Subgroups — C₂×C₃₁×#3475 #21519467

Order 7936.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3475	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#555	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#552	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#551	C₂	1	4	yes	maximal, complemented
9	C₂×C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#529	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₁×#529	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×#41×C₃₁	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₃₁×#117	C₂	1	2	yes	maximal, complemented
19	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₃₁	C₂²	1	2	yes	—
21	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
23	C₃₁×#556	C₂²	1	16	yes	complemented
24	C₃₁×#555	C₂²	1	16	yes	complemented
25	C₃₁×#554	C₂²	1	16	yes	complemented
26	C₃₁×#553	C₂²	1	32	yes	complemented
27	C₃₁×#552	C₂²	1	32	yes	complemented
28	C₃₁×#552	C₂²	1	32	yes	complemented
29	C₃₁×#551	C₂²	1	64	yes	complemented
30	C₃₁×#547	C₂²	1	16	yes	complemented
31	C₃₁×#546	C₂²	1	32	yes	complemented
32	C₃₁×#533	C₂²	1	16	yes	complemented
33	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₃₁×#529	C₂²	1	64	yes	complemented
36	C₃₁×#529	C₂²	1	32	yes	complemented
37	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
38	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
39	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#125	C₂²	1	4	yes	complemented
41	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
42	C₂×C₃₁×#125	C₂²	1	2	yes	complemented
43	C₂×C₃₁×#124	C₂²	1	2	yes	—
44	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
45	C₃₁×#525	C₂²	1	32	yes	complemented
46	C₂×C₃₁×#123	C₂²	1	4	yes	—
47	C₂×C₃₁×#123	C₂²	1	4	yes	—
48	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
49	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
50	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
53	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
55	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×C₃₁×#121	C₂²	1	4	yes	—
57	C₂×C₃₁×#121	C₂²	1	2	yes	—
58	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
59	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
60	C₂×C₃₁×#120	C₂²	1	4	yes	—
61	C₄×#41×C₃₁	C₂²	1	16	yes	complemented
62	C₄×#41×C₃₁	C₂²	1	32	yes	complemented
63	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
64	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
66	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
68	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
71	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
73	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
74	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
75	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
76	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₃₁	C₂²	1	16	yes	complemented
78	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
83	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
84	C₂×C₃₁×#117	C₂²	1	2	yes	—
85	C₂×C₃₁×#117	C₂²	1	4	yes	—
86	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
87	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
88	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
89	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
90	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
91	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
92	C₂×C₃₁×#117	C₂²	1	32	yes	complemented
93	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
95	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
96	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
97	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
98	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
99	C₂²×C₄²×C₃₁	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₃₁	C₂²	1	2	yes	complemented
101	C₂⁵×C₃₁	C₂³	1	2	yes	—
102	C₂×#41×C₃₁	—	2	16	no	—
103	C₂×#41×C₃₁	—	2	8	no	—
104	C₂×#41×C₃₁	C₂³	1	8	yes	—
105	C₂×#41×C₃₁	C₂³	1	16	yes	—
106	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
107	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	—	2	8	no	—
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
114	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
116	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
117	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₃₁	—	2	16	no	—
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
121	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	16	yes	—
126	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
129	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
131	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
134	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
135	C₃₁×#126	C₂³	1	32	yes	complemented
136	C₃₁×#126	C₂³	1	32	yes	complemented
137	C₃₁×#126	C₂³	1	32	yes	complemented
138	C₃₁×#125	C₂³	1	32	yes	complemented
139	C₃₁×#125	C₂³	1	16	yes	complemented
