Subgroups — C₃₁×#60772 #21517531

Order 7936.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3489	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3203	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3200	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3198	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3197	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3196	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3194	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3193	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3097	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3096	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3054	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3013	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3012	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3010	C₂	1	1	yes	maximal, characteristic, complemented
22	C₃₁×#3009	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
30	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#550	—	2	1	no	—
34	D₄×Q₈×C₃₁	—	2	1	no	—
35	C₃₁×#548	—	2	1	no	—
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	—	2	2	no	—
38	C₃₁×#547	—	2	1	no	—
39	C₃₁×#546	—	2	2	no	—
40	C₃₁×#546	—	2	1	no	—
41	C₃₁×#546	—	2	2	no	—
42	C₃₁×#546	—	2	1	no	—
43	D₄²×C₃₁	—	2	2	no	—
44	D₄²×C₃₁	—	2	1	no	—
45	C₃₁×#537	C₂²	1	1	yes	characteristic
46	C₃₁×#537	C₂²	1	1	yes	characteristic
47	C₃₁×#537	C₂²	1	2	yes	—
48	C₃₁×#537	C₂²	1	2	yes	complemented
49	C₃₁×#536	C₂²	1	1	yes	characteristic
50	C₃₁×#536	C₂²	1	2	yes	complemented
51	C₃₁×#535	C₂²	1	1	yes	characteristic
52	C₃₁×#535	C₂²	1	2	yes	—
53	C₃₁×#525	C₂²	1	2	yes	—
54	C₃₁×#525	C₂²	1	1	yes	characteristic
55	C₃₁×#525	C₂²	1	2	yes	complemented
56	C₃₁×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₃₁×#121	C₂²	1	2	yes	—
60	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
61	C₃₁×#520	C₂²	1	1	yes	characteristic
62	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#485	C₂²	1	2	yes	complemented
64	C₃₁×#485	C₂²	1	2	yes	complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#485	C₂²	1	2	yes	complemented
67	C₃₁×#484	C₂²	1	2	yes	complemented
68	C₃₁×#484	C₂²	1	2	yes	complemented
69	C₃₁×#484	C₂²	1	2	yes	complemented
70	C₃₁×#483	C₂²	1	2	yes	complemented
71	C₃₁×#482	C₂²	1	2	yes	complemented
72	C₃₁×#482	C₂²	1	2	yes	complemented
73	C₃₁×#482	C₂²	1	2	yes	complemented
74	C₃₁×#482	C₂²	1	2	yes	complemented
75	C₃₁×#481	C₂²	1	2	yes	complemented
76	C₃₁×#480	C₂²	1	2	yes	complemented
77	C₃₁×#480	C₂²	1	2	yes	complemented
78	C₃₁×#480	C₂²	1	2	yes	complemented
79	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
80	C₃₁×#470	C₂²	1	2	yes	complemented
81	C₃₁×#470	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#469	C₂²	1	2	yes	complemented
84	C₃₁×#469	C₂²	1	1	yes	characteristic, complemented
85	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#468	C₂²	1	2	yes	complemented
87	C₃₁×#468	C₂²	1	2	yes	complemented
88	C₃₁×#468	C₂²	1	2	yes	complemented
89	C₃₁×#468	C₂²	1	2	yes	complemented
90	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#468	C₂²	1	2	yes	complemented
92	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#468	C₂²	1	2	yes	complemented
94	C₃₁×#468	C₂²	1	1	yes	characteristic, complemented
95	C₃₁×#467	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	complemented
97	C₃₁×#465	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#452	C₂²	1	2	yes	complemented
100	C₃₁×#452	C₂²	1	2	yes	complemented
101	C₃₁×#452	C₂²	1	2	yes	complemented
102	C₃₁×#452	C₂²	1	2	yes	complemented
103	C₃₁×#451	C₂²	1	2	yes	complemented
104	C₃₁×#450	C₂²	1	2	yes	complemented
105	C₃₁×#450	C₂²	1	2	yes	complemented
106	C₃₁×#450	C₂²	1	2	yes	complemented
107	C₃₁×#449	C₂²	1	2	yes	complemented
108	C₃₁×#449	C₂²	1	2	yes	complemented
109	C₃₁×#449	C₂²	1	2	yes	complemented
110	C₃₁×#449	C₂²	1	2	yes	complemented
111	C₃₁×#448	C₂²	1	2	yes	complemented
112	C₃₁×#448	C₂²	1	2	yes	complemented
113	C₃₁×#448	C₂²	1	2	yes	complemented
114	C₃₁×#447	C₂²	1	2	yes	complemented
115	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
116	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
117	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic, complemented
119	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
120	C₃₁×#418	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#417	C₂²	1	1	yes	characteristic, complemented
123	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
124	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#408	C₂²	1	1	yes	characteristic
128	C₃₁×#408	C₂²	1	1	yes	characteristic
129	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
130	C₃₁×#408	C₂²	1	1	yes	characteristic, complemented
131	C₃₁×#408	C₂²	1	2	yes	complemented
132	C₃₁×#408	C₂²	1	2	yes	complemented
133	C₃₁×#407	C₂²	1	2	yes	complemented
134	C₃₁×#407	C₂²	1	2	yes	complemented
135	C₃₁×2₋¹⁺⁴	—	4	2	no	—
136	C₃₁×2₋¹⁺⁴	—	4	2	no	—
137	C₃₁×H(5,𝔽₂)	—	4	2	no	—
138	C₃₁×H(5,𝔽₂)	—	4	2	no	—
139	C₂×#41×C₃₁	—	2	1	no	—
140	C₂×#41×C₃₁	—	2	2	no	—
141	C₂×#41×C₃₁	—	2	1	no	—
142	C₂×#41×C₃₁	—	4	2	no	—
143	C₂×#41×C₃₁	—	4	2	no	—
144	C₂×#41×C₃₁	D₄	1	2	yes	—
145	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
146	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
147	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×#41×C₃₁	C₂³	1	2	yes	—
150	C₂×#41×C₃₁	C₂³	1	2	yes	—
151	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×#41×C₃₁	C₂³	1	2	yes	—
154	C₂²×Q₈×C₃₁	—	2	1	no	—
155	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
156	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
157	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
158	C₂²×D₄×C₃₁	—	2	1	no	—
159	C₂²×D₄×C₃₁	—	2	2	no	—
160	C₂²×D₄×C₃₁	—	2	2	no	—
161	C₂²×D₄×C₃₁	—	2	1	no	—
162	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
163	C₂²×D₄×C₃₁	D₄	1	2	yes	—
164	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
165	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
166	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
167	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
168	C₃₁×#137	—	4	2	no	—
169	C₃₁×AGL(1,ℤ/8)	—	4	2	no	—
170	C₃₁×#135	—	4	2	no	—
