Subgroups — C₃₁×#62017 #21518776

Order 7936.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3561	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3402	C₂	1	2	yes	maximal, complemented
4	C₃₁×#3367	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3314	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3308	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3299	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3269	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3266	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3262	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3225	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#3124	C₂	1	2	yes	maximal, complemented
16	C₃₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#3046	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
21	C₂×C₃₁×#135	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#563	—	2	1	no	—
25	C₃₁×#562	—	2	1	no	—
26	C₃₁×#556	C₂²	1	2	yes	complemented
27	C₃₁×#556	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#554	C₂²	1	2	yes	—
29	C₃₁×#552	—	2	1	no	—
30	C₃₁×#551	—	2	2	no	—
31	C₃₁×#551	—	2	2	no	—
32	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
33	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#548	—	2	1	no	—
35	C₃₁×#548	C₂²	1	2	yes	complemented
36	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#547	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#546	C₂²	1	2	yes	—
39	C₃₁×#546	C₂²	1	2	yes	—
40	C₃₁×#543	—	2	1	no	—
41	C₃₁×#542	—	2	2	no	—
42	C₃₁×#542	C₂²	1	2	yes	complemented
43	C₃₁×#542	C₂²	1	2	yes	complemented
44	C₃₁×#539	—	2	2	no	—
45	C₃₁×#538	—	2	1	no	—
46	C₃₁×#536	C₂²	1	2	yes	complemented
47	C₃₁×#533	C₂²	1	1	yes	characteristic
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#529	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
51	C₃₁×#525	—	2	1	no	—
52	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
53	C₃₁×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
55	C₃₁×#497	C₂²	1	2	yes	complemented
56	C₃₁×#497	C₂²	1	2	yes	complemented
57	C₃₁×#495	C₂²	1	2	yes	—
58	C₃₁×#489	C₂²	1	2	yes	complemented
59	C₃₁×#489	C₂²	1	2	yes	complemented
60	C₃₁×#487	C₂²	1	2	yes	complemented
61	C₃₁×#484	C₂²	1	2	yes	—
62	C₃₁×#484	C₂²	1	2	yes	complemented
63	C₃₁×#480	C₂²	1	2	yes	complemented
64	C₃₁×#477	C₂²	1	2	yes	complemented
65	C₃₁×#477	C₂²	1	2	yes	complemented
66	C₃₁×#477	C₂²	1	2	yes	complemented
67	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#474	C₂²	1	1	yes	characteristic, complemented
69	C₃₁×#474	C₂²	1	2	yes	complemented
70	C₃₁×#468	C₂²	1	2	yes	complemented
71	C₃₁×#468	C₂²	1	2	yes	complemented
72	C₃₁×#467	C₂²	1	2	yes	—
73	C₃₁×#467	C₂²	1	2	yes	—
74	C₃₁×#467	C₂²	1	2	yes	complemented
75	C₃₁×#466	C₂²	1	2	yes	—
76	C₃₁×#464	C₂²	1	2	yes	complemented
77	C₃₁×#464	C₂²	1	2	yes	complemented
78	C₃₁×#464	C₂²	1	2	yes	complemented
79	C₃₁×#464	C₂²	1	2	yes	complemented
80	C₃₁×#463	C₂²	1	2	yes	—
81	C₃₁×#463	C₂²	1	2	yes	—
82	C₃₁×#463	C₂²	1	2	yes	—
83	C₃₁×#463	C₂²	1	2	yes	—
84	C₃₁×#463	C₂²	1	2	yes	—
85	C₃₁×#463	C₂²	1	2	yes	—
86	C₃₁×#462	C₂²	1	2	yes	complemented
87	C₃₁×#462	C₂²	1	2	yes	complemented
88	C₃₁×#462	C₂²	1	2	yes	complemented
89	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#461	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#461	C₂²	1	2	yes	complemented
92	C₃₁×#452	C₂²	1	2	yes	complemented
93	C₃₁×#452	C₂²	1	2	yes	complemented
94	C₃₁×#451	C₂²	1	2	yes	—
95	C₃₁×#451	C₂²	1	2	yes	complemented
96	C₃₁×#450	C₂²	1	2	yes	—
97	C₃₁×#450	C₂²	1	2	yes	—
98	C₃₁×#449	C₂²	1	2	yes	—
99	C₃₁×#449	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	complemented
101	C₃₁×#446	C₂²	1	2	yes	complemented
102	C₃₁×#440	C₂²	1	2	yes	complemented
103	C₃₁×#440	C₂²	1	2	yes	complemented
104	C₃₁×#440	C₂²	1	2	yes	complemented
105	C₃₁×#440	C₂²	1	2	yes	complemented
106	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
107	C₄×D₈×C₃₁	C₂²	1	2	yes	—
108	C₃₁×#435	C₂²	1	2	yes	—
109	C₃₁×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₃₁	C₂²	1	2	yes	—
111	C₃₁×#433	C₂²	1	2	yes	complemented
112	C₃₁×#432	C₂²	1	1	yes	characteristic
113	C₃₁×#424	C₂²	1	2	yes	complemented
114	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₃₁×#417	C₂²	1	2	yes	complemented
116	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
117	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
