Subgroups — C₂×C₃₁×#3546 #21519506

Order 7936.

8046 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3546	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#560	C₂	1	4	yes	maximal, complemented
3	C₂×C₃₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#550	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
10	C₂×D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#538	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₁×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#535	C₂	1	2	yes	maximal, complemented
15	C₂×C₃₁×#535	C₂	1	2	yes	maximal, complemented
16	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
20	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
21	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
22	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
23	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
24	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
25	C₃₁×#560	C₂²	1	64	yes	complemented
26	C₃₁×#556	C₂²	1	16	yes	complemented
27	C₃₁×#553	C₂²	1	32	yes	complemented
28	C₃₁×#550	C₂²	1	32	yes	complemented
29	C₃₁×#550	C₂²	1	16	yes	complemented
30	C₃₁×#547	C₂²	1	16	yes	complemented
31	C₃₁×#546	C₂²	1	32	yes	complemented
32	C₃₁×#546	C₂²	1	32	yes	complemented
33	D₄²×C₃₁	C₂²	1	16	yes	complemented
34	C₃₁×#542	C₂²	1	32	yes	complemented
35	C₃₁×#538	C₂²	1	64	yes	complemented
36	C₃₁×#537	C₂²	1	32	yes	complemented
37	C₃₁×#535	C₂²	1	32	yes	complemented
38	C₃₁×#535	C₂²	1	32	yes	complemented
39	C₃₁×#532	C₂²	1	16	yes	complemented
40	C₃₁×#532	C₂²	1	16	yes	complemented
41	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
44	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
46	C₂×C₃₁×#127	C₂²	1	4	yes	complemented
47	C₃₁×#529	C₂²	1	16	yes	complemented
48	C₂×C₃₁×#126	C₂²	1	2	yes	complemented
49	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
50	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
51	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
53	C₂×C₃₁×#124	C₂²	1	2	yes	—
54	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
55	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
57	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
58	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
59	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
60	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
66	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
67	C₂×C₃₁×#121	C₂²	1	2	yes	—
68	C₂×C₃₁×#121	C₂²	1	2	yes	—
69	C₂×C₃₁×#121	C₂²	1	2	yes	—
70	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
71	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
73	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
74	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
75	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
76	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
77	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
78	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
79	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
80	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
81	C₂×C₃₁×#120	C₂²	1	4	yes	—
82	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
83	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
84	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
85	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
87	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
88	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
89	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
90	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
91	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
92	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
93	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
95	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
96	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
97	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
98	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
99	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
100	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₃₁	C₂³	1	4	yes	—
102	C₂×#41×C₃₁	—	4	8	no	—
103	C₂×#41×C₃₁	—	4	8	no	—
104	C₂×#41×C₃₁	—	4	8	no	—
105	C₂×#41×C₃₁	—	4	8	no	—
106	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
107	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
108	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
109	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
110	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
112	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×D₄×C₃₁	—	4	8	no	—
114	C₂²×D₄×C₃₁	—	4	8	no	—
115	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
119	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
121	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
122	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
123	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
124	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
125	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
126	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
128	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
130	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
131	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
132	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
133	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
134	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
138	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
141	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
142	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
143	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
