Subgroups — C₃₁×#61457 #21518216

Order 7936.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3482	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3344	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3316	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3312	C₂	1	2	yes	maximal, complemented
11	C₃₁×#3299	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3270	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×#3181	C₂	1	2	yes	maximal, complemented
17	C₃₁×#3117	C₂	1	2	yes	maximal, complemented
18	C₃₁×#3116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₃₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
20	C₃₁×#3113	C₂	1	2	yes	maximal, complemented
21	C₃₁×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₃₁×#441	C₂	1	2	yes	maximal, complemented
24	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
26	Q₈²×C₃₁	C₂²	1	1	yes	characteristic
27	C₃₁×#557	—	2	1	no	—
28	C₃₁×#557	C₂²	1	1	yes	characteristic
29	C₃₁×#557	C₂²	1	1	yes	characteristic
30	C₃₁×#556	—	2	1	no	—
31	C₃₁×#556	C₂²	1	1	yes	characteristic
32	C₃₁×#554	—	2	1	no	—
33	C₃₁×#554	—	2	2	no	—
34	C₃₁×#554	C₂²	1	1	yes	characteristic
35	C₃₁×#554	C₂²	1	2	yes	—
36	C₃₁×#552	—	2	2	no	—
37	C₃₁×#552	C₂²	1	2	yes	—
38	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
39	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
41	C₃₁×#548	C₂²	1	2	yes	—
42	C₃₁×#547	—	2	1	no	—
43	C₃₁×#547	C₂²	1	1	yes	characteristic
44	C₃₁×#533	—	2	1	no	—
45	C₃₁×#533	—	2	2	no	—
46	C₃₁×#533	—	2	1	no	—
47	C₃₁×#533	C₂²	1	2	yes	—
48	C₃₁×#533	C₂²	1	1	yes	characteristic
49	C₃₁×#533	C₂²	1	1	yes	characteristic
50	C₃₁×#529	—	2	2	no	—
51	C₃₁×#529	C₂²	1	2	yes	—
52	C₄×#41×C₃₁	—	2	1	no	—
53	C₄×#41×C₃₁	—	2	1	no	—
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
59	C₃₁×#501	C₂²	1	2	yes	—
60	C₃₁×#498	C₂²	1	1	yes	characteristic
61	C₃₁×#497	C₂²	1	2	yes	—
62	C₃₁×#494	C₂²	1	1	yes	characteristic
63	C₃₁×#491	C₂²	1	2	yes	—
64	C₃₁×#489	C₂²	1	2	yes	—
65	C₃₁×#487	C₂²	1	1	yes	characteristic
66	C₃₁×#487	C₂²	1	1	yes	characteristic
67	C₃₁×#485	C₂²	1	2	yes	—
68	C₃₁×#484	C₂²	1	2	yes	—
69	C₃₁×#483	C₂²	1	2	yes	—
70	C₃₁×#483	C₂²	1	2	yes	—
71	C₃₁×#483	C₂²	1	2	yes	—
72	C₃₁×#481	C₂²	1	2	yes	—
73	C₃₁×#479	C₂²	1	2	yes	—
74	C₃₁×#479	C₂²	1	2	yes	—
75	C₃₁×#477	C₂²	1	1	yes	characteristic
76	C₃₁×#476	C₂²	1	1	yes	characteristic
77	C₃₁×#475	C₂²	1	1	yes	characteristic
78	C₃₁×#475	C₂²	1	2	yes	—
79	C₃₁×#475	C₂²	1	1	yes	characteristic
80	C₃₁×#475	C₂²	1	2	yes	—
81	C₃₁×#470	C₂²	1	2	yes	—
82	C₃₁×#470	C₂²	1	2	yes	—
83	C₃₁×#467	C₂²	1	2	yes	—
84	C₃₁×#467	C₂²	1	2	yes	—
85	C₃₁×#465	C₂²	1	2	yes	—
86	C₃₁×#465	C₂²	1	2	yes	—
87	C₃₁×#464	C₂²	1	2	yes	—
88	C₃₁×#464	C₂²	1	2	yes	—
89	C₃₁×#462	C₂²	1	1	yes	characteristic
90	C₃₁×#462	C₂²	1	2	yes	—
91	C₃₁×#462	C₂²	1	1	yes	characteristic
92	C₃₁×#462	C₂²	1	2	yes	—
93	C₃₁×#462	C₂²	1	1	yes	characteristic
94	C₃₁×#461	C₂²	1	1	yes	characteristic
95	C₃₁×#452	C₂²	1	2	yes	—
96	C₃₁×#451	C₂²	1	2	yes	—
97	C₃₁×#451	C₂²	1	2	yes	—
98	C₃₁×#451	C₂²	1	2	yes	—
99	C₃₁×#451	C₂²	1	2	yes	—
100	C₃₁×#448	C₂²	1	2	yes	—
101	C₃₁×#446	C₂²	1	1	yes	characteristic
102	C₃₁×#446	C₂²	1	1	yes	characteristic
103	C₃₁×#441	C₂²	1	2	yes	—
104	C₃₁×#441	C₂²	1	2	yes	—
105	C₃₁×#441	C₂²	1	1	yes	characteristic
106	C₃₁×#441	C₂²	1	2	yes	—
107	C₃₁×#441	C₂²	1	2	yes	—
108	C₃₁×#441	C₂²	1	2	yes	—
109	C₃₁×#441	C₂²	1	2	yes	—
110	C₃₁×#441	C₂²	1	2	yes	—
111	C₃₁×#441	C₂²	1	2	yes	—
112	C₃₁×#441	C₂²	1	2	yes	—
113	C₃₁×#441	C₂²	1	1	yes	characteristic
114	C₃₁×#440	C₂²	1	2	yes	—
115	C₃₁×#440	C₂²	1	1	yes	characteristic
116	C₃₁×#440	C₂²	1	1	yes	characteristic
117	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
118	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
119	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
121	C₃₁×#435	C₂²	1	2	yes	—
122	C₃₁×#435	C₂²	1	2	yes	—
123	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
125	C₃₁×#432	C₂²	1	1	yes	characteristic
126	C₃₁×#432	C₂²	1	2	yes	—
127	C₃₁×#428	C₂²	1	1	yes	characteristic
