Subgroups — C₃₁×#61776 #21518535

Order 7936.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3356	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3354	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3343	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3327	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3322	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3321	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3311	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3244	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3204	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3196	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3194	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3098	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3095	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#3094	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2978	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#562	—	2	2	no	—
21	C₃₁×#556	—	2	1	no	—
22	C₃₁×#556	C₂²	1	2	yes	—
23	C₃₁×#555	—	2	1	no	—
24	C₃₁×#555	C₂²	1	2	yes	complemented
25	C₃₁×#554	C₂²	1	2	yes	—
26	C₃₁×#553	—	2	1	no	—
27	C₃₁×#553	C₂²	1	2	yes	—
28	C₃₁×#552	—	2	1	no	—
29	C₃₁×#552	C₂²	1	2	yes	complemented
30	C₃₁×#548	C₂²	1	2	yes	—
31	C₃₁×#547	C₂²	1	2	yes	—
32	C₃₁×#546	—	2	2	no	—
33	C₃₁×#546	C₂²	1	2	yes	—
34	C₃₁×#544	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#543	—	2	1	no	—
36	C₃₁×#542	C₂²	1	2	yes	—
37	C₃₁×#539	—	2	1	no	—
38	C₃₁×#538	—	2	1	no	—
39	C₃₁×#538	—	2	2	no	—
40	C₃₁×#537	—	2	1	no	—
41	C₃₁×#537	C₂²	1	2	yes	—
42	C₃₁×#537	C₂²	1	1	yes	characteristic, complemented
43	C₃₁×#529	—	2	2	no	—
44	C₃₁×#525	C₂²	1	1	yes	characteristic
45	C₃₁×#525	C₂²	1	1	yes	characteristic
46	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
47	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
48	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
49	C₃₁×#520	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	complemented
52	C₃₁×#498	C₂²	1	2	yes	complemented
53	C₃₁×#489	C₂²	1	2	yes	complemented
54	C₃₁×#488	C₂²	1	2	yes	complemented
55	C₃₁×#485	C₂²	1	2	yes	—
56	C₃₁×#485	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	complemented
58	C₃₁×#485	C₂²	1	2	yes	complemented
59	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#484	C₂²	1	2	yes	complemented
61	C₃₁×#484	C₂²	1	2	yes	complemented
62	C₃₁×#483	C₂²	1	1	yes	characteristic
63	C₃₁×#483	C₂²	1	2	yes	complemented
64	C₃₁×#483	C₂²	1	2	yes	complemented
65	C₃₁×#482	C₂²	1	2	yes	—
66	C₃₁×#482	C₂²	1	2	yes	—
67	C₃₁×#482	C₂²	1	2	yes	—
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#481	C₂²	1	2	yes	—
70	C₃₁×#481	C₂²	1	2	yes	complemented
71	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#480	C₂²	1	1	yes	characteristic
73	C₃₁×#480	C₂²	1	2	yes	—
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	2	yes	complemented
77	C₃₁×#477	C₂²	1	2	yes	complemented
78	C₃₁×#476	C₂²	1	2	yes	complemented
79	C₃₁×#475	C₂²	1	2	yes	complemented
80	C₃₁×#474	C₂²	1	2	yes	complemented
81	C₃₁×#470	C₂²	1	2	yes	—
82	C₃₁×#470	C₂²	1	2	yes	complemented
83	C₃₁×#469	C₂²	1	2	yes	—
84	C₃₁×#469	C₂²	1	2	yes	complemented
85	C₃₁×#468	C₂²	1	2	yes	—
86	C₃₁×#468	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	complemented
88	C₃₁×#465	C₂²	1	2	yes	complemented
89	C₃₁×#464	C₂²	1	2	yes	complemented
90	C₃₁×#463	C₂²	1	2	yes	complemented
91	C₃₁×#452	C₂²	1	2	yes	complemented
92	C₃₁×#452	C₂²	1	2	yes	complemented
93	C₃₁×#451	C₂²	1	1	yes	characteristic, complemented
94	C₃₁×#450	C₂²	1	1	yes	characteristic
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#449	C₂²	1	2	yes	complemented
97	C₃₁×#448	C₂²	1	1	yes	characteristic, complemented
98	C₃₁×#447	C₂²	1	1	yes	characteristic
99	C₃₁×#440	C₂²	1	2	yes	complemented
100	C₃₁×#440	C₂²	1	2	yes	complemented
101	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
102	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
103	C₃₁×#436	C₂²	1	2	yes	—
104	C₃₁×#436	C₂²	1	2	yes	complemented
105	C₃₁×#435	C₂²	1	2	yes	—
