Subgroups — C₂×C₃₁×#3270 #21517787

Order 7936.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#548	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#3270	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₃₁×#497	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₃₁×#137	—	2	8	no	—
22	C₂×C₃₁×#137	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₃₁	—	2	8	no	—
24	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
27	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
29	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
30	C₂²×Q₁₆×C₃₁	C₂²	1	8	yes	complemented
31	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₃₁	—	2	4	no	—
37	D₄×Q₈×C₃₁	C₂²	1	8	yes	complemented
38	C₃₁×#548	—	2	4	no	—
39	C₃₁×#548	C₂²	1	8	yes	—
40	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₃₁×#124	—	2	1	no	—
43	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
45	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
46	C₂×C₃₁×C₂²⋊Q₈	—	2	1	no	—
47	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
50	C₂×C₃₁×#121	—	2	1	no	—
51	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
52	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
53	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₃₁	—	2	1	no	—
55	C₂×C₄×D₄×C₃₁	—	2	1	no	—
56	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
57	C₃₁×#497	C₂²	1	8	yes	complemented
58	C₃₁×#470	C₂²	1	8	yes	complemented
59	C₃₁×#465	C₂²	1	8	yes	complemented
60	C₃₁×#464	C₂²	1	8	yes	complemented
61	C₃₁×#462	C₂²	1	8	yes	complemented
62	C₃₁×#452	C₂²	1	8	yes	complemented
63	C₃₁×#451	C₂²	1	8	yes	complemented
64	C₃₁×#451	C₂²	1	8	yes	complemented
65	C₃₁×#448	C₂²	1	8	yes	complemented
66	C₃₁×#441	C₂²	1	8	yes	complemented
67	C₃₁×#435	C₂²	1	8	yes	complemented
68	C₂×C₃₁×#106	C₂²	1	1	yes	characteristic
69	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
71	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
73	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
74	C₂×C₃₁×#103	C₂²	1	1	yes	characteristic
75	C₂×C₃₁×#102	C₂²	1	1	yes	characteristic
76	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
77	C₂×C₃₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
78	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
79	C₂×#41×C₃₁	—	2	2	no	—
80	C₂×#41×C₃₁	—	2	4	no	—
81	C₂×#41×C₃₁	—	4	2	no	—
82	C₂×#41×C₃₁	C₂³	1	4	yes	—
83	C₂²×Q₈×C₃₁	—	2	1	no	—
84	C₂²×Q₈×C₃₁	—	2	1	no	—
85	C₂²×Q₈×C₃₁	—	2	1	no	—
86	C₂²×Q₈×C₃₁	—	2	2	no	—
87	C₂²×Q₈×C₃₁	—	2	2	no	—
88	C₂²×Q₈×C₃₁	—	2	2	no	—
89	C₂²×Q₈×C₃₁	—	2	4	no	—
90	C₂²×Q₈×C₃₁	—	2	4	no	—
91	C₂²×Q₈×C₃₁	—	2	4	no	—
92	C₂²×Q₈×C₃₁	—	4	2	no	—
93	C₂²×Q₈×C₃₁	—	4	2	no	—
94	C₂²×Q₈×C₃₁	—	4	2	no	—
95	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
101	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₁	—	2	1	no	—
104	C₂²×D₄×C₃₁	—	2	1	no	—
105	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	—	2	1	no	—
108	C₂³×C₄×C₃₁	—	2	1	no	—
109	C₂³×C₄×C₃₁	—	2	1	no	—
110	C₂³×C₄×C₃₁	—	2	1	no	—
111	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₃₁×#137	—	2	32	no	—
114	C₂×Q₁₆×C₃₁	—	2	4	no	—
115	C₂×Q₁₆×C₃₁	—	2	4	no	—
116	C₂×Q₁₆×C₃₁	—	2	4	no	—
117	C₂×Q₁₆×C₃₁	—	2	32	no	—
118	C₂×Q₁₆×C₃₁	—	2	4	no	—
119	C₂×Q₁₆×C₃₁	—	4	2	no	—