171	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
172	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
173	C₂×SD₁₆×C₃₁	—	4	2	no	—
174	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
175	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
176	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
177	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
178	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
179	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
180	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
181	C₂×D₈×C₃₁	C₂³	1	2	yes	—
182	C₂×M₁₆×C₃₁	—	4	2	no	—
183	C₂×M₁₆×C₃₁	—	4	2	no	—
184	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
185	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
186	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
188	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
193	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
194	C₃₁×C₄⋊Q₈	—	2	1	no	—
195	C₃₁×C₄⋊Q₈	—	2	2	no	—
196	C₃₁×#127	—	2	1	no	—
197	C₃₁×#127	—	2	2	no	—
198	C₃₁×#124	—	2	1	no	—
199	C₃₁×#124	—	2	2	no	—
200	C₃₁×#124	—	2	1	no	—
201	C₃₁×#124	—	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	1	no	—
206	C₃₁×#123	—	2	2	no	—
207	C₃₁×#123	—	2	1	no	—
208	C₃₁×#123	—	2	2	no	—
209	C₃₁×C₂²⋊Q₈	—	2	1	no	—
210	C₃₁×C₂²⋊Q₈	—	2	2	no	—
211	C₃₁×C₂²⋊Q₈	—	2	1	no	—
212	C₃₁×C₂²⋊Q₈	—	2	2	no	—
213	C₃₁×C₂²⋊Q₈	—	2	1	no	—
214	C₃₁×C₂²⋊Q₈	—	2	2	no	—
215	C₃₁×C₂²⋊Q₈	—	2	1	no	—
216	C₃₁×C₂²⋊Q₈	—	2	2	no	—
217	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
219	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
222	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
225	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
226	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₃₁×#121	—	2	2	no	—
228	C₃₁×#121	—	2	2	no	—
229	C₃₁×#121	—	2	2	no	—
230	C₃₁×#121	—	2	1	no	—
231	C₃₁×#121	—	2	2	no	—
232	C₃₁×#121	—	2	2	no	—
233	C₃₁×#121	—	2	1	no	—
234	C₃₁×#121	—	2	2	no	—
235	C₃₁×#121	—	2	2	no	—
236	C₃₁×#121	—	2	2	no	—
237	C₃₁×#121	—	2	1	no	—
238	C₃₁×#121	—	2	2	no	—
239	C₃₁×#121	—	2	1	no	—
240	C₃₁×#121	—	2	2	no	—
241	C₃₁×#121	C₂³	1	2	yes	—
242	C₃₁×#121	C₂³	1	2	yes	—
243	C₃₁×#121	C₂³	1	2	yes	—
244	C₃₁×#121	C₂³	1	2	yes	—
245	C₃₁×#121	C₂³	1	1	yes	characteristic
246	C₃₁×#121	C₂³	1	2	yes	—
247	C₃₁×#121	C₂³	1	1	yes	characteristic
248	C₃₁×#121	C₂³	1	1	yes	characteristic
249	C₃₁×#121	C₂³	1	2	yes	—
250	C₃₁×#121	C₂³	1	1	yes	characteristic
251	C₃₁×#120	—	2	1	no	—
252	C₃₁×#120	—	2	2	no	—
253	C₃₁×#120	—	2	1	no	—
254	C₃₁×#120	—	2	2	no	—
255	C₃₁×#120	—	2	2	no	—
256	C₃₁×#120	—	2	2	no	—
257	C₃₁×#120	—	2	2	no	—
258	C₄×Q₈×C₃₁	—	2	1	no	—
259	C₄×Q₈×C₃₁	—	2	1	no	—
260	C₄×D₄×C₃₁	—	2	2	no	—
261	C₄×D₄×C₃₁	—	2	1	no	—
262	C₄×D₄×C₃₁	—	2	2	no	—
263	C₄×D₄×C₃₁	—	2	1	no	—
264	C₄×D₄×C₃₁	—	2	1	no	—
265	C₄×D₄×C₃₁	—	2	2	no	—
266	C₄×D₄×C₃₁	—	2	1	no	—
267	C₄×D₄×C₃₁	—	2	2	no	—
268	C₄×D₄×C₃₁	—	2	1	no	—
269	C₄×D₄×C₃₁	—	2	2	no	—
270	C₄×D₄×C₃₁	—	2	1	no	—
271	C₄×D₄×C₃₁	—	2	2	no	—
272	C₃₁×#117	C₂³	1	1	yes	characteristic
273	C₃₁×#117	C₂³	1	1	yes	characteristic
274	C₃₁×#117	C₂³	1	2	yes	—
275	C₃₁×#117	C₂³	1	2	yes	—
276	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
277	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
278	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
281	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
282	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
283	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
284	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
285	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
286	C₃₁×#107	C₂³	1	2	yes	—
287	C₃₁×#107	C₂³	1	2	yes	—
288	C₃₁×#107	C₂³	1	1	yes	characteristic
289	C₃₁×#107	C₂³	1	1	yes	characteristic
290	C₃₁×#107	C₂³	1	2	yes	—
291	C₃₁×#107	C₂³	1	2	yes	—
292	C₃₁×#106	C₂³	1	1	yes	characteristic
293	C₃₁×#106	C₂³	1	1	yes	characteristic
294	C₃₁×#106	C₂³	1	2	yes	—
295	C₃₁×#106	C₂³	1	2	yes	—
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	1	yes	characteristic
299	C₃₁×#103	C₂³	1	1	yes	characteristic
300	C₃₁×#103	C₂³	1	1	yes	characteristic
301	C₃₁×#103	C₂³	1	1	yes	characteristic
302	C₃₁×#103	C₂³	1	2	yes	—
303	C₃₁×#103	C₂³	1	2	yes	—
304	C₃₁×#103	C₂³	1	2	yes	—
305	C₃₁×#103	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	1	yes	characteristic
310	C₃₁×#102	C₂³	1	1	yes	characteristic
311	C₃₁×#102	C₂³	1	1	yes	characteristic
312	C₃₁×#102	C₂³	1	2	yes	—
313	C₃₁×#102	C₂³	1	2	yes	—
314	C₃₁×#102	C₂³	1	2	yes	—
315	C₃₁×#102	C₂³	1	2	yes	—
316	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
321	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
322	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
323	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
324	C₂⁴×C₃₁	—	2	2	no	—
325	C₂⁴×C₃₁	—	2	1	no	—
326	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
327	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
328	#41×C₃₁	—	2	2	no	—
329	#41×C₃₁	—	2	2	no	—
330	#41×C₃₁	—	2	2	no	—
331	#41×C₃₁	—	2	2	no	—
332	#41×C₃₁	—	2	2	no	—
333	#41×C₃₁	—	2	2	no	—
334	#41×C₃₁	—	2	2	no	—
335	#41×C₃₁	—	2	2	no	—
336	#41×C₃₁	—	4	2	no	—
337	#41×C₃₁	—	4	2	no	—
338	#41×C₃₁	—	4	4	no	—
339	#41×C₃₁	—	4	2	no	—
340	#41×C₃₁	—	4	2	no	—
341	#41×C₃₁	—	4	2	no	—
342	#41×C₃₁	—	4	2	no	—
343	#41×C₃₁	—	4	2	no	—
344	#41×C₃₁	—	4	2	no	—
345	#41×C₃₁	—	4	8	no	—
346	#41×C₃₁	—	4	4	no	—
347	#41×C₃₁	—	4	4	no	—
348	C₂×Q₈×C₃₁	—	2	2	no	—
349	C₂×Q₈×C₃₁	—	2	1	no	—
350	C₂×Q₈×C₃₁	—	2	2	no	—
351	C₂×Q₈×C₃₁	—	2	2	no	—
352	C₂×Q₈×C₃₁	—	4	2	no	—
353	C₂×Q₈×C₃₁	—	4	2	no	—
354	C₂×Q₈×C₃₁	—	4	2	no	—
355	C₂×Q₈×C₃₁	—	4	4	no	—
356	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
357	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
358	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
359	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
360	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
361	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
362	C₂×D₄×C₃₁	—	2	1	no	—
363	C₂×D₄×C₃₁	—	2	1	no	—
364	C₂×D₄×C₃₁	—	2	2	no	—
365	C₂×D₄×C₃₁	—	2	2	no	—
366	C₂×D₄×C₃₁	—	2	1	no	—
367	C₂×D₄×C₃₁	—	2	2	no	—
368	C₂×D₄×C₃₁	—	2	1	no	—
369	C₂×D₄×C₃₁	—	2	1	no	—
370	C₂×D₄×C₃₁	—	2	2	no	—
371	C₂×D₄×C₃₁	—	2	2	no	—
