Subgroups — C₃₁×#61087 #21517846

Order 7936.

2786 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#577	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#3284	C₂	1	4	yes	maximal, complemented
5	D₄×SD₁₆×C₃₁	C₂	1	4	yes	maximal, complemented
6	C₃₁×#3278	C₂	1	4	yes	maximal, complemented
7	C₃₁×#3272	C₂	1	4	yes	maximal, complemented
8	C₂×C₃₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#3057	C₂	1	2	yes	maximal, complemented
10	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×#3010	C₂	1	2	yes	maximal, complemented
13	C₃₁×#3009	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#2931	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	2	yes	—
18	C₃₁×#577	—	2	16	no	—
19	C₂×C₃₁×#137	C₂²	1	2	yes	—
20	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
21	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
23	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
24	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
25	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
27	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
28	C₂×C₃₁×#131	C₂²	1	2	yes	complemented
29	C₃₁×#550	C₂²	1	4	yes	—
30	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
31	C₃₁×#547	—	2	4	no	—
32	C₃₁×#547	C₂²	1	4	yes	complemented
33	D₄²×C₃₁	—	2	4	no	—
34	D₄²×C₃₁	C₂²	1	4	yes	—
35	C₃₁×#536	—	2	2	no	—
36	C₃₁×#536	C₂²	1	2	yes	complemented
37	C₃₁×#535	—	2	2	no	—
38	C₃₁×#535	C₂²	1	2	yes	—
39	C₃₁×#532	—	2	1	no	—
40	C₃₁×#532	—	2	1	no	—
41	C₃₁×#532	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
43	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₃₁×#127	—	2	1	no	—
45	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
46	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
47	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	C₃₁×#492	C₂²	1	4	yes	complemented
49	C₃₁×#492	C₂²	1	4	yes	complemented
50	C₃₁×#468	C₂²	1	8	yes	complemented
51	C₃₁×#465	C₂²	1	8	yes	complemented
52	C₃₁×#462	C₂²	1	4	yes	complemented
53	C₃₁×#461	C₂²	1	4	yes	complemented
54	C₃₁×#460	C₂²	1	4	yes	complemented
55	C₃₁×#459	C₂²	1	4	yes	complemented
56	C₃₁×#452	C₂²	1	8	yes	complemented
57	C₃₁×#450	C₂²	1	8	yes	complemented
58	C₃₁×#449	C₂²	1	8	yes	complemented
59	C₃₁×#448	C₂²	1	8	yes	complemented
60	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
62	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
63	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
64	C₃₁×#436	C₂²	1	4	yes	complemented
65	C₈×D₄×C₃₁	C₂²	1	4	yes	complemented
66	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
67	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
68	C₃₁×#419	C₂²	1	2	yes	complemented
69	C₃₁×#418	C₂²	1	2	yes	complemented
70	C₃₁×#416	C₂²	1	1	yes	characteristic
71	C₃₁×#416	C₂²	1	1	yes	characteristic, complemented
72	C₃₁×#408	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
74	C₃₁×2₋¹⁺⁴	—	2	8	no	—
75	C₃₁×2₋¹⁺⁴	—	4	4	no	—
76	C₃₁×H(5,𝔽₂)	—	2	8	no	—
77	C₃₁×H(5,𝔽₂)	—	4	4	no	—
78	C₂×#41×C₃₁	—	2	2	no	—
79	C₂×#41×C₃₁	—	2	2	no	—
80	C₂×#41×C₃₁	—	2	4	no	—
81	C₂×#41×C₃₁	C₂³	1	4	yes	—
82	C₂×#41×C₃₁	C₂³	1	4	yes	—
83	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
84	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
85	C₂×#41×C₃₁	C₂³	1	2	yes	—
86	C₂²×Q₈×C₃₁	—	2	2	no	—
87	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
