Subgroups — C₂×C₃₁×#3551 #21519498

Order 7936.

7354 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3551	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#555	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#548	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#540	C₂	1	4	yes	maximal, complemented
11	C₂×C₃₁×#538	C₂	1	4	yes	maximal, complemented
12	C₂×C₃₁×#537	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#529	C₂	1	2	yes	maximal, complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₃₁	C₂²	1	2	yes	—
19	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₃₁×#563	C₂²	1	32	yes	complemented
23	C₃₁×#560	C₂²	1	32	yes	complemented
24	C₃₁×#555	C₂²	1	32	yes	complemented
25	C₃₁×#553	C₂²	1	32	yes	complemented
26	C₃₁×#552	C₂²	1	32	yes	complemented
27	C₃₁×#551	C₂²	1	32	yes	complemented
28	C₃₁×#548	C₂²	1	32	yes	complemented
29	C₃₁×#546	C₂²	1	32	yes	complemented
30	C₃₁×#540	C₂²	1	64	yes	complemented
31	C₃₁×#538	C₂²	1	64	yes	complemented
32	C₃₁×#537	C₂²	1	32	yes	complemented
33	C₃₁×#536	C₂²	1	16	yes	complemented
34	C₃₁×#535	C₂²	1	16	yes	complemented
35	C₃₁×#532	C₂²	1	16	yes	complemented
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
38	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
39	C₂×C₃₁×#127	C₂²	1	2	yes	—
40	C₃₁×#529	C₂²	1	32	yes	complemented
41	C₂×C₃₁×#126	C₂²	1	4	yes	—
42	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
43	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
44	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
45	C₂×C₃₁×#125	C₂²	1	4	yes	complemented
46	C₂×C₃₁×#124	C₂²	1	2	yes	—
47	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×#124	C₂²	1	2	yes	—
49	C₂×C₃₁×#124	C₂²	1	2	yes	—
50	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
52	C₂×C₃₁×#123	C₂²	1	2	yes	—
53	C₂×C₃₁×#123	C₂²	1	4	yes	—
54	C₂×C₃₁×#123	C₂²	1	4	yes	—
55	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
56	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
57	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
58	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
62	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₃₁×#121	C₂²	1	2	yes	—
64	C₂×C₃₁×#121	C₂²	1	2	yes	—
65	C₂×C₃₁×#121	C₂²	1	2	yes	—
66	C₂×C₃₁×#121	C₂²	1	2	yes	—
67	C₂×C₃₁×#121	C₂²	1	4	yes	—
68	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
69	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
70	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
71	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
72	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
73	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
74	C₂×C₃₁×#120	C₂²	1	2	yes	—
75	C₂×C₃₁×#120	C₂²	1	2	yes	—
76	C₂×C₃₁×#120	C₂²	1	4	yes	—
77	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
78	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
83	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
84	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
85	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
86	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
88	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
89	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
90	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
91	C₂⁵×C₃₁	C₂³	1	2	yes	—
92	C₂×#41×C₃₁	—	4	4	no	—
93	C₂×#41×C₃₁	—	4	4	no	—
94	C₂×#41×C₃₁	—	4	8	no	—
95	C₂×#41×C₃₁	C₂³	1	8	yes	—
96	C₂×#41×C₃₁	C₂³	1	16	yes	—
97	C₂×#41×C₃₁	C₂³	1	8	yes	complemented
98	C₂²×Q₈×C₃₁	—	4	4	no	—
99	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
102	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₃₁	C₂³	1	8	yes	complemented
104	C₂²×D₄×C₃₁	—	4	4	no	—
105	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
106	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
107	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
108	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
116	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
126	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
129	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₃₁×#127	C₂³	1	8	yes	—
131	C₃₁×#127	C₂³	1	16	yes	—
132	C₃₁×#126	C₂³	1	32	yes	—
133	C₃₁×#126	C₂³	1	32	yes	complemented
134	C₃₁×#126	C₂³	1	32	yes	complemented
135	C₃₁×#125	C₂³	1	16	yes	complemented