120	C₂×Q₁₆×C₃₁	D₄	1	8	yes	complemented
121	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
122	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
123	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
124	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
125	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
126	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
127	C₂×SD₁₆×C₃₁	—	2	4	no	—
128	C₂×SD₁₆×C₃₁	—	2	4	no	—
129	C₂×SD₁₆×C₃₁	—	4	2	no	—
130	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
132	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
133	C₂×M₁₆×C₃₁	—	2	4	no	—
134	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
135	C₂²×C₈×C₃₁	—	2	4	no	—
136	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
140	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
141	C₃₁×C₄⋊Q₈	—	2	8	no	—
142	C₃₁×C₄⋊Q₈	—	2	2	no	—
143	C₃₁×C₄⋊Q₈	C₂³	1	4	yes	—
144	C₃₁×#124	—	2	8	no	—
145	C₃₁×#124	—	2	2	no	—
146	C₃₁×#124	C₂³	1	4	yes	—
147	C₃₁×C₂²⋊Q₈	—	2	2	no	—
148	C₃₁×C₂²⋊Q₈	—	2	2	no	—
149	C₃₁×C₂²⋊Q₈	—	2	2	no	—
150	C₃₁×C₂²⋊Q₈	—	2	8	no	—
151	C₃₁×C₂²⋊Q₈	—	2	8	no	—
152	C₃₁×C₂²⋊Q₈	—	2	8	no	—
153	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
155	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₃₁×#121	—	2	8	no	—
157	C₃₁×#121	—	2	2	no	—
158	C₃₁×#121	C₂³	1	4	yes	—
159	C₄×Q₈×C₃₁	—	2	2	no	—
160	C₄×Q₈×C₃₁	—	2	2	no	—
161	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
162	C₄×Q₈×C₃₁	C₂³	1	4	yes	—
163	C₄×D₄×C₃₁	—	2	8	no	—
164	C₄×D₄×C₃₁	—	2	8	no	—
165	C₄×D₄×C₃₁	D₄	1	4	yes	—
166	C₄×D₄×C₃₁	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
168	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
171	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
172	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
173	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
174	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₃₁	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₃₁	—	2	1	no	—
186	C₂×C₄²×C₃₁	—	2	1	no	—
187	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
188	C₃₁×#106	C₂³	1	4	yes	—
189	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
190	C₃₁×#103	C₂³	1	4	yes	—
191	C₃₁×#103	C₂³	1	4	yes	—
192	C₃₁×#103	C₂³	1	4	yes	—
193	C₃₁×#103	C₂³	1	4	yes	—
194	C₃₁×#103	C₂³	1	4	yes	—
195	C₃₁×#102	C₂³	1	4	yes	—
196	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₃₁×#97	C₂³	1	4	yes	—
199	C₂⁴×C₃₁	—	2	1	no	—
200	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
202	#41×C₃₁	—	2	8	no	—
203	#41×C₃₁	—	4	4	no	—
204	#41×C₃₁	—	4	8	no	—
205	C₂×Q₈×C₃₁	—	2	1	no	—
206	C₂×Q₈×C₃₁	—	2	1	no	—
207	C₂×Q₈×C₃₁	—	2	4	no	—
208	C₂×Q₈×C₃₁	—	2	1	no	—
209	C₂×Q₈×C₃₁	—	2	4	no	—
210	C₂×Q₈×C₃₁	—	2	4	no	—
211	C₂×Q₈×C₃₁	—	2	1	no	—
212	C₂×Q₈×C₃₁	—	2	1	no	—
213	C₂×Q₈×C₃₁	—	2	2	no	—
214	C₂×Q₈×C₃₁	—	2	2	no	—
215	C₂×Q₈×C₃₁	—	2	8	no	—
216	C₂×Q₈×C₃₁	—	2	8	no	—
217	C₂×Q₈×C₃₁	—	2	8	no	—
218	C₂×Q₈×C₃₁	—	2	2	no	—
219	C₂×Q₈×C₃₁	—	2	2	no	—
220	C₂×Q₈×C₃₁	—	2	2	no	—
221	C₂×Q₈×C₃₁	—	2	2	no	—
222	C₂×Q₈×C₃₁	—	2	2	no	—
223	C₂×Q₈×C₃₁	—	2	2	no	—
224	C₂×Q₈×C₃₁	—	4	4	no	—
225	C₂×Q₈×C₃₁	—	4	4	no	—
226	C₂×Q₈×C₃₁	—	4	4	no	—
227	C₂×Q₈×C₃₁	—	4	4	no	—
228	C₂×Q₈×C₃₁	—	4	4	no	—
229	C₂×Q₈×C₃₁	—	4	4	no	—