140	C₃₁×#125	C₂³	1	16	yes	complemented
141	C₃₁×#124	C₂³	1	16	yes	—
142	C₃₁×#124	C₂³	1	32	yes	complemented
143	C₃₁×#123	C₂³	1	32	yes	—
144	C₃₁×#123	C₂³	1	32	yes	—
145	C₃₁×#123	C₂³	1	32	yes	complemented
146	C₃₁×#123	C₂³	1	32	yes	complemented
147	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
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×#121	C₂³	1	32	yes	—
154	C₃₁×#121	C₂³	1	16	yes	—
155	C₃₁×#121	C₂³	1	16	yes	complemented
156	C₃₁×#121	C₂³	1	16	yes	complemented
157	C₃₁×#120	C₂³	1	32	yes	—
158	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
159	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
160	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
161	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
162	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
163	C₄×D₄×C₃₁	C₂³	1	8	yes	—
164	C₄×D₄×C₃₁	C₂³	1	8	yes	—
165	C₄×D₄×C₃₁	C₂³	1	16	yes	—
166	C₄×D₄×C₃₁	C₂³	1	8	yes	—
167	C₄×D₄×C₃₁	C₂³	1	16	yes	—
168	C₄×D₄×C₃₁	C₂³	1	8	yes	—
169	C₄×D₄×C₃₁	C₂³	1	16	yes	—
170	C₄×D₄×C₃₁	C₂³	1	16	yes	—
171	C₄×D₄×C₃₁	C₂³	1	16	yes	—
172	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
173	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
174	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
175	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
176	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
177	C₃₁×#117	C₂³	1	8	yes	—
178	C₃₁×#117	C₂³	1	16	yes	—
179	C₃₁×#117	C₂³	1	32	yes	—
180	C₃₁×#117	C₂³	1	32	yes	complemented
181	C₃₁×#117	C₂³	1	16	yes	complemented
182	C₃₁×#117	C₂³	1	16	yes	complemented
183	C₃₁×#117	C₂³	1	16	yes	complemented
184	C₃₁×#117	C₂³	1	32	yes	complemented
185	C₃₁×#117	C₂³	1	16	yes	complemented
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
205	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
210	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
211	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	—
212	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
216	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
222	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
225	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
226	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
227	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
228	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
229	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
232	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
233	C₂×C₄²×C₃₁	C₂³	1	32	yes	complemented
234	C₂×C₄²×C₃₁	C₂³	1	16	yes	complemented
235	C₂⁴×C₃₁	—	2	8	no	—
236	C₂⁴×C₃₁	—	2	8	no	—
237	C₂⁴×C₃₁	—	4	4	no	—
238	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
239	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
240	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
241	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
243	#41×C₃₁	—	2	64	no	—
244	#41×C₃₁	—	2	32	no	—
245	C₂×Q₈×C₃₁	—	2	4	no	—
246	C₂×Q₈×C₃₁	—	2	8	no	—
247	C₂×Q₈×C₃₁	—	4	4	no	—
248	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
249	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
250	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
251	C₂×D₄×C₃₁	—	2	8	no	—
252	C₂×D₄×C₃₁	—	2	8	no	—
253	C₂×D₄×C₃₁	—	2	16	no	—
254	C₂×D₄×C₃₁	—	2	32	no	—
255	C₂×D₄×C₃₁	—	2	4	no	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	4	8	no	—
258	C₂×D₄×C₃₁	#41	1	8	yes	complemented
259	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
260	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
261	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
262	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
263	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
264	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
265	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₃₁	—	2	8	no	—
267	C₂²×C₄×C₃₁	—	2	16	no	—
268	C₂²×C₄×C₃₁	—	2	8	no	—
269	C₂²×C₄×C₃₁	—	2	8	no	—
270	C₂²×C₄×C₃₁	—	2	8	no	—
271	C₂²×C₄×C₃₁	—	2	8	no	—
272	C₂²×C₄×C₃₁	—	2	4	no	—
273	C₂²×C₄×C₃₁	—	2	8	no	—
274	C₂²×C₄×C₃₁	—	2	8	no	—
275	C₂²×C₄×C₃₁	—	2	64	no	—
276	C₂²×C₄×C₃₁	—	4	4	no	—
277	C₂²×C₄×C₃₁	—	4	8	no	—
278	C₂²×C₄×C₃₁	—	4	2	no	—
279	C₂²×C₄×C₃₁	#41	1	8	yes	complemented
280	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
288	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
290	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
291	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
296	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
300	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
301	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
302	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
314	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
315	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
319	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
320	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
321	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
