Subgroups — C₃₁×#61645 #21518404

Order 7936.

2026 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3539	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3486	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×#3320	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3276	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3271	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3223	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3221	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3201	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3197	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3013	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3004	C₂	1	2	yes	maximal, complemented
19	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
21	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
22	C₂×C₃₁×#137	C₂²	1	2	yes	—
23	C₂×C₃₁×#137	C₂²	1	2	yes	—
24	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#135	C₂²	1	2	yes	complemented
26	C₃₁×#560	—	2	2	no	—
27	C₃₁×#553	—	2	2	no	—
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#552	C₂²	1	2	yes	—
30	C₃₁×#550	C₂²	1	2	yes	—
31	D₄×Q₈×C₃₁	—	2	2	no	—
32	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
33	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
34	C₃₁×#548	—	2	2	no	—
35	C₃₁×#548	C₂²	1	2	yes	—
36	C₃₁×#548	C₂²	1	2	yes	—
37	C₃₁×#547	C₂²	1	2	yes	—
38	C₃₁×#541	C₂²	1	1	yes	characteristic
39	C₃₁×#540	—	2	2	no	—
40	C₃₁×#540	C₂²	1	1	yes	characteristic
41	C₃₁×#539	—	2	2	no	—
42	C₃₁×#537	C₂²	1	2	yes	—
43	C₃₁×#536	—	2	2	no	—
44	C₃₁×#536	C₂²	1	1	yes	characteristic
45	C₃₁×#536	C₂²	1	1	yes	characteristic
46	C₃₁×#525	—	2	2	no	—
47	C₃₁×#525	C₂²	1	1	yes	characteristic
48	C₃₁×#525	C₂²	1	2	yes	—
49	C₃₁×#525	C₂²	1	1	yes	characteristic
50	C₃₁×#519	C₂²	1	1	yes	characteristic
51	C₃₁×#497	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#496	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#494	C₂²	1	1	yes	characteristic, complemented
54	C₃₁×#492	C₂²	1	1	yes	characteristic, complemented
55	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
56	C₃₁×#491	C₂²	1	1	yes	characteristic, complemented
57	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
58	C₃₁×#488	C₂²	1	1	yes	characteristic, complemented
59	C₃₁×#485	C₂²	1	2	yes	—
60	C₃₁×#485	C₂²	1	2	yes	—
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	2	yes	complemented
63	C₃₁×#482	C₂²	1	2	yes	—
64	C₃₁×#482	C₂²	1	2	yes	—
65	C₃₁×#479	C₂²	1	2	yes	complemented
66	C₃₁×#479	C₂²	1	2	yes	complemented
67	C₃₁×#470	C₂²	1	2	yes	—
68	C₃₁×#470	C₂²	1	2	yes	complemented
69	C₃₁×#469	C₂²	1	2	yes	—
70	C₃₁×#468	C₂²	1	2	yes	—
71	C₃₁×#468	C₂²	1	2	yes	—
72	C₃₁×#468	C₂²	1	2	yes	complemented
73	C₃₁×#467	C₂²	1	2	yes	complemented
74	C₃₁×#465	C₂²	1	2	yes	complemented
75	C₃₁×#464	C₂²	1	2	yes	complemented
76	C₃₁×#463	C₂²	1	2	yes	complemented
77	C₃₁×#462	C₂²	1	2	yes	complemented
78	C₃₁×#462	C₂²	1	2	yes	complemented
79	C₃₁×#461	C₂²	1	2	yes	complemented
80	C₃₁×#460	C₂²	1	2	yes	complemented
81	C₃₁×#452	C₂²	1	2	yes	—
82	C₃₁×#452	C₂²	1	2	yes	—
83	C₃₁×#452	C₂²	1	2	yes	complemented
84	C₃₁×#452	C₂²	1	2	yes	complemented
85	C₃₁×#452	C₂²	1	2	yes	complemented
86	C₃₁×#451	C₂²	1	2	yes	—
87	C₃₁×#451	C₂²	1	2	yes	—
88	C₃₁×#451	C₂²	1	2	yes	—
89	C₃₁×#451	C₂²	1	2	yes	—
90	C₃₁×#451	C₂²	1	2	yes	complemented
91	C₃₁×#449	C₂²	1	2	yes	—
92	C₃₁×#449	C₂²	1	2	yes	—
93	C₃₁×#449	C₂²	1	2	yes	complemented
94	C₃₁×#448	C₂²	1	2	yes	—
95	C₃₁×#448	C₂²	1	2	yes	—
96	C₃₁×#448	C₂²	1	2	yes	—
97	C₃₁×#448	C₂²	1	2	yes	—
98	C₃₁×#448	C₂²	1	2	yes	complemented
99	C₃₁×#441	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#436	C₂²	1	2	yes	—
104	C₃₁×#436	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	—
106	C₃₁×#435	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	1	yes	characteristic
108	C₃₁×#433	C₂²	1	1	yes	characteristic
109	C₃₁×#419	C₂²	1	2	yes	—
110	C₃₁×#419	C₂²	1	2	yes	—
111	C₃₁×#417	C₂²	1	2	yes	complemented