230	C₂×Q₈×C₃₁	—	4	8	no	—
231	C₂×Q₈×C₃₁	—	4	8	no	—
232	C₂×Q₈×C₃₁	—	4	8	no	—
233	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
234	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
235	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
236	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
237	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
240	C₂×D₄×C₃₁	—	2	4	no	—
241	C₂×D₄×C₃₁	—	2	4	no	—
242	C₂×D₄×C₃₁	—	2	4	no	—
243	C₂×D₄×C₃₁	—	2	2	no	—
244	C₂×D₄×C₃₁	—	2	1	no	—
245	C₂×D₄×C₃₁	—	2	2	no	—
246	C₂×D₄×C₃₁	—	4	4	no	—
247	C₂×D₄×C₃₁	—	4	4	no	—
248	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
249	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₃₁	—	2	1	no	—
251	C₂²×C₄×C₃₁	—	2	1	no	—
252	C₂²×C₄×C₃₁	—	2	2	no	—
253	C₂²×C₄×C₃₁	—	2	2	no	—
254	C₂²×C₄×C₃₁	—	2	2	no	—
255	C₂²×C₄×C₃₁	—	2	2	no	—
256	C₂²×C₄×C₃₁	—	2	4	no	—
257	C₂²×C₄×C₃₁	—	2	4	no	—
258	C₂²×C₄×C₃₁	—	2	4	no	—
259	C₂²×C₄×C₃₁	—	2	1	no	—
260	C₂²×C₄×C₃₁	—	2	1	no	—
261	C₂²×C₄×C₃₁	—	2	1	no	—
262	C₂²×C₄×C₃₁	—	2	1	no	—
263	C₂²×C₄×C₃₁	—	2	1	no	—
264	C₂²×C₄×C₃₁	—	2	4	no	—
265	C₂²×C₄×C₃₁	—	4	4	no	—
266	C₂²×C₄×C₃₁	—	4	4	no	—
267	C₂²×C₄×C₃₁	—	4	4	no	—
268	C₂²×C₄×C₃₁	—	4	4	no	—
269	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
278	Q₁₆×C₃₁	—	2	8	no	—
279	Q₁₆×C₃₁	—	2	8	no	—
280	Q₁₆×C₃₁	—	2	8	no	—
281	Q₁₆×C₃₁	—	2	8	no	—
282	Q₁₆×C₃₁	—	4	4	no	—
283	Q₁₆×C₃₁	C₂×D₄	1	16	yes	complemented
284	SD₁₆×C₃₁	—	2	8	no	—
285	SD₁₆×C₃₁	—	2	8	no	—
286	SD₁₆×C₃₁	—	4	4	no	—
287	M₁₆×C₃₁	—	2	8	no	—
288	C₂×C₈×C₃₁	—	2	2	no	—
289	C₂×C₈×C₃₁	—	2	2	no	—
290	C₂×C₈×C₃₁	—	2	2	no	—
291	C₂×C₈×C₃₁	—	2	8	no	—
292	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
293	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
294	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
295	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
296	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
297	C₄⋊C₄×C₃₁	—	2	4	no	—
298	C₄⋊C₄×C₃₁	—	2	4	no	—
299	C₄⋊C₄×C₃₁	—	2	4	no	—
300	C₄⋊C₄×C₃₁	—	2	4	no	—
301	C₄⋊C₄×C₃₁	—	2	4	no	—
302	C₄⋊C₄×C₃₁	—	2	4	no	—
303	C₄⋊C₄×C₃₁	—	2	4	no	—
304	C₄⋊C₄×C₃₁	—	2	1	no	—
305	C₄⋊C₄×C₃₁	—	2	1	no	—
306	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
309	C₂²⋊C₄×C₃₁	—	2	4	no	—
310	C₂²⋊C₄×C₃₁	—	2	4	no	—
311	C₂²⋊C₄×C₃₁	—	2	4	no	—
312	C₂²⋊C₄×C₃₁	—	2	4	no	—
313	C₂²⋊C₄×C₃₁	—	2	4	no	—
314	C₂²⋊C₄×C₃₁	—	2	4	no	—
315	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
316	C₂²⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
317	C₄²×C₃₁	—	2	4	no	—
318	C₄²×C₃₁	—	2	4	no	—
319	C₄²×C₃₁	C₂×D₄	1	2	yes	—
320	C₄²×C₃₁	C₂⁴	1	2	yes	—
321	C₂×#3270	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₃₁	—	2	2	no	—
323	C₂³×C₃₁	—	2	2	no	—
324	C₂³×C₃₁	—	2	2	no	—
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	—	2	2	no	—
327	C₂³×C₃₁	—	2	2	no	—
328	C₂³×C₃₁	—	4	2	no	—
329	C₂³×C₃₁	—	4	2	no	—
330	C₂³×C₃₁	—	4	2	no	—
331	C₂³×C₃₁	#137	1	4	yes	complemented
332	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
333	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
334	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₃₁	—	2	4	no	—
336	Q₈×C₃₁	—	2	4	no	—
337	Q₈×C₃₁	—	2	2	no	—
338	Q₈×C₃₁	—	2	2	no	—
339	Q₈×C₃₁	—	2	2	no	—