88	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
89	C₂²×D₄×C₃₁	—	2	2	no	—
90	C₂²×D₄×C₃₁	—	2	4	no	—
91	C₂²×D₄×C₃₁	—	2	4	no	—
92	C₂²×D₄×C₃₁	—	2	2	no	—
93	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
95	C₃₁×#137	—	2	8	no	—
96	C₃₁×#137	—	2	16	no	—
97	C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
98	C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
99	C₃₁×#135	—	2	16	no	—
100	C₃₁×#135	D₄	1	8	yes	complemented
101	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
103	C₂×SD₁₆×C₃₁	—	2	16	no	—
104	C₂×SD₁₆×C₃₁	—	2	8	no	—
105	C₂×SD₁₆×C₃₁	—	4	4	no	—
106	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
111	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
112	C₂×SD₁₆×C₃₁	C₂³	1	1	yes	characteristic
113	C₂×D₈×C₃₁	C₂³	1	4	yes	—
114	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
115	C₃₁×#131	—	2	8	no	—
116	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
117	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
118	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
120	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
121	C₃₁×C₄⋊Q₈	—	2	2	no	—
122	C₃₁×C₄⋊Q₈	—	2	4	no	—
123	C₃₁×C₄⋊Q₈	—	2	1	no	—
124	C₃₁×C₄⋊Q₈	—	2	1	no	—
125	C₃₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
126	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
127	C₃₁×#127	—	2	2	no	—
128	C₃₁×#127	—	2	4	no	—
129	C₃₁×#127	—	2	1	no	—
130	C₃₁×#127	—	2	1	no	—
131	C₃₁×#127	D₄	1	1	yes	characteristic
132	C₃₁×#127	C₂³	1	4	yes	—
133	C₃₁×#124	—	2	2	no	—
134	C₃₁×#124	—	2	2	no	—
135	C₃₁×#124	D₄	1	2	yes	—
136	C₃₁×#123	—	2	4	no	—
137	C₃₁×#123	—	2	8	no	—
138	C₃₁×C₂²⋊Q₈	—	2	8	no	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
140	C₃₁×#121	—	2	4	no	—
141	C₃₁×#121	—	2	4	no	—
142	C₃₁×#121	—	2	8	no	—
143	C₃₁×#121	D₄	1	4	yes	—
144	C₃₁×#121	C₂³	1	8	yes	—
145	C₃₁×#120	—	2	4	no	—
146	C₃₁×#120	—	2	8	no	—
147	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
149	C₄×D₄×C₃₁	—	2	4	no	—
150	C₄×D₄×C₃₁	—	2	2	no	—
151	C₄×D₄×C₃₁	—	2	2	no	—
152	C₄×D₄×C₃₁	—	2	4	no	—
153	C₄×D₄×C₃₁	C₂³	1	2	yes	—
154	C₄×D₄×C₃₁	C₂³	1	2	yes	—
155	C₄×D₄×C₃₁	C₂³	1	4	yes	—
156	C₃₁×#117	—	2	1	no	—
157	C₃₁×#117	—	2	1	no	—
158	C₃₁×#117	C₂³	1	1	yes	characteristic
159	C₃₁×#117	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
161	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
162	C₂×C₄²×C₃₁	—	2	1	no	—
163	C₂×C₄²×C₃₁	—	2	1	no	—
164	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
165	C₃₁×#107	C₂³	1	2	yes	—
166	C₃₁×#106	C₂³	1	2	yes	—
167	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
168	C₃₁×#103	C₂³	1	2	yes	—
169	C₃₁×#103	C₂³	1	2	yes	—
170	C₃₁×#103	C₂³	1	8	yes	—
171	C₃₁×#102	C₂³	1	2	yes	—
172	C₃₁×#102	C₂³	1	2	yes	—
173	C₃₁×#102	C₂³	1	8	yes	—
174	C₃₁×C₂²⋊C₈	C₂³	1	8	yes	—
175	C₄×C₈×C₃₁	C₂³	1	2	yes	—
176	C₄×C₈×C₃₁	C₂³	1	2	yes	—
177	C₂⁴×C₃₁	—	2	4	no	—
178	C₂⁴×C₃₁	—	2	2	no	—
179	#41×C₃₁	—	2	4	no	—
180	#41×C₃₁	—	2	2	no	—
181	#41×C₃₁	—	2	4	no	—
182	#41×C₃₁	—	2	2	no	—
183	#41×C₃₁	—	2	8	no	—
184	#41×C₃₁	—	2	8	no	—
185	#41×C₃₁	—	4	4	no	—
186	#41×C₃₁	—	4	4	no	—
187	#41×C₃₁	—	4	8	no	—
188	#41×C₃₁	—	4	8	no	—
189	#41×C₃₁	—	4	16	no	—
190	#41×C₃₁	C₂×D₄	1	4	yes	—
191	#41×C₃₁	C₂×D₄	1	4	yes	complemented
192	C₂×Q₈×C₃₁	—	2	4	no	—
193	C₂×Q₈×C₃₁	—	2	2	no	—
194	C₂×Q₈×C₃₁	—	2	8	no	—
195	C₂×Q₈×C₃₁	—	2	4	no	—
196	C₂×Q₈×C₃₁	—	2	4	no	—
197	C₂×Q₈×C₃₁	—	4	4	no	—
198	C₂×Q₈×C₃₁	—	4	8	no	—