136	C₃₁×#125	C₂³	1	32	yes	complemented
137	C₃₁×#124	C₂³	1	16	yes	—
138	C₃₁×#124	C₂³	1	8	yes	—
139	C₃₁×#124	C₂³	1	16	yes	—
140	C₃₁×#124	C₂³	1	16	yes	—
141	C₃₁×#124	C₂³	1	8	yes	complemented
142	C₃₁×#124	C₂³	1	32	yes	complemented
143	C₃₁×#123	C₂³	1	16	yes	—
144	C₃₁×#123	C₂³	1	32	yes	—
145	C₃₁×#123	C₂³	1	32	yes	—
146	C₃₁×#123	C₂³	1	32	yes	complemented
147	C₃₁×#123	C₂³	1	16	yes	complemented
148	C₃₁×#123	C₂³	1	32	yes	complemented
149	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₃₁×#121	C₂³	1	16	yes	—
155	C₃₁×#121	C₂³	1	16	yes	—
156	C₃₁×#121	C₂³	1	16	yes	—
157	C₃₁×#121	C₂³	1	16	yes	—
158	C₃₁×#121	C₂³	1	32	yes	—
159	C₃₁×#121	C₂³	1	16	yes	complemented
160	C₃₁×#121	C₂³	1	32	yes	complemented
161	C₃₁×#121	C₂³	1	32	yes	complemented
162	C₃₁×#121	C₂³	1	32	yes	complemented
163	C₃₁×#121	C₂³	1	32	yes	complemented
164	C₃₁×#121	C₂³	1	32	yes	complemented
165	C₃₁×#120	C₂³	1	16	yes	—
166	C₃₁×#120	C₂³	1	16	yes	—
167	C₃₁×#120	C₂³	1	32	yes	—
168	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
169	C₄×D₄×C₃₁	C₂³	1	16	yes	—
170	C₄×D₄×C₃₁	C₂³	1	16	yes	—
171	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
172	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
173	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
174	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
175	C₃₁×#117	C₂³	1	8	yes	—
176	C₃₁×#117	C₂³	1	32	yes	complemented
177	C₃₁×#117	C₂³	1	8	yes	complemented
178	C₃₁×#117	C₂³	1	32	yes	complemented
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
211	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
212	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
214	C₂⁴×C₃₁	—	4	4	no	—
215	C₂⁴×C₃₁	—	4	8	no	—
216	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
218	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
220	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
222	#41×C₃₁	—	4	16	no	—
223	#41×C₃₁	—	4	16	no	—
224	#41×C₃₁	—	4	32	no	—
225	C₂×Q₈×C₃₁	—	2	8	no	—
226	C₂×Q₈×C₃₁	—	4	4	no	—
227	C₂×Q₈×C₃₁	—	4	2	no	—
228	C₂×Q₈×C₃₁	—	4	2	no	—
229	C₂×Q₈×C₃₁	—	4	16	no	—
230	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
231	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
234	C₂×D₄×C₃₁	—	2	8	no	—
235	C₂×D₄×C₃₁	—	4	16	no	—
236	C₂×D₄×C₃₁	—	4	4	no	—
237	C₂×D₄×C₃₁	—	4	8	no	—
238	C₂×D₄×C₃₁	—	4	4	no	—
239	C₂×D₄×C₃₁	—	4	8	no	—
240	C₂×D₄×C₃₁	—	4	8	no	—
241	C₂×D₄×C₃₁	—	4	4	no	—
242	C₂×D₄×C₃₁	—	4	4	no	—
243	C₂×D₄×C₃₁	—	4	2	no	—
244	C₂×D₄×C₃₁	—	4	2	no	—
245	C₂×D₄×C₃₁	—	4	2	no	—
246	C₂×D₄×C₃₁	—	4	2	no	—
247	C₂×D₄×C₃₁	—	4	8	no	—
248	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
249	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
250	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
251	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
252	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
253	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
254	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
255	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
256	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
259	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
260	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₃₁	—	2	4	no	—
262	C₂²×C₄×C₃₁	—	2	4	no	—
263	C₂²×C₄×C₃₁	—	2	8	no	—
264	C₂²×C₄×C₃₁	—	2	4	no	—
265	C₂²×C₄×C₃₁	—	4	8	no	—
266	C₂²×C₄×C₃₁	—	4	4	no	—
267	C₂²×C₄×C₃₁	—	4	8	no	—
268	C₂²×C₄×C₃₁	—	4	4	no	—
269	C₂²×C₄×C₃₁	—	4	8	no	—
270	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
287	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
290	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
291	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
292	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
293	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
294	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
295	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
296	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
298	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
299	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
300	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
301	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
302	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