118	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
119	C₂×#41×C₃₁	—	2	1	no	—
120	C₂×#41×C₃₁	C₂³	1	2	yes	—
121	C₂×#41×C₃₁	C₂³	1	2	yes	—
122	C₂²×Q₈×C₃₁	—	2	1	no	—
123	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₃₁	—	2	1	no	—
128	C₃₁×#137	—	4	4	no	—
129	C₃₁×#135	—	4	4	no	—
130	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
131	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
132	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
133	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₃₁	—	4	2	no	—
135	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
141	C₂×D₈×C₃₁	—	4	2	no	—
142	C₂×D₈×C₃₁	C₂³	1	2	yes	—
143	C₂×D₈×C₃₁	C₂³	1	2	yes	—
144	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
148	C₃₁×C₄⋊Q₈	—	2	2	no	—
149	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
150	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
151	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×#126	—	2	2	no	—
156	C₃₁×#126	—	2	2	no	—
157	C₃₁×#126	—	2	2	no	—
158	C₃₁×#126	—	2	2	no	—
159	C₃₁×#126	—	2	2	no	—
160	C₃₁×#126	D₄	1	2	yes	—
161	C₃₁×#125	—	2	2	no	—
162	C₃₁×#125	—	2	1	no	—
163	C₃₁×#125	—	2	1	no	—
164	C₃₁×#125	D₄	1	1	yes	characteristic
165	C₃₁×#124	—	2	2	no	—
166	C₃₁×#124	—	2	2	no	—
167	C₃₁×#124	—	2	2	no	—
168	C₃₁×#124	—	2	1	no	—
169	C₃₁×#124	—	2	1	no	—
170	C₃₁×#124	D₄	1	1	yes	characteristic
171	C₃₁×#124	C₂³	1	2	yes	—
172	C₃₁×#124	C₂³	1	2	yes	—
173	C₃₁×#124	C₂³	1	2	yes	—
174	C₃₁×#124	C₂³	1	2	yes	—
175	C₃₁×#123	—	2	2	no	—
176	C₃₁×#123	—	2	2	no	—
177	C₃₁×#123	—	2	2	no	—
178	C₃₁×#123	—	2	2	no	—
179	C₃₁×#123	—	2	2	no	—
180	C₃₁×#123	—	2	2	no	—
181	C₃₁×#123	—	2	2	no	—
182	C₃₁×#123	—	2	2	no	—
183	C₃₁×#123	D₄	1	2	yes	—
184	C₃₁×C₂²⋊Q₈	—	2	1	no	—
185	C₃₁×C₂²⋊Q₈	—	2	2	no	—
186	C₃₁×C₂²⋊Q₈	—	2	1	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	2	no	—
189	C₃₁×C₂²⋊Q₈	—	2	1	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	2	no	—
192	C₃₁×C₂²⋊Q₈	—	2	2	no	—
193	C₃₁×C₂²⋊Q₈	—	2	2	no	—
194	C₃₁×C₂²⋊Q₈	—	2	2	no	—
195	C₃₁×C₂²⋊Q₈	—	2	2	no	—
196	C₃₁×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
201	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₃₁×#121	—	2	1	no	—
206	C₃₁×#121	—	2	2	no	—
207	C₃₁×#121	—	2	2	no	—
208	C₃₁×#121	—	2	2	no	—
209	C₃₁×#121	D₄	1	1	yes	characteristic
210	C₃₁×#121	C₂³	1	2	yes	—
211	C₃₁×#121	C₂³	1	2	yes	—
212	C₃₁×#120	—	2	2	no	—
213	C₃₁×#120	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	1	no	—
216	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
217	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
218	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
219	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₃₁	—	2	2	no	—
222	C₄×D₄×C₃₁	—	2	2	no	—
223	C₄×D₄×C₃₁	—	2	2	no	—
224	C₄×D₄×C₃₁	—	2	2	no	—
225	C₄×D₄×C₃₁	—	2	2	no	—
226	C₄×D₄×C₃₁	—	2	1	no	—
227	C₄×D₄×C₃₁	—	2	1	no	—
228	C₄×D₄×C₃₁	C₂³	1	2	yes	—
229	C₄×D₄×C₃₁	C₂³	1	2	yes	—
230	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₄×D₄×C₃₁	C₂³	1	2	yes	—
235	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₃₁×#117	—	2	1	no	—
237	C₃₁×#117	—	2	1	no	—
238	C₃₁×#117	—	2	2	no	—
239	C₃₁×#117	—	2	1	no	—
240	C₃₁×#117	—	2	2	no	—
241	C₃₁×#117	C₂³	1	2	yes	—
242	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
243	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
244	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
246	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
247	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
248	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
249	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
250	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
251	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
252	C₃₁×#107	C₂³	1	2	yes	—
253	C₃₁×#107	C₂³	1	2	yes	—
254	C₃₁×#107	C₂³	1	2	yes	—
255	C₃₁×#107	C₂³	1	2	yes	—
256	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
257	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
258	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
260	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
261	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₃₁×#103	C₂³	1	2	yes	—
263	C₃₁×#103	C₂³	1	2	yes	—
264	C₃₁×#103	C₂³	1	2	yes	—
265	C₃₁×#103	C₂³	1	2	yes	—
266	C₃₁×#103	C₂³	1	2	yes	—
267	C₃₁×#103	C₂³	1	2	yes	—