128	C₂×C₃₁×#106	C₂²	1	2	yes	—
129	C₃₁×#419	C₂²	1	1	yes	characteristic
130	C₃₁×#417	C₂²	1	1	yes	characteristic
131	C₂×C₃₁×#103	C₂²	1	2	yes	—
132	C₂×C₃₁×#103	C₂²	1	2	yes	—
133	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
134	C₂×C₃₁×#97	C₂²	1	2	yes	—
135	C₂×#41×C₃₁	—	2	1	no	—
136	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
137	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
139	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
140	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₃₁×#137	—	2	4	no	—
142	C₂×Q₁₆×C₃₁	—	2	8	no	—
143	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
144	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
153	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
155	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
156	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
157	C₃₁×C₄⋊Q₈	—	2	1	no	—
158	C₃₁×C₄⋊Q₈	—	2	1	no	—
159	C₃₁×C₄⋊Q₈	—	2	2	no	—
160	C₃₁×C₄⋊Q₈	—	2	1	no	—
161	C₃₁×C₄⋊Q₈	—	2	1	no	—
162	C₃₁×C₄⋊Q₈	—	2	2	no	—
163	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
169	C₃₁×#126	—	2	2	no	—
170	C₃₁×#126	—	2	2	no	—
171	C₃₁×#126	—	2	2	no	—
172	C₃₁×#125	—	2	2	no	—
173	C₃₁×#125	—	2	2	no	—
174	C₃₁×#125	—	2	1	no	—
175	C₃₁×#125	—	2	2	no	—
176	C₃₁×#125	—	2	2	no	—
177	C₃₁×#125	—	2	1	no	—
178	C₃₁×#125	—	2	1	no	—
179	C₃₁×#125	—	2	1	no	—
180	C₃₁×#125	—	2	2	no	—
181	C₃₁×#125	C₂³	1	2	yes	—
182	C₃₁×#124	—	2	2	no	—
183	C₃₁×#124	C₂³	1	2	yes	—
184	C₃₁×#123	—	2	2	no	—
185	C₃₁×#123	—	2	2	no	—
186	C₃₁×#123	—	2	2	no	—
187	C₃₁×C₂²⋊Q₈	—	2	1	no	—
188	C₃₁×C₂²⋊Q₈	—	2	1	no	—
189	C₃₁×C₂²⋊Q₈	—	2	2	no	—
190	C₃₁×C₂²⋊Q₈	—	2	1	no	—
191	C₃₁×C₂²⋊Q₈	—	2	1	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	C₂³	1	2	yes	—
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	2	no	—
206	C₃₁×#121	C₂³	1	2	yes	—
207	C₄×Q₈×C₃₁	—	2	1	no	—
208	C₄×Q₈×C₃₁	—	2	1	no	—
209	C₄×Q₈×C₃₁	—	2	1	no	—
210	C₄×Q₈×C₃₁	—	2	2	no	—
211	C₄×Q₈×C₃₁	—	2	1	no	—
212	C₄×Q₈×C₃₁	—	2	2	no	—
213	C₄×Q₈×C₃₁	—	2	2	no	—
214	C₄×Q₈×C₃₁	—	2	1	no	—
215	C₄×Q₈×C₃₁	—	2	2	no	—
216	C₄×Q₈×C₃₁	—	2	1	no	—
217	C₄×Q₈×C₃₁	—	2	1	no	—
218	C₄×Q₈×C₃₁	—	2	2	no	—
219	C₄×Q₈×C₃₁	D₄	1	1	yes	characteristic
220	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
225	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
228	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
229	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
230	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
231	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
232	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₃₁	—	2	1	no	—
234	C₄×D₄×C₃₁	—	2	2	no	—
235	C₄×D₄×C₃₁	—	2	1	no	—
236	C₄×D₄×C₃₁	—	2	2	no	—
237	C₄×D₄×C₃₁	—	2	1	no	—
238	C₄×D₄×C₃₁	—	2	2	no	—
239	C₄×D₄×C₃₁	—	2	1	no	—
240	C₄×D₄×C₃₁	—	2	1	no	—
241	C₄×D₄×C₃₁	—	2	2	no	—
242	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
243	C₄×D₄×C₃₁	D₄	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	1	yes	characteristic
247	C₄×D₄×C₃₁	C₂³	1	2	yes	—
248	C₃₁×#117	—	2	2	no	—
249	C₃₁×#117	—	2	1	no	—
250	C₃₁×#117	—	2	1	no	—
251	C₃₁×#117	—	2	1	no	—
252	C₃₁×#117	—	2	2	no	—
253	C₃₁×#117	—	2	1	no	—
254	C₃₁×#117	—	2	2	no	—
255	C₃₁×#117	D₄	1	2	yes	—
256	C₃₁×#117	D₄	1	1	yes	characteristic
257	C₃₁×#117	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
259	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
260	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
261	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
264	C₂×C₄²×C₃₁	—	2	2	no	—
265	C₂×C₄²×C₃₁	—	2	2	no	—
266	C₂×C₄²×C₃₁	—	2	1	no	—
267	C₂×C₄²×C₃₁	—	2	1	no	—
268	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
269	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
270	C₃₁×#107	C₂³	1	1	yes	characteristic
271	C₃₁×#107	C₂³	1	1	yes	characteristic
272	C₃₁×#107	C₂³	1	2	yes	—
273	C₃₁×#106	C₂³	1	1	yes	characteristic
274	C₃₁×#106	C₂³	1	2	yes	—
275	C₃₁×#106	C₂³	1	2	yes	—
276	C₃₁×#106	C₂³	1	2	yes	—
277	C₃₁×#106	C₂³	1	1	yes	characteristic
278	C₃₁×#106	C₂³	1	2	yes	—
