Subgroups — C₃₁×#62170 #21518929

Order 7936.

1740 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3385	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3370	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3345	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3334	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3309	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3301	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3243	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3119	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3083	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#479	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#563	—	2	1	no	—
21	C₃₁×#562	—	2	1	no	—
22	C₃₁×#559	—	2	1	no	—
23	C₃₁×#559	C₂²	1	1	yes	characteristic
24	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#554	—	2	1	no	—
26	C₃₁×#554	C₂²	1	2	yes	—
27	C₃₁×#554	C₂²	1	1	yes	characteristic
28	C₃₁×#553	C₂²	1	2	yes	—
29	C₃₁×#553	C₂²	1	2	yes	—
30	C₃₁×#550	C₂²	1	1	yes	characteristic
31	C₃₁×#548	C₂²	1	2	yes	—
32	C₃₁×#547	—	2	2	no	—
33	C₃₁×#547	—	2	2	no	—
34	C₃₁×#547	C₂²	1	2	yes	—
35	C₃₁×#547	C₂²	1	2	yes	—
36	C₃₁×#544	C₂²	1	2	yes	—
37	C₃₁×#542	—	2	2	no	—
38	C₃₁×#542	C₂²	1	2	yes	—
39	C₃₁×#540	C₂²	1	2	yes	—
40	C₃₁×#539	—	2	2	no	—
41	C₃₁×#539	—	2	1	no	—
42	C₃₁×#537	—	2	1	no	—
43	C₃₁×#532	—	2	1	no	—
44	C₃₁×#532	C₂²	1	1	yes	characteristic
45	C₃₁×#532	C₂²	1	1	yes	characteristic
46	C₃₁×#529	—	2	1	no	—
47	C₃₁×#529	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
49	C₃₁×#520	C₂²	1	2	yes	—
50	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
51	C₃₁×#501	C₂²	1	2	yes	—
52	C₃₁×#501	C₂²	1	2	yes	—
53	C₃₁×#500	C₂²	1	2	yes	—
54	C₃₁×#490	C₂²	1	2	yes	—
55	C₃₁×#489	C₂²	1	2	yes	—
56	C₃₁×#488	C₂²	1	2	yes	—
57	C₃₁×#485	C₂²	1	2	yes	—
58	C₃₁×#484	C₂²	1	2	yes	—
59	C₃₁×#482	C₂²	1	2	yes	—
60	C₃₁×#481	C₂²	1	2	yes	—
61	C₃₁×#481	C₂²	1	2	yes	—
62	C₃₁×#480	C₂²	1	2	yes	—
63	C₃₁×#480	C₂²	1	2	yes	—
64	C₃₁×#480	C₂²	1	2	yes	—
65	C₃₁×#480	C₂²	1	2	yes	—
66	C₃₁×#479	C₂²	1	2	yes	—
67	C₃₁×#479	C₂²	1	2	yes	—
68	C₃₁×#479	C₂²	1	2	yes	—
69	C₃₁×#479	C₂²	1	2	yes	—
70	C₃₁×#479	C₂²	1	2	yes	—
71	C₃₁×#478	C₂²	1	2	yes	—
72	C₃₁×#478	C₂²	1	2	yes	—
73	C₃₁×#478	C₂²	1	2	yes	—
74	C₃₁×#477	C₂²	1	1	yes	characteristic
75	C₃₁×#477	C₂²	1	2	yes	—
76	C₃₁×#477	C₂²	1	1	yes	characteristic
77	C₃₁×#476	C₂²	1	2	yes	—
78	C₃₁×#474	C₂²	1	2	yes	—
79	C₃₁×#474	C₂²	1	2	yes	—
80	C₃₁×#474	C₂²	1	2	yes	—
81	C₃₁×#474	C₂²	1	2	yes	—
82	C₃₁×#469	C₂²	1	2	yes	—
83	C₃₁×#468	C₂²	1	2	yes	—
84	C₃₁×#466	C₂²	1	2	yes	—
85	C₃₁×#466	C₂²	1	2	yes	—
86	C₃₁×#466	C₂²	1	2	yes	—
87	C₃₁×#465	C₂²	1	2	yes	—
88	C₃₁×#463	C₂²	1	2	yes	—
89	C₃₁×#463	C₂²	1	2	yes	—
90	C₃₁×#460	C₂²	1	1	yes	characteristic
91	C₃₁×#460	C₂²	1	1	yes	characteristic
92	C₃₁×#459	C₂²	1	2	yes	—
93	C₃₁×#459	C₂²	1	2	yes	—
94	C₃₁×#449	C₂²	1	2	yes	—
95	C₃₁×#449	C₂²	1	2	yes	—
96	C₃₁×#448	C₂²	1	2	yes	—
97	C₃₁×#446	C₂²	1	2	yes	—
98	C₃₁×#442	C₂²	1	2	yes	—
99	C₃₁×#440	C₂²	1	2	yes	—
100	C₃₁×#440	C₂²	1	2	yes	—
101	C₃₁×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
103	C₄×D₈×C₃₁	C₂²	1	2	yes	—
104	C₃₁×#435	C₂²	1	2	yes	—
105	C₃₁×#435	C₂²	1	2	yes	—
106	C₈×D₄×C₃₁	C₂²	1	2	yes	—
107	C₃₁×#433	C₂²	1	2	yes	—
108	C₃₁×#432	C₂²	1	1	yes	characteristic
109	C₃₁×#428	C₂²	1	2	yes	—
110	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
111	C₂×C₃₁×#107	C₂²	1	2	yes	—
