Subgroups — C₃₁×#61216 #21517975

Order 7936.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3326	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3323	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3300	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3297	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3296	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3080	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
25	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
29	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
30	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#553	—	2	2	no	—
32	C₃₁×#553	—	2	2	no	—
33	C₃₁×#553	C₂²	1	2	yes	complemented
34	C₃₁×#553	C₂²	1	2	yes	complemented
35	C₃₁×#552	C₂²	1	2	yes	complemented
36	C₃₁×#552	C₂²	1	2	yes	complemented
37	C₃₁×#548	C₂²	1	2	yes	—
38	C₃₁×#548	C₂²	1	2	yes	—
39	C₃₁×#546	—	2	2	no	—
40	C₃₁×#546	—	2	2	no	—
41	C₃₁×#546	C₂²	1	2	yes	—
42	C₃₁×#546	C₂²	1	2	yes	—
43	C₃₁×#541	—	2	1	no	—
44	C₃₁×#540	—	2	1	no	—
45	C₃₁×#537	C₂²	1	1	yes	characteristic
46	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#536	—	2	1	no	—
48	C₃₁×#536	C₂²	1	1	yes	characteristic
49	C₃₁×#535	—	2	1	no	—
50	C₃₁×#535	C₂²	1	1	yes	characteristic
51	C₃₁×#532	—	2	1	no	—
52	C₃₁×#532	C₂²	1	1	yes	characteristic
53	C₃₁×#529	—	2	1	no	—
54	C₃₁×#529	—	2	1	no	—
55	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₃₁×#124	—	2	1	no	—
57	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
58	C₃₁×#520	C₂²	1	1	yes	characteristic
59	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
61	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
62	C₃₁×#488	C₂²	1	2	yes	complemented
63	C₃₁×#488	C₂²	1	2	yes	complemented
64	C₃₁×#488	C₂²	1	2	yes	complemented
65	C₃₁×#488	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#485	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#483	C₂²	1	2	yes	complemented
70	C₃₁×#482	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#480	C₂²	1	2	yes	complemented
74	C₃₁×#479	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#478	C₂²	1	2	yes	complemented
78	C₃₁×#470	C₂²	1	2	yes	complemented
79	C₃₁×#469	C₂²	1	2	yes	complemented
80	C₃₁×#468	C₂²	1	2	yes	complemented
81	C₃₁×#468	C₂²	1	2	yes	complemented
82	C₃₁×#467	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×#464	C₂²	1	2	yes	complemented
87	C₃₁×#464	C₂²	1	2	yes	complemented
88	C₃₁×#463	C₂²	1	2	yes	complemented
89	C₃₁×#463	C₂²	1	2	yes	complemented
90	C₃₁×#452	C₂²	1	2	yes	—
91	C₃₁×#452	C₂²	1	2	yes	complemented
92	C₃₁×#451	C₂²	1	2	yes	complemented
93	C₃₁×#450	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	complemented
96	C₃₁×#448	C₂²	1	2	yes	complemented
97	C₃₁×#447	C₂²	1	2	yes	—
98	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
100	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, 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×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#436	C₂²	1	2	yes	complemented
107	C₃₁×#436	C₂²	1	2	yes	complemented
108	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
109	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
110	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
111	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
112	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
114	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
115	C₃₁×#419	C₂²	1	2	yes	complemented
116	C₃₁×#418	C₂²	1	1	yes	characteristic
117	C₃₁×#418	C₂²	1	2	yes	—
118	C₃₁×#417	C₂²	1	1	yes	characteristic
119	C₃₁×#417	C₂²	1	1	yes	characteristic
120	C₃₁×#417	C₂²	1	2	yes	—
121	C₃₁×#417	C₂²	1	2	yes	complemented
122	C₃₁×#416	C₂²	1	1	yes	characteristic
123	C₃₁×#416	C₂²	1	2	yes	—
124	C₃₁×#416	C₂²	1	2	yes	complemented
125	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
129	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
130	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#102	C₂²	1	2	yes	—
132	C₃₁×#408	C₂²	1	1	yes	characteristic
133	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
135	C₃₁×2₋¹⁺⁴	—	2	4	no	—
136	C₃₁×2₋¹⁺⁴	—	4	2	no	—
137	C₃₁×H(5,𝔽₂)	—	2	4	no	—
138	C₃₁×H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	1	no	—
141	C₂×#41×C₃₁	—	2	2	no	—
142	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
143	C₂×#41×C₃₁	C₂³	1	2	yes	—
144	C₂×#41×C₃₁	C₂³	1	2	yes	—
145	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₃₁	—	2	1	no	—
149	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