372	C₂×D₄×C₃₁	—	2	1	no	—
373	C₂×D₄×C₃₁	—	2	2	no	—
374	C₂×D₄×C₃₁	—	2	2	no	—
375	C₂×D₄×C₃₁	—	2	2	no	—
376	C₂×D₄×C₃₁	—	2	2	no	—
377	C₂×D₄×C₃₁	—	2	1	no	—
378	C₂×D₄×C₃₁	—	2	2	no	—
379	C₂×D₄×C₃₁	—	2	2	no	—
380	C₂×D₄×C₃₁	—	4	2	no	—
381	C₂×D₄×C₃₁	—	4	2	no	—
382	C₂×D₄×C₃₁	—	4	2	no	—
383	C₂×D₄×C₃₁	—	4	4	no	—
384	C₂×D₄×C₃₁	—	4	8	no	—
385	C₂×D₄×C₃₁	—	4	4	no	—
386	C₂×D₄×C₃₁	—	8	2	no	—
387	C₂×D₄×C₃₁	—	8	4	no	—
388	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
391	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
392	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
397	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₃₁	—	2	2	no	—
399	C₂²×C₄×C₃₁	—	2	2	no	—
400	C₂²×C₄×C₃₁	—	2	2	no	—
401	C₂²×C₄×C₃₁	—	2	1	no	—
402	C₂²×C₄×C₃₁	—	2	2	no	—
403	C₂²×C₄×C₃₁	—	2	1	no	—
404	C₂²×C₄×C₃₁	—	2	2	no	—
405	C₂²×C₄×C₃₁	—	2	1	no	—
406	C₂²×C₄×C₃₁	—	2	2	no	—
407	C₂²×C₄×C₃₁	—	2	1	no	—
408	C₂²×C₄×C₃₁	—	2	2	no	—
409	C₂²×C₄×C₃₁	—	2	1	no	—
410	C₂²×C₄×C₃₁	—	4	2	no	—
411	C₂²×C₄×C₃₁	—	4	2	no	—
412	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
416	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
417	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
418	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
420	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
423	Q₁₆×C₃₁	—	4	1	no	—
424	Q₁₆×C₃₁	—	4	2	no	—
425	SD₁₆×C₃₁	—	4	2	no	—
426	SD₁₆×C₃₁	—	4	2	no	—
427	SD₁₆×C₃₁	—	4	1	no	—
428	SD₁₆×C₃₁	—	4	1	no	—
429	SD₁₆×C₃₁	—	4	2	no	—
430	SD₁₆×C₃₁	—	4	2	no	—
431	D₈×C₃₁	—	4	1	no	—
432	D₈×C₃₁	—	4	2	no	—
433	M₁₆×C₃₁	—	2	2	no	—
434	M₁₆×C₃₁	—	2	2	no	—
435	M₁₆×C₃₁	—	4	1	no	—
436	M₁₆×C₃₁	—	4	1	no	—
437	M₁₆×C₃₁	—	4	1	no	—
438	M₁₆×C₃₁	—	4	1	no	—
439	M₁₆×C₃₁	—	4	2	no	—
440	C₂×C₈×C₃₁	—	2	2	no	—
441	C₂×C₈×C₃₁	—	2	2	no	—
442	C₂×C₈×C₃₁	—	4	2	no	—
443	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
444	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
445	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
446	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
447	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
448	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
449	C₄⋊C₄×C₃₁	—	2	2	no	—
450	C₄⋊C₄×C₃₁	—	2	1	no	—
451	C₄⋊C₄×C₃₁	—	2	2	no	—
452	C₄⋊C₄×C₃₁	—	2	2	no	—
453	C₄⋊C₄×C₃₁	—	2	2	no	—
454	C₄⋊C₄×C₃₁	—	2	2	no	—
455	C₄⋊C₄×C₃₁	—	2	1	no	—
456	C₄⋊C₄×C₃₁	—	2	2	no	—
457	C₄⋊C₄×C₃₁	—	2	1	no	—
458	C₄⋊C₄×C₃₁	—	2	1	no	—
459	C₄⋊C₄×C₃₁	—	2	2	no	—
460	C₄⋊C₄×C₃₁	—	2	1	no	—
461	C₄⋊C₄×C₃₁	—	2	2	no	—
462	C₄⋊C₄×C₃₁	—	2	1	no	—
463	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
465	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
467	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
468	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
469	C₂²⋊C₄×C₃₁	—	2	2	no	—
470	C₂²⋊C₄×C₃₁	—	2	1	no	—
471	C₂²⋊C₄×C₃₁	—	2	2	no	—
472	C₂²⋊C₄×C₃₁	—	2	2	no	—
473	C₂²⋊C₄×C₃₁	—	2	2	no	—
474	C₂²⋊C₄×C₃₁	—	2	2	no	—
475	C₂²⋊C₄×C₃₁	—	2	1	no	—
476	C₂²⋊C₄×C₃₁	—	2	2	no	—
477	C₂²⋊C₄×C₃₁	—	2	1	no	—
478	C₂²⋊C₄×C₃₁	—	2	1	no	—
479	C₂²⋊C₄×C₃₁	—	2	1	no	—
480	C₂²⋊C₄×C₃₁	—	2	2	no	—
481	C₂²⋊C₄×C₃₁	—	2	2	no	—
482	C₂²⋊C₄×C₃₁	—	2	1	no	—
483	C₂²⋊C₄×C₃₁	—	2	2	no	—
484	C₂²⋊C₄×C₃₁	—	2	1	no	—
485	C₂²⋊C₄×C₃₁	—	2	2	no	—
486	C₂²⋊C₄×C₃₁	—	2	2	no	—
487	C₂²⋊C₄×C₃₁	—	2	2	no	—
488	C₂²⋊C₄×C₃₁	—	2	1	no	—
489	C₂²⋊C₄×C₃₁	—	2	2	no	—
490	C₂²⋊C₄×C₃₁	—	2	1	no	—
491	C₂²⋊C₄×C₃₁	—	2	2	no	—
492	C₂²⋊C₄×C₃₁	—	2	1	no	—
493	C₄²×C₃₁	—	2	2	no	—
494	C₄²×C₃₁	—	2	1	no	—
495	C₄²×C₃₁	—	2	2	no	—
496	C₄²×C₃₁	—	2	1	no	—
497	#60772	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
498	C₂³×C₃₁	—	2	2	no	—
499	C₂³×C₃₁	—	2	1	no	—
500	C₂³×C₃₁	—	2	2	no	—
501	C₂³×C₃₁	—	2	1	no	—
502	C₂³×C₃₁	—	4	2	no	—
503	C₂³×C₃₁	—	4	1	no	—
504	C₂³×C₃₁	—	4	2	no	—
505	C₂³×C₃₁	—	4	1	no	—
506	C₂³×C₃₁	—	4	2	no	—
507	C₂³×C₃₁	—	4	4	no	—
508	C₂³×C₃₁	—	4	2	no	—
509	C₂³×C₃₁	—	8	1	no	—
510	C₂³×C₃₁	—	8	2	no	—
511	C₂³×C₃₁	—	8	1	no	—
512	C₂³×C₃₁	—	8	2	no	—
513	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
514	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
515	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
516	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
517	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	Q₈×C₃₁	—	2	2	no	—
519	Q₈×C₃₁	—	2	2	no	—
520	Q₈×C₃₁	—	2	2	no	—
521	Q₈×C₃₁	—	2	1	no	—
522	Q₈×C₃₁	—	2	2	no	—
523	Q₈×C₃₁	—	2	1	no	—
524	Q₈×C₃₁	—	2	1	no	—
525	Q₈×C₃₁	—	2	1	no	—
526	Q₈×C₃₁	—	4	2	no	—
527	Q₈×C₃₁	—	4	4	no	—
528	Q₈×C₃₁	—	4	2	no	—
529	D₄×C₃₁	—	2	4	no	—
530	D₄×C₃₁	—	2	4	no	—
531	D₄×C₃₁	—	2	2	no	—
532	D₄×C₃₁	—	2	2	no	—
533	D₄×C₃₁	—	2	1	no	—
534	D₄×C₃₁	—	2	2	no	—
535	D₄×C₃₁	—	2	1	no	—
536	D₄×C₃₁	—	2	1	no	—
537	D₄×C₃₁	—	2	2	no	—
538	D₄×C₃₁	—	2	1	no	—
539	D₄×C₃₁	—	4	2	no	—
540	D₄×C₃₁	—	4	2	no	—
541	D₄×C₃₁	—	4	2	no	—
542	D₄×C₃₁	—	4	4	no	—
543	D₄×C₃₁	—	4	2	no	—
544	D₄×C₃₁	—	4	4	no	—
545	D₄×C₃₁	—	4	4	no	—
546	D₄×C₃₁	—	4	2	no	—
547	D₄×C₃₁	—	4	4	no	—
548	D₄×C₃₁	—	4	2	no	—
549	D₄×C₃₁	—	4	2	no	—
550	D₄×C₃₁	—	4	2	no	—
551	D₄×C₃₁	—	8	2	no	—
552	D₄×C₃₁	—	8	1	no	—
553	D₄×C₃₁	—	8	1	no	—
554	D₄×C₃₁	—	8	2	no	—
555	D₄×C₃₁	—	8	2	no	—
556	D₄×C₃₁	—	8	2	no	—
557	D₄×C₃₁	—	8	2	no	—
558	C₂×C₄×C₃₁	—	2	2	no	—
559	C₂×C₄×C₃₁	—	2	2	no	—
560	C₂×C₄×C₃₁	—	2	2	no	—
561	C₂×C₄×C₃₁	—	2	1	no	—
562	C₂×C₄×C₃₁	—	2	1	no	—
563	C₂×C₄×C₃₁	—	2	1	no	—
564	C₂×C₄×C₃₁	—	2	1	no	—
565	C₂×C₄×C₃₁	—	2	2	no	—
566	C₂×C₄×C₃₁	—	2	2	no	—
567	C₂×C₄×C₃₁	—	2	2	no	—
568	C₂×C₄×C₃₁	—	2	2	no	—
569	C₂×C₄×C₃₁	—	2	1	no	—
570	C₂×C₄×C₃₁	—	2	1	no	—
571	C₂×C₄×C₃₁	—	2	2	no	—
572	C₂×C₄×C₃₁	—	2	1	no	—
573	C₂×C₄×C₃₁	—	2	2	no	—
574	C₂×C₄×C₃₁	—	2	1	no	—
575	C₂×C₄×C₃₁	—	2	1	no	—
576	C₂×C₄×C₃₁	—	2	2	no	—
577	C₂×C₄×C₃₁	—	2	1	no	—
578	C₂×C₄×C₃₁	—	4	2	no	—
579	C₂×C₄×C₃₁	—	4	2	no	—
580	C₂×C₄×C₃₁	—	4	2	no	—
581	C₂×C₄×C₃₁	—	4	4	no	—
582	C₂×C₄×C₃₁	—	4	4	no	—
583	C₂×C₄×C₃₁	—	4	4	no	—
584	C₂×C₄×C₃₁	—	4	2	no	—
585	C₂×C₄×C₃₁	—	4	2	no	—
586	C₂×C₄×C₃₁	—	4	2	no	—
587	C₂×C₄×C₃₁	—	8	1	no	—
588	C₂×C₄×C₃₁	—	8	2	no	—
589	C₂×C₄×C₃₁	—	8	1	no	—
590	C₂×C₄×C₃₁	—	8	2	no	—
591	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
592	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
593	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
594	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