279	C₃₁×#106	C₂³	1	2	yes	—
280	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
283	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
284	C₃₁×#103	C₂³	1	1	yes	characteristic
285	C₃₁×#103	C₂³	1	1	yes	characteristic
286	C₃₁×#103	C₂³	1	2	yes	—
287	C₃₁×#103	C₂³	1	2	yes	—
288	C₃₁×#103	C₂³	1	2	yes	—
289	C₃₁×#103	C₂³	1	2	yes	—
290	C₃₁×#103	C₂³	1	2	yes	—
291	C₃₁×#103	C₂³	1	2	yes	—
292	C₃₁×#103	C₂³	1	1	yes	characteristic
293	C₃₁×#103	C₂³	1	1	yes	characteristic
294	C₃₁×#103	C₂³	1	1	yes	characteristic
295	C₃₁×#103	C₂³	1	1	yes	characteristic
296	C₃₁×#103	C₂³	1	2	yes	—
297	C₃₁×#103	C₂³	1	2	yes	—
298	C₃₁×#103	C₂³	1	2	yes	—
299	C₃₁×#103	C₂³	1	2	yes	—
300	C₃₁×#103	C₂³	1	2	yes	—
301	C₃₁×#102	C₂³	1	1	yes	characteristic
302	C₃₁×#102	C₂³	1	1	yes	characteristic
303	C₃₁×#102	C₂³	1	2	yes	—
304	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₃₁×#97	C₂³	1	1	yes	characteristic
308	C₃₁×#97	C₂³	1	2	yes	—
309	C₃₁×#97	C₂³	1	2	yes	—
310	C₃₁×#97	C₂³	1	2	yes	—
311	C₃₁×#97	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
314	#41×C₃₁	—	2	4	no	—
315	#41×C₃₁	—	2	2	no	—
316	#41×C₃₁	—	4	1	no	—
317	#41×C₃₁	—	4	4	no	—
318	C₂×Q₈×C₃₁	—	2	2	no	—
319	C₂×Q₈×C₃₁	—	2	1	no	—
320	C₂×Q₈×C₃₁	—	2	2	no	—
321	C₂×Q₈×C₃₁	—	2	1	no	—
322	C₂×Q₈×C₃₁	—	2	2	no	—
323	C₂×Q₈×C₃₁	—	2	1	no	—
324	C₂×Q₈×C₃₁	—	2	4	no	—
325	C₂×Q₈×C₃₁	—	2	4	no	—
326	C₂×Q₈×C₃₁	—	2	2	no	—
327	C₂×Q₈×C₃₁	—	4	2	no	—
328	C₂×Q₈×C₃₁	—	4	2	no	—
329	C₂×Q₈×C₃₁	—	4	1	no	—
330	C₂×Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₃₁	—	2	1	no	—
337	C₂×D₄×C₃₁	—	2	2	no	—
338	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
339	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₃₁	—	2	2	no	—
342	C₂²×C₄×C₃₁	—	2	2	no	—
343	C₂²×C₄×C₃₁	—	2	1	no	—
344	C₂²×C₄×C₃₁	—	2	2	no	—
345	C₂²×C₄×C₃₁	—	2	1	no	—
346	C₂²×C₄×C₃₁	—	2	2	no	—
347	C₂²×C₄×C₃₁	—	2	1	no	—
348	C₂²×C₄×C₃₁	—	2	1	no	—
349	C₂²×C₄×C₃₁	—	2	1	no	—
350	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
351	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
355	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
356	Q₁₆×C₃₁	—	2	4	no	—
357	Q₁₆×C₃₁	—	2	4	no	—
358	Q₁₆×C₃₁	—	2	2	no	—
359	Q₁₆×C₃₁	—	2	4	no	—
360	Q₁₆×C₃₁	—	4	2	no	—
361	Q₁₆×C₃₁	—	4	2	no	—
362	Q₁₆×C₃₁	#41	1	4	yes	complemented
363	SD₁₆×C₃₁	—	2	2	no	—
364	SD₁₆×C₃₁	—	2	2	no	—
365	SD₁₆×C₃₁	—	4	2	no	—
366	M₁₆×C₃₁	—	2	2	no	—
367	M₁₆×C₃₁	—	4	1	no	—
368	C₂×C₈×C₃₁	—	2	4	no	—
369	C₂×C₈×C₃₁	—	4	2	no	—
370	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
374	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
375	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₃₁	—	2	1	no	—
377	C₄⋊C₄×C₃₁	—	2	1	no	—
378	C₄⋊C₄×C₃₁	—	2	2	no	—
379	C₄⋊C₄×C₃₁	—	2	2	no	—
380	C₄⋊C₄×C₃₁	—	2	1	no	—
381	C₄⋊C₄×C₃₁	—	2	2	no	—
382	C₄⋊C₄×C₃₁	—	2	1	no	—
383	C₄⋊C₄×C₃₁	—	2	2	no	—
384	C₄⋊C₄×C₃₁	—	2	1	no	—
385	C₄⋊C₄×C₃₁	—	2	2	no	—
386	C₄⋊C₄×C₃₁	—	2	2	no	—
387	C₄⋊C₄×C₃₁	—	2	1	no	—
388	C₄⋊C₄×C₃₁	—	2	2	no	—
389	C₄⋊C₄×C₃₁	—	2	2	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	1	no	—
396	C₄⋊C₄×C₃₁	—	2	2	no	—
397	C₄⋊C₄×C₃₁	—	2	1	no	—
398	C₄⋊C₄×C₃₁	—	2	1	no	—
399	C₄⋊C₄×C₃₁	—	2	2	no	—
400	C₄⋊C₄×C₃₁	—	2	1	no	—
401	C₄⋊C₄×C₃₁	—	2	2	no	—
402	C₄⋊C₄×C₃₁	—	2	2	no	—
403	C₄⋊C₄×C₃₁	—	2	1	no	—
404	C₄⋊C₄×C₃₁	—	2	2	no	—
405	C₄⋊C₄×C₃₁	—	2	2	no	—
406	C₄⋊C₄×C₃₁	—	2	2	no	—
407	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
409	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
410	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
414	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
417	C₂²⋊C₄×C₃₁	—	2	2	no	—
418	C₂²⋊C₄×C₃₁	—	2	2	no	—
419	C₂²⋊C₄×C₃₁	—	2	2	no	—
420	C₂²⋊C₄×C₃₁	—	2	2	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	C₂×D₄	1	2	yes	—
429	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
430	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
431	C₄²×C₃₁	—	2	1	no	—
432	C₄²×C₃₁	—	2	1	no	—
433	C₄²×C₃₁	—	2	1	no	—
434	C₄²×C₃₁	—	2	2	no	—
435	C₄²×C₃₁	—	2	2	no	—
436	C₄²×C₃₁	—	2	1	no	—
