	#135	—	2	4	no	—
759	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
764	C₂×D₈	—	2	4	no	—
765	C₂×D₈	C₂³×C₃₁	1	2	yes	—
766	C₂×D₈	C₂³×C₃₁	1	2	yes	—
767	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
768	C₂×D₈	C₂³×C₃₁	1	2	yes	—
769	C₂×D₈	C₂³×C₃₁	1	2	yes	—
770	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
771	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
776	#127	—	2	1	no	—
777	#127	C₂³×C₃₁	1	2	yes	—
778	#126	—	2	2	no	—
779	#126	—	2	2	no	—
780	#125	—	2	1	no	—
781	#125	C₂³×C₃₁	1	2	yes	—
782	#124	—	2	1	no	—
783	#124	—	2	2	no	—
784	#124	—	2	2	no	—
785	#124	C₂³×C₃₁	1	2	yes	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
794	#121	—	2	2	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	C₂³×C₃₁	1	2	yes	—
802	#121	C₂³×C₃₁	1	2	yes	—
803	#121	C₂³×C₃₁	1	2	yes	—
804	#120	—	2	2	no	—
805	#120	—	2	2	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
808	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
809	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
810	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
812	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
813	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
814	C₄×D₄	—	2	2	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	1	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	2	2	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
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	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	2	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	2	no	—
837	C₄×D₄	D₄×C₃₁	1	2	yes	—
838	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
839	C₄×D₄	D₄×C₃₁	1	2	yes	—
840	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₃₁	1	2	yes	—
842	C₄×D₄	C₂³×C₃₁	1	2	yes	—
843	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
844	C₄×D₄	C₂³×C₃₁	1	2	yes	—
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	1	yes	characteristic
849	C₄×D₄	C₂³×C₃₁	1	2	yes	—
850	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
851	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
852	#117	—	2	1	no	—
853	#117	—	2	2	no	—
854	#117	—	2	1	no	—
855	#117	—	2	2	no	—
856	#117	—	2	1	no	—
857	#117	—	2	2	no	—
858	#117	C₂³×C₃₁	1	1	yes	characteristic
859	#117	C₂³×C₃₁	1	2	yes	—
860	#117	C₂³×C₃₁	1	1	yes	characteristic
861	#117	C₂³×C₃₁	1	1	yes	characteristic
862	#117	C₂³×C₃₁	1	2	yes	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	2	no	—
865	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
867	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
868	C₂×C₂²⋊C₄	—	2	1	no	—
869	C₂×C₂²⋊C₄	—	2	2	no	—
870	C₂×C₂²⋊C₄	—	2	1	no	—
871	C₂×C₂²⋊C₄	—	2	2	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	C₂×C₂²⋊C₄	—	2	2	no	—
874	C₂×C₄²	—	2	1	no	—
875	C₂×C₄²	—	2	2	no	—
876	C₂×C₄²	—	2	1	no	—
877	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
878	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
879	#107	C₂³×C₃₁	1	2	yes	—
880	#107	C₂³×C₃₁	1	2	yes	—
881	#107	C₂³×C₃₁	1	1	yes	characteristic
882	#107	C₂³×C₃₁	1	1	yes	characteristic
883	#107	C₂³×C₃₁	1	2	yes	—
884	#107	C₂³×C₃₁	1	2	yes	—
885	#106	C₂³×C₃₁	1	1	yes	characteristic
886	#106	C₂³×C₃₁	1	1	yes	characteristic
887	#106	C₂³×C₃₁	1	2	yes	—
888	#106	C₂³×C₃₁	1	2	yes	—
889	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
890	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
891	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
892	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
893	#103	C₂³×C₃₁	1	1	yes	characteristic