595	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
596	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
597	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
598	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
599	C₈×C₃₁	—	2	1	no	—
600	C₈×C₃₁	—	2	1	no	—
601	C₈×C₃₁	—	2	1	no	—
602	C₈×C₃₁	—	2	1	no	—
603	C₈×C₃₁	—	2	2	no	—
604	C₈×C₃₁	—	2	2	no	—
605	#3489	C₂×C₃₁	1	1	yes	characteristic, complemented
606	#3488	C₂×C₃₁	1	1	yes	characteristic, complemented
607	#3203	C₂×C₃₁	1	2	yes	complemented
608	#3201	C₂×C₃₁	1	2	yes	complemented
609	#3200	C₂×C₃₁	1	2	yes	complemented
610	#3198	C₂×C₃₁	1	2	yes	complemented
611	#3197	C₂×C₃₁	1	2	yes	complemented
612	#3196	C₂×C₃₁	1	2	yes	complemented
613	#3194	C₂×C₃₁	1	2	yes	complemented
614	#3193	C₂×C₃₁	1	2	yes	complemented
615	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
616	#3098	C₂×C₃₁	1	1	yes	characteristic, complemented
617	#3097	C₂×C₃₁	1	1	yes	characteristic, complemented
618	#3096	C₂×C₃₁	1	1	yes	characteristic, complemented
619	#3056	C₂×C₃₁	1	1	yes	characteristic, complemented
620	#3055	C₂×C₃₁	1	1	yes	characteristic, complemented
621	#3054	C₂×C₃₁	1	1	yes	characteristic, complemented
622	C₂×#468	C₂×C₃₁	1	1	yes	characteristic, complemented
623	#3013	C₂×C₃₁	1	1	yes	characteristic, complemented
624	#3012	C₂×C₃₁	1	1	yes	characteristic, complemented
625	#3010	C₂×C₃₁	1	1	yes	characteristic, complemented
626	#3009	C₂×C₃₁	1	1	yes	characteristic, complemented
627	#2879	C₂×C₃₁	1	1	yes	characteristic, complemented
628	C₂²×C₃₁	—	2	1	no	—
629	C₂²×C₃₁	—	2	1	no	—
630	C₂²×C₃₁	—	2	2	no	—
631	C₂²×C₃₁	—	2	2	no	—
632	C₂²×C₃₁	—	2	1	no	—
633	C₂²×C₃₁	—	2	1	no	—
634	C₂²×C₃₁	—	2	1	no	—
635	C₂²×C₃₁	—	2	1	no	—
636	C₂²×C₃₁	—	2	2	no	—
637	C₂²×C₃₁	—	2	2	no	—
638	C₂²×C₃₁	—	2	1	no	—
639	C₂²×C₃₁	—	2	1	no	—
640	C₂²×C₃₁	—	2	2	no	—
641	C₂²×C₃₁	—	2	2	no	—
642	C₂²×C₃₁	—	4	2	no	—
643	C₂²×C₃₁	—	4	1	no	—
644	C₂²×C₃₁	—	4	1	no	—
645	C₂²×C₃₁	—	4	1	no	—
646	C₂²×C₃₁	—	4	2	no	—
647	C₂²×C₃₁	—	4	1	no	—
648	C₂²×C₃₁	—	4	1	no	—
649	C₂²×C₃₁	—	4	2	no	—
650	C₂²×C₃₁	—	4	1	no	—
651	C₂²×C₃₁	—	8	2	no	—
652	C₂²×C₃₁	—	8	4	no	—
653	C₂²×C₃₁	—	16	2	no	—
654	C₂²×C₃₁	—	16	4	no	—
655	C₂²×C₃₁	#534	1	2	yes	—
656	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
657	C₄×C₃₁	—	2	1	no	—
658	C₄×C₃₁	—	2	1	no	—
659	C₄×C₃₁	—	2	2	no	—
660	C₄×C₃₁	—	2	2	no	—
661	C₄×C₃₁	—	4	2	no	—
662	C₄×C₃₁	—	4	1	no	—
663	C₄×C₃₁	—	4	2	no	—
664	C₄×C₃₁	—	4	1	no	—
665	C₄×C₃₁	—	4	1	no	—
666	C₄×C₃₁	—	4	1	no	—
667	C₄×C₃₁	—	4	1	no	—
668	C₄×C₃₁	—	4	2	no	—
669	C₄×C₃₁	—	4	1	no	—
670	C₄×C₃₁	#534	1	2	yes	—
671	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
672	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic, complemented
674	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	1	yes	characteristic
675	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
676	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic, complemented
677	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	1	yes	characteristic, complemented
678	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
681	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
682	#550	—	2	1	no	—
683	D₄×Q₈	—	2	1	no	—
684	#548	—	2	1	no	—
685	#548	—	2	1	no	—
686	#547	—	2	2	no	—
687	#547	—	2	1	no	—
688	#546	—	2	2	no	—
689	#546	—	2	1	no	—
690	#546	—	2	2	no	—
691	#546	—	2	1	no	—
692	D₄²	—	2	2	no	—
693	D₄²	—	2	1	no	—
694	#537	C₂²×C₃₁	1	1	yes	characteristic
695	#537	C₂²×C₃₁	1	1	yes	characteristic
696	#537	C₂²×C₃₁	1	2	yes	—
697	#537	C₂²×C₃₁	1	2	yes	complemented
698	#536	C₂²×C₃₁	1	1	yes	characteristic
699	#536	C₂²×C₃₁	1	2	yes	complemented
700	#535	C₂²×C₃₁	1	1	yes	characteristic
701	#535	C₂²×C₃₁	1	2	yes	—
702	#525	C₂²×C₃₁	1	2	yes	—
703	#525	C₂²×C₃₁	1	1	yes	characteristic
704	#525	C₂²×C₃₁	1	2	yes	complemented
705	#525	C₂²×C₃₁	1	1	yes	characteristic, complemented
706	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
707	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
708	C₂×#121	C₂²×C₃₁	1	2	yes	—
709	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
710	#520	C₂²×C₃₁	1	1	yes	characteristic
711	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
712	#485	C₂²×C₃₁	1	2	yes	complemented
713	#485	C₂²×C₃₁	1	2	yes	complemented
714	#485	C₂²×C₃₁	1	2	yes	complemented
715	#485	C₂²×C₃₁	1	2	yes	complemented
716	#484	C₂²×C₃₁	1	2	yes	complemented
717	#484	C₂²×C₃₁	1	2	yes	complemented
718	#484	C₂²×C₃₁	1	2	yes	complemented
719	#483	C₂²×C₃₁	1	2	yes	complemented
720	#482	C₂²×C₃₁	1	2	yes	complemented
721	#482	C₂²×C₃₁	1	2	yes	complemented
722	#482	C₂²×C₃₁	1	2	yes	complemented
723	#482	C₂²×C₃₁	1	2	yes	complemented
724	#481	C₂²×C₃₁	1	2	yes	complemented
725	#480	C₂²×C₃₁	1	2	yes	complemented
726	#480	C₂²×C₃₁	1	2	yes	complemented
727	#480	C₂²×C₃₁	1	2	yes	complemented
728	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
729	#470	C₂²×C₃₁	1	2	yes	complemented
730	#470	C₂²×C₃₁	1	1	yes	characteristic, complemented
731	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
732	#469	C₂²×C₃₁	1	2	yes	complemented
733	#469	C₂²×C₃₁	1	1	yes	characteristic, complemented
734	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
735	#468	C₂²×C₃₁	1	2	yes	complemented
736	#468	C₂²×C₃₁	1	2	yes	complemented
737	#468	C₂²×C₃₁	1	2	yes	complemented
738	#468	C₂²×C₃₁	1	2	yes	complemented
739	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
740	#468	C₂²×C₃₁	1	2	yes	complemented
741	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
742	#468	C₂²×C₃₁	1	2	yes	complemented
743	#468	C₂²×C₃₁	1	1	yes	characteristic, complemented
744	#467	C₂²×C₃₁	1	2	yes	complemented
745	#466	C₂²×C₃₁	1	2	yes	complemented
746	#465	C₂²×C₃₁	1	2	yes	complemented
747	#465	C₂²×C₃₁	1	2	yes	complemented
748	#452	C₂²×C₃₁	1	2	yes	complemented
749	#452	C₂²×C₃₁	1	2	yes	complemented
750	#452	C₂²×C₃₁	1	2	yes	complemented
751	#452	C₂²×C₃₁	1	2	yes	complemented
752	#451	C₂²×C₃₁	1	2	yes	complemented
753	#450	C₂²×C₃₁	1	2	yes	complemented
754	#450	C₂²×C₃₁	1	2	yes	complemented
755	#450	C₂²×C₃₁	1	2	yes	complemented
756	#449	C₂²×C₃₁	1	2	yes	complemented
757	#449	C₂²×C₃₁	1	2	yes	complemented
758	#449	C₂²×C₃₁	1	2	yes	complemented