151	C₂²×D₄×C₃₁	—	2	1	no	—
152	C₂²×D₄×C₃₁	—	2	2	no	—
153	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
155	C₃₁×#137	—	4	2	no	—
156	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
157	C₃₁×#135	—	2	4	no	—
158	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
159	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
164	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₃₁	C₂³	1	2	yes	—
166	C₃₁×#131	—	4	2	no	—
167	C₃₁×#131	—	4	2	no	—
168	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
171	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
172	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
175	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
176	C₃₁×C₄⋊Q₈	—	2	1	no	—
177	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
178	C₃₁×#127	—	2	1	no	—
179	C₃₁×#127	D₄	1	1	yes	characteristic
180	C₃₁×#126	—	2	2	no	—
181	C₃₁×#126	—	2	2	no	—
182	C₃₁×#126	—	2	2	no	—
183	C₃₁×#126	—	2	2	no	—
184	C₃₁×#125	—	2	2	no	—
185	C₃₁×#125	—	2	2	no	—
186	C₃₁×#125	—	2	1	no	—
187	C₃₁×#125	—	2	1	no	—
188	C₃₁×#125	C₂³	1	2	yes	—
189	C₃₁×#125	C₂³	1	2	yes	—
190	C₃₁×#124	—	2	1	no	—
191	C₃₁×#124	—	2	1	no	—
192	C₃₁×#124	—	2	2	no	—
193	C₃₁×#124	—	2	2	no	—
194	C₃₁×#124	—	2	1	no	—
195	C₃₁×#124	—	2	1	no	—
196	C₃₁×#124	D₄	1	1	yes	characteristic
197	C₃₁×#124	D₄	1	1	yes	characteristic
198	C₃₁×#124	C₂³	1	2	yes	—
199	C₃₁×#124	C₂³	1	2	yes	—
200	C₃₁×#123	—	2	2	no	—
201	C₃₁×#123	—	2	2	no	—
202	C₃₁×#123	—	2	2	no	—
203	C₃₁×#123	—	2	2	no	—
204	C₃₁×#123	—	2	2	no	—
205	C₃₁×#123	—	2	2	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×C₂²⋊Q₈	—	2	1	no	—
208	C₃₁×C₂²⋊Q₈	—	2	1	no	—
209	C₃₁×C₂²⋊Q₈	—	2	2	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₃₁×#121	—	2	1	no	—
216	C₃₁×#121	—	2	1	no	—
217	C₃₁×#121	—	2	2	no	—
218	C₃₁×#121	—	2	2	no	—
219	C₃₁×#121	—	2	2	no	—
220	C₃₁×#121	—	2	2	no	—
221	C₃₁×#121	—	2	2	no	—
222	C₃₁×#121	—	2	2	no	—
223	C₃₁×#121	—	2	2	no	—
224	C₃₁×#121	—	2	2	no	—
225	C₃₁×#121	D₄	1	2	yes	—
226	C₃₁×#121	D₄	1	2	yes	—
227	C₃₁×#121	C₂³	1	2	yes	—
228	C₃₁×#121	C₂³	1	2	yes	—
229	C₃₁×#121	C₂³	1	2	yes	—
230	C₃₁×#121	C₂³	1	2	yes	—
231	C₃₁×#120	—	2	2	no	—
232	C₃₁×#120	—	2	2	no	—
233	C₃₁×#120	—	2	2	no	—
234	C₄×Q₈×C₃₁	—	2	1	no	—
235	C₄×Q₈×C₃₁	—	2	1	no	—
236	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	—	2	1	no	—
243	C₄×D₄×C₃₁	—	2	2	no	—
244	C₄×D₄×C₃₁	—	2	1	no	—
245	C₄×D₄×C₃₁	—	2	1	no	—
246	C₄×D₄×C₃₁	—	2	1	no	—
247	C₄×D₄×C₃₁	—	2	1	no	—
248	C₄×D₄×C₃₁	—	2	2	no	—
249	C₄×D₄×C₃₁	—	2	2	no	—
250	C₄×D₄×C₃₁	—	2	2	no	—
251	C₄×D₄×C₃₁	—	2	2	no	—
252	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₃₁	C₂³	1	2	yes	—
257	C₄×D₄×C₃₁	C₂³	1	2	yes	—
258	C₃₁×#117	—	2	2	no	—
259	C₃₁×#117	—	2	2	no	—
260	C₃₁×#117	—	2	1	no	—
261	C₃₁×#117	—	2	1	no	—
262	C₃₁×#117	C₂³	1	1	yes	characteristic
263	C₃₁×#117	C₂³	1	2	yes	—
264	C₃₁×#117	C₂³	1	2	yes	—
265	C₃₁×#117	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
267	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
268	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
271	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
272	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
273	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
274	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
276	C₂×C₄²×C₃₁	—	2	1	no	—
277	C₂×C₄²×C₃₁	—	2	1	no	—
278	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
279	C₃₁×#107	C₂³	1	1	yes	characteristic
280	C₃₁×#107	C₂³	1	1	yes	characteristic
281	C₃₁×#107	C₂³	1	2	yes	—
282	C₃₁×#107	C₂³	1	2	yes	—
283	C₃₁×#106	C₂³	1	1	yes	characteristic
284	C₃₁×#106	C₂³	1	1	yes	characteristic
285	C₃₁×#106	C₂³	1	2	yes	—
286	C₃₁×#106	C₂³	1	2	yes	—
287	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
288	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	1	yes	characteristic
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	2	yes	—
293	C₃₁×#103	C₂³	1	2	yes	—
294	C₃₁×#103	C₂³	1	2	yes	—
295	C₃₁×#103	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	1	yes	characteristic
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	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×#102	C₂³	1	1	yes	characteristic
309	C₃₁×#102	C₂³	1	2	yes	—
310	C₃₁×#102	C₂³	1	2	yes	—
311	C₃₁×#102	C₂³	1	1	yes	characteristic
312	C₃₁×#102	C₂³	1	1	yes	characteristic
313	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
314	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
315	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