112	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
113	C₃₁×#408	C₂²	1	2	yes	—
114	C₃₁×#407	C₂²	1	2	yes	—
115	C₃₁×2₋¹⁺⁴	—	4	4	no	—
116	C₂×#41×C₃₁	—	2	2	no	—
117	C₂×#41×C₃₁	—	2	1	no	—
118	C₂×#41×C₃₁	C₂³	1	2	yes	—
119	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	—	2	1	no	—
124	C₂²×Q₈×C₃₁	—	2	1	no	—
125	C₂²×Q₈×C₃₁	—	2	2	no	—
126	C₂²×Q₈×C₃₁	—	4	4	no	—
127	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
128	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
129	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
130	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
131	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₃₁	—	2	1	no	—
133	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
134	C₃₁×#137	—	4	4	no	—
135	C₃₁×#137	—	4	4	no	—
136	C₃₁×#137	—	4	4	no	—
137	C₃₁×#135	—	4	4	no	—
138	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
151	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	—	2	1	no	—
155	C₃₁×C₄⋊Q₈	—	2	2	no	—
156	C₃₁×C₄⋊Q₈	—	2	2	no	—
157	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×#127	—	2	2	no	—
161	C₃₁×#127	C₂³	1	1	yes	characteristic
162	C₃₁×#126	—	2	2	no	—
163	C₃₁×#126	—	2	2	no	—
164	C₃₁×#126	—	2	2	no	—
165	C₃₁×#125	—	2	2	no	—
166	C₃₁×#125	—	2	2	no	—
167	C₃₁×#125	C₂³	1	1	yes	characteristic
168	C₃₁×#125	C₂³	1	1	yes	characteristic
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	—	2	2	no	—
171	C₃₁×#124	—	2	2	no	—
172	C₃₁×#124	C₂³	1	1	yes	characteristic
173	C₃₁×#124	C₂³	1	1	yes	characteristic
174	C₃₁×#123	—	2	2	no	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	1	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	D₄	1	2	yes	—
184	C₃₁×C₂²⋊Q₈	—	2	2	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	2	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	2	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	D₄	1	2	yes	—
193	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
195	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₃₁×#121	—	2	2	no	—
200	C₃₁×#121	—	2	2	no	—
201	C₃₁×#121	—	2	2	no	—
202	C₃₁×#121	—	2	2	no	—
203	C₃₁×#121	—	2	2	no	—
204	C₃₁×#121	—	2	2	no	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	D₄	1	2	yes	—
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#121	C₂³	1	2	yes	—
213	C₃₁×#121	C₂³	1	2	yes	—
214	C₃₁×#120	—	2	1	no	—
215	C₃₁×#120	—	2	2	no	—
216	C₃₁×#120	D₄	1	2	yes	—
217	C₄×Q₈×C₃₁	—	2	2	no	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
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	2	no	—
226	C₄×D₄×C₃₁	—	2	2	no	—
227	C₄×D₄×C₃₁	—	2	2	no	—
228	C₄×D₄×C₃₁	—	2	2	no	—
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	C₂³	1	2	yes	—
231	C₄×D₄×C₃₁	C₂³	1	2	yes	—
232	C₄×D₄×C₃₁	C₂³	1	2	yes	—
233	C₃₁×#117	—	2	2	no	—
234	C₃₁×#117	—	2	2	no	—
235	C₃₁×#117	C₂³	1	2	yes	—
236	C₃₁×#117	C₂³	1	1	yes	characteristic
237	C₃₁×#117	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#106	C₂³	1	2	yes	—
243	C₃₁×#106	C₂³	1	2	yes	—
244	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
245	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
246	C₃₁×#103	C₂³	1	2	yes	—
247	C₃₁×#103	C₂³	1	2	yes	—
248	C₃₁×#103	C₂³	1	2	yes	—
249	C₃₁×#103	C₂³	1	2	yes	—
250	C₃₁×#103	C₂³	1	2	yes	—
251	C₃₁×#103	C₂³	1	2	yes	—
252	C₃₁×#103	C₂³	1	2	yes	—
253	C₃₁×#103	C₂³	1	2	yes	—
254	C₃₁×#103	C₂³	1	2	yes	—
255	C₃₁×#103	C₂³	1	2	yes	—
256	C₃₁×#103	C₂³	1	2	yes	—
257	C₃₁×#103	C₂³	1	2	yes	—
258	C₃₁×#102	C₂³	1	2	yes	—
259	C₃₁×#102	C₂³	1	2	yes	—
260	C₃₁×#102	C₂³	1	2	yes	—
261	C₃₁×#102	C₂³	1	2	yes	—
262	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
265	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
266	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₃₁×#97	C₂³	1	1	yes	characteristic
269	C₃₁×#97	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
271	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
272	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
273	#41×C₃₁	—	2	4	no	—
274	#41×C₃₁	—	4	2	no	—