112	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
113	C₃₁×#424	C₂²	1	2	yes	—
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₃₁×#417	C₂²	1	2	yes	—
116	C₃₁×#416	C₂²	1	2	yes	—
117	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
118	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	2	no	—
120	C₂×#41×C₃₁	—	2	2	no	—
121	C₂×#41×C₃₁	—	2	1	no	—
122	C₂×#41×C₃₁	—	2	1	no	—
123	C₂×#41×C₃₁	C₂³	1	2	yes	—
124	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
127	C₂×D₈×C₃₁	C₂³	1	2	yes	—
128	C₂×D₈×C₃₁	C₂³	1	2	yes	—
129	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
130	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
133	C₃₁×C₄⋊Q₈	—	2	1	no	—
134	C₃₁×C₄⋊Q₈	—	2	2	no	—
135	C₃₁×C₄⋊Q₈	—	2	2	no	—
136	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
137	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₃₁×#127	—	2	1	no	—
141	C₃₁×#127	C₂³	1	1	yes	characteristic
142	C₃₁×#127	C₂³	1	1	yes	characteristic
143	C₃₁×#126	—	2	2	no	—
144	C₃₁×#126	—	2	2	no	—
145	C₃₁×#126	—	2	2	no	—
146	C₃₁×#126	D₄	1	2	yes	—
147	C₃₁×#125	—	2	1	no	—
148	C₃₁×#125	—	2	2	no	—
149	C₃₁×#125	—	2	1	no	—
150	C₃₁×#125	—	2	1	no	—
151	C₃₁×#125	D₄	1	1	yes	characteristic
152	C₃₁×#125	C₂³	1	2	yes	—
153	C₃₁×#125	C₂³	1	2	yes	—
154	C₃₁×#125	C₂³	1	2	yes	—
155	C₃₁×#124	—	2	1	no	—
156	C₃₁×#124	—	2	2	no	—
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	—	2	1	no	—
159	C₃₁×#124	—	2	1	no	—
160	C₃₁×#124	D₄	1	1	yes	characteristic
161	C₃₁×#124	C₂³	1	2	yes	—
162	C₃₁×#123	—	2	2	no	—
163	C₃₁×#123	—	2	2	no	—
164	C₃₁×#123	—	2	2	no	—
165	C₃₁×#123	—	2	2	no	—
166	C₃₁×#123	—	2	2	no	—
167	C₃₁×#123	—	2	2	no	—
168	C₃₁×#123	—	2	2	no	—
169	C₃₁×#123	—	2	2	no	—
170	C₃₁×#123	—	2	2	no	—
171	C₃₁×#123	—	2	2	no	—
172	C₃₁×#123	D₄	1	2	yes	—
173	C₃₁×C₂²⋊Q₈	—	2	2	no	—
174	C₃₁×C₂²⋊Q₈	—	2	2	no	—
175	C₃₁×C₂²⋊Q₈	—	2	2	no	—
176	C₃₁×C₂²⋊Q₈	—	2	2	no	—
177	C₃₁×C₂²⋊Q₈	—	2	2	no	—
178	C₃₁×C₂²⋊Q₈	—	2	2	no	—
179	C₃₁×C₂²⋊Q₈	—	2	2	no	—
180	C₃₁×C₂²⋊Q₈	—	2	2	no	—
181	C₃₁×C₂²⋊Q₈	—	2	2	no	—
182	C₃₁×C₂²⋊Q₈	—	2	2	no	—
183	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
184	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
185	C₃₁×#121	—	2	2	no	—
186	C₃₁×#121	—	2	2	no	—
187	C₃₁×#121	—	2	2	no	—
188	C₃₁×#121	—	2	1	no	—
189	C₃₁×#121	—	2	1	no	—
190	C₃₁×#121	—	2	2	no	—
191	C₃₁×#121	—	2	2	no	—
192	C₃₁×#121	—	2	2	no	—
193	C₃₁×#121	D₄	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×#121	C₂³	1	2	yes	—
199	C₄×Q₈×C₃₁	—	2	1	no	—
200	C₄×Q₈×C₃₁	—	2	1	no	—
201	C₄×Q₈×C₃₁	—	2	1	no	—
202	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
203	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
204	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₃₁	—	2	1	no	—
209	C₄×D₄×C₃₁	—	2	1	no	—
210	C₄×D₄×C₃₁	—	2	1	no	—
211	C₄×D₄×C₃₁	—	2	2	no	—
212	C₄×D₄×C₃₁	—	2	2	no	—
213	C₄×D₄×C₃₁	—	2	2	no	—
214	C₄×D₄×C₃₁	—	2	2	no	—
215	C₄×D₄×C₃₁	—	2	2	no	—
216	C₄×D₄×C₃₁	—	2	1	no	—
217	C₄×D₄×C₃₁	—	2	1	no	—
218	C₄×D₄×C₃₁	C₂³	1	2	yes	—
219	C₄×D₄×C₃₁	C₂³	1	2	yes	—
220	C₄×D₄×C₃₁	C₂³	1	2	yes	—
221	C₄×D₄×C₃₁	C₂³	1	2	yes	—
222	C₄×D₄×C₃₁	C₂³	1	2	yes	—
223	C₄×D₄×C₃₁	C₂³	1	2	yes	—
224	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
225	C₃₁×#117	—	2	2	no	—
226	C₃₁×#117	C₂³	1	2	yes	—
227	C₃₁×#117	C₂³	1	2	yes	—
228	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
229	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
