Subgroups — C₃₁×#34932 #21491691

Order 7936.

2428 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	C₂×C₃₁×#529	C₂	1	2	yes	maximal, complemented
2	C₃₁×#2553	C₂	1	4	yes	maximal, complemented
3	C₃₁×#2552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2537	C₂	1	1	yes	maximal, characteristic
7	C₃₁×#2496	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2489	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2427	C₂	1	2	yes	maximal, complemented
10	C₃₁×#2422	C₂	1	2	yes	maximal, complemented
11	C₃₁×#2395	C₂	1	4	yes	maximal, complemented
12	C₄×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₃₁×#121	C₂	1	2	yes	maximal, complemented
15	C₃₁×#2285	C₂	1	2	yes	maximal, complemented
16	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃₁×#529	—	2	16	no	—
20	C₂×C₃₁×#126	C₂²	1	4	yes	—
21	C₂×C₃₁×#125	C₂²	1	2	yes	—
22	C₂×C₃₁×#124	C₂²	1	2	yes	—
23	C₂×C₃₁×#123	C₂²	1	4	yes	—
24	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₃₁×#121	C₂²	1	2	yes	—
27	C₂×C₃₁×#121	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
36	C₂×C₃₁×#117	C₂²	1	4	yes	—
37	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
38	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
39	C₃₁×#400	C₂²	1	4	yes	—
40	C₃₁×#399	C₂²	1	4	yes	—
41	C₃₁×#398	C₂²	1	4	yes	—
42	C₃₁×#397	C₂²	1	4	yes	—
43	C₃₁×#397	C₂²	1	4	yes	—
44	C₃₁×#397	C₂²	1	4	yes	—
45	C₃₁×#394	C₂²	1	4	yes	—
46	C₃₁×#394	C₂²	1	4	yes	—
47	C₃₁×#391	C₂²	1	2	yes	—
48	C₃₁×#391	C₂²	1	2	yes	—
49	C₃₁×#390	C₂²	1	2	yes	—
50	C₃₁×#389	C₂²	1	2	yes	—
51	C₃₁×#389	C₂²	1	2	yes	—
52	C₃₁×#389	C₂²	1	2	yes	—
53	C₃₁×#389	C₂²	1	2	yes	—
54	C₃₁×#388	C₂²	1	4	yes	—
55	C₃₁×#387	C₂²	1	4	yes	—
56	C₃₁×#386	C₂²	1	4	yes	—
57	C₃₁×#385	C₂²	1	4	yes	—
58	C₃₁×#384	C₂²	1	1	yes	characteristic
59	C₃₁×#384	C₂²	1	2	yes	—
60	C₃₁×#384	C₂²	1	2	yes	—
61	C₃₁×#382	C₂²	1	4	yes	—
62	C₃₁×#380	C₂²	1	2	yes	—
63	C₃₁×#380	C₂²	1	4	yes	—
64	C₃₁×#380	C₂²	1	2	yes	—
65	C₃₁×#380	C₂²	1	2	yes	—
66	C₃₁×#380	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
69	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
70	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
71	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
72	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
73	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
74	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
78	C₄×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
79	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
80	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
81	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
83	C₄³×C₃₁	C₂²	1	1	yes	characteristic
84	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
85	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
89	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
90	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
91	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
92	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
93	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
94	C₃₁×C₄⋊Q₈	—	2	4	no	—
95	C₃₁×#126	—	2	16	no	—
96	C₃₁×#125	—	2	8	no	—
97	C₃₁×#124	—	2	8	no	—
98	C₃₁×#123	—	2	16	no	—
99	C₃₁×C₂²⋊Q₈	—	2	8	no	—
100	C₃₁×C₂²⋊Q₈	—	2	8	no	—
101	C₃₁×#121	—	2	8	no	—
102	C₃₁×#121	—	2	8	no	—
103	C₄×Q₈×C₃₁	—	2	8	no	—
104	C₄×D₄×C₃₁	—	2	4	no	—
105	C₄×D₄×C₃₁	—	2	16	no	—
106	C₄×D₄×C₃₁	—	2	4	no	—
107	C₄×D₄×C₃₁	—	2	4	no	—
108	C₄×D₄×C₃₁	—	2	4	no	—