199	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
200	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
201	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
203	C₂×D₄×C₃₁	—	2	1	no	—
204	C₂×D₄×C₃₁	—	2	1	no	—
205	C₂×D₄×C₃₁	—	2	8	no	—
206	C₂×D₄×C₃₁	—	2	4	no	—
207	C₂×D₄×C₃₁	—	2	4	no	—
208	C₂×D₄×C₃₁	—	2	8	no	—
209	C₂×D₄×C₃₁	—	2	4	no	—
210	C₂×D₄×C₃₁	—	2	4	no	—
211	C₂×D₄×C₃₁	—	2	4	no	—
212	C₂×D₄×C₃₁	—	2	2	no	—
213	C₂×D₄×C₃₁	—	2	4	no	—
214	C₂×D₄×C₃₁	—	2	4	no	—
215	C₂×D₄×C₃₁	—	4	4	no	—
216	C₂×D₄×C₃₁	—	4	8	no	—
217	C₂×D₄×C₃₁	—	4	16	no	—
218	C₂×D₄×C₃₁	—	8	4	no	—
219	C₂×D₄×C₃₁	—	8	8	no	—
220	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
224	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
225	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₃₁	—	2	1	no	—
227	C₂²×C₄×C₃₁	—	2	1	no	—
228	C₂²×C₄×C₃₁	—	2	2	no	—
229	C₂²×C₄×C₃₁	—	2	4	no	—
230	C₂²×C₄×C₃₁	—	2	2	no	—
231	C₂²×C₄×C₃₁	—	2	2	no	—
232	C₂²×C₄×C₃₁	—	2	4	no	—
233	C₂²×C₄×C₃₁	—	2	4	no	—
234	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
237	Q₁₆×C₃₁	—	2	8	no	—
238	Q₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
239	SD₁₆×C₃₁	—	2	8	no	—
240	SD₁₆×C₃₁	—	2	8	no	—
241	SD₁₆×C₃₁	—	2	8	no	—
242	SD₁₆×C₃₁	—	2	8	no	—
243	SD₁₆×C₃₁	—	4	8	no	—
244	SD₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
245	SD₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
246	D₈×C₃₁	—	2	8	no	—
247	D₈×C₃₁	C₂×D₄	1	4	yes	complemented
248	M₁₆×C₃₁	—	2	4	no	—
249	M₁₆×C₃₁	—	2	8	no	—
250	C₂×C₈×C₃₁	—	2	2	no	—
251	C₂×C₈×C₃₁	—	2	8	no	—
252	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	complemented
253	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
254	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
255	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₄⋊C₄×C₃₁	—	2	4	no	—
258	C₄⋊C₄×C₃₁	—	2	4	no	—
259	C₄⋊C₄×C₃₁	—	2	8	no	—
260	C₄⋊C₄×C₃₁	—	2	2	no	—
261	C₄⋊C₄×C₃₁	—	2	2	no	—
262	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
265	C₂²⋊C₄×C₃₁	—	2	1	no	—
266	C₂²⋊C₄×C₃₁	—	2	1	no	—
267	C₂²⋊C₄×C₃₁	—	2	8	no	—
268	C₂²⋊C₄×C₃₁	—	2	2	no	—
269	C₂²⋊C₄×C₃₁	—	2	2	no	—
270	C₂²⋊C₄×C₃₁	—	2	8	no	—
271	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
272	C₄²×C₃₁	—	2	1	no	—
273	C₄²×C₃₁	—	2	1	no	—
274	C₄²×C₃₁	—	2	2	no	—
275	C₄²×C₃₁	—	2	2	no	—
276	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₃₁	C₂⁴	1	2	yes	—
279	#61087	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂³×C₃₁	—	2	1	no	—
281	C₂³×C₃₁	—	2	1	no	—
282	C₂³×C₃₁	—	2	4	no	—
283	C₂³×C₃₁	—	4	8	no	—
284	C₂³×C₃₁	—	4	4	no	—
285	C₂³×C₃₁	—	8	4	no	—
286	C₂³×C₃₁	—	8	8	no	—
287	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
288	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₃₁	—	2	4	no	—
290	Q₈×C₃₁	—	2	1	no	—
291	Q₈×C₃₁	—	2	1	no	—
292	Q₈×C₃₁	—	2	4	no	—
293	Q₈×C₃₁	—	2	4	no	—
294	Q₈×C₃₁	—	4	8	no	—
295	Q₈×C₃₁	—	4	4	no	—
296	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
297	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
298	D₄×C₃₁	—	2	4	no	—
299	D₄×C₃₁	—	2	4	no	—
300	D₄×C₃₁	—	2	8	no	—
301	D₄×C₃₁	—	2	4	no	—
302	D₄×C₃₁	—	2	8	no	—
303	D₄×C₃₁	—	2	4	no	—
304	D₄×C₃₁	—	2	1	no	—
305	D₄×C₃₁	—	2	1	no	—
306	D₄×C₃₁	—	2	4	no	—
307	D₄×C₃₁	—	4	8	no	—
308	D₄×C₃₁	—	4	8	no	—
309	D₄×C₃₁	—	4	8	no	—
310	D₄×C₃₁	—	4	4	no	—
311	D₄×C₃₁	—	4	8	no	—
312	D₄×C₃₁	—	8	4	no	—
313	D₄×C₃₁	—	8	8	no	—
314	D₄×C₃₁	C₂²×D₄	1	2	yes	—