230	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
231	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
232	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
233	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
236	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
238	C₂×C₄²×C₃₁	—	2	1	no	—
239	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
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×#107	C₂³	1	2	yes	—
247	C₃₁×#107	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×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
263	C₃₁×#103	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×#102	C₂³	1	2	yes	—
271	C₃₁×#102	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₃₁×#97	C₂³	1	2	yes	—
278	C₃₁×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₃₁	C₂³	1	2	yes	—
280	#41×C₃₁	—	2	4	no	—
281	#41×C₃₁	—	4	2	no	—
282	#41×C₃₁	—	8	2	no	—
283	#41×C₃₁	—	8	2	no	—
284	#41×C₃₁	—	8	4	no	—
285	#41×C₃₁	—	8	4	no	—
286	C₂×Q₈×C₃₁	—	2	1	no	—
287	C₂×Q₈×C₃₁	—	2	2	no	—
288	C₂×Q₈×C₃₁	—	2	2	no	—
289	C₂×Q₈×C₃₁	—	2	1	no	—
290	C₂×Q₈×C₃₁	—	2	1	no	—
291	C₂×Q₈×C₃₁	—	2	2	no	—
292	C₂×Q₈×C₃₁	—	4	1	no	—
293	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
295	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂×D₄×C₃₁	—	2	2	no	—
297	C₂×D₄×C₃₁	—	2	2	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	—	2	1	no	—
304	C₂×D₄×C₃₁	—	2	1	no	—
305	C₂×D₄×C₃₁	—	2	1	no	—
306	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
307	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
308	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
309	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₃₁	—	2	1	no	—
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	2	no	—
315	C₂²×C₄×C₃₁	—	2	2	no	—
316	C₂²×C₄×C₃₁	—	2	2	no	—
317	C₂²×C₄×C₃₁	—	2	2	no	—
318	C₂²×C₄×C₃₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
326	SD₁₆×C₃₁	—	2	4	no	—
327	SD₁₆×C₃₁	—	4	2	no	—
328	D₈×C₃₁	—	4	2	no	—
329	D₈×C₃₁	—	4	2	no	—
330	M₁₆×C₃₁	—	4	2	no	—
331	C₂×C₈×C₃₁	—	4	1	no	—
332	C₂×C₈×C₃₁	—	4	2	no	—
333	C₂×C₈×C₃₁	—	4	1	no	—
334	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
335	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
337	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	1	no	—
343	C₄⋊C₄×C₃₁	—	2	1	no	—
344	C₄⋊C₄×C₃₁	—	2	1	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	2	no	—
347	C₄⋊C₄×C₃₁	—	2	2	no	—
348	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
354	C₄⋊C₄×C₃₁	—	2	1	no	—
355	C₄⋊C₄×C₃₁	—	2	1	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	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
365	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
370	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
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	2	no	—
376	C₂²⋊C₄×C₃₁	—	2	2	no	—
377	C₂²⋊C₄×C₃₁	—	2	2	no	—
378	C₂²⋊C₄×C₃₁	—	2	2	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	2	no	—
385	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
390	C₄²×C₃₁	—	2	1	no	—
391	C₄²×C₃₁	—	2	1	no	—
392	C₄²×C₃₁	—	2	1	no	—
393	C₄²×C₃₁	—	2	1	no	—
394	C₄²×C₃₁	—	2	2	no	—
395	C₄²×C₃₁	—	2	2	no	—
396	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
397	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₃₁	C₂⁴	1	2	yes	—
399	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
400	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