109	C₄×D₄×C₃₁	—	2	4	no	—
110	C₄×D₄×C₃₁	D₄	1	8	yes	complemented
111	C₃₁×#117	—	2	16	no	—
112	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
141	C₂×C₄²×C₃₁	—	2	8	no	—
142	C₂×C₄²×C₃₁	—	2	8	no	—
143	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
144	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
145	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
146	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
147	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
148	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
150	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
151	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
152	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
157	C₃₁×#95	C₂³	1	2	yes	—
158	C₃₁×#95	C₂³	1	2	yes	—
159	C₃₁×#95	C₂³	1	2	yes	—
160	C₃₁×#95	C₂³	1	4	yes	—
161	C₃₁×#95	C₂³	1	4	yes	—
162	C₃₁×#95	C₂³	1	4	yes	—
163	C₃₁×#95	C₂³	1	4	yes	—
164	C₃₁×#95	C₂³	1	2	yes	—
165	C₃₁×#95	C₂³	1	4	yes	—
166	C₃₁×#95	C₂³	1	2	yes	—
167	C₃₁×#95	C₂³	1	2	yes	—
168	C₃₁×#95	C₂³	1	4	yes	—
169	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
170	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
171	C₂×Q₈×C₃₁	—	2	4	no	—
172	C₂×Q₈×C₃₁	—	2	4	no	—
173	C₂×Q₈×C₃₁	—	2	4	no	—
174	C₂×D₄×C₃₁	—	2	8	no	—
175	C₂×D₄×C₃₁	—	2	8	no	—
176	C₂×D₄×C₃₁	—	2	2	no	—
177	C₂×D₄×C₃₁	—	2	2	no	—
178	C₂×D₄×C₃₁	—	2	2	no	—
179	C₂×D₄×C₃₁	—	2	2	no	—
180	C₂×D₄×C₃₁	—	4	4	no	—
181	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
182	C₂×D₄×C₃₁	#41	1	4	yes	—
183	C₂²×C₄×C₃₁	—	2	4	no	—
184	C₂²×C₄×C₃₁	—	2	4	no	—
185	C₂²×C₄×C₃₁	—	2	4	no	—
186	C₂²×C₄×C₃₁	—	2	4	no	—
187	C₂²×C₄×C₃₁	—	2	4	no	—
188	C₂²×C₄×C₃₁	—	2	4	no	—
189	C₂²×C₄×C₃₁	—	2	4	no	—
190	C₂²×C₄×C₃₁	—	2	4	no	—
191	C₂²×C₄×C₃₁	—	2	4	no	—
192	C₂²×C₄×C₃₁	—	2	4	no	—
193	C₂²×C₄×C₃₁	—	2	4	no	—
194	C₂²×C₄×C₃₁	—	2	4	no	—
195	C₂²×C₄×C₃₁	—	2	4	no	—
196	C₂²×C₄×C₃₁	—	2	4	no	—
197	C₂²×C₄×C₃₁	—	2	4	no	—
198	C₂²×C₄×C₃₁	—	4	2	no	—
199	C₂²×C₄×C₃₁	—	4	2	no	—
200	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₃₁	—	2	8	no	—
217	C₄⋊C₄×C₃₁	—	2	8	no	—
218	C₄⋊C₄×C₃₁	—	2	8	no	—
219	C₄⋊C₄×C₃₁	—	2	4	no	—
220	C₄⋊C₄×C₃₁	—	2	8	no	—
221	C₄⋊C₄×C₃₁	—	2	2	no	—
222	C₄⋊C₄×C₃₁	—	2	2	no	—
223	C₄⋊C₄×C₃₁	—	2	2	no	—
224	C₄⋊C₄×C₃₁	—	2	2	no	—
225	C₄⋊C₄×C₃₁	—	2	4	no	—
226	C₄⋊C₄×C₃₁	—	2	8	no	—
227	C₄⋊C₄×C₃₁	—	2	4	no	—
228	C₄⋊C₄×C₃₁	—	2	4	no	—
229	C₄⋊C₄×C₃₁	—	4	2	no	—
230	C₄⋊C₄×C₃₁	—	4	4	no	—
231	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₃₁	#41	1	4	yes	—
233	C₂²⋊C₄×C₃₁	—	2	8	no	—
234	C₂²⋊C₄×C₃₁	—	2	8	no	—
235	C₂²⋊C₄×C₃₁	—	2	8	no	—
236	C₂²⋊C₄×C₃₁	—	2	4	no	—
237	C₂²⋊C₄×C₃₁	—	2	8	no	—
238	C₂²⋊C₄×C₃₁	—	2	8	no	—
239	C₂²⋊C₄×C₃₁	—	2	4	no	—
240	C₂²⋊C₄×C₃₁	—	2	4	no	—
241	C₂²⋊C₄×C₃₁	—	2	4	no	—
242	C₂²⋊C₄×C₃₁	—	2	4	no	—
243	C₂²⋊C₄×C₃₁	—	2	8	no	—
244	C₂²⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
245	C₄²×C₃₁	—	2	4	no	—
246	C₄²×C₃₁	—	2	4	no	—
247	C₄²×C₃₁	—	2	4	no	—
248	C₄²×C₃₁	—	2	8	no	—
249	C₄²×C₃₁	—	2	4	no	—
250	C₄²×C₃₁	—	2	4	no	—
251	C₄²×C₃₁	—	2	4	no	—
252	C₄²×C₃₁	—	2	2	no	—
253	C₄²×C₃₁	—	2	2	no	—
254	C₄²×C₃₁	—	2	2	no	—
255	C₄²×C₃₁	—	4	1	no	—
256	C₄²×C₃₁	C₂×D₄	1	4	yes	—
257	C₄²×C₃₁	#41	1	4	yes	—
258	C₄²×C₃₁	#41	1	4	yes	—
259	#34932	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂³×C₃₁	—	2	2	no	—
261	C₂³×C₃₁	—	2	2	no	—
262	C₂³×C₃₁	—	2	2	no	—
263	C₂³×C₃₁	—	2	2	no	—
264	C₂³×C₃₁	—	2	2	no	—
265	C₂³×C₃₁	—	2	2	no	—
266	C₂³×C₃₁	—	2	2	no	—
267	C₂³×C₃₁	—	2	2	no	—