315	D₄×C₃₁	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₃₁	—	2	1	no	—
317	C₂×C₄×C₃₁	—	2	1	no	—
318	C₂×C₄×C₃₁	—	2	4	no	—
319	C₂×C₄×C₃₁	—	2	4	no	—
320	C₂×C₄×C₃₁	—	2	4	no	—
321	C₂×C₄×C₃₁	—	2	4	no	—
322	C₂×C₄×C₃₁	—	2	4	no	—
323	C₂×C₄×C₃₁	—	2	2	no	—
324	C₂×C₄×C₃₁	—	2	2	no	—
325	C₂×C₄×C₃₁	—	2	4	no	—
326	C₂×C₄×C₃₁	—	4	8	no	—
327	C₂×C₄×C₃₁	—	4	8	no	—
328	C₂×C₄×C₃₁	—	4	8	no	—
329	C₂×C₄×C₃₁	—	4	4	no	—
330	C₂×C₄×C₃₁	—	4	4	no	—
331	C₂×C₄×C₃₁	—	4	4	no	—
332	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
338	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
339	C₈×C₃₁	—	2	4	no	—
340	C₈×C₃₁	—	2	2	no	—
341	C₈×C₃₁	C₂²×D₄	1	2	yes	—
342	C₈×C₃₁	C₂²×D₄	1	2	yes	—
343	C₂×#577	C₂×C₃₁	1	2	yes	complemented
344	#3499	C₂×C₃₁	1	1	yes	characteristic, complemented
345	#3498	C₂×C₃₁	1	1	yes	characteristic, complemented
346	#3284	C₂×C₃₁	1	4	yes	complemented
347	D₄×SD₁₆	C₂×C₃₁	1	4	yes	complemented
348	#3278	C₂×C₃₁	1	4	yes	complemented
349	#3272	C₂×C₃₁	1	4	yes	complemented
350	C₂×#492	C₂×C₃₁	1	1	yes	characteristic, complemented
351	#3057	C₂×C₃₁	1	2	yes	complemented
352	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
353	#3038	C₂×C₃₁	1	1	yes	characteristic, complemented
354	#3010	C₂×C₃₁	1	2	yes	complemented
355	#3009	C₂×C₃₁	1	2	yes	complemented
356	C₄×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
357	#2931	C₂×C₃₁	1	1	yes	characteristic, complemented
358	C₂²×C₃₁	—	2	2	no	—
359	C₂²×C₃₁	—	2	2	no	—
360	C₂²×C₃₁	—	2	4	no	—
361	C₂²×C₃₁	—	2	2	no	—
362	C₂²×C₃₁	—	2	8	no	—
363	C₂²×C₃₁	—	4	2	no	—
364	C₂²×C₃₁	—	4	2	no	—
365	C₂²×C₃₁	—	4	4	no	—
366	C₂²×C₃₁	—	4	8	no	—
367	C₂²×C₃₁	—	16	4	no	—
368	C₂²×C₃₁	—	16	8	no	—
369	C₂²×C₃₁	D₄²	1	2	yes	—
370	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₃₁	—	2	2	no	—
372	C₄×C₃₁	—	2	2	no	—
373	C₄×C₃₁	—	2	4	no	—
374	C₄×C₃₁	—	2	2	no	—
375	C₄×C₃₁	—	4	4	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	D₄²	1	2	yes	—
379	C₄×C₃₁	#577	1	4	yes	complemented
380	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×2₋¹⁺⁴	C₂²×C₃₁	1	2	yes	complemented
383	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	2	yes	—
384	#577	—	2	16	no	—
385	C₂×#137	C₂²×C₃₁	1	2	yes	—
386	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
387	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	2	yes	complemented
388	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	4	yes	complemented
389	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
390	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
391	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
392	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
393	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
394	C₂×#131	C₂²×C₃₁	1	2	yes	complemented
395	#550	C₂²×C₃₁	1	4	yes	—
396	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
397	#547	—	2	4	no	—
398	#547	C₂²×C₃₁	1	4	yes	complemented
399	D₄²	—	2	4	no	—
400	D₄²	C₂²×C₃₁	1	4	yes	—
401	#536	—	2	2	no	—
402	#536	C₂²×C₃₁	1	2	yes	complemented
403	#535	—	2	2	no	—
404	#535	C₂²×C₃₁	1	2	yes	—
405	#532	—	2	1	no	—
406	#532	—	2	1	no	—
407	#532	C₂²×C₃₁	1	1	yes	characteristic
408	C₂×C₄⋊Q₈	—	2	1	no	—
409	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
410	C₂×#127	—	2	1	no	—
411	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
412	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