275	#41×C₃₁	—	4	2	no	—
276	#41×C₃₁	—	4	2	no	—
277	#41×C₃₁	—	4	8	no	—
278	#41×C₃₁	—	4	2	no	—
279	#41×C₃₁	—	4	2	no	—
280	#41×C₃₁	—	4	2	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	4	4	no	—
283	C₂×Q₈×C₃₁	—	2	4	no	—
284	C₂×Q₈×C₃₁	—	2	1	no	—
285	C₂×Q₈×C₃₁	—	2	2	no	—
286	C₂×Q₈×C₃₁	—	2	2	no	—
287	C₂×Q₈×C₃₁	—	2	1	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	4	no	—
290	C₂×Q₈×C₃₁	—	2	4	no	—
291	C₂×Q₈×C₃₁	—	2	4	no	—
292	C₂×Q₈×C₃₁	—	4	2	no	—
293	C₂×Q₈×C₃₁	—	4	2	no	—
294	C₂×Q₈×C₃₁	—	4	2	no	—
295	C₂×Q₈×C₃₁	—	4	2	no	—
296	C₂×Q₈×C₃₁	—	4	4	no	—
297	C₂×Q₈×C₃₁	—	4	8	no	—
298	C₂×Q₈×C₃₁	—	4	4	no	—
299	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
301	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
302	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	1	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	2	no	—
311	C₂×D₄×C₃₁	—	2	2	no	—
312	C₂×D₄×C₃₁	—	2	2	no	—
313	C₂×D₄×C₃₁	—	2	2	no	—
314	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
317	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
318	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₃₁	—	2	1	no	—
321	C₂²×C₄×C₃₁	—	2	2	no	—
322	C₂²×C₄×C₃₁	—	2	2	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	1	no	—
325	C₂²×C₄×C₃₁	—	2	2	no	—
326	C₂²×C₄×C₃₁	—	2	2	no	—
327	C₂²×C₄×C₃₁	—	2	1	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	2	no	—
331	C₂²×C₄×C₃₁	—	4	2	no	—
332	C₂²×C₄×C₃₁	—	4	4	no	—
333	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
334	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
338	Q₁₆×C₃₁	—	2	4	no	—
339	Q₁₆×C₃₁	—	2	4	no	—
340	Q₁₆×C₃₁	—	4	2	no	—
341	Q₁₆×C₃₁	—	4	2	no	—
342	Q₁₆×C₃₁	—	4	2	no	—
343	SD₁₆×C₃₁	—	2	4	no	—
344	SD₁₆×C₃₁	—	2	4	no	—
345	SD₁₆×C₃₁	—	4	2	no	—
346	SD₁₆×C₃₁	—	4	2	no	—
347	SD₁₆×C₃₁	—	4	2	no	—
348	SD₁₆×C₃₁	—	4	2	no	—
349	D₈×C₃₁	—	4	2	no	—
350	M₁₆×C₃₁	—	4	2	no	—
351	M₁₆×C₃₁	—	4	2	no	—
352	M₁₆×C₃₁	—	4	2	no	—
353	C₂×C₈×C₃₁	—	4	2	no	—
354	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
355	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
356	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
357	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	2	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	2	no	—
365	C₄⋊C₄×C₃₁	—	2	2	no	—
366	C₄⋊C₄×C₃₁	—	2	2	no	—
367	C₄⋊C₄×C₃₁	—	2	2	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
378	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
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	2	no	—
383	C₂²⋊C₄×C₃₁	—	2	2	no	—
384	C₂²⋊C₄×C₃₁	—	2	2	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	2	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	2	no	—
393	C₂²⋊C₄×C₃₁	—	2	2	no	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
399	C₄²×C₃₁	—	2	2	no	—
400	C₄²×C₃₁	—	2	2	no	—
401	C₄²×C₃₁	—	2	2	no	—
402	C₄²×C₃₁	—	2	2	no	—
403	C₄²×C₃₁	—	2	1	no	—
404	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
405	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
406	#61645	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂³×C₃₁	—	2	1	no	—
408	C₂³×C₃₁	—	2	2	no	—
409	C₂³×C₃₁	—	4	1	no	—
410	C₂³×C₃₁	—	4	2	no	—
411	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
412	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
414	Q₈×C₃₁	—	2	4	no	—
415	Q₈×C₃₁	—	2	2	no	—
416	Q₈×C₃₁	—	2	2	no	—
417	Q₈×C₃₁	—	2	2	no	—
418	Q₈×C₃₁	—	2	2	no	—
419	Q₈×C₃₁	—	2	2	no	—
420	Q₈×C₃₁	—	2	2	no	—
421	Q₈×C₃₁	—	4	1	no	—
422	Q₈×C₃₁	—	4	4	no	—
423	Q₈×C₃₁	—	4	4	no	—
424	Q₈×C₃₁	—	4	4	no	—
425	Q₈×C₃₁	—	4	2	no	—
426	Q₈×C₃₁	H(5,𝔽₂)	1	4	yes	—
427	D₄×C₃₁	—	2	2	no	—
428	D₄×C₃₁	—	2	2	no	—
429	D₄×C₃₁	—	2	2	no	—
430	D₄×C₃₁	—	4	2	no	—
431	D₄×C₃₁	—	4	2	no	—
432	D₄×C₃₁	—	4	1	no	—
433	D₄×C₃₁	—	4	2	no	—
434	D₄×C₃₁	—	4	4	no	—
435	D₄×C₃₁	—	4	4	no	—
436	D₄×C₃₁	—	4	2	no	—
437	D₄×C₃₁	—	8	2	no	—
438	D₄×C₃₁	—	8	2	no	—
439	D₄×C₃₁	—	8	2	no	—
440	D₄×C₃₁	—	8	2	no	—
441	D₄×C₃₁	—	8	2	no	—
442	D₄×C₃₁	—	8	2	no	—
443	C₂×C₄×C₃₁	—	2	4	no	—
444	C₂×C₄×C₃₁	—	2	2	no	—