303	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
304	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
305	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
306	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
307	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
308	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
309	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
310	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
311	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
313	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
315	C₄²×C₃₁	C₂⁴	1	4	yes	—
316	C₄²×C₃₁	C₂⁴	1	8	yes	—
317	C₄²×C₃₁	C₂⁴	1	4	yes	—
318	C₄²×C₃₁	C₂⁴	1	8	yes	—
319	C₄²×C₃₁	C₂⁴	1	16	yes	—
320	C₄²×C₃₁	C₂⁴	1	8	yes	—
321	C₂×#3551	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₃₁	—	2	2	no	—
323	C₂³×C₃₁	—	2	4	no	—
324	C₂³×C₃₁	—	2	2	no	—
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	—	2	8	no	—
327	C₂³×C₃₁	—	2	4	no	—
328	C₂³×C₃₁	—	2	4	no	—
329	C₂³×C₃₁	—	2	8	no	—
330	C₂³×C₃₁	—	2	4	no	—
331	C₂³×C₃₁	—	2	4	no	—
332	C₂³×C₃₁	—	2	8	no	—
333	C₂³×C₃₁	—	2	4	no	—
334	C₂³×C₃₁	—	4	8	no	—
335	C₂³×C₃₁	—	4	16	no	—
336	C₂³×C₃₁	—	8	16	no	—
337	C₂³×C₃₁	C₂⁵	1	2	yes	—
338	C₂³×C₃₁	C₂⁵	1	8	yes	—
339	C₂³×C₃₁	C₂⁵	1	2	yes	—
340	C₂³×C₃₁	C₂⁵	1	4	yes	—
341	C₂³×C₃₁	C₂⁵	1	2	yes	—
342	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
343	Q₈×C₃₁	—	2	16	no	—
344	Q₈×C₃₁	—	4	8	no	—
345	Q₈×C₃₁	—	4	4	no	—
346	Q₈×C₃₁	—	4	4	no	—
347	D₄×C₃₁	—	2	16	no	—
348	D₄×C₃₁	—	4	8	no	—
349	D₄×C₃₁	—	4	16	no	—
350	D₄×C₃₁	—	4	8	no	—
351	D₄×C₃₁	—	4	16	no	—
352	D₄×C₃₁	—	4	16	no	—
353	D₄×C₃₁	—	4	8	no	—
354	D₄×C₃₁	—	4	8	no	—
355	D₄×C₃₁	—	4	4	no	—
356	D₄×C₃₁	—	4	4	no	—
357	D₄×C₃₁	—	4	4	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	16	no	—
360	C₂×C₄×C₃₁	—	2	4	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	8	no	—
365	C₂×C₄×C₃₁	—	2	4	no	—
366	C₂×C₄×C₃₁	—	2	8	no	—
367	C₂×C₄×C₃₁	—	2	4	no	—
368	C₂×C₄×C₃₁	—	2	8	no	—
369	C₂×C₄×C₃₁	—	2	8	no	—
370	C₂×C₄×C₃₁	—	2	8	no	—
371	C₂×C₄×C₃₁	—	2	16	no	—
372	C₂×C₄×C₃₁	—	2	8	no	—
373	C₂×C₄×C₃₁	—	4	16	no	—
374	C₂×C₄×C₃₁	—	4	8	no	—
375	C₂×C₄×C₃₁	—	4	16	no	—
376	C₂×C₄×C₃₁	—	4	8	no	—
377	C₂×C₄×C₃₁	—	4	16	no	—
378	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
379	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
380	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
381	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
382	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
383	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
384	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
385	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
386	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
387	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
388	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
389	#3551	C₂×C₃₁	1	32	yes	direct product factor
390	C₂×#563	C₂×C₃₁	1	2	yes	complemented
391	C₂×#560	C₂×C₃₁	1	2	yes	complemented
392	C₂×#555	C₂×C₃₁	1	2	yes	complemented
393	C₂×#553	C₂×C₃₁	1	2	yes	complemented
394	C₂×#552	C₂×C₃₁	1	2	yes	complemented
395	C₂×#551	C₂×C₃₁	1	2	yes	complemented
396	C₂×#548	C₂×C₃₁	1	2	yes	complemented
397	C₂×#546	C₂×C₃₁	1	2	yes	complemented
398	C₂×#540	C₂×C₃₁	1	4	yes	complemented
399	C₂×#538	C₂×C₃₁	1	4	yes	complemented
400	C₂×#537	C₂×C₃₁	1	2	yes	complemented
401	C₂×#536	C₂×C₃₁	1	1	yes	characteristic, complemented
402	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
403	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
404	C₂×#529	C₂×C₃₁	1	2	yes	complemented
405	C₂²×C₃₁	—	2	2	no	—
406	C₂²×C₃₁	—	2	4	no	—
407	C₂²×C₃₁	—	2	2	no	—
408	C₂²×C₃₁	—	2	2	no	—
409	C₂²×C₃₁	—	2	8	no	—
410	C₂²×C₃₁	—	2	4	no	—
411	C₂²×C₃₁	—	2	4	no	—
412	C₂²×C₃₁	—	2	8	no	—
413	C₂²×C₃₁	—	2	4	no	—
414	C₂²×C₃₁	—	2	4	no	—
415	C₂²×C₃₁	—	2	8	no	—
416	C₂²×C₃₁	—	2	4	no	—
417	C₂²×C₃₁	—	4	4	no	—
418	C₂²×C₃₁	—	4	8	no	—
419	C₂²×C₃₁	—	4	4	no	—
420	C₂²×C₃₁	—	4	16	no	—
421	C₂²×C₃₁	—	4	4	no	—
422	C₂²×C₃₁	—	8	16	no	—
423	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
424	C₂²×C₃₁	#585	1	4	yes	—
425	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
426	C₄×C₃₁	—	2	4	no	—
427	C₄×C₃₁	—	2	2	no	—
428	C₄×C₃₁	—	2	2	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	8	no	—
431	C₄×C₃₁	—	2	4	no	—