268	C₂³×C₃₁	—	2	2	no	—
269	C₂³×C₃₁	—	2	2	no	—
270	C₂³×C₃₁	—	2	2	no	—
271	C₂³×C₃₁	—	2	2	no	—
272	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
273	C₂³×C₃₁	C₂×#41	1	4	yes	—
274	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
275	Q₈×C₃₁	—	4	8	no	—
276	D₄×C₃₁	—	2	8	no	—
277	D₄×C₃₁	—	2	8	no	—
278	D₄×C₃₁	—	4	16	no	—
279	C₂×C₄×C₃₁	—	2	2	no	—
280	C₂×C₄×C₃₁	—	2	2	no	—
281	C₂×C₄×C₃₁	—	2	1	no	—
282	C₂×C₄×C₃₁	—	2	1	no	—
283	C₂×C₄×C₃₁	—	2	1	no	—
284	C₂×C₄×C₃₁	—	2	2	no	—
285	C₂×C₄×C₃₁	—	2	1	no	—
286	C₂×C₄×C₃₁	—	2	1	no	—
287	C₂×C₄×C₃₁	—	2	1	no	—
288	C₂×C₄×C₃₁	—	2	2	no	—
289	C₂×C₄×C₃₁	—	2	16	no	—
290	C₂×C₄×C₃₁	—	2	2	no	—
291	C₂×C₄×C₃₁	—	2	2	no	—
292	C₂×C₄×C₃₁	—	2	2	no	—
293	C₂×C₄×C₃₁	—	2	4	no	—
294	C₂×C₄×C₃₁	—	2	4	no	—
295	C₂×C₄×C₃₁	—	2	2	no	—
296	C₂×C₄×C₃₁	—	2	1	no	—
297	C₂×C₄×C₃₁	—	2	1	no	—
298	C₂×C₄×C₃₁	—	2	2	no	—
299	C₂×C₄×C₃₁	—	2	2	no	—
300	C₂×C₄×C₃₁	—	2	2	no	—
301	C₂×C₄×C₃₁	—	2	2	no	—
302	C₂×C₄×C₃₁	—	2	2	no	—
303	C₂×C₄×C₃₁	—	2	4	no	—
304	C₂×C₄×C₃₁	—	2	4	no	—
305	C₂×C₄×C₃₁	—	2	2	no	—
306	C₂×C₄×C₃₁	—	2	4	no	—
307	C₂×C₄×C₃₁	—	2	1	no	—
308	C₂×C₄×C₃₁	—	2	2	no	—
309	C₂×C₄×C₃₁	—	2	2	no	—
310	C₂×C₄×C₃₁	—	2	4	no	—
311	C₂×C₄×C₃₁	—	4	8	no	—
312	C₂×C₄×C₃₁	—	4	8	no	—
313	C₂×C₄×C₃₁	—	4	8	no	—
314	C₂×C₄×C₃₁	—	4	8	no	—
315	C₂×C₄×C₃₁	—	4	8	no	—
316	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
321	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
322	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
323	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
324	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
325	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
326	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
327	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
328	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
329	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
330	C₂×#529	C₂×C₃₁	1	2	yes	complemented
331	#2553	C₂×C₃₁	1	4	yes	complemented
332	#2552	C₂×C₃₁	1	1	yes	characteristic, complemented
333	#2547	C₂×C₃₁	1	1	yes	characteristic, complemented
334	#2542	C₂×C₃₁	1	1	yes	characteristic, complemented
335	#2537	C₂×C₃₁	1	1	yes	characteristic
336	#2496	C₂×C₃₁	1	2	yes	complemented
337	#2489	C₂×C₃₁	1	2	yes	complemented
338	#2427	C₂×C₃₁	1	2	yes	complemented
339	#2422	C₂×C₃₁	1	2	yes	complemented
340	#2395	C₂×C₃₁	1	4	yes	complemented
341	C₄×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
342	C₄×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
343	C₄×#121	C₂×C₃₁	1	2	yes	complemented
344	#2285	C₂×C₃₁	1	2	yes	complemented
345	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
346	C₄²×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
347	C₂²×C₃₁	—	2	4	no	—
348	C₂²×C₃₁	—	2	4	no	—
349	C₂²×C₃₁	—	2	4	no	—
350	C₂²×C₃₁	—	2	4	no	—
351	C₂²×C₃₁	—	2	4	no	—
352	C₂²×C₃₁	—	2	4	no	—
353	C₂²×C₃₁	—	4	2	no	—
354	C₂²×C₃₁	—	4	2	no	—
355	C₂²×C₃₁	—	4	2	no	—
356	C₂²×C₃₁	—	4	2	no	—
357	C₂²×C₃₁	—	4	2	no	—
358	C₂²×C₃₁	—	4	2	no	—
359	C₂²×C₃₁	—	4	2	no	—
360	C₂²×C₃₁	—	4	2	no	—
361	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
366	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
367	C₂²×C₃₁	#585	1	1	yes	characteristic
368	C₄×C₃₁	—	2	2	no	—
369	C₄×C₃₁	—	2	4	no	—
370	C₄×C₃₁	—	2	2	no	—
371	C₄×C₃₁	—	2	2	no	—
372	C₄×C₃₁	—	2	4	no	—
373	C₄×C₃₁	—	4	2	no	—
374	C₄×C₃₁	—	4	2	no	—
375	C₄×C₃₁	—	4	4	no	—
376	C₄×C₃₁	—	4	2	no	—
377	C₄×C₃₁	—	4	2	no	—