316	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
318	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
319	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
320	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
321	C₂⁴×C₃₁	—	2	2	no	—
322	C₂⁴×C₃₁	—	2	1	no	—
323	#41×C₃₁	—	2	2	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	4	no	—
329	#41×C₃₁	—	2	4	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	4	2	no	—
333	#41×C₃₁	—	4	2	no	—
334	#41×C₃₁	—	4	4	no	—
335	#41×C₃₁	—	4	4	no	—
336	#41×C₃₁	—	4	8	no	—
337	#41×C₃₁	#41	1	4	yes	—
338	C₂×Q₈×C₃₁	—	2	2	no	—
339	C₂×Q₈×C₃₁	—	2	1	no	—
340	C₂×Q₈×C₃₁	—	2	4	no	—
341	C₂×Q₈×C₃₁	—	2	2	no	—
342	C₂×Q₈×C₃₁	—	2	2	no	—
343	C₂×Q₈×C₃₁	—	4	2	no	—
344	C₂×Q₈×C₃₁	—	4	4	no	—
345	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
346	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
348	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₃₁	—	2	1	no	—
351	C₂×D₄×C₃₁	—	2	4	no	—
352	C₂×D₄×C₃₁	—	2	1	no	—
353	C₂×D₄×C₃₁	—	2	2	no	—
354	C₂×D₄×C₃₁	—	2	2	no	—
355	C₂×D₄×C₃₁	—	2	2	no	—
356	C₂×D₄×C₃₁	—	2	2	no	—
357	C₂×D₄×C₃₁	—	2	2	no	—
358	C₂×D₄×C₃₁	—	2	2	no	—
359	C₂×D₄×C₃₁	—	2	2	no	—
360	C₂×D₄×C₃₁	—	2	1	no	—
361	C₂×D₄×C₃₁	—	2	2	no	—
362	C₂×D₄×C₃₁	—	2	2	no	—
363	C₂×D₄×C₃₁	—	4	2	no	—
364	C₂×D₄×C₃₁	—	4	4	no	—
365	C₂×D₄×C₃₁	—	4	8	no	—
366	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
373	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₃₁	—	2	1	no	—
376	C₂²×C₄×C₃₁	—	2	1	no	—
377	C₂²×C₄×C₃₁	—	2	2	no	—
378	C₂²×C₄×C₃₁	—	2	1	no	—
379	C₂²×C₄×C₃₁	—	2	1	no	—
380	C₂²×C₄×C₃₁	—	2	2	no	—
381	C₂²×C₄×C₃₁	—	2	2	no	—
382	C₂²×C₄×C₃₁	—	2	1	no	—
383	C₂²×C₄×C₃₁	—	2	2	no	—
384	C₂²×C₄×C₃₁	—	2	2	no	—
385	C₂²×C₄×C₃₁	—	2	1	no	—
386	C₂²×C₄×C₃₁	—	2	1	no	—
387	C₂²×C₄×C₃₁	—	2	1	no	—
388	C₂²×C₄×C₃₁	—	2	1	no	—
389	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
394	Q₁₆×C₃₁	—	2	2	no	—
395	Q₁₆×C₃₁	—	4	2	no	—
396	SD₁₆×C₃₁	—	2	2	no	—
397	SD₁₆×C₃₁	—	2	2	no	—
398	SD₁₆×C₃₁	—	4	2	no	—
399	SD₁₆×C₃₁	—	4	2	no	—
400	D₈×C₃₁	—	2	2	no	—
401	D₈×C₃₁	—	4	2	no	—
402	M₁₆×C₃₁	—	2	2	no	—
403	M₁₆×C₃₁	—	2	2	no	—
404	M₁₆×C₃₁	—	4	2	no	—
405	M₁₆×C₃₁	—	4	2	no	—
406	C₂×C₈×C₃₁	—	2	2	no	—
407	C₂×C₈×C₃₁	—	2	2	no	—
408	C₂×C₈×C₃₁	—	4	2	no	—
409	C₂×C₈×C₃₁	—	4	2	no	—
410	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
415	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	—	2	2	no	—
417	C₄⋊C₄×C₃₁	—	2	2	no	—
418	C₄⋊C₄×C₃₁	—	2	2	no	—
419	C₄⋊C₄×C₃₁	—	2	2	no	—
420	C₄⋊C₄×C₃₁	—	2	1	no	—
421	C₄⋊C₄×C₃₁	—	2	1	no	—
422	C₄⋊C₄×C₃₁	—	2	2	no	—
423	C₄⋊C₄×C₃₁	—	2	2	no	—
424	C₄⋊C₄×C₃₁	—	2	1	no	—
425	C₄⋊C₄×C₃₁	—	2	1	no	—
426	C₄⋊C₄×C₃₁	—	2	1	no	—
427	C₄⋊C₄×C₃₁	—	2	1	no	—
428	C₄⋊C₄×C₃₁	—	2	2	no	—
429	C₄⋊C₄×C₃₁	—	2	2	no	—
430	C₄⋊C₄×C₃₁	—	2	2	no	—
431	C₄⋊C₄×C₃₁	—	2	2	no	—
432	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
437	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
445	C₂²⋊C₄×C₃₁	—	2	1	no	—
446	C₂²⋊C₄×C₃₁	—	2	2	no	—
447	C₂²⋊C₄×C₃₁	—	2	2	no	—
448	C₂²⋊C₄×C₃₁	—	2	2	no	—
449	C₂²⋊C₄×C₃₁	—	2	2	no	—
450	C₂²⋊C₄×C₃₁	—	2	2	no	—
451	C₂²⋊C₄×C₃₁	—	2	2	no	—
452	C₂²⋊C₄×C₃₁	—	2	2	no	—
453	C₂²⋊C₄×C₃₁	—	2	2	no	—
454	C₂²⋊C₄×C₃₁	—	2	1	no	—
455	C₂²⋊C₄×C₃₁	—	2	1	no	—
456	C₂²⋊C₄×C₃₁	—	2	1	no	—
457	C₂²⋊C₄×C₃₁	—	2	1	no	—
458	C₂²⋊C₄×C₃₁	—	2	2	no	—
459	C₂²⋊C₄×C₃₁	—	2	2	no	—
460	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
464	C₄²×C₃₁	—	2	1	no	—
465	C₄²×C₃₁	—	2	1	no	—
466	C₄²×C₃₁	—	2	1	no	—
467	C₄²×C₃₁	—	2	1	no	—
468	C₄²×C₃₁	—	2	1	no	—
469	C₄²×C₃₁	—	2	1	no	—
470	C₄²×C₃₁	—	2	2	no	—
471	C₄²×C₃₁	—	2	2	no	—
472	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
475	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
476	#61216	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
477	C₂³×C₃₁	—	2	1	no	—
478	C₂³×C₃₁	—	2	1	no	—
479	C₂³×C₃₁	—	2	2	no	—
480	C₂³×C₃₁	—	4	4	no	—
481	C₂³×C₃₁	—	4	2	no	—
482	C₂³×C₃₁	—	8	1	no	—
483	C₂³×C₃₁	—	8	1	no	—
484	C₂³×C₃₁	—	8	2	no	—
485	C₂³×C₃₁	—	8	2	no	—
486	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
487	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
488	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
489	Q₈×C₃₁	—	2	2	no	—
490	Q₈×C₃₁	—	2	2	no	—
491	Q₈×C₃₁	—	2	1	no	—
492	Q₈×C₃₁	—	2	1	no	—
493	Q₈×C₃₁	—	2	2	no	—
494	Q₈×C₃₁	—	2	1	no	—
495	Q₈×C₃₁	—	2	2	no	—
496	Q₈×C₃₁	—	4	4	no	—
497	Q₈×C₃₁	—	4	2	no	—
498	Q₈×C₃₁	C₂×#41	1	2	yes	—
499	D₄×C₃₁	—	2	4	no	—
500	D₄×C₃₁	—	2	4	no	—
501	D₄×C₃₁	—	2	4	no	—
502	D₄×C₃₁	—	2	2	no	—