322	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
326	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
328	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
329	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
330	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
331	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
332	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
333	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
334	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
335	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
336	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
337	C₄²×C₃₁	C₂⁴	1	4	yes	—
338	C₄²×C₃₁	C₂⁴	1	4	yes	—
339	C₄²×C₃₁	C₂⁴	1	4	yes	—
340	C₄²×C₃₁	C₂⁴	1	4	yes	—
341	C₄²×C₃₁	C₂⁴	1	8	yes	—
342	C₄²×C₃₁	C₂⁴	1	16	yes	—
343	C₄²×C₃₁	C₂⁴	1	16	yes	—
344	C₄²×C₃₁	C₂⁴	1	16	yes	—
345	C₄²×C₃₁	C₂⁴	1	8	yes	—
346	C₄²×C₃₁	C₂⁴	1	8	yes	—
347	C₂×#3475	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
348	C₂³×C₃₁	—	2	4	no	—
349	C₂³×C₃₁	—	2	2	no	—
350	C₂³×C₃₁	—	2	4	no	—
351	C₂³×C₃₁	—	2	2	no	—
352	C₂³×C₃₁	—	2	16	no	—
353	C₂³×C₃₁	—	2	4	no	—
354	C₂³×C₃₁	—	2	4	no	—
355	C₂³×C₃₁	—	2	4	no	—
356	C₂³×C₃₁	—	2	16	no	—
357	C₂³×C₃₁	—	2	4	no	—
358	C₂³×C₃₁	—	2	4	no	—
359	C₂³×C₃₁	—	2	4	no	—
360	C₂³×C₃₁	—	4	8	no	—
361	C₂³×C₃₁	—	4	32	no	—
362	C₂³×C₃₁	C₂×#41	1	4	yes	—
363	C₂³×C₃₁	C₂×#41	1	8	yes	—
364	C₂³×C₃₁	C₂⁵	1	4	yes	—
365	C₂³×C₃₁	C₂⁵	1	4	yes	—
366	C₂³×C₃₁	C₂⁵	1	2	yes	—
367	C₂³×C₃₁	C₂⁵	1	4	yes	—
368	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
369	Q₈×C₃₁	—	2	8	no	—
370	Q₈×C₃₁	—	2	16	no	—
371	Q₈×C₃₁	—	4	8	no	—
372	D₄×C₃₁	—	2	16	no	—
373	D₄×C₃₁	—	2	16	no	—
374	D₄×C₃₁	—	2	32	no	—
375	D₄×C₃₁	—	2	8	no	—
376	D₄×C₃₁	—	2	8	no	—
377	D₄×C₃₁	—	4	16	no	—
378	D₄×C₃₁	C₂×#41	1	16	yes	complemented
379	C₂×C₄×C₃₁	—	2	16	no	—
380	C₂×C₄×C₃₁	—	2	4	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	4	no	—
383	C₂×C₄×C₃₁	—	2	2	no	—
384	C₂×C₄×C₃₁	—	2	8	no	—
385	C₂×C₄×C₃₁	—	2	4	no	—
386	C₂×C₄×C₃₁	—	2	32	no	—
387	C₂×C₄×C₃₁	—	2	2	no	—
388	C₂×C₄×C₃₁	—	2	4	no	—
389	C₂×C₄×C₃₁	—	2	8	no	—
390	C₂×C₄×C₃₁	—	2	2	no	—
391	C₂×C₄×C₃₁	—	2	16	no	—
392	C₂×C₄×C₃₁	—	2	16	no	—
393	C₂×C₄×C₃₁	—	2	16	no	—
394	C₂×C₄×C₃₁	—	2	16	no	—
395	C₂×C₄×C₃₁	—	2	8	no	—
396	C₂×C₄×C₃₁	—	2	16	no	—
397	C₂×C₄×C₃₁	—	2	16	no	—
398	C₂×C₄×C₃₁	—	4	8	no	—
399	C₂×C₄×C₃₁	—	4	16	no	—
400	C₂×C₄×C₃₁	—	4	4	no	—
401	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
402	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
403	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
404	C₂×C₄×C₃₁	C₂×#41	1	16	yes	complemented
405	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
406	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
407	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
408	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
409	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
410	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
411	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
412	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
413	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
414	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
415	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
416	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
417	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
418	#3475	C₂×C₃₁	1	32	yes	direct product factor
419	C₂×#556	C₂×C₃₁	1	1	yes	characteristic, complemented
420	C₂×#555	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₂×#554	C₂×C₃₁	1	1	yes	characteristic, complemented
422	C₂×#553	C₂×C₃₁	1	2	yes	complemented
423	C₂×#552	C₂×C₃₁	1	2	yes	complemented
424	C₂×#552	C₂×C₃₁	1	2	yes	complemented
425	C₂×#551	C₂×C₃₁	1	4	yes	complemented
426	C₂×#547	C₂×C₃₁	1	1	yes	characteristic, complemented
427	C₂×#546	C₂×C₃₁	1	2	yes	complemented
428	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
429	C₂×#529	C₂×C₃₁	1	4	yes	complemented
430	C₂×#529	C₂×C₃₁	1	2	yes	complemented
431	C₂×#525	C₂×C₃₁	1	2	yes	complemented
432	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
433	C₂×C₄×#41	C₂×C₃₁	1	2	yes	complemented
434	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
435	C₂²×#117	C₂×C₃₁	1	2	yes	complemented
436	C₂²×C₃₁	—	2	4	no	—
437	C₂²×C₃₁	—	2	2	no	—
438	C₂²×C₃₁	—	2	4	no	—
439	C₂²×C₃₁	—	2	2	no	—
440	C₂²×C₃₁	—	2	8	no	—
441	C₂²×C₃₁	—	2	16	no	—
442	C₂²×C₃₁	—	2	4	no	—
443	C₂²×C₃₁	—	2	4	no	—
444	C₂²×C₃₁	—	2	4	no	—
445	C₂²×C₃₁	—	2	4	no	—
446	C₂²×C₃₁	—	2	4	no	—
447	C₂²×C₃₁	—	2	4	no	—
448	C₂²×C₃₁	—	4	32	no	—
449	C₂²×C₃₁	—	4	8	no	—
450	C₂²×C₃₁	—	4	8	no	—
451	C₂²×C₃₁	C₂²×#41	1	4	yes	—
452	C₂²×C₃₁	C₂²×#41	1	8	yes	—
453	C₂²×C₃₁	C₂²×#41	1	2	yes	—
454	C₂²×C₃₁	C₂²×#41	1	2	yes	—
455	C₂²×C₃₁	#585	1	2	yes	—
456	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
457	C₄×C₃₁	—	2	4	no	—
458	C₄×C₃₁	—	2	4	no	—
459	C₄×C₃₁	—	2	4	no	—
460	C₄×C₃₁	—	2	2	no	—
461	C₄×C₃₁	—	2	8	no	—