759	#449	C₂²×C₃₁	1	2	yes	complemented
760	#448	C₂²×C₃₁	1	2	yes	complemented
761	#448	C₂²×C₃₁	1	2	yes	complemented
762	#448	C₂²×C₃₁	1	2	yes	complemented
763	#447	C₂²×C₃₁	1	2	yes	complemented
764	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
765	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
766	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
767	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic, complemented
768	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
769	#418	C₂²×C₃₁	1	1	yes	characteristic, complemented
770	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
771	#417	C₂²×C₃₁	1	1	yes	characteristic, complemented
772	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
773	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
774	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic, complemented
775	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic, complemented
776	#408	C₂²×C₃₁	1	1	yes	characteristic
777	#408	C₂²×C₃₁	1	1	yes	characteristic
778	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
779	#408	C₂²×C₃₁	1	1	yes	characteristic, complemented
780	#408	C₂²×C₃₁	1	2	yes	complemented
781	#408	C₂²×C₃₁	1	2	yes	complemented
782	#407	C₂²×C₃₁	1	2	yes	complemented
783	#407	C₂²×C₃₁	1	2	yes	complemented
784	C₂×C₃₁	—	2	2	no	—
785	C₂×C₃₁	—	4	2	no	—
786	C₂×C₃₁	—	4	1	no	—
787	C₂×C₃₁	—	4	1	no	—
788	C₂×C₃₁	—	4	2	no	—
789	C₂×C₃₁	—	8	1	no	—
790	C₂×C₃₁	—	8	2	no	—
791	C₂×C₃₁	—	8	1	no	—
792	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
793	C₂×C₃₁	#3585	1	1	yes	characteristic
794	C₂×C₃₁	#3586	1	1	yes	characteristic
795	2₋¹⁺⁴	—	4	2	no	—
796	2₋¹⁺⁴	—	4	2	no	—
797	H(5,𝔽₂)	—	4	2	no	—
798	H(5,𝔽₂)	—	4	2	no	—
799	C₂×#41	—	2	1	no	—
800	C₂×#41	—	2	2	no	—
801	C₂×#41	—	2	1	no	—
802	C₂×#41	—	4	2	no	—
803	C₂×#41	—	4	2	no	—
804	C₂×#41	D₄×C₃₁	1	2	yes	—
805	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
806	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
807	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
808	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
809	C₂×#41	C₂³×C₃₁	1	2	yes	—
810	C₂×#41	C₂³×C₃₁	1	2	yes	—
811	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
812	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
813	C₂×#41	C₂³×C₃₁	1	2	yes	—
814	C₂²×Q₈	—	2	1	no	—
815	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
816	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
817	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
818	C₂²×D₄	—	2	1	no	—
819	C₂²×D₄	—	2	2	no	—
820	C₂²×D₄	—	2	2	no	—
821	C₂²×D₄	—	2	1	no	—
822	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
823	C₂²×D₄	D₄×C₃₁	1	2	yes	—
824	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
825	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
826	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
827	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
828	#137	—	4	2	no	—
829	AGL(1,ℤ/8)	—	4	2	no	—
830	#135	—	4	2	no	—
831	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
832	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
833	C₂×SD₁₆	—	4	2	no	—
834	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
835	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
836	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
837	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
838	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
839	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
840	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
841	C₂×D₈	C₂³×C₃₁	1	2	yes	—
842	C₂×M₁₆	—	4	2	no	—
843	C₂×M₁₆	—	4	2	no	—
844	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
845	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
846	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
847	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
848	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
849	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
850	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
851	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
852	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
853	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
854	C₄⋊Q₈	—	2	1	no	—
855	C₄⋊Q₈	—	2	2	no	—
856	#127	—	2	1	no	—
857	#127	—	2	2	no	—
858	#124	—	2	1	no	—
859	#124	—	2	2	no	—
860	#124	—	2	1	no	—
861	#124	—	2	2	no	—
862	#123	—	2	2	no	—
863	#123	—	2	2	no	—
864	#123	—	2	2	no	—
865	#123	—	2	1	no	—
866	#123	—	2	2	no	—
867	#123	—	2	1	no	—
868	#123	—	2	2	no	—
869	C₂²⋊Q₈	—	2	1	no	—
870	C₂²⋊Q₈	—	2	2	no	—
871	C₂²⋊Q₈	—	2	1	no	—
872	C₂²⋊Q₈	—	2	2	no	—
873	C₂²⋊Q₈	—	2	1	no	—
874	C₂²⋊Q₈	—	2	2	no	—
875	C₂²⋊Q₈	—	2	1	no	—
876	C₂²⋊Q₈	—	2	2	no	—
877	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
878	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
879	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
881	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
882	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
883	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
884	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
885	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
886	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
887	#121	—	2	2	no	—
888	#121	—	2	2	no	—
889	#121	—	2	2	no	—
890	#121	—	2	1	no	—
891	#121	—	2	2	no	—
892	#121	—	2	2	no	—
893	#121	—	2	1	no	—
894	#121	—	2	2	no	—
895	#121	—	2	2	no	—
896	#121	—	2	2	no	—
897	#121	—	2	1	no	—
898	#121	—	2	2	no	—
899	#121	—	2	1	no	—
900	#121	—	2	2	no	—
901	#121	C₂³×C₃₁	1	1	yes	characteristic
902	#121	C₂³×C₃₁	1	2	yes	—
903	#121	C₂³×C₃₁	1	2	yes	—
904	#121	C₂³×C₃₁	1	2	yes	—
905	#121	C₂³×C₃₁	1	2	yes	—
906	#121	C₂³×C₃₁	1	2	yes	—
907	#121	C₂³×C₃₁	1	1	yes	characteristic
908	#121	C₂³×C₃₁	1	1	yes	characteristic
909	#121	C₂³×C₃₁	1	2	yes	—
910	#121	C₂³×C₃₁	1	1	yes	characteristic
911	#120	—	2	1	no	—
912	#120	—	2	2	no	—
913	#120	—	2	1	no	—
914	#120	—	2	2	no	—
915	#120	—	2	2	no	—
916	#120	—	2	2	no	—
917	#120	—	2	2	no	—
918	C₄×Q₈	—	2	1	no	—
919	C₄×Q₈	—	2	1	no	—
920	C₄×D₄	—	2	2	no	—
921	C₄×D₄	—	2	1	no	—
922	C₄×D₄	—	2	2	no	—
923	C₄×D₄	—	2	1	no	—
924	C₄×D₄	—	2	1	no	—
925	C₄×D₄	—	2	2	no	—