445	C₂×C₄×C₃₁	—	2	2	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	2	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	2	2	no	—
452	C₂×C₄×C₃₁	—	2	2	no	—
453	C₂×C₄×C₃₁	—	2	2	no	—
454	C₂×C₄×C₃₁	—	2	1	no	—
455	C₂×C₄×C₃₁	—	2	1	no	—
456	C₂×C₄×C₃₁	—	2	1	no	—
457	C₂×C₄×C₃₁	—	4	2	no	—
458	C₂×C₄×C₃₁	—	4	1	no	—
459	C₂×C₄×C₃₁	—	4	4	no	—
460	C₂×C₄×C₃₁	—	4	4	no	—
461	C₂×C₄×C₃₁	—	4	4	no	—
462	C₂×C₄×C₃₁	—	4	4	no	—
463	C₂×C₄×C₃₁	—	4	2	no	—
464	C₂×C₄×C₃₁	—	4	2	no	—
465	C₂×C₄×C₃₁	—	8	2	no	—
466	C₂×C₄×C₃₁	—	8	2	no	—
467	C₂×C₄×C₃₁	—	8	2	no	—
468	C₂×C₄×C₃₁	—	8	2	no	—
469	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
475	C₈×C₃₁	—	2	2	no	—
476	C₈×C₃₁	—	2	2	no	—
477	C₈×C₃₁	—	2	2	no	—
478	C₈×C₃₁	—	2	2	no	—
479	#3539	C₂×C₃₁	1	1	yes	characteristic, complemented
480	#3486	C₂×C₃₁	1	1	yes	characteristic, complemented
481	#3327	C₂×C₃₁	1	2	yes	complemented
482	#3326	C₂×C₃₁	1	2	yes	complemented
483	#3320	C₂×C₃₁	1	2	yes	complemented
484	#3312	C₂×C₃₁	1	2	yes	complemented
485	#3278	C₂×C₃₁	1	2	yes	complemented
486	#3276	C₂×C₃₁	1	2	yes	complemented
487	#3271	C₂×C₃₁	1	2	yes	complemented
488	#3269	C₂×C₃₁	1	2	yes	complemented
489	#3223	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3221	C₂×C₃₁	1	1	yes	characteristic, complemented
491	#3201	C₂×C₃₁	1	2	yes	complemented
492	#3197	C₂×C₃₁	1	2	yes	complemented
493	#3127	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#3126	C₂×C₃₁	1	1	yes	characteristic, complemented
495	#3013	C₂×C₃₁	1	2	yes	complemented
496	#3004	C₂×C₃₁	1	2	yes	complemented
497	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
498	C₂²×C₃₁	—	2	2	no	—
499	C₂²×C₃₁	—	2	2	no	—
500	C₂²×C₃₁	—	2	2	no	—
501	C₂²×C₃₁	—	2	2	no	—
502	C₂²×C₃₁	—	2	2	no	—
503	C₂²×C₃₁	—	2	1	no	—
504	C₂²×C₃₁	—	2	2	no	—
505	C₂²×C₃₁	—	2	2	no	—
506	C₂²×C₃₁	—	4	4	no	—
507	C₂²×C₃₁	—	4	2	no	—
508	C₂²×C₃₁	—	4	2	no	—
509	C₂²×C₃₁	—	4	2	no	—
510	C₂²×C₃₁	—	4	1	no	—
511	C₂²×C₃₁	—	4	2	no	—
512	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
513	C₄×C₃₁	—	2	2	no	—
514	C₄×C₃₁	—	2	2	no	—
515	C₄×C₃₁	—	2	4	no	—
516	C₄×C₃₁	—	2	1	no	—
517	C₄×C₃₁	—	2	2	no	—
518	C₄×C₃₁	—	2	2	no	—
519	C₄×C₃₁	—	4	2	no	—
520	C₄×C₃₁	—	4	2	no	—
521	C₄×C₃₁	—	4	2	no	—
522	C₄×C₃₁	—	4	1	no	—
523	C₄×C₃₁	—	4	1	no	—
524	C₄×C₃₁	—	4	1	no	—
525	C₄×C₃₁	—	4	2	no	—
526	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
527	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	1	yes	characteristic
528	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
529	C₂×#137	C₂²×C₃₁	1	2	yes	—
530	C₂×#137	C₂²×C₃₁	1	2	yes	—
531	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
532	C₂×#135	C₂²×C₃₁	1	2	yes	complemented
533	#560	—	2	2	no	—
534	#553	—	2	2	no	—
535	#553	C₂²×C₃₁	1	2	yes	—
536	#552	C₂²×C₃₁	1	2	yes	—
537	#550	C₂²×C₃₁	1	2	yes	—
538	D₄×Q₈	—	2	2	no	—
539	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
540	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
541	#548	—	2	2	no	—
542	#548	C₂²×C₃₁	1	2	yes	—
543	#548	C₂²×C₃₁	1	2	yes	—
544	#547	C₂²×C₃₁	1	2	yes	—
545	#541	C₂²×C₃₁	1	1	yes	characteristic
546	#540	—	2	2	no	—
547	#540	C₂²×C₃₁	1	1	yes	characteristic
548	#539	—	2	2	no	—
549	#537	C₂²×C₃₁	1	2	yes	—
550	#536	—	2	2	no	—
551	#536	C₂²×C₃₁	1	1	yes	characteristic
552	#536	C₂²×C₃₁	1	1	yes	characteristic
553	#525	—	2	2	no	—
554	#525	C₂²×C₃₁	1	1	yes	characteristic
555	#525	C₂²×C₃₁	1	2	yes	—
556	#525	C₂²×C₃₁	1	1	yes	characteristic
557	#519	C₂²×C₃₁	1	1	yes	characteristic
558	#497	C₂²×C₃₁	1	1	yes	characteristic, complemented
559	#496	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#494	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	#492	C₂²×C₃₁	1	1	yes	characteristic, complemented
562	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
563	#491	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
565	#488	C₂²×C₃₁	1	1	yes	characteristic, complemented
566	#485	C₂²×C₃₁	1	2	yes	—
567	#485	C₂²×C₃₁	1	2	yes	—
568	#484	C₂²×C₃₁	1	2	yes	complemented