106	C₃₁×#435	C₂²	1	2	yes	complemented
107	C₃₁×#433	C₂²	1	2	yes	complemented
108	C₃₁×#428	C₂²	1	2	yes	—
109	C₃₁×#428	C₂²	1	2	yes	complemented
110	C₃₁×#428	C₂²	1	2	yes	complemented
111	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
112	C₃₁×#419	C₂²	1	2	yes	complemented
113	C₃₁×#418	C₂²	1	2	yes	—
114	C₃₁×#417	C₂²	1	2	yes	complemented
115	C₃₁×#416	C₂²	1	2	yes	complemented
116	C₃₁×#408	C₂²	1	2	yes	complemented
117	C₃₁×#407	C₂²	1	1	yes	characteristic
118	C₃₁×#407	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
122	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₃₁	—	2	1	no	—
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂×D₈×C₃₁	C₂³	1	2	yes	—
131	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
135	C₃₁×C₄⋊Q₈	—	2	1	no	—
136	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₃₁×#126	—	2	2	no	—
139	C₃₁×#126	—	2	2	no	—
140	C₃₁×#126	—	2	2	no	—
141	C₃₁×#126	—	2	2	no	—
142	C₃₁×#126	—	2	2	no	—
143	C₃₁×#125	—	2	2	no	—
144	C₃₁×#125	—	2	2	no	—
145	C₃₁×#125	—	2	1	no	—
146	C₃₁×#125	C₂³	1	2	yes	—
147	C₃₁×#124	—	2	2	no	—
148	C₃₁×#124	—	2	2	no	—
149	C₃₁×#124	—	2	2	no	—
150	C₃₁×#124	—	2	2	no	—
151	C₃₁×#124	—	2	2	no	—
152	C₃₁×#124	C₂³	1	2	yes	—
153	C₃₁×#123	—	2	2	no	—
154	C₃₁×#123	—	2	1	no	—
155	C₃₁×#123	—	2	2	no	—
156	C₃₁×#123	—	2	2	no	—
157	C₃₁×#123	—	2	2	no	—
158	C₃₁×#123	—	2	2	no	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	D₄	1	2	yes	—
161	C₃₁×C₂²⋊Q₈	—	2	2	no	—
162	C₃₁×C₂²⋊Q₈	—	2	1	no	—
163	C₃₁×C₂²⋊Q₈	—	2	1	no	—
164	C₃₁×C₂²⋊Q₈	—	2	1	no	—
165	C₃₁×C₂²⋊Q₈	—	2	2	no	—
166	C₃₁×C₂²⋊Q₈	—	2	2	no	—
167	C₃₁×C₂²⋊Q₈	—	2	2	no	—
168	C₃₁×C₂²⋊Q₈	—	2	2	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	—	2	2	no	—
171	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
172	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
173	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
174	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
175	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
176	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	—	2	2	no	—
182	C₃₁×#121	—	2	2	no	—
183	C₃₁×#121	—	2	2	no	—
184	C₃₁×#121	—	2	1	no	—
185	C₃₁×#121	—	2	2	no	—
186	C₃₁×#121	—	2	2	no	—
187	C₃₁×#121	—	2	1	no	—
188	C₃₁×#121	—	2	1	no	—
189	C₃₁×#121	—	2	2	no	—
190	C₃₁×#121	D₄	1	1	yes	characteristic
191	C₃₁×#121	D₄	1	1	yes	characteristic
192	C₃₁×#121	C₂³	1	1	yes	characteristic
193	C₃₁×#121	C₂³	1	1	yes	characteristic
194	C₃₁×#121	C₂³	1	2	yes	—
195	C₃₁×#121	C₂³	1	2	yes	—
196	C₃₁×#121	C₂³	1	2	yes	—
197	C₃₁×#121	C₂³	1	2	yes	—
198	C₃₁×#120	—	2	1	no	—
199	C₃₁×#120	—	2	2	no	—
200	C₃₁×#120	D₄	1	2	yes	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	—	2	2	no	—
203	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
204	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
205	C₄×D₄×C₃₁	—	2	2	no	—
206	C₄×D₄×C₃₁	—	2	1	no	—
207	C₄×D₄×C₃₁	—	2	2	no	—
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	2	no	—
211	C₄×D₄×C₃₁	—	2	2	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	C₂³	1	2	yes	—
214	C₄×D₄×C₃₁	C₂³	1	2	yes	—
215	C₄×D₄×C₃₁	C₂³	1	2	yes	—
216	C₄×D₄×C₃₁	C₂³	1	2	yes	—
217	C₃₁×#117	—	2	1	no	—
218	C₃₁×#117	—	2	1	no	—
219	C₃₁×#117	—	2	1	no	—
220	C₃₁×#117	—	2	2	no	—
221	C₃₁×#117	—	2	2	no	—
222	C₃₁×#117	C₂³	1	2	yes	—
223	C₃₁×#117	C₂³	1	2	yes	—
224	C₃₁×#117	C₂³	1	2	yes	—
225	C₃₁×#117	C₂³	1	1	yes	characteristic
226	C₃₁×#117	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
230	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
236	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
239	C₂×C₄²×C₃₁	—	2	1	no	—
240	C₃₁×#107	C₂³	1	2	yes	—
241	C₃₁×#107	C₂³	1	2	yes	—
242	C₃₁×#107	C₂³	1	2	yes	—
243	C₃₁×#107	C₂³	1	2	yes	—
244	C₃₁×#107	C₂³	1	2	yes	—
245	C₃₁×#107	C₂³	1	2	yes	—
246	C₃₁×#106	C₂³	1	2	yes	—
247	C₃₁×#106	C₂³	1	2	yes	—
248	C₃₁×#106	C₂³	1	2	yes	—
249	C₃₁×#106	C₂³	1	2	yes	—
250	C₃₁×#106	C₂³	1	2	yes	—
251	C₃₁×#106	C₂³	1	2	yes	—
252	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
253	C₃₁×C₄⋊C₈	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×#103	C₂³	1	2	yes	—