926	C₄×D₄	—	2	1	no	—
927	C₄×D₄	—	2	2	no	—
928	C₄×D₄	—	2	1	no	—
929	C₄×D₄	—	2	2	no	—
930	C₄×D₄	—	2	1	no	—
931	C₄×D₄	—	2	2	no	—
932	#117	C₂³×C₃₁	1	1	yes	characteristic
933	#117	C₂³×C₃₁	1	2	yes	—
934	#117	C₂³×C₃₁	1	1	yes	characteristic
935	#117	C₂³×C₃₁	1	2	yes	—
936	C₂×C₄⋊C₄	—	2	1	no	—
937	C₂×C₄⋊C₄	—	2	2	no	—
938	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
940	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
942	C₂×C₂²⋊C₄	—	2	1	no	—
943	C₂×C₂²⋊C₄	—	2	2	no	—
944	C₂×C₂²⋊C₄	—	2	1	no	—
945	C₂×C₂²⋊C₄	—	2	2	no	—
946	#107	C₂³×C₃₁	1	2	yes	—
947	#107	C₂³×C₃₁	1	2	yes	—
948	#107	C₂³×C₃₁	1	1	yes	characteristic
949	#107	C₂³×C₃₁	1	1	yes	characteristic
950	#107	C₂³×C₃₁	1	2	yes	—
951	#107	C₂³×C₃₁	1	2	yes	—
952	#106	C₂³×C₃₁	1	1	yes	characteristic
953	#106	C₂³×C₃₁	1	1	yes	characteristic
954	#106	C₂³×C₃₁	1	2	yes	—
955	#106	C₂³×C₃₁	1	2	yes	—
956	#103	C₂³×C₃₁	1	2	yes	—
957	#103	C₂³×C₃₁	1	2	yes	—
958	#103	C₂³×C₃₁	1	1	yes	characteristic
959	#103	C₂³×C₃₁	1	1	yes	characteristic
960	#103	C₂³×C₃₁	1	1	yes	characteristic
961	#103	C₂³×C₃₁	1	1	yes	characteristic
962	#103	C₂³×C₃₁	1	2	yes	—
963	#103	C₂³×C₃₁	1	2	yes	—
964	#103	C₂³×C₃₁	1	2	yes	—
965	#103	C₂³×C₃₁	1	2	yes	—
966	#102	C₂³×C₃₁	1	2	yes	—
967	#102	C₂³×C₃₁	1	2	yes	—
968	#102	C₂³×C₃₁	1	1	yes	characteristic
969	#102	C₂³×C₃₁	1	1	yes	characteristic
970	#102	C₂³×C₃₁	1	1	yes	characteristic
971	#102	C₂³×C₃₁	1	1	yes	characteristic
972	#102	C₂³×C₃₁	1	2	yes	—
973	#102	C₂³×C₃₁	1	2	yes	—
974	#102	C₂³×C₃₁	1	2	yes	—
975	#102	C₂³×C₃₁	1	2	yes	—
976	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
977	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
978	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
979	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
980	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
981	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
982	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
983	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
984	C₃₁	#60772	1	1	yes	characteristic, direct product factor, Sylow
985	C₂⁴	—	2	2	no	—
986	C₂⁴	—	2	1	no	—
987	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
988	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
989	#41	—	2	2	no	—
990	#41	—	2	2	no	—
991	#41	—	2	2	no	—
992	#41	—	2	2	no	—
993	#41	—	2	2	no	—
994	#41	—	2	2	no	—
995	#41	—	2	2	no	—
996	#41	—	2	2	no	—
997	#41	—	4	2	no	—
998	#41	—	4	2	no	—
999	#41	—	4	4	no	—
1000	#41	—	4	2	no	—
1001	#41	—	4	2	no	—
1002	#41	—	4	2	no	—
1003	#41	—	4	2	no	—
1004	#41	—	4	2	no	—
1005	#41	—	4	2	no	—
1006	#41	—	4	8	no	—
1007	#41	—	4	4	no	—
1008	#41	—	4	4	no	—
1009	C₂×Q₈	—	2	2	no	—
1010	C₂×Q₈	—	2	1	no	—
1011	C₂×Q₈	—	2	2	no	—
1012	C₂×Q₈	—	2	2	no	—
1013	C₂×Q₈	—	4	2	no	—
1014	C₂×Q₈	—	4	2	no	—
1015	C₂×Q₈	—	4	2	no	—
1016	C₂×Q₈	—	4	4	no	—
1017	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1018	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
1019	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
1020	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
1021	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1022	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₂×D₄	—	2	1	no	—
1024	C₂×D₄	—	2	1	no	—
1025	C₂×D₄	—	2	2	no	—
1026	C₂×D₄	—	2	2	no	—
1027	C₂×D₄	—	2	1	no	—
1028	C₂×D₄	—	2	2	no	—
1029	C₂×D₄	—	2	1	no	—
1030	C₂×D₄	—	2	1	no	—
1031	C₂×D₄	—	2	2	no	—
1032	C₂×D₄	—	2	2	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	2	no	—
1040	C₂×D₄	—	2	2	no	—
1041	C₂×D₄	—	4	2	no	—
1042	C₂×D₄	—	4	2	no	—
1043	C₂×D₄	—	4	2	no	—
1044	C₂×D₄	—	4	4	no	—
1045	C₂×D₄	—	4	8	no	—
1046	C₂×D₄	—	4	4	no	—
1047	C₂×D₄	—	8	2	no	—
1048	C₂×D₄	—	8	4	no	—
1049	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1050	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1051	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1052	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1053	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1054	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1055	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
1056	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1057	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
1058	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
1059	C₂²×C₄	—	2	2	no	—
1060	C₂²×C₄	—	2	2	no	—
1061	C₂²×C₄	—	2	2	no	—
1062	C₂²×C₄	—	2	1	no	—
1063	C₂²×C₄	—	2	2	no	—
1064	C₂²×C₄	—	2	1	no	—
1065	C₂²×C₄	—	2	2	no	—
1066	C₂²×C₄	—	2	1	no	—
1067	C₂²×C₄	—	2	2	no	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	2	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	4	2	no	—
1072	C₂²×C₄	—	4	2	no	—
1073	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1074	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1075	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
1076	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1077	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1078	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
1079	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1080	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
1081	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1082	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1083	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1084	Q₁₆	—	4	1	no	—
1085	Q₁₆	—	4	2	no	—
1086	SD₁₆	—	4	2	no	—
1087	SD₁₆	—	4	2	no	—
1088	SD₁₆	—	4	1	no	—
1089	SD₁₆	—	4	1	no	—
1090	SD₁₆	—	4	2	no	—
1091	SD₁₆	—	4	2	no	—
1092	D₈	—	4	1	no	—
1093	D₈	—	4	2	no	—
1094	M₁₆	—	2	2	no	—
1095	M₁₆	—	2	2	no	—
1096	M₁₆	—	4	1	no	—
1097	M₁₆	—	4	1	no	—
1098	M₁₆	—	4	1	no	—
1099	M₁₆	—	4	1	no	—
1100	M₁₆	—	4	2	no	—
1101	C₂×C₈	—	2	2	no	—
1102	C₂×C₈	—	2	2	no	—
1103	C₂×C₈	—	4	2	no	—
1104	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1105	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1106	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1107	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1108	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
1109	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
1110	C₄⋊C₄	—	2	2	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	2	no	—
1113	C₄⋊C₄	—	2	2	no	—
1114	C₄⋊C₄	—	2	2	no	—