268	C₃₁×#103	C₂³	1	2	yes	—
269	C₃₁×#103	C₂³	1	2	yes	—
270	C₃₁×#103	C₂³	1	2	yes	—
271	C₃₁×#103	C₂³	1	2	yes	—
272	C₃₁×#102	C₂³	1	2	yes	—
273	C₃₁×#102	C₂³	1	2	yes	—
274	C₃₁×#102	C₂³	1	2	yes	—
275	C₃₁×#102	C₂³	1	2	yes	—
276	C₃₁×#102	C₂³	1	2	yes	—
277	C₃₁×#102	C₂³	1	2	yes	—
278	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₃₁×#97	C₂³	1	2	yes	—
282	C₃₁×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₃₁	C₂³	1	2	yes	—
284	C₂⁴×C₃₁	—	2	1	no	—
285	C₂⁴×C₃₁	—	2	1	no	—
286	#41×C₃₁	—	2	4	no	—
287	#41×C₃₁	—	4	2	no	—
288	#41×C₃₁	—	4	2	no	—
289	#41×C₃₁	—	4	2	no	—
290	#41×C₃₁	—	8	2	no	—
291	C₂×Q₈×C₃₁	—	2	1	no	—
292	C₂×Q₈×C₃₁	—	2	1	no	—
293	C₂×Q₈×C₃₁	—	2	2	no	—
294	C₂×Q₈×C₃₁	—	2	2	no	—
295	C₂×Q₈×C₃₁	—	2	1	no	—
296	C₂×Q₈×C₃₁	—	4	1	no	—
297	C₂×Q₈×C₃₁	—	4	2	no	—
298	C₂×Q₈×C₃₁	—	4	1	no	—
299	C₂×Q₈×C₃₁	—	4	2	no	—
300	C₂×Q₈×C₃₁	—	8	2	no	—
301	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
302	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
303	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
305	C₂×D₄×C₃₁	—	2	2	no	—
306	C₂×D₄×C₃₁	—	2	2	no	—
307	C₂×D₄×C₃₁	—	2	2	no	—
308	C₂×D₄×C₃₁	—	2	2	no	—
309	C₂×D₄×C₃₁	—	2	2	no	—
310	C₂×D₄×C₃₁	—	2	1	no	—
311	C₂×D₄×C₃₁	—	2	1	no	—
312	C₂×D₄×C₃₁	—	4	1	no	—
313	C₂×D₄×C₃₁	—	4	1	no	—
314	C₂×D₄×C₃₁	—	4	1	no	—
315	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₃₁	—	2	1	no	—
321	C₂²×C₄×C₃₁	—	2	1	no	—
322	C₂²×C₄×C₃₁	—	2	2	no	—
323	C₂²×C₄×C₃₁	—	2	2	no	—
324	C₂²×C₄×C₃₁	—	2	2	no	—
325	C₂²×C₄×C₃₁	—	2	1	no	—
326	C₂²×C₄×C₃₁	—	2	1	no	—
327	C₂²×C₄×C₃₁	—	2	2	no	—
328	C₂²×C₄×C₃₁	—	2	2	no	—
329	C₂²×C₄×C₃₁	—	2	2	no	—
330	C₂²×C₄×C₃₁	—	2	1	no	—
331	C₂²×C₄×C₃₁	—	2	1	no	—
332	C₂²×C₄×C₃₁	—	8	2	no	—
333	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
337	Q₁₆×C₃₁	—	4	2	no	—
338	Q₁₆×C₃₁	—	4	2	no	—
339	Q₁₆×C₃₁	—	4	2	no	—
340	Q₁₆×C₃₁	—	4	2	no	—
341	SD₁₆×C₃₁	—	2	4	no	—
342	SD₁₆×C₃₁	—	2	4	no	—
343	SD₁₆×C₃₁	—	4	2	no	—
344	SD₁₆×C₃₁	—	4	2	no	—
345	SD₁₆×C₃₁	—	4	2	no	—
346	SD₁₆×C₃₁	—	4	2	no	—
347	D₈×C₃₁	—	2	4	no	—
348	D₈×C₃₁	—	4	2	no	—
349	M₁₆×C₃₁	—	4	2	no	—
350	C₂×C₈×C₃₁	—	4	1	no	—
351	C₂×C₈×C₃₁	—	4	1	no	—
352	C₂×C₈×C₃₁	—	4	2	no	—
353	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
354	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
355	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
356	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₃₁	—	2	2	no	—
358	C₄⋊C₄×C₃₁	—	2	1	no	—
359	C₄⋊C₄×C₃₁	—	2	2	no	—
360	C₄⋊C₄×C₃₁	—	2	2	no	—
361	C₄⋊C₄×C₃₁	—	2	2	no	—
362	C₄⋊C₄×C₃₁	—	2	1	no	—
363	C₄⋊C₄×C₃₁	—	2	2	no	—
364	C₄⋊C₄×C₃₁	—	2	1	no	—
365	C₄⋊C₄×C₃₁	—	2	1	no	—
366	C₄⋊C₄×C₃₁	—	2	1	no	—
367	C₄⋊C₄×C₃₁	—	2	1	no	—
368	C₄⋊C₄×C₃₁	—	2	2	no	—
369	C₄⋊C₄×C₃₁	—	2	2	no	—
370	C₄⋊C₄×C₃₁	—	2	2	no	—
371	C₄⋊C₄×C₃₁	—	2	2	no	—
372	C₄⋊C₄×C₃₁	—	2	2	no	—
373	C₄⋊C₄×C₃₁	—	2	1	no	—
374	C₄⋊C₄×C₃₁	—	2	2	no	—
375	C₄⋊C₄×C₃₁	—	2	2	no	—
376	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
386	C₂²⋊C₄×C₃₁	—	2	2	no	—
387	C₂²⋊C₄×C₃₁	—	2	2	no	—
388	C₂²⋊C₄×C₃₁	—	2	2	no	—
389	C₂²⋊C₄×C₃₁	—	2	2	no	—
390	C₂²⋊C₄×C₃₁	—	2	1	no	—
391	C₂²⋊C₄×C₃₁	—	2	2	no	—
392	C₂²⋊C₄×C₃₁	—	2	1	no	—
393	C₂²⋊C₄×C₃₁	—	2	1	no	—
394	C₂²⋊C₄×C₃₁	—	2	1	no	—
395	C₂²⋊C₄×C₃₁	—	2	2	no	—
396	C₂²⋊C₄×C₃₁	—	2	2	no	—
397	C₂²⋊C₄×C₃₁	—	2	2	no	—
398	C₂²⋊C₄×C₃₁	—	2	2	no	—
399	C₂²⋊C₄×C₃₁	—	2	2	no	—
400	C₂²⋊C₄×C₃₁	—	2	2	no	—
401	C₂²⋊C₄×C₃₁	—	2	2	no	—
402	C₂²⋊C₄×C₃₁	—	2	2	no	—
403	C₂²⋊C₄×C₃₁	—	2	2	no	—
404	C₂²⋊C₄×C₃₁	—	2	2	no	—
405	C₂²⋊C₄×C₃₁	—	2	2	no	—
406	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
407	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
408	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
411	C₄²×C₃₁	—	2	2	no	—
412	C₄²×C₃₁	—	2	2	no	—
413	C₄²×C₃₁	—	2	2	no	—
414	C₄²×C₃₁	—	2	2	no	—
415	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
416	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
417	C₄²×C₃₁	C₂⁴	1	2	yes	—
418	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
419	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
420	#62017	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
421	C₂³×C₃₁	—	2	1	no	—
422	C₂³×C₃₁	—	2	1	no	—
423	C₂³×C₃₁	—	2	2	no	—
424	C₂³×C₃₁	—	4	2	no	—
425	C₂³×C₃₁	—	4	2	no	—
426	C₂³×C₃₁	—	4	2	no	—
427	C₂³×C₃₁	—	8	1	no	—
428	C₂³×C₃₁	—	8	1	no	—
429	C₂³×C₃₁	—	8	1	no	—
430	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