259	C₃₁×#103	C₂³	1	2	yes	—
260	C₃₁×#103	C₂³	1	2	yes	—
261	C₃₁×#103	C₂³	1	2	yes	—
262	C₃₁×#102	C₂³	1	2	yes	—
263	C₃₁×#102	C₂³	1	2	yes	—
264	C₃₁×#102	C₂³	1	2	yes	—
265	C₃₁×#102	C₂³	1	2	yes	—
266	C₃₁×#102	C₂³	1	2	yes	—
267	C₃₁×#102	C₂³	1	2	yes	—
268	C₃₁×#102	C₂³	1	2	yes	—
269	C₃₁×#102	C₂³	1	2	yes	—
270	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
271	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
272	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
275	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	C₂⁴×C₃₁	—	2	1	no	—
281	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
282	#41×C₃₁	—	4	2	no	—
283	#41×C₃₁	—	4	2	no	—
284	#41×C₃₁	—	4	2	no	—
285	#41×C₃₁	—	4	2	no	—
286	#41×C₃₁	—	8	4	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	1	no	—
289	C₂×Q₈×C₃₁	—	2	2	no	—
290	C₂×Q₈×C₃₁	—	4	2	no	—
291	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
293	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
294	C₂×D₄×C₃₁	—	2	1	no	—
295	C₂×D₄×C₃₁	—	2	2	no	—
296	C₂×D₄×C₃₁	—	2	1	no	—
297	C₂×D₄×C₃₁	—	2	1	no	—
298	C₂×D₄×C₃₁	—	2	2	no	—
299	C₂×D₄×C₃₁	—	2	2	no	—
300	C₂×D₄×C₃₁	—	2	2	no	—
301	C₂×D₄×C₃₁	—	2	2	no	—
302	C₂×D₄×C₃₁	—	2	1	no	—
303	C₂×D₄×C₃₁	—	4	2	no	—
304	C₂×D₄×C₃₁	—	8	2	no	—
305	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
306	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
309	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
310	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	—	2	1	no	—
312	C₂²×C₄×C₃₁	—	2	1	no	—
313	C₂²×C₄×C₃₁	—	2	1	no	—
314	C₂²×C₄×C₃₁	—	2	1	no	—
315	C₂²×C₄×C₃₁	—	2	1	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	1	no	—
319	C₂²×C₄×C₃₁	—	2	2	no	—
320	C₂²×C₄×C₃₁	—	2	2	no	—
321	C₂²×C₄×C₃₁	—	2	2	no	—
322	C₂²×C₄×C₃₁	—	4	2	no	—
323	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
330	Q₁₆×C₃₁	—	4	2	no	—
331	SD₁₆×C₃₁	—	4	2	no	—
332	SD₁₆×C₃₁	—	4	2	no	—
333	D₈×C₃₁	—	4	2	no	—
334	M₁₆×C₃₁	—	4	2	no	—
335	M₁₆×C₃₁	—	4	2	no	—
336	M₁₆×C₃₁	—	4	2	no	—
337	C₂×C₈×C₃₁	—	4	2	no	—
338	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
339	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
340	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
341	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	1	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	2	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	—	2	2	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	2	no	—
356	C₄⋊C₄×C₃₁	—	2	2	no	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	2	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₂²⋊C₄×C₃₁	—	2	2	no	—
371	C₂²⋊C₄×C₃₁	—	2	2	no	—
372	C₂²⋊C₄×C₃₁	—	2	2	no	—
373	C₂²⋊C₄×C₃₁	—	2	2	no	—
374	C₂²⋊C₄×C₃₁	—	2	2	no	—
375	C₂²⋊C₄×C₃₁	—	2	1	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	1	no	—
378	C₂²⋊C₄×C₃₁	—	2	1	no	—
379	C₂²⋊C₄×C₃₁	—	2	2	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	1	no	—
385	C₂²⋊C₄×C₃₁	—	2	2	no	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	1	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	—	2	2	no	—
397	C₄²×C₃₁	—	2	2	no	—
398	C₄²×C₃₁	—	2	2	no	—
399	C₄²×C₃₁	—	2	1	no	—
400	C₄²×C₃₁	—	2	2	no	—
401	C₄²×C₃₁	C₂⁴	1	2	yes	—
402	#61776	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
403	C₂³×C₃₁	—	2	1	no	—
404	C₂³×C₃₁	—	2	2	no	—
405	C₂³×C₃₁	—	4	1	no	—
406	C₂³×C₃₁	—	4	1	no	—
407	C₂³×C₃₁	—	4	1	no	—
408	C₂³×C₃₁	—	4	2	no	—
409	C₂³×C₃₁	—	8	1	no	—
410	C₂³×C₃₁	—	8	1	no	—
411	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
412	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
413	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
414	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
415	Q₈×C₃₁	—	2	2	no	—
416	Q₈×C₃₁	—	2	2	no	—
417	Q₈×C₃₁	—	2	2	no	—
418	Q₈×C₃₁	—	4	1	no	—
419	Q₈×C₃₁	—	8	2	no	—
420	Q₈×C₃₁	—	8	1	no	—
421	Q₈×C₃₁	—	8	2	no	—
422	D₄×C₃₁	—	2	2	no	—
423	D₄×C₃₁	—	2	2	no	—
424	D₄×C₃₁	—	2	2	no	—
425	D₄×C₃₁	—	4	2	no	—
426	D₄×C₃₁	—	4	1	no	—
427	D₄×C₃₁	—	4	2	no	—
428	D₄×C₃₁	—	4	2	no	—
429	D₄×C₃₁	—	4	4	no	—
430	D₄×C₃₁	—	4	2	no	—
431	D₄×C₃₁	—	8	1	no	—