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	—	2	1	no	—
442	C₄²×C₃₁	—	2	2	no	—
443	C₄²×C₃₁	—	2	1	no	—
444	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
445	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
446	C₄²×C₃₁	C₂×D₄	1	2	yes	—
447	C₄²×C₃₁	C₂×D₄	1	2	yes	—
448	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
449	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
450	C₄²×C₃₁	C₂⁴	1	2	yes	—
451	#61457	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂³×C₃₁	—	2	1	no	—
453	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
455	Q₈×C₃₁	—	2	2	no	—
456	Q₈×C₃₁	—	2	1	no	—
457	Q₈×C₃₁	—	2	1	no	—
458	Q₈×C₃₁	—	2	1	no	—
459	Q₈×C₃₁	—	2	2	no	—
460	Q₈×C₃₁	—	2	2	no	—
461	Q₈×C₃₁	—	2	2	no	—
462	Q₈×C₃₁	—	2	2	no	—
463	Q₈×C₃₁	—	2	1	no	—
464	Q₈×C₃₁	—	4	2	no	—
465	Q₈×C₃₁	—	4	4	no	—
466	Q₈×C₃₁	—	4	4	no	—
467	Q₈×C₃₁	—	4	2	no	—
468	Q₈×C₃₁	—	8	2	no	—
469	Q₈×C₃₁	—	8	1	no	—
470	Q₈×C₃₁	C₂×#41	1	2	yes	—
471	Q₈×C₃₁	C₂×#41	1	2	yes	—
472	D₄×C₃₁	—	2	4	no	—
473	D₄×C₃₁	—	2	1	no	—
474	D₄×C₃₁	—	2	1	no	—
475	D₄×C₃₁	—	4	2	no	—
476	D₄×C₃₁	—	4	4	no	—
477	D₄×C₃₁	#137	1	4	yes	complemented
478	C₂×C₄×C₃₁	—	2	4	no	—
479	C₂×C₄×C₃₁	—	2	1	no	—
480	C₂×C₄×C₃₁	—	2	1	no	—
481	C₂×C₄×C₃₁	—	2	2	no	—
482	C₂×C₄×C₃₁	—	2	2	no	—
483	C₂×C₄×C₃₁	—	2	1	no	—
484	C₂×C₄×C₃₁	—	2	2	no	—
485	C₂×C₄×C₃₁	—	2	1	no	—
486	C₂×C₄×C₃₁	—	2	1	no	—
487	C₂×C₄×C₃₁	—	2	1	no	—
488	C₂×C₄×C₃₁	—	2	1	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	2	no	—
493	C₂×C₄×C₃₁	—	2	2	no	—
494	C₂×C₄×C₃₁	—	2	1	no	—
495	C₂×C₄×C₃₁	—	4	2	no	—
496	C₂×C₄×C₃₁	—	4	1	no	—
497	C₂×C₄×C₃₁	—	4	2	no	—
498	C₂×C₄×C₃₁	—	4	4	no	—
499	C₂×C₄×C₃₁	—	4	4	no	—
500	C₂×C₄×C₃₁	—	4	2	no	—
501	C₂×C₄×C₃₁	—	4	2	no	—
502	C₂×C₄×C₃₁	—	4	4	no	—
503	C₂×C₄×C₃₁	—	4	2	no	—
504	C₂×C₄×C₃₁	—	8	2	no	—
505	C₂×C₄×C₃₁	—	8	1	no	—
506	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
515	C₈×C₃₁	—	2	2	no	—
516	C₈×C₃₁	—	2	1	no	—
517	C₈×C₃₁	—	2	1	no	—
518	C₈×C₃₁	—	2	2	no	—
519	C₈×C₃₁	—	2	1	no	—
520	C₈×C₃₁	C₂×#41	1	2	yes	—
521	#3482	C₂×C₃₁	1	1	yes	characteristic
522	Q₈×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
523	#3398	C₂×C₃₁	1	1	yes	characteristic, complemented
524	#3387	C₂×C₃₁	1	1	yes	characteristic, complemented
525	#3374	C₂×C₃₁	1	1	yes	characteristic, complemented
526	#3369	C₂×C₃₁	1	1	yes	characteristic, complemented
527	#3344	C₂×C₃₁	1	2	yes	complemented
528	#3335	C₂×C₃₁	1	1	yes	characteristic, complemented
529	#3316	C₂×C₃₁	1	2	yes	complemented
530	#3312	C₂×C₃₁	1	2	yes	complemented
531	#3299	C₂×C₃₁	1	1	yes	characteristic, complemented
532	#3298	C₂×C₃₁	1	1	yes	characteristic, complemented
533	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
534	#3270	C₂×C₃₁	1	2	yes	complemented
535	#3185	C₂×C₃₁	1	1	yes	characteristic, complemented
536	#3181	C₂×C₃₁	1	2	yes	complemented
537	#3117	C₂×C₃₁	1	2	yes	complemented
538	#3116	C₂×C₃₁	1	1	yes	characteristic, complemented
539	#3113	C₂×C₃₁	1	2	yes	complemented
540	#3113	C₂×C₃₁	1	1	yes	characteristic, complemented
541	#2970	C₂×C₃₁	1	1	yes	characteristic, complemented
542	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
543	C₂×#441	C₂×C₃₁	1	2	yes	complemented
544	C₂²×C₃₁	—	2	2	no	—
545	C₂²×C₃₁	—	2	2	no	—
546	C₂²×C₃₁	—	2	1	no	—
547	C₂²×C₃₁	—	2	1	no	—
548	C₂²×C₃₁	—	2	1	no	—
549	C₂²×C₃₁	—	4	1	no	—
550	C₂²×C₃₁	—	4	1	no	—
551	C₂²×C₃₁	—	4	1	no	—
552	C₂²×C₃₁	C₂×#137	1	4	yes	—
553	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₃₁	—	2	1	no	—
555	C₄×C₃₁	—	2	2	no	—
556	C₄×C₃₁	—	2	1	no	—
557	C₄×C₃₁	—	2	1	no	—
558	C₄×C₃₁	—	2	2	no	—
559	C₄×C₃₁	—	2	2	no	—
560	C₄×C₃₁	—	2	2	no	—
561	C₄×C₃₁	—	2	1	no	—
562	C₄×C₃₁	—	2	2	no	—
563	C₄×C₃₁	—	4	1	no	—
564	C₄×C₃₁	—	4	1	no	—
565	C₄×C₃₁	—	4	2	no	—
566	C₄×C₃₁	—	4	1	no	—
567	C₄×C₃₁	—	4	2	no	—
568	C₄×C₃₁	—	4	1	no	—
569	C₄×C₃₁	—	4	2	no	—
570	C₄×C₃₁	—	4	1	no	—
571	C₄×C₃₁	—	4	2	no	—
572	C₄×C₃₁	C₂×#137	1	2	yes	—
573	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
574	C₄×C₃₁	#585	1	1	yes	characteristic
575	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