144	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	complemented
145	C₃₁×#127	C₂³	1	8	yes	—
146	C₃₁×#127	C₂³	1	8	yes	—
147	C₃₁×#127	C₂³	1	16	yes	complemented
148	C₃₁×#127	C₂³	1	32	yes	complemented
149	C₃₁×#126	C₂³	1	16	yes	complemented
150	C₃₁×#126	C₂³	1	32	yes	complemented
151	C₃₁×#126	C₂³	1	32	yes	complemented
152	C₃₁×#125	C₂³	1	8	yes	complemented
153	C₃₁×#124	C₂³	1	8	yes	—
154	C₃₁×#124	C₂³	1	16	yes	—
155	C₃₁×#124	C₂³	1	16	yes	complemented
156	C₃₁×#124	C₂³	1	16	yes	complemented
157	C₃₁×#124	C₂³	1	32	yes	complemented
158	C₃₁×#123	C₂³	1	16	yes	complemented
159	C₃₁×#123	C₂³	1	32	yes	complemented
160	C₃₁×#123	C₂³	1	32	yes	complemented
161	C₃₁×#123	C₂³	1	32	yes	complemented
162	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	complemented
163	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
164	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
165	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
166	C₃₁×#121	C₂³	1	8	yes	—
167	C₃₁×#121	C₂³	1	8	yes	—
168	C₃₁×#121	C₂³	1	16	yes	—
169	C₃₁×#121	C₂³	1	16	yes	—
170	C₃₁×#121	C₂³	1	16	yes	—
171	C₃₁×#121	C₂³	1	16	yes	complemented
172	C₃₁×#121	C₂³	1	8	yes	complemented
173	C₃₁×#121	C₂³	1	16	yes	complemented
174	C₃₁×#121	C₂³	1	16	yes	complemented
175	C₃₁×#121	C₂³	1	32	yes	complemented
176	C₃₁×#121	C₂³	1	16	yes	complemented
177	C₃₁×#121	C₂³	1	32	yes	complemented
178	C₃₁×#121	C₂³	1	32	yes	complemented
179	C₃₁×#121	C₂³	1	32	yes	complemented
180	C₃₁×#121	C₂³	1	32	yes	complemented
181	C₃₁×#121	C₂³	1	32	yes	complemented
182	C₃₁×#120	C₂³	1	32	yes	—
183	C₃₁×#120	C₂³	1	32	yes	complemented
184	C₃₁×#120	C₂³	1	32	yes	complemented
185	C₃₁×#120	C₂³	1	32	yes	complemented
186	C₄×Q₈×C₃₁	C₂³	1	8	yes	complemented
187	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
188	C₄×D₄×C₃₁	C₂³	1	8	yes	—
189	C₄×D₄×C₃₁	C₂³	1	8	yes	—
190	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
191	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
192	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
193	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
194	C₄×D₄×C₃₁	C₂³	1	8	yes	complemented
195	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
196	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
197	C₃₁×#117	C₂³	1	16	yes	complemented
198	C₃₁×#117	C₂³	1	16	yes	complemented
199	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
209	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
210	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
211	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
212	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
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	4	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	4	yes	—
219	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
225	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
226	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
227	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	complemented
230	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
235	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
236	C₂×C₄²×C₃₁	C₂³	1	8	yes	complemented
237	C₂⁴×C₃₁	—	4	8	no	—
238	C₂⁴×C₃₁	—	4	8	no	—
239	C₂⁴×C₃₁	—	4	8	no	—
240	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
241	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
242	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
243	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
245	C₂⁴×C₃₁	C₂⁴	1	16	yes	—
246	#41×C₃₁	—	4	32	no	—
247	#41×C₃₁	—	4	32	no	—
248	#41×C₃₁	—	4	32	no	—
249	#41×C₃₁	—	4	32	no	—
250	C₂×Q₈×C₃₁	—	2	4	no	—
251	C₂×Q₈×C₃₁	—	2	8	no	—
252	C₂×Q₈×C₃₁	—	4	4	no	—
253	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
255	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
256	C₂×D₄×C₃₁	—	2	4	no	—
257	C₂×D₄×C₃₁	—	2	4	no	—
258	C₂×D₄×C₃₁	—	2	8	no	—
259	C₂×D₄×C₃₁	—	2	8	no	—
260	C₂×D₄×C₃₁	—	2	4	no	—
261	C₂×D₄×C₃₁	—	4	32	no	—
262	C₂×D₄×C₃₁	—	4	32	no	—
263	C₂×D₄×C₃₁	—	4	8	no	—
264	C₂×D₄×C₃₁	—	4	8	no	—
265	C₂×D₄×C₃₁	—	4	4	no	—
266	C₂×D₄×C₃₁	—	4	4	no	—
267	C₂×D₄×C₃₁	—	4	4	no	—
268	C₂×D₄×C₃₁	—	4	8	no	—
269	C₂×D₄×C₃₁	—	4	4	no	—
270	C₂×D₄×C₃₁	—	4	4	no	—
271	C₂×D₄×C₃₁	—	4	4	no	—
272	C₂×D₄×C₃₁	—	4	8	no	—
273	C₂×D₄×C₃₁	—	4	8	no	—
274	C₂×D₄×C₃₁	—	4	8	no	—
275	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
276	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
277	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
278	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
279	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
280	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
281	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
282	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
283	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
284	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
285	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
286	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
287	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
288	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
289	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
290	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
291	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
292	C₂²×C₄×C₃₁	—	2	8	no	—
293	C₂²×C₄×C₃₁	—	2	8	no	—
294	C₂²×C₄×C₃₁	—	2	4	no	—
295	C₂²×C₄×C₃₁	—	2	8	no	—
296	C₂²×C₄×C₃₁	—	2	4	no	—
297	C₂²×C₄×C₃₁	—	4	2	no	—
298	C₂²×C₄×C₃₁	—	4	8	no	—
299	C₂²×C₄×C₃₁	—	4	8	no	—
300	C₂²×C₄×C₃₁	—	4	8	no	—
301	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
302	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
305	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
306	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