432	D₄×C₃₁	—	8	1	no	—
433	D₄×C₃₁	—	8	2	no	—
434	D₄×C₃₁	—	8	1	no	—
435	D₄×C₃₁	—	8	2	no	—
436	D₄×C₃₁	—	8	2	no	—
437	D₄×C₃₁	—	8	2	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	2	no	—
441	C₂×C₄×C₃₁	—	2	2	no	—
442	C₂×C₄×C₃₁	—	2	2	no	—
443	C₂×C₄×C₃₁	—	2	2	no	—
444	C₂×C₄×C₃₁	—	2	1	no	—
445	C₂×C₄×C₃₁	—	2	1	no	—
446	C₂×C₄×C₃₁	—	2	2	no	—
447	C₂×C₄×C₃₁	—	2	2	no	—
448	C₂×C₄×C₃₁	—	2	1	no	—
449	C₂×C₄×C₃₁	—	2	2	no	—
450	C₂×C₄×C₃₁	—	2	2	no	—
451	C₂×C₄×C₃₁	—	4	1	no	—
452	C₂×C₄×C₃₁	—	4	1	no	—
453	C₂×C₄×C₃₁	—	4	1	no	—
454	C₂×C₄×C₃₁	—	4	2	no	—
455	C₂×C₄×C₃₁	—	4	2	no	—
456	C₂×C₄×C₃₁	—	8	2	no	—
457	C₂×C₄×C₃₁	—	8	2	no	—
458	C₂×C₄×C₃₁	—	8	2	no	—
459	C₂×C₄×C₃₁	—	8	1	no	—
460	C₂×C₄×C₃₁	—	8	2	no	—
461	C₂×C₄×C₃₁	—	8	1	no	—
462	C₂×C₄×C₃₁	—	8	1	no	—
463	C₂×C₄×C₃₁	—	8	1	no	—
464	C₂×C₄×C₃₁	—	8	2	no	—
465	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
469	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
472	C₈×C₃₁	—	2	2	no	—
473	C₈×C₃₁	—	2	2	no	—
474	C₈×C₃₁	—	2	2	no	—
475	C₈×C₃₁	—	2	2	no	—
476	#3536	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#3493	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#3356	C₂×C₃₁	1	2	yes	complemented
479	#3354	C₂×C₃₁	1	2	yes	complemented
480	#3346	C₂×C₃₁	1	2	yes	complemented
481	#3343	C₂×C₃₁	1	2	yes	complemented
482	#3327	C₂×C₃₁	1	2	yes	complemented
483	#3322	C₂×C₃₁	1	2	yes	complemented
484	#3321	C₂×C₃₁	1	2	yes	complemented
485	#3311	C₂×C₃₁	1	2	yes	complemented
486	#3244	C₂×C₃₁	1	2	yes	complemented
487	#3204	C₂×C₃₁	1	2	yes	complemented
488	#3196	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#3194	C₂×C₃₁	1	1	yes	characteristic, complemented
490	#3124	C₂×C₃₁	1	2	yes	complemented
491	#3098	C₂×C₃₁	1	2	yes	complemented
492	#3095	C₂×C₃₁	1	1	yes	characteristic, complemented
493	#3094	C₂×C₃₁	1	1	yes	characteristic, complemented
494	#2978	C₂×C₃₁	1	1	yes	characteristic, complemented
495	C₂²×C₃₁	—	2	1	no	—
496	C₂²×C₃₁	—	2	2	no	—
497	C₂²×C₃₁	—	2	1	no	—
498	C₂²×C₃₁	—	2	1	no	—
499	C₂²×C₃₁	—	2	1	no	—
500	C₂²×C₃₁	—	2	1	no	—
501	C₂²×C₃₁	—	2	2	no	—
502	C₂²×C₃₁	—	2	1	no	—
503	C₂²×C₃₁	—	2	1	no	—
504	C₂²×C₃₁	—	2	1	no	—
505	C₂²×C₃₁	—	2	1	no	—
506	C₂²×C₃₁	—	2	2	no	—
507	C₂²×C₃₁	—	4	1	no	—
508	C₂²×C₃₁	—	4	2	no	—
509	C₂²×C₃₁	—	4	1	no	—
510	C₂²×C₃₁	—	4	2	no	—
511	C₂²×C₃₁	—	4	1	no	—
512	C₂²×C₃₁	—	4	2	no	—
513	C₂²×C₃₁	—	8	2	no	—
514	C₂²×C₃₁	—	16	2	no	—
515	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
516	C₄×C₃₁	—	2	2	no	—
517	C₄×C₃₁	—	2	2	no	—
518	C₄×C₃₁	—	2	1	no	—
519	C₄×C₃₁	—	2	1	no	—
520	C₄×C₃₁	—	2	1	no	—
521	C₄×C₃₁	—	2	2	no	—
522	C₄×C₃₁	—	4	2	no	—
523	C₄×C₃₁	—	4	2	no	—
524	C₄×C₃₁	—	4	2	no	—
525	C₄×C₃₁	—	4	1	no	—
526	C₄×C₃₁	—	4	2	no	—
527	C₄×C₃₁	—	4	1	no	—
528	C₄×C₃₁	—	4	1	no	—
529	C₄×C₃₁	—	4	2	no	—
530	C₄×C₃₁	#585	1	2	yes	—
531	#562	—	2	2	no	—
532	#556	—	2	1	no	—
533	#556	C₂²×C₃₁	1	2	yes	—
534	#555	—	2	1	no	—
535	#555	C₂²×C₃₁	1	2	yes	complemented
536	#554	C₂²×C₃₁	1	2	yes	—
537	#553	—	2	1	no	—
538	#553	C₂²×C₃₁	1	2	yes	—
539	#552	—	2	1	no	—
540	#552	C₂²×C₃₁	1	2	yes	complemented
541	#548	C₂²×C₃₁	1	2	yes	—
542	#547	C₂²×C₃₁	1	2	yes	—
543	#546	—	2	2	no	—
544	#546	C₂²×C₃₁	1	2	yes	—
545	#544	C₂²×C₃₁	1	1	yes	characteristic, complemented
546	#543	—	2	1	no	—
547	#542	C₂²×C₃₁	1	2	yes	—
548	#539	—	2	1	no	—
549	#538	—	2	1	no	—
550	#538	—	2	2	no	—
551	#537	—	2	1	no	—
552	#537	C₂²×C₃₁	1	2	yes	—
553	#537	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	#529	—	2	2	no	—
555	#525	C₂²×C₃₁	1	1	yes	characteristic
556	#525	C₂²×C₃₁	1	1	yes	characteristic
557	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
558	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
559	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
560	#520	C₂²×C₃₁	1	1	yes	characteristic, complemented
561	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
562	#501	C₂²×C₃₁	1	2	yes	complemented
563	#498	C₂²×C₃₁	1	2	yes	complemented
564	#489	C₂²×C₃₁	1	2	yes	complemented
565	#488	C₂²×C₃₁	1	2	yes	complemented
566	#485	C₂²×C₃₁	1	2	yes	—
567	#485	C₂²×C₃₁	1	2	yes	—
568	#485	C₂²×C₃₁	1	2	yes	complemented
