Subgroups — C₃₁×#61234 #21517993

Order 7936.

1874 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3342	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3340	C₂	1	2	yes	maximal, complemented
5	C₃₁×#3339	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#3337	C₂	1	4	yes	maximal, complemented
8	C₃₁×#3336	C₂	1	2	yes	maximal, complemented
9	C₃₁×#3335	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3091	C₂	1	4	yes	maximal, complemented
13	C₃₁×#3076	C₂	1	2	yes	maximal, complemented
14	C₃₁×#3050	C₂	1	2	yes	maximal, complemented
15	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#427	C₂	1	2	yes	maximal, complemented
18	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#556	C₂²	1	2	yes	—
21	C₃₁×#555	C₂²	1	2	yes	—
22	C₃₁×#554	C₂²	1	2	yes	—
23	C₃₁×#553	C₂²	1	4	yes	—
24	C₃₁×#552	—	2	2	no	—
25	C₃₁×#552	C₂²	1	4	yes	—
26	C₃₁×#551	—	2	4	no	—
27	C₃₁×#547	C₂²	1	2	yes	—
28	C₃₁×#546	—	2	2	no	—
29	C₃₁×#533	C₂²	1	2	yes	—
30	C₃₁×#529	—	2	4	no	—
31	C₃₁×#529	—	2	2	no	—
32	C₃₁×#525	C₂²	1	4	yes	—
33	C₄×#41×C₃₁	—	2	2	no	—
34	C₄×#41×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#117	C₂²	1	4	yes	—
37	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#500	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#499	C₂²	1	2	yes	complemented
40	C₃₁×#499	C₂²	1	2	yes	complemented
41	C₃₁×#498	C₂²	1	2	yes	complemented
42	C₃₁×#485	C₂²	1	4	yes	complemented
43	C₃₁×#485	C₂²	1	4	yes	complemented
44	C₃₁×#484	C₂²	1	4	yes	complemented
45	C₃₁×#483	C₂²	1	4	yes	complemented
46	C₃₁×#482	C₂²	1	4	yes	complemented
47	C₃₁×#482	C₂²	1	4	yes	complemented
48	C₃₁×#481	C₂²	1	4	yes	complemented
49	C₃₁×#480	C₂²	1	4	yes	complemented
50	C₃₁×#479	C₂²	1	4	yes	complemented
51	C₃₁×#478	C₂²	1	4	yes	complemented
52	C₃₁×#477	C₂²	1	2	yes	complemented
53	C₃₁×#476	C₂²	1	2	yes	complemented
54	C₃₁×#475	C₂²	1	2	yes	complemented
55	C₃₁×#474	C₂²	1	2	yes	complemented
56	C₃₁×#467	C₂²	1	2	yes	complemented
57	C₃₁×#467	C₂²	1	2	yes	complemented
58	C₃₁×#466	C₂²	1	2	yes	complemented
59	C₃₁×#466	C₂²	1	2	yes	complemented
60	C₃₁×#465	C₂²	1	4	yes	complemented
61	C₃₁×#465	C₂²	1	4	yes	complemented
62	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
63	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
64	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
65	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
66	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
67	C₄×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
68	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
69	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₈×D₄×C₃₁	C₂²	1	2	yes	—
71	C₈×D₄×C₃₁	C₂²	1	2	yes	—
72	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
73	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
74	C₃₁×#427	C₂²	1	4	yes	—
75	C₃₁×#427	C₂²	1	2	yes	—
76	C₃₁×#427	C₂²	1	2	yes	—
77	C₃₁×#427	C₂²	1	1	yes	characteristic
78	C₃₁×#427	C₂²	1	2	yes	complemented
79	C₃₁×#427	C₂²	1	4	yes	complemented
80	C₃₁×#427	C₂²	1	2	yes	complemented
81	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
82	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