401	#62170	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂³×C₃₁	—	2	2	no	—
403	C₂³×C₃₁	—	2	2	no	—
404	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
405	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
406	Q₈×C₃₁	—	2	1	no	—
407	Q₈×C₃₁	—	2	1	no	—
408	Q₈×C₃₁	—	2	1	no	—
409	Q₈×C₃₁	—	4	1	no	—
410	Q₈×C₃₁	—	4	2	no	—
411	Q₈×C₃₁	—	8	1	no	—
412	Q₈×C₃₁	—	8	1	no	—
413	Q₈×C₃₁	—	8	2	no	—
414	Q₈×C₃₁	—	8	2	no	—
415	Q₈×C₃₁	2₋¹⁺⁴	1	2	yes	—
416	D₄×C₃₁	—	2	4	no	—
417	D₄×C₃₁	—	2	2	no	—
418	D₄×C₃₁	—	2	2	no	—
419	D₄×C₃₁	—	2	2	no	—
420	D₄×C₃₁	—	2	2	no	—
421	D₄×C₃₁	—	4	1	no	—
422	D₄×C₃₁	—	4	4	no	—
423	D₄×C₃₁	—	4	2	no	—
424	D₄×C₃₁	—	4	4	no	—
425	D₄×C₃₁	—	4	4	no	—
426	D₄×C₃₁	—	8	1	no	—
427	D₄×C₃₁	—	8	1	no	—
428	D₄×C₃₁	—	8	1	no	—
429	D₄×C₃₁	—	8	2	no	—
430	D₄×C₃₁	—	8	2	no	—
431	D₄×C₃₁	—	8	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	1	no	—
434	C₂×C₄×C₃₁	—	2	1	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	2	no	—
438	C₂×C₄×C₃₁	—	2	1	no	—
439	C₂×C₄×C₃₁	—	2	1	no	—
440	C₂×C₄×C₃₁	—	2	1	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	2	no	—
445	C₂×C₄×C₃₁	—	4	1	no	—
446	C₂×C₄×C₃₁	—	4	4	no	—
447	C₂×C₄×C₃₁	—	4	2	no	—
448	C₂×C₄×C₃₁	—	4	2	no	—
449	C₂×C₄×C₃₁	—	4	2	no	—
450	C₂×C₄×C₃₁	—	8	2	no	—
451	C₂×C₄×C₃₁	—	8	2	no	—
452	C₂×C₄×C₃₁	—	8	2	no	—
453	C₂×C₄×C₃₁	—	8	2	no	—
454	C₂×C₄×C₃₁	—	8	2	no	—
455	C₂×C₄×C₃₁	—	8	1	no	—
456	C₂×C₄×C₃₁	—	8	2	no	—
457	C₂×C₄×C₃₁	—	8	2	no	—
458	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
461	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
467	C₈×C₃₁	—	2	2	no	—
468	C₈×C₃₁	—	2	2	no	—
469	C₈×C₃₁	—	2	2	no	—
470	C₈×C₃₁	—	2	2	no	—
471	#3559	C₂×C₃₁	1	1	yes	characteristic, complemented
472	#3522	C₂×C₃₁	1	1	yes	characteristic, complemented
473	#3385	C₂×C₃₁	1	2	yes	complemented
474	#3370	C₂×C₃₁	1	2	yes	complemented
475	#3346	C₂×C₃₁	1	2	yes	complemented
476	#3345	C₂×C₃₁	1	2	yes	complemented
477	#3334	C₂×C₃₁	1	2	yes	complemented
478	#3309	C₂×C₃₁	1	2	yes	complemented
479	#3308	C₂×C₃₁	1	2	yes	complemented
480	#3301	C₂×C₃₁	1	2	yes	complemented
481	#3257	C₂×C₃₁	1	2	yes	complemented
482	#3245	C₂×C₃₁	1	1	yes	characteristic, complemented
483	#3243	C₂×C₃₁	1	2	yes	complemented
484	#3234	C₂×C₃₁	1	1	yes	characteristic, complemented
485	#3119	C₂×C₃₁	1	2	yes	complemented
486	#3112	C₂×C₃₁	1	1	yes	characteristic, complemented
487	#3083	C₂×C₃₁	1	2	yes	complemented
488	C₂×#479	C₂×C₃₁	1	1	yes	characteristic, complemented
489	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
490	C₂²×C₃₁	—	2	1	no	—
491	C₂²×C₃₁	—	2	1	no	—
492	C₂²×C₃₁	—	2	2	no	—
493	C₂²×C₃₁	—	2	2	no	—
494	C₂²×C₃₁	—	2	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	4	2	no	—
497	C₂²×C₃₁	—	4	2	no	—
498	C₂²×C₃₁	—	4	2	no	—
499	C₂²×C₃₁	—	4	2	no	—
500	C₂²×C₃₁	—	4	2	no	—
501	C₂²×C₃₁	#576	1	2	yes	—
502	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
503	C₄×C₃₁	—	2	1	no	—
504	C₄×C₃₁	—	2	1	no	—
505	C₄×C₃₁	—	2	2	no	—
506	C₄×C₃₁	—	2	2	no	—
507	C₄×C₃₁	—	2	1	no	—
508	C₄×C₃₁	—	2	2	no	—
509	C₄×C₃₁	—	2	1	no	—
510	C₄×C₃₁	—	2	1	no	—
511	C₄×C₃₁	—	2	2	no	—
512	C₄×C₃₁	—	4	2	no	—
513	C₄×C₃₁	—	4	1	no	—
514	C₄×C₃₁	—	4	1	no	—
515	C₄×C₃₁	—	4	2	no	—
516	C₄×C₃₁	—	4	1	no	—
517	C₄×C₃₁	—	4	2	no	—
518	C₄×C₃₁	—	4	2	no	—
519	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
520	C₄×C₃₁	#585	1	1	yes	characteristic
521	#563	—	2	1	no	—
522	#562	—	2	1	no	—