432	C₄×C₃₁	—	2	8	no	—
433	C₄×C₃₁	—	2	4	no	—
434	C₄×C₃₁	—	2	8	no	—
435	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
436	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
437	C₂²×#41	C₂²×C₃₁	1	2	yes	—
438	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
439	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
440	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
441	#563	C₂²×C₃₁	1	32	yes	complemented
442	#560	C₂²×C₃₁	1	32	yes	complemented
443	#555	C₂²×C₃₁	1	32	yes	complemented
444	#553	C₂²×C₃₁	1	32	yes	complemented
445	#552	C₂²×C₃₁	1	32	yes	complemented
446	#551	C₂²×C₃₁	1	32	yes	complemented
447	#548	C₂²×C₃₁	1	32	yes	complemented
448	#546	C₂²×C₃₁	1	32	yes	complemented
449	#540	C₂²×C₃₁	1	64	yes	complemented
450	#538	C₂²×C₃₁	1	64	yes	complemented
451	#537	C₂²×C₃₁	1	32	yes	complemented
452	#536	C₂²×C₃₁	1	16	yes	complemented
453	#535	C₂²×C₃₁	1	16	yes	complemented
454	#532	C₂²×C₃₁	1	16	yes	complemented
455	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
456	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
457	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
458	C₂×#127	C₂²×C₃₁	1	2	yes	—
459	#529	C₂²×C₃₁	1	32	yes	complemented
460	C₂×#126	C₂²×C₃₁	1	4	yes	—
461	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
462	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
463	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
464	C₂×#125	C₂²×C₃₁	1	4	yes	complemented
465	C₂×#124	C₂²×C₃₁	1	2	yes	—
466	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
467	C₂×#124	C₂²×C₃₁	1	2	yes	—
468	C₂×#124	C₂²×C₃₁	1	2	yes	—
469	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
470	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
471	C₂×#123	C₂²×C₃₁	1	2	yes	—
472	C₂×#123	C₂²×C₃₁	1	4	yes	—
473	C₂×#123	C₂²×C₃₁	1	4	yes	—
474	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
475	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
476	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
477	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
478	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
479	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
480	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
481	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
482	C₂×#121	C₂²×C₃₁	1	2	yes	—
483	C₂×#121	C₂²×C₃₁	1	2	yes	—
484	C₂×#121	C₂²×C₃₁	1	2	yes	—
485	C₂×#121	C₂²×C₃₁	1	2	yes	—
486	C₂×#121	C₂²×C₃₁	1	4	yes	—
487	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
488	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
489	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
490	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
491	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
492	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
493	C₂×#120	C₂²×C₃₁	1	2	yes	—
494	C₂×#120	C₂²×C₃₁	1	2	yes	—
495	C₂×#120	C₂²×C₃₁	1	4	yes	—
496	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
497	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
498	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
500	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
501	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
502	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
503	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
504	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
505	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
506	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
507	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
508	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
509	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	C₂×C₃₁	—	4	2	no	—
511	C₂×C₃₁	—	4	4	no	—
512	C₂×C₃₁	—	4	2	no	—
513	C₂×C₃₁	—	4	8	no	—
514	C₂×C₃₁	—	4	2	no	—
515	C₂×C₃₁	#3551	1	4	yes	direct product factor
516	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
517	C₂×C₃₁	C₂×#585	1	2	yes	—
518	C₂⁵	C₂³×C₃₁	1	2	yes	—
519	C₂×#41	—	4	4	no	—
520	C₂×#41	—	4	4	no	—
521	C₂×#41	—	4	8	no	—
522	C₂×#41	C₂³×C₃₁	1	8	yes	—
523	C₂×#41	C₂³×C₃₁	1	16	yes	—
524	C₂×#41	C₂³×C₃₁	1	8	yes	complemented
525	C₂²×Q₈	—	4	4	no	—
526	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
527	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
528	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