83	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
84	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₃₁×#416	C₂²	1	4	yes	—
86	C₃₁×#416	C₂²	1	2	yes	—
87	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
89	C₂×#41×C₃₁	—	2	2	no	—
90	C₂×#41×C₃₁	C₂³	1	2	yes	—
91	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
93	C₃₁×#135	—	2	4	no	—
94	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
95	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
96	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₃₁	—	2	8	no	—
98	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
100	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
102	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
103	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
104	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
105	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₃₁×#126	—	2	4	no	—
108	C₃₁×#126	—	2	4	no	—
109	C₃₁×#126	—	2	4	no	—
110	C₃₁×#125	—	2	4	no	—
111	C₃₁×#125	—	2	2	no	—
112	C₃₁×#125	C₂³	1	4	yes	—
113	C₃₁×#124	—	2	2	no	—
114	C₃₁×#124	—	2	4	no	—
115	C₃₁×#123	—	2	4	no	—
116	C₃₁×#123	—	2	4	no	—
117	C₃₁×#123	—	2	4	no	—
118	C₃₁×#123	—	2	4	no	—
119	C₃₁×C₂²⋊Q₈	—	2	2	no	—
120	C₃₁×C₂²⋊Q₈	—	2	2	no	—
121	C₃₁×C₂²⋊Q₈	—	2	2	no	—
122	C₃₁×C₂²⋊Q₈	—	2	4	no	—
123	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
124	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₃₁×#121	—	2	4	no	—
126	C₃₁×#121	—	2	2	no	—
127	C₃₁×#121	C₂³	1	4	yes	—
128	C₃₁×#121	C₂³	1	4	yes	—
129	C₃₁×#120	—	2	4	no	—
130	C₄×Q₈×C₃₁	—	2	2	no	—
131	C₄×Q₈×C₃₁	—	2	2	no	—
132	C₄×Q₈×C₃₁	—	2	2	no	—
133	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
134	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
135	C₄×D₄×C₃₁	—	2	2	no	—
136	C₄×D₄×C₃₁	—	2	4	no	—
137	C₄×D₄×C₃₁	—	2	2	no	—
138	C₄×D₄×C₃₁	—	2	2	no	—
139	C₄×D₄×C₃₁	—	2	4	no	—
140	C₄×D₄×C₃₁	—	2	4	no	—
141	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
142	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
143	C₄×D₄×C₃₁	D₄	1	2	yes	—
144	C₄×D₄×C₃₁	C₂³	1	2	yes	—
145	C₄×D₄×C₃₁	C₂³	1	2	yes	—
146	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₄×D₄×C₃₁	C₂³	1	2	yes	—
148	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
149	C₃₁×#117	—	2	4	no	—
150	C₃₁×#117	—	2	4	no	—
151	C₃₁×#117	—	2	2	no	—
152	C₃₁×#117	—	2	4	no	—
153	C₃₁×#117	—	2	2	no	—
154	C₃₁×#117	C₂³	1	2	yes	—
155	C₃₁×#117	C₂³	1	4	yes	—
156	C₃₁×#117	C₂³	1	4	yes	—
157	C₃₁×#117	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
162	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
163	C₂×C₄²×C₃₁	—	2	4	no	—
164	C₂×C₄²×C₃₁	—	2	2	no	—
165	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
166	C₃₁×#107	C₂³	1	1	yes	characteristic
167	C₃₁×#107	C₂³	1	1	yes	characteristic
168	C₃₁×#107	C₂³	1	2	yes	—
169	C₃₁×#107	C₂³	1	2	yes	—
170	C₃₁×#107	C₂³	1	4	yes	—
171	C₃₁×#107	C₂³	1	4	yes	—
172	C₃₁×#107	C₂³	1	2	yes	—
173	C₃₁×#107	C₂³	1	2	yes	—
174	C₃₁×#106	C₂³	1	2	yes	—
175	C₃₁×#106	C₂³	1	4	yes	—
176	C₃₁×#106	C₂³	1	4	yes	—
177	C₃₁×#106	C₂³	1	4	yes	—
178	C₃₁×#106	C₂³	1	4	yes	—
179	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