894	#103	C₂³×C₃₁	1	1	yes	characteristic
895	#103	C₂³×C₃₁	1	1	yes	characteristic
896	#103	C₂³×C₃₁	1	1	yes	characteristic
897	#103	C₂³×C₃₁	1	2	yes	—
898	#103	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	#102	C₂³×C₃₁	1	1	yes	characteristic
904	#102	C₂³×C₃₁	1	1	yes	characteristic
905	#102	C₂³×C₃₁	1	1	yes	characteristic
906	#102	C₂³×C₃₁	1	1	yes	characteristic
907	#102	C₂³×C₃₁	1	2	yes	—
908	#102	C₂³×C₃₁	1	2	yes	—
909	#102	C₂³×C₃₁	1	2	yes	—
910	#102	C₂³×C₃₁	1	2	yes	—
911	#102	C₂³×C₃₁	1	2	yes	—
912	#102	C₂³×C₃₁	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
916	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
917	#97	C₂³×C₃₁	1	2	yes	—
918	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
919	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
920	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
921	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
922	C₄×C₈	C₂³×C₃₁	1	2	yes	—
923	C₃₁	#60570	1	1	yes	characteristic, direct product factor, Sylow
924	C₂⁴	—	2	2	no	—
925	C₂⁴	—	2	1	no	—
926	C₂⁴	—	2	1	no	—
927	#41	—	2	8	no	—
928	#41	—	2	4	no	—
929	#41	—	2	4	no	—
930	#41	—	2	2	no	—
931	#41	—	2	2	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	8	4	no	—
936	#41	#41×C₃₁	1	4	yes	complemented
937	C₂×Q₈	—	2	2	no	—
938	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
939	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
940	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
941	C₂×D₄	—	2	16	no	—
942	C₂×D₄	—	2	8	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	4	no	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	1	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	2	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
960	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₂×D₄	#41×C₃₁	1	4	yes	complemented
962	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
963	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
965	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	2	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	2	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	8	2	no	—
984	C₂²×C₄	—	8	2	no	—
985	C₂²×C₄	—	8	4	no	—
986	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
987	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
989	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
990	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
991	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
992	Q₁₆	—	2	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	4	no	—
995	SD₁₆	—	2	2	no	—
996	SD₁₆	—	2	4	no	—
997	D₈	—	2	4	no	—
998	D₈	—	2	4	no	—
999	D₈	—	2	2	no	—
1000	D₈	—	2	4	no	—
1001	D₈	—	2	4	no	—
1002	M₁₆	—	2	2	no	—
1003	M₁₆	—	2	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1009	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1011	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	—	2	2	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	2	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1025	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1026	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1027	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1028	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1029	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1030	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1031	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1032	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1033	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	2	no	—