431	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
432	Q₈×C₃₁	—	2	2	no	—
433	Q₈×C₃₁	—	2	2	no	—
434	Q₈×C₃₁	—	2	2	no	—
435	Q₈×C₃₁	—	2	2	no	—
436	Q₈×C₃₁	—	2	2	no	—
437	Q₈×C₃₁	—	2	2	no	—
438	Q₈×C₃₁	—	4	1	no	—
439	Q₈×C₃₁	—	4	2	no	—
440	Q₈×C₃₁	—	8	1	no	—
441	Q₈×C₃₁	—	8	2	no	—
442	Q₈×C₃₁	—	8	1	no	—
443	Q₈×C₃₁	—	8	2	no	—
444	D₄×C₃₁	—	2	4	no	—
445	D₄×C₃₁	—	2	2	no	—
446	D₄×C₃₁	—	2	1	no	—
447	D₄×C₃₁	—	2	1	no	—
448	D₄×C₃₁	—	2	1	no	—
449	D₄×C₃₁	—	2	2	no	—
450	D₄×C₃₁	—	4	1	no	—
451	D₄×C₃₁	—	4	2	no	—
452	D₄×C₃₁	—	4	4	no	—
453	D₄×C₃₁	—	8	1	no	—
454	D₄×C₃₁	—	8	2	no	—
455	D₄×C₃₁	—	8	2	no	—
456	D₄×C₃₁	—	8	2	no	—
457	D₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄×C₃₁	—	2	2	no	—
459	C₂×C₄×C₃₁	—	2	1	no	—
460	C₂×C₄×C₃₁	—	2	2	no	—
461	C₂×C₄×C₃₁	—	2	1	no	—
462	C₂×C₄×C₃₁	—	2	2	no	—
463	C₂×C₄×C₃₁	—	2	2	no	—
464	C₂×C₄×C₃₁	—	2	2	no	—
465	C₂×C₄×C₃₁	—	2	1	no	—
466	C₂×C₄×C₃₁	—	2	2	no	—
467	C₂×C₄×C₃₁	—	2	2	no	—
468	C₂×C₄×C₃₁	—	2	2	no	—
469	C₂×C₄×C₃₁	—	2	1	no	—
470	C₂×C₄×C₃₁	—	4	1	no	—
471	C₂×C₄×C₃₁	—	4	4	no	—
472	C₂×C₄×C₃₁	—	4	2	no	—
473	C₂×C₄×C₃₁	—	4	2	no	—
474	C₂×C₄×C₃₁	—	8	2	no	—
475	C₂×C₄×C₃₁	—	8	1	no	—
476	C₂×C₄×C₃₁	—	8	1	no	—
477	C₂×C₄×C₃₁	—	8	2	no	—
478	C₂×C₄×C₃₁	—	8	2	no	—
479	C₂×C₄×C₃₁	—	8	1	no	—
480	C₂×C₄×C₃₁	—	8	2	no	—
481	C₂×C₄×C₃₁	—	8	1	no	—
482	C₂×C₄×C₃₁	—	8	2	no	—
483	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
486	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
492	C₈×C₃₁	—	2	2	no	—
493	C₈×C₃₁	—	2	2	no	—
494	C₈×C₃₁	—	2	2	no	—
495	C₈×C₃₁	—	2	2	no	—
496	#3561	C₂×C₃₁	1	1	yes	characteristic, complemented
497	#3520	C₂×C₃₁	1	1	yes	characteristic, complemented
498	#3402	C₂×C₃₁	1	2	yes	complemented
499	#3367	C₂×C₃₁	1	2	yes	complemented
500	#3314	C₂×C₃₁	1	2	yes	complemented
501	#3308	C₂×C₃₁	1	2	yes	complemented
502	#3299	C₂×C₃₁	1	2	yes	complemented
503	#3280	C₂×C₃₁	1	2	yes	complemented
504	#3269	C₂×C₃₁	1	2	yes	complemented
505	#3266	C₂×C₃₁	1	2	yes	complemented
506	#3262	C₂×C₃₁	1	2	yes	complemented
507	#3249	C₂×C₃₁	1	1	yes	characteristic, complemented
508	#3225	C₂×C₃₁	1	2	yes	complemented
509	#3215	C₂×C₃₁	1	1	yes	characteristic, complemented
510	#3124	C₂×C₃₁	1	2	yes	complemented
511	#3110	C₂×C₃₁	1	1	yes	characteristic, complemented
512	#3046	C₂×C₃₁	1	2	yes	complemented
513	C₂×#463	C₂×C₃₁	1	1	yes	characteristic, complemented
514	#2992	C₂×C₃₁	1	1	yes	characteristic, complemented
515	C₂²×C₃₁	—	2	1	no	—
516	C₂²×C₃₁	—	2	1	no	—
517	C₂²×C₃₁	—	2	2	no	—
518	C₂²×C₃₁	—	2	2	no	—
519	C₂²×C₃₁	—	2	2	no	—
520	C₂²×C₃₁	—	2	2	no	—
521	C₂²×C₃₁	—	4	1	no	—
522	C₂²×C₃₁	—	4	1	no	—
523	C₂²×C₃₁	—	4	1	no	—
524	C₂²×C₃₁	—	4	2	no	—
525	C₂²×C₃₁	—	4	2	no	—
526	C₂²×C₃₁	—	4	1	no	—
527	C₂²×C₃₁	—	4	1	no	—
528	C₂²×C₃₁	—	4	2	no	—
529	C₂²×C₃₁	—	8	4	no	—
530	C₂²×C₃₁	—	16	2	no	—
531	C₂²×C₃₁	#578	1	2	yes	—
532	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
533	C₄×C₃₁	—	2	1	no	—
534	C₄×C₃₁	—	2	1	no	—
535	C₄×C₃₁	—	2	2	no	—
536	C₄×C₃₁	—	2	2	no	—
537	C₄×C₃₁	—	2	1	no	—
538	C₄×C₃₁	—	2	1	no	—
539	C₄×C₃₁	—	2	1	no	—
540	C₄×C₃₁	—	2	2	no	—
541	C₄×C₃₁	—	4	1	no	—
542	C₄×C₃₁	—	4	1	no	—
543	C₄×C₃₁	—	4	2	no	—
544	C₄×C₃₁	—	4	2	no	—
545	C₄×C₃₁	—	4	2	no	—
546	C₄×C₃₁	—	4	2	no	—
547	C₄×C₃₁	—	4	2	no	—
548	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
549	C₄×C₃₁	#585	1	1	yes	characteristic
550	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
551	C₂×#135	C₂²×C₃₁	1	2	yes	—
552	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
553	C₂²×D₈	C₂²×C₃₁	1	1	yes	characteristic
554	#563	—	2	1	no	—
555	#562	—	2	1	no	—
556	#556	C₂²×C₃₁	1	2	yes	complemented
557	#556	C₂²×C₃₁	1	1	yes	characteristic, complemented
558	#554	C₂²×C₃₁	1	2	yes	—
559	#552	—	2	1	no	—
560	#551	—	2	2	no	—
561	#551	—	2	2	no	—
562	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
563	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
564	#548	—	2	1	no	—
565	#548	C₂²×C₃₁	1	2	yes	complemented
566	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
567	#547	C₂²×C₃₁	1	1	yes	characteristic, complemented
568	#546	C₂²×C₃₁	1	2	yes	—
569	#546	C₂²×C₃₁	1	2	yes	—
570	#543	—	2	1	no	—
571	#542	—	2	2	no	—
572	#542	C₂²×C₃₁	1	2	yes	complemented
573	#542	C₂²×C₃₁	1	2	yes	complemented
574	#539	—	2	2	no	—
575	#538	—	2	1	no	—
576	#536	C₂²×C₃₁	1	2	yes	complemented
577	#533	C₂²×C₃₁	1	1	yes	characteristic
578	#533	C₂²×C₃₁	1	1	yes	characteristic