413	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
414	#492	C₂²×C₃₁	1	4	yes	complemented
415	#492	C₂²×C₃₁	1	4	yes	complemented
416	#468	C₂²×C₃₁	1	8	yes	complemented
417	#465	C₂²×C₃₁	1	8	yes	complemented
418	#462	C₂²×C₃₁	1	4	yes	complemented
419	#461	C₂²×C₃₁	1	4	yes	complemented
420	#460	C₂²×C₃₁	1	4	yes	complemented
421	#459	C₂²×C₃₁	1	4	yes	complemented
422	#452	C₂²×C₃₁	1	8	yes	complemented
423	#450	C₂²×C₃₁	1	8	yes	complemented
424	#449	C₂²×C₃₁	1	8	yes	complemented
425	#448	C₂²×C₃₁	1	8	yes	complemented
426	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
427	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
428	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
429	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
430	#436	C₂²×C₃₁	1	4	yes	complemented
431	C₈×D₄	C₂²×C₃₁	1	4	yes	complemented
432	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
433	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
434	#419	C₂²×C₃₁	1	2	yes	complemented
435	#418	C₂²×C₃₁	1	2	yes	complemented
436	#416	C₂²×C₃₁	1	1	yes	characteristic
437	#416	C₂²×C₃₁	1	1	yes	characteristic, complemented
438	#408	C₂²×C₃₁	1	2	yes	complemented
439	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	C₂×C₃₁	—	2	2	no	—
441	C₂×C₃₁	—	4	4	no	—
442	C₂×C₃₁	—	4	2	no	—
443	C₂×C₃₁	—	4	2	no	—
444	C₂×C₃₁	—	8	4	no	—
445	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
446	C₂×C₃₁	C₂×#577	1	2	yes	—
447	2₋¹⁺⁴	—	2	8	no	—
448	2₋¹⁺⁴	—	4	4	no	—
449	H(5,𝔽₂)	—	2	8	no	—
450	H(5,𝔽₂)	—	4	4	no	—
451	C₂×#41	—	2	2	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	4	no	—
454	C₂×#41	C₂³×C₃₁	1	4	yes	—
455	C₂×#41	C₂³×C₃₁	1	4	yes	—
456	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
457	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
458	C₂×#41	C₂³×C₃₁	1	2	yes	—
459	C₂²×Q₈	—	2	2	no	—
460	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
461	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	4	no	—
464	C₂²×D₄	—	2	4	no	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
467	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
468	#137	—	2	8	no	—
469	#137	—	2	16	no	—
470	AGL(1,ℤ/8)	—	2	8	no	—
471	AGL(1,ℤ/8)	—	2	16	no	—
472	#135	—	2	16	no	—
473	#135	D₄×C₃₁	1	8	yes	complemented
474	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
475	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
476	C₂×SD₁₆	—	2	16	no	—
477	C₂×SD₁₆	—	2	8	no	—
478	C₂×SD₁₆	—	4	4	no	—
479	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
480	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
481	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
482	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
483	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
484	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
485	C₂×SD₁₆	C₂³×C₃₁	1	1	yes	characteristic
486	C₂×D₈	C₂³×C₃₁	1	4	yes	—
487	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
488	#131	—	2	8	no	—
489	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
490	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
491	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
492	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
494	C₄⋊Q₈	—	2	2	no	—
495	C₄⋊Q₈	—	2	4	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	C₄⋊Q₈	D₄×C₃₁	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
500	#127	—	2	2	no	—