1038	C₂²⋊C₄	—	2	1	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	—	2	1	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1055	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1056	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1057	C₄²	—	2	1	no	—
1058	C₄²	—	2	1	no	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	2	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1066	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1067	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1068	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1069	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1070	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1071	C₄²	C₂⁴×C₃₁	1	2	yes	—
1072	C₂³	—	2	8	no	—
1073	C₂³	—	2	2	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	2	4	no	—
1076	C₂³	—	2	2	no	—
1077	C₂³	—	2	1	no	—
1078	C₂³	—	4	2	no	—
1079	C₂³	—	8	1	no	—
1080	C₂³	—	8	1	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	—	8	1	no	—
1083	C₂³	—	8	1	no	—
1084	C₂³	—	8	2	no	—
1085	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1086	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1087	Q₈	—	2	2	no	—
1088	Q₈	—	2	1	no	—
1089	Q₈	—	2	1	no	—
1090	Q₈	—	2	1	no	—
1091	Q₈	—	8	2	no	—
1092	Q₈	C₂×#41×C₃₁	1	2	yes	—
1093	D₄	—	2	8	no	—
1094	D₄	—	2	8	no	—
1095	D₄	—	2	4	no	—
1096	D₄	—	2	4	no	—
1097	D₄	—	2	2	no	—
1098	D₄	—	2	4	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	8	2	no	—
1108	D₄	—	8	2	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	C₂×#41×C₃₁	1	2	yes	—
1113	D₄	C₂×#41×C₃₁	1	4	yes	—
1114	C₂×C₄	—	2	8	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	4	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	4	no	—
1119	C₂×C₄	—	2	2	no	—
1120	C₂×C₄	—	2	2	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	2	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	4	2	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	4	no	—
1133	C₂×C₄	—	4	4	no	—
1134	C₂×C₄	—	4	2	no	—
1135	C₂×C₄	—	8	1	no	—
1136	C₂×C₄	—	8	1	no	—
1137	C₂×C₄	—	8	2	no	—
1138	C₂×C₄	—	8	2	no	—
1139	C₂×C₄	—	8	2	no	—
1140	C₂×C₄	—	8	2	no	—
1141	C₂×C₄	—	8	2	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	—	8	1	no	—
1145	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1146	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1147	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1148	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1149	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1150	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1151	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1152	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1153	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1154	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1155	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	2	2	no	—
1161	C₈	—	2	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	4	no	—
1166	C₂²	—	2	2	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	2	no	—
1169	C₂²	—	4	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	1	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	8	4	no	—
1180	C₂²	—	8	4	no	—
1181	C₂²	—	8	8	no	—
1182	C₂²	C₃₁×#525	1	2	yes	—
1183	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1184	C₄	—	2	2	no	—
1185	C₄	—	2	2	no	—
1186	C₄	—	2	1	no	—
1187	C₄	—	2	2	no	—
1188	C₄	—	2	1	no	—
1189	C₄	—	2	1	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	4	1	no	—
1192	C₄	—	4	2	no	—
1193	C₄	—	4	1	no	—
