Subgroups — C₃₁×#62199 #21518958

Order 7936.

1808 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3384	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3354	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#3346	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3340	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3324	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3318	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3295	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3257	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3241	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3227	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3118	C₂	1	2	yes	maximal, complemented
20	C₃₁×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₃₁×#3081	C₂	1	2	yes	maximal, complemented
22	C₂×C₃₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₃₁×#563	—	2	2	no	—
25	C₃₁×#557	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
27	C₃₁×#555	C₂²	1	1	yes	characteristic
28	C₃₁×#554	C₂²	1	1	yes	characteristic
29	C₃₁×#554	C₂²	1	2	yes	complemented
30	C₃₁×#553	—	2	1	no	—
31	C₃₁×#553	C₂²	1	2	yes	—
32	C₃₁×#553	C₂²	1	2	yes	complemented
33	C₃₁×#550	C₂²	1	1	yes	characteristic
34	D₄×Q₈×C₃₁	—	2	1	no	—
35	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#548	—	2	1	no	—
37	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#546	—	2	1	no	—
39	C₃₁×#546	—	2	2	no	—
40	D₄²×C₃₁	C₂²	1	1	yes	characteristic
41	D₄²×C₃₁	C₂²	1	2	yes	—
42	C₃₁×#544	C₂²	1	2	yes	complemented
43	C₃₁×#542	C₂²	1	2	yes	complemented
44	C₃₁×#541	—	2	1	no	—
45	C₃₁×#540	C₂²	1	2	yes	—
46	C₃₁×#539	—	2	2	no	—
47	C₃₁×#538	—	2	2	no	—
48	C₃₁×#536	—	2	1	no	—
49	C₃₁×#532	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
51	C₃₁×#529	C₂²	1	1	yes	characteristic
52	C₃₁×#529	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#525	—	2	1	no	—
54	C₂×C₃₁×#121	—	2	1	no	—
55	C₃₁×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#501	C₂²	1	2	yes	complemented
58	C₃₁×#499	C₂²	1	2	yes	complemented
59	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
60	C₃₁×#498	C₂²	1	1	yes	characteristic, complemented
61	C₃₁×#490	C₂²	1	2	yes	complemented
62	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
63	C₃₁×#486	C₂²	1	2	yes	complemented
64	C₃₁×#486	C₂²	1	1	yes	characteristic, complemented
65	C₃₁×#485	C₂²	1	2	yes	complemented
66	C₃₁×#484	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#482	C₂²	1	2	yes	complemented
68	C₃₁×#482	C₂²	1	2	yes	complemented
69	C₃₁×#482	C₂²	1	2	yes	complemented
70	C₃₁×#481	C₂²	1	1	yes	characteristic, complemented
71	C₃₁×#481	C₂²	1	2	yes	complemented
72	C₃₁×#481	C₂²	1	2	yes	complemented
73	C₃₁×#481	C₂²	1	2	yes	complemented
74	C₃₁×#480	C₂²	1	2	yes	complemented
75	C₃₁×#479	C₂²	1	2	yes	complemented
76	C₃₁×#478	C₂²	1	1	yes	characteristic
77	C₃₁×#478	C₂²	1	2	yes	—
78	C₃₁×#478	C₂²	1	2	yes	complemented
79	C₃₁×#478	C₂²	1	2	yes	complemented
80	C₃₁×#478	C₂²	1	2	yes	complemented
81	C₃₁×#478	C₂²	1	1	yes	characteristic, complemented
82	C₃₁×#477	C₂²	1	1	yes	characteristic, complemented
83	C₃₁×#476	C₂²	1	2	yes	—
84	C₃₁×#476	C₂²	1	2	yes	complemented
85	C₃₁×#476	C₂²	1	1	yes	characteristic, complemented
86	C₃₁×#476	C₂²	1	2	yes	complemented
87	C₃₁×#474	C₂²	1	2	yes	—
88	C₃₁×#474	C₂²	1	1	yes	characteristic
89	C₃₁×#474	C₂²	1	1	yes	characteristic
90	C₃₁×#474	C₂²	1	2	yes	complemented
91	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
92	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
93	C₃₁×#474	C₂²	1	2	yes	complemented
94	C₃₁×#469	C₂²	1	2	yes	complemented
95	C₃₁×#468	C₂²	1	2	yes	complemented
96	C₃₁×#466	C₂²	1	2	yes	complemented
97	C₃₁×#466	C₂²	1	2	yes	complemented
98	C₃₁×#465	C₂²	1	2	yes	complemented
99	C₃₁×#465	C₂²	1	2	yes	complemented
100	C₃₁×#463	C₂²	1	1	yes	characteristic
101	C₃₁×#463	C₂²	1	1	yes	characteristic, complemented
102	C₃₁×#463	C₂²	1	2	yes	complemented
103	C₃₁×#460	C₂²	1	1	yes	characteristic, complemented
104	C₃₁×#460	C₂²	1	2	yes	complemented
105	C₃₁×#459	C₂²	1	1	yes	characteristic, complemented
106	C₃₁×#459	C₂²	1	2	yes	complemented
107	C₃₁×#450	C₂²	1	1	yes	characteristic
108	C₃₁×#450	C₂²	1	2	yes	—
109	C₃₁×#447	C₂²	1	1	yes	characteristic
110	C₃₁×#447	C₂²	1	2	yes	—
111	C₃₁×#446	C₂²	1	1	yes	characteristic, complemented
112	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
113	C₃₁×#442	C₂²	1	2	yes	—
114	C₃₁×#440	C₂²	1	2	yes	complemented
115	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
120	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