378	C₄×C₃₁	—	4	4	no	—
379	C₄×C₃₁	—	4	1	no	—
380	C₄×C₃₁	#529	1	4	yes	complemented
381	C₄×C₃₁	#532	1	4	yes	—
382	C₄×C₃₁	#547	1	4	yes	—
383	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
384	#529	—	2	16	no	—
385	C₂×#126	C₂²×C₃₁	1	4	yes	—
386	C₂×#125	C₂²×C₃₁	1	2	yes	—
387	C₂×#124	C₂²×C₃₁	1	2	yes	—
388	C₂×#123	C₂²×C₃₁	1	4	yes	—
389	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
391	C₂×#121	C₂²×C₃₁	1	2	yes	—
392	C₂×#121	C₂²×C₃₁	1	2	yes	—
393	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
394	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
395	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
396	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
397	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
398	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
400	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
401	C₂×#117	C₂²×C₃₁	1	4	yes	—
402	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
403	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
404	#400	C₂²×C₃₁	1	4	yes	—
405	#399	C₂²×C₃₁	1	4	yes	—
406	#398	C₂²×C₃₁	1	4	yes	—
407	#397	C₂²×C₃₁	1	4	yes	—
408	#397	C₂²×C₃₁	1	4	yes	—
409	#397	C₂²×C₃₁	1	4	yes	—
410	#394	C₂²×C₃₁	1	4	yes	—
411	#394	C₂²×C₃₁	1	4	yes	—
412	#391	C₂²×C₃₁	1	2	yes	—
413	#391	C₂²×C₃₁	1	2	yes	—
414	#390	C₂²×C₃₁	1	2	yes	—
415	#389	C₂²×C₃₁	1	2	yes	—
416	#389	C₂²×C₃₁	1	2	yes	—
417	#389	C₂²×C₃₁	1	2	yes	—
418	#389	C₂²×C₃₁	1	2	yes	—
419	#388	C₂²×C₃₁	1	4	yes	—
420	#387	C₂²×C₃₁	1	4	yes	—
421	#386	C₂²×C₃₁	1	4	yes	—
422	#385	C₂²×C₃₁	1	4	yes	—
423	#384	C₂²×C₃₁	1	1	yes	characteristic
424	#384	C₂²×C₃₁	1	2	yes	—
425	#384	C₂²×C₃₁	1	2	yes	—
426	#382	C₂²×C₃₁	1	4	yes	—
427	#380	C₂²×C₃₁	1	2	yes	—
428	#380	C₂²×C₃₁	1	4	yes	—
429	#380	C₂²×C₃₁	1	2	yes	—
430	#380	C₂²×C₃₁	1	2	yes	—
431	#380	C₂²×C₃₁	1	2	yes	—
432	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
433	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
434	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
435	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
436	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
438	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
439	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
441	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
445	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
446	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
447	C₄×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
448	C₄³	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×C₃₁	—	4	4	no	—
450	C₂×C₃₁	—	4	4	no	—
451	C₂×C₃₁	C₂×#529	1	1	yes	characteristic
452	C₂×C₃₁	C₂×#532	1	1	yes	characteristic
453	C₂×C₃₁	#3461	1	1	yes	characteristic
454	C₂×C₃₁	C₂×#547	1	1	yes	characteristic
455	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
456	C₂×C₃₁	#3475	1	1	yes	characteristic
457	C₂×C₃₁	#3482	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
459	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
460	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
463	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
464	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
465	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
466	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
467	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
468	C₄⋊Q₈	—	2	4	no	—
469	#126	—	2	16	no	—
470	#125	—	2	8	no	—
471	#124	—	2	8	no	—
472	#123	—	2	16	no	—