569	#483	C₂²×C₃₁	1	2	yes	complemented
570	#482	C₂²×C₃₁	1	2	yes	—
571	#482	C₂²×C₃₁	1	2	yes	—
572	#479	C₂²×C₃₁	1	2	yes	complemented
573	#479	C₂²×C₃₁	1	2	yes	complemented
574	#470	C₂²×C₃₁	1	2	yes	—
575	#470	C₂²×C₃₁	1	2	yes	complemented
576	#469	C₂²×C₃₁	1	2	yes	—
577	#468	C₂²×C₃₁	1	2	yes	—
578	#468	C₂²×C₃₁	1	2	yes	—
579	#468	C₂²×C₃₁	1	2	yes	complemented
580	#467	C₂²×C₃₁	1	2	yes	complemented
581	#465	C₂²×C₃₁	1	2	yes	complemented
582	#464	C₂²×C₃₁	1	2	yes	complemented
583	#463	C₂²×C₃₁	1	2	yes	complemented
584	#462	C₂²×C₃₁	1	2	yes	complemented
585	#462	C₂²×C₃₁	1	2	yes	complemented
586	#461	C₂²×C₃₁	1	2	yes	complemented
587	#460	C₂²×C₃₁	1	2	yes	complemented
588	#452	C₂²×C₃₁	1	2	yes	—
589	#452	C₂²×C₃₁	1	2	yes	—
590	#452	C₂²×C₃₁	1	2	yes	complemented
591	#452	C₂²×C₃₁	1	2	yes	complemented
592	#452	C₂²×C₃₁	1	2	yes	complemented
593	#451	C₂²×C₃₁	1	2	yes	—
594	#451	C₂²×C₃₁	1	2	yes	—
595	#451	C₂²×C₃₁	1	2	yes	—
596	#451	C₂²×C₃₁	1	2	yes	—
597	#451	C₂²×C₃₁	1	2	yes	complemented
598	#449	C₂²×C₃₁	1	2	yes	—
599	#449	C₂²×C₃₁	1	2	yes	—
600	#449	C₂²×C₃₁	1	2	yes	complemented
601	#448	C₂²×C₃₁	1	2	yes	—
602	#448	C₂²×C₃₁	1	2	yes	—
603	#448	C₂²×C₃₁	1	2	yes	—
604	#448	C₂²×C₃₁	1	2	yes	—
605	#448	C₂²×C₃₁	1	2	yes	complemented
606	#441	C₂²×C₃₁	1	2	yes	complemented
607	#440	C₂²×C₃₁	1	2	yes	complemented
608	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
609	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
610	#436	C₂²×C₃₁	1	2	yes	—
611	#436	C₂²×C₃₁	1	2	yes	—
612	#435	C₂²×C₃₁	1	2	yes	—
613	#435	C₂²×C₃₁	1	2	yes	—
614	#433	C₂²×C₃₁	1	1	yes	characteristic
615	#433	C₂²×C₃₁	1	1	yes	characteristic
616	#419	C₂²×C₃₁	1	2	yes	—
617	#419	C₂²×C₃₁	1	2	yes	—
618	#417	C₂²×C₃₁	1	2	yes	complemented
619	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
620	#408	C₂²×C₃₁	1	2	yes	—
621	#407	C₂²×C₃₁	1	2	yes	—
622	C₂×C₃₁	—	4	2	no	—
623	C₂×C₃₁	—	4	2	no	—
624	C₂×C₃₁	—	4	1	no	—
625	C₂×C₃₁	—	8	2	no	—
626	C₂×C₃₁	—	8	1	no	—
627	C₂×C₃₁	#3484	1	1	yes	characteristic
628	C₂×C₃₁	#3586	1	2	yes	—
629	2₋¹⁺⁴	—	4	4	no	—
630	C₂×#41	—	2	2	no	—
631	C₂×#41	—	2	1	no	—
632	C₂×#41	C₂³×C₃₁	1	2	yes	—
633	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
634	C₂×#41	C₂³×C₃₁	1	2	yes	—
635	C₂×#41	C₂³×C₃₁	1	2	yes	—
636	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
637	C₂²×Q₈	—	2	1	no	—
638	C₂²×Q₈	—	2	1	no	—
639	C₂²×Q₈	—	2	2	no	—
640	C₂²×Q₈	—	4	4	no	—
641	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
642	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
643	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
644	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
645	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
646	C₂³×C₄	—	2	1	no	—
647	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
648	#137	—	4	4	no	—
649	#137	—	4	4	no	—
650	#137	—	4	4	no	—
651	#135	—	4	4	no	—
652	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
653	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
654	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
655	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
656	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
657	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
658	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
659	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
660	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
661	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
662	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
663	C₂×D₈	C₂³×C₃₁	1	2	yes	—
664	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
665	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
666	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
667	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
668	C₄⋊Q₈	—	2	1	no	—
669	C₄⋊Q₈	—	2	2	no	—
670	C₄⋊Q₈	—	2	2	no	—
671	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
672	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