462	C₄×C₃₁	—	2	4	no	—
463	C₄×C₃₁	—	2	2	no	—
464	C₄×C₃₁	—	2	4	no	—
465	C₄×C₃₁	—	2	8	no	—
466	C₄×C₃₁	—	2	2	no	—
467	C₄×C₃₁	C₂²×#41	1	4	yes	—
468	C₄×C₃₁	C₂²×#41	1	4	yes	—
469	C₄×C₃₁	C₂²×#41	1	4	yes	—
470	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
471	C₂²×#41	C₂²×C₃₁	1	2	yes	—
472	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
473	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
474	#556	C₂²×C₃₁	1	16	yes	complemented
475	#555	C₂²×C₃₁	1	16	yes	complemented
476	#554	C₂²×C₃₁	1	16	yes	complemented
477	#553	C₂²×C₃₁	1	32	yes	complemented
478	#552	C₂²×C₃₁	1	32	yes	complemented
479	#552	C₂²×C₃₁	1	32	yes	complemented
480	#551	C₂²×C₃₁	1	64	yes	complemented
481	#547	C₂²×C₃₁	1	16	yes	complemented
482	#546	C₂²×C₃₁	1	32	yes	complemented
483	#533	C₂²×C₃₁	1	16	yes	complemented
484	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
485	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
486	#529	C₂²×C₃₁	1	64	yes	complemented
487	#529	C₂²×C₃₁	1	32	yes	complemented
488	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
489	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
490	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
491	C₂×#125	C₂²×C₃₁	1	4	yes	complemented
492	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
493	C₂×#125	C₂²×C₃₁	1	2	yes	complemented
494	C₂×#124	C₂²×C₃₁	1	2	yes	—
495	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
496	#525	C₂²×C₃₁	1	32	yes	complemented
497	C₂×#123	C₂²×C₃₁	1	4	yes	—
498	C₂×#123	C₂²×C₃₁	1	4	yes	—
499	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
500	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
501	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
502	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
503	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
504	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
505	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
506	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
507	C₂×#121	C₂²×C₃₁	1	4	yes	—
508	C₂×#121	C₂²×C₃₁	1	2	yes	—
509	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
510	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
511	C₂×#120	C₂²×C₃₁	1	4	yes	—
512	C₄×#41	C₂²×C₃₁	1	16	yes	complemented
513	C₄×#41	C₂²×C₃₁	1	32	yes	complemented
514	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
515	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
516	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
517	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
518	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
519	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
520	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
522	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
524	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
525	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
526	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
527	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₃₁	1	16	yes	complemented
529	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
530	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
531	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
532	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
533	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
534	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
535	C₂×#117	C₂²×C₃₁	1	2	yes	—
536	C₂×#117	C₂²×C₃₁	1	4	yes	—
537	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
538	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
539	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
540	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
541	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
542	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
543	C₂×#117	C₂²×C₃₁	1	32	yes	complemented
544	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
545	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
546	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
547	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
548	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
549	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
550	C₂²×C₄²	C₂²×C₃₁	1	4	yes	complemented
551	C₂²×C₄²	C₂²×C₃₁	1	2	yes	complemented
552	C₂×C₃₁	—	2	4	no	—
553	C₂×C₃₁	—	2	8	no	—
554	C₂×C₃₁	—	4	4	no	—
555	C₂×C₃₁	—	4	4	no	—
556	C₂×C₃₁	#3475	1	4	yes	direct product factor
557	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
558	C₂×C₃₁	C₂³×#41	1	1	yes	characteristic
559	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
560	C₂⁵	C₂³×C₃₁	1	2	yes	—
561	C₂×#41	—	2	16	no	—
562	C₂×#41	—	2	8	no	—
563	C₂×#41	C₂³×C₃₁	1	8	yes	—
564	C₂×#41	C₂³×C₃₁	1	16	yes	—
565	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
566	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
568	C₂²×D₄	—	2	8	no	—
569	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