501	#127	—	2	4	no	—
502	#127	—	2	1	no	—
503	#127	—	2	1	no	—
504	#127	D₄×C₃₁	1	1	yes	characteristic
505	#127	C₂³×C₃₁	1	4	yes	—
506	#124	—	2	2	no	—
507	#124	—	2	2	no	—
508	#124	D₄×C₃₁	1	2	yes	—
509	#123	—	2	4	no	—
510	#123	—	2	8	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
513	#121	—	2	4	no	—
514	#121	—	2	4	no	—
515	#121	—	2	8	no	—
516	#121	D₄×C₃₁	1	4	yes	—
517	#121	C₂³×C₃₁	1	8	yes	—
518	#120	—	2	4	no	—
519	#120	—	2	8	no	—
520	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
521	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
522	C₄×D₄	—	2	4	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	C₂³×C₃₁	1	2	yes	—
527	C₄×D₄	C₂³×C₃₁	1	2	yes	—
528	C₄×D₄	C₂³×C₃₁	1	4	yes	—
529	#117	—	2	1	no	—
530	#117	—	2	1	no	—
531	#117	C₂³×C₃₁	1	1	yes	characteristic
532	#117	C₂³×C₃₁	1	1	yes	characteristic
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	4	no	—
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	—	2	1	no	—
537	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
538	#107	C₂³×C₃₁	1	2	yes	—
539	#106	C₂³×C₃₁	1	2	yes	—
540	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
541	#103	C₂³×C₃₁	1	2	yes	—
542	#103	C₂³×C₃₁	1	2	yes	—
543	#103	C₂³×C₃₁	1	8	yes	—
544	#102	C₂³×C₃₁	1	2	yes	—
545	#102	C₂³×C₃₁	1	2	yes	—
546	#102	C₂³×C₃₁	1	8	yes	—
547	C₂²⋊C₈	C₂³×C₃₁	1	8	yes	—
548	C₄×C₈	C₂³×C₃₁	1	2	yes	—
549	C₄×C₈	C₂³×C₃₁	1	2	yes	—
550	C₃₁	#61087	1	1	yes	characteristic, direct product factor, Sylow
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	2	no	—
553	#41	—	2	4	no	—
554	#41	—	2	2	no	—
555	#41	—	2	4	no	—
556	#41	—	2	2	no	—
557	#41	—	2	8	no	—
558	#41	—	2	8	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	#41	—	4	8	no	—
562	#41	—	4	8	no	—
563	#41	—	4	16	no	—
564	#41	C₂×D₄×C₃₁	1	4	yes	—
565	#41	C₂×D₄×C₃₁	1	4	yes	complemented
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	4	4	no	—
572	C₂×Q₈	—	4	8	no	—
573	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
574	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
575	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
576	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	—	2	8	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	8	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	4	4	no	—
590	C₂×D₄	—	4	8	no	—
591	C₂×D₄	—	4	16	no	—
592	C₂×D₄	—	8	4	no	—
593	C₂×D₄	—	8	8	no	—
594	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
595	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
596	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
597	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
598	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
599	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
611	Q₁₆	—	2	8	no	—
612	Q₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	2	8	no	—
615	SD₁₆	—	2	8	no	—
616	SD₁₆	—	2	8	no	—
617	SD₁₆	—	4	8	no	—
618	SD₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
619	SD₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
620	D₈	—	2	8	no	—
621	D₈	C₂×D₄×C₃₁	1	4	yes	complemented
622	M₁₆	—	2	4	no	—
623	M₁₆	—	2	8	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	8	no	—
626	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	complemented
627	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
628	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