340	Q₈×C₃₁	—	2	2	no	—
341	Q₈×C₃₁	—	2	2	no	—
342	Q₈×C₃₁	—	2	2	no	—
343	Q₈×C₃₁	—	2	2	no	—
344	Q₈×C₃₁	—	2	2	no	—
345	Q₈×C₃₁	—	4	8	no	—
346	Q₈×C₃₁	—	4	8	no	—
347	Q₈×C₃₁	—	4	8	no	—
348	Q₈×C₃₁	—	4	2	no	—
349	Q₈×C₃₁	—	4	2	no	—
350	Q₈×C₃₁	—	4	2	no	—
351	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
352	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
353	D₄×C₃₁	—	2	8	no	—
354	D₄×C₃₁	—	2	2	no	—
355	D₄×C₃₁	—	2	2	no	—
356	D₄×C₃₁	—	4	8	no	—
357	D₄×C₃₁	—	4	8	no	—
358	D₄×C₃₁	—	4	2	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	4	no	—
362	C₂×C₄×C₃₁	—	2	4	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	2	no	—
366	C₂×C₄×C₃₁	—	2	2	no	—
367	C₂×C₄×C₃₁	—	2	4	no	—
368	C₂×C₄×C₃₁	—	2	4	no	—
369	C₂×C₄×C₃₁	—	2	2	no	—
370	C₂×C₄×C₃₁	—	2	2	no	—
371	C₂×C₄×C₃₁	—	2	2	no	—
372	C₂×C₄×C₃₁	—	2	2	no	—
373	C₂×C₄×C₃₁	—	2	2	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	2	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	2	no	—
378	C₂×C₄×C₃₁	—	4	8	no	—
379	C₂×C₄×C₃₁	—	4	8	no	—
380	C₂×C₄×C₃₁	—	4	8	no	—
381	C₂×C₄×C₃₁	—	4	8	no	—
382	C₂×C₄×C₃₁	—	4	2	no	—
383	C₂×C₄×C₃₁	—	4	2	no	—
384	C₂×C₄×C₃₁	—	4	2	no	—
385	C₂×C₄×C₃₁	—	4	2	no	—
386	C₂×C₄×C₃₁	—	4	2	no	—
387	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
390	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
395	C₈×C₃₁	—	2	2	no	—
396	C₈×C₃₁	—	2	2	no	—
397	C₈×C₃₁	—	2	2	no	—
398	C₈×C₃₁	C₂²×D₄	1	4	yes	—
399	C₂²×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
400	C₂³×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
401	C₂×D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
402	C₂×#548	C₂×C₃₁	1	1	yes	characteristic
403	#3270	C₂×C₃₁	1	16	yes	direct product factor
404	C₂×#497	C₂×C₃₁	1	1	yes	characteristic, complemented
405	C₂×#470	C₂×C₃₁	1	1	yes	characteristic, complemented
406	C₂×#465	C₂×C₃₁	1	1	yes	characteristic, complemented
407	C₂×#464	C₂×C₃₁	1	1	yes	characteristic, complemented
408	C₂×#462	C₂×C₃₁	1	1	yes	characteristic, complemented
409	C₂×#452	C₂×C₃₁	1	1	yes	characteristic, complemented
410	C₂×#451	C₂×C₃₁	1	1	yes	characteristic, complemented
411	C₂×#451	C₂×C₃₁	1	1	yes	characteristic, complemented
412	C₂×#448	C₂×C₃₁	1	1	yes	characteristic, complemented
413	C₂×#441	C₂×C₃₁	1	1	yes	characteristic, complemented
414	C₂×#435	C₂×C₃₁	1	1	yes	characteristic, complemented
415	C₂²×C₃₁	—	2	2	no	—
416	C₂²×C₃₁	—	2	8	no	—
417	C₂²×C₃₁	—	2	2	no	—
418	C₂²×C₃₁	—	2	2	no	—
419	C₂²×C₃₁	—	2	2	no	—
420	C₂²×C₃₁	—	2	2	no	—
421	C₂²×C₃₁	—	4	4	no	—
422	C₂²×C₃₁	—	4	2	no	—
423	C₂²×C₃₁	—	4	2	no	—
424	C₂²×C₃₁	—	4	2	no	—
425	C₂²×C₃₁	—	8	4	no	—
426	C₂²×C₃₁	D₄²	1	2	yes	—
427	C₂²×C₃₁	C₂×#137	1	2	yes	—
428	C₂²×C₃₁	C₂×#137	1	4	yes	complemented
429	C₂²×C₃₁	#578	1	2	yes	—
430	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	2	no	—
433	C₄×C₃₁	—	2	4	no	—
434	C₄×C₃₁	—	2	4	no	—
435	C₄×C₃₁	—	2	2	no	—
436	C₄×C₃₁	—	2	2	no	—
437	C₄×C₃₁	—	4	2	no	—
438	C₄×C₃₁	—	4	2	no	—
439	C₄×C₃₁	—	4	2	no	—
440	C₄×C₃₁	—	4	2	no	—
441	C₄×C₃₁	—	4	2	no	—
442	C₄×C₃₁	D₄²	1	2	yes	—
443	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
444	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
446	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
447	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