314	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
317	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
318	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
319	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
320	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
324	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
325	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
327	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
328	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
329	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
330	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
331	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
332	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
333	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
334	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
335	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
338	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
339	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
340	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
341	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
342	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
343	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
344	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
345	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
346	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
347	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
348	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
349	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
350	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
351	C₄²×C₃₁	C₂⁴	1	4	yes	—
352	C₄²×C₃₁	C₂⁴	1	4	yes	—
353	C₄²×C₃₁	C₂⁴	1	4	yes	—
354	C₄²×C₃₁	C₂⁴	1	4	yes	—
355	C₄²×C₃₁	C₂⁴	1	8	yes	—
356	C₄²×C₃₁	C₂⁴	1	16	yes	—
357	C₂×#3546	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂³×C₃₁	—	2	2	no	—
359	C₂³×C₃₁	—	2	2	no	—
360	C₂³×C₃₁	—	2	4	no	—
361	C₂³×C₃₁	—	2	4	no	—
362	C₂³×C₃₁	—	2	4	no	—
363	C₂³×C₃₁	—	2	4	no	—
364	C₂³×C₃₁	—	2	8	no	—
365	C₂³×C₃₁	—	2	8	no	—
366	C₂³×C₃₁	—	2	4	no	—
367	C₂³×C₃₁	—	2	4	no	—
368	C₂³×C₃₁	—	2	2	no	—
369	C₂³×C₃₁	—	2	4	no	—
370	C₂³×C₃₁	—	2	8	no	—
371	C₂³×C₃₁	—	2	4	no	—
372	C₂³×C₃₁	—	2	4	no	—
373	C₂³×C₃₁	—	4	16	no	—
374	C₂³×C₃₁	—	4	16	no	—
375	C₂³×C₃₁	—	4	16	no	—
376	C₂³×C₃₁	—	8	32	no	—
377	C₂³×C₃₁	C₂⁵	1	4	yes	—
378	C₂³×C₃₁	C₂⁵	1	4	yes	—
379	C₂³×C₃₁	C₂⁵	1	8	yes	—
380	C₂³×C₃₁	C₂⁵	1	2	yes	—
381	C₂³×C₃₁	C₂⁵	1	4	yes	—
382	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
383	Q₈×C₃₁	—	2	8	no	—
384	Q₈×C₃₁	—	2	16	no	—
385	Q₈×C₃₁	—	4	8	no	—
386	D₄×C₃₁	—	2	8	no	—
387	D₄×C₃₁	—	2	8	no	—
388	D₄×C₃₁	—	2	16	no	—
389	D₄×C₃₁	—	2	16	no	—
390	D₄×C₃₁	—	2	8	no	—
391	D₄×C₃₁	—	4	16	no	—
392	D₄×C₃₁	—	4	16	no	—
393	D₄×C₃₁	—	4	8	no	—
394	D₄×C₃₁	—	4	8	no	—
395	D₄×C₃₁	—	4	8	no	—
396	D₄×C₃₁	—	4	16	no	—
397	D₄×C₃₁	—	4	8	no	—
398	D₄×C₃₁	—	4	8	no	—
399	D₄×C₃₁	—	4	8	no	—
400	D₄×C₃₁	—	4	16	no	—
401	D₄×C₃₁	—	4	16	no	—
402	D₄×C₃₁	—	4	16	no	—
403	C₂×C₄×C₃₁	—	2	2	no	—
404	C₂×C₄×C₃₁	—	2	4	no	—
405	C₂×C₄×C₃₁	—	2	4	no	—
406	C₂×C₄×C₃₁	—	2	4	no	—
407	C₂×C₄×C₃₁	—	2	2	no	—
408	C₂×C₄×C₃₁	—	2	8	no	—
409	C₂×C₄×C₃₁	—	2	4	no	—
410	C₂×C₄×C₃₁	—	2	2	no	—
411	C₂×C₄×C₃₁	—	2	2	no	—
412	C₂×C₄×C₃₁	—	2	4	no	—
413	C₂×C₄×C₃₁	—	2	16	no	—
414	C₂×C₄×C₃₁	—	2	16	no	—
415	C₂×C₄×C₃₁	—	2	8	no	—
416	C₂×C₄×C₃₁	—	2	16	no	—
417	C₂×C₄×C₃₁	—	2	8	no	—
418	C₂×C₄×C₃₁	—	4	4	no	—
419	C₂×C₄×C₃₁	—	4	16	no	—
420	C₂×C₄×C₃₁	—	4	16	no	—
421	C₂×C₄×C₃₁	—	4	16	no	—
422	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
423	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
424	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
425	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
426	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
427	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
428	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
429	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
430	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
431	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
432	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
433	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
434	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
435	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
436	#3546	C₂×C₃₁	1	32	yes	direct product factor
437	C₂×#560	C₂×C₃₁	1	4	yes	complemented
438	C₂×#556	C₂×C₃₁	1	1	yes	characteristic, complemented
439	C₂×#553	C₂×C₃₁	1	2	yes	complemented
440	C₂×#550	C₂×C₃₁	1	2	yes	complemented
441	C₂×#550	C₂×C₃₁	1	1	yes	characteristic, complemented
442	C₂×#547	C₂×C₃₁	1	1	yes	characteristic, complemented
443	C₂×#546	C₂×C₃₁	1	2	yes	complemented
444	C₂×#546	C₂×C₃₁	1	2	yes	complemented
445	C₂×D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
446	C₂×#542	C₂×C₃₁	1	2	yes	complemented
447	C₂×#538	C₂×C₃₁	1	4	yes	complemented
448	C₂×#537	C₂×C₃₁	1	2	yes	complemented
449	C₂×#535	C₂×C₃₁	1	2	yes	complemented
450	C₂×#535	C₂×C₃₁	1	2	yes	complemented
451	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
452	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
453	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
454	C₂²×C₃₁	—	2	2	no	—
455	C₂²×C₃₁	—	2	2	no	—
456	C₂²×C₃₁	—	2	4	no	—
457	C₂²×C₃₁	—	2	4	no	—
458	C₂²×C₃₁	—	2	4	no	—
459	C₂²×C₃₁	—	2	4	no	—
460	C₂²×C₃₁	—	2	8	no	—
461	C₂²×C₃₁	—	2	8	no	—
462	C₂²×C₃₁	—	2	4	no	—
463	C₂²×C₃₁	—	2	4	no	—
464	C₂²×C₃₁	—	2	2	no	—
465	C₂²×C₃₁	—	2	4	no	—
466	C₂²×C₃₁	—	2	8	no	—
467	C₂²×C₃₁	—	2	4	no	—
468	C₂²×C₃₁	—	2	4	no	—
469	C₂²×C₃₁	—	4	4	no	—
470	C₂²×C₃₁	—	4	8	no	—
471	C₂²×C₃₁	—	4	16	no	—
472	C₂²×C₃₁	—	4	8	no	—