503	D₄×C₃₁	—	2	2	no	—
504	D₄×C₃₁	—	2	1	no	—
505	D₄×C₃₁	—	2	2	no	—
506	D₄×C₃₁	—	2	1	no	—
507	D₄×C₃₁	—	2	1	no	—
508	D₄×C₃₁	—	2	2	no	—
509	D₄×C₃₁	—	4	2	no	—
510	D₄×C₃₁	—	4	2	no	—
511	D₄×C₃₁	—	4	4	no	—
512	D₄×C₃₁	—	4	4	no	—
513	D₄×C₃₁	—	4	4	no	—
514	D₄×C₃₁	—	4	2	no	—
515	D₄×C₃₁	—	4	2	no	—
516	D₄×C₃₁	—	8	2	no	—
517	D₄×C₃₁	—	8	2	no	—
518	D₄×C₃₁	—	8	2	no	—
519	D₄×C₃₁	—	8	2	no	—
520	D₄×C₃₁	C₂×#41	1	2	yes	—
521	C₂×C₄×C₃₁	—	2	1	no	—
522	C₂×C₄×C₃₁	—	2	4	no	—
523	C₂×C₄×C₃₁	—	2	2	no	—
524	C₂×C₄×C₃₁	—	2	2	no	—
525	C₂×C₄×C₃₁	—	2	2	no	—
526	C₂×C₄×C₃₁	—	2	2	no	—
527	C₂×C₄×C₃₁	—	2	1	no	—
528	C₂×C₄×C₃₁	—	2	1	no	—
529	C₂×C₄×C₃₁	—	2	1	no	—
530	C₂×C₄×C₃₁	—	2	1	no	—
531	C₂×C₄×C₃₁	—	2	1	no	—
532	C₂×C₄×C₃₁	—	2	2	no	—
533	C₂×C₄×C₃₁	—	2	2	no	—
534	C₂×C₄×C₃₁	—	2	2	no	—
535	C₂×C₄×C₃₁	—	4	1	no	—
536	C₂×C₄×C₃₁	—	4	1	no	—
537	C₂×C₄×C₃₁	—	4	4	no	—
538	C₂×C₄×C₃₁	—	4	4	no	—
539	C₂×C₄×C₃₁	—	4	4	no	—
540	C₂×C₄×C₃₁	—	4	2	no	—
541	C₂×C₄×C₃₁	—	4	2	no	—
542	C₂×C₄×C₃₁	—	8	1	no	—
543	C₂×C₄×C₃₁	—	8	1	no	—
544	C₂×C₄×C₃₁	—	8	1	no	—
545	C₂×C₄×C₃₁	—	8	1	no	—
546	C₂×C₄×C₃₁	—	8	2	no	—
547	C₂×C₄×C₃₁	—	8	2	no	—
548	C₂×C₄×C₃₁	—	8	1	no	—
549	C₂×C₄×C₃₁	—	8	1	no	—
550	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
557	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
558	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
559	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
560	C₈×C₃₁	—	2	1	no	—
561	C₈×C₃₁	—	2	1	no	—
562	C₈×C₃₁	—	2	1	no	—
563	C₈×C₃₁	—	2	1	no	—
564	C₈×C₃₁	—	2	2	no	—
565	C₈×C₃₁	—	2	2	no	—
566	#3512	C₂×C₃₁	1	1	yes	characteristic, complemented
567	#3500	C₂×C₃₁	1	1	yes	characteristic, complemented
568	#3327	C₂×C₃₁	1	2	yes	complemented
569	#3326	C₂×C₃₁	1	2	yes	complemented
570	#3323	C₂×C₃₁	1	2	yes	complemented
571	#3322	C₂×C₃₁	1	2	yes	complemented
572	#3301	C₂×C₃₁	1	2	yes	complemented
573	#3300	C₂×C₃₁	1	2	yes	complemented
574	#3297	C₂×C₃₁	1	2	yes	complemented
575	#3296	C₂×C₃₁	1	2	yes	complemented
576	C₂×#488	C₂×C₃₁	1	1	yes	characteristic, complemented
577	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
578	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
579	#3080	C₂×C₃₁	1	1	yes	characteristic, complemented
580	#3063	C₂×C₃₁	1	1	yes	characteristic, complemented
581	#3062	C₂×C₃₁	1	1	yes	characteristic, complemented
582	#3040	C₂×C₃₁	1	1	yes	characteristic, complemented
583	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
584	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
585	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
586	#2931	C₂×C₃₁	1	1	yes	characteristic, complemented
587	#2898	C₂×C₃₁	1	1	yes	characteristic, complemented
588	#2897	C₂×C₃₁	1	1	yes	characteristic, complemented
589	C₂²×C₃₁	—	2	1	no	—
590	C₂²×C₃₁	—	2	1	no	—
591	C₂²×C₃₁	—	2	2	no	—
592	C₂²×C₃₁	—	2	2	no	—
593	C₂²×C₃₁	—	2	2	no	—
594	C₂²×C₃₁	—	2	2	no	—
595	C₂²×C₃₁	—	2	2	no	—
596	C₂²×C₃₁	—	2	2	no	—
597	C₂²×C₃₁	—	2	2	no	—
598	C₂²×C₃₁	—	4	1	no	—
599	C₂²×C₃₁	—	4	1	no	—
600	C₂²×C₃₁	—	4	1	no	—
601	C₂²×C₃₁	—	4	1	no	—
602	C₂²×C₃₁	—	4	2	no	—
603	C₂²×C₃₁	—	4	2	no	—
604	C₂²×C₃₁	—	4	2	no	—
605	C₂²×C₃₁	—	4	1	no	—
606	C₂²×C₃₁	—	16	2	no	—
607	C₂²×C₃₁	—	16	4	no	—
608	C₂²×C₃₁	#546	1	2	yes	—
609	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
610	C₄×C₃₁	—	2	1	no	—
611	C₄×C₃₁	—	2	1	no	—
612	C₄×C₃₁	—	2	1	no	—
613	C₄×C₃₁	—	2	1	no	—
614	C₄×C₃₁	—	2	2	no	—
615	C₄×C₃₁	—	2	2	no	—
616	C₄×C₃₁	—	2	2	no	—
617	C₄×C₃₁	—	4	1	no	—
618	C₄×C₃₁	—	4	1	no	—
619	C₄×C₃₁	—	4	2	no	—
620	C₄×C₃₁	—	4	2	no	—
621	C₄×C₃₁	—	4	1	no	—
622	C₄×C₃₁	—	4	1	no	—
623	C₄×C₃₁	—	4	2	no	—
624	C₄×C₃₁	—	4	1	no	—
625	C₄×C₃₁	#546	1	2	yes	—
626	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
627	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
629	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
630	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
631	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic
632	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
633	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
634	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic, complemented
635	#553	—	2	2	no	—
636	#553	—	2	2	no	—
637	#553	C₂²×C₃₁	1	2	yes	complemented
638	#553	C₂²×C₃₁	1	2	yes	complemented
639	#552	C₂²×C₃₁	1	2	yes	complemented
640	#552	C₂²×C₃₁	1	2	yes	complemented
641	#548	C₂²×C₃₁	1	2	yes	—
642	#548	C₂²×C₃₁	1	2	yes	—
643	#546	—	2	2	no	—
644	#546	—	2	2	no	—
645	#546	C₂²×C₃₁	1	2	yes	—
646	#546	C₂²×C₃₁	1	2	yes	—
647	#541	—	2	1	no	—