121	C₃₁×#436	C₂²	1	1	yes	characteristic, complemented
122	C₃₁×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₃₁	C₂²	1	2	yes	complemented
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
125	C₃₁×#433	C₂²	1	2	yes	complemented
126	C₃₁×#431	C₂²	1	1	yes	characteristic, complemented
127	C₃₁×#428	C₂²	1	2	yes	complemented
128	C₃₁×#427	C₂²	1	2	yes	complemented
129	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
130	C₃₁×#424	C₂²	1	2	yes	complemented
131	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₃₁×#418	C₂²	1	2	yes	—
133	C₂×C₃₁×#102	C₂²	1	2	yes	—
134	C₂×C₃₁×#102	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	—	2	1	no	—
137	C₂×#41×C₃₁	—	2	1	no	—
138	C₂²×Q₈×C₃₁	—	2	1	no	—
139	C₂²×Q₈×C₃₁	—	2	1	no	—
140	C₂²×D₄×C₃₁	—	2	1	no	—
141	C₂²×D₄×C₃₁	—	2	2	no	—
142	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
144	C₂³×C₄×C₃₁	—	2	1	no	—
145	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
146	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×D₈×C₃₁	C₂³	1	2	yes	—
150	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
152	C₂²×C₈×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	1	no	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₃₁×#127	C₂³	1	1	yes	characteristic
164	C₃₁×#127	C₂³	1	2	yes	—
165	C₃₁×#126	—	2	2	no	—
166	C₃₁×#126	—	2	2	no	—
167	C₃₁×#126	—	2	2	no	—
168	C₃₁×#126	—	2	2	no	—
169	C₃₁×#126	—	2	1	no	—
170	C₃₁×#126	D₄	1	2	yes	—
171	C₃₁×#125	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	D₄	1	1	yes	characteristic
175	C₃₁×#125	C₂³	1	1	yes	characteristic
176	C₃₁×#125	C₂³	1	2	yes	—
177	C₃₁×#125	C₂³	1	2	yes	—
178	C₃₁×#124	—	2	1	no	—
179	C₃₁×#124	—	2	2	no	—
180	C₃₁×#124	—	2	2	no	—
181	C₃₁×#124	—	2	1	no	—
182	C₃₁×#124	D₄	1	1	yes	characteristic
183	C₃₁×#124	C₂³	1	1	yes	characteristic
184	C₃₁×#123	—	2	1	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×#123	—	2	2	no	—
188	C₃₁×#123	—	2	2	no	—
189	C₃₁×#123	—	2	2	no	—
190	C₃₁×#123	—	2	2	no	—
191	C₃₁×#123	D₄	1	2	yes	—
192	C₃₁×C₂²⋊Q₈	—	2	1	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	1	no	—
196	C₃₁×C₂²⋊Q₈	—	2	1	no	—
197	C₃₁×C₂²⋊Q₈	—	2	2	no	—
198	C₃₁×C₂²⋊Q₈	—	2	2	no	—
199	C₃₁×C₂²⋊Q₈	—	2	2	no	—
200	C₃₁×C₂²⋊Q₈	—	2	2	no	—
201	C₃₁×C₂²⋊Q₈	—	2	2	no	—
202	C₃₁×C₂²⋊Q₈	D₄	1	1	yes	characteristic
203	C₃₁×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×#121	—	2	2	no	—
206	C₃₁×#121	—	2	1	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	1	no	—
209	C₃₁×#121	—	2	1	no	—
210	C₃₁×#121	—	2	1	no	—
211	C₃₁×#121	—	2	2	no	—
212	C₃₁×#121	—	2	2	no	—
213	C₃₁×#121	—	2	2	no	—
214	C₃₁×#121	—	2	2	no	—
215	C₃₁×#121	D₄	1	1	yes	characteristic
216	C₃₁×#121	C₂³	1	1	yes	characteristic
217	C₃₁×#121	C₂³	1	2	yes	—
218	C₃₁×#121	C₂³	1	2	yes	—
219	C₃₁×#121	C₂³	1	2	yes	—
220	C₃₁×#121	C₂³	1	2	yes	—
221	C₃₁×#120	—	2	2	no	—
222	C₃₁×#120	—	2	2	no	—
223	C₃₁×#120	—	2	2	no	—
224	C₄×Q₈×C₃₁	—	2	1	no	—
225	C₄×Q₈×C₃₁	—	2	1	no	—
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₃₁	—	2	2	no	—
230	C₄×D₄×C₃₁	—	2	1	no	—
231	C₄×D₄×C₃₁	—	2	2	no	—
232	C₄×D₄×C₃₁	—	2	2	no	—
233	C₄×D₄×C₃₁	—	2	2	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	1	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₃₁	C₂³	1	2	yes	—
242	C₄×D₄×C₃₁	C₂³	1	2	yes	—
243	C₄×D₄×C₃₁	C₂³	1	2	yes	—
244	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₃₁	C₂³	1	2	yes	—
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	C₂³	1	2	yes	—
252	C₃₁×#117	C₂³	1	2	yes	—
253	C₃₁×#117	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
255	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
256	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
260	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₃₁×#107	C₂³	1	2	yes	—
264	C₃₁×#107	C₂³	1	2	yes	—
265	C₃₁×#107	C₂³	1	2	yes	—
266	C₃₁×#107	C₂³	1	2	yes	—
267	C₃₁×#107	C₂³	1	2	yes	—
268	C₃₁×#107	C₂³	1	1	yes	characteristic
269	C₃₁×#107	C₂³	1	1	yes	characteristic
270	C₃₁×#106	C₂³	1	1	yes	characteristic
271	C₃₁×#106	C₂³	1	2	yes	—
272	C₃₁×#106	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	2	yes	—
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	1	yes	characteristic
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
278	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
279	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₃₁×#103	C₂³	1	2	yes	—
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	1	yes	characteristic
287	C₃₁×#102	C₂³	1	1	yes	characteristic
288	C₃₁×#102	C₂³	1	2	yes	—
289	C₃₁×#102	C₂³	1	2	yes	—
290	C₃₁×#102	C₂³	1	2	yes	—