473	C₂²×C₃₁	—	4	8	no	—
474	C₂²×C₃₁	—	8	32	no	—
475	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
476	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
477	C₂²×C₃₁	#585	1	2	yes	—
478	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
479	C₄×C₃₁	—	2	2	no	—
480	C₄×C₃₁	—	2	4	no	—
481	C₄×C₃₁	—	2	4	no	—
482	C₄×C₃₁	—	2	4	no	—
483	C₄×C₃₁	—	2	2	no	—
484	C₄×C₃₁	—	2	8	no	—
485	C₄×C₃₁	—	2	4	no	—
486	C₄×C₃₁	—	2	2	no	—
487	C₄×C₃₁	—	2	2	no	—
488	C₄×C₃₁	—	2	4	no	—
489	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
490	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
491	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
492	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
493	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
494	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
495	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
496	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
497	#560	C₂²×C₃₁	1	64	yes	complemented
498	#556	C₂²×C₃₁	1	16	yes	complemented
499	#553	C₂²×C₃₁	1	32	yes	complemented
500	#550	C₂²×C₃₁	1	32	yes	complemented
501	#550	C₂²×C₃₁	1	16	yes	complemented
502	#547	C₂²×C₃₁	1	16	yes	complemented
503	#546	C₂²×C₃₁	1	32	yes	complemented
504	#546	C₂²×C₃₁	1	32	yes	complemented
505	D₄²	C₂²×C₃₁	1	16	yes	complemented
506	#542	C₂²×C₃₁	1	32	yes	complemented
507	#538	C₂²×C₃₁	1	64	yes	complemented
508	#537	C₂²×C₃₁	1	32	yes	complemented
509	#535	C₂²×C₃₁	1	32	yes	complemented
510	#535	C₂²×C₃₁	1	32	yes	complemented
511	#532	C₂²×C₃₁	1	16	yes	complemented
512	#532	C₂²×C₃₁	1	16	yes	complemented
513	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
514	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
515	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
516	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
517	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
518	C₂×#127	C₂²×C₃₁	1	4	yes	complemented
519	#529	C₂²×C₃₁	1	16	yes	complemented
520	C₂×#126	C₂²×C₃₁	1	2	yes	complemented
521	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
522	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
523	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic, complemented
524	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
525	C₂×#124	C₂²×C₃₁	1	2	yes	—
526	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
527	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
528	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
529	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
530	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
531	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
532	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
533	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
534	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
535	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
536	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
537	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
538	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
539	C₂×#121	C₂²×C₃₁	1	2	yes	—
540	C₂×#121	C₂²×C₃₁	1	2	yes	—
541	C₂×#121	C₂²×C₃₁	1	2	yes	—
542	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
543	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
544	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
545	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
546	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
547	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
548	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
549	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
550	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
551	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
552	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
553	C₂×#120	C₂²×C₃₁	1	4	yes	—
554	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
555	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
556	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
557	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
558	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
559	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
560	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
562	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
563	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
564	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
565	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
566	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
567	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
568	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
569	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
570	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
571	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
572	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
573	C₂×C₃₁	—	4	2	no	—
574	C₂×C₃₁	—	4	4	no	—
575	C₂×C₃₁	—	4	8	no	—
576	C₂×C₃₁	—	4	4	no	—
577	C₂×C₃₁	—	4	4	no	—
578	C₂×C₃₁	#3546	1	4	yes	direct product factor
579	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
580	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
581	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
582	C₂⁵	C₂³×C₃₁	1	4	yes	—
583	C₂×#41	—	4	8	no	—
584	C₂×#41	—	4	8	no	—
585	C₂×#41	—	4	8	no	—
586	C₂×#41	—	4	8	no	—
587	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
588	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
589	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
590	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
591	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
592	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