648	#540	—	2	1	no	—
649	#537	C₂²×C₃₁	1	1	yes	characteristic
650	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
651	#536	—	2	1	no	—
652	#536	C₂²×C₃₁	1	1	yes	characteristic
653	#535	—	2	1	no	—
654	#535	C₂²×C₃₁	1	1	yes	characteristic
655	#532	—	2	1	no	—
656	#532	C₂²×C₃₁	1	1	yes	characteristic
657	#529	—	2	1	no	—
658	#529	—	2	1	no	—
659	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	C₂×#124	—	2	1	no	—
661	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
662	#520	C₂²×C₃₁	1	1	yes	characteristic
663	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
664	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
665	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
666	#488	C₂²×C₃₁	1	2	yes	complemented
667	#488	C₂²×C₃₁	1	2	yes	complemented
668	#488	C₂²×C₃₁	1	2	yes	complemented
669	#488	C₂²×C₃₁	1	2	yes	complemented
670	#485	C₂²×C₃₁	1	2	yes	complemented
671	#485	C₂²×C₃₁	1	2	yes	complemented
672	#484	C₂²×C₃₁	1	2	yes	complemented
673	#483	C₂²×C₃₁	1	2	yes	complemented
674	#482	C₂²×C₃₁	1	2	yes	complemented
675	#482	C₂²×C₃₁	1	2	yes	complemented
676	#481	C₂²×C₃₁	1	2	yes	complemented
677	#480	C₂²×C₃₁	1	2	yes	complemented
678	#479	C₂²×C₃₁	1	2	yes	complemented
679	#479	C₂²×C₃₁	1	2	yes	complemented
680	#478	C₂²×C₃₁	1	2	yes	complemented
681	#478	C₂²×C₃₁	1	2	yes	complemented
682	#470	C₂²×C₃₁	1	2	yes	complemented
683	#469	C₂²×C₃₁	1	2	yes	complemented
684	#468	C₂²×C₃₁	1	2	yes	complemented
685	#468	C₂²×C₃₁	1	2	yes	complemented
686	#467	C₂²×C₃₁	1	2	yes	complemented
687	#466	C₂²×C₃₁	1	2	yes	complemented
688	#465	C₂²×C₃₁	1	2	yes	complemented
689	#465	C₂²×C₃₁	1	2	yes	complemented
690	#464	C₂²×C₃₁	1	2	yes	complemented
691	#464	C₂²×C₃₁	1	2	yes	complemented
692	#463	C₂²×C₃₁	1	2	yes	complemented
693	#463	C₂²×C₃₁	1	2	yes	complemented
694	#452	C₂²×C₃₁	1	2	yes	—
695	#452	C₂²×C₃₁	1	2	yes	complemented
696	#451	C₂²×C₃₁	1	2	yes	complemented
697	#450	C₂²×C₃₁	1	2	yes	—
698	#449	C₂²×C₃₁	1	2	yes	—
699	#449	C₂²×C₃₁	1	2	yes	complemented
700	#448	C₂²×C₃₁	1	2	yes	complemented
701	#447	C₂²×C₃₁	1	2	yes	—
702	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
703	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
704	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
705	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
707	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, 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	2	yes	complemented
711	#436	C₂²×C₃₁	1	2	yes	complemented
712	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
713	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
714	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
715	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
716	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
717	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
718	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
719	#419	C₂²×C₃₁	1	2	yes	complemented
720	#418	C₂²×C₃₁	1	1	yes	characteristic
721	#418	C₂²×C₃₁	1	2	yes	—
722	#417	C₂²×C₃₁	1	1	yes	characteristic
723	#417	C₂²×C₃₁	1	1	yes	characteristic
724	#417	C₂²×C₃₁	1	2	yes	—
725	#417	C₂²×C₃₁	1	2	yes	complemented
726	#416	C₂²×C₃₁	1	1	yes	characteristic
727	#416	C₂²×C₃₁	1	2	yes	—
728	#416	C₂²×C₃₁	1	2	yes	complemented
729	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
730	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
733	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
734	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
735	C₂×#102	C₂²×C₃₁	1	2	yes	—
736	#408	C₂²×C₃₁	1	1	yes	characteristic
737	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
738	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
739	C₂×C₃₁	—	2	2	no	—
740	C₂×C₃₁	—	4	2	no	—
741	C₂×C₃₁	—	4	2	no	—
742	C₂×C₃₁	—	4	2	no	—
743	C₂×C₃₁	—	8	1	no	—
744	C₂×C₃₁	—	8	2	no	—
745	C₂×C₃₁	C₂×#546	1	1	yes	characteristic
746	C₂×C₃₁	#3584	1	1	yes	characteristic
747	C₂×C₃₁	#3584	1	1	yes	characteristic
748	2₋¹⁺⁴	—	2	4	no	—
749	2₋¹⁺⁴	—	4	2	no	—
750	H(5,𝔽₂)	—	2	4	no	—
751	H(5,𝔽₂)	—	4	2	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	2	no	—
755	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
756	C₂×#41	C₂³×C₃₁	1	2	yes	—
757	C₂×#41	C₂³×C₃₁	1	2	yes	—
758	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
759	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
760	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
761	C₂²×Q₈	—	2	1	no	—
762	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