570	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
571	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
573	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
574	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
575	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
576	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂³×C₄	—	2	16	no	—
578	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
580	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
582	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
583	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
584	C₂³×C₄	C₂³×C₃₁	1	16	yes	—
585	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
586	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
587	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
588	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
590	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
591	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
592	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
593	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
594	#126	C₂³×C₃₁	1	32	yes	complemented
595	#126	C₂³×C₃₁	1	32	yes	complemented
596	#126	C₂³×C₃₁	1	32	yes	complemented
597	#125	C₂³×C₃₁	1	32	yes	complemented
598	#125	C₂³×C₃₁	1	16	yes	complemented
599	#125	C₂³×C₃₁	1	16	yes	complemented
600	#124	C₂³×C₃₁	1	16	yes	—
601	#124	C₂³×C₃₁	1	32	yes	complemented
602	#123	C₂³×C₃₁	1	32	yes	—
603	#123	C₂³×C₃₁	1	32	yes	—
604	#123	C₂³×C₃₁	1	32	yes	complemented
605	#123	C₂³×C₃₁	1	32	yes	complemented
606	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
607	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
608	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
609	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
610	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
611	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
612	#121	C₂³×C₃₁	1	32	yes	—
613	#121	C₂³×C₃₁	1	16	yes	—
614	#121	C₂³×C₃₁	1	16	yes	complemented
615	#121	C₂³×C₃₁	1	16	yes	complemented
616	#120	C₂³×C₃₁	1	32	yes	—
617	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
618	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
619	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
620	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
621	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
622	C₄×D₄	C₂³×C₃₁	1	8	yes	—
623	C₄×D₄	C₂³×C₃₁	1	8	yes	—
624	C₄×D₄	C₂³×C₃₁	1	16	yes	—
625	C₄×D₄	C₂³×C₃₁	1	8	yes	—
626	C₄×D₄	C₂³×C₃₁	1	16	yes	—
627	C₄×D₄	C₂³×C₃₁	1	8	yes	—
628	C₄×D₄	C₂³×C₃₁	1	16	yes	—
629	C₄×D₄	C₂³×C₃₁	1	16	yes	—
630	C₄×D₄	C₂³×C₃₁	1	16	yes	—
631	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
632	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
633	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
634	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
635	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
636	#117	C₂³×C₃₁	1	8	yes	—
637	#117	C₂³×C₃₁	1	16	yes	—
638	#117	C₂³×C₃₁	1	32	yes	—
639	#117	C₂³×C₃₁	1	32	yes	complemented
640	#117	C₂³×C₃₁	1	16	yes	complemented
641	#117	C₂³×C₃₁	1	16	yes	complemented
642	#117	C₂³×C₃₁	1	16	yes	complemented
643	#117	C₂³×C₃₁	1	32	yes	complemented
644	#117	C₂³×C₃₁	1	16	yes	complemented
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
649	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
654	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
655	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
659	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
660	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
661	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
662	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
664	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
665	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
681	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
682	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
683	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
684	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
685	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
687	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
692	C₂×C₄²	C₂³×C₃₁	1	32	yes	complemented
693	C₂×C₄²	C₂³×C₃₁	1	16	yes	complemented
694	C₃₁	C₂×#3475	1	1	yes	characteristic, direct product factor, Sylow
695	C₂⁴	—	2	8	no	—
696	C₂⁴	—	2	8	no	—
697	C₂⁴	—	4	4	no	—
698	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
699	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
700	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
701	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
702	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
703	#41	—	2	64	no	—
704	#41	—	2	32	no	—
705	C₂×Q₈	—	2	4	no	—
706	C₂×Q₈	—	2	8	no	—
707	C₂×Q₈	—	4	4	no	—
708	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
709	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