291	C₃₁×#102	C₂³	1	2	yes	—
292	C₃₁×#102	C₂³	1	2	yes	—
293	C₃₁×#102	C₂³	1	2	yes	—
294	C₃₁×#102	C₂³	1	1	yes	characteristic
295	C₃₁×#102	C₂³	1	2	yes	—
296	C₃₁×#102	C₂³	1	2	yes	—
297	C₃₁×#102	C₂³	1	1	yes	characteristic
298	C₃₁×#102	C₂³	1	1	yes	characteristic
299	C₃₁×#102	C₂³	1	2	yes	—
300	C₃₁×#102	C₂³	1	1	yes	characteristic
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	2	yes	—
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₃₁×C₂²⋊C₈	C₂³	1	1	yes	characteristic
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₃₁	C₂³	1	2	yes	—
312	C₂⁴×C₃₁	—	2	1	no	—
313	C₂⁴×C₃₁	—	2	2	no	—
314	#41×C₃₁	—	8	2	no	—
315	#41×C₃₁	—	8	2	no	—
316	#41×C₃₁	—	8	2	no	—
317	C₂×Q₈×C₃₁	—	2	1	no	—
318	C₂×Q₈×C₃₁	—	2	1	no	—
319	C₂×Q₈×C₃₁	—	2	2	no	—
320	C₂×Q₈×C₃₁	—	2	1	no	—
321	C₂×Q₈×C₃₁	—	2	2	no	—
322	C₂×Q₈×C₃₁	—	8	2	no	—
323	C₂×Q₈×C₃₁	—	8	2	no	—
324	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₃₁	—	2	2	no	—
327	C₂×D₄×C₃₁	—	2	4	no	—
328	C₂×D₄×C₃₁	—	2	1	no	—
329	C₂×D₄×C₃₁	—	2	2	no	—
330	C₂×D₄×C₃₁	—	2	2	no	—
331	C₂×D₄×C₃₁	—	2	2	no	—
332	C₂×D₄×C₃₁	—	2	2	no	—
333	C₂×D₄×C₃₁	—	2	2	no	—
334	C₂×D₄×C₃₁	—	2	1	no	—
335	C₂×D₄×C₃₁	—	2	1	no	—
336	C₂×D₄×C₃₁	—	2	2	no	—
337	C₂×D₄×C₃₁	—	2	1	no	—
338	C₂×D₄×C₃₁	—	2	2	no	—
339	C₂×D₄×C₃₁	—	4	1	no	—
340	C₂×D₄×C₃₁	—	4	2	no	—
341	C₂×D₄×C₃₁	—	8	2	no	—
342	C₂×D₄×C₃₁	—	8	4	no	—
343	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
347	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	—	2	2	no	—
351	C₂²×C₄×C₃₁	—	2	2	no	—
352	C₂²×C₄×C₃₁	—	2	1	no	—
353	C₂²×C₄×C₃₁	—	2	1	no	—
354	C₂²×C₄×C₃₁	—	2	1	no	—
355	C₂²×C₄×C₃₁	—	2	1	no	—
356	C₂²×C₄×C₃₁	—	2	2	no	—
357	C₂²×C₄×C₃₁	—	2	2	no	—
358	C₂²×C₄×C₃₁	—	2	2	no	—
359	C₂²×C₄×C₃₁	—	2	1	no	—
360	C₂²×C₄×C₃₁	—	2	2	no	—
361	C₂²×C₄×C₃₁	—	8	2	no	—
362	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
366	SD₁₆×C₃₁	—	2	2	no	—
367	SD₁₆×C₃₁	—	4	1	no	—
368	SD₁₆×C₃₁	—	4	2	no	—
369	D₈×C₃₁	—	2	2	no	—
370	D₈×C₃₁	—	4	2	no	—
371	D₈×C₃₁	—	4	1	no	—
372	M₁₆×C₃₁	—	4	2	no	—
373	C₂×C₈×C₃₁	—	4	2	no	—
374	C₂×C₈×C₃₁	—	4	2	no	—
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
380	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
381	C₄⋊C₄×C₃₁	—	2	1	no	—
382	C₄⋊C₄×C₃₁	—	2	2	no	—
383	C₄⋊C₄×C₃₁	—	2	1	no	—
384	C₄⋊C₄×C₃₁	—	2	2	no	—
385	C₄⋊C₄×C₃₁	—	2	1	no	—
386	C₄⋊C₄×C₃₁	—	2	1	no	—
387	C₄⋊C₄×C₃₁	—	2	2	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	1	no	—
390	C₄⋊C₄×C₃₁	—	2	1	no	—
391	C₄⋊C₄×C₃₁	—	2	2	no	—
392	C₄⋊C₄×C₃₁	—	2	2	no	—
393	C₄⋊C₄×C₃₁	—	2	1	no	—
394	C₄⋊C₄×C₃₁	—	2	2	no	—
395	C₄⋊C₄×C₃₁	—	2	2	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	2	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
403	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
405	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
407	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
408	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₂²⋊C₄×C₃₁	—	2	2	no	—
413	C₂²⋊C₄×C₃₁	—	2	2	no	—
414	C₂²⋊C₄×C₃₁	—	2	1	no	—
415	C₂²⋊C₄×C₃₁	—	2	2	no	—
416	C₂²⋊C₄×C₃₁	—	2	1	no	—
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	1	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	1	no	—
421	C₂²⋊C₄×C₃₁	—	2	2	no	—
422	C₂²⋊C₄×C₃₁	—	2	1	no	—
423	C₂²⋊C₄×C₃₁	—	2	2	no	—
424	C₂²⋊C₄×C₃₁	—	2	1	no	—
425	C₂²⋊C₄×C₃₁	—	2	1	no	—
426	C₂²⋊C₄×C₃₁	—	2	2	no	—
427	C₂²⋊C₄×C₃₁	—	2	2	no	—
428	C₂²⋊C₄×C₃₁	—	2	2	no	—
429	C₂²⋊C₄×C₃₁	—	2	1	no	—
430	C₂²⋊C₄×C₃₁	—	2	2	no	—
431	C₂²⋊C₄×C₃₁	—	2	1	no	—
432	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
433	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
437	C₄²×C₃₁	—	2	2	no	—
438	C₄²×C₃₁	—	2	1	no	—
439	C₄²×C₃₁	—	2	2	no	—
440	C₄²×C₃₁	—	2	2	no	—
441	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
444	C₄²×C₃₁	C₂⁴	1	2	yes	—
445	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
446	#62199	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
447	C₂³×C₃₁	—	2	1	no	—
448	C₂³×C₃₁	—	2	1	no	—
449	C₂³×C₃₁	—	2	1	no	—
450	C₂³×C₃₁	—	2	2	no	—
451	C₂³×C₃₁	—	4	2	no	—
452	C₂³×C₃₁	—	4	4	no	—
453	C₂³×C₃₁	—	4	2	no	—
454	C₂³×C₃₁	—	8	1	no	—
455	C₂³×C₃₁	—	8	2	no	—
456	C₂³×C₃₁	—	8	2	no	—
457	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
458	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	1	no	—
461	Q₈×C₃₁	—	2	1	no	—
462	Q₈×C₃₁	—	4	2	no	—
463	Q₈×C₃₁	—	4	2	no	—
464	Q₈×C₃₁	—	8	2	no	—
465	Q₈×C₃₁	—	8	2	no	—
466	Q₈×C₃₁	—	8	1	no	—
467	D₄×C₃₁	—	2	4	no	—
468	D₄×C₃₁	—	2	2	no	—
469	D₄×C₃₁	—	2	1	no	—
470	D₄×C₃₁	—	2	1	no	—
471	D₄×C₃₁	—	2	2	no	—
472	D₄×C₃₁	—	2	1	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	2	2	no	—