448	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
449	C₂×#137	—	2	8	no	—
450	C₂×#137	C₂²×C₃₁	1	8	yes	complemented
451	C₂²×Q₁₆	—	2	8	no	—
452	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
453	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
454	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
455	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
456	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
457	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
458	C₂²×Q₁₆	C₂²×C₃₁	1	8	yes	complemented
459	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
460	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
461	C₂²×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic
462	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
463	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
464	D₄×Q₈	—	2	4	no	—
465	D₄×Q₈	C₂²×C₃₁	1	8	yes	complemented
466	#548	—	2	4	no	—
467	#548	C₂²×C₃₁	1	8	yes	—
468	C₂×C₄⋊Q₈	—	2	1	no	—
469	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
470	C₂×#124	—	2	1	no	—
471	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
472	C₂×C₂²⋊Q₈	—	2	1	no	—
473	C₂×C₂²⋊Q₈	—	2	1	no	—
474	C₂×C₂²⋊Q₈	—	2	1	no	—
475	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
476	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
477	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
478	C₂×#121	—	2	1	no	—
479	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
481	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
482	C₂×C₄×D₄	—	2	1	no	—
483	C₂×C₄×D₄	—	2	1	no	—
484	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
485	#497	C₂²×C₃₁	1	8	yes	complemented
486	#470	C₂²×C₃₁	1	8	yes	complemented
487	#465	C₂²×C₃₁	1	8	yes	complemented
488	#464	C₂²×C₃₁	1	8	yes	complemented
489	#462	C₂²×C₃₁	1	8	yes	complemented
490	#452	C₂²×C₃₁	1	8	yes	complemented
491	#451	C₂²×C₃₁	1	8	yes	complemented
492	#451	C₂²×C₃₁	1	8	yes	complemented
493	#448	C₂²×C₃₁	1	8	yes	complemented
494	#441	C₂²×C₃₁	1	8	yes	complemented
495	#435	C₂²×C₃₁	1	8	yes	complemented
496	C₂×#106	C₂²×C₃₁	1	1	yes	characteristic
497	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
498	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
499	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
500	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
501	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
502	C₂×#103	C₂²×C₃₁	1	1	yes	characteristic
503	C₂×#102	C₂²×C₃₁	1	1	yes	characteristic
504	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
505	C₂×C₂²⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
506	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
507	C₂×C₃₁	—	2	4	no	—
508	C₂×C₃₁	—	4	2	no	—
509	C₂×C₃₁	—	8	2	no	—
510	C₂×C₃₁	#3270	1	4	yes	direct product factor
511	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
512	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
513	C₂×C₃₁	C₂×#578	1	1	yes	characteristic
514	C₂×#41	—	2	2	no	—
515	C₂×#41	—	2	4	no	—
516	C₂×#41	—	4	2	no	—
517	C₂×#41	C₂³×C₃₁	1	4	yes	—
518	C₂²×Q₈	—	2	1	no	—
519	C₂²×Q₈	—	2	1	no	—
520	C₂²×Q₈	—	2	1	no	—
521	C₂²×Q₈	—	2	2	no	—
522	C₂²×Q₈	—	2	2	no	—
523	C₂²×Q₈	—	2	2	no	—