473	C₂²⋊Q₈	—	2	8	no	—
474	C₂²⋊Q₈	—	2	8	no	—
475	#121	—	2	8	no	—
476	#121	—	2	8	no	—
477	C₄×Q₈	—	2	8	no	—
478	C₄×D₄	—	2	4	no	—
479	C₄×D₄	—	2	16	no	—
480	C₄×D₄	—	2	4	no	—
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	4	no	—
484	C₄×D₄	D₄×C₃₁	1	8	yes	complemented
485	#117	—	2	16	no	—
486	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
491	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
493	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
503	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
515	C₂×C₄²	—	2	8	no	—
516	C₂×C₄²	—	2	8	no	—
517	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
518	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
519	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
522	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
523	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
524	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
525	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
526	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
527	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
531	#95	C₂³×C₃₁	1	2	yes	—
532	#95	C₂³×C₃₁	1	2	yes	—
533	#95	C₂³×C₃₁	1	2	yes	—
534	#95	C₂³×C₃₁	1	2	yes	—
535	#95	C₂³×C₃₁	1	2	yes	—
536	#95	C₂³×C₃₁	1	2	yes	—
537	#95	C₂³×C₃₁	1	4	yes	—
538	#95	C₂³×C₃₁	1	4	yes	—
539	#95	C₂³×C₃₁	1	4	yes	—
540	#95	C₂³×C₃₁	1	4	yes	—
541	#95	C₂³×C₃₁	1	4	yes	—
542	#95	C₂³×C₃₁	1	4	yes	—
543	C₃₁	#34932	1	1	yes	characteristic, direct product factor, Sylow
544	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
545	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	4	no	—
548	C₂×Q₈	—	2	4	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	8	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
557	C₂×D₄	#41×C₃₁	1	4	yes	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	4	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
576	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
582	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
583	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
584	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	8	no	—
593	C₄⋊C₄	—	2	8	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	8	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	4	2	no	—
605	C₄⋊C₄	—	4	4	no	—
606	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
607	C₄⋊C₄	#41×C₃₁	1	4	yes	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	4	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	—	2	4	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
620	C₄²	—	2	4	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	8	no	—
624	C₄²	—	2	4	no	—
625	C₄²	—	2	4	no	—
626	C₄²	—	2	4	no	—
627	C₄²	—	2	2	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	4	1	no	—
631	C₄²	C₂×D₄×C₃₁	1	4	yes	—
632	C₄²	#41×C₃₁	1	4	yes	—
633	C₄²	#41×C₃₁	1	4	yes	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
647	C₂³	C₂×#41×C₃₁	1	4	yes	—
648	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
649	Q₈	—	4	8	no	—
650	D₄	—	2	8	no	—
651	D₄	—	2	8	no	—
652	D₄	—	4	16	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	16	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	4	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	4	8	no	—
686	C₂×C₄	—	4	8	no	—
687	C₂×C₄	—	4	8	no	—
688	C₂×C₄	—	4	8	no	—
689	C₂×C₄	—	4	8	no	—
690	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