476	D₄×C₃₁	—	4	2	no	—
477	D₄×C₃₁	—	4	4	no	—
478	D₄×C₃₁	—	4	2	no	—
479	D₄×C₃₁	—	4	4	no	—
480	D₄×C₃₁	—	4	2	no	—
481	D₄×C₃₁	—	8	2	no	—
482	D₄×C₃₁	—	8	2	no	—
483	D₄×C₃₁	—	8	1	no	—
484	D₄×C₃₁	—	8	2	no	—
485	D₄×C₃₁	—	8	2	no	—
486	D₄×C₃₁	—	8	2	no	—
487	D₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄×C₃₁	—	2	2	no	—
489	C₂×C₄×C₃₁	—	2	2	no	—
490	C₂×C₄×C₃₁	—	2	1	no	—
491	C₂×C₄×C₃₁	—	2	2	no	—
492	C₂×C₄×C₃₁	—	2	1	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	2	1	no	—
496	C₂×C₄×C₃₁	—	2	1	no	—
497	C₂×C₄×C₃₁	—	2	2	no	—
498	C₂×C₄×C₃₁	—	2	2	no	—
499	C₂×C₄×C₃₁	—	2	2	no	—
500	C₂×C₄×C₃₁	—	2	1	no	—
501	C₂×C₄×C₃₁	—	2	1	no	—
502	C₂×C₄×C₃₁	—	4	2	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	4	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	—	8	1	no	—
507	C₂×C₄×C₃₁	—	8	2	no	—
508	C₂×C₄×C₃₁	—	8	2	no	—
509	C₂×C₄×C₃₁	—	8	2	no	—
510	C₂×C₄×C₃₁	—	8	2	no	—
511	C₂×C₄×C₃₁	—	8	1	no	—
512	C₂×C₄×C₃₁	—	8	2	no	—
513	C₂×C₄×C₃₁	—	8	2	no	—
514	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
523	C₈×C₃₁	—	2	1	no	—
524	C₈×C₃₁	—	2	1	no	—
525	C₈×C₃₁	—	2	2	no	—
526	C₈×C₃₁	—	2	1	no	—
527	C₈×C₃₁	—	2	2	no	—
528	C₈×C₃₁	—	2	1	no	—
529	#3552	C₂×C₃₁	1	1	yes	characteristic, complemented
530	#3519	C₂×C₃₁	1	1	yes	characteristic, complemented
531	#3384	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3381	C₂×C₃₁	1	1	yes	characteristic, complemented
533	#3368	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3358	C₂×C₃₁	1	1	yes	characteristic, complemented
535	#3354	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3346	C₂×C₃₁	1	2	yes	complemented
537	#3340	C₂×C₃₁	1	1	yes	characteristic, complemented
538	#3339	C₂×C₃₁	1	2	yes	complemented
539	#3324	C₂×C₃₁	1	1	yes	characteristic, complemented
540	#3318	C₂×C₃₁	1	2	yes	complemented
541	#3295	C₂×C₃₁	1	2	yes	complemented
542	#3294	C₂×C₃₁	1	1	yes	characteristic, complemented
543	#3257	C₂×C₃₁	1	2	yes	complemented
544	#3247	C₂×C₃₁	1	1	yes	characteristic, complemented
545	#3241	C₂×C₃₁	1	2	yes	complemented
546	#3227	C₂×C₃₁	1	1	yes	characteristic, complemented
547	#3118	C₂×C₃₁	1	2	yes	complemented
548	#3105	C₂×C₃₁	1	1	yes	characteristic, complemented
549	#3081	C₂×C₃₁	1	2	yes	complemented
550	C₂×#474	C₂×C₃₁	1	1	yes	characteristic, complemented
551	#2994	C₂×C₃₁	1	1	yes	characteristic, complemented
552	C₂²×C₃₁	—	2	1	no	—
553	C₂²×C₃₁	—	2	1	no	—
554	C₂²×C₃₁	—	2	2	no	—
555	C₂²×C₃₁	—	2	2	no	—
556	C₂²×C₃₁	—	2	2	no	—
557	C₂²×C₃₁	—	2	2	no	—
558	C₂²×C₃₁	—	4	1	no	—
559	C₂²×C₃₁	—	4	1	no	—
560	C₂²×C₃₁	—	4	1	no	—
561	C₂²×C₃₁	—	4	2	no	—
562	C₂²×C₃₁	—	4	1	no	—
563	C₂²×C₃₁	—	4	1	no	—
564	C₂²×C₃₁	—	4	1	no	—
565	C₂²×C₃₁	—	4	2	no	—
566	C₂²×C₃₁	—	4	2	no	—
567	C₂²×C₃₁	—	4	1	no	—
568	C₂²×C₃₁	—	4	1	no	—
569	C₂²×C₃₁	—	8	4	no	—
570	C₂²×C₃₁	—	16	4	no	—
571	C₂²×C₃₁	#577	1	2	yes	—
572	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₃₁	—	2	1	no	—
574	C₄×C₃₁	—	2	2	no	—
575	C₄×C₃₁	—	2	1	no	—
576	C₄×C₃₁	—	2	2	no	—
577	C₄×C₃₁	—	2	1	no	—
578	C₄×C₃₁	—	2	1	no	—
579	C₄×C₃₁	—	2	2	no	—
580	C₄×C₃₁	—	4	1	no	—
581	C₄×C₃₁	—	4	1	no	—
582	C₄×C₃₁	—	4	1	no	—
583	C₄×C₃₁	—	4	1	no	—
584	C₄×C₃₁	—	4	2	no	—
585	C₄×C₃₁	—	4	2	no	—
586	C₄×C₃₁	—	4	2	no	—
587	C₄×C₃₁	—	4	1	no	—
588	C₄×C₃₁	#576	1	2	yes	—
589	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
590	C₄×C₃₁	#585	1	1	yes	characteristic
591	#563	—	2	2	no	—
592	#557	C₂²×C₃₁	1	1	yes	characteristic, complemented
593	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	#555	C₂²×C₃₁	1	1	yes	characteristic
595	#554	C₂²×C₃₁	1	1	yes	characteristic
596	#554	C₂²×C₃₁	1	2	yes	complemented
597	#553	—	2	1	no	—
598	#553	C₂²×C₃₁	1	2	yes	—
599	#553	C₂²×C₃₁	1	2	yes	complemented
600	#550	C₂²×C₃₁	1	1	yes	characteristic
601	D₄×Q₈	—	2	1	no	—
602	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
603	#548	—	2	1	no	—
604	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
605	#546	—	2	1	no	—
606	#546	—	2	2	no	—
607	D₄²	C₂²×C₃₁	1	1	yes	characteristic
608	D₄²	C₂²×C₃₁	1	2	yes	—
609	#544	C₂²×C₃₁	1	2	yes	complemented
610	#542	C₂²×C₃₁	1	2	yes	complemented
611	#541	—	2	1	no	—
612	#540	C₂²×C₃₁	1	2	yes	—
613	#539	—	2	2	no	—
614	#538	—	2	2	no	—
615	#536	—	2	1	no	—
616	#532	C₂²×C₃₁	1	1	yes	characteristic
617	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
618	#529	C₂²×C₃₁	1	1	yes	characteristic
619	#529	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#525	—	2	1	no	—
621	C₂×#121	—	2	1	no	—
622	#518	C₂²×C₃₁	1	2	yes	—
623	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