524	C₂²×Q₈	—	2	4	no	—
525	C₂²×Q₈	—	2	4	no	—
526	C₂²×Q₈	—	2	4	no	—
527	C₂²×Q₈	—	4	2	no	—
528	C₂²×Q₈	—	4	2	no	—
529	C₂²×Q₈	—	4	2	no	—
530	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
533	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
534	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
535	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
536	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
541	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂³×C₄	—	2	1	no	—
543	C₂³×C₄	—	2	1	no	—
544	C₂³×C₄	—	2	1	no	—
545	C₂³×C₄	—	2	1	no	—
546	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
548	#137	—	2	32	no	—
549	C₂×Q₁₆	—	2	4	no	—
550	C₂×Q₁₆	—	2	4	no	—
551	C₂×Q₁₆	—	2	4	no	—
552	C₂×Q₁₆	—	2	32	no	—
553	C₂×Q₁₆	—	2	4	no	—
554	C₂×Q₁₆	—	4	2	no	—
555	C₂×Q₁₆	D₄×C₃₁	1	8	yes	complemented
556	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
557	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
558	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
559	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
560	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
561	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
562	C₂×SD₁₆	—	2	4	no	—
563	C₂×SD₁₆	—	2	4	no	—
564	C₂×SD₁₆	—	4	2	no	—
565	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
566	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
568	C₂×M₁₆	—	2	4	no	—
569	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
570	C₂²×C₈	—	2	4	no	—
571	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
573	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
574	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
575	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
576	C₄⋊Q₈	—	2	8	no	—
577	C₄⋊Q₈	—	2	2	no	—
578	C₄⋊Q₈	C₂³×C₃₁	1	4	yes	—
579	#124	—	2	8	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₃₁	1	4	yes	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	8	no	—
586	C₂²⋊Q₈	—	2	8	no	—
587	C₂²⋊Q₈	—	2	8	no	—
588	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
589	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
590	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
591	#121	—	2	8	no	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₃₁	1	4	yes	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
597	C₄×Q₈	C₂³×C₃₁	1	4	yes	—
598	C₄×D₄	—	2	8	no	—
599	C₄×D₄	—	2	8	no	—
600	C₄×D₄	D₄×C₃₁	1	4	yes	—
601	C₄×D₄	C₂³×C₃₁	1	4	yes	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	D₄×C₃₁	1	1	yes	characteristic
620	C₂×C₄²	—	2	1	no	—
621	C₂×C₄²	—	2	1	no	—
622	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
623	#106	C₂³×C₃₁	1	4	yes	—
624	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
625	#103	C₂³×C₃₁	1	4	yes	—
626	#103	C₂³×C₃₁	1	4	yes	—
627	#103	C₂³×C₃₁	1	4	yes	—
628	#103	C₂³×C₃₁	1	4	yes	—
629	#103	C₂³×C₃₁	1	4	yes	—
630	#102	C₂³×C₃₁	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
632	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
633	#97	C₂³×C₃₁	1	4	yes	—
634	C₃₁	C₂×#3270	1	1	yes	characteristic, direct product factor, Sylow
635	C₂⁴	—	2	1	no	—
636	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
637	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