764	C₂²×D₄	—	2	1	no	—
765	C₂²×D₄	—	2	2	no	—
766	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
768	#137	—	4	2	no	—
769	AGL(1,ℤ/8)	—	4	2	no	—
770	#135	—	2	4	no	—
771	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
772	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
773	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
774	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
775	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
776	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
777	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₂×D₈	C₂³×C₃₁	1	2	yes	—
779	#131	—	4	2	no	—
780	#131	—	4	2	no	—
781	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
782	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
784	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
785	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
788	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
789	C₄⋊Q₈	—	2	1	no	—
790	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
791	#127	—	2	1	no	—
792	#127	D₄×C₃₁	1	1	yes	characteristic
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#125	—	2	2	no	—
798	#125	—	2	2	no	—
799	#125	—	2	1	no	—
800	#125	—	2	1	no	—
801	#125	C₂³×C₃₁	1	2	yes	—
802	#125	C₂³×C₃₁	1	2	yes	—
803	#124	—	2	1	no	—
804	#124	—	2	1	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	1	no	—
808	#124	—	2	1	no	—
809	#124	D₄×C₃₁	1	1	yes	characteristic
810	#124	D₄×C₃₁	1	1	yes	characteristic
811	#124	C₂³×C₃₁	1	2	yes	—
812	#124	C₂³×C₃₁	1	2	yes	—
813	#123	—	2	2	no	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	2	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
825	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	D₄×C₃₁	1	2	yes	—
839	#121	D₄×C₃₁	1	2	yes	—
840	#121	C₂³×C₃₁	1	2	yes	—
841	#121	C₂³×C₃₁	1	2	yes	—
842	#121	C₂³×C₃₁	1	2	yes	—
843	#121	C₂³×C₃₁	1	2	yes	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
850	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
866	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₃₁	1	2	yes	—
870	C₄×D₄	C₂³×C₃₁	1	2	yes	—
871	#117	—	2	2	no	—
872	#117	—	2	2	no	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	C₂³×C₃₁	1	1	yes	characteristic
876	#117	C₂³×C₃₁	1	1	yes	characteristic
877	#117	C₂³×C₃₁	1	2	yes	—
878	#117	C₂³×C₃₁	1	2	yes	—
879	C₂×C₄⋊C₄	—	2	1	no	—
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
883	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₄²	—	2	1	no	—
890	C₂×C₄²	—	2	1	no	—
891	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
892	#107	C₂³×C₃₁	1	1	yes	characteristic
893	#107	C₂³×C₃₁	1	1	yes	characteristic
894	#107	C₂³×C₃₁	1	2	yes	—
895	#107	C₂³×C₃₁	1	2	yes	—
896	#106	C₂³×C₃₁	1	1	yes	characteristic
897	#106	C₂³×C₃₁	1	1	yes	characteristic
898	#106	C₂³×C₃₁	1	2	yes	—
899	#106	C₂³×C₃₁	1	2	yes	—
900	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
901	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
902	#103	C₂³×C₃₁	1	1	yes	characteristic
903	#103	C₂³×C₃₁	1	2	yes	—
904	#103	C₂³×C₃₁	1	2	yes	—
905	#103	C₂³×C₃₁	1	2	yes	—
906	#103	C₂³×C₃₁	1	2	yes	—
907	#103	C₂³×C₃₁	1	2	yes	—
908	#103	C₂³×C₃₁	1	2	yes	—
909	#103	C₂³×C₃₁	1	1	yes	characteristic
910	#103	C₂³×C₃₁	1	2	yes	—
911	#103	C₂³×C₃₁	1	2	yes	—
912	#103	C₂³×C₃₁	1	1	yes	characteristic
913	#103	C₂³×C₃₁	1	1	yes	characteristic
914	#102	C₂³×C₃₁	1	1	yes	characteristic
915	#102	C₂³×C₃₁	1	2	yes	—
916	#102	C₂³×C₃₁	1	2	yes	—
917	#102	C₂³×C₃₁	1	2	yes	—
918	#102	C₂³×C₃₁	1	2	yes	—
919	#102	C₂³×C₃₁	1	2	yes	—
920	#102	C₂³×C₃₁	1	2	yes	—
921	#102	C₂³×C₃₁	1	1	yes	characteristic
922	#102	C₂³×C₃₁	1	2	yes	—
923	#102	C₂³×C₃₁	1	2	yes	—
924	#102	C₂³×C₃₁	1	1	yes	characteristic
925	#102	C₂³×C₃₁	1	1	yes	characteristic
926	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
927	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
930	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
931	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
932	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
933	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
934	C₃₁	#61216	1	1	yes	characteristic, direct product factor, Sylow
935	C₂⁴	—	2	2	no	—
936	C₂⁴	—	2	1	no	—
937	#41	—	2	2	no	—
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	4	no	—
949	#41	—	4	4	no	—
950	#41	—	4	8	no	—
951	#41	#41×C₃₁	1	4	yes	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	1	no	—
954	C₂×Q₈	—	2	4	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	4	2	no	—