569	#485	C₂²×C₃₁	1	2	yes	complemented
570	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
571	#484	C₂²×C₃₁	1	2	yes	complemented
572	#484	C₂²×C₃₁	1	2	yes	complemented
573	#483	C₂²×C₃₁	1	1	yes	characteristic
574	#483	C₂²×C₃₁	1	2	yes	complemented
575	#483	C₂²×C₃₁	1	2	yes	complemented
576	#482	C₂²×C₃₁	1	2	yes	—
577	#482	C₂²×C₃₁	1	2	yes	—
578	#482	C₂²×C₃₁	1	2	yes	—
579	#482	C₂²×C₃₁	1	2	yes	complemented
580	#481	C₂²×C₃₁	1	2	yes	—
581	#481	C₂²×C₃₁	1	2	yes	complemented
582	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
583	#480	C₂²×C₃₁	1	1	yes	characteristic
584	#480	C₂²×C₃₁	1	2	yes	—
585	#480	C₂²×C₃₁	1	2	yes	complemented
586	#479	C₂²×C₃₁	1	2	yes	complemented
587	#478	C₂²×C₃₁	1	2	yes	complemented
588	#477	C₂²×C₃₁	1	2	yes	complemented
589	#476	C₂²×C₃₁	1	2	yes	complemented
590	#475	C₂²×C₃₁	1	2	yes	complemented
591	#474	C₂²×C₃₁	1	2	yes	complemented
592	#470	C₂²×C₃₁	1	2	yes	—
593	#470	C₂²×C₃₁	1	2	yes	complemented
594	#469	C₂²×C₃₁	1	2	yes	—
595	#469	C₂²×C₃₁	1	2	yes	complemented
596	#468	C₂²×C₃₁	1	2	yes	—
597	#468	C₂²×C₃₁	1	2	yes	—
598	#465	C₂²×C₃₁	1	2	yes	complemented
599	#465	C₂²×C₃₁	1	2	yes	complemented
600	#464	C₂²×C₃₁	1	2	yes	complemented
601	#463	C₂²×C₃₁	1	2	yes	complemented
602	#452	C₂²×C₃₁	1	2	yes	complemented
603	#452	C₂²×C₃₁	1	2	yes	complemented
604	#451	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#450	C₂²×C₃₁	1	1	yes	characteristic
606	#449	C₂²×C₃₁	1	2	yes	—
607	#449	C₂²×C₃₁	1	2	yes	complemented
608	#448	C₂²×C₃₁	1	1	yes	characteristic, complemented
609	#447	C₂²×C₃₁	1	1	yes	characteristic
610	#440	C₂²×C₃₁	1	2	yes	complemented
611	#440	C₂²×C₃₁	1	2	yes	complemented
612	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
613	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
614	#436	C₂²×C₃₁	1	2	yes	—
615	#436	C₂²×C₃₁	1	2	yes	complemented
616	#435	C₂²×C₃₁	1	2	yes	—
617	#435	C₂²×C₃₁	1	2	yes	complemented
618	#433	C₂²×C₃₁	1	2	yes	complemented
619	#428	C₂²×C₃₁	1	2	yes	—
620	#428	C₂²×C₃₁	1	2	yes	complemented
621	#428	C₂²×C₃₁	1	2	yes	complemented
622	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
623	#419	C₂²×C₃₁	1	2	yes	complemented
624	#418	C₂²×C₃₁	1	2	yes	—
625	#417	C₂²×C₃₁	1	2	yes	complemented
626	#416	C₂²×C₃₁	1	2	yes	complemented
627	#408	C₂²×C₃₁	1	2	yes	complemented
628	#407	C₂²×C₃₁	1	1	yes	characteristic
629	#407	C₂²×C₃₁	1	1	yes	characteristic
630	C₂×C₃₁	—	4	2	no	—
631	C₂×C₃₁	—	4	1	no	—
632	C₂×C₃₁	—	4	1	no	—
633	C₂×C₃₁	—	4	1	no	—
634	C₂×C₃₁	—	8	1	no	—
635	C₂×C₃₁	—	8	2	no	—
636	C₂×C₃₁	#3485	1	1	yes	characteristic
637	C₂×C₃₁	#3585	1	1	yes	characteristic
638	C₂×C₃₁	#3586	1	1	yes	characteristic
639	C₂×#41	—	2	2	no	—
640	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
641	C₂×#41	C₂³×C₃₁	1	2	yes	—
642	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
643	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
644	C₂²×D₄	—	2	1	no	—
645	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
648	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
649	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
650	C₂×D₈	C₂³×C₃₁	1	2	yes	—
651	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
652	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
653	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
654	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
655	C₄⋊Q₈	—	2	1	no	—
656	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
657	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	2	no	—
665	#125	—	2	1	no	—
666	#125	C₂³×C₃₁	1	2	yes	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	2	no	—
672	#124	C₂³×C₃₁	1	2	yes	—
673	#123	—	2	2	no	—
674	#123	—	2	1	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	D₄×C₃₁	1	2	yes	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	1	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
692	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
693	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