710	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
711	C₂×D₄	—	2	8	no	—
712	C₂×D₄	—	2	8	no	—
713	C₂×D₄	—	2	16	no	—
714	C₂×D₄	—	2	32	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	4	8	no	—
718	C₂×D₄	#41×C₃₁	1	8	yes	complemented
719	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
720	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
721	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
722	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
723	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
724	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
725	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
726	C₂²×C₄	—	2	8	no	—
727	C₂²×C₄	—	2	16	no	—
728	C₂²×C₄	—	2	8	no	—
729	C₂²×C₄	—	2	8	no	—
730	C₂²×C₄	—	2	8	no	—
731	C₂²×C₄	—	2	8	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	8	no	—
734	C₂²×C₄	—	2	8	no	—
735	C₂²×C₄	—	2	64	no	—
736	C₂²×C₄	—	4	4	no	—
737	C₂²×C₄	—	4	8	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	#41×C₃₁	1	8	yes	complemented
740	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
746	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
748	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
750	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
751	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
752	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
753	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
754	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
756	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
757	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
758	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
759	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
760	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
761	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
762	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
766	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
767	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
768	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
769	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
771	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
772	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
773	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
774	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
775	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
778	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
779	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
780	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
781	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
782	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
783	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
784	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
785	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
786	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
787	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
788	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
791	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
792	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
794	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
797	C₄²	C₂⁴×C₃₁	1	4	yes	—
798	C₄²	C₂⁴×C₃₁	1	4	yes	—
799	C₄²	C₂⁴×C₃₁	1	4	yes	—
800	C₄²	C₂⁴×C₃₁	1	4	yes	—
801	C₄²	C₂⁴×C₃₁	1	8	yes	—
802	C₄²	C₂⁴×C₃₁	1	16	yes	—
803	C₄²	C₂⁴×C₃₁	1	16	yes	—
804	C₄²	C₂⁴×C₃₁	1	16	yes	—
805	C₄²	C₂⁴×C₃₁	1	8	yes	—
806	C₄²	C₂⁴×C₃₁	1	8	yes	—
807	C₂³	—	2	4	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	4	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	16	no	—
812	C₂³	—	2	4	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	16	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	32	no	—
821	C₂³	C₂×#41×C₃₁	1	4	yes	—
822	C₂³	C₂×#41×C₃₁	1	8	yes	—
823	C₂³	C₂⁵×C₃₁	1	4	yes	—
824	C₂³	C₂⁵×C₃₁	1	4	yes	—
825	C₂³	C₂⁵×C₃₁	1	2	yes	—
826	C₂³	C₂⁵×C₃₁	1	4	yes	—
827	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
828	Q₈	—	2	8	no	—
829	Q₈	—	2	16	no	—
830	Q₈	—	4	8	no	—
831	D₄	—	2	16	no	—
832	D₄	—	2	16	no	—
833	D₄	—	2	32	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	8	no	—
836	D₄	—	4	16	no	—
837	D₄	C₂×#41×C₃₁	1	16	yes	complemented
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	2	4	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	32	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	8	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	16	no	—
851	C₂×C₄	—	2	16	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	2	16	no	—
854	C₂×C₄	—	2	8	no	—
855	C₂×C₄	—	2	16	no	—
856	C₂×C₄	—	2	16	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	16	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
861	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
862	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
863	C₂×C₄	C₂×#41×C₃₁	1	16	yes	complemented