579	#529	C₂²×C₃₁	1	1	yes	characteristic
580	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
581	#525	—	2	1	no	—
582	C₂×C₂²⋊Q₈	—	2	1	no	—
583	#520	C₂²×C₃₁	1	2	yes	complemented
584	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
585	#497	C₂²×C₃₁	1	2	yes	complemented
586	#497	C₂²×C₃₁	1	2	yes	complemented
587	#495	C₂²×C₃₁	1	2	yes	—
588	#489	C₂²×C₃₁	1	2	yes	complemented
589	#489	C₂²×C₃₁	1	2	yes	complemented
590	#487	C₂²×C₃₁	1	2	yes	complemented
591	#484	C₂²×C₃₁	1	2	yes	—
592	#484	C₂²×C₃₁	1	2	yes	complemented
593	#480	C₂²×C₃₁	1	2	yes	complemented
594	#477	C₂²×C₃₁	1	2	yes	complemented
595	#477	C₂²×C₃₁	1	2	yes	complemented
596	#477	C₂²×C₃₁	1	2	yes	complemented
597	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
598	#474	C₂²×C₃₁	1	1	yes	characteristic, complemented
599	#474	C₂²×C₃₁	1	2	yes	complemented
600	#468	C₂²×C₃₁	1	2	yes	complemented
601	#468	C₂²×C₃₁	1	2	yes	complemented
602	#467	C₂²×C₃₁	1	2	yes	—
603	#467	C₂²×C₃₁	1	2	yes	—
604	#467	C₂²×C₃₁	1	2	yes	complemented
605	#466	C₂²×C₃₁	1	2	yes	—
606	#464	C₂²×C₃₁	1	2	yes	complemented
607	#464	C₂²×C₃₁	1	2	yes	complemented
608	#464	C₂²×C₃₁	1	2	yes	complemented
609	#464	C₂²×C₃₁	1	2	yes	complemented
610	#463	C₂²×C₃₁	1	2	yes	—
611	#463	C₂²×C₃₁	1	2	yes	—
612	#463	C₂²×C₃₁	1	2	yes	—
613	#463	C₂²×C₃₁	1	2	yes	—
614	#463	C₂²×C₃₁	1	2	yes	—
615	#463	C₂²×C₃₁	1	2	yes	—
616	#462	C₂²×C₃₁	1	2	yes	complemented
617	#462	C₂²×C₃₁	1	2	yes	complemented
618	#462	C₂²×C₃₁	1	2	yes	complemented
619	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
620	#461	C₂²×C₃₁	1	1	yes	characteristic, complemented
621	#461	C₂²×C₃₁	1	2	yes	complemented
622	#452	C₂²×C₃₁	1	2	yes	complemented
623	#452	C₂²×C₃₁	1	2	yes	complemented
624	#451	C₂²×C₃₁	1	2	yes	—
625	#451	C₂²×C₃₁	1	2	yes	complemented
626	#450	C₂²×C₃₁	1	2	yes	—
627	#450	C₂²×C₃₁	1	2	yes	—
628	#449	C₂²×C₃₁	1	2	yes	—
629	#449	C₂²×C₃₁	1	2	yes	—
630	#448	C₂²×C₃₁	1	2	yes	complemented
631	#446	C₂²×C₃₁	1	2	yes	complemented
632	#440	C₂²×C₃₁	1	2	yes	complemented
633	#440	C₂²×C₃₁	1	2	yes	complemented
634	#440	C₂²×C₃₁	1	2	yes	complemented
635	#440	C₂²×C₃₁	1	2	yes	complemented
636	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
637	C₄×D₈	C₂²×C₃₁	1	2	yes	—
638	#435	C₂²×C₃₁	1	2	yes	—
639	#435	C₂²×C₃₁	1	2	yes	complemented
640	C₈×D₄	C₂²×C₃₁	1	2	yes	—
641	#433	C₂²×C₃₁	1	2	yes	complemented
642	#432	C₂²×C₃₁	1	1	yes	characteristic
643	#424	C₂²×C₃₁	1	2	yes	complemented
644	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
645	#417	C₂²×C₃₁	1	2	yes	complemented
646	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
647	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
648	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
649	C₂×C₃₁	—	2	2	no	—
650	C₂×C₃₁	—	4	2	no	—
651	C₂×C₃₁	—	4	2	no	—
652	C₂×C₃₁	—	8	1	no	—
653	C₂×C₃₁	—	8	2	no	—
654	C₂×C₃₁	#3488	1	1	yes	characteristic
655	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
656	C₂×C₃₁	#3585	1	1	yes	characteristic
657	C₂×#41	—	2	1	no	—
658	C₂×#41	C₂³×C₃₁	1	2	yes	—
659	C₂×#41	C₂³×C₃₁	1	2	yes	—
660	C₂²×Q₈	—	2	1	no	—
661	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
662	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
663	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
664	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
665	C₂³×C₄	—	2	1	no	—
666	#137	—	4	4	no	—
667	#135	—	4	4	no	—
668	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
669	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
670	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
671	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
672	C₂×SD₁₆	—	4	2	no	—
673	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
674	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
675	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
676	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
677	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
678	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
679	C₂×D₈	—	4	2	no	—
680	C₂×D₈	C₂³×C₃₁	1	2	yes	—
681	C₂×D₈	C₂³×C₃₁	1	2	yes	—
682	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
683	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
684	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
685	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
686	C₄⋊Q₈	—	2	2	no	—