576	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
577	Q₈²	C₂²×C₃₁	1	1	yes	characteristic
578	#557	—	2	1	no	—
579	#557	C₂²×C₃₁	1	1	yes	characteristic
580	#557	C₂²×C₃₁	1	1	yes	characteristic
581	#556	—	2	1	no	—
582	#556	C₂²×C₃₁	1	1	yes	characteristic
583	#554	—	2	1	no	—
584	#554	—	2	2	no	—
585	#554	C₂²×C₃₁	1	1	yes	characteristic
586	#554	C₂²×C₃₁	1	2	yes	—
587	#552	—	2	2	no	—
588	#552	C₂²×C₃₁	1	2	yes	—
589	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
590	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
591	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
592	#548	C₂²×C₃₁	1	2	yes	—
593	#547	—	2	1	no	—
594	#547	C₂²×C₃₁	1	1	yes	characteristic
595	#533	—	2	1	no	—
596	#533	—	2	2	no	—
597	#533	—	2	1	no	—
598	#533	C₂²×C₃₁	1	2	yes	—
599	#533	C₂²×C₃₁	1	1	yes	characteristic
600	#533	C₂²×C₃₁	1	1	yes	characteristic
601	#529	—	2	2	no	—
602	#529	C₂²×C₃₁	1	2	yes	—
603	C₄×#41	—	2	1	no	—
604	C₄×#41	—	2	1	no	—
605	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
606	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
607	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
608	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
609	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
610	#501	C₂²×C₃₁	1	2	yes	—
611	#498	C₂²×C₃₁	1	1	yes	characteristic
612	#497	C₂²×C₃₁	1	2	yes	—
613	#494	C₂²×C₃₁	1	1	yes	characteristic
614	#491	C₂²×C₃₁	1	2	yes	—
615	#489	C₂²×C₃₁	1	2	yes	—
616	#487	C₂²×C₃₁	1	1	yes	characteristic
617	#487	C₂²×C₃₁	1	1	yes	characteristic
618	#485	C₂²×C₃₁	1	2	yes	—
619	#484	C₂²×C₃₁	1	2	yes	—
620	#483	C₂²×C₃₁	1	2	yes	—
621	#483	C₂²×C₃₁	1	2	yes	—
622	#483	C₂²×C₃₁	1	2	yes	—
623	#481	C₂²×C₃₁	1	2	yes	—
624	#479	C₂²×C₃₁	1	2	yes	—
625	#479	C₂²×C₃₁	1	2	yes	—
626	#477	C₂²×C₃₁	1	1	yes	characteristic
627	#476	C₂²×C₃₁	1	1	yes	characteristic
628	#475	C₂²×C₃₁	1	1	yes	characteristic
629	#475	C₂²×C₃₁	1	2	yes	—
630	#475	C₂²×C₃₁	1	1	yes	characteristic
631	#475	C₂²×C₃₁	1	2	yes	—
632	#470	C₂²×C₃₁	1	2	yes	—
633	#470	C₂²×C₃₁	1	2	yes	—
634	#467	C₂²×C₃₁	1	2	yes	—
635	#467	C₂²×C₃₁	1	2	yes	—
636	#465	C₂²×C₃₁	1	2	yes	—
637	#465	C₂²×C₃₁	1	2	yes	—
638	#464	C₂²×C₃₁	1	2	yes	—
639	#464	C₂²×C₃₁	1	2	yes	—
640	#462	C₂²×C₃₁	1	1	yes	characteristic
641	#462	C₂²×C₃₁	1	2	yes	—
642	#462	C₂²×C₃₁	1	1	yes	characteristic
643	#462	C₂²×C₃₁	1	2	yes	—
644	#462	C₂²×C₃₁	1	1	yes	characteristic
645	#461	C₂²×C₃₁	1	1	yes	characteristic
646	#452	C₂²×C₃₁	1	2	yes	—
647	#451	C₂²×C₃₁	1	2	yes	—
648	#451	C₂²×C₃₁	1	2	yes	—
649	#451	C₂²×C₃₁	1	2	yes	—
650	#451	C₂²×C₃₁	1	2	yes	—
651	#448	C₂²×C₃₁	1	2	yes	—
652	#446	C₂²×C₃₁	1	1	yes	characteristic
653	#446	C₂²×C₃₁	1	1	yes	characteristic
654	#441	C₂²×C₃₁	1	2	yes	—
655	#441	C₂²×C₃₁	1	2	yes	—
656	#441	C₂²×C₃₁	1	1	yes	characteristic
657	#441	C₂²×C₃₁	1	2	yes	—
658	#441	C₂²×C₃₁	1	2	yes	—
659	#441	C₂²×C₃₁	1	2	yes	—
660	#441	C₂²×C₃₁	1	2	yes	—
661	#441	C₂²×C₃₁	1	2	yes	—
662	#441	C₂²×C₃₁	1	2	yes	—
663	#441	C₂²×C₃₁	1	2	yes	—
664	#441	C₂²×C₃₁	1	1	yes	characteristic
665	#440	C₂²×C₃₁	1	2	yes	—
666	#440	C₂²×C₃₁	1	1	yes	characteristic
667	#440	C₂²×C₃₁	1	1	yes	characteristic
668	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
669	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
671	C₄×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
672	#435	C₂²×C₃₁	1	2	yes	—
673	#435	C₂²×C₃₁	1	2	yes	—
674	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
675	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
676	#432	C₂²×C₃₁	1	1	yes	characteristic
677	#432	C₂²×C₃₁	1	2	yes	—
678	#428	C₂²×C₃₁	1	1	yes	characteristic
679	C₂×#106	C₂²×C₃₁	1	2	yes	—
680	#419	C₂²×C₃₁	1	1	yes	characteristic
681	#417	C₂²×C₃₁	1	1	yes	characteristic
682	C₂×#103	C₂²×C₃₁	1	2	yes	—
683	C₂×#103	C₂²×C₃₁	1	2	yes	—
684	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
685	C₂×#97	C₂²×C₃₁	1	2	yes	—
686	C₂×C₃₁	—	2	4	no	—
687	C₂×C₃₁	—	4	1	no	—
688	C₂×C₃₁	—	8	1	no	—
689	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