638	#41	—	2	8	no	—
639	#41	—	4	4	no	—
640	#41	—	4	8	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	1	no	—
643	C₂×Q₈	—	2	4	no	—
644	C₂×Q₈	—	2	1	no	—
645	C₂×Q₈	—	2	4	no	—
646	C₂×Q₈	—	2	4	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	2	8	no	—
652	C₂×Q₈	—	2	8	no	—
653	C₂×Q₈	—	2	8	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	—	4	4	no	—
663	C₂×Q₈	—	4	4	no	—
664	C₂×Q₈	—	4	4	no	—
665	C₂×Q₈	—	4	4	no	—
666	C₂×Q₈	—	4	8	no	—
667	C₂×Q₈	—	4	8	no	—
668	C₂×Q₈	—	4	8	no	—
669	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
670	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
671	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
675	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	4	4	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
685	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	4	4	no	—
702	C₂²×C₄	—	4	4	no	—
703	C₂²×C₄	—	4	4	no	—
704	C₂²×C₄	—	4	4	no	—
705	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
706	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
707	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
714	Q₁₆	—	2	8	no	—
715	Q₁₆	—	2	8	no	—
716	Q₁₆	—	2	8	no	—
717	Q₁₆	—	2	8	no	—
718	Q₁₆	—	4	4	no	—
719	Q₁₆	C₂×D₄×C₃₁	1	16	yes	complemented
720	SD₁₆	—	2	8	no	—
721	SD₁₆	—	2	8	no	—
722	SD₁₆	—	4	4	no	—
723	M₁₆	—	2	8	no	—
724	C₂×C₈	—	2	2	no	—
725	C₂×C₈	—	2	2	no	—
726	C₂×C₈	—	2	2	no	—
727	C₂×C₈	—	2	8	no	—
728	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
729	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
730	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
731	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
732	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	4	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
752	C₂²⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	C₂×D₄×C₃₁	1	2	yes	—
756	C₄²	C₂⁴×C₃₁	1	2	yes	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	4	2	no	—
764	C₂³	—	4	2	no	—
765	C₂³	—	4	2	no	—
766	C₂³	C₃₁×#137	1	4	yes	complemented
767	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
768	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
769	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
770	Q₈	—	2	4	no	—
771	Q₈	—	2	4	no	—
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	2	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	2	no	—
780	Q₈	—	4	8	no	—
781	Q₈	—	4	8	no	—
782	Q₈	—	4	8	no	—
783	Q₈	—	4	2	no	—
784	Q₈	—	4	2	no	—
785	Q₈	—	4	2	no	—
786	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
787	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
788	D₄	—	2	8	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	2	no	—
791	D₄	—	4	8	no	—
792	D₄	—	4	8	no	—
793	D₄	—	4	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	8	no	—
816	C₂×C₄	—	4	8	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	2	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
823	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
824	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
828	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
829	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	C₂²×D₄×C₃₁	1	4	yes	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	8	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	4	no	—