687	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
688	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
689	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
690	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
691	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
692	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
693	#126	—	2	2	no	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	D₄×C₃₁	1	2	yes	—
699	#125	—	2	2	no	—
700	#125	—	2	1	no	—
701	#125	—	2	1	no	—
702	#125	D₄×C₃₁	1	1	yes	characteristic
703	#124	—	2	2	no	—
704	#124	—	2	2	no	—
705	#124	—	2	2	no	—
706	#124	—	2	1	no	—
707	#124	—	2	1	no	—
708	#124	D₄×C₃₁	1	1	yes	characteristic
709	#124	C₂³×C₃₁	1	2	yes	—
710	#124	C₂³×C₃₁	1	2	yes	—
711	#124	C₂³×C₃₁	1	2	yes	—
712	#124	C₂³×C₃₁	1	2	yes	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	D₄×C₃₁	1	2	yes	—
722	C₂²⋊Q₈	—	2	1	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	1	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	2	no	—
738	C₂²⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
739	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
740	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
741	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
742	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
743	#121	—	2	1	no	—
744	#121	—	2	2	no	—
745	#121	—	2	2	no	—
746	#121	—	2	2	no	—
747	#121	D₄×C₃₁	1	1	yes	characteristic
748	#121	C₂³×C₃₁	1	2	yes	—
749	#121	C₂³×C₃₁	1	2	yes	—
750	#120	—	2	2	no	—
751	#120	—	2	2	no	—
752	C₄×Q₈	—	2	1	no	—
753	C₄×Q₈	—	2	1	no	—
754	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
755	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
756	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
757	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
758	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
767	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
770	C₄×D₄	C₂³×C₃₁	1	2	yes	—
771	C₄×D₄	C₂³×C₃₁	1	2	yes	—
772	C₄×D₄	C₂³×C₃₁	1	2	yes	—
773	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
774	#117	—	2	1	no	—
775	#117	—	2	1	no	—
776	#117	—	2	2	no	—
777	#117	—	2	1	no	—
778	#117	—	2	2	no	—
779	#117	C₂³×C₃₁	1	2	yes	—
780	C₂×C₄⋊C₄	—	2	2	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
783	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
784	C₂×C₂²⋊C₄	—	2	1	no	—
785	C₂×C₂²⋊C₄	—	2	1	no	—
786	C₂×C₂²⋊C₄	—	2	1	no	—
787	C₂×C₂²⋊C₄	—	2	2	no	—
788	C₂×C₂²⋊C₄	—	2	2	no	—
789	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
790	#107	C₂³×C₃₁	1	2	yes	—
791	#107	C₂³×C₃₁	1	2	yes	—
792	#107	C₂³×C₃₁	1	2	yes	—
793	#107	C₂³×C₃₁	1	2	yes	—
794	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
795	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
796	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
797	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
798	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
799	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
800	#103	C₂³×C₃₁	1	2	yes	—
801	#103	C₂³×C₃₁	1	2	yes	—
802	#103	C₂³×C₃₁	1	2	yes	—
803	#103	C₂³×C₃₁	1	2	yes	—
804	#103	C₂³×C₃₁	1	2	yes	—
805	#103	C₂³×C₃₁	1	2	yes	—
806	#103	C₂³×C₃₁	1	2	yes	—
807	#103	C₂³×C₃₁	1	2	yes	—
808	#103	C₂³×C₃₁	1	2	yes	—
809	#103	C₂³×C₃₁	1	2	yes	—
810	#102	C₂³×C₃₁	1	2	yes	—
811	#102	C₂³×C₃₁	1	2	yes	—
812	#102	C₂³×C₃₁	1	2	yes	—
813	#102	C₂³×C₃₁	1	2	yes	—
814	#102	C₂³×C₃₁	1	2	yes	—
815	#102	C₂³×C₃₁	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
818	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
819	#97	C₂³×C₃₁	1	2	yes	—
820	#97	C₂³×C₃₁	1	2	yes	—
821	C₄×C₈	C₂³×C₃₁	1	2	yes	—
822	C₃₁	#62017	1	1	yes	characteristic, direct product factor, Sylow
823	C₂⁴	—	2	1	no	—
824	C₂⁴	—	2	1	no	—
825	#41	—	2	4	no	—
826	#41	—	4	2	no	—
827	#41	—	4	2	no	—
828	#41	—	4	2	no	—
829	#41	—	8	2	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	2	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	4	1	no	—
836	C₂×Q₈	—	4	2	no	—
837	C₂×Q₈	—	4	1	no	—
838	C₂×Q₈	—	4	2	no	—
839	C₂×Q₈	—	8	2	no	—
840	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
841	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
842	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
843	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	1	no	—
851	C₂×D₄	—	4	1	no	—
852	C₂×D₄	—	4	1	no	—
853	C₂×D₄	—	4	1	no	—