523	#559	—	2	1	no	—
524	#559	C₂²×C₃₁	1	1	yes	characteristic
525	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
526	#554	—	2	1	no	—
527	#554	C₂²×C₃₁	1	2	yes	—
528	#554	C₂²×C₃₁	1	1	yes	characteristic
529	#553	C₂²×C₃₁	1	2	yes	—
530	#553	C₂²×C₃₁	1	2	yes	—
531	#550	C₂²×C₃₁	1	1	yes	characteristic
532	#548	C₂²×C₃₁	1	2	yes	—
533	#547	—	2	2	no	—
534	#547	—	2	2	no	—
535	#547	C₂²×C₃₁	1	2	yes	—
536	#547	C₂²×C₃₁	1	2	yes	—
537	#544	C₂²×C₃₁	1	2	yes	—
538	#542	—	2	2	no	—
539	#542	C₂²×C₃₁	1	2	yes	—
540	#540	C₂²×C₃₁	1	2	yes	—
541	#539	—	2	2	no	—
542	#539	—	2	1	no	—
543	#537	—	2	1	no	—
544	#532	—	2	1	no	—
545	#532	C₂²×C₃₁	1	1	yes	characteristic
546	#532	C₂²×C₃₁	1	1	yes	characteristic
547	#529	—	2	1	no	—
548	#529	C₂²×C₃₁	1	1	yes	characteristic
549	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
550	#520	C₂²×C₃₁	1	2	yes	—
551	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
552	#501	C₂²×C₃₁	1	2	yes	—
553	#501	C₂²×C₃₁	1	2	yes	—
554	#500	C₂²×C₃₁	1	2	yes	—
555	#490	C₂²×C₃₁	1	2	yes	—
556	#489	C₂²×C₃₁	1	2	yes	—
557	#488	C₂²×C₃₁	1	2	yes	—
558	#485	C₂²×C₃₁	1	2	yes	—
559	#484	C₂²×C₃₁	1	2	yes	—
560	#482	C₂²×C₃₁	1	2	yes	—
561	#481	C₂²×C₃₁	1	2	yes	—
562	#481	C₂²×C₃₁	1	2	yes	—
563	#480	C₂²×C₃₁	1	2	yes	—
564	#480	C₂²×C₃₁	1	2	yes	—
565	#480	C₂²×C₃₁	1	2	yes	—
566	#480	C₂²×C₃₁	1	2	yes	—
567	#479	C₂²×C₃₁	1	2	yes	—
568	#479	C₂²×C₃₁	1	2	yes	—
569	#479	C₂²×C₃₁	1	2	yes	—
570	#479	C₂²×C₃₁	1	2	yes	—
571	#479	C₂²×C₃₁	1	2	yes	—
572	#478	C₂²×C₃₁	1	2	yes	—
573	#478	C₂²×C₃₁	1	2	yes	—
574	#478	C₂²×C₃₁	1	2	yes	—
575	#477	C₂²×C₃₁	1	1	yes	characteristic
576	#477	C₂²×C₃₁	1	2	yes	—
577	#477	C₂²×C₃₁	1	1	yes	characteristic
578	#476	C₂²×C₃₁	1	2	yes	—
579	#474	C₂²×C₃₁	1	2	yes	—
580	#474	C₂²×C₃₁	1	2	yes	—
581	#474	C₂²×C₃₁	1	2	yes	—
582	#474	C₂²×C₃₁	1	2	yes	—
583	#469	C₂²×C₃₁	1	2	yes	—
584	#468	C₂²×C₃₁	1	2	yes	—
585	#466	C₂²×C₃₁	1	2	yes	—
586	#466	C₂²×C₃₁	1	2	yes	—
587	#466	C₂²×C₃₁	1	2	yes	—
588	#465	C₂²×C₃₁	1	2	yes	—
589	#463	C₂²×C₃₁	1	2	yes	—
590	#463	C₂²×C₃₁	1	2	yes	—
591	#460	C₂²×C₃₁	1	1	yes	characteristic
592	#460	C₂²×C₃₁	1	1	yes	characteristic
593	#459	C₂²×C₃₁	1	2	yes	—
594	#459	C₂²×C₃₁	1	2	yes	—
595	#449	C₂²×C₃₁	1	2	yes	—
596	#449	C₂²×C₃₁	1	2	yes	—
597	#448	C₂²×C₃₁	1	2	yes	—
598	#446	C₂²×C₃₁	1	2	yes	—
599	#442	C₂²×C₃₁	1	2	yes	—
600	#440	C₂²×C₃₁	1	2	yes	—
601	#440	C₂²×C₃₁	1	2	yes	—
602	#440	C₂²×C₃₁	1	2	yes	—
603	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
604	C₄×D₈	C₂²×C₃₁	1	2	yes	—
605	#435	C₂²×C₃₁	1	2	yes	—
606	#435	C₂²×C₃₁	1	2	yes	—
607	C₈×D₄	C₂²×C₃₁	1	2	yes	—
608	#433	C₂²×C₃₁	1	2	yes	—
609	#432	C₂²×C₃₁	1	1	yes	characteristic
610	#428	C₂²×C₃₁	1	2	yes	—
611	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
612	C₂×#107	C₂²×C₃₁	1	2	yes	—
613	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
614	#424	C₂²×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
616	#417	C₂²×C₃₁	1	2	yes	—
617	#416	C₂²×C₃₁	1	2	yes	—
618	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
619	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
620	C₂×C₃₁	—	2	2	no	—
621	C₂×C₃₁	—	4	2	no	—
622	C₂×C₃₁	—	8	2	no	—
623	C₂×C₃₁	—	8	2	no	—
624	C₂×C₃₁	#3489	1	1	yes	characteristic
625	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
626	C₂×C₃₁	#3586	1	1	yes	characteristic
627	C₂×#41	—	2	2	no	—
628	C₂×#41	—	2	2	no	—
629	C₂×#41	—	2	1	no	—
630	C₂×#41	—	2	1	no	—
631	C₂×#41	C₂³×C₃₁	1	2	yes	—