529	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
530	C₂²×Q₈	C₂³×C₃₁	1	8	yes	complemented
531	C₂²×D₄	—	4	4	no	—
532	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
533	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
534	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
535	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
536	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
537	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
538	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
539	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
541	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
542	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
543	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
545	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
546	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
547	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
551	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
552	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
553	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
554	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
556	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
557	#127	C₂³×C₃₁	1	8	yes	—
558	#127	C₂³×C₃₁	1	16	yes	—
559	#126	C₂³×C₃₁	1	32	yes	—
560	#126	C₂³×C₃₁	1	32	yes	complemented
561	#126	C₂³×C₃₁	1	32	yes	complemented
562	#125	C₂³×C₃₁	1	16	yes	complemented
563	#125	C₂³×C₃₁	1	32	yes	complemented
564	#124	C₂³×C₃₁	1	16	yes	—
565	#124	C₂³×C₃₁	1	8	yes	—
566	#124	C₂³×C₃₁	1	16	yes	—
567	#124	C₂³×C₃₁	1	16	yes	—
568	#124	C₂³×C₃₁	1	8	yes	complemented
569	#124	C₂³×C₃₁	1	32	yes	complemented
570	#123	C₂³×C₃₁	1	16	yes	—
571	#123	C₂³×C₃₁	1	32	yes	—
572	#123	C₂³×C₃₁	1	32	yes	—
573	#123	C₂³×C₃₁	1	32	yes	complemented
574	#123	C₂³×C₃₁	1	16	yes	complemented
575	#123	C₂³×C₃₁	1	32	yes	complemented
576	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
577	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
578	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
579	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
580	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
581	#121	C₂³×C₃₁	1	16	yes	—
582	#121	C₂³×C₃₁	1	16	yes	—
583	#121	C₂³×C₃₁	1	16	yes	—
584	#121	C₂³×C₃₁	1	16	yes	—
585	#121	C₂³×C₃₁	1	32	yes	—
586	#121	C₂³×C₃₁	1	16	yes	complemented
587	#121	C₂³×C₃₁	1	32	yes	complemented
588	#121	C₂³×C₃₁	1	32	yes	complemented
589	#121	C₂³×C₃₁	1	32	yes	complemented
590	#121	C₂³×C₃₁	1	32	yes	complemented
591	#121	C₂³×C₃₁	1	32	yes	complemented
592	#120	C₂³×C₃₁	1	16	yes	—
593	#120	C₂³×C₃₁	1	16	yes	—
594	#120	C₂³×C₃₁	1	32	yes	—
595	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
596	C₄×D₄	C₂³×C₃₁	1	16	yes	—
597	C₄×D₄	C₂³×C₃₁	1	16	yes	—
598	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
599	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
600	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
601	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
602	#117	C₂³×C₃₁	1	8	yes	—
603	#117	C₂³×C₃₁	1	32	yes	complemented
604	#117	C₂³×C₃₁	1	8	yes	complemented
605	#117	C₂³×C₃₁	1	32	yes	complemented
606	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
618	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
634	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
635	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
637	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
641	C₃₁	C₂×#3551	1	1	yes	characteristic, direct product factor, Sylow
642	C₂⁴	—	4	4	no	—
643	C₂⁴	—	4	8	no	—
644	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
645	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
646	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
647	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
648	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
649	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
650	#41	—	4	16	no	—
651	#41	—	4	16	no	—
652	#41	—	4	32	no	—
653	C₂×Q₈	—	2	8	no	—
654	C₂×Q₈	—	4	4	no	—
655	C₂×Q₈	—	4	2	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	4	16	no	—
658	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
659	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