1194	C₄	—	4	2	no	—
1195	C₄	—	4	1	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	C₃₁×#525	1	2	yes	—
1199	C₄	C₃₁×#576	1	2	yes	—
1200	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1201	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1202	C₂	—	2	2	no	—
1203	C₂	—	4	2	no	—
1204	C₂	—	4	4	no	—
1205	C₂	—	4	2	no	—
1206	C₂	—	8	2	no	—
1207	C₂	—	8	1	no	—
1208	C₂	C₂×C₃₁×#525	1	1	yes	characteristic
1209	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1210	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3460	C₂	semidirect
2. C₄×C₃₁×H(5,𝔽₂)	C₂	semidirect
3. C₃₁×#3124	C₂	semidirect
4. C₃₁×#3122	C₂	semidirect
5. C₃₁×#3119	C₂	semidirect
6. C₃₁×#3118	C₂	semidirect
7. C₃₁×#3106	C₂	semidirect
8. C₃₁×#3105	C₂	semidirect
9. C₃₁×#3102	C₂	semidirect
10. C₃₁×#3100	C₂	semidirect
11. C₃₁×#3098	C₂	semidirect
12. C₃₁×#3096	C₂	semidirect
13. C₃₁×#3083	C₂	semidirect
14. C₃₁×#3081	C₂	semidirect
15. C₃₁×#3045	C₂	semidirect
16. C₃₁×#3041	C₂	semidirect
17. C₃₁×#3012	C₂	semidirect
18. C₃₁×#3008	C₂	semidirect
19. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
20. C₄×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
21. C₄×C₃₁×#135	C₂	semidirect
22. C₂×C₄×D₈×C₃₁	C₂	semidirect
23. C₃₁×#2922	C₂	semidirect
29. C₃₁×#544	C₂²	semidirect
31. C₃₁×#542	C₂²	semidirect
33. C₃₁×#540	C₂²	semidirect
37. C₃₁×#535	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
41. C₃₁×#529	C₂²	semidirect
46. C₃₁×#520	C₂²	semidirect
50. C₃₁×#518	C₂²	semidirect
54. C₄×#41×C₃₁	C₂²	semidirect
55. C₄×#41×C₃₁	C₂²	semidirect
59. C₂×C₄×D₄×C₃₁	C₂²	semidirect
60. C₂×C₄×D₄×C₃₁	C₂²	semidirect
61. C₃₁×#485	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
63. C₃₁×#482	C₂²	semidirect
64. C₃₁×#482	C₂²	semidirect
65. C₃₁×#482	C₂²	semidirect
66. C₃₁×#481	C₂²	semidirect
67. C₃₁×#480	C₂²	semidirect
68. C₃₁×#480	C₂²	semidirect
69. C₃₁×#479	C₂²	semidirect
70. C₃₁×#478	C₂²	semidirect
71. C₃₁×#478	C₂²	semidirect
72. C₃₁×#478	C₂²	semidirect
73. C₃₁×#477	C₂²	semidirect
74. C₃₁×#476	C₂²	semidirect
75. C₃₁×#474	C₂²	semidirect
76. C₃₁×#474	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#463	C₂²	semidirect
79. C₃₁×#463	C₂²	semidirect
80. C₃₁×#463	C₂²	semidirect
81. C₃₁×#460	C₂²	semidirect
82. C₃₁×#459	C₂²	semidirect
83. C₃₁×#459	C₂²	semidirect
84. C₃₁×#459	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
86. C₃₁×#450	C₂²	semidirect
89. C₃₁×#449	C₂²	semidirect
92. C₃₁×#447	C₂²	semidirect
93. C₃₁×#442	C₂²	semidirect
94. C₃₁×#442	C₂²	semidirect
95. C₃₁×#440	C₂²	semidirect
96. C₃₁×#440	C₂²	semidirect
97. C₄×Q₁₆×C₃₁	C₂²	semidirect
98. C₄×Q₁₆×C₃₁	C₂²	semidirect
99. C₄×SD₁₆×C₃₁	C₂²	semidirect
100. C₄×SD₁₆×C₃₁	C₂²	semidirect
101. C₄×SD₁₆×C₃₁	C₂²	semidirect
102. C₄×SD₁₆×C₃₁	C₂²	semidirect
103. C₄×SD₁₆×C₃₁	C₂²	semidirect
104. C₄×SD₁₆×C₃₁	C₂²	semidirect
105. C₄×D₈×C₃₁	C₂²	semidirect
106. C₄×D₈×C₃₁	C₂²	semidirect
107. C₄×D₈×C₃₁	C₂²	semidirect
108. C₄×D₈×C₃₁	C₂²	semidirect
109. C₄×D₈×C₃₁	C₂²	semidirect
110. C₄×D₈×C₃₁	C₂²	semidirect
111. C₄×D₈×C₃₁	C₂²	semidirect
112. C₄×D₈×C₃₁	C₂²	semidirect
113. C₃₁×#433	C₂²	semidirect
114. C₃₁×#433	C₂²	semidirect
115. C₃₁×#431	C₂²	semidirect
116. C₃₁×#431	C₂²	semidirect
117. C₃₁×#428	C₂²	semidirect
118. C₃₁×#428	C₂²	semidirect
119. C₃₁×#427	C₂²	semidirect
120. C₂×C₃₁×#107	C₂²	semidirect
121. C₃₁×#424	C₂²	semidirect
122. C₃₁×#424	C₂²	semidirect
124. C₃₁×#418	C₂²	semidirect
126. C₃₁×#417	C₂²	semidirect
128. C₃₁×#416	C₂²	semidirect
130. C₂×C₃₁×#102	C₂²	semidirect
133. C₄×M₁₆×C₃₁	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