690	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
691	C₂×C₃₁	#3586	1	1	yes	characteristic
692	C₂×#41	—	2	1	no	—
693	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
694	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
695	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
696	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
697	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	#137	—	2	4	no	—
699	C₂×Q₁₆	—	2	8	no	—
700	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
701	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
702	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
703	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
704	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
705	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
706	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
707	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
708	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
709	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
710	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
711	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
712	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
713	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	1	no	—
716	C₄⋊Q₈	—	2	2	no	—
717	C₄⋊Q₈	—	2	1	no	—
718	C₄⋊Q₈	—	2	1	no	—
719	C₄⋊Q₈	—	2	2	no	—
720	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
721	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
723	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
724	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
725	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	1	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	—	2	2	no	—
738	#125	C₂³×C₃₁	1	2	yes	—
739	#124	—	2	2	no	—
740	#124	C₂³×C₃₁	1	2	yes	—
741	#123	—	2	2	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	C₂²⋊Q₈	—	2	1	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	1	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
758	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
761	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
762	#121	—	2	2	no	—
763	#121	C₂³×C₃₁	1	2	yes	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	2	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	D₄×C₃₁	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
779	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
780	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
781	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
782	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
783	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
785	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
786	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
788	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
800	C₄×D₄	D₄×C₃₁	1	2	yes	—
801	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
803	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₃₁	1	2	yes	—
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	2	1	no	—
808	#117	—	2	1	no	—
809	#117	—	2	2	no	—
810	#117	—	2	1	no	—
811	#117	—	2	2	no	—
812	#117	D₄×C₃₁	1	2	yes	—
813	#117	D₄×C₃₁	1	1	yes	characteristic
814	#117	C₂³×C₃₁	1	1	yes	characteristic
815	C₂×C₄⋊C₄	—	2	2	no	—
816	C₂×C₄⋊C₄	—	2	2	no	—
817	C₂×C₄⋊C₄	—	2	1	no	—
818	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
819	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
820	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
821	C₂×C₄²	—	2	2	no	—
822	C₂×C₄²	—	2	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	—	2	1	no	—
825	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
826	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
827	#107	C₂³×C₃₁	1	1	yes	characteristic
828	#107	C₂³×C₃₁	1	1	yes	characteristic
829	#107	C₂³×C₃₁	1	2	yes	—
830	#106	C₂³×C₃₁	1	1	yes	characteristic
831	#106	C₂³×C₃₁	1	2	yes	—
832	#106	C₂³×C₃₁	1	2	yes	—
833	#106	C₂³×C₃₁	1	2	yes	—
834	#106	C₂³×C₃₁	1	1	yes	characteristic