854	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
855	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
856	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
857	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
858	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	1	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	1	no	—
871	C₂²×C₄	—	8	2	no	—
872	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
873	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
876	Q₁₆	—	4	2	no	—
877	Q₁₆	—	4	2	no	—
878	Q₁₆	—	4	2	no	—
879	Q₁₆	—	4	2	no	—
880	SD₁₆	—	2	4	no	—
881	SD₁₆	—	2	4	no	—
882	SD₁₆	—	4	2	no	—
883	SD₁₆	—	4	2	no	—
884	SD₁₆	—	4	2	no	—
885	SD₁₆	—	4	2	no	—
886	D₈	—	2	4	no	—
887	D₈	—	4	2	no	—
888	M₁₆	—	4	2	no	—
889	C₂×C₈	—	4	1	no	—
890	C₂×C₈	—	4	1	no	—
891	C₂×C₈	—	4	2	no	—
892	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
893	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
894	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
895	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	1	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
918	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
920	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
921	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	1	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	1	no	—
933	C₂²⋊C₄	—	2	1	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
946	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
947	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
948	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
949	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
955	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
956	C₄²	C₂⁴×C₃₁	1	2	yes	—
957	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
958	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
959	C₂³	—	2	1	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	1	no	—
962	C₂³	—	4	2	no	—
963	C₂³	—	4	2	no	—
964	C₂³	—	4	2	no	—
965	C₂³	—	8	1	no	—
966	C₂³	—	8	1	no	—
967	C₂³	—	8	1	no	—
968	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
969	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	2	2	no	—
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	4	1	no	—
977	Q₈	—	4	2	no	—
978	Q₈	—	8	1	no	—
979	Q₈	—	8	2	no	—
980	Q₈	—	8	1	no	—
981	Q₈	—	8	2	no	—
982	D₄	—	2	4	no	—
983	D₄	—	2	2	no	—
984	D₄	—	2	1	no	—
985	D₄	—	2	1	no	—
986	D₄	—	2	1	no	—
987	D₄	—	2	2	no	—
988	D₄	—	4	1	no	—
989	D₄	—	4	2	no	—
990	D₄	—	4	4	no	—
991	D₄	—	8	1	no	—
992	D₄	—	8	2	no	—
993	D₄	—	8	2	no	—
994	D₄	—	8	2	no	—
995	D₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	4	1	no	—
1009	C₂×C₄	—	4	4	no	—
1010	C₂×C₄	—	4	2	no	—
1011	C₂×C₄	—	4	2	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	8	1	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	8	2	no	—
1017	C₂×C₄	—	8	1	no	—
1018	C₂×C₄	—	8	2	no	—
1019	C₂×C₄	—	8	1	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1024	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1026	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1027	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1028	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1029	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1030	C₈	—	2	2	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₈	—	2	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	2	2	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	8	4	no	—
1049	C₂²	—	16	2	no	—
1050	C₂²	C₃₁×#578	1	2	yes	—
1051	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1052	C₄	—	2	2	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	2	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1068	C₄	C₃₁×#585	1	1	yes	characteristic
1069	C₂	—	2	2	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	4	2	no	—
1072	C₂	—	8	1	no	—
1073	C₂	—	8	2	no	—
1074	C₂	C₃₁×#3488	1	1	yes	characteristic
1075	C₂	C₂×C₃₁×#578	1	1	yes	characteristic
1076	C₂	C₃₁×#3585	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×#3561	C₂	semidirect
2. C₃₁×#3520	C₂	semidirect
3. C₃₁×#3402	C₂	semidirect
4. C₃₁×#3367	C₂	semidirect
5. C₃₁×#3314	C₂	semidirect
6. C₃₁×#3308	C₂	semidirect
7. C₃₁×#3299	C₂	semidirect
8. C₃₁×#3280	C₂	semidirect
9. C₃₁×#3269	C₂	semidirect
10. C₃₁×#3266	C₂	semidirect
11. C₃₁×#3262	C₂	semidirect