593	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
594	C₂²×D₄	—	4	8	no	—
595	C₂²×D₄	—	4	8	no	—
596	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
597	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
598	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
599	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
600	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
601	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
602	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
603	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
604	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
605	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
606	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
607	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
608	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
609	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
610	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
611	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
612	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
613	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
614	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
615	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
616	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
617	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
618	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
619	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
620	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
621	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
622	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
623	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
624	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
625	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
626	#127	C₂³×C₃₁	1	8	yes	—
627	#127	C₂³×C₃₁	1	8	yes	—
628	#127	C₂³×C₃₁	1	16	yes	complemented
629	#127	C₂³×C₃₁	1	32	yes	complemented
630	#126	C₂³×C₃₁	1	16	yes	complemented
631	#126	C₂³×C₃₁	1	32	yes	complemented
632	#126	C₂³×C₃₁	1	32	yes	complemented
633	#125	C₂³×C₃₁	1	8	yes	complemented
634	#124	C₂³×C₃₁	1	8	yes	—
635	#124	C₂³×C₃₁	1	16	yes	—
636	#124	C₂³×C₃₁	1	16	yes	complemented
637	#124	C₂³×C₃₁	1	16	yes	complemented
638	#124	C₂³×C₃₁	1	32	yes	complemented
639	#123	C₂³×C₃₁	1	16	yes	complemented
640	#123	C₂³×C₃₁	1	32	yes	complemented
641	#123	C₂³×C₃₁	1	32	yes	complemented
642	#123	C₂³×C₃₁	1	32	yes	complemented
643	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
644	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
645	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
646	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
647	#121	C₂³×C₃₁	1	8	yes	—
648	#121	C₂³×C₃₁	1	8	yes	—
649	#121	C₂³×C₃₁	1	16	yes	—
650	#121	C₂³×C₃₁	1	16	yes	—
651	#121	C₂³×C₃₁	1	16	yes	—
652	#121	C₂³×C₃₁	1	16	yes	complemented
653	#121	C₂³×C₃₁	1	8	yes	complemented
654	#121	C₂³×C₃₁	1	16	yes	complemented
655	#121	C₂³×C₃₁	1	16	yes	complemented
656	#121	C₂³×C₃₁	1	32	yes	complemented
657	#121	C₂³×C₃₁	1	16	yes	complemented
658	#121	C₂³×C₃₁	1	32	yes	complemented
659	#121	C₂³×C₃₁	1	32	yes	complemented
660	#121	C₂³×C₃₁	1	32	yes	complemented
661	#121	C₂³×C₃₁	1	32	yes	complemented
662	#121	C₂³×C₃₁	1	32	yes	complemented
663	#120	C₂³×C₃₁	1	32	yes	—
664	#120	C₂³×C₃₁	1	32	yes	complemented
665	#120	C₂³×C₃₁	1	32	yes	complemented
666	#120	C₂³×C₃₁	1	32	yes	complemented
667	C₄×Q₈	C₂³×C₃₁	1	8	yes	complemented
668	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
669	C₄×D₄	C₂³×C₃₁	1	8	yes	—
670	C₄×D₄	C₂³×C₃₁	1	8	yes	—
671	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
672	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
673	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
674	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
675	C₄×D₄	C₂³×C₃₁	1	8	yes	complemented
676	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
677	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
678	#117	C₂³×C₃₁	1	16	yes	complemented
679	#117	C₂³×C₃₁	1	16	yes	complemented
680	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
682	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
683	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
687	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
692	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
693	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
694	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	complemented
711	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
712	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
713	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
714	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
716	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
717	C₂×C₄²	C₂³×C₃₁	1	8	yes	complemented
718	C₃₁	C₂×#3546	1	1	yes	characteristic, direct product factor, Sylow
719	C₂⁴	—	4	8	no	—
720	C₂⁴	—	4	8	no	—
721	C₂⁴	—	4	8	no	—
722	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
723	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
724	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
725	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
726	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
727	C₂⁴	C₂⁴×C₃₁	1	16	yes	—
728	#41	—	4	32	no	—
729	#41	—	4	32	no	—
730	#41	—	4	32	no	—
731	#41	—	4	32	no	—
732	C₂×Q₈	—	2	4	no	—
733	C₂×Q₈	—	2	8	no	—
734	C₂×Q₈	—	4	4	no	—
735	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
736	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
737	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	4	no	—
740	C₂×D₄	—	2	8	no	—