180	C₃₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
181	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
182	C₃₁×#103	C₂³	1	2	yes	—
183	C₃₁×#103	C₂³	1	2	yes	—
184	C₃₁×#103	C₂³	1	4	yes	—
185	C₃₁×#103	C₂³	1	4	yes	—
186	C₃₁×#102	C₂³	1	2	yes	—
187	C₃₁×#102	C₂³	1	2	yes	—
188	C₃₁×#102	C₂³	1	4	yes	—
189	C₃₁×#102	C₂³	1	4	yes	—
190	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
193	C₃₁×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
198	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
199	#41×C₃₁	—	2	4	no	—
200	#41×C₃₁	—	2	4	no	—
201	#41×C₃₁	—	4	8	no	—
202	C₂×Q₈×C₃₁	—	2	2	no	—
203	C₂×Q₈×C₃₁	—	2	2	no	—
204	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
205	C₂×D₄×C₃₁	—	2	4	no	—
206	C₂×D₄×C₃₁	—	2	2	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	4	no	—
209	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
211	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₃₁	—	2	4	no	—
214	C₂²×C₄×C₃₁	—	2	4	no	—
215	C₂²×C₄×C₃₁	—	2	4	no	—
216	C₂²×C₄×C₃₁	—	2	4	no	—
217	C₂²×C₄×C₃₁	—	2	2	no	—
218	C₂²×C₄×C₃₁	—	2	2	no	—
219	C₂²×C₄×C₃₁	—	2	2	no	—
220	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
224	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
228	Q₁₆×C₃₁	—	2	2	no	—
229	SD₁₆×C₃₁	—	2	4	no	—
230	D₈×C₃₁	—	2	2	no	—
231	C₂×C₈×C₃₁	—	2	4	no	—
232	C₂×C₈×C₃₁	—	2	2	no	—
233	C₂×C₈×C₃₁	—	2	4	no	—
234	C₂×C₈×C₃₁	—	2	4	no	—
235	C₂×C₈×C₃₁	—	2	4	no	—
236	C₂×C₈×C₃₁	—	2	4	no	—
237	C₂×C₈×C₃₁	#41	1	4	yes	complemented
238	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
242	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₃₁	—	2	4	no	—
245	C₄⋊C₄×C₃₁	—	2	4	no	—
246	C₄⋊C₄×C₃₁	—	2	2	no	—
247	C₄⋊C₄×C₃₁	—	2	4	no	—
248	C₄⋊C₄×C₃₁	—	2	4	no	—
249	C₄⋊C₄×C₃₁	—	2	2	no	—
250	C₄⋊C₄×C₃₁	—	2	2	no	—
251	C₄⋊C₄×C₃₁	—	2	4	no	—
252	C₄⋊C₄×C₃₁	—	2	4	no	—
253	C₄⋊C₄×C₃₁	—	2	2	no	—
254	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
255	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
260	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
261	C₂²⋊C₄×C₃₁	—	2	2	no	—
262	C₂²⋊C₄×C₃₁	—	2	4	no	—
263	C₂²⋊C₄×C₃₁	—	2	4	no	—
264	C₂²⋊C₄×C₃₁	—	2	4	no	—
265	C₂²⋊C₄×C₃₁	—	2	4	no	—
266	C₂²⋊C₄×C₃₁	—	2	4	no	—
267	C₂²⋊C₄×C₃₁	—	2	4	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	4	no	—
271	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
273	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
275	C₄²×C₃₁	—	2	4	no	—
276	C₄²×C₃₁	—	2	2	no	—
277	C₄²×C₃₁	—	2	4	no	—
278	C₄²×C₃₁	—	2	2	no	—
279	C₄²×C₃₁	—	2	2	no	—
280	C₄²×C₃₁	—	2	4	no	—
281	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
284	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
285	#61234	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₃₁	—	2	4	no	—
287	C₂³×C₃₁	—	2	4	no	—
288	C₂³×C₃₁	—	2	2	no	—
289	C₂³×C₃₁	—	4	2	no	—
290	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
291	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
293	Q₈×C₃₁	—	2	2	no	—
294	Q₈×C₃₁	—	2	2	no	—
295	Q₈×C₃₁	—	4	4	no	—
296	Q₈×C₃₁	—	8	2	no	—
297	D₄×C₃₁	—	2	4	no	—
298	D₄×C₃₁	—	2	2	no	—
299	D₄×C₃₁	—	2	2	no	—
300	D₄×C₃₁	—	2	2	no	—
301	D₄×C₃₁	—	4	4	no	—
302	D₄×C₃₁	—	4	8	no	—