660	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
661	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
662	C₂×D₄	—	2	8	no	—
663	C₂×D₄	—	4	16	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	8	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	8	no	—
668	C₂×D₄	—	4	8	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	4	2	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	8	no	—
676	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
677	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
678	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
679	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
680	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
681	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
682	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
683	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
684	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
685	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
686	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
687	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
688	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	8	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	8	no	—
694	C₂²×C₄	—	4	4	no	—
695	C₂²×C₄	—	4	8	no	—
696	C₂²×C₄	—	4	4	no	—
697	C₂²×C₄	—	4	8	no	—
698	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
701	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
705	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
706	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
707	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
709	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
710	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
712	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
713	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
717	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
718	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
720	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
722	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
723	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
725	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
726	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
727	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
728	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
729	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
730	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
731	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
732	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
733	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
734	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
735	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
736	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
737	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
738	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
739	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
740	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
741	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
742	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
743	C₄²	C₂⁴×C₃₁	1	4	yes	—
744	C₄²	C₂⁴×C₃₁	1	8	yes	—
745	C₄²	C₂⁴×C₃₁	1	4	yes	—
746	C₄²	C₂⁴×C₃₁	1	8	yes	—
747	C₄²	C₂⁴×C₃₁	1	16	yes	—
748	C₄²	C₂⁴×C₃₁	1	8	yes	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	4	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	8	no	—
754	C₂³	—	2	4	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	8	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	8	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	8	16	no	—
764	C₂³	C₂⁵×C₃₁	1	2	yes	—
765	C₂³	C₂⁵×C₃₁	1	8	yes	—
766	C₂³	C₂⁵×C₃₁	1	2	yes	—
767	C₂³	C₂⁵×C₃₁	1	4	yes	—
768	C₂³	C₂⁵×C₃₁	1	2	yes	—
769	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
770	Q₈	—	2	16	no	—
771	Q₈	—	4	8	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	4	4	no	—
774	D₄	—	2	16	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	16	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	16	no	—
779	D₄	—	4	16	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	4	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	4	no	—
786	D₄	—	4	16	no	—