698	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	1	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	—	2	1	no	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	D₄×C₃₁	1	1	yes	characteristic
711	#121	D₄×C₃₁	1	1	yes	characteristic
712	#121	C₂³×C₃₁	1	2	yes	—
713	#121	C₂³×C₃₁	1	2	yes	—
714	#121	C₂³×C₃₁	1	1	yes	characteristic
715	#121	C₂³×C₃₁	1	1	yes	characteristic
716	#121	C₂³×C₃₁	1	2	yes	—
717	#121	C₂³×C₃₁	1	2	yes	—
718	#120	—	2	1	no	—
719	#120	—	2	2	no	—
720	#120	D₄×C₃₁	1	2	yes	—
721	C₄×Q₈	—	2	1	no	—
722	C₄×Q₈	—	2	2	no	—
723	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
724	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	C₂³×C₃₁	1	2	yes	—
734	C₄×D₄	C₂³×C₃₁	1	2	yes	—
735	C₄×D₄	C₂³×C₃₁	1	2	yes	—
736	C₄×D₄	C₂³×C₃₁	1	2	yes	—
737	#117	—	2	1	no	—
738	#117	—	2	1	no	—
739	#117	—	2	1	no	—
740	#117	—	2	2	no	—
741	#117	—	2	2	no	—
742	#117	C₂³×C₃₁	1	2	yes	—
743	#117	C₂³×C₃₁	1	2	yes	—
744	#117	C₂³×C₃₁	1	1	yes	characteristic
745	#117	C₂³×C₃₁	1	2	yes	—
746	#117	C₂³×C₃₁	1	1	yes	characteristic
747	C₂×C₄⋊C₄	—	2	1	no	—
748	C₂×C₄⋊C₄	—	2	1	no	—
749	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
752	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
753	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
755	C₂×C₂²⋊C₄	—	2	1	no	—
756	C₂×C₂²⋊C₄	—	2	1	no	—
757	C₂×C₂²⋊C₄	—	2	1	no	—
758	C₂×C₂²⋊C₄	—	2	2	no	—
759	C₂×C₄²	—	2	1	no	—
760	#107	C₂³×C₃₁	1	2	yes	—
761	#107	C₂³×C₃₁	1	2	yes	—
762	#107	C₂³×C₃₁	1	2	yes	—
763	#107	C₂³×C₃₁	1	2	yes	—
764	#107	C₂³×C₃₁	1	2	yes	—
765	#107	C₂³×C₃₁	1	2	yes	—
766	#106	C₂³×C₃₁	1	2	yes	—
767	#106	C₂³×C₃₁	1	2	yes	—
768	#106	C₂³×C₃₁	1	2	yes	—
769	#106	C₂³×C₃₁	1	2	yes	—
770	#106	C₂³×C₃₁	1	2	yes	—
771	#106	C₂³×C₃₁	1	2	yes	—
772	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
773	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
774	#103	C₂³×C₃₁	1	2	yes	—
775	#103	C₂³×C₃₁	1	2	yes	—
776	#103	C₂³×C₃₁	1	2	yes	—
777	#103	C₂³×C₃₁	1	2	yes	—
778	#103	C₂³×C₃₁	1	2	yes	—
779	#103	C₂³×C₃₁	1	2	yes	—
780	#103	C₂³×C₃₁	1	2	yes	—
781	#103	C₂³×C₃₁	1	2	yes	—
782	#102	C₂³×C₃₁	1	2	yes	—
783	#102	C₂³×C₃₁	1	2	yes	—
784	#102	C₂³×C₃₁	1	2	yes	—
785	#102	C₂³×C₃₁	1	2	yes	—
786	#102	C₂³×C₃₁	1	2	yes	—
787	#102	C₂³×C₃₁	1	2	yes	—
788	#102	C₂³×C₃₁	1	2	yes	—
789	#102	C₂³×C₃₁	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
793	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
794	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
795	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
796	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
797	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
798	#97	C₂³×C₃₁	1	2	yes	—
799	C₄×C₈	C₂³×C₃₁	1	2	yes	—
800	C₃₁	#61776	1	1	yes	characteristic, direct product factor, Sylow
801	C₂⁴	—	2	1	no	—
802	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	#41	—	4	2	no	—
806	#41	—	4	2	no	—
807	#41	—	8	4	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	1	no	—
810	C₂×Q₈	—	2	2	no	—
811	C₂×Q₈	—	4	2	no	—
812	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
813	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
814	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	2	1	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	1	no	—
824	C₂×D₄	—	4	2	no	—
825	C₂×D₄	—	8	2	no	—
826	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
827	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
828	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
829	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
830	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
831	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	1	no	—
836	C₂²×C₄	—	2	1	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	2	no	—
843	C₂²×C₄	—	4	2	no	—
844	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
845	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
846	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
851	Q₁₆	—	4	2	no	—
852	SD₁₆	—	4	2	no	—
853	SD₁₆	—	4	2	no	—
854	D₈	—	4	2	no	—
855	M₁₆	—	4	2	no	—
856	M₁₆	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	C₂×C₈	—	4	2	no	—