624	#501	C₂²×C₃₁	1	2	yes	complemented
625	#499	C₂²×C₃₁	1	2	yes	complemented
626	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
627	#498	C₂²×C₃₁	1	1	yes	characteristic, complemented
628	#490	C₂²×C₃₁	1	2	yes	complemented
629	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
630	#486	C₂²×C₃₁	1	2	yes	complemented
631	#486	C₂²×C₃₁	1	1	yes	characteristic, complemented
632	#485	C₂²×C₃₁	1	2	yes	complemented
633	#484	C₂²×C₃₁	1	1	yes	characteristic, complemented
634	#482	C₂²×C₃₁	1	2	yes	complemented
635	#482	C₂²×C₃₁	1	2	yes	complemented
636	#482	C₂²×C₃₁	1	2	yes	complemented
637	#481	C₂²×C₃₁	1	1	yes	characteristic, complemented
638	#481	C₂²×C₃₁	1	2	yes	complemented
639	#481	C₂²×C₃₁	1	2	yes	complemented
640	#481	C₂²×C₃₁	1	2	yes	complemented
641	#480	C₂²×C₃₁	1	2	yes	complemented
642	#479	C₂²×C₃₁	1	2	yes	complemented
643	#478	C₂²×C₃₁	1	1	yes	characteristic
644	#478	C₂²×C₃₁	1	2	yes	—
645	#478	C₂²×C₃₁	1	2	yes	complemented
646	#478	C₂²×C₃₁	1	2	yes	complemented
647	#478	C₂²×C₃₁	1	2	yes	complemented
648	#478	C₂²×C₃₁	1	1	yes	characteristic, complemented
649	#477	C₂²×C₃₁	1	1	yes	characteristic, complemented
650	#476	C₂²×C₃₁	1	2	yes	—
651	#476	C₂²×C₃₁	1	2	yes	complemented
652	#476	C₂²×C₃₁	1	1	yes	characteristic, complemented
653	#476	C₂²×C₃₁	1	2	yes	complemented
654	#474	C₂²×C₃₁	1	2	yes	—
655	#474	C₂²×C₃₁	1	1	yes	characteristic
656	#474	C₂²×C₃₁	1	1	yes	characteristic
657	#474	C₂²×C₃₁	1	2	yes	complemented
658	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
659	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
660	#474	C₂²×C₃₁	1	2	yes	complemented
661	#469	C₂²×C₃₁	1	2	yes	complemented
662	#468	C₂²×C₃₁	1	2	yes	complemented
663	#466	C₂²×C₃₁	1	2	yes	complemented
664	#466	C₂²×C₃₁	1	2	yes	complemented
665	#465	C₂²×C₃₁	1	2	yes	complemented
666	#465	C₂²×C₃₁	1	2	yes	complemented
667	#463	C₂²×C₃₁	1	1	yes	characteristic
668	#463	C₂²×C₃₁	1	1	yes	characteristic, complemented
669	#463	C₂²×C₃₁	1	2	yes	complemented
670	#460	C₂²×C₃₁	1	1	yes	characteristic, complemented
671	#460	C₂²×C₃₁	1	2	yes	complemented
672	#459	C₂²×C₃₁	1	1	yes	characteristic, complemented
673	#459	C₂²×C₃₁	1	2	yes	complemented
674	#450	C₂²×C₃₁	1	1	yes	characteristic
675	#450	C₂²×C₃₁	1	2	yes	—
676	#447	C₂²×C₃₁	1	1	yes	characteristic
677	#447	C₂²×C₃₁	1	2	yes	—
678	#446	C₂²×C₃₁	1	1	yes	characteristic, complemented
679	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
680	#442	C₂²×C₃₁	1	2	yes	—
681	#440	C₂²×C₃₁	1	2	yes	complemented
682	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
683	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
685	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic
686	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
687	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
688	#436	C₂²×C₃₁	1	1	yes	characteristic, complemented
689	#435	C₂²×C₃₁	1	2	yes	complemented
690	C₈×D₄	C₂²×C₃₁	1	2	yes	complemented
691	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
692	#433	C₂²×C₃₁	1	2	yes	complemented
693	#431	C₂²×C₃₁	1	1	yes	characteristic, complemented
694	#428	C₂²×C₃₁	1	2	yes	complemented
695	#427	C₂²×C₃₁	1	2	yes	complemented
696	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
697	#424	C₂²×C₃₁	1	2	yes	complemented
698	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
699	#418	C₂²×C₃₁	1	2	yes	—
700	C₂×#102	C₂²×C₃₁	1	2	yes	—
701	C₂×#102	C₂²×C₃₁	1	2	yes	—
702	C₂×C₃₁	—	2	2	no	—
703	C₂×C₃₁	—	4	2	no	—
704	C₂×C₃₁	—	4	2	no	—
705	C₂×C₃₁	—	8	1	no	—
706	C₂×C₃₁	—	8	1	no	—
707	C₂×C₃₁	—	8	2	no	—
708	C₂×C₃₁	#3489	1	1	yes	characteristic
709	C₂×C₃₁	C₂×#576	1	1	yes	characteristic
710	C₂×C₃₁	C₂×#577	1	1	yes	characteristic
711	C₂×#41	—	2	1	no	—
712	C₂×#41	—	2	1	no	—
713	C₂×#41	—	2	1	no	—
714	C₂²×Q₈	—	2	1	no	—
715	C₂²×Q₈	—	2	1	no	—
716	C₂²×D₄	—	2	1	no	—
717	C₂²×D₄	—	2	2	no	—
718	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
719	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
720	C₂³×C₄	—	2	1	no	—
721	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
722	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
723	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
724	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
725	C₂×D₈	C₂³×C₃₁	1	2	yes	—
726	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
728	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
729	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	1	no	—
734	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
735	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