864	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
865	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
866	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
867	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
868	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
869	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
870	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
871	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
872	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
873	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
874	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
875	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
876	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	4	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	16	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	4	32	no	—
890	C₂²	—	4	8	no	—
891	C₂²	—	4	8	no	—
892	C₂²	C₂²×#41×C₃₁	1	4	yes	—
893	C₂²	C₂²×#41×C₃₁	1	8	yes	—
894	C₂²	C₂²×#41×C₃₁	1	2	yes	—
895	C₂²	C₂²×#41×C₃₁	1	2	yes	—
896	C₂²	C₃₁×#585	1	2	yes	—
897	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	8	no	—
903	C₄	—	2	4	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	8	no	—
907	C₄	—	2	2	no	—
908	C₄	C₂²×#41×C₃₁	1	4	yes	—
909	C₄	C₂²×#41×C₃₁	1	4	yes	—
910	C₄	C₂²×#41×C₃₁	1	4	yes	—
911	C₂	—	2	4	no	—
912	C₂	—	2	8	no	—
913	C₂	—	4	4	no	—
914	C₂	—	4	4	no	—
915	C₂	C₃₁×#3475	1	4	yes	direct product factor
916	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
917	C₂	C₂³×#41×C₃₁	1	1	yes	characteristic
918	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂³×C₃₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3475	C₂	direct (N × H)
2. C₂×C₃₁×#556	C₂	semidirect
3. C₂×C₃₁×#555	C₂	semidirect
4. C₂×C₃₁×#554	C₂	semidirect
5. C₂×C₃₁×#553	C₂	semidirect
6. C₂×C₃₁×#552	C₂	semidirect
7. C₂×C₃₁×#552	C₂	semidirect
8. C₂×C₃₁×#551	C₂	semidirect
9. C₂×C₃₁×#547	C₂	semidirect
10. C₂×C₃₁×#546	C₂	semidirect
11. C₂×C₃₁×#533	C₂	semidirect
12. C₂×C₃₁×#529	C₂	semidirect
13. C₂×C₃₁×#529	C₂	semidirect
14. C₂×C₃₁×#525	C₂	semidirect
15. C₂×C₄×#41×C₃₁	C₂	semidirect
16. C₂×C₄×#41×C₃₁	C₂	semidirect
17. C₂²×C₄×D₄×C₃₁	C₂	semidirect
18. C₂²×C₃₁×#117	C₂	semidirect
23. C₃₁×#556	C₂²	semidirect
24. C₃₁×#555	C₂²	semidirect
25. C₃₁×#554	C₂²	semidirect
26. C₃₁×#553	C₂²	semidirect
27. C₃₁×#552	C₂²	semidirect
28. C₃₁×#552	C₂²	semidirect
29. C₃₁×#551	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
31. C₃₁×#546	C₂²	semidirect
32. C₃₁×#533	C₂²	semidirect
33. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
35. C₃₁×#529	C₂²	semidirect
36. C₃₁×#529	C₂²	semidirect
37. C₂×C₃₁×#126	C₂²	semidirect
38. C₂×C₃₁×#126	C₂²	semidirect
39. C₂×C₃₁×#126	C₂²	semidirect
40. C₂×C₃₁×#125	C₂²	semidirect
41. C₂×C₃₁×#125	C₂²	semidirect
42. C₂×C₃₁×#125	C₂²	semidirect
44. C₂×C₃₁×#124	C₂²	semidirect
45. C₃₁×#525	C₂²	semidirect
48. C₂×C₃₁×#123	C₂²	semidirect
49. C₂×C₃₁×#123	C₂²	semidirect
52. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₃₁×#121	C₂²	semidirect
59. C₂×C₃₁×#121	C₂²	semidirect
61. C₄×#41×C₃₁	C₂²	semidirect
62. C₄×#41×C₃₁	C₂²	semidirect
63. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
64. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
65. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
66. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
67. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
77. C₂×C₄×D₄×C₃₁	C₂²	semidirect
78. C₂×C₄×D₄×C₃₁	C₂²	semidirect
79. C₂×C₄×D₄×C₃₁	C₂²	semidirect
80. C₂×C₄×D₄×C₃₁	C₂²	semidirect
81. C₂×C₄×D₄×C₃₁	C₂²	semidirect
82. C₂×C₄×D₄×C₃₁	C₂²	semidirect
86. C₂×C₃₁×#117	C₂²	semidirect
87. C₂×C₃₁×#117	C₂²	semidirect
88. C₂×C₃₁×#117	C₂²	semidirect
89. C₂×C₃₁×#117	C₂²	semidirect
90. C₂×C₃₁×#117	C₂²	semidirect
91. C₂×C₃₁×#117	C₂²	semidirect
92. C₂×C₃₁×#117	C₂²	semidirect
94. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
95. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
99. C₂²×C₄²×C₃₁	C₂²	semidirect
100. C₂²×C₄²×C₃₁	C₂²	semidirect
133. C₃₁×C₄⋊Q₈	C₂³	semidirect
134. C₃₁×C₄⋊Q₈	C₂³	semidirect
135. C₃₁×#126	C₂³	semidirect
136. C₃₁×#126	C₂³	semidirect
137. C₃₁×#126	C₂³	semidirect
138. C₃₁×#125	C₂³	semidirect
139. C₃₁×#125	C₂³	semidirect
140. C₃₁×#125	C₂³	semidirect
142. C₃₁×#124	C₂³	semidirect
145. C₃₁×#123	C₂³	semidirect
146. C₃₁×#123	C₂³	semidirect
149. C₃₁×C₂²⋊Q₈	C₂³	semidirect
150. C₃₁×C₂²⋊Q₈	C₂³	semidirect
151. C₃₁×C₂²⋊Q₈	C₂³	semidirect
152. C₃₁×C₂²⋊Q₈	C₂³	semidirect
155. C₃₁×#121	C₂³	semidirect
156. C₃₁×#121	C₂³	semidirect
158. C₄×Q₈×C₃₁	C₂³	semidirect
159. C₄×Q₈×C₃₁	C₂³	semidirect
160. C₄×Q₈×C₃₁	C₂³	semidirect
161. C₄×Q₈×C₃₁	C₂³	semidirect
162. C₄×Q₈×C₃₁	C₂³	semidirect
172. C₄×D₄×C₃₁	C₂³	semidirect
173. C₄×D₄×C₃₁	C₂³	semidirect
174. C₄×D₄×C₃₁	C₂³	semidirect
175. C₄×D₄×C₃₁	C₂³	semidirect
176. C₄×D₄×C₃₁	C₂³	semidirect
180. C₃₁×#117	C₂³	semidirect
181. C₃₁×#117	C₂³	semidirect
182. C₃₁×#117	C₂³	semidirect