692	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
694	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
695	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
696	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
697	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
698	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
699	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
700	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
701	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
702	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
703	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
704	C₂²	—	2	4	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	2	4	no	—
707	C₂²	—	2	4	no	—
708	C₂²	—	2	4	no	—
709	C₂²	—	2	4	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
719	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
720	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
721	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
722	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
723	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
724	C₂²	C₃₁×#585	1	1	yes	characteristic
725	C₄	—	2	2	no	—
726	C₄	—	2	4	no	—
727	C₄	—	2	2	no	—
728	C₄	—	2	2	no	—
729	C₄	—	2	4	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	4	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	4	no	—
736	C₄	—	4	1	no	—
737	C₄	C₃₁×#529	1	4	yes	complemented
738	C₄	C₃₁×#532	1	4	yes	—
739	C₄	C₃₁×#547	1	4	yes	—
740	C₂	—	4	4	no	—
741	C₂	—	4	4	no	—
742	C₂	C₂×C₃₁×#529	1	1	yes	characteristic
743	C₂	C₂×C₃₁×#532	1	1	yes	characteristic
744	C₂	C₃₁×#3461	1	1	yes	characteristic
745	C₂	C₂×C₃₁×#547	1	1	yes	characteristic
746	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
747	C₂	C₃₁×#3475	1	1	yes	characteristic
748	C₂	C₃₁×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₃₁×#2537	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#529	C₂	semidirect
2. C₃₁×#2553	C₂	semidirect
3. C₃₁×#2552	C₂	semidirect
4. C₃₁×#2547	C₂	semidirect
5. C₃₁×#2542	C₂	semidirect
7. C₃₁×#2496	C₂	semidirect
8. C₃₁×#2489	C₂	semidirect
9. C₃₁×#2427	C₂	semidirect
10. C₃₁×#2422	C₂	semidirect
11. C₃₁×#2395	C₂	semidirect
12. C₄×C₃₁×C₄⋊Q₈	C₂	semidirect
13. C₄×C₃₁×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₃₁×#121	C₂	semidirect
15. C₃₁×#2285	C₂	semidirect
16. C₄²×D₄×C₃₁	C₂	semidirect
17. C₄²×D₄×C₃₁	C₂	semidirect
110. C₄×D₄×C₃₁	D₄	semidirect
259. #34932	C₃₁	direct (N × H)
330. C₂×#529	C₂×C₃₁	semidirect
331. #2553	C₂×C₃₁	semidirect
332. #2552	C₂×C₃₁	semidirect
333. #2547	C₂×C₃₁	semidirect
334. #2542	C₂×C₃₁	semidirect
336. #2496	C₂×C₃₁	semidirect
337. #2489	C₂×C₃₁	semidirect
338. #2427	C₂×C₃₁	semidirect
339. #2422	C₂×C₃₁	semidirect
340. #2395	C₂×C₃₁	semidirect
341. C₄×C₄⋊Q₈	C₂×C₃₁	semidirect
342. C₄×C₂²⋊Q₈	C₂×C₃₁	semidirect
343. C₄×#121	C₂×C₃₁	semidirect
344. #2285	C₂×C₃₁	semidirect
345. C₄²×D₄	C₂×C₃₁	semidirect
346. C₄²×D₄	C₂×C₃₁	semidirect
380. C₄×C₃₁	#529	semidirect
484. C₄×D₄	D₄×C₃₁	semidirect
543. C₃₁	#34932	direct (N × H)
737. C₄	C₃₁×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#529	2
C₃₁×#2553	2
C₃₁×#2552	2
C₃₁×#2547	2
C₃₁×#2542	2
C₃₁×#2537	2
C₃₁×#2496	2
C₃₁×#2489	2
C₃₁×#2427	2
C₃₁×#2422	2
C₃₁×#2395	2
C₄×C₃₁×C₄⋊Q₈	2
C₄×C₃₁×C₂²⋊Q₈	2
C₄×C₃₁×#121	2
C₃₁×#2285	2
C₄²×D₄×C₃₁	2
#34932	31

Subgroups — C31×#34932 #21491691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34932 #21491691