673	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
674	#127	—	2	2	no	—
675	#127	C₂³×C₃₁	1	1	yes	characteristic
676	#126	—	2	2	no	—
677	#126	—	2	2	no	—
678	#126	—	2	2	no	—
679	#125	—	2	2	no	—
680	#125	—	2	2	no	—
681	#125	C₂³×C₃₁	1	1	yes	characteristic
682	#125	C₂³×C₃₁	1	1	yes	characteristic
683	#124	—	2	1	no	—
684	#124	—	2	2	no	—
685	#124	—	2	2	no	—
686	#124	C₂³×C₃₁	1	1	yes	characteristic
687	#124	C₂³×C₃₁	1	1	yes	characteristic
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	#123	—	2	1	no	—
691	#123	—	2	2	no	—
692	#123	—	2	2	no	—
693	#123	—	2	2	no	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	D₄×C₃₁	1	2	yes	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	D₄×C₃₁	1	2	yes	—
707	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
708	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
709	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
710	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
711	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
712	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
713	#121	—	2	2	no	—
714	#121	—	2	2	no	—
715	#121	—	2	2	no	—
716	#121	—	2	2	no	—
717	#121	—	2	2	no	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	—	2	2	no	—
721	#121	—	2	2	no	—
722	#121	—	2	2	no	—
723	#121	D₄×C₃₁	1	2	yes	—
724	#121	C₂³×C₃₁	1	2	yes	—
725	#121	C₂³×C₃₁	1	2	yes	—
726	#121	C₂³×C₃₁	1	2	yes	—
727	#121	C₂³×C₃₁	1	2	yes	—
728	#120	—	2	1	no	—
729	#120	—	2	2	no	—
730	#120	D₄×C₃₁	1	2	yes	—
731	C₄×Q₈	—	2	2	no	—
732	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
733	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
734	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	—	2	2	no	—
737	C₄×D₄	—	2	2	no	—
738	C₄×D₄	—	2	2	no	—
739	C₄×D₄	—	2	2	no	—
740	C₄×D₄	—	2	2	no	—
741	C₄×D₄	—	2	2	no	—
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	2	no	—
744	C₄×D₄	C₂³×C₃₁	1	2	yes	—
745	C₄×D₄	C₂³×C₃₁	1	2	yes	—
746	C₄×D₄	C₂³×C₃₁	1	2	yes	—
747	#117	—	2	2	no	—
748	#117	—	2	2	no	—
749	#117	C₂³×C₃₁	1	1	yes	characteristic
750	#117	C₂³×C₃₁	1	2	yes	—
751	#117	C₂³×C₃₁	1	1	yes	characteristic
752	C₂×C₄⋊C₄	—	2	2	no	—
753	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
754	#107	C₂³×C₃₁	1	2	yes	—
755	#107	C₂³×C₃₁	1	2	yes	—
756	#106	C₂³×C₃₁	1	2	yes	—
757	#106	C₂³×C₃₁	1	2	yes	—
758	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
759	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
760	#103	C₂³×C₃₁	1	2	yes	—
761	#103	C₂³×C₃₁	1	2	yes	—
762	#103	C₂³×C₃₁	1	2	yes	—
763	#103	C₂³×C₃₁	1	2	yes	—
764	#103	C₂³×C₃₁	1	2	yes	—
765	#103	C₂³×C₃₁	1	2	yes	—
766	#103	C₂³×C₃₁	1	2	yes	—
767	#103	C₂³×C₃₁	1	2	yes	—
768	#103	C₂³×C₃₁	1	2	yes	—
769	#103	C₂³×C₃₁	1	2	yes	—
770	#103	C₂³×C₃₁	1	2	yes	—
771	#103	C₂³×C₃₁	1	2	yes	—
772	#102	C₂³×C₃₁	1	2	yes	—
773	#102	C₂³×C₃₁	1	2	yes	—
774	#102	C₂³×C₃₁	1	2	yes	—
775	#102	C₂³×C₃₁	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
782	#97	C₂³×C₃₁	1	1	yes	characteristic
783	#97	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
785	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
786	C₃₁	#61645	1	1	yes	characteristic, direct product factor, Sylow
787	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
788	#41	—	2	4	no	—
789	#41	—	4	2	no	—
790	#41	—	4	2	no	—
791	#41	—	4	2	no	—
792	#41	—	4	8	no	—
793	#41	—	4	2	no	—
794	#41	—	4	2	no	—
795	#41	—	4	2	no	—
796	#41	—	4	2	no	—
797	#41	—	4	4	no	—
798	C₂×Q₈	—	2	4	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	4	no	—
805	C₂×Q₈	—	2	4	no	—
806	C₂×Q₈	—	2	4	no	—
807	C₂×Q₈	—	4	2	no	—
808	C₂×Q₈	—	4	2	no	—
809	C₂×Q₈	—	4	2	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	—	4	4	no	—
812	C₂×Q₈	—	4	8	no	—
813	C₂×Q₈	—	4	4	no	—
814	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
815	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
816	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
817	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
818	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