741	C₂×D₄	—	2	8	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	4	32	no	—
744	C₂×D₄	—	4	32	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	8	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	4	4	no	—
749	C₂×D₄	—	4	4	no	—
750	C₂×D₄	—	4	8	no	—
751	C₂×D₄	—	4	4	no	—
752	C₂×D₄	—	4	4	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	8	no	—
755	C₂×D₄	—	4	8	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
758	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
759	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
760	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
761	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
762	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
763	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
764	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
765	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
766	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
767	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
768	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
769	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
770	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
771	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
772	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
773	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
774	C₂²×C₄	—	2	8	no	—
775	C₂²×C₄	—	2	8	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	8	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	8	no	—
781	C₂²×C₄	—	4	8	no	—
782	C₂²×C₄	—	4	8	no	—
783	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
786	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
788	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
789	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
791	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
792	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
793	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
794	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
795	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
796	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
797	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
798	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
799	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
800	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
801	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
802	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
804	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
805	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
806	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
807	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
808	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
809	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
810	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
811	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
812	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
813	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
814	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
815	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
816	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
817	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
818	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
819	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
820	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
821	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
822	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
823	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
824	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
825	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
826	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
827	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
828	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
829	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
830	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
831	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
832	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
833	C₄²	C₂⁴×C₃₁	1	4	yes	—
834	C₄²	C₂⁴×C₃₁	1	4	yes	—
835	C₄²	C₂⁴×C₃₁	1	4	yes	—
836	C₄²	C₂⁴×C₃₁	1	4	yes	—
837	C₄²	C₂⁴×C₃₁	1	8	yes	—
838	C₄²	C₂⁴×C₃₁	1	16	yes	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	4	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	2	4	no	—
845	C₂³	—	2	8	no	—
846	C₂³	—	2	8	no	—
847	C₂³	—	2	4	no	—
848	C₂³	—	2	4	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	4	no	—
851	C₂³	—	2	8	no	—
852	C₂³	—	2	4	no	—
853	C₂³	—	2	4	no	—
854	C₂³	—	4	16	no	—
855	C₂³	—	4	16	no	—
856	C₂³	—	4	16	no	—
857	C₂³	—	8	32	no	—
858	C₂³	C₂⁵×C₃₁	1	4	yes	—
859	C₂³	C₂⁵×C₃₁	1	4	yes	—
860	C₂³	C₂⁵×C₃₁	1	8	yes	—
861	C₂³	C₂⁵×C₃₁	1	2	yes	—
862	C₂³	C₂⁵×C₃₁	1	4	yes	—
863	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
864	Q₈	—	2	8	no	—
865	Q₈	—	2	16	no	—
866	Q₈	—	4	8	no	—
867	D₄	—	2	8	no	—
868	D₄	—	2	8	no	—
869	D₄	—	2	16	no	—
870	D₄	—	2	16	no	—
871	D₄	—	2	8	no	—
872	D₄	—	4	16	no	—
873	D₄	—	4	16	no	—
874	D₄	—	4	8	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	16	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	8	no	—
880	D₄	—	4	8	no	—
881	D₄	—	4	16	no	—
882	D₄	—	4	16	no	—
883	D₄	—	4	16	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	4	no	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	2	4	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	4	no	—
894	C₂×C₄	—	2	16	no	—
895	C₂×C₄	—	2	16	no	—
896	C₂×C₄	—	2	8	no	—
897	C₂×C₄	—	2	16	no	—
898	C₂×C₄	—	2	8	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	16	no	—