787	C₂×C₄	—	2	4	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	16	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	4	16	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	4	16	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	4	16	no	—
805	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
806	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
807	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
808	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
809	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
810	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
811	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
812	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
813	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
814	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
815	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	8	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	2	4	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	8	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	4	no	—
829	C₂²	—	4	16	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	8	16	no	—
834	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
835	C₂²	C₃₁×#585	1	4	yes	—
836	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
837	C₄	—	2	4	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	8	no	—
842	C₄	—	2	4	no	—
843	C₄	—	2	8	no	—
844	C₄	—	2	4	no	—
845	C₄	—	2	8	no	—
846	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
847	C₂	—	4	2	no	—
848	C₂	—	4	8	no	—
849	C₂	—	4	2	no	—
850	C₂	—	4	4	no	—
851	C₂	—	4	2	no	—
852	C₂	C₃₁×#3551	1	4	yes	direct product factor
853	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂	C₂×C₃₁×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3551	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×#560	C₂	semidirect
4. C₂×C₃₁×#555	C₂	semidirect
5. C₂×C₃₁×#553	C₂	semidirect
6. C₂×C₃₁×#552	C₂	semidirect
7. C₂×C₃₁×#551	C₂	semidirect
8. C₂×C₃₁×#548	C₂	semidirect
9. C₂×C₃₁×#546	C₂	semidirect
10. C₂×C₃₁×#540	C₂	semidirect
11. C₂×C₃₁×#538	C₂	semidirect
12. C₂×C₃₁×#537	C₂	semidirect
13. C₂×C₃₁×#536	C₂	semidirect
14. C₂×C₃₁×#535	C₂	semidirect
15. C₂×C₃₁×#532	C₂	semidirect
16. C₂×C₃₁×#529	C₂	semidirect
19. C₂²×#41×C₃₁	C₂²	semidirect
20. C₂³×Q₈×C₃₁	C₂²	semidirect
22. C₃₁×#563	C₂²	semidirect
23. C₃₁×#560	C₂²	semidirect
24. C₃₁×#555	C₂²	semidirect
25. C₃₁×#553	C₂²	semidirect
26. C₃₁×#552	C₂²	semidirect
27. C₃₁×#551	C₂²	semidirect
28. C₃₁×#548	C₂²	semidirect
29. C₃₁×#546	C₂²	semidirect
30. C₃₁×#540	C₂²	semidirect
31. C₃₁×#538	C₂²	semidirect
32. C₃₁×#537	C₂²	semidirect
33. C₃₁×#536	C₂²	semidirect
34. C₃₁×#535	C₂²	semidirect
35. C₃₁×#532	C₂²	semidirect
36. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
40. C₃₁×#529	C₂²	semidirect
42. C₂×C₃₁×#126	C₂²	semidirect
43. C₂×C₃₁×#126	C₂²	semidirect
44. C₂×C₃₁×#125	C₂²	semidirect
45. C₂×C₃₁×#125	C₂²	semidirect
50. C₂×C₃₁×#124	C₂²	semidirect
51. C₂×C₃₁×#124	C₂²	semidirect
55. C₂×C₃₁×#123	C₂²	semidirect
56. C₂×C₃₁×#123	C₂²	semidirect
57. C₂×C₃₁×#123	C₂²	semidirect
59. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₃₁×#121	C₂²	semidirect
69. C₂×C₃₁×#121	C₂²	semidirect
70. C₂×C₃₁×#121	C₂²	semidirect
71. C₂×C₃₁×#121	C₂²	semidirect
72. C₂×C₃₁×#121	C₂²	semidirect
73. C₂×C₃₁×#121	C₂²	semidirect
77. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
80. C₂×C₄×D₄×C₃₁	C₂²	semidirect
81. C₂×C₄×D₄×C₃₁	C₂²	semidirect
82. C₂×C₄×D₄×C₃₁	C₂²	semidirect
83. C₂×C₄×D₄×C₃₁	C₂²	semidirect
85. C₂×C₃₁×#117	C₂²	semidirect
86. C₂×C₃₁×#117	C₂²	semidirect
87. C₂×C₃₁×#117	C₂²	semidirect
88. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
90. C₂²×C₄²×C₃₁	C₂²	semidirect
97. C₂×#41×C₃₁	C₂³	semidirect
103. C₂²×Q₈×C₃₁	C₂³	semidirect
128. C₃₁×C₄⋊Q₈	C₂³	semidirect
129. C₃₁×C₄⋊Q₈	C₂³	semidirect
133. C₃₁×#126	C₂³	semidirect
134. C₃₁×#126	C₂³	semidirect
135. C₃₁×#125	C₂³	semidirect
136. C₃₁×#125	C₂³	semidirect
141. C₃₁×#124	C₂³	semidirect
142. C₃₁×#124	C₂³	semidirect
146. C₃₁×#123	C₂³	semidirect
147. C₃₁×#123	C₂³	semidirect
148. C₃₁×#123	C₂³	semidirect
150. C₃₁×C₂²⋊Q₈	C₂³	semidirect
151. C₃₁×C₂²⋊Q₈	C₂³	semidirect
152. C₃₁×C₂²⋊Q₈	C₂³	semidirect
153. C₃₁×C₂²⋊Q₈	C₂³	semidirect
159. C₃₁×#121	C₂³	semidirect