958	C₂×Q₈	—	4	4	no	—
959	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
960	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
961	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
963	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	4	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	4	no	—
979	C₂×D₄	—	4	8	no	—
980	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
983	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
986	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
987	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	4	2	no	—
1010	SD₁₆	—	2	2	no	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	4	2	no	—
1013	SD₁₆	—	4	2	no	—
1014	D₈	—	2	2	no	—
1015	D₈	—	4	2	no	—
1016	M₁₆	—	2	2	no	—
1017	M₁₆	—	2	2	no	—
1018	M₁₆	—	4	2	no	—
1019	M₁₆	—	4	2	no	—
1020	C₂×C₈	—	2	2	no	—
1021	C₂×C₈	—	2	2	no	—
1022	C₂×C₈	—	4	2	no	—
1023	C₂×C₈	—	4	2	no	—
1024	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1025	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1047	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1087	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1088	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1089	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	8	1	no	—
1096	C₂³	—	8	1	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	—	8	2	no	—
1099	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1100	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1101	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	4	4	no	—
1110	Q₈	—	4	2	no	—
1111	Q₈	C₂×#41×C₃₁	1	2	yes	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	4	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	2	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	4	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	C₂×#41×C₃₁	1	2	yes	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	1	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1166	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1170	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
1171	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1172	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	2	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	16	2	no	—
1197	C₂²	—	16	4	no	—
1198	C₂²	C₃₁×#546	1	2	yes	—
1199	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1200	C₄	—	2	2	no	—
1201	C₄	—	2	2	no	—
1202	C₄	—	2	2	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	1	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	4	2	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	4	2	no	—
1212	C₄	—	4	2	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	C₃₁×#546	1	2	yes	—
1216	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1217	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1218	C₂	—	2	2	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	4	2	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	C₂×C₃₁×#546	1	1	yes	characteristic
1225	C₂	C₃₁×#3584	1	1	yes	characteristic
1226	C₂	C₃₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3512	C₂	semidirect
2. C₃₁×#3500	C₂	semidirect
3. C₃₁×#3327	C₂	semidirect
4. C₃₁×#3326	C₂	semidirect
5. C₃₁×#3323	C₂	semidirect
6. C₃₁×#3322	C₂	semidirect
7. C₃₁×#3301	C₂	semidirect
8. C₃₁×#3300	C₂	semidirect
9. C₃₁×#3297	C₂	semidirect
10. C₃₁×#3296	C₂	semidirect
11. C₂×C₃₁×#488	C₂	semidirect
12. C₃₁×#3097	C₂	semidirect
13. C₃₁×#3096	C₂	semidirect
14. C₃₁×#3080	C₂	semidirect
15. C₃₁×#3063	C₂	semidirect
16. C₃₁×#3062	C₂	semidirect
17. C₃₁×#3040	C₂	semidirect
18. C₃₁×#3013	C₂	semidirect
19. C₃₁×#3012	C₂	semidirect
20. C₄×C₃₁×#135	C₂	semidirect
21. C₃₁×#2931	C₂	semidirect
22. C₃₁×#2898	C₂	semidirect
23. C₃₁×#2897	C₂	semidirect
26. C₂×C₃₁×#137	C₂²	semidirect
30. C₂×C₃₁×#131	C₂²	semidirect
33. C₃₁×#553	C₂²	semidirect
34. C₃₁×#553	C₂²	semidirect
35. C₃₁×#552	C₂²	semidirect
36. C₃₁×#552	C₂²	semidirect
46. C₃₁×#537	C₂²	semidirect
55. C₂×C₃₁×#125	C₂²	semidirect
59. C₃₁×#520	C₂²	semidirect
61. C₄×#41×C₃₁	C₂²	semidirect
62. C₃₁×#488	C₂²	semidirect
63. C₃₁×#488	C₂²	semidirect
64. C₃₁×#488	C₂²	semidirect
65. C₃₁×#488	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#485	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
69. C₃₁×#483	C₂²	semidirect
70. C₃₁×#482	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
73. C₃₁×#480	C₂²	semidirect
74. C₃₁×#479	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#478	C₂²	semidirect