901	C₂×C₄	—	4	16	no	—
902	C₂×C₄	—	4	16	no	—
903	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
904	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
905	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
906	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
907	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
908	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
909	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
910	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
911	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
912	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
913	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
914	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
915	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
916	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	4	no	—
920	C₂²	—	2	4	no	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	8	no	—
924	C₂²	—	2	8	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	2	8	no	—
930	C₂²	—	2	4	no	—
931	C₂²	—	2	4	no	—
932	C₂²	—	4	8	no	—
933	C₂²	—	4	8	no	—
934	C₂²	—	4	16	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	4	8	no	—
937	C₂²	—	8	32	no	—
938	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
939	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
940	C₂²	C₃₁×#585	1	2	yes	—
941	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	4	no	—
945	C₄	—	2	4	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	8	no	—
948	C₄	—	2	4	no	—
949	C₄	—	2	2	no	—
950	C₄	—	2	2	no	—
951	C₄	—	2	4	no	—
952	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
953	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
954	C₂	—	4	4	no	—
955	C₂	—	4	4	no	—
956	C₂	—	4	8	no	—
957	C₂	—	4	2	no	—
958	C₂	—	4	4	no	—
959	C₂	C₃₁×#3546	1	4	yes	direct product factor
960	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
961	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
962	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	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×#3546	C₂	direct (N × H)
2. C₂×C₃₁×#560	C₂	semidirect
3. C₂×C₃₁×#556	C₂	semidirect
4. C₂×C₃₁×#553	C₂	semidirect
5. C₂×C₃₁×#550	C₂	semidirect
6. C₂×C₃₁×#550	C₂	semidirect
7. C₂×C₃₁×#547	C₂	semidirect
8. C₂×C₃₁×#546	C₂	semidirect
9. C₂×C₃₁×#546	C₂	semidirect
10. C₂×D₄²×C₃₁	C₂	semidirect
11. C₂×C₃₁×#542	C₂	semidirect
12. C₂×C₃₁×#538	C₂	semidirect
13. C₂×C₃₁×#537	C₂	semidirect
14. C₂×C₃₁×#535	C₂	semidirect
15. C₂×C₃₁×#535	C₂	semidirect
16. C₂×C₃₁×#532	C₂	semidirect
17. C₂×C₃₁×#532	C₂	semidirect
18. C₂×C₃₁×#529	C₂	semidirect
19. C₂²×#41×C₃₁	C₂²	semidirect
20. C₂²×#41×C₃₁	C₂²	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
25. C₃₁×#560	C₂²	semidirect
26. C₃₁×#556	C₂²	semidirect
27. C₃₁×#553	C₂²	semidirect
28. C₃₁×#550	C₂²	semidirect
29. C₃₁×#550	C₂²	semidirect
30. C₃₁×#547	C₂²	semidirect
31. C₃₁×#546	C₂²	semidirect
32. C₃₁×#546	C₂²	semidirect
33. D₄²×C₃₁	C₂²	semidirect
34. C₃₁×#542	C₂²	semidirect
35. C₃₁×#538	C₂²	semidirect
36. C₃₁×#537	C₂²	semidirect
37. C₃₁×#535	C₂²	semidirect
38. C₃₁×#535	C₂²	semidirect
39. C₃₁×#532	C₂²	semidirect
40. C₃₁×#532	C₂²	semidirect
41. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
45. C₂×C₃₁×#127	C₂²	semidirect
46. C₂×C₃₁×#127	C₂²	semidirect
47. C₃₁×#529	C₂²	semidirect
48. C₂×C₃₁×#126	C₂²	semidirect
49. C₂×C₃₁×#126	C₂²	semidirect
50. C₂×C₃₁×#126	C₂²	semidirect
51. C₂×C₃₁×#125	C₂²	semidirect
54. C₂×C₃₁×#124	C₂²	semidirect
55. C₂×C₃₁×#124	C₂²	semidirect
56. C₂×C₃₁×#124	C₂²	semidirect
57. C₂×C₃₁×#123	C₂²	semidirect
58. C₂×C₃₁×#123	C₂²	semidirect
59. C₂×C₃₁×#123	C₂²	semidirect
60. C₂×C₃₁×#123	C₂²	semidirect
61. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₃₁×C₂²⋊Q₈	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
74. C₂×C₃₁×#121	C₂²	semidirect
75. C₂×C₃₁×#121	C₂²	semidirect
76. C₂×C₃₁×#121	C₂²	semidirect
77. C₂×C₃₁×#121	C₂²	semidirect
78. C₂×C₃₁×#121	C₂²	semidirect
79. C₂×C₃₁×#121	C₂²	semidirect
80. C₂×C₃₁×#121	C₂²	semidirect
82. C₂×C₃₁×#120	C₂²	semidirect
83. C₂×C₃₁×#120	C₂²	semidirect
84. C₂×C₃₁×#120	C₂²	semidirect
85. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
86. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
89. C₂×C₄×D₄×C₃₁	C₂²	semidirect
90. C₂×C₄×D₄×C₃₁	C₂²	semidirect
91. C₂×C₄×D₄×C₃₁	C₂²	semidirect
92. C₂×C₄×D₄×C₃₁	C₂²	semidirect
93. C₂×C₄×D₄×C₃₁	C₂²	semidirect
94. C₂×C₄×D₄×C₃₁	C₂²	semidirect
95. C₂×C₄×D₄×C₃₁	C₂²	semidirect
96. C₂×C₃₁×#117	C₂²	semidirect
97. C₂×C₃₁×#117	C₂²	semidirect
98. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
99. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
100. C₂²×C₄²×C₃₁	C₂²	semidirect
106. C₂×#41×C₃₁	C₂³	semidirect
107. C₂×#41×C₃₁	C₂³	semidirect
108. C₂×#41×C₃₁	C₂³	semidirect
109. C₂×#41×C₃₁	C₂³	semidirect
143. C₃₁×C₄⋊Q₈	C₂³	semidirect
144. C₃₁×C₄⋊Q₈	C₂³	semidirect
147. C₃₁×#127	C₂³	semidirect
148. C₃₁×#127	C₂³	semidirect
149. C₃₁×#126	C₂³	semidirect
150. C₃₁×#126	C₂³	semidirect
151. C₃₁×#126	C₂³	semidirect
152. C₃₁×#125	C₂³	semidirect
155. C₃₁×#124	C₂³	semidirect
156. C₃₁×#124	C₂³	semidirect
157. C₃₁×#124	C₂³	semidirect
158. C₃₁×#123	C₂³	semidirect
159. C₃₁×#123	C₂³	semidirect
160. C₃₁×#123	C₂³	semidirect
161. C₃₁×#123	C₂³	semidirect
162. C₃₁×C₂²⋊Q₈	C₂³	semidirect
163. C₃₁×C₂²⋊Q₈	C₂³	semidirect
164. C₃₁×C₂²⋊Q₈	C₂³	semidirect
165. C₃₁×C₂²⋊Q₈	C₂³	semidirect
171. C₃₁×#121	C₂³	semidirect
172. C₃₁×#121	C₂³	semidirect
173. C₃₁×#121	C₂³	semidirect
174. C₃₁×#121	C₂³	semidirect
175. C₃₁×#121	C₂³	semidirect
176. C₃₁×#121	C₂³	semidirect
177. C₃₁×#121	C₂³	semidirect
178. C₃₁×#121	C₂³	semidirect
179. C₃₁×#121	C₂³	semidirect
180. C₃₁×#121	C₂³	semidirect
181. C₃₁×#121	C₂³	semidirect