632	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
633	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
635	C₂×D₈	C₂³×C₃₁	1	2	yes	—
636	C₂×D₈	C₂³×C₃₁	1	2	yes	—
637	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
638	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
639	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
640	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	—	2	2	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
646	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
648	#127	—	2	1	no	—
649	#127	C₂³×C₃₁	1	1	yes	characteristic
650	#127	C₂³×C₃₁	1	1	yes	characteristic
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	D₄×C₃₁	1	2	yes	—
655	#125	—	2	1	no	—
656	#125	—	2	2	no	—
657	#125	—	2	1	no	—
658	#125	—	2	1	no	—
659	#125	D₄×C₃₁	1	1	yes	characteristic
660	#125	C₂³×C₃₁	1	2	yes	—
661	#125	C₂³×C₃₁	1	2	yes	—
662	#125	C₂³×C₃₁	1	2	yes	—
663	#124	—	2	1	no	—
664	#124	—	2	2	no	—
665	#124	—	2	2	no	—
666	#124	—	2	1	no	—
667	#124	—	2	1	no	—
668	#124	D₄×C₃₁	1	1	yes	characteristic
669	#124	C₂³×C₃₁	1	2	yes	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	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	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	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	C₂³×C₃₁	1	2	yes	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	1	no	—
697	#121	—	2	1	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	D₄×C₃₁	1	1	yes	characteristic
702	#121	C₂³×C₃₁	1	2	yes	—
703	#121	C₂³×C₃₁	1	2	yes	—
704	#121	C₂³×C₃₁	1	2	yes	—
705	#121	C₂³×C₃₁	1	2	yes	—
706	#121	C₂³×C₃₁	1	2	yes	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
711	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
712	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
713	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
714	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
715	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	C₂³×C₃₁	1	2	yes	—
727	C₄×D₄	C₂³×C₃₁	1	2	yes	—
728	C₄×D₄	C₂³×C₃₁	1	2	yes	—
729	C₄×D₄	C₂³×C₃₁	1	2	yes	—
730	C₄×D₄	C₂³×C₃₁	1	2	yes	—
731	C₄×D₄	C₂³×C₃₁	1	2	yes	—
732	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
733	#117	—	2	2	no	—
734	#117	C₂³×C₃₁	1	2	yes	—
735	#117	C₂³×C₃₁	1	2	yes	—
736	C₂×C₄⋊C₄	—	2	1	no	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	—	2	1	no	—
739	C₂×C₄⋊C₄	—	2	2	no	—
740	C₂×C₄⋊C₄	—	2	2	no	—
741	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
743	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
744	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
745	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
746	C₂×C₄²	—	2	1	no	—
747	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
748	#107	C₂³×C₃₁	1	2	yes	—
749	#107	C₂³×C₃₁	1	2	yes	—
750	#107	C₂³×C₃₁	1	2	yes	—
751	#107	C₂³×C₃₁	1	2	yes	—
752	#107	C₂³×C₃₁	1	2	yes	—
753	#107	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	#106	C₂³×C₃₁	1	2	yes	—
759	#106	C₂³×C₃₁	1	2	yes	—
760	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
761	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
762	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
763	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
764	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
765	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