859	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
860	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
861	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
862	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	1	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	C₂×D₄×C₃₁	1	1	yes	characteristic
882	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
883	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
884	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
885	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
886	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
888	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
890	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	1	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	1	no	—
899	C₂²⋊C₄	—	2	1	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	1	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	1	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
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	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
915	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
916	C₄²	—	2	2	no	—
917	C₄²	—	2	2	no	—
918	C₄²	—	2	2	no	—
919	C₄²	—	2	2	no	—
920	C₄²	—	2	1	no	—
921	C₄²	—	2	2	no	—
922	C₄²	C₂⁴×C₃₁	1	2	yes	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	4	1	no	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	1	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	8	1	no	—
930	C₂³	—	8	1	no	—
931	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
932	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
933	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
934	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
935	Q₈	—	2	2	no	—
936	Q₈	—	2	2	no	—
937	Q₈	—	2	2	no	—
938	Q₈	—	4	1	no	—
939	Q₈	—	8	2	no	—
940	Q₈	—	8	1	no	—
941	Q₈	—	8	2	no	—
942	D₄	—	2	2	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	2	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	4	no	—
950	D₄	—	4	2	no	—
951	D₄	—	8	1	no	—
952	D₄	—	8	1	no	—
953	D₄	—	8	2	no	—
954	D₄	—	8	1	no	—
955	D₄	—	8	2	no	—
956	D₄	—	8	2	no	—
957	D₄	—	8	2	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	1	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	8	2	no	—
977	C₂×C₄	—	8	2	no	—
978	C₂×C₄	—	8	2	no	—
979	C₂×C₄	—	8	1	no	—
980	C₂×C₄	—	8	2	no	—
981	C₂×C₄	—	8	1	no	—
982	C₂×C₄	—	8	1	no	—
983	C₂×C₄	—	8	1	no	—
984	C₂×C₄	—	8	2	no	—
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	1	yes	characteristic
988	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
989	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
991	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
992	C₈	—	2	2	no	—
993	C₈	—	2	2	no	—
994	C₈	—	2	2	no	—
995	C₈	—	2	2	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	1	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	2	no	—
1010	C₂²	—	4	1	no	—
1011	C₂²	—	4	2	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	2	no	—
1014	C₂²	—	8	2	no	—
1015	C₂²	—	16	2	no	—
1016	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1017	C₄	—	2	1	no	—
1018	C₄	—	2	1	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	4	1	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	1	no	—
1031	C₄	C₃₁×#585	1	2	yes	—
1032	C₂	—	4	1	no	—
1033	C₂	—	4	1	no	—
1034	C₂	—	4	1	no	—
1035	C₂	—	4	2	no	—
1036	C₂	—	8	2	no	—
1037	C₂	—	8	1	no	—
1038	C₂	C₃₁×#3485	1	1	yes	characteristic
1039	C₂	C₃₁×#3585	1	1	yes	characteristic
1040	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 ◁ C₃₁×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3536	C₂	semidirect
2. C₃₁×#3493	C₂	semidirect
3. C₃₁×#3356	C₂	semidirect
4. C₃₁×#3354	C₂	semidirect
5. C₃₁×#3346	C₂	semidirect
6. C₃₁×#3343	C₂	semidirect
7. C₃₁×#3327	C₂	semidirect
8. C₃₁×#3322	C₂	semidirect
9. C₃₁×#3321	C₂	semidirect
10. C₃₁×#3311	C₂	semidirect
11. C₃₁×#3244	C₂	semidirect
12. C₃₁×#3204	C₂	semidirect
13. C₃₁×#3196	C₂	semidirect
14. C₃₁×#3194	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3098	C₂	semidirect
17. C₃₁×#3095	C₂	semidirect