160. C₃₁×#121	C₂³	semidirect
161. C₃₁×#121	C₂³	semidirect
162. C₃₁×#121	C₂³	semidirect
163. C₃₁×#121	C₂³	semidirect
164. C₃₁×#121	C₂³	semidirect
168. C₄×Q₈×C₃₁	C₂³	semidirect
171. C₄×D₄×C₃₁	C₂³	semidirect
172. C₄×D₄×C₃₁	C₂³	semidirect
173. C₄×D₄×C₃₁	C₂³	semidirect
174. C₄×D₄×C₃₁	C₂³	semidirect
176. C₃₁×#117	C₂³	semidirect
177. C₃₁×#117	C₂³	semidirect
178. C₃₁×#117	C₂³	semidirect
190. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
213. C₂×C₄²×C₃₁	C₂³	semidirect
321. C₂×#3551	C₃₁	direct (N × H)
389. #3551	C₂×C₃₁	direct (N × H)
390. C₂×#563	C₂×C₃₁	semidirect
391. C₂×#560	C₂×C₃₁	semidirect
392. C₂×#555	C₂×C₃₁	semidirect
393. C₂×#553	C₂×C₃₁	semidirect
394. C₂×#552	C₂×C₃₁	semidirect
395. C₂×#551	C₂×C₃₁	semidirect
396. C₂×#548	C₂×C₃₁	semidirect
397. C₂×#546	C₂×C₃₁	semidirect
398. C₂×#540	C₂×C₃₁	semidirect
399. C₂×#538	C₂×C₃₁	semidirect
400. C₂×#537	C₂×C₃₁	semidirect
401. C₂×#536	C₂×C₃₁	semidirect
402. C₂×#535	C₂×C₃₁	semidirect
403. C₂×#532	C₂×C₃₁	semidirect
404. C₂×#529	C₂×C₃₁	semidirect
438. C₂²×#41	C₂²×C₃₁	semidirect
439. C₂³×Q₈	C₂²×C₃₁	semidirect
441. #563	C₂²×C₃₁	semidirect
442. #560	C₂²×C₃₁	semidirect
443. #555	C₂²×C₃₁	semidirect
444. #553	C₂²×C₃₁	semidirect
445. #552	C₂²×C₃₁	semidirect
446. #551	C₂²×C₃₁	semidirect
447. #548	C₂²×C₃₁	semidirect
448. #546	C₂²×C₃₁	semidirect
449. #540	C₂²×C₃₁	semidirect
450. #538	C₂²×C₃₁	semidirect
451. #537	C₂²×C₃₁	semidirect
452. #536	C₂²×C₃₁	semidirect
453. #535	C₂²×C₃₁	semidirect
454. #532	C₂²×C₃₁	semidirect
455. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
456. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
459. #529	C₂²×C₃₁	semidirect
461. C₂×#126	C₂²×C₃₁	semidirect
462. C₂×#126	C₂²×C₃₁	semidirect
463. C₂×#125	C₂²×C₃₁	semidirect
464. C₂×#125	C₂²×C₃₁	semidirect
469. C₂×#124	C₂²×C₃₁	semidirect
470. C₂×#124	C₂²×C₃₁	semidirect
474. C₂×#123	C₂²×C₃₁	semidirect
475. C₂×#123	C₂²×C₃₁	semidirect
476. C₂×#123	C₂²×C₃₁	semidirect
478. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
479. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
480. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
481. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
487. C₂×#121	C₂²×C₃₁	semidirect
488. C₂×#121	C₂²×C₃₁	semidirect
489. C₂×#121	C₂²×C₃₁	semidirect
490. C₂×#121	C₂²×C₃₁	semidirect
491. C₂×#121	C₂²×C₃₁	semidirect
492. C₂×#121	C₂²×C₃₁	semidirect
496. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
499. C₂×C₄×D₄	C₂²×C₃₁	semidirect
500. C₂×C₄×D₄	C₂²×C₃₁	semidirect
501. C₂×C₄×D₄	C₂²×C₃₁	semidirect
502. C₂×C₄×D₄	C₂²×C₃₁	semidirect
504. C₂×#117	C₂²×C₃₁	semidirect
505. C₂×#117	C₂²×C₃₁	semidirect
506. C₂×#117	C₂²×C₃₁	semidirect
507. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
509. C₂²×C₄²	C₂²×C₃₁	semidirect
515. C₂×C₃₁	#3551	direct (N × H)
524. C₂×#41	C₂³×C₃₁	semidirect
530. C₂²×Q₈	C₂³×C₃₁	semidirect
555. C₄⋊Q₈	C₂³×C₃₁	semidirect
556. C₄⋊Q₈	C₂³×C₃₁	semidirect
560. #126	C₂³×C₃₁	semidirect
561. #126	C₂³×C₃₁	semidirect
562. #125	C₂³×C₃₁	semidirect
563. #125	C₂³×C₃₁	semidirect
568. #124	C₂³×C₃₁	semidirect
569. #124	C₂³×C₃₁	semidirect
573. #123	C₂³×C₃₁	semidirect
574. #123	C₂³×C₃₁	semidirect
575. #123	C₂³×C₃₁	semidirect
577. C₂²⋊Q₈	C₂³×C₃₁	semidirect
578. C₂²⋊Q₈	C₂³×C₃₁	semidirect
579. C₂²⋊Q₈	C₂³×C₃₁	semidirect
580. C₂²⋊Q₈	C₂³×C₃₁	semidirect
586. #121	C₂³×C₃₁	semidirect
587. #121	C₂³×C₃₁	semidirect
588. #121	C₂³×C₃₁	semidirect
589. #121	C₂³×C₃₁	semidirect
590. #121	C₂³×C₃₁	semidirect
591. #121	C₂³×C₃₁	semidirect
595. C₄×Q₈	C₂³×C₃₁	semidirect
598. C₄×D₄	C₂³×C₃₁	semidirect
599. C₄×D₄	C₂³×C₃₁	semidirect
600. C₄×D₄	C₂³×C₃₁	semidirect
601. C₄×D₄	C₂³×C₃₁	semidirect
603. #117	C₂³×C₃₁	semidirect
604. #117	C₂³×C₃₁	semidirect
605. #117	C₂³×C₃₁	semidirect
617. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
640. C₂×C₄²	C₂³×C₃₁	semidirect
641. C₃₁	C₂×#3551	direct (N × H)
852. C₂	C₃₁×#3551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#3551	2
C₂×C₃₁×#563	2
C₂×C₃₁×#560	2
C₂×C₃₁×#555	2
C₂×C₃₁×#553	2
C₂×C₃₁×#552	2
C₂×C₃₁×#551	2
C₂×C₃₁×#548	2
C₂×C₃₁×#546	2
C₂×C₃₁×#540	2
C₂×C₃₁×#538	2
C₂×C₃₁×#537	2
C₂×C₃₁×#536	2
C₂×C₃₁×#535	2
C₂×C₃₁×#532	2
C₂×C₃₁×#529	2
C₂×#3551	31

Subgroups — C2×C31×#3551 #21519498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3551 #21519498