303	D₄×C₃₁	—	8	4	no	—
304	D₄×C₃₁	#135	1	4	yes	complemented
305	C₂×C₄×C₃₁	—	2	4	no	—
306	C₂×C₄×C₃₁	—	2	4	no	—
307	C₂×C₄×C₃₁	—	2	4	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	2	no	—
311	C₂×C₄×C₃₁	—	2	2	no	—
312	C₂×C₄×C₃₁	—	2	2	no	—
313	C₂×C₄×C₃₁	—	2	2	no	—
314	C₂×C₄×C₃₁	—	2	2	no	—
315	C₂×C₄×C₃₁	—	2	2	no	—
316	C₂×C₄×C₃₁	—	2	4	no	—
317	C₂×C₄×C₃₁	—	2	4	no	—
318	C₂×C₄×C₃₁	—	4	1	no	—
319	C₂×C₄×C₃₁	—	4	8	no	—
320	C₂×C₄×C₃₁	—	4	4	no	—
321	C₂×C₄×C₃₁	—	4	4	no	—
322	C₂×C₄×C₃₁	—	8	2	no	—
323	C₂×C₄×C₃₁	—	8	4	no	—
324	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
332	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
333	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
334	C₈×C₃₁	—	2	2	no	—
335	C₈×C₃₁	—	2	2	no	—
336	C₈×C₃₁	—	2	1	no	—
337	C₈×C₃₁	—	2	1	no	—
338	C₈×C₃₁	C₂×#41	1	2	yes	—
339	C₈×C₃₁	C₂×#41	1	2	yes	—
340	#3475	C₂×C₃₁	1	2	yes	complemented
341	#3342	C₂×C₃₁	1	1	yes	characteristic, complemented
342	#3341	C₂×C₃₁	1	1	yes	characteristic, complemented
343	#3340	C₂×C₃₁	1	2	yes	complemented
344	#3339	C₂×C₃₁	1	2	yes	complemented
345	#3338	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3337	C₂×C₃₁	1	4	yes	complemented
347	#3336	C₂×C₃₁	1	2	yes	complemented
348	#3335	C₂×C₃₁	1	2	yes	complemented
349	#3334	C₂×C₃₁	1	1	yes	characteristic, complemented
350	#3160	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3091	C₂×C₃₁	1	4	yes	complemented
352	#3076	C₂×C₃₁	1	2	yes	complemented
353	#3050	C₂×C₃₁	1	2	yes	complemented
354	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
355	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
356	C₂×#427	C₂×C₃₁	1	2	yes	complemented
357	C₂²×C₃₁	—	2	1	no	—
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	2	2	no	—
360	C₂²×C₃₁	—	2	1	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	2	no	—
363	C₂²×C₃₁	—	2	2	no	—
364	C₂²×C₃₁	—	4	8	no	—
365	C₂²×C₃₁	—	4	2	no	—
366	C₂²×C₃₁	—	4	2	no	—
367	C₂²×C₃₁	—	4	2	no	—
368	C₂²×C₃₁	#547	1	2	yes	—
369	C₂²×C₃₁	C₂×#135	1	4	yes	—
370	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₃₁	—	2	1	no	—
372	C₄×C₃₁	—	2	1	no	—
373	C₄×C₃₁	—	2	2	no	—
374	C₄×C₃₁	—	2	2	no	—
375	C₄×C₃₁	—	2	1	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	4	no	—
378	C₄×C₃₁	—	4	2	no	—
379	C₄×C₃₁	—	4	2	no	—
380	C₄×C₃₁	—	4	4	no	—
381	C₄×C₃₁	#547	1	2	yes	—
382	C₄×C₃₁	C₂×#135	1	2	yes	—
383	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
384	C₄×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
385	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
386	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
387	#556	C₂²×C₃₁	1	2	yes	—
388	#555	C₂²×C₃₁	1	2	yes	—
389	#554	C₂²×C₃₁	1	2	yes	—
390	#553	C₂²×C₃₁	1	4	yes	—
391	#552	—	2	2	no	—
392	#552	C₂²×C₃₁	1	4	yes	—
393	#551	—	2	4	no	—
394	#547	C₂²×C₃₁	1	2	yes	—
395	#546	—	2	2	no	—
396	#533	C₂²×C₃₁	1	2	yes	—
397	#529	—	2	4	no	—
398	#529	—	2	2	no	—
399	#525	C₂²×C₃₁	1	4	yes	—
400	C₄×#41	—	2	2	no	—
401	C₄×#41	C₂²×C₃₁	1	2	yes	—
402	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
403	C₂×#117	C₂²×C₃₁	1	4	yes	—
404	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
405	#500	C₂²×C₃₁	1	1	yes	characteristic, complemented