629	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	8	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
637	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	8	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	8	no	—
645	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
651	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
652	C₄²	C₂⁴×C₃₁	1	2	yes	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	4	8	no	—
657	C₂³	—	4	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	—	8	8	no	—
660	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
661	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
662	Q₈	—	2	4	no	—
663	Q₈	—	2	1	no	—
664	Q₈	—	2	1	no	—
665	Q₈	—	2	4	no	—
666	Q₈	—	2	4	no	—
667	Q₈	—	4	8	no	—
668	Q₈	—	4	4	no	—
669	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
670	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	8	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	8	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	1	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	4	no	—
680	D₄	—	4	8	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	8	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	8	no	—
687	D₄	C₂²×D₄×C₃₁	1	2	yes	—
688	D₄	C₂²×D₄×C₃₁	1	2	yes	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	4	8	no	—
700	C₂×C₄	—	4	8	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
706	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
710	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
711	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
712	C₈	—	2	4	no	—
713	C₈	—	2	2	no	—
714	C₈	C₂²×D₄×C₃₁	1	2	yes	—
715	C₈	C₂²×D₄×C₃₁	1	2	yes	—
716	C₂²	—	2	2	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	4	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	8	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	8	no	—
725	C₂²	—	16	4	no	—
726	C₂²	—	16	8	no	—
727	C₂²	D₄²×C₃₁	1	2	yes	—
728	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	2	no	—
733	C₄	—	4	4	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	D₄²×C₃₁	1	2	yes	—
737	C₄	C₃₁×#577	1	4	yes	complemented
738	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
739	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
740	C₂	—	2	2	no	—
741	C₂	—	4	4	no	—
742	C₂	—	4	2	no	—
743	C₂	—	4	2	no	—
744	C₂	—	8	4	no	—
745	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
746	C₂	C₂×C₃₁×#577	1	2	yes	—

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#577	C₂	semidirect
2. C₃₁×#3499	C₂	semidirect
3. C₃₁×#3498	C₂	semidirect
4. C₃₁×#3284	C₂	semidirect
5. D₄×SD₁₆×C₃₁	C₂	semidirect
6. C₃₁×#3278	C₂	semidirect
7. C₃₁×#3272	C₂	semidirect
8. C₂×C₃₁×#492	C₂	semidirect
9. C₃₁×#3057	C₂	semidirect
10. C₃₁×#3039	C₂	semidirect
11. C₃₁×#3038	C₂	semidirect
12. C₃₁×#3010	C₂	semidirect
13. C₃₁×#3009	C₂	semidirect
14. C₄×C₃₁×#135	C₂	semidirect
15. C₃₁×#2931	C₂	semidirect
16. C₂×C₃₁×2₋¹⁺⁴	C₂²	semidirect
20. C₂×C₃₁×#137	C₂²	semidirect
21. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₃₁×#135	C₂²	semidirect
25. C₂²×SD₁₆×C₃₁	C₂²	semidirect
26. C₂²×SD₁₆×C₃₁	C₂²	semidirect
27. C₂²×SD₁₆×C₃₁	C₂²	semidirect
28. C₂×C₃₁×#131	C₂²	semidirect
30. D₄×Q₈×C₃₁	C₂²	semidirect
32. C₃₁×#547	C₂²	semidirect
36. C₃₁×#536	C₂²	semidirect
43. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
47. C₄×#41×C₃₁	C₂²	semidirect
48. C₃₁×#492	C₂²	semidirect