819	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	2	no	—
828	C₂×D₄	—	2	2	no	—
829	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
830	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
831	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
832	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
833	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
834	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	1	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	1	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	2	2	no	—
846	C₂²×C₄	—	4	2	no	—
847	C₂²×C₄	—	4	4	no	—
848	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
849	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
853	Q₁₆	—	2	4	no	—
854	Q₁₆	—	2	4	no	—
855	Q₁₆	—	4	2	no	—
856	Q₁₆	—	4	2	no	—
857	Q₁₆	—	4	2	no	—
858	SD₁₆	—	2	4	no	—
859	SD₁₆	—	2	4	no	—
860	SD₁₆	—	4	2	no	—
861	SD₁₆	—	4	2	no	—
862	SD₁₆	—	4	2	no	—
863	SD₁₆	—	4	2	no	—
864	D₈	—	4	2	no	—
865	M₁₆	—	4	2	no	—
866	M₁₆	—	4	2	no	—
867	M₁₆	—	4	2	no	—
868	C₂×C₈	—	4	2	no	—
869	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
870	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
871	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
872	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	2	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
889	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
890	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
891	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
892	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
893	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
910	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
911	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
912	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
913	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	1	no	—
919	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
920	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
921	C₂³	—	2	1	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	2	no	—
925	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
926	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
927	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
928	Q₈	—	2	4	no	—
929	Q₈	—	2	2	no	—
930	Q₈	—	2	2	no	—
931	Q₈	—	2	2	no	—
932	Q₈	—	2	2	no	—
933	Q₈	—	2	2	no	—
934	Q₈	—	2	2	no	—
935	Q₈	—	4	1	no	—
936	Q₈	—	4	4	no	—
937	Q₈	—	4	4	no	—
938	Q₈	—	4	4	no	—
939	Q₈	—	4	2	no	—
940	Q₈	C₃₁×H(5,𝔽₂)	1	4	yes	—
941	D₄	—	2	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	4	no	—
949	D₄	—	4	4	no	—
950	D₄	—	4	2	no	—
951	D₄	—	8	2	no	—
952	D₄	—	8	2	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	2	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	C₂×C₄	—	2	4	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	4	2	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	4	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	4	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	2	no	—
979	C₂×C₄	—	8	2	no	—
980	C₂×C₄	—	8	2	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	8	2	no	—
983	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
984	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
985	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
986	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
987	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
988	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
989	C₈	—	2	2	no	—
990	C₈	—	2	2	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	2	no	—
993	C₂²	—	2	1	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	2	2	no	—
996	C₂²	—	2	2	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	4	4	no	—
1002	C₂²	—	4	1	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	2	no	—
1005	C₂²	—	4	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1008	C₄	—	2	4	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	1	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