406	#499	C₂²×C₃₁	1	2	yes	complemented
407	#499	C₂²×C₃₁	1	2	yes	complemented
408	#498	C₂²×C₃₁	1	2	yes	complemented
409	#485	C₂²×C₃₁	1	4	yes	complemented
410	#485	C₂²×C₃₁	1	4	yes	complemented
411	#484	C₂²×C₃₁	1	4	yes	complemented
412	#483	C₂²×C₃₁	1	4	yes	complemented
413	#482	C₂²×C₃₁	1	4	yes	complemented
414	#482	C₂²×C₃₁	1	4	yes	complemented
415	#481	C₂²×C₃₁	1	4	yes	complemented
416	#480	C₂²×C₃₁	1	4	yes	complemented
417	#479	C₂²×C₃₁	1	4	yes	complemented
418	#478	C₂²×C₃₁	1	4	yes	complemented
419	#477	C₂²×C₃₁	1	2	yes	complemented
420	#476	C₂²×C₃₁	1	2	yes	complemented
421	#475	C₂²×C₃₁	1	2	yes	complemented
422	#474	C₂²×C₃₁	1	2	yes	complemented
423	#467	C₂²×C₃₁	1	2	yes	complemented
424	#467	C₂²×C₃₁	1	2	yes	complemented
425	#466	C₂²×C₃₁	1	2	yes	complemented
426	#466	C₂²×C₃₁	1	2	yes	complemented
427	#465	C₂²×C₃₁	1	4	yes	complemented
428	#465	C₂²×C₃₁	1	4	yes	complemented
429	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
430	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
431	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
432	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
433	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	C₄×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
435	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
436	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
437	C₈×D₄	C₂²×C₃₁	1	2	yes	—
438	C₈×D₄	C₂²×C₃₁	1	2	yes	—
439	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
440	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
441	#427	C₂²×C₃₁	1	4	yes	—
442	#427	C₂²×C₃₁	1	2	yes	—
443	#427	C₂²×C₃₁	1	2	yes	—
444	#427	C₂²×C₃₁	1	1	yes	characteristic
445	#427	C₂²×C₃₁	1	2	yes	complemented
446	#427	C₂²×C₃₁	1	4	yes	complemented
447	#427	C₂²×C₃₁	1	2	yes	complemented
448	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
449	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
450	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
451	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
452	#416	C₂²×C₃₁	1	4	yes	—
453	#416	C₂²×C₃₁	1	2	yes	—
454	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
455	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
456	C₂×C₃₁	—	2	2	no	—
457	C₂×C₃₁	—	2	4	no	—
458	C₂×C₃₁	—	4	2	no	—
459	C₂×C₃₁	—	8	2	no	—
460	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
461	C₂×C₃₁	C₂²×#135	1	1	yes	characteristic
462	C₂×C₃₁	#3584	1	1	yes	characteristic
463	C₂×#41	—	2	2	no	—
464	C₂×#41	C₂³×C₃₁	1	2	yes	—
465	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
467	#135	—	2	4	no	—
468	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
469	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
470	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
471	C₂²×C₈	—	2	8	no	—
472	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
473	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
474	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
475	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
476	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
477	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