739	#127	C₂³×C₃₁	1	1	yes	characteristic
740	#127	C₂³×C₃₁	1	2	yes	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	1	no	—
746	#126	D₄×C₃₁	1	2	yes	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	D₄×C₃₁	1	1	yes	characteristic
751	#125	C₂³×C₃₁	1	1	yes	characteristic
752	#125	C₂³×C₃₁	1	2	yes	—
753	#125	C₂³×C₃₁	1	2	yes	—
754	#124	—	2	1	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	1	no	—
758	#124	D₄×C₃₁	1	1	yes	characteristic
759	#124	C₂³×C₃₁	1	1	yes	characteristic
760	#123	—	2	1	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	D₄×C₃₁	1	2	yes	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	1	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
780	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
781	#121	—	2	2	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	—	2	2	no	—
789	#121	—	2	2	no	—
790	#121	—	2	2	no	—
791	#121	D₄×C₃₁	1	1	yes	characteristic
792	#121	C₂³×C₃₁	1	1	yes	characteristic
793	#121	C₂³×C₃₁	1	2	yes	—
794	#121	C₂³×C₃₁	1	2	yes	—
795	#121	C₂³×C₃₁	1	2	yes	—
796	#121	C₂³×C₃₁	1	2	yes	—
797	#120	—	2	2	no	—
798	#120	—	2	2	no	—
799	#120	—	2	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
804	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₃₁	1	2	yes	—
819	C₄×D₄	C₂³×C₃₁	1	2	yes	—
820	C₄×D₄	C₂³×C₃₁	1	2	yes	—
821	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₃₁	1	2	yes	—
823	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₃₁	1	2	yes	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	C₂³×C₃₁	1	2	yes	—
828	#117	C₂³×C₃₁	1	2	yes	—
829	#117	C₂³×C₃₁	1	2	yes	—
830	C₂×C₄⋊C₄	—	2	1	no	—
831	C₂×C₄⋊C₄	—	2	1	no	—
832	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
833	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
834	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
835	C₂×C₂²⋊C₄	—	2	1	no	—
836	C₂×C₂²⋊C₄	—	2	2	no	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
839	#107	C₂³×C₃₁	1	2	yes	—
840	#107	C₂³×C₃₁	1	2	yes	—
841	#107	C₂³×C₃₁	1	2	yes	—
842	#107	C₂³×C₃₁	1	2	yes	—
843	#107	C₂³×C₃₁	1	2	yes	—
844	#107	C₂³×C₃₁	1	1	yes	characteristic
845	#107	C₂³×C₃₁	1	1	yes	characteristic
846	#106	C₂³×C₃₁	1	1	yes	characteristic
847	#106	C₂³×C₃₁	1	2	yes	—
848	#106	C₂³×C₃₁	1	2	yes	—
849	#106	C₂³×C₃₁	1	2	yes	—
850	#106	C₂³×C₃₁	1	2	yes	—
851	#106	C₂³×C₃₁	1	1	yes	characteristic
852	#106	C₂³×C₃₁	1	2	yes	—
853	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
854	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
858	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
859	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
860	#103	C₂³×C₃₁	1	2	yes	—
861	#103	C₂³×C₃₁	1	1	yes	characteristic
862	#103	C₂³×C₃₁	1	1	yes	characteristic
863	#102	C₂³×C₃₁	1	1	yes	characteristic
864	#102	C₂³×C₃₁	1	2	yes	—
865	#102	C₂³×C₃₁	1	2	yes	—
866	#102	C₂³×C₃₁	1	2	yes	—
867	#102	C₂³×C₃₁	1	2	yes	—
868	#102	C₂³×C₃₁	1	2	yes	—
869	#102	C₂³×C₃₁	1	2	yes	—
870	#102	C₂³×C₃₁	1	1	yes	characteristic
871	#102	C₂³×C₃₁	1	2	yes	—
872	#102	C₂³×C₃₁	1	2	yes	—
873	#102	C₂³×C₃₁	1	1	yes	characteristic
874	#102	C₂³×C₃₁	1	1	yes	characteristic
875	#102	C₂³×C₃₁	1	2	yes	—
876	#102	C₂³×C₃₁	1	1	yes	characteristic
877	#102	C₂³×C₃₁	1	1	yes	characteristic
878	#102	C₂³×C₃₁	1	2	yes	—
879	#102	C₂³×C₃₁	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
884	#97	C₂³×C₃₁	1	2	yes	—
885	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
886	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
887	C₄×C₈	C₂³×C₃₁	1	2	yes	—
888	C₃₁	#62199	1	1	yes	characteristic, direct product factor, Sylow
889	C₂⁴	—	2	1	no	—
890	C₂⁴	—	2	2	no	—
891	#41	—	8	2	no	—
892	#41	—	8	2	no	—
893	#41	—	8	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	8	2	no	—
900	C₂×Q₈	—	8	2	no	—
901	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
902	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	2	1	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	1	no	—
915	C₂×D₄	—	2	2	no	—
916	C₂×D₄	—	4	1	no	—
917	C₂×D₄	—	4	2	no	—
918	C₂×D₄	—	8	2	no	—
919	C₂×D₄	—	8	4	no	—
920	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
921	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
922	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
924	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
925	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	2	2	no	—
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	8	2	no	—
939	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
940	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	4	1	no	—