183. C₃₁×#117	C₂³	semidirect
184. C₃₁×#117	C₂³	semidirect
185. C₃₁×#117	C₂³	semidirect
204. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
205. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
233. C₂×C₄²×C₃₁	C₂³	semidirect
234. C₂×C₄²×C₃₁	C₂³	semidirect
258. C₂×D₄×C₃₁	#41	semidirect
279. C₂²×C₄×C₃₁	#41	semidirect
347. C₂×#3475	C₃₁	direct (N × H)
378. D₄×C₃₁	C₂×#41	semidirect
404. C₂×C₄×C₃₁	C₂×#41	semidirect
418. #3475	C₂×C₃₁	direct (N × H)
419. C₂×#556	C₂×C₃₁	semidirect
420. C₂×#555	C₂×C₃₁	semidirect
421. C₂×#554	C₂×C₃₁	semidirect
422. C₂×#553	C₂×C₃₁	semidirect
423. C₂×#552	C₂×C₃₁	semidirect
424. C₂×#552	C₂×C₃₁	semidirect
425. C₂×#551	C₂×C₃₁	semidirect
426. C₂×#547	C₂×C₃₁	semidirect
427. C₂×#546	C₂×C₃₁	semidirect
428. C₂×#533	C₂×C₃₁	semidirect
429. C₂×#529	C₂×C₃₁	semidirect
430. C₂×#529	C₂×C₃₁	semidirect
431. C₂×#525	C₂×C₃₁	semidirect
432. C₂×C₄×#41	C₂×C₃₁	semidirect
433. C₂×C₄×#41	C₂×C₃₁	semidirect
434. C₂²×C₄×D₄	C₂×C₃₁	semidirect
435. C₂²×#117	C₂×C₃₁	semidirect
474. #556	C₂²×C₃₁	semidirect
475. #555	C₂²×C₃₁	semidirect
476. #554	C₂²×C₃₁	semidirect
477. #553	C₂²×C₃₁	semidirect
478. #552	C₂²×C₃₁	semidirect
479. #552	C₂²×C₃₁	semidirect
480. #551	C₂²×C₃₁	semidirect
481. #547	C₂²×C₃₁	semidirect
482. #546	C₂²×C₃₁	semidirect
483. #533	C₂²×C₃₁	semidirect
484. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
485. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
486. #529	C₂²×C₃₁	semidirect
487. #529	C₂²×C₃₁	semidirect
488. C₂×#126	C₂²×C₃₁	semidirect
489. C₂×#126	C₂²×C₃₁	semidirect
490. C₂×#126	C₂²×C₃₁	semidirect
491. C₂×#125	C₂²×C₃₁	semidirect
492. C₂×#125	C₂²×C₃₁	semidirect
493. C₂×#125	C₂²×C₃₁	semidirect
495. C₂×#124	C₂²×C₃₁	semidirect
496. #525	C₂²×C₃₁	semidirect
499. C₂×#123	C₂²×C₃₁	semidirect
500. C₂×#123	C₂²×C₃₁	semidirect
503. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
504. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
505. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
506. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
509. C₂×#121	C₂²×C₃₁	semidirect
510. C₂×#121	C₂²×C₃₁	semidirect
512. C₄×#41	C₂²×C₃₁	semidirect
513. C₄×#41	C₂²×C₃₁	semidirect
514. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
515. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
516. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
517. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
518. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
528. C₂×C₄×D₄	C₂²×C₃₁	semidirect
529. C₂×C₄×D₄	C₂²×C₃₁	semidirect
530. C₂×C₄×D₄	C₂²×C₃₁	semidirect
531. C₂×C₄×D₄	C₂²×C₃₁	semidirect
532. C₂×C₄×D₄	C₂²×C₃₁	semidirect
533. C₂×C₄×D₄	C₂²×C₃₁	semidirect
537. C₂×#117	C₂²×C₃₁	semidirect
538. C₂×#117	C₂²×C₃₁	semidirect
539. C₂×#117	C₂²×C₃₁	semidirect
540. C₂×#117	C₂²×C₃₁	semidirect
541. C₂×#117	C₂²×C₃₁	semidirect
542. C₂×#117	C₂²×C₃₁	semidirect
543. C₂×#117	C₂²×C₃₁	semidirect
545. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
546. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
550. C₂²×C₄²	C₂²×C₃₁	semidirect
551. C₂²×C₄²	C₂²×C₃₁	semidirect
556. C₂×C₃₁	#3475	direct (N × H)
592. C₄⋊Q₈	C₂³×C₃₁	semidirect
593. C₄⋊Q₈	C₂³×C₃₁	semidirect
594. #126	C₂³×C₃₁	semidirect
595. #126	C₂³×C₃₁	semidirect
596. #126	C₂³×C₃₁	semidirect
597. #125	C₂³×C₃₁	semidirect
598. #125	C₂³×C₃₁	semidirect
599. #125	C₂³×C₃₁	semidirect
601. #124	C₂³×C₃₁	semidirect
604. #123	C₂³×C₃₁	semidirect
605. #123	C₂³×C₃₁	semidirect
608. C₂²⋊Q₈	C₂³×C₃₁	semidirect
609. C₂²⋊Q₈	C₂³×C₃₁	semidirect
610. C₂²⋊Q₈	C₂³×C₃₁	semidirect
611. C₂²⋊Q₈	C₂³×C₃₁	semidirect
614. #121	C₂³×C₃₁	semidirect
615. #121	C₂³×C₃₁	semidirect
617. C₄×Q₈	C₂³×C₃₁	semidirect
618. C₄×Q₈	C₂³×C₃₁	semidirect
619. C₄×Q₈	C₂³×C₃₁	semidirect
620. C₄×Q₈	C₂³×C₃₁	semidirect
621. C₄×Q₈	C₂³×C₃₁	semidirect
631. C₄×D₄	C₂³×C₃₁	semidirect
632. C₄×D₄	C₂³×C₃₁	semidirect
633. C₄×D₄	C₂³×C₃₁	semidirect
634. C₄×D₄	C₂³×C₃₁	semidirect
635. C₄×D₄	C₂³×C₃₁	semidirect
639. #117	C₂³×C₃₁	semidirect
640. #117	C₂³×C₃₁	semidirect
641. #117	C₂³×C₃₁	semidirect
642. #117	C₂³×C₃₁	semidirect
643. #117	C₂³×C₃₁	semidirect
644. #117	C₂³×C₃₁	semidirect
663. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
664. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
692. C₂×C₄²	C₂³×C₃₁	semidirect
693. C₂×C₄²	C₂³×C₃₁	semidirect
694. C₃₁	C₂×#3475	direct (N × H)
718. C₂×D₄	#41×C₃₁	semidirect
739. C₂²×C₄	#41×C₃₁	semidirect
837. D₄	C₂×#41×C₃₁	semidirect
863. C₂×C₄	C₂×#41×C₃₁	semidirect
915. C₂	C₃₁×#3475	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×#3475	2
C₂×C₃₁×#556	2
C₂×C₃₁×#555	2
C₂×C₃₁×#554	2
C₂×C₃₁×#553	2
C₂×C₃₁×#552	2
C₂×C₃₁×#551	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×C₃₁×#533	2
C₂×C₃₁×#529	2
C₂×C₃₁×#525	2
C₂×C₄×#41×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₂²×C₃₁×#117	2
C₂×#3475	31

Subgroups — C2×C31×#3475 #21519467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3475 #21519467