480	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
481	#126	—	2	4	no	—
482	#126	—	2	4	no	—
483	#126	—	2	4	no	—
484	#125	—	2	4	no	—
485	#125	—	2	2	no	—
486	#125	C₂³×C₃₁	1	4	yes	—
487	#124	—	2	2	no	—
488	#124	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
498	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
499	#121	—	2	4	no	—
500	#121	—	2	2	no	—
501	#121	C₂³×C₃₁	1	4	yes	—
502	#121	C₂³×C₃₁	1	4	yes	—
503	#120	—	2	4	no	—
504	C₄×Q₈	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
508	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
516	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
517	C₄×D₄	D₄×C₃₁	1	2	yes	—
518	C₄×D₄	C₂³×C₃₁	1	2	yes	—
519	C₄×D₄	C₂³×C₃₁	1	2	yes	—
520	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
521	C₄×D₄	C₂³×C₃₁	1	2	yes	—
522	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
523	#117	—	2	4	no	—
524	#117	—	2	4	no	—
525	#117	—	2	2	no	—
526	#117	—	2	4	no	—
527	#117	—	2	2	no	—
528	#117	C₂³×C₃₁	1	2	yes	—
529	#117	C₂³×C₃₁	1	4	yes	—
530	#117	C₂³×C₃₁	1	4	yes	—
531	#117	C₂³×C₃₁	1	4	yes	—
532	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
534	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
535	C₂×C₂²⋊C₄	—	2	4	no	—
536	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
537	C₂×C₄²	—	2	4	no	—
538	C₂×C₄²	—	2	2	no	—
539	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
540	#107	C₂³×C₃₁	1	1	yes	characteristic
541	#107	C₂³×C₃₁	1	1	yes	characteristic
542	#107	C₂³×C₃₁	1	2	yes	—
543	#107	C₂³×C₃₁	1	2	yes	—
544	#107	C₂³×C₃₁	1	4	yes	—
545	#107	C₂³×C₃₁	1	4	yes	—
546	#107	C₂³×C₃₁	1	2	yes	—
547	#107	C₂³×C₃₁	1	2	yes	—
548	#106	C₂³×C₃₁	1	2	yes	—
549	#106	C₂³×C₃₁	1	4	yes	—
550	#106	C₂³×C₃₁	1	4	yes	—
551	#106	C₂³×C₃₁	1	4	yes	—
552	#106	C₂³×C₃₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
554	C₄⋊C₈	C₂³×C₃₁	1	1	yes	characteristic
555	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
556	#103	C₂³×C₃₁	1	2	yes	—
557	#103	C₂³×C₃₁	1	2	yes	—
558	#103	C₂³×C₃₁	1	4	yes	—
559	#103	C₂³×C₃₁	1	4	yes	—
560	#102	C₂³×C₃₁	1	2	yes	—
561	#102	C₂³×C₃₁	1	2	yes	—
562	#102	C₂³×C₃₁	1	4	yes	—
563	#102	C₂³×C₃₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
567	C₂²⋊C₈	C₂³×C₃₁	1	2	yes	—
568	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₃₁	#61234	1	1	yes	characteristic, direct product factor, Sylow
573	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
574	#41	—	2	4	no	—
575	#41	—	2	4	no	—
576	#41	—	4	8	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
585	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
586	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
587	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
596	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
599	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
603	Q₁₆	—	2	2	no	—
604	SD₁₆	—	2	4	no	—
605	D₈	—	2	2	no	—
606	C₂×C₈	—	2	4	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	4	no	—
609	C₂×C₈	—	2	4	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#41×C₃₁	1	4	yes	complemented
613	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