49. C₃₁×#492	C₂²	semidirect
50. C₃₁×#468	C₂²	semidirect
51. C₃₁×#465	C₂²	semidirect
52. C₃₁×#462	C₂²	semidirect
53. C₃₁×#461	C₂²	semidirect
54. C₃₁×#460	C₂²	semidirect
55. C₃₁×#459	C₂²	semidirect
56. C₃₁×#452	C₂²	semidirect
57. C₃₁×#450	C₂²	semidirect
58. C₃₁×#449	C₂²	semidirect
59. C₃₁×#448	C₂²	semidirect
60. C₄×Q₁₆×C₃₁	C₂²	semidirect
61. C₄×SD₁₆×C₃₁	C₂²	semidirect
62. C₄×SD₁₆×C₃₁	C₂²	semidirect
63. C₄×D₈×C₃₁	C₂²	semidirect
64. C₃₁×#436	C₂²	semidirect
65. C₈×D₄×C₃₁	C₂²	semidirect
66. C₃₁×#427	C₂²	semidirect
67. C₃₁×#423	C₂²	semidirect
68. C₃₁×#419	C₂²	semidirect
69. C₃₁×#418	C₂²	semidirect
71. C₃₁×#416	C₂²	semidirect
72. C₃₁×#408	C₂²	semidirect
73. C₂×C₄×C₈×C₃₁	C₂²	semidirect
100. C₃₁×#135	D₄	semidirect
191. #41×C₃₁	C₂×D₄	semidirect
238. Q₁₆×C₃₁	C₂×D₄	semidirect
244. SD₁₆×C₃₁	C₂×D₄	semidirect
245. SD₁₆×C₃₁	C₂×D₄	semidirect
247. D₈×C₃₁	C₂×D₄	semidirect
252. C₂×C₈×C₃₁	C₂×D₄	semidirect
279. #61087	C₃₁	direct (N × H)
343. C₂×#577	C₂×C₃₁	semidirect
344. #3499	C₂×C₃₁	semidirect
345. #3498	C₂×C₃₁	semidirect
346. #3284	C₂×C₃₁	semidirect
347. D₄×SD₁₆	C₂×C₃₁	semidirect
348. #3278	C₂×C₃₁	semidirect
349. #3272	C₂×C₃₁	semidirect
350. C₂×#492	C₂×C₃₁	semidirect
351. #3057	C₂×C₃₁	semidirect
352. #3039	C₂×C₃₁	semidirect
353. #3038	C₂×C₃₁	semidirect
354. #3010	C₂×C₃₁	semidirect
355. #3009	C₂×C₃₁	semidirect
356. C₄×#135	C₂×C₃₁	semidirect
357. #2931	C₂×C₃₁	semidirect
379. C₄×C₃₁	#577	semidirect
382. C₂×2₋¹⁺⁴	C₂²×C₃₁	semidirect
386. C₂×#137	C₂²×C₃₁	semidirect
387. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
388. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
390. C₂×#135	C₂²×C₃₁	semidirect
391. C₂²×SD₁₆	C₂²×C₃₁	semidirect
392. C₂²×SD₁₆	C₂²×C₃₁	semidirect
393. C₂²×SD₁₆	C₂²×C₃₁	semidirect
394. C₂×#131	C₂²×C₃₁	semidirect
396. D₄×Q₈	C₂²×C₃₁	semidirect
398. #547	C₂²×C₃₁	semidirect
402. #536	C₂²×C₃₁	semidirect
409. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
413. C₄×#41	C₂²×C₃₁	semidirect
414. #492	C₂²×C₃₁	semidirect
415. #492	C₂²×C₃₁	semidirect
416. #468	C₂²×C₃₁	semidirect
417. #465	C₂²×C₃₁	semidirect
418. #462	C₂²×C₃₁	semidirect
419. #461	C₂²×C₃₁	semidirect
420. #460	C₂²×C₃₁	semidirect
421. #459	C₂²×C₃₁	semidirect
422. #452	C₂²×C₃₁	semidirect
423. #450	C₂²×C₃₁	semidirect
424. #449	C₂²×C₃₁	semidirect
425. #448	C₂²×C₃₁	semidirect
426. C₄×Q₁₆	C₂²×C₃₁	semidirect
427. C₄×SD₁₆	C₂²×C₃₁	semidirect
428. C₄×SD₁₆	C₂²×C₃₁	semidirect
429. C₄×D₈	C₂²×C₃₁	semidirect
430. #436	C₂²×C₃₁	semidirect
431. C₈×D₄	C₂²×C₃₁	semidirect
432. #427	C₂²×C₃₁	semidirect
433. #423	C₂²×C₃₁	semidirect
434. #419	C₂²×C₃₁	semidirect
435. #418	C₂²×C₃₁	semidirect
437. #416	C₂²×C₃₁	semidirect
438. #408	C₂²×C₃₁	semidirect
439. C₂×C₄×C₈	C₂²×C₃₁	semidirect
473. #135	D₄×C₃₁	semidirect
550. C₃₁	#61087	direct (N × H)
565. #41	C₂×D₄×C₃₁	semidirect
612. Q₁₆	C₂×D₄×C₃₁	semidirect
618. SD₁₆	C₂×D₄×C₃₁	semidirect
619. SD₁₆	C₂×D₄×C₃₁	semidirect
621. D₈	C₂×D₄×C₃₁	semidirect
626. C₂×C₈	C₂×D₄×C₃₁	semidirect
737. C₄	C₃₁×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#577	2
C₃₁×#3499	2
C₃₁×#3498	2
C₃₁×#3284	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3278	2
C₃₁×#3272	2
C₂×C₃₁×#492	2
C₃₁×#3057	2
C₃₁×#3039	2
C₃₁×#3038	2
C₃₁×#3010	2
C₃₁×#3009	2
C₄×C₃₁×#135	2
C₃₁×#2931	2
#61087	31

Subgroups — C31×#61087 #21517846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#61087 #21517846