945	SD₁₆	—	4	2	no	—
946	D₈	—	2	2	no	—
947	D₈	—	4	2	no	—
948	D₈	—	4	1	no	—
949	M₁₆	—	4	2	no	—
950	C₂×C₈	—	4	2	no	—
951	C₂×C₈	—	4	2	no	—
952	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
953	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
954	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
955	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
956	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
957	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
981	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
987	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1011	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1012	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1013	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1020	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₃₁	1	2	yes	—
1022	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1023	C₂³	—	2	1	no	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	4	no	—
1029	C₂³	—	4	2	no	—
1030	C₂³	—	8	1	no	—
1031	C₂³	—	8	2	no	—
1032	C₂³	—	8	2	no	—
1033	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1034	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	4	2	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	2	no	—
1042	Q₈	—	8	1	no	—
1043	D₄	—	2	4	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	1	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	4	2	no	—
1055	D₄	—	4	4	no	—
1056	D₄	—	4	2	no	—
1057	D₄	—	8	2	no	—
1058	D₄	—	8	2	no	—
1059	D₄	—	8	1	no	—
1060	D₄	—	8	2	no	—
1061	D₄	—	8	2	no	—
1062	D₄	—	8	2	no	—
1063	D₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	—	8	1	no	—
1088	C₂×C₄	—	8	2	no	—
1089	C₂×C₄	—	8	2	no	—
1090	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1095	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1096	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1097	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1098	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1099	C₈	—	2	1	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	2	no	—
1102	C₈	—	2	1	no	—
1103	C₈	—	2	2	no	—
1104	C₈	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	2	2	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	1	no	—
1116	C₂²	—	4	1	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	8	4	no	—
1123	C₂²	—	16	4	no	—
1124	C₂²	C₃₁×#577	1	2	yes	—
1125	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	2	no	—
1130	C₄	—	2	1	no	—
1131	C₄	—	2	1	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	C₃₁×#576	1	2	yes	—
1142	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
1143	C₄	C₃₁×#585	1	1	yes	characteristic
1144	C₂	—	2	2	no	—
1145	C₂	—	4	2	no	—
1146	C₂	—	4	2	no	—
1147	C₂	—	8	1	no	—
1148	C₂	—	8	2	no	—
1149	C₂	—	8	1	no	—
1150	C₂	C₃₁×#3489	1	1	yes	characteristic
1151	C₂	C₂×C₃₁×#576	1	1	yes	characteristic
1152	C₂	C₂×C₃₁×#577	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×#3552	C₂	semidirect
2. C₃₁×#3519	C₂	semidirect
3. C₃₁×#3384	C₂	semidirect
4. C₃₁×#3381	C₂	semidirect
5. C₃₁×#3368	C₂	semidirect
6. C₃₁×#3358	C₂	semidirect
7. C₃₁×#3354	C₂	semidirect
8. C₃₁×#3346	C₂	semidirect
9. C₃₁×#3340	C₂	semidirect
10. C₃₁×#3339	C₂	semidirect
11. C₃₁×#3324	C₂	semidirect
12. C₃₁×#3318	C₂	semidirect
13. C₃₁×#3295	C₂	semidirect
14. C₃₁×#3294	C₂	semidirect
15. C₃₁×#3257	C₂	semidirect
16. C₃₁×#3247	C₂	semidirect
17. C₃₁×#3241	C₂	semidirect
18. C₃₁×#3227	C₂	semidirect
19. C₃₁×#3118	C₂	semidirect
20. C₃₁×#3105	C₂	semidirect
21. C₃₁×#3081	C₂	semidirect
22. C₂×C₃₁×#474	C₂	semidirect
23. C₃₁×#2994	C₂	semidirect
25. C₃₁×#557	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
29. C₃₁×#554	C₂²	semidirect
32. C₃₁×#553	C₂²	semidirect
35. D₄×Q₈×C₃₁	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
42. C₃₁×#544	C₂²	semidirect
43. C₃₁×#542	C₂²	semidirect
50. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
52. C₃₁×#529	C₂²	semidirect
57. C₃₁×#501	C₂²	semidirect
58. C₃₁×#499	C₂²	semidirect
59. C₃₁×#498	C₂²	semidirect
60. C₃₁×#498	C₂²	semidirect
61. C₃₁×#490	C₂²	semidirect
62. C₃₁×#486	C₂²	semidirect
63. C₃₁×#486	C₂²	semidirect
64. C₃₁×#486	C₂²	semidirect
65. C₃₁×#485	C₂²	semidirect
66. C₃₁×#484	C₂²	semidirect
67. C₃₁×#482	C₂²	semidirect
68. C₃₁×#482	C₂²	semidirect
69. C₃₁×#482	C₂²	semidirect
70. C₃₁×#481	C₂²	semidirect
71. C₃₁×#481	C₂²	semidirect
72. C₃₁×#481	C₂²	semidirect
73. C₃₁×#481	C₂²	semidirect
74. C₃₁×#480	C₂²	semidirect
75. C₃₁×#479	C₂²	semidirect
78. C₃₁×#478	C₂²	semidirect
79. C₃₁×#478	C₂²	semidirect