1115	C₄⋊C₄	—	2	2	no	—
1116	C₄⋊C₄	—	2	1	no	—
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	1	no	—
1119	C₄⋊C₄	—	2	1	no	—
1120	C₄⋊C₄	—	2	2	no	—
1121	C₄⋊C₄	—	2	1	no	—
1122	C₄⋊C₄	—	2	2	no	—
1123	C₄⋊C₄	—	2	1	no	—
1124	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1125	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1126	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1127	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1128	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
1129	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
1130	C₂²⋊C₄	—	2	2	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	2	no	—
1133	C₂²⋊C₄	—	2	2	no	—
1134	C₂²⋊C₄	—	2	2	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	1	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	1	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	2	no	—
1142	C₂²⋊C₄	—	2	2	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	2	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	2	no	—
1147	C₂²⋊C₄	—	2	2	no	—
1148	C₂²⋊C₄	—	2	2	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	—	2	2	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	2	no	—
1153	C₂²⋊C₄	—	2	1	no	—
1154	C₄²	—	2	2	no	—
1155	C₄²	—	2	1	no	—
1156	C₄²	—	2	2	no	—
1157	C₄²	—	2	1	no	—
1158	C₂³	—	2	2	no	—
1159	C₂³	—	2	1	no	—
1160	C₂³	—	2	2	no	—
1161	C₂³	—	2	1	no	—
1162	C₂³	—	4	2	no	—
1163	C₂³	—	4	1	no	—
1164	C₂³	—	4	2	no	—
1165	C₂³	—	4	1	no	—
1166	C₂³	—	4	2	no	—
1167	C₂³	—	4	4	no	—
1168	C₂³	—	4	2	no	—
1169	C₂³	—	8	1	no	—
1170	C₂³	—	8	2	no	—
1171	C₂³	—	8	1	no	—
1172	C₂³	—	8	2	no	—
1173	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1174	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1175	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1176	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1177	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1178	Q₈	—	2	2	no	—
1179	Q₈	—	2	2	no	—
1180	Q₈	—	2	2	no	—
1181	Q₈	—	2	1	no	—
1182	Q₈	—	2	2	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	2	1	no	—
1185	Q₈	—	2	1	no	—
1186	Q₈	—	4	2	no	—
1187	Q₈	—	4	4	no	—
1188	Q₈	—	4	2	no	—
1189	D₄	—	2	4	no	—
1190	D₄	—	2	4	no	—
1191	D₄	—	2	2	no	—
1192	D₄	—	2	2	no	—
1193	D₄	—	2	1	no	—
1194	D₄	—	2	2	no	—
1195	D₄	—	2	1	no	—
1196	D₄	—	2	1	no	—
1197	D₄	—	2	2	no	—
1198	D₄	—	2	1	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	4	2	no	—
1201	D₄	—	4	2	no	—
1202	D₄	—	4	4	no	—
1203	D₄	—	4	2	no	—
1204	D₄	—	4	4	no	—
1205	D₄	—	4	4	no	—
1206	D₄	—	4	2	no	—
1207	D₄	—	4	4	no	—
1208	D₄	—	4	2	no	—
1209	D₄	—	4	2	no	—
1210	D₄	—	4	2	no	—
1211	D₄	—	8	2	no	—
1212	D₄	—	8	1	no	—
1213	D₄	—	8	1	no	—
1214	D₄	—	8	2	no	—
1215	D₄	—	8	2	no	—
1216	D₄	—	8	2	no	—
1217	D₄	—	8	2	no	—
1218	C₂×C₄	—	2	2	no	—
1219	C₂×C₄	—	2	2	no	—
1220	C₂×C₄	—	2	2	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	2	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	2	2	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	2	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	2	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	4	2	no	—
1239	C₂×C₄	—	4	2	no	—
1240	C₂×C₄	—	4	2	no	—
1241	C₂×C₄	—	4	4	no	—
1242	C₂×C₄	—	4	4	no	—
1243	C₂×C₄	—	4	4	no	—
1244	C₂×C₄	—	4	2	no	—
1245	C₂×C₄	—	4	2	no	—
1246	C₂×C₄	—	4	2	no	—
1247	C₂×C₄	—	8	1	no	—
1248	C₂×C₄	—	8	2	no	—
1249	C₂×C₄	—	8	1	no	—
1250	C₂×C₄	—	8	2	no	—
1251	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1252	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1253	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1254	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1255	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1256	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1257	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
1258	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1259	C₈	—	2	1	no	—
1260	C₈	—	2	1	no	—
1261	C₈	—	2	1	no	—
1262	C₈	—	2	1	no	—
1263	C₈	—	2	2	no	—
1264	C₈	—	2	2	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	2	2	no	—
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	2	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	1	no	—
1275	C₂²	—	2	1	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	2	2	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	2	no	—
1281	C₂²	—	4	1	no	—
1282	C₂²	—	4	2	no	—
1283	C₂²	—	4	1	no	—
1284	C₂²	—	4	1	no	—
1285	C₂²	—	4	1	no	—
1286	C₂²	—	4	2	no	—
1287	C₂²	—	4	1	no	—
1288	C₂²	—	8	2	no	—
1289	C₂²	—	8	4	no	—
1290	C₂²	—	16	2	no	—
1291	C₂²	—	16	4	no	—
1292	C₂²	C₃₁×#534	1	2	yes	—
1293	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1294	C₄	—	2	1	no	—
1295	C₄	—	2	1	no	—
1296	C₄	—	2	2	no	—
1297	C₄	—	2	2	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	2	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	2	no	—
1304	C₄	—	4	1	no	—
1305	C₄	—	4	1	no	—
1306	C₄	—	4	1	no	—
1307	C₄	C₃₁×#534	1	2	yes	—
1308	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1309	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1310	C₂	—	2	2	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	4	2	no	—
1313	C₂	—	4	1	no	—
1314	C₂	—	4	2	no	—
1315	C₂	—	8	2	no	—
1316	C₂	—	8	1	no	—
1317	C₂	—	8	1	no	—
1318	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
1319	C₂	C₃₁×#3585	1	1	yes	characteristic
1320	C₂	C₃₁×#3586	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 ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3489	C₂	semidirect
2. C₃₁×#3488	C₂	semidirect
3. C₃₁×#3203	C₂	semidirect
4. C₃₁×#3201	C₂	semidirect
5. C₃₁×#3200	C₂	semidirect
6. C₃₁×#3198	C₂	semidirect
7. C₃₁×#3197	C₂	semidirect
8. C₃₁×#3196	C₂	semidirect
9. C₃₁×#3194	C₂	semidirect
10. C₃₁×#3193	C₂	semidirect
11. C₃₁×#3098	C₂	semidirect
12. C₃₁×#3098	C₂	semidirect
13. C₃₁×#3097	C₂	semidirect
14. C₃₁×#3096	C₂	semidirect
15. C₃₁×#3056	C₂	semidirect
16. C₃₁×#3055	C₂	semidirect
17. C₃₁×#3054	C₂	semidirect
18. C₂×C₃₁×#468	C₂	semidirect
19. C₃₁×#3013	C₂	semidirect
20. C₃₁×#3012	C₂	semidirect
21. C₃₁×#3010	C₂	semidirect
22. C₃₁×#3009	C₂	semidirect
23. C₃₁×#2879	C₂	semidirect
24. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
28. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
29. C₂×C₃₁×#135	C₂²	semidirect