614	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
615	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
616	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
617	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
630	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
631	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
635	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
647	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
648	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
649	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	—	2	2	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	—	2	2	no	—
656	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
657	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
658	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
659	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
660	C₂³	—	2	4	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
665	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
666	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
667	Q₈	—	2	2	no	—
668	Q₈	—	2	2	no	—
669	Q₈	—	4	4	no	—
670	Q₈	—	8	2	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	2	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	8	no	—
677	D₄	—	8	4	no	—
678	D₄	C₃₁×#135	1	4	yes	complemented
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	4	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	—	8	4	no	—
698	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
699	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
705	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
706	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
707	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
708	C₈	—	2	2	no	—
709	C₈	—	2	2	no	—
710	C₈	—	2	1	no	—
711	C₈	—	2	1	no	—
712	C₈	C₂×#41×C₃₁	1	2	yes	—
713	C₈	C₂×#41×C₃₁	1	2	yes	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	8	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	C₃₁×#547	1	2	yes	—
726	C₂²	C₂×C₃₁×#135	1	4	yes	—
727	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
728	C₄	—	2	2	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	C₃₁×#547	1	2	yes	—
739	C₄	C₂×C₃₁×#135	1	2	yes	—
740	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
741	C₄	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	4	no	—
744	C₂	—	4	2	no	—
745	C₂	—	8	2	no	—
746	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
747	C₂	C₂²×C₃₁×#135	1	1	yes	characteristic
748	C₂	C₃₁×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	semidirect
2. C₃₁×#3342	C₂	semidirect
3. C₃₁×#3341	C₂	semidirect
4. C₃₁×#3340	C₂	semidirect
5. C₃₁×#3339	C₂	semidirect
6. C₃₁×#3338	C₂	semidirect
7. C₃₁×#3337	C₂	semidirect
8. C₃₁×#3336	C₂	semidirect
9. C₃₁×#3335	C₂	semidirect
10. C₃₁×#3334	C₂	semidirect
11. C₃₁×#3160	C₂	semidirect
12. C₃₁×#3091	C₂	semidirect
13. C₃₁×#3076	C₂	semidirect
14. C₃₁×#3050	C₂	semidirect
15. C₄×C₃₁×#135	C₂	semidirect
16. C₂×C₈×D₄×C₃₁	C₂	semidirect
17. C₂×C₃₁×#427	C₂	semidirect
37. C₃₁×#500	C₂²	semidirect
38. C₃₁×#500	C₂²	semidirect
39. C₃₁×#499	C₂²	semidirect
40. C₃₁×#499	C₂²	semidirect