835	#106	C₂³×C₃₁	1	2	yes	—
836	#106	C₂³×C₃₁	1	2	yes	—
837	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
838	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
839	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
840	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
841	#103	C₂³×C₃₁	1	1	yes	characteristic
842	#103	C₂³×C₃₁	1	1	yes	characteristic
843	#103	C₂³×C₃₁	1	2	yes	—
844	#103	C₂³×C₃₁	1	2	yes	—
845	#103	C₂³×C₃₁	1	2	yes	—
846	#103	C₂³×C₃₁	1	2	yes	—
847	#103	C₂³×C₃₁	1	2	yes	—
848	#103	C₂³×C₃₁	1	2	yes	—
849	#103	C₂³×C₃₁	1	1	yes	characteristic
850	#103	C₂³×C₃₁	1	1	yes	characteristic
851	#103	C₂³×C₃₁	1	1	yes	characteristic
852	#103	C₂³×C₃₁	1	1	yes	characteristic
853	#103	C₂³×C₃₁	1	2	yes	—
854	#103	C₂³×C₃₁	1	2	yes	—
855	#103	C₂³×C₃₁	1	2	yes	—
856	#103	C₂³×C₃₁	1	2	yes	—
857	#103	C₂³×C₃₁	1	2	yes	—
858	#102	C₂³×C₃₁	1	1	yes	characteristic
859	#102	C₂³×C₃₁	1	1	yes	characteristic
860	#102	C₂³×C₃₁	1	2	yes	—
861	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
862	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
863	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
864	#97	C₂³×C₃₁	1	1	yes	characteristic
865	#97	C₂³×C₃₁	1	2	yes	—
866	#97	C₂³×C₃₁	1	2	yes	—
867	#97	C₂³×C₃₁	1	2	yes	—
868	#97	C₂³×C₃₁	1	1	yes	characteristic
869	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
870	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
871	C₃₁	#61457	1	1	yes	characteristic, direct product factor, Sylow
872	#41	—	2	4	no	—
873	#41	—	2	2	no	—
874	#41	—	4	1	no	—
875	#41	—	4	4	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	2	1	no	—
880	C₂×Q₈	—	2	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	4	no	—
883	C₂×Q₈	—	2	4	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	4	2	no	—
886	C₂×Q₈	—	4	2	no	—
887	C₂×Q₈	—	4	1	no	—
888	C₂×Q₈	C₂×D₄×C₃₁	1	1	yes	characteristic
889	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
890	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
892	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
893	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	2	2	no	—
896	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
897	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
898	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	—	2	2	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
909	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
910	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
911	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
914	Q₁₆	—	2	4	no	—
915	Q₁₆	—	2	4	no	—
916	Q₁₆	—	2	2	no	—
917	Q₁₆	—	2	4	no	—
918	Q₁₆	—	4	2	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	#41×C₃₁	1	4	yes	complemented
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	2	no	—
924	M₁₆	—	2	2	no	—
925	M₁₆	—	4	1	no	—
926	C₂×C₈	—	2	4	no	—
927	C₂×C₈	—	4	2	no	—
928	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
929	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
930	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
931	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
932	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
933	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	1	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
966	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
969	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
972	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
974	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
987	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
988	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	2	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1003	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
1004	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1005	C₄²	C₂×D₄×C₃₁	1	2	yes	—
1006	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₃₁	1	2	yes	—
1009	C₂³	—	2	1	no	—
1010	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