30. C₂²×SD₁₆×C₃₁	C₂²	semidirect
31. C₂²×M₁₆×C₃₁	C₂²	semidirect
32. C₂²×M₁₆×C₃₁	C₂²	semidirect
48. C₃₁×#537	C₂²	semidirect
50. C₃₁×#536	C₂²	semidirect
55. C₃₁×#525	C₂²	semidirect
56. C₃₁×#525	C₂²	semidirect
57. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₃₁×#520	C₂²	semidirect
63. C₃₁×#485	C₂²	semidirect
64. C₃₁×#485	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#485	C₂²	semidirect
67. C₃₁×#484	C₂²	semidirect
68. C₃₁×#484	C₂²	semidirect
69. C₃₁×#484	C₂²	semidirect
70. C₃₁×#483	C₂²	semidirect
71. C₃₁×#482	C₂²	semidirect
72. C₃₁×#482	C₂²	semidirect
73. C₃₁×#482	C₂²	semidirect
74. C₃₁×#482	C₂²	semidirect
75. C₃₁×#481	C₂²	semidirect
76. C₃₁×#480	C₂²	semidirect
77. C₃₁×#480	C₂²	semidirect
78. C₃₁×#480	C₂²	semidirect
79. C₃₁×#470	C₂²	semidirect
80. C₃₁×#470	C₂²	semidirect
81. C₃₁×#470	C₂²	semidirect
82. C₃₁×#469	C₂²	semidirect
83. C₃₁×#469	C₂²	semidirect
84. C₃₁×#469	C₂²	semidirect
85. C₃₁×#468	C₂²	semidirect
86. C₃₁×#468	C₂²	semidirect
87. C₃₁×#468	C₂²	semidirect
88. C₃₁×#468	C₂²	semidirect
89. C₃₁×#468	C₂²	semidirect
90. C₃₁×#468	C₂²	semidirect
91. C₃₁×#468	C₂²	semidirect
92. C₃₁×#468	C₂²	semidirect
93. C₃₁×#468	C₂²	semidirect
94. C₃₁×#468	C₂²	semidirect
95. C₃₁×#467	C₂²	semidirect
96. C₃₁×#466	C₂²	semidirect
97. C₃₁×#465	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#452	C₂²	semidirect
100. C₃₁×#452	C₂²	semidirect
101. C₃₁×#452	C₂²	semidirect
102. C₃₁×#452	C₂²	semidirect
103. C₃₁×#451	C₂²	semidirect
104. C₃₁×#450	C₂²	semidirect
105. C₃₁×#450	C₂²	semidirect
106. C₃₁×#450	C₂²	semidirect
107. C₃₁×#449	C₂²	semidirect
108. C₃₁×#449	C₂²	semidirect
109. C₃₁×#449	C₂²	semidirect
110. C₃₁×#449	C₂²	semidirect
111. C₃₁×#448	C₂²	semidirect
112. C₃₁×#448	C₂²	semidirect
113. C₃₁×#448	C₂²	semidirect
114. C₃₁×#447	C₂²	semidirect
115. C₃₁×#428	C₂²	semidirect
116. C₃₁×#428	C₂²	semidirect
117. C₃₁×#427	C₂²	semidirect
118. C₂×C₃₁×#107	C₂²	semidirect
119. C₃₁×#419	C₂²	semidirect
120. C₃₁×#418	C₂²	semidirect
121. C₃₁×#417	C₂²	semidirect
122. C₃₁×#417	C₂²	semidirect
123. C₃₁×#416	C₂²	semidirect
124. C₃₁×#416	C₂²	semidirect
125. C₂×C₃₁×#103	C₂²	semidirect
126. C₂×C₃₁×#102	C₂²	semidirect
129. C₃₁×#408	C₂²	semidirect
130. C₃₁×#408	C₂²	semidirect
131. C₃₁×#408	C₂²	semidirect
132. C₃₁×#408	C₂²	semidirect
133. C₃₁×#407	C₂²	semidirect
134. C₃₁×#407	C₂²	semidirect
497. #60772	C₃₁	direct (N × H)
605. #3489	C₂×C₃₁	semidirect
606. #3488	C₂×C₃₁	semidirect
607. #3203	C₂×C₃₁	semidirect
608. #3201	C₂×C₃₁	semidirect
609. #3200	C₂×C₃₁	semidirect
610. #3198	C₂×C₃₁	semidirect
611. #3197	C₂×C₃₁	semidirect
612. #3196	C₂×C₃₁	semidirect
613. #3194	C₂×C₃₁	semidirect
614. #3193	C₂×C₃₁	semidirect
615. #3098	C₂×C₃₁	semidirect
616. #3098	C₂×C₃₁	semidirect
617. #3097	C₂×C₃₁	semidirect
618. #3096	C₂×C₃₁	semidirect
619. #3056	C₂×C₃₁	semidirect
620. #3055	C₂×C₃₁	semidirect
621. #3054	C₂×C₃₁	semidirect
622. C₂×#468	C₂×C₃₁	semidirect
623. #3013	C₂×C₃₁	semidirect
624. #3012	C₂×C₃₁	semidirect
625. #3010	C₂×C₃₁	semidirect
626. #3009	C₂×C₃₁	semidirect
627. #2879	C₂×C₃₁	semidirect
673. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
676. C₂×#137	C₂²×C₃₁	semidirect
677. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
678. C₂×#135	C₂²×C₃₁	semidirect
679. C₂²×SD₁₆	C₂²×C₃₁	semidirect
680. C₂²×M₁₆	C₂²×C₃₁	semidirect
681. C₂²×M₁₆	C₂²×C₃₁	semidirect
697. #537	C₂²×C₃₁	semidirect
699. #536	C₂²×C₃₁	semidirect
704. #525	C₂²×C₃₁	semidirect
705. #525	C₂²×C₃₁	semidirect
706. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
707. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
711. #520	C₂²×C₃₁	semidirect
712. #485	C₂²×C₃₁	semidirect
713. #485	C₂²×C₃₁	semidirect
714. #485	C₂²×C₃₁	semidirect
715. #485	C₂²×C₃₁	semidirect
716. #484	C₂²×C₃₁	semidirect
717. #484	C₂²×C₃₁	semidirect
718. #484	C₂²×C₃₁	semidirect
719. #483	C₂²×C₃₁	semidirect
720. #482	C₂²×C₃₁	semidirect
721. #482	C₂²×C₃₁	semidirect
722. #482	C₂²×C₃₁	semidirect
723. #482	C₂²×C₃₁	semidirect
724. #481	C₂²×C₃₁	semidirect
725. #480	C₂²×C₃₁	semidirect
726. #480	C₂²×C₃₁	semidirect
727. #480	C₂²×C₃₁	semidirect
728. #470	C₂²×C₃₁	semidirect
729. #470	C₂²×C₃₁	semidirect
730. #470	C₂²×C₃₁	semidirect
731. #469	C₂²×C₃₁	semidirect
732. #469	C₂²×C₃₁	semidirect
733. #469	C₂²×C₃₁	semidirect
734. #468	C₂²×C₃₁	semidirect
735. #468	C₂²×C₃₁	semidirect
736. #468	C₂²×C₃₁	semidirect
737. #468	C₂²×C₃₁	semidirect
738. #468	C₂²×C₃₁	semidirect
739. #468	C₂²×C₃₁	semidirect
740. #468	C₂²×C₃₁	semidirect
741. #468	C₂²×C₃₁	semidirect
742. #468	C₂²×C₃₁	semidirect
743. #468	C₂²×C₃₁	semidirect
744. #467	C₂²×C₃₁	semidirect
745. #466	C₂²×C₃₁	semidirect
746. #465	C₂²×C₃₁	semidirect
747. #465	C₂²×C₃₁	semidirect
748. #452	C₂²×C₃₁	semidirect
749. #452	C₂²×C₃₁	semidirect
750. #452	C₂²×C₃₁	semidirect
751. #452	C₂²×C₃₁	semidirect
752. #451	C₂²×C₃₁	semidirect
753. #450	C₂²×C₃₁	semidirect
754. #450	C₂²×C₃₁	semidirect
755. #450	C₂²×C₃₁	semidirect
756. #449	C₂²×C₃₁	semidirect
757. #449	C₂²×C₃₁	semidirect
758. #449	C₂²×C₃₁	semidirect
759. #449	C₂²×C₃₁	semidirect
760. #448	C₂²×C₃₁	semidirect
761. #448	C₂²×C₃₁	semidirect
762. #448	C₂²×C₃₁	semidirect
763. #447	C₂²×C₃₁	semidirect
764. #428	C₂²×C₃₁	semidirect
765. #428	C₂²×C₃₁	semidirect
766. #427	C₂²×C₃₁	semidirect
767. C₂×#107	C₂²×C₃₁	semidirect
768. #419	C₂²×C₃₁	semidirect
769. #418	C₂²×C₃₁	semidirect
770. #417	C₂²×C₃₁	semidirect
771. #417	C₂²×C₃₁	semidirect
772. #416	C₂²×C₃₁	semidirect
773. #416	C₂²×C₃₁	semidirect
774. C₂×#103	C₂²×C₃₁	semidirect
775. C₂×#102	C₂²×C₃₁	semidirect
778. #408	C₂²×C₃₁	semidirect
779. #408	C₂²×C₃₁	semidirect
780. #408	C₂²×C₃₁	semidirect
781. #408	C₂²×C₃₁	semidirect
782. #407	C₂²×C₃₁	semidirect
783. #407	C₂²×C₃₁	semidirect
984. C₃₁	#60772	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×#3489	2
C₃₁×#3488	2
C₃₁×#3203	2
C₃₁×#3201	2
C₃₁×#3200	2
C₃₁×#3198	2
C₃₁×#3197	2
C₃₁×#3196	2
C₃₁×#3194	2
C₃₁×#3193	2
C₃₁×#3098	2
C₃₁×#3097	2
C₃₁×#3096	2
C₃₁×#3056	2
C₃₁×#3055	2
C₃₁×#3054	2
C₂×C₃₁×#468	2
C₃₁×#3013	2
C₃₁×#3012	2
C₃₁×#3010	2
C₃₁×#3009	2
C₃₁×#2879	2
#60772	31

Subgroups — C31×#60772 #21517531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#60772 #21517531