18. C₃₁×#3094	C₂	semidirect
19. C₃₁×#2978	C₂	semidirect
24. C₃₁×#555	C₂²	semidirect
29. C₃₁×#552	C₂²	semidirect
34. C₃₁×#544	C₂²	semidirect
42. C₃₁×#537	C₂²	semidirect
48. C₃₁×#520	C₂²	semidirect
49. C₃₁×#520	C₂²	semidirect
51. C₃₁×#501	C₂²	semidirect
52. C₃₁×#498	C₂²	semidirect
53. C₃₁×#489	C₂²	semidirect
54. C₃₁×#488	C₂²	semidirect
57. C₃₁×#485	C₂²	semidirect
58. C₃₁×#485	C₂²	semidirect
59. C₃₁×#484	C₂²	semidirect
60. C₃₁×#484	C₂²	semidirect
61. C₃₁×#484	C₂²	semidirect
63. C₃₁×#483	C₂²	semidirect
64. C₃₁×#483	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
76. C₃₁×#478	C₂²	semidirect
77. C₃₁×#477	C₂²	semidirect
78. C₃₁×#476	C₂²	semidirect
79. C₃₁×#475	C₂²	semidirect
80. C₃₁×#474	C₂²	semidirect
82. C₃₁×#470	C₂²	semidirect
84. C₃₁×#469	C₂²	semidirect
87. C₃₁×#465	C₂²	semidirect
88. C₃₁×#465	C₂²	semidirect
89. C₃₁×#464	C₂²	semidirect
90. C₃₁×#463	C₂²	semidirect
91. C₃₁×#452	C₂²	semidirect
92. C₃₁×#452	C₂²	semidirect
93. C₃₁×#451	C₂²	semidirect
96. C₃₁×#449	C₂²	semidirect
97. C₃₁×#448	C₂²	semidirect
99. C₃₁×#440	C₂²	semidirect
100. C₃₁×#440	C₂²	semidirect
101. C₄×Q₁₆×C₃₁	C₂²	semidirect
102. C₄×D₈×C₃₁	C₂²	semidirect
104. C₃₁×#436	C₂²	semidirect
106. C₃₁×#435	C₂²	semidirect
107. C₃₁×#433	C₂²	semidirect
109. C₃₁×#428	C₂²	semidirect
110. C₃₁×#428	C₂²	semidirect
111. C₂×C₃₁×#107	C₂²	semidirect
112. C₃₁×#419	C₂²	semidirect
114. C₃₁×#417	C₂²	semidirect
115. C₃₁×#416	C₂²	semidirect
116. C₃₁×#408	C₂²	semidirect
402. #61776	C₃₁	direct (N × H)
476. #3536	C₂×C₃₁	semidirect
477. #3493	C₂×C₃₁	semidirect
478. #3356	C₂×C₃₁	semidirect
479. #3354	C₂×C₃₁	semidirect
480. #3346	C₂×C₃₁	semidirect
481. #3343	C₂×C₃₁	semidirect
482. #3327	C₂×C₃₁	semidirect
483. #3322	C₂×C₃₁	semidirect
484. #3321	C₂×C₃₁	semidirect
485. #3311	C₂×C₃₁	semidirect
486. #3244	C₂×C₃₁	semidirect
487. #3204	C₂×C₃₁	semidirect
488. #3196	C₂×C₃₁	semidirect
489. #3194	C₂×C₃₁	semidirect
490. #3124	C₂×C₃₁	semidirect
491. #3098	C₂×C₃₁	semidirect
492. #3095	C₂×C₃₁	semidirect
493. #3094	C₂×C₃₁	semidirect
494. #2978	C₂×C₃₁	semidirect
535. #555	C₂²×C₃₁	semidirect
540. #552	C₂²×C₃₁	semidirect
545. #544	C₂²×C₃₁	semidirect
553. #537	C₂²×C₃₁	semidirect
559. #520	C₂²×C₃₁	semidirect
560. #520	C₂²×C₃₁	semidirect
562. #501	C₂²×C₃₁	semidirect
563. #498	C₂²×C₃₁	semidirect
564. #489	C₂²×C₃₁	semidirect
565. #488	C₂²×C₃₁	semidirect
568. #485	C₂²×C₃₁	semidirect
569. #485	C₂²×C₃₁	semidirect
570. #484	C₂²×C₃₁	semidirect
571. #484	C₂²×C₃₁	semidirect
572. #484	C₂²×C₃₁	semidirect
574. #483	C₂²×C₃₁	semidirect
575. #483	C₂²×C₃₁	semidirect
579. #482	C₂²×C₃₁	semidirect
581. #481	C₂²×C₃₁	semidirect
582. #481	C₂²×C₃₁	semidirect
585. #480	C₂²×C₃₁	semidirect
586. #479	C₂²×C₃₁	semidirect
587. #478	C₂²×C₃₁	semidirect
588. #477	C₂²×C₃₁	semidirect
589. #476	C₂²×C₃₁	semidirect
590. #475	C₂²×C₃₁	semidirect
591. #474	C₂²×C₃₁	semidirect
593. #470	C₂²×C₃₁	semidirect
595. #469	C₂²×C₃₁	semidirect
598. #465	C₂²×C₃₁	semidirect
599. #465	C₂²×C₃₁	semidirect
600. #464	C₂²×C₃₁	semidirect
601. #463	C₂²×C₃₁	semidirect
602. #452	C₂²×C₃₁	semidirect
603. #452	C₂²×C₃₁	semidirect
604. #451	C₂²×C₃₁	semidirect
607. #449	C₂²×C₃₁	semidirect
608. #448	C₂²×C₃₁	semidirect
610. #440	C₂²×C₃₁	semidirect
611. #440	C₂²×C₃₁	semidirect
612. C₄×Q₁₆	C₂²×C₃₁	semidirect
613. C₄×D₈	C₂²×C₃₁	semidirect
615. #436	C₂²×C₃₁	semidirect
617. #435	C₂²×C₃₁	semidirect
618. #433	C₂²×C₃₁	semidirect
620. #428	C₂²×C₃₁	semidirect
621. #428	C₂²×C₃₁	semidirect
622. C₂×#107	C₂²×C₃₁	semidirect
623. #419	C₂²×C₃₁	semidirect
625. #417	C₂²×C₃₁	semidirect
626. #416	C₂²×C₃₁	semidirect
627. #408	C₂²×C₃₁	semidirect
800. C₃₁	#61776	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×#3536	2
C₃₁×#3493	2
C₃₁×#3356	2
C₃₁×#3354	2
C₃₁×#3346	2
C₃₁×#3343	2
C₃₁×#3327	2
C₃₁×#3322	2
C₃₁×#3321	2
C₃₁×#3311	2
C₃₁×#3244	2
C₃₁×#3204	2
C₃₁×#3196	2
C₃₁×#3194	2
C₃₁×#3124	2
C₃₁×#3098	2
C₃₁×#3095	2
C₃₁×#3094	2
C₃₁×#2978	2
#61776	31

Subgroups — C31×#61776 #21518535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61776 #21518535