78. C₃₁×#470	C₂²	semidirect
79. C₃₁×#469	C₂²	semidirect
80. C₃₁×#468	C₂²	semidirect
81. C₃₁×#468	C₂²	semidirect
82. C₃₁×#467	C₂²	semidirect
83. C₃₁×#466	C₂²	semidirect
84. C₃₁×#465	C₂²	semidirect
85. C₃₁×#465	C₂²	semidirect
86. C₃₁×#464	C₂²	semidirect
87. C₃₁×#464	C₂²	semidirect
88. C₃₁×#463	C₂²	semidirect
89. C₃₁×#463	C₂²	semidirect
91. C₃₁×#452	C₂²	semidirect
92. C₃₁×#451	C₂²	semidirect
95. C₃₁×#449	C₂²	semidirect
96. C₃₁×#448	C₂²	semidirect
98. C₄×Q₁₆×C₃₁	C₂²	semidirect
99. C₄×Q₁₆×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×D₈×C₃₁	C₂²	semidirect
105. C₄×D₈×C₃₁	C₂²	semidirect
106. C₃₁×#436	C₂²	semidirect
107. C₃₁×#436	C₂²	semidirect
108. C₈×D₄×C₃₁	C₂²	semidirect
109. C₈×D₄×C₃₁	C₂²	semidirect
110. C₃₁×#428	C₂²	semidirect
111. C₃₁×#428	C₂²	semidirect
112. C₃₁×#427	C₂²	semidirect
113. C₃₁×#423	C₂²	semidirect
114. C₃₁×#419	C₂²	semidirect
115. C₃₁×#419	C₂²	semidirect
121. C₃₁×#417	C₂²	semidirect
124. C₃₁×#416	C₂²	semidirect
125. C₃₁×#416	C₂²	semidirect
126. C₂×C₃₁×#103	C₂²	semidirect
127. C₂×C₃₁×#103	C₂²	semidirect
128. C₂×C₃₁×#103	C₂²	semidirect
133. C₃₁×#408	C₂²	semidirect
134. C₂×C₄×C₈×C₃₁	C₂²	semidirect
476. #61216	C₃₁	direct (N × H)
566. #3512	C₂×C₃₁	semidirect
567. #3500	C₂×C₃₁	semidirect
568. #3327	C₂×C₃₁	semidirect
569. #3326	C₂×C₃₁	semidirect
570. #3323	C₂×C₃₁	semidirect
571. #3322	C₂×C₃₁	semidirect
572. #3301	C₂×C₃₁	semidirect
573. #3300	C₂×C₃₁	semidirect
574. #3297	C₂×C₃₁	semidirect
575. #3296	C₂×C₃₁	semidirect
576. C₂×#488	C₂×C₃₁	semidirect
577. #3097	C₂×C₃₁	semidirect
578. #3096	C₂×C₃₁	semidirect
579. #3080	C₂×C₃₁	semidirect
580. #3063	C₂×C₃₁	semidirect
581. #3062	C₂×C₃₁	semidirect
582. #3040	C₂×C₃₁	semidirect
583. #3013	C₂×C₃₁	semidirect
584. #3012	C₂×C₃₁	semidirect
585. C₄×#135	C₂×C₃₁	semidirect
586. #2931	C₂×C₃₁	semidirect
587. #2898	C₂×C₃₁	semidirect
588. #2897	C₂×C₃₁	semidirect
630. C₂×#137	C₂²×C₃₁	semidirect
634. C₂×#131	C₂²×C₃₁	semidirect
637. #553	C₂²×C₃₁	semidirect
638. #553	C₂²×C₃₁	semidirect
639. #552	C₂²×C₃₁	semidirect
640. #552	C₂²×C₃₁	semidirect
650. #537	C₂²×C₃₁	semidirect
659. C₂×#125	C₂²×C₃₁	semidirect
663. #520	C₂²×C₃₁	semidirect
665. C₄×#41	C₂²×C₃₁	semidirect
666. #488	C₂²×C₃₁	semidirect
667. #488	C₂²×C₃₁	semidirect
668. #488	C₂²×C₃₁	semidirect
669. #488	C₂²×C₃₁	semidirect
670. #485	C₂²×C₃₁	semidirect
671. #485	C₂²×C₃₁	semidirect
672. #484	C₂²×C₃₁	semidirect
673. #483	C₂²×C₃₁	semidirect
674. #482	C₂²×C₃₁	semidirect
675. #482	C₂²×C₃₁	semidirect
676. #481	C₂²×C₃₁	semidirect
677. #480	C₂²×C₃₁	semidirect
678. #479	C₂²×C₃₁	semidirect
679. #479	C₂²×C₃₁	semidirect
680. #478	C₂²×C₃₁	semidirect
681. #478	C₂²×C₃₁	semidirect
682. #470	C₂²×C₃₁	semidirect
683. #469	C₂²×C₃₁	semidirect
684. #468	C₂²×C₃₁	semidirect
685. #468	C₂²×C₃₁	semidirect
686. #467	C₂²×C₃₁	semidirect
687. #466	C₂²×C₃₁	semidirect
688. #465	C₂²×C₃₁	semidirect
689. #465	C₂²×C₃₁	semidirect
690. #464	C₂²×C₃₁	semidirect
691. #464	C₂²×C₃₁	semidirect
692. #463	C₂²×C₃₁	semidirect
693. #463	C₂²×C₃₁	semidirect
695. #452	C₂²×C₃₁	semidirect
696. #451	C₂²×C₃₁	semidirect
699. #449	C₂²×C₃₁	semidirect
700. #448	C₂²×C₃₁	semidirect
702. C₄×Q₁₆	C₂²×C₃₁	semidirect
703. C₄×Q₁₆	C₂²×C₃₁	semidirect
704. C₄×SD₁₆	C₂²×C₃₁	semidirect
705. C₄×SD₁₆	C₂²×C₃₁	semidirect
706. C₄×SD₁₆	C₂²×C₃₁	semidirect
707. C₄×SD₁₆	C₂²×C₃₁	semidirect
708. C₄×D₈	C₂²×C₃₁	semidirect
709. C₄×D₈	C₂²×C₃₁	semidirect
710. #436	C₂²×C₃₁	semidirect
711. #436	C₂²×C₃₁	semidirect
712. C₈×D₄	C₂²×C₃₁	semidirect
713. C₈×D₄	C₂²×C₃₁	semidirect
714. #428	C₂²×C₃₁	semidirect
715. #428	C₂²×C₃₁	semidirect
716. #427	C₂²×C₃₁	semidirect
717. #423	C₂²×C₃₁	semidirect
718. #419	C₂²×C₃₁	semidirect
719. #419	C₂²×C₃₁	semidirect
725. #417	C₂²×C₃₁	semidirect
728. #416	C₂²×C₃₁	semidirect
729. #416	C₂²×C₃₁	semidirect
730. C₂×#103	C₂²×C₃₁	semidirect
731. C₂×#103	C₂²×C₃₁	semidirect
732. C₂×#103	C₂²×C₃₁	semidirect
737. #408	C₂²×C₃₁	semidirect
738. C₂×C₄×C₈	C₂²×C₃₁	semidirect
934. C₃₁	#61216	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3512	2
C₃₁×#3500	2
C₃₁×#3327	2
C₃₁×#3326	2
C₃₁×#3323	2
C₃₁×#3322	2
C₃₁×#3301	2
C₃₁×#3300	2
C₃₁×#3297	2
C₃₁×#3296	2
C₂×C₃₁×#488	2
C₃₁×#3097	2
C₃₁×#3096	2
C₃₁×#3080	2
C₃₁×#3063	2
C₃₁×#3062	2
C₃₁×#3040	2
C₃₁×#3013	2
C₃₁×#3012	2
C₄×C₃₁×#135	2
C₃₁×#2931	2
C₃₁×#2898	2
C₃₁×#2897	2
#61216	31

Subgroups — C31×#61216 #21517975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61216 #21517975