183. C₃₁×#120	C₂³	semidirect
184. C₃₁×#120	C₂³	semidirect
185. C₃₁×#120	C₂³	semidirect
186. C₄×Q₈×C₃₁	C₂³	semidirect
187. C₄×Q₈×C₃₁	C₂³	semidirect
190. C₄×D₄×C₃₁	C₂³	semidirect
191. C₄×D₄×C₃₁	C₂³	semidirect
192. C₄×D₄×C₃₁	C₂³	semidirect
193. C₄×D₄×C₃₁	C₂³	semidirect
194. C₄×D₄×C₃₁	C₂³	semidirect
195. C₄×D₄×C₃₁	C₂³	semidirect
196. C₄×D₄×C₃₁	C₂³	semidirect
197. C₃₁×#117	C₂³	semidirect
198. C₃₁×#117	C₂³	semidirect
212. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
229. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
236. C₂×C₄²×C₃₁	C₂³	semidirect
357. C₂×#3546	C₃₁	direct (N × H)
436. #3546	C₂×C₃₁	direct (N × H)
437. C₂×#560	C₂×C₃₁	semidirect
438. C₂×#556	C₂×C₃₁	semidirect
439. C₂×#553	C₂×C₃₁	semidirect
440. C₂×#550	C₂×C₃₁	semidirect
441. C₂×#550	C₂×C₃₁	semidirect
442. C₂×#547	C₂×C₃₁	semidirect
443. C₂×#546	C₂×C₃₁	semidirect
444. C₂×#546	C₂×C₃₁	semidirect
445. C₂×D₄²	C₂×C₃₁	semidirect
446. C₂×#542	C₂×C₃₁	semidirect
447. C₂×#538	C₂×C₃₁	semidirect
448. C₂×#537	C₂×C₃₁	semidirect
449. C₂×#535	C₂×C₃₁	semidirect
450. C₂×#535	C₂×C₃₁	semidirect
451. C₂×#532	C₂×C₃₁	semidirect
452. C₂×#532	C₂×C₃₁	semidirect
453. C₂×#529	C₂×C₃₁	semidirect
491. C₂²×#41	C₂²×C₃₁	semidirect
492. C₂²×#41	C₂²×C₃₁	semidirect
493. C₂²×#41	C₂²×C₃₁	semidirect
494. C₂²×#41	C₂²×C₃₁	semidirect
497. #560	C₂²×C₃₁	semidirect
498. #556	C₂²×C₃₁	semidirect
499. #553	C₂²×C₃₁	semidirect
500. #550	C₂²×C₃₁	semidirect
501. #550	C₂²×C₃₁	semidirect
502. #547	C₂²×C₃₁	semidirect
503. #546	C₂²×C₃₁	semidirect
504. #546	C₂²×C₃₁	semidirect
505. D₄²	C₂²×C₃₁	semidirect
506. #542	C₂²×C₃₁	semidirect
507. #538	C₂²×C₃₁	semidirect
508. #537	C₂²×C₃₁	semidirect
509. #535	C₂²×C₃₁	semidirect
510. #535	C₂²×C₃₁	semidirect
511. #532	C₂²×C₃₁	semidirect
512. #532	C₂²×C₃₁	semidirect
513. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
514. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
517. C₂×#127	C₂²×C₃₁	semidirect
518. C₂×#127	C₂²×C₃₁	semidirect
519. #529	C₂²×C₃₁	semidirect
520. C₂×#126	C₂²×C₃₁	semidirect
521. C₂×#126	C₂²×C₃₁	semidirect
522. C₂×#126	C₂²×C₃₁	semidirect
523. C₂×#125	C₂²×C₃₁	semidirect
526. C₂×#124	C₂²×C₃₁	semidirect
527. C₂×#124	C₂²×C₃₁	semidirect
528. C₂×#124	C₂²×C₃₁	semidirect
529. C₂×#123	C₂²×C₃₁	semidirect
530. C₂×#123	C₂²×C₃₁	semidirect
531. C₂×#123	C₂²×C₃₁	semidirect
532. C₂×#123	C₂²×C₃₁	semidirect
533. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
534. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
535. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
536. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
542. C₂×#121	C₂²×C₃₁	semidirect
543. C₂×#121	C₂²×C₃₁	semidirect
544. C₂×#121	C₂²×C₃₁	semidirect
545. C₂×#121	C₂²×C₃₁	semidirect
546. C₂×#121	C₂²×C₃₁	semidirect
547. C₂×#121	C₂²×C₃₁	semidirect
548. C₂×#121	C₂²×C₃₁	semidirect
549. C₂×#121	C₂²×C₃₁	semidirect
550. C₂×#121	C₂²×C₃₁	semidirect
551. C₂×#121	C₂²×C₃₁	semidirect
552. C₂×#121	C₂²×C₃₁	semidirect
554. C₂×#120	C₂²×C₃₁	semidirect
555. C₂×#120	C₂²×C₃₁	semidirect
556. C₂×#120	C₂²×C₃₁	semidirect
557. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
558. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
561. C₂×C₄×D₄	C₂²×C₃₁	semidirect
562. C₂×C₄×D₄	C₂²×C₃₁	semidirect
563. C₂×C₄×D₄	C₂²×C₃₁	semidirect
564. C₂×C₄×D₄	C₂²×C₃₁	semidirect
565. C₂×C₄×D₄	C₂²×C₃₁	semidirect
566. C₂×C₄×D₄	C₂²×C₃₁	semidirect
567. C₂×C₄×D₄	C₂²×C₃₁	semidirect
568. C₂×#117	C₂²×C₃₁	semidirect
569. C₂×#117	C₂²×C₃₁	semidirect
570. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
571. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
572. C₂²×C₄²	C₂²×C₃₁	semidirect
578. C₂×C₃₁	#3546	direct (N × H)
587. C₂×#41	C₂³×C₃₁	semidirect
588. C₂×#41	C₂³×C₃₁	semidirect
589. C₂×#41	C₂³×C₃₁	semidirect
590. C₂×#41	C₂³×C₃₁	semidirect
624. C₄⋊Q₈	C₂³×C₃₁	semidirect
625. C₄⋊Q₈	C₂³×C₃₁	semidirect
628. #127	C₂³×C₃₁	semidirect
629. #127	C₂³×C₃₁	semidirect
630. #126	C₂³×C₃₁	semidirect
631. #126	C₂³×C₃₁	semidirect
632. #126	C₂³×C₃₁	semidirect
633. #125	C₂³×C₃₁	semidirect
636. #124	C₂³×C₃₁	semidirect
637. #124	C₂³×C₃₁	semidirect
638. #124	C₂³×C₃₁	semidirect
639. #123	C₂³×C₃₁	semidirect
640. #123	C₂³×C₃₁	semidirect
641. #123	C₂³×C₃₁	semidirect
642. #123	C₂³×C₃₁	semidirect
643. C₂²⋊Q₈	C₂³×C₃₁	semidirect
644. C₂²⋊Q₈	C₂³×C₃₁	semidirect
645. C₂²⋊Q₈	C₂³×C₃₁	semidirect
646. C₂²⋊Q₈	C₂³×C₃₁	semidirect
652. #121	C₂³×C₃₁	semidirect
653. #121	C₂³×C₃₁	semidirect
654. #121	C₂³×C₃₁	semidirect
655. #121	C₂³×C₃₁	semidirect
656. #121	C₂³×C₃₁	semidirect
657. #121	C₂³×C₃₁	semidirect
658. #121	C₂³×C₃₁	semidirect
659. #121	C₂³×C₃₁	semidirect
660. #121	C₂³×C₃₁	semidirect
661. #121	C₂³×C₃₁	semidirect
662. #121	C₂³×C₃₁	semidirect
664. #120	C₂³×C₃₁	semidirect
665. #120	C₂³×C₃₁	semidirect
666. #120	C₂³×C₃₁	semidirect
667. C₄×Q₈	C₂³×C₃₁	semidirect
668. C₄×Q₈	C₂³×C₃₁	semidirect
671. C₄×D₄	C₂³×C₃₁	semidirect
672. C₄×D₄	C₂³×C₃₁	semidirect
673. C₄×D₄	C₂³×C₃₁	semidirect
674. C₄×D₄	C₂³×C₃₁	semidirect
675. C₄×D₄	C₂³×C₃₁	semidirect
676. C₄×D₄	C₂³×C₃₁	semidirect
677. C₄×D₄	C₂³×C₃₁	semidirect
678. #117	C₂³×C₃₁	semidirect
679. #117	C₂³×C₃₁	semidirect
693. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
710. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
717. C₂×C₄²	C₂³×C₃₁	semidirect
718. C₃₁	C₂×#3546	direct (N × H)
959. C₂	C₃₁×#3546	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×#3546	2
C₂×C₃₁×#560	2
C₂×C₃₁×#556	2
C₂×C₃₁×#553	2
C₂×C₃₁×#550	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×D₄²×C₃₁	2
C₂×C₃₁×#542	2
C₂×C₃₁×#538	2
C₂×C₃₁×#537	2
C₂×C₃₁×#535	2
C₂×C₃₁×#532	2
C₂×C₃₁×#529	2
C₂×#3546	31

Subgroups — C2×C31×#3546 #21519506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3546 #21519506