41. C₃₁×#498	C₂²	semidirect
42. C₃₁×#485	C₂²	semidirect
43. C₃₁×#485	C₂²	semidirect
44. C₃₁×#484	C₂²	semidirect
45. C₃₁×#483	C₂²	semidirect
46. C₃₁×#482	C₂²	semidirect
47. C₃₁×#482	C₂²	semidirect
48. C₃₁×#481	C₂²	semidirect
49. C₃₁×#480	C₂²	semidirect
50. C₃₁×#479	C₂²	semidirect
51. C₃₁×#478	C₂²	semidirect
52. C₃₁×#477	C₂²	semidirect
53. C₃₁×#476	C₂²	semidirect
54. C₃₁×#475	C₂²	semidirect
55. C₃₁×#474	C₂²	semidirect
56. C₃₁×#467	C₂²	semidirect
57. C₃₁×#467	C₂²	semidirect
58. C₃₁×#466	C₂²	semidirect
59. C₃₁×#466	C₂²	semidirect
60. C₃₁×#465	C₂²	semidirect
61. C₃₁×#465	C₂²	semidirect
62. C₄×Q₁₆×C₃₁	C₂²	semidirect
63. C₄×Q₁₆×C₃₁	C₂²	semidirect
64. C₄×SD₁₆×C₃₁	C₂²	semidirect
65. C₄×SD₁₆×C₃₁	C₂²	semidirect
66. C₄×D₈×C₃₁	C₂²	semidirect
67. C₄×D₈×C₃₁	C₂²	semidirect
78. C₃₁×#427	C₂²	semidirect
79. C₃₁×#427	C₂²	semidirect
80. C₃₁×#427	C₂²	semidirect
81. C₂×C₃₁×#107	C₂²	semidirect
82. C₂×C₃₁×#107	C₂²	semidirect
83. C₂×C₃₁×#106	C₂²	semidirect
237. C₂×C₈×C₃₁	#41	semidirect
285. #61234	C₃₁	direct (N × H)
304. D₄×C₃₁	#135	semidirect
340. #3475	C₂×C₃₁	semidirect
341. #3342	C₂×C₃₁	semidirect
342. #3341	C₂×C₃₁	semidirect
343. #3340	C₂×C₃₁	semidirect
344. #3339	C₂×C₃₁	semidirect
345. #3338	C₂×C₃₁	semidirect
346. #3337	C₂×C₃₁	semidirect
347. #3336	C₂×C₃₁	semidirect
348. #3335	C₂×C₃₁	semidirect
349. #3334	C₂×C₃₁	semidirect
350. #3160	C₂×C₃₁	semidirect
351. #3091	C₂×C₃₁	semidirect
352. #3076	C₂×C₃₁	semidirect
353. #3050	C₂×C₃₁	semidirect
354. C₄×#135	C₂×C₃₁	semidirect
355. C₂×C₈×D₄	C₂×C₃₁	semidirect
356. C₂×#427	C₂×C₃₁	semidirect
404. #500	C₂²×C₃₁	semidirect
405. #500	C₂²×C₃₁	semidirect
406. #499	C₂²×C₃₁	semidirect
407. #499	C₂²×C₃₁	semidirect
408. #498	C₂²×C₃₁	semidirect
409. #485	C₂²×C₃₁	semidirect
410. #485	C₂²×C₃₁	semidirect
411. #484	C₂²×C₃₁	semidirect
412. #483	C₂²×C₃₁	semidirect
413. #482	C₂²×C₃₁	semidirect
414. #482	C₂²×C₃₁	semidirect
415. #481	C₂²×C₃₁	semidirect
416. #480	C₂²×C₃₁	semidirect
417. #479	C₂²×C₃₁	semidirect
418. #478	C₂²×C₃₁	semidirect
419. #477	C₂²×C₃₁	semidirect
420. #476	C₂²×C₃₁	semidirect
421. #475	C₂²×C₃₁	semidirect
422. #474	C₂²×C₃₁	semidirect
423. #467	C₂²×C₃₁	semidirect
424. #467	C₂²×C₃₁	semidirect
425. #466	C₂²×C₃₁	semidirect
426. #466	C₂²×C₃₁	semidirect
427. #465	C₂²×C₃₁	semidirect
428. #465	C₂²×C₃₁	semidirect
429. C₄×Q₁₆	C₂²×C₃₁	semidirect
430. C₄×Q₁₆	C₂²×C₃₁	semidirect
431. C₄×SD₁₆	C₂²×C₃₁	semidirect
432. C₄×SD₁₆	C₂²×C₃₁	semidirect
433. C₄×D₈	C₂²×C₃₁	semidirect
434. C₄×D₈	C₂²×C₃₁	semidirect
445. #427	C₂²×C₃₁	semidirect
446. #427	C₂²×C₃₁	semidirect
447. #427	C₂²×C₃₁	semidirect
448. C₂×#107	C₂²×C₃₁	semidirect
449. C₂×#107	C₂²×C₃₁	semidirect
450. C₂×#106	C₂²×C₃₁	semidirect
572. C₃₁	#61234	direct (N × H)
612. C₂×C₈	#41×C₃₁	semidirect
678. D₄	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3475	2
C₃₁×#3342	2
C₃₁×#3341	2
C₃₁×#3340	2
C₃₁×#3339	2
C₃₁×#3338	2
C₃₁×#3337	2
C₃₁×#3336	2
C₃₁×#3335	2
C₃₁×#3334	2
C₃₁×#3160	2
C₃₁×#3091	2
C₃₁×#3076	2
C₃₁×#3050	2
C₄×C₃₁×#135	2
C₂×C₈×D₄×C₃₁	2
C₂×C₃₁×#427	2
#61234	31

Subgroups — C31×#61234 #21517993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61234 #21517993