80. C₃₁×#478	C₂²	semidirect
81. C₃₁×#478	C₂²	semidirect
82. C₃₁×#477	C₂²	semidirect
84. C₃₁×#476	C₂²	semidirect
85. C₃₁×#476	C₂²	semidirect
86. C₃₁×#476	C₂²	semidirect
90. C₃₁×#474	C₂²	semidirect
91. C₃₁×#474	C₂²	semidirect
92. C₃₁×#474	C₂²	semidirect
93. C₃₁×#474	C₂²	semidirect
94. C₃₁×#469	C₂²	semidirect
95. C₃₁×#468	C₂²	semidirect
96. C₃₁×#466	C₂²	semidirect
97. C₃₁×#466	C₂²	semidirect
98. C₃₁×#465	C₂²	semidirect
99. C₃₁×#465	C₂²	semidirect
101. C₃₁×#463	C₂²	semidirect
102. C₃₁×#463	C₂²	semidirect
103. C₃₁×#460	C₂²	semidirect
104. C₃₁×#460	C₂²	semidirect
105. C₃₁×#459	C₂²	semidirect
106. C₃₁×#459	C₂²	semidirect
111. C₃₁×#446	C₂²	semidirect
112. C₈×Q₈×C₃₁	C₂²	semidirect
114. C₃₁×#440	C₂²	semidirect
117. C₄×SD₁₆×C₃₁	C₂²	semidirect
119. C₄×D₈×C₃₁	C₂²	semidirect
120. C₄×D₈×C₃₁	C₂²	semidirect
121. C₃₁×#436	C₂²	semidirect
122. C₃₁×#435	C₂²	semidirect
123. C₈×D₄×C₃₁	C₂²	semidirect
124. C₈×D₄×C₃₁	C₂²	semidirect
125. C₃₁×#433	C₂²	semidirect
126. C₃₁×#431	C₂²	semidirect
127. C₃₁×#428	C₂²	semidirect
128. C₃₁×#427	C₂²	semidirect
129. C₂×C₃₁×#107	C₂²	semidirect
130. C₃₁×#424	C₂²	semidirect
131. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
446. #62199	C₃₁	direct (N × H)
529. #3552	C₂×C₃₁	semidirect
530. #3519	C₂×C₃₁	semidirect
531. #3384	C₂×C₃₁	semidirect
532. #3381	C₂×C₃₁	semidirect
533. #3368	C₂×C₃₁	semidirect
534. #3358	C₂×C₃₁	semidirect
535. #3354	C₂×C₃₁	semidirect
536. #3346	C₂×C₃₁	semidirect
537. #3340	C₂×C₃₁	semidirect
538. #3339	C₂×C₃₁	semidirect
539. #3324	C₂×C₃₁	semidirect
540. #3318	C₂×C₃₁	semidirect
541. #3295	C₂×C₃₁	semidirect
542. #3294	C₂×C₃₁	semidirect
543. #3257	C₂×C₃₁	semidirect
544. #3247	C₂×C₃₁	semidirect
545. #3241	C₂×C₃₁	semidirect
546. #3227	C₂×C₃₁	semidirect
547. #3118	C₂×C₃₁	semidirect
548. #3105	C₂×C₃₁	semidirect
549. #3081	C₂×C₃₁	semidirect
550. C₂×#474	C₂×C₃₁	semidirect
551. #2994	C₂×C₃₁	semidirect
592. #557	C₂²×C₃₁	semidirect
593. #556	C₂²×C₃₁	semidirect
596. #554	C₂²×C₃₁	semidirect
599. #553	C₂²×C₃₁	semidirect
602. D₄×Q₈	C₂²×C₃₁	semidirect
604. #547	C₂²×C₃₁	semidirect
609. #544	C₂²×C₃₁	semidirect
610. #542	C₂²×C₃₁	semidirect
617. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
619. #529	C₂²×C₃₁	semidirect
624. #501	C₂²×C₃₁	semidirect
625. #499	C₂²×C₃₁	semidirect
626. #498	C₂²×C₃₁	semidirect
627. #498	C₂²×C₃₁	semidirect
628. #490	C₂²×C₃₁	semidirect
629. #486	C₂²×C₃₁	semidirect
630. #486	C₂²×C₃₁	semidirect
631. #486	C₂²×C₃₁	semidirect
632. #485	C₂²×C₃₁	semidirect
633. #484	C₂²×C₃₁	semidirect
634. #482	C₂²×C₃₁	semidirect
635. #482	C₂²×C₃₁	semidirect
636. #482	C₂²×C₃₁	semidirect
637. #481	C₂²×C₃₁	semidirect
638. #481	C₂²×C₃₁	semidirect
639. #481	C₂²×C₃₁	semidirect
640. #481	C₂²×C₃₁	semidirect
641. #480	C₂²×C₃₁	semidirect
642. #479	C₂²×C₃₁	semidirect
645. #478	C₂²×C₃₁	semidirect
646. #478	C₂²×C₃₁	semidirect
647. #478	C₂²×C₃₁	semidirect
648. #478	C₂²×C₃₁	semidirect
649. #477	C₂²×C₃₁	semidirect
651. #476	C₂²×C₃₁	semidirect
652. #476	C₂²×C₃₁	semidirect
653. #476	C₂²×C₃₁	semidirect
657. #474	C₂²×C₃₁	semidirect
658. #474	C₂²×C₃₁	semidirect
659. #474	C₂²×C₃₁	semidirect
660. #474	C₂²×C₃₁	semidirect
661. #469	C₂²×C₃₁	semidirect
662. #468	C₂²×C₃₁	semidirect
663. #466	C₂²×C₃₁	semidirect
664. #466	C₂²×C₃₁	semidirect
665. #465	C₂²×C₃₁	semidirect
666. #465	C₂²×C₃₁	semidirect
668. #463	C₂²×C₃₁	semidirect
669. #463	C₂²×C₃₁	semidirect
670. #460	C₂²×C₃₁	semidirect
671. #460	C₂²×C₃₁	semidirect
672. #459	C₂²×C₃₁	semidirect
673. #459	C₂²×C₃₁	semidirect
678. #446	C₂²×C₃₁	semidirect
679. C₈×Q₈	C₂²×C₃₁	semidirect
681. #440	C₂²×C₃₁	semidirect
684. C₄×SD₁₆	C₂²×C₃₁	semidirect
686. C₄×D₈	C₂²×C₃₁	semidirect
687. C₄×D₈	C₂²×C₃₁	semidirect
688. #436	C₂²×C₃₁	semidirect
689. #435	C₂²×C₃₁	semidirect
690. C₈×D₄	C₂²×C₃₁	semidirect
691. C₈×D₄	C₂²×C₃₁	semidirect
692. #433	C₂²×C₃₁	semidirect
693. #431	C₂²×C₃₁	semidirect
694. #428	C₂²×C₃₁	semidirect
695. #427	C₂²×C₃₁	semidirect
696. C₂×#107	C₂²×C₃₁	semidirect
697. #424	C₂²×C₃₁	semidirect
698. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
888. C₃₁	#62199	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×#3552	2
C₃₁×#3519	2
C₃₁×#3384	2
C₃₁×#3381	2
C₃₁×#3368	2
C₃₁×#3358	2
C₃₁×#3354	2
C₃₁×#3346	2
C₃₁×#3340	2
C₃₁×#3339	2
C₃₁×#3324	2
C₃₁×#3318	2
C₃₁×#3295	2
C₃₁×#3294	2
C₃₁×#3257	2
C₃₁×#3247	2
C₃₁×#3241	2
C₃₁×#3227	2
C₃₁×#3118	2
C₃₁×#3105	2
C₃₁×#3081	2
C₂×C₃₁×#474	2
C₃₁×#2994	2
#62199	31

Subgroups — C31×#62199 #21518958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62199 #21518958