12. C₃₁×#3249	C₂	semidirect
13. C₃₁×#3225	C₂	semidirect
14. C₃₁×#3215	C₂	semidirect
15. C₃₁×#3124	C₂	semidirect
16. C₃₁×#3110	C₂	semidirect
17. C₃₁×#3046	C₂	semidirect
18. C₂×C₃₁×#463	C₂	semidirect
19. C₃₁×#2992	C₂	semidirect
20. C₂×C₃₁×#137	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
27. C₃₁×#556	C₂²	semidirect
33. D₄×Q₈×C₃₁	C₂²	semidirect
35. C₃₁×#548	C₂²	semidirect
36. C₃₁×#547	C₂²	semidirect
37. C₃₁×#547	C₂²	semidirect
42. C₃₁×#542	C₂²	semidirect
43. C₃₁×#542	C₂²	semidirect
46. C₃₁×#536	C₂²	semidirect
53. C₃₁×#520	C₂²	semidirect
55. C₃₁×#497	C₂²	semidirect
56. C₃₁×#497	C₂²	semidirect
58. C₃₁×#489	C₂²	semidirect
59. C₃₁×#489	C₂²	semidirect
60. C₃₁×#487	C₂²	semidirect
62. C₃₁×#484	C₂²	semidirect
63. C₃₁×#480	C₂²	semidirect
64. C₃₁×#477	C₂²	semidirect
65. C₃₁×#477	C₂²	semidirect
66. C₃₁×#477	C₂²	semidirect
67. C₃₁×#474	C₂²	semidirect
68. C₃₁×#474	C₂²	semidirect
69. C₃₁×#474	C₂²	semidirect
70. C₃₁×#468	C₂²	semidirect
71. C₃₁×#468	C₂²	semidirect
74. C₃₁×#467	C₂²	semidirect
76. C₃₁×#464	C₂²	semidirect
77. C₃₁×#464	C₂²	semidirect
78. C₃₁×#464	C₂²	semidirect
79. C₃₁×#464	C₂²	semidirect
86. C₃₁×#462	C₂²	semidirect
87. C₃₁×#462	C₂²	semidirect
88. C₃₁×#462	C₂²	semidirect
89. C₃₁×#461	C₂²	semidirect
90. C₃₁×#461	C₂²	semidirect
91. C₃₁×#461	C₂²	semidirect
92. C₃₁×#452	C₂²	semidirect
93. C₃₁×#452	C₂²	semidirect
95. C₃₁×#451	C₂²	semidirect
100. C₃₁×#448	C₂²	semidirect
101. C₃₁×#446	C₂²	semidirect
102. C₃₁×#440	C₂²	semidirect
103. C₃₁×#440	C₂²	semidirect
104. C₃₁×#440	C₂²	semidirect
105. C₃₁×#440	C₂²	semidirect
106. C₄×Q₁₆×C₃₁	C₂²	semidirect
109. C₃₁×#435	C₂²	semidirect
111. C₃₁×#433	C₂²	semidirect
113. C₃₁×#424	C₂²	semidirect
115. C₃₁×#417	C₂²	semidirect
117. C₂×C₃₁×#103	C₂²	semidirect
420. #62017	C₃₁	direct (N × H)
496. #3561	C₂×C₃₁	semidirect
497. #3520	C₂×C₃₁	semidirect
498. #3402	C₂×C₃₁	semidirect
499. #3367	C₂×C₃₁	semidirect
500. #3314	C₂×C₃₁	semidirect
501. #3308	C₂×C₃₁	semidirect
502. #3299	C₂×C₃₁	semidirect
503. #3280	C₂×C₃₁	semidirect
504. #3269	C₂×C₃₁	semidirect
505. #3266	C₂×C₃₁	semidirect
506. #3262	C₂×C₃₁	semidirect
507. #3249	C₂×C₃₁	semidirect
508. #3225	C₂×C₃₁	semidirect
509. #3215	C₂×C₃₁	semidirect
510. #3124	C₂×C₃₁	semidirect
511. #3110	C₂×C₃₁	semidirect
512. #3046	C₂×C₃₁	semidirect
513. C₂×#463	C₂×C₃₁	semidirect
514. #2992	C₂×C₃₁	semidirect
550. C₂×#137	C₂²×C₃₁	semidirect
556. #556	C₂²×C₃₁	semidirect
557. #556	C₂²×C₃₁	semidirect
563. D₄×Q₈	C₂²×C₃₁	semidirect
565. #548	C₂²×C₃₁	semidirect
566. #547	C₂²×C₃₁	semidirect
567. #547	C₂²×C₃₁	semidirect
572. #542	C₂²×C₃₁	semidirect
573. #542	C₂²×C₃₁	semidirect
576. #536	C₂²×C₃₁	semidirect
583. #520	C₂²×C₃₁	semidirect
585. #497	C₂²×C₃₁	semidirect
586. #497	C₂²×C₃₁	semidirect
588. #489	C₂²×C₃₁	semidirect
589. #489	C₂²×C₃₁	semidirect
590. #487	C₂²×C₃₁	semidirect
592. #484	C₂²×C₃₁	semidirect
593. #480	C₂²×C₃₁	semidirect
594. #477	C₂²×C₃₁	semidirect
595. #477	C₂²×C₃₁	semidirect
596. #477	C₂²×C₃₁	semidirect
597. #474	C₂²×C₃₁	semidirect
598. #474	C₂²×C₃₁	semidirect
599. #474	C₂²×C₃₁	semidirect
600. #468	C₂²×C₃₁	semidirect
601. #468	C₂²×C₃₁	semidirect
604. #467	C₂²×C₃₁	semidirect
606. #464	C₂²×C₃₁	semidirect
607. #464	C₂²×C₃₁	semidirect
608. #464	C₂²×C₃₁	semidirect
609. #464	C₂²×C₃₁	semidirect
616. #462	C₂²×C₃₁	semidirect
617. #462	C₂²×C₃₁	semidirect
618. #462	C₂²×C₃₁	semidirect
619. #461	C₂²×C₃₁	semidirect
620. #461	C₂²×C₃₁	semidirect
621. #461	C₂²×C₃₁	semidirect
622. #452	C₂²×C₃₁	semidirect
623. #452	C₂²×C₃₁	semidirect
625. #451	C₂²×C₃₁	semidirect
630. #448	C₂²×C₃₁	semidirect
631. #446	C₂²×C₃₁	semidirect
632. #440	C₂²×C₃₁	semidirect
633. #440	C₂²×C₃₁	semidirect
634. #440	C₂²×C₃₁	semidirect
635. #440	C₂²×C₃₁	semidirect
636. C₄×Q₁₆	C₂²×C₃₁	semidirect
639. #435	C₂²×C₃₁	semidirect
641. #433	C₂²×C₃₁	semidirect
643. #424	C₂²×C₃₁	semidirect
645. #417	C₂²×C₃₁	semidirect
647. C₂×#103	C₂²×C₃₁	semidirect
822. C₃₁	#62017	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×#3561	2
C₃₁×#3520	2
C₃₁×#3402	2
C₃₁×#3367	2
C₃₁×#3314	2
C₃₁×#3308	2
C₃₁×#3299	2
C₃₁×#3280	2
C₃₁×#3269	2
C₃₁×#3266	2
C₃₁×#3262	2
C₃₁×#3249	2
C₃₁×#3225	2
C₃₁×#3215	2
C₃₁×#3124	2
C₃₁×#3110	2
C₃₁×#3046	2
C₂×C₃₁×#463	2
C₃₁×#2992	2
#62017	31

Subgroups — C31×#62017 #21518776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#62017 #21518776