845	C₂²	D₄²×C₃₁	1	2	yes	—
846	C₂²	C₂×C₃₁×#137	1	2	yes	—
847	C₂²	C₂×C₃₁×#137	1	4	yes	complemented
848	C₂²	C₃₁×#578	1	2	yes	—
849	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	D₄²×C₃₁	1	2	yes	—
862	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
863	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂	—	2	4	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	C₃₁×#3270	1	4	yes	direct product factor
868	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
869	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
870	C₂	C₂×C₃₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#137	C₂	semidirect
2. C₂³×Q₁₆×C₃₁	C₂	semidirect
3. C₂×D₄×Q₈×C₃₁	C₂	semidirect
5. C₃₁×#3270	C₂	direct (N × H)
6. C₂×C₃₁×#497	C₂	semidirect
7. C₂×C₃₁×#470	C₂	semidirect
8. C₂×C₃₁×#465	C₂	semidirect
9. C₂×C₃₁×#464	C₂	semidirect
10. C₂×C₃₁×#462	C₂	semidirect
11. C₂×C₃₁×#452	C₂	semidirect
12. C₂×C₃₁×#451	C₂	semidirect
13. C₂×C₃₁×#451	C₂	semidirect
14. C₂×C₃₁×#448	C₂	semidirect
15. C₂×C₃₁×#441	C₂	semidirect
16. C₂×C₃₁×#435	C₂	semidirect
22. C₂×C₃₁×#137	C₂²	semidirect
30. C₂²×Q₁₆×C₃₁	C₂²	semidirect
37. D₄×Q₈×C₃₁	C₂²	semidirect
57. C₃₁×#497	C₂²	semidirect
58. C₃₁×#470	C₂²	semidirect
59. C₃₁×#465	C₂²	semidirect
60. C₃₁×#464	C₂²	semidirect
61. C₃₁×#462	C₂²	semidirect
62. C₃₁×#452	C₂²	semidirect
63. C₃₁×#451	C₂²	semidirect
64. C₃₁×#451	C₂²	semidirect
65. C₃₁×#448	C₂²	semidirect
66. C₃₁×#441	C₂²	semidirect
67. C₃₁×#435	C₂²	semidirect
120. C₂×Q₁₆×C₃₁	D₄	semidirect
283. Q₁₆×C₃₁	C₂×D₄	semidirect
321. C₂×#3270	C₃₁	direct (N × H)
331. C₂³×C₃₁	#137	semidirect
399. C₂²×#137	C₂×C₃₁	semidirect
400. C₂³×Q₁₆	C₂×C₃₁	semidirect
401. C₂×D₄×Q₈	C₂×C₃₁	semidirect
403. #3270	C₂×C₃₁	direct (N × H)
404. C₂×#497	C₂×C₃₁	semidirect
405. C₂×#470	C₂×C₃₁	semidirect
406. C₂×#465	C₂×C₃₁	semidirect
407. C₂×#464	C₂×C₃₁	semidirect
408. C₂×#462	C₂×C₃₁	semidirect
409. C₂×#452	C₂×C₃₁	semidirect
410. C₂×#451	C₂×C₃₁	semidirect
411. C₂×#451	C₂×C₃₁	semidirect
412. C₂×#448	C₂×C₃₁	semidirect
413. C₂×#441	C₂×C₃₁	semidirect
414. C₂×#435	C₂×C₃₁	semidirect
428. C₂²×C₃₁	C₂×#137	semidirect
450. C₂×#137	C₂²×C₃₁	semidirect
458. C₂²×Q₁₆	C₂²×C₃₁	semidirect
465. D₄×Q₈	C₂²×C₃₁	semidirect
485. #497	C₂²×C₃₁	semidirect
486. #470	C₂²×C₃₁	semidirect
487. #465	C₂²×C₃₁	semidirect
488. #464	C₂²×C₃₁	semidirect
489. #462	C₂²×C₃₁	semidirect
490. #452	C₂²×C₃₁	semidirect
491. #451	C₂²×C₃₁	semidirect
492. #451	C₂²×C₃₁	semidirect
493. #448	C₂²×C₃₁	semidirect
494. #441	C₂²×C₃₁	semidirect
495. #435	C₂²×C₃₁	semidirect
510. C₂×C₃₁	#3270	direct (N × H)
555. C₂×Q₁₆	D₄×C₃₁	semidirect
634. C₃₁	C₂×#3270	direct (N × H)
719. Q₁₆	C₂×D₄×C₃₁	semidirect
766. C₂³	C₃₁×#137	semidirect
847. C₂²	C₂×C₃₁×#137	semidirect
867. C₂	C₃₁×#3270	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#137	2
C₂³×Q₁₆×C₃₁	2
C₂×D₄×Q₈×C₃₁	2
C₂×C₃₁×#548	2
C₃₁×#3270	2
C₂×C₃₁×#497	2
C₂×C₃₁×#470	2
C₂×C₃₁×#465	2
C₂×C₃₁×#464	2
C₂×C₃₁×#462	2
C₂×C₃₁×#452	2
C₂×C₃₁×#451	2
C₂×C₃₁×#448	2
C₂×C₃₁×#441	2
C₂×C₃₁×#435	2
C₂×#3270	31

Subgroups — C2×C31×#3270 #21517787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3270 #21517787