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	#102	C₂³×C₃₁	1	2	yes	—
777	#102	C₂³×C₃₁	1	2	yes	—
778	#102	C₂³×C₃₁	1	2	yes	—
779	#102	C₂³×C₃₁	1	2	yes	—
780	#102	C₂³×C₃₁	1	2	yes	—
781	#102	C₂³×C₃₁	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
785	#97	C₂³×C₃₁	1	2	yes	—
786	#97	C₂³×C₃₁	1	2	yes	—
787	C₄×C₈	C₂³×C₃₁	1	2	yes	—
788	C₃₁	#62170	1	1	yes	characteristic, direct product factor, Sylow
789	#41	—	2	4	no	—
790	#41	—	4	2	no	—
791	#41	—	8	2	no	—
792	#41	—	8	2	no	—
793	#41	—	8	4	no	—
794	#41	—	8	4	no	—
795	C₂×Q₈	—	2	1	no	—
796	C₂×Q₈	—	2	2	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	1	no	—
799	C₂×Q₈	—	2	1	no	—
800	C₂×Q₈	—	2	2	no	—
801	C₂×Q₈	—	4	1	no	—
802	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
803	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	2	2	no	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	1	no	—
812	C₂×D₄	—	2	1	no	—
813	C₂×D₄	—	2	1	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
816	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
817	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
818	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
819	C₂²×C₄	—	2	1	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	2	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
835	SD₁₆	—	2	4	no	—
836	SD₁₆	—	4	2	no	—
837	D₈	—	4	2	no	—
838	D₈	—	4	2	no	—
839	M₁₆	—	4	2	no	—
840	C₂×C₈	—	4	1	no	—
841	C₂×C₈	—	4	2	no	—
842	C₂×C₈	—	4	1	no	—
843	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
844	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
845	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
846	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
847	C₄⋊C₄	—	2	1	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	1	no	—
860	C₄⋊C₄	—	2	1	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
869	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
870	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
871	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
872	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
874	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
875	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
876	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
877	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
878	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
879	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
895	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
896	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
898	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
899	C₄²	—	2	1	no	—
900	C₄²	—	2	1	no	—
901	C₄²	—	2	1	no	—
902	C₄²	—	2	1	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
906	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
907	C₄²	C₂⁴×C₃₁	1	2	yes	—
908	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
909	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
913	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
914	Q₈	—	2	1	no	—
915	Q₈	—	2	1	no	—
916	Q₈	—	2	1	no	—
917	Q₈	—	4	1	no	—
918	Q₈	—	4	2	no	—
919	Q₈	—	8	1	no	—
920	Q₈	—	8	1	no	—
921	Q₈	—	8	2	no	—
922	Q₈	—	8	2	no	—
923	Q₈	C₃₁×2₋¹⁺⁴	1	2	yes	—
924	D₄	—	2	4	no	—
925	D₄	—	2	2	no	—
926	D₄	—	2	2	no	—
927	D₄	—	2	2	no	—
928	D₄	—	2	2	no	—
929	D₄	—	4	1	no	—
930	D₄	—	4	4	no	—
931	D₄	—	4	2	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	8	1	no	—