330. #41×C₃₁	#41	semidirect
355. C₂×D₄×C₃₁	#41	semidirect
466. #60570	C₃₁	direct (N × H)
557. #3460	C₂×C₃₁	semidirect
558. C₄×H(5,𝔽₂)	C₂×C₃₁	semidirect
559. #3124	C₂×C₃₁	semidirect
560. #3122	C₂×C₃₁	semidirect
561. #3119	C₂×C₃₁	semidirect
562. #3118	C₂×C₃₁	semidirect
563. #3106	C₂×C₃₁	semidirect
564. #3105	C₂×C₃₁	semidirect
565. #3102	C₂×C₃₁	semidirect
566. #3100	C₂×C₃₁	semidirect
567. #3098	C₂×C₃₁	semidirect
568. #3096	C₂×C₃₁	semidirect
569. #3083	C₂×C₃₁	semidirect
570. #3081	C₂×C₃₁	semidirect
571. #3045	C₂×C₃₁	semidirect
572. #3041	C₂×C₃₁	semidirect
573. #3012	C₂×C₃₁	semidirect
574. #3008	C₂×C₃₁	semidirect
575. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
576. C₄×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
577. C₄×#135	C₂×C₃₁	semidirect
578. C₂×C₄×D₈	C₂×C₃₁	semidirect
579. #2922	C₂×C₃₁	semidirect
625. #544	C₂²×C₃₁	semidirect
627. #542	C₂²×C₃₁	semidirect
629. #540	C₂²×C₃₁	semidirect
633. #535	C₂²×C₃₁	semidirect
635. #532	C₂²×C₃₁	semidirect
637. #529	C₂²×C₃₁	semidirect
642. #520	C₂²×C₃₁	semidirect
646. #518	C₂²×C₃₁	semidirect
650. C₄×#41	C₂²×C₃₁	semidirect
651. C₄×#41	C₂²×C₃₁	semidirect
655. C₂×C₄×D₄	C₂²×C₃₁	semidirect
656. C₂×C₄×D₄	C₂²×C₃₁	semidirect
657. #485	C₂²×C₃₁	semidirect
658. #484	C₂²×C₃₁	semidirect
659. #482	C₂²×C₃₁	semidirect
660. #482	C₂²×C₃₁	semidirect
661. #482	C₂²×C₃₁	semidirect
662. #481	C₂²×C₃₁	semidirect
663. #480	C₂²×C₃₁	semidirect
664. #480	C₂²×C₃₁	semidirect
665. #479	C₂²×C₃₁	semidirect
666. #478	C₂²×C₃₁	semidirect
667. #478	C₂²×C₃₁	semidirect
668. #478	C₂²×C₃₁	semidirect
669. #477	C₂²×C₃₁	semidirect
670. #476	C₂²×C₃₁	semidirect
671. #474	C₂²×C₃₁	semidirect
672. #474	C₂²×C₃₁	semidirect
673. #464	C₂²×C₃₁	semidirect
674. #463	C₂²×C₃₁	semidirect
675. #463	C₂²×C₃₁	semidirect
676. #463	C₂²×C₃₁	semidirect
677. #460	C₂²×C₃₁	semidirect
678. #459	C₂²×C₃₁	semidirect
679. #459	C₂²×C₃₁	semidirect
680. #459	C₂²×C₃₁	semidirect
681. #452	C₂²×C₃₁	semidirect
682. #450	C₂²×C₃₁	semidirect
685. #449	C₂²×C₃₁	semidirect
688. #447	C₂²×C₃₁	semidirect
689. #442	C₂²×C₃₁	semidirect
690. #442	C₂²×C₃₁	semidirect
691. #440	C₂²×C₃₁	semidirect
692. #440	C₂²×C₃₁	semidirect
693. C₄×Q₁₆	C₂²×C₃₁	semidirect
694. C₄×Q₁₆	C₂²×C₃₁	semidirect
695. C₄×SD₁₆	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
701. C₄×D₈	C₂²×C₃₁	semidirect
702. C₄×D₈	C₂²×C₃₁	semidirect
703. C₄×D₈	C₂²×C₃₁	semidirect
704. C₄×D₈	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. #433	C₂²×C₃₁	semidirect
710. #433	C₂²×C₃₁	semidirect
711. #431	C₂²×C₃₁	semidirect
712. #431	C₂²×C₃₁	semidirect
713. #428	C₂²×C₃₁	semidirect
714. #428	C₂²×C₃₁	semidirect
715. #427	C₂²×C₃₁	semidirect
716. C₂×#107	C₂²×C₃₁	semidirect
717. #424	C₂²×C₃₁	semidirect
718. #424	C₂²×C₃₁	semidirect
720. #418	C₂²×C₃₁	semidirect
722. #417	C₂²×C₃₁	semidirect
724. #416	C₂²×C₃₁	semidirect
726. C₂×#102	C₂²×C₃₁	semidirect
729. C₄×M₁₆	C₂²×C₃₁	semidirect
730. C₂×C₄×C₈	C₂²×C₃₁	semidirect
923. C₃₁	#60570	direct (N × H)
936. #41	#41×C₃₁	semidirect
961. C₂×D₄	#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×#3460	2
C₄×C₃₁×H(5,𝔽₂)	2
C₃₁×#3124	2
C₃₁×#3122	2
C₃₁×#3119	2
C₃₁×#3118	2
C₃₁×#3106	2
C₃₁×#3105	2
C₃₁×#3102	2
C₃₁×#3100	2
C₃₁×#3098	2
C₃₁×#3096	2
C₃₁×#3083	2
C₃₁×#3081	2
C₃₁×#3045	2
C₃₁×#3041	2
C₃₁×#3012	2
C₃₁×#3008	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₄×C₃₁×#135	2
C₂×C₄×D₈×C₃₁	2
C₃₁×#2922	2
#60570	31

Subgroups — C31×#60570 #21517329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60570 #21517329