1022	C₂	—	4	1	no	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	8	1	no	—
1026	C₂	—	8	2	no	—
1027	C₂	C₃₁×#3484	1	1	yes	characteristic
1028	C₂	C₃₁×#3586	1	2	yes	—

	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3539	C₂	semidirect
2. C₃₁×#3486	C₂	semidirect
3. C₃₁×#3327	C₂	semidirect
4. C₃₁×#3326	C₂	semidirect
5. C₃₁×#3320	C₂	semidirect
6. C₃₁×#3312	C₂	semidirect
7. C₃₁×#3278	C₂	semidirect
8. C₃₁×#3276	C₂	semidirect
9. C₃₁×#3271	C₂	semidirect
10. C₃₁×#3269	C₂	semidirect
11. C₃₁×#3223	C₂	semidirect
12. C₃₁×#3221	C₂	semidirect
13. C₃₁×#3201	C₂	semidirect
14. C₃₁×#3197	C₂	semidirect
15. C₃₁×#3127	C₂	semidirect
16. C₃₁×#3126	C₂	semidirect
17. C₃₁×#3013	C₂	semidirect
18. C₃₁×#3004	C₂	semidirect
19. C₃₁×#2978	C₂	semidirect
24. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#135	C₂²	semidirect
51. C₃₁×#497	C₂²	semidirect
52. C₃₁×#496	C₂²	semidirect
53. C₃₁×#494	C₂²	semidirect
54. C₃₁×#492	C₂²	semidirect
55. C₃₁×#491	C₂²	semidirect
56. C₃₁×#491	C₂²	semidirect
57. C₃₁×#488	C₂²	semidirect
58. C₃₁×#488	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
62. C₃₁×#483	C₂²	semidirect
65. C₃₁×#479	C₂²	semidirect
66. C₃₁×#479	C₂²	semidirect
68. C₃₁×#470	C₂²	semidirect
72. C₃₁×#468	C₂²	semidirect
73. C₃₁×#467	C₂²	semidirect
74. C₃₁×#465	C₂²	semidirect
75. C₃₁×#464	C₂²	semidirect
76. C₃₁×#463	C₂²	semidirect
77. C₃₁×#462	C₂²	semidirect
78. C₃₁×#462	C₂²	semidirect
79. C₃₁×#461	C₂²	semidirect
80. C₃₁×#460	C₂²	semidirect
83. C₃₁×#452	C₂²	semidirect
84. C₃₁×#452	C₂²	semidirect
85. C₃₁×#452	C₂²	semidirect
90. C₃₁×#451	C₂²	semidirect
93. C₃₁×#449	C₂²	semidirect
98. C₃₁×#448	C₂²	semidirect
99. C₃₁×#441	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×SD₁₆×C₃₁	C₂²	semidirect
111. C₃₁×#417	C₂²	semidirect
112. C₂×C₃₁×#103	C₂²	semidirect
406. #61645	C₃₁	direct (N × H)
479. #3539	C₂×C₃₁	semidirect
480. #3486	C₂×C₃₁	semidirect
481. #3327	C₂×C₃₁	semidirect
482. #3326	C₂×C₃₁	semidirect
483. #3320	C₂×C₃₁	semidirect
484. #3312	C₂×C₃₁	semidirect
485. #3278	C₂×C₃₁	semidirect
486. #3276	C₂×C₃₁	semidirect
487. #3271	C₂×C₃₁	semidirect
488. #3269	C₂×C₃₁	semidirect
489. #3223	C₂×C₃₁	semidirect
490. #3221	C₂×C₃₁	semidirect
491. #3201	C₂×C₃₁	semidirect
492. #3197	C₂×C₃₁	semidirect
493. #3127	C₂×C₃₁	semidirect
494. #3126	C₂×C₃₁	semidirect
495. #3013	C₂×C₃₁	semidirect
496. #3004	C₂×C₃₁	semidirect
497. #2978	C₂×C₃₁	semidirect
531. C₂×#137	C₂²×C₃₁	semidirect
532. C₂×#135	C₂²×C₃₁	semidirect
558. #497	C₂²×C₃₁	semidirect
559. #496	C₂²×C₃₁	semidirect
560. #494	C₂²×C₃₁	semidirect
561. #492	C₂²×C₃₁	semidirect
562. #491	C₂²×C₃₁	semidirect
563. #491	C₂²×C₃₁	semidirect
564. #488	C₂²×C₃₁	semidirect
565. #488	C₂²×C₃₁	semidirect
568. #484	C₂²×C₃₁	semidirect
569. #483	C₂²×C₃₁	semidirect
572. #479	C₂²×C₃₁	semidirect
573. #479	C₂²×C₃₁	semidirect
575. #470	C₂²×C₃₁	semidirect
579. #468	C₂²×C₃₁	semidirect
580. #467	C₂²×C₃₁	semidirect
581. #465	C₂²×C₃₁	semidirect
582. #464	C₂²×C₃₁	semidirect
583. #463	C₂²×C₃₁	semidirect
584. #462	C₂²×C₃₁	semidirect
585. #462	C₂²×C₃₁	semidirect
586. #461	C₂²×C₃₁	semidirect
587. #460	C₂²×C₃₁	semidirect
590. #452	C₂²×C₃₁	semidirect
591. #452	C₂²×C₃₁	semidirect
592. #452	C₂²×C₃₁	semidirect
597. #451	C₂²×C₃₁	semidirect
600. #449	C₂²×C₃₁	semidirect
605. #448	C₂²×C₃₁	semidirect
606. #441	C₂²×C₃₁	semidirect
607. #440	C₂²×C₃₁	semidirect
608. C₄×Q₁₆	C₂²×C₃₁	semidirect
609. C₄×SD₁₆	C₂²×C₃₁	semidirect
618. #417	C₂²×C₃₁	semidirect
619. C₂×#103	C₂²×C₃₁	semidirect
786. C₃₁	#61645	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×#3539	2
C₃₁×#3486	2
C₃₁×#3327	2
C₃₁×#3326	2
C₃₁×#3320	2
C₃₁×#3312	2
C₃₁×#3278	2
C₃₁×#3276	2
C₃₁×#3271	2
C₃₁×#3269	2
C₃₁×#3223	2
C₃₁×#3221	2
C₃₁×#3201	2
C₃₁×#3197	2
C₃₁×#3127	2
C₃₁×#3126	2
C₃₁×#3013	2
C₃₁×#3004	2
C₃₁×#2978	2
#61645	31

Subgroups — C31×#61645 #21518404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61645 #21518404