935	D₄	—	8	1	no	—
936	D₄	—	8	1	no	—
937	D₄	—	8	2	no	—
938	D₄	—	8	2	no	—
939	D₄	—	8	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	4	1	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	2	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	4	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	8	2	no	—
961	C₂×C₄	—	8	2	no	—
962	C₂×C₄	—	8	2	no	—
963	C₂×C₄	—	8	1	no	—
964	C₂×C₄	—	8	2	no	—
965	C₂×C₄	—	8	2	no	—
966	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
969	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
970	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
971	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
972	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
973	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
974	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
975	C₈	—	2	2	no	—
976	C₈	—	2	2	no	—
977	C₈	—	2	2	no	—
978	C₈	—	2	2	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	2	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	2	no	—
990	C₂²	C₃₁×#576	1	2	yes	—
991	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
992	C₄	—	2	2	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	2	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	2	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	2	no	—
1001	C₄	—	4	1	no	—
1002	C₄	—	4	1	no	—
1003	C₄	—	4	2	no	—
1004	C₄	—	4	1	no	—
1005	C₄	—	4	2	no	—
1006	C₄	—	4	2	no	—
1007	C₄	—	4	2	no	—
1008	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1009	C₄	C₃₁×#585	1	1	yes	characteristic
1010	C₂	—	2	2	no	—
1011	C₂	—	4	2	no	—
1012	C₂	—	8	2	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₃₁×#3489	1	1	yes	characteristic
1015	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1016	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3559	C₂	semidirect
2. C₃₁×#3522	C₂	semidirect
3. C₃₁×#3385	C₂	semidirect
4. C₃₁×#3370	C₂	semidirect
5. C₃₁×#3346	C₂	semidirect
6. C₃₁×#3345	C₂	semidirect
7. C₃₁×#3334	C₂	semidirect
8. C₃₁×#3309	C₂	semidirect
9. C₃₁×#3308	C₂	semidirect
10. C₃₁×#3301	C₂	semidirect
11. C₃₁×#3257	C₂	semidirect
12. C₃₁×#3245	C₂	semidirect
13. C₃₁×#3243	C₂	semidirect
14. C₃₁×#3234	C₂	semidirect
15. C₃₁×#3119	C₂	semidirect
16. C₃₁×#3112	C₂	semidirect
17. C₃₁×#3083	C₂	semidirect
18. C₂×C₃₁×#479	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
401. #62170	C₃₁	direct (N × H)
471. #3559	C₂×C₃₁	semidirect
472. #3522	C₂×C₃₁	semidirect
473. #3385	C₂×C₃₁	semidirect
474. #3370	C₂×C₃₁	semidirect
475. #3346	C₂×C₃₁	semidirect
476. #3345	C₂×C₃₁	semidirect
477. #3334	C₂×C₃₁	semidirect
478. #3309	C₂×C₃₁	semidirect
479. #3308	C₂×C₃₁	semidirect
480. #3301	C₂×C₃₁	semidirect
481. #3257	C₂×C₃₁	semidirect
482. #3245	C₂×C₃₁	semidirect
483. #3243	C₂×C₃₁	semidirect
484. #3234	C₂×C₃₁	semidirect
485. #3119	C₂×C₃₁	semidirect
486. #3112	C₂×C₃₁	semidirect
487. #3083	C₂×C₃₁	semidirect
488. C₂×#479	C₂×C₃₁	semidirect
489. #2992	C₂×C₃₁	semidirect
788. C₃₁	#62170	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×#3559	2
C₃₁×#3522	2
C₃₁×#3385	2
C₃₁×#3370	2
C₃₁×#3346	2
C₃₁×#3345	2
C₃₁×#3334	2
C₃₁×#3309	2
C₃₁×#3308	2
C₃₁×#3301	2
C₃₁×#3257	2
C₃₁×#3245	2
C₃₁×#3243	2
C₃₁×#3234	2
C₃₁×#3119	2
C₃₁×#3112	2
C₃₁×#3083	2
C₂×C₃₁×#479	2
C₃₁×#2992	2
#62170	31

Subgroups — C31×#62170 #21518929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62170 #21518929