1011	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	2	2	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	4	no	—
1023	Q₈	—	4	4	no	—
1024	Q₈	—	4	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	—	8	1	no	—
1027	Q₈	C₂×#41×C₃₁	1	2	yes	—
1028	Q₈	C₂×#41×C₃₁	1	2	yes	—
1029	D₄	—	2	4	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	4	2	no	—
1033	D₄	—	4	4	no	—
1034	D₄	C₃₁×#137	1	4	yes	complemented
1035	C₂×C₄	—	2	4	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	2	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	4	1	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	4	no	—
1056	C₂×C₄	—	4	4	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	8	2	no	—
1062	C₂×C₄	—	8	1	no	—
1063	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1064	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1065	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1066	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1067	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1068	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
1069	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
1071	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
1072	C₈	—	2	2	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	2	2	no	—
1076	C₈	—	2	1	no	—
1077	C₈	C₂×#41×C₃₁	1	2	yes	—
1078	C₂²	—	2	2	no	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	C₂×C₃₁×#137	1	4	yes	—
1087	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	2	2	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	4	2	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	1	no	—
1101	C₄	—	4	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	C₂×C₃₁×#137	1	2	yes	—
1107	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
1108	C₄	C₃₁×#585	1	1	yes	characteristic
1109	C₂	—	2	4	no	—
1110	C₂	—	4	1	no	—
1111	C₂	—	8	1	no	—
1112	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
1113	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
1114	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₃₁×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×#41×C₃₁	C₂	semidirect
3. C₃₁×#3398	C₂	semidirect
4. C₃₁×#3387	C₂	semidirect
5. C₃₁×#3374	C₂	semidirect
6. C₃₁×#3369	C₂	semidirect
7. C₃₁×#3344	C₂	semidirect
8. C₃₁×#3335	C₂	semidirect
9. C₃₁×#3316	C₂	semidirect
10. C₃₁×#3312	C₂	semidirect
11. C₃₁×#3299	C₂	semidirect
12. C₃₁×#3298	C₂	semidirect
13. D₄×Q₁₆×C₃₁	C₂	semidirect
14. C₃₁×#3270	C₂	semidirect
15. C₃₁×#3185	C₂	semidirect
16. C₃₁×#3181	C₂	semidirect
17. C₃₁×#3117	C₂	semidirect
18. C₃₁×#3116	C₂	semidirect
19. C₃₁×#3113	C₂	semidirect
20. C₃₁×#3113	C₂	semidirect
21. C₃₁×#2970	C₂	semidirect
22. C₄×C₃₁×#137	C₂	semidirect
23. C₂×C₃₁×#441	C₂	semidirect
362. Q₁₆×C₃₁	#41	semidirect
451. #61457	C₃₁	direct (N × H)
477. D₄×C₃₁	#137	semidirect
522. Q₈×#41	C₂×C₃₁	semidirect
523. #3398	C₂×C₃₁	semidirect
524. #3387	C₂×C₃₁	semidirect
525. #3374	C₂×C₃₁	semidirect
526. #3369	C₂×C₃₁	semidirect
527. #3344	C₂×C₃₁	semidirect
528. #3335	C₂×C₃₁	semidirect
529. #3316	C₂×C₃₁	semidirect
530. #3312	C₂×C₃₁	semidirect
531. #3299	C₂×C₃₁	semidirect
532. #3298	C₂×C₃₁	semidirect
533. D₄×Q₁₆	C₂×C₃₁	semidirect
534. #3270	C₂×C₃₁	semidirect
535. #3185	C₂×C₃₁	semidirect
536. #3181	C₂×C₃₁	semidirect
537. #3117	C₂×C₃₁	semidirect
538. #3116	C₂×C₃₁	semidirect
539. #3113	C₂×C₃₁	semidirect
540. #3113	C₂×C₃₁	semidirect
541. #2970	C₂×C₃₁	semidirect
542. C₄×#137	C₂×C₃₁	semidirect
543. C₂×#441	C₂×C₃₁	semidirect
871. C₃₁	#61457	direct (N × H)
920. Q₁₆	#41×C₃₁	semidirect
1034. D₄	C₃₁×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#3482	2
Q₈×#41×C₃₁	2
C₃₁×#3398	2
C₃₁×#3387	2
C₃₁×#3374	2
C₃₁×#3369	2
C₃₁×#3344	2
C₃₁×#3335	2
C₃₁×#3316	2
C₃₁×#3312	2
C₃₁×#3299	2
C₃₁×#3298	2
D₄×Q₁₆×C₃₁	2
C₃₁×#3270	2
C₃₁×#3185	2
C₃₁×#3181	2
C₃₁×#3117	2
C₃₁×#3116	2
C₃₁×#3113	2
C₃₁×#2970	2
C₄×C₃₁×#137	2
C₂×C₃₁×#441	2
#61457	31

Subgroups — C31×#61457 #21518216

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61457 #21518216