Subgroups — C₂×C₃₁×#3536 #21519482

Order 7936.

7962 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3536	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#562	C₂	1	4	yes	maximal, complemented
3	C₂×C₃₁×#554	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#548	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#547	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#546	C₂	1	4	yes	maximal, complemented
7	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#543	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#539	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#538	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#537	C₂	1	2	yes	maximal, complemented
13	C₂×C₃₁×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₃₁×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	4	yes	complemented
19	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
20	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
23	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#562	C₂²	1	64	yes	complemented
25	C₃₁×#554	C₂²	1	32	yes	complemented
26	C₃₁×#548	C₂²	1	32	yes	complemented
27	C₃₁×#547	C₂²	1	32	yes	complemented
28	C₃₁×#546	C₂²	1	64	yes	complemented
29	C₃₁×#546	C₂²	1	32	yes	complemented
30	C₃₁×#543	C₂²	1	32	yes	complemented
31	C₃₁×#542	C₂²	1	32	yes	complemented
32	C₃₁×#539	C₂²	1	32	yes	complemented
33	C₃₁×#538	C₂²	1	32	yes	complemented
34	C₃₁×#537	C₂²	1	32	yes	complemented
35	C₃₁×#537	C₂²	1	32	yes	complemented
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
38	C₂×C₃₁×#125	C₂²	1	4	yes	complemented
39	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
41	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
42	C₃₁×#525	C₂²	1	16	yes	complemented
43	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
44	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
45	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
46	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
47	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
48	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	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	1	yes	characteristic, complemented
55	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	16	yes	complemented
62	C₂×C₃₁×#121	C₂²	1	2	yes	—
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	1	yes	characteristic
67	C₂×C₃₁×#121	C₂²	1	16	yes	complemented
68	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
70	C₂×C₃₁×#121	C₂²	1	2	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×#121	C₂²	1	4	yes	complemented
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	4	yes	—
80	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
81	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
82	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
83	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
85	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
86	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
87	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
89	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	—
91	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
92	C₂⁵×C₃₁	C₂³	1	2	yes	—
93	C₂×#41×C₃₁	—	4	4	no	—
94	C₂×#41×C₃₁	—	4	16	no	—
95	C₂×#41×C₃₁	—	4	8	no	—
96	C₂×#41×C₃₁	C₂³	1	8	yes	complemented
97	C₂×#41×C₃₁	C₂³	1	32	yes	complemented
98	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
99	C₂²×Q₈×C₃₁	—	4	4	no	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
103	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
104	C₂²×Q₈×C₃₁	C₂³	1	8	yes	complemented
105	C₂²×D₄×C₃₁	—	4	4	no	—
106	C₂²×D₄×C₃₁	—	4	8	no	—
107	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
111	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
113	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
116	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
117	C₂²×D₄×C₃₁	C₂³	1	8	yes	—
118	C₂²×D₄×C₃₁	C₂³	1	16	yes	—
119	C₂³×C₄×C₃₁	—	4	4	no	—
120	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
121	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
127	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
128	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
129	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
130	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
132	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
134	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
135	C₃₁×#126	C₂³	1	32	yes	complemented
136	C₃₁×#125	C₂³	1	32	yes	complemented
137	C₃₁×#124	C₂³	1	32	yes	complemented
138	C₃₁×#124	C₂³	1	16	yes	complemented
139	C₃₁×#124	C₂³	1	32	yes	complemented
140	C₃₁×#123	C₂³	1	16	yes	complemented
141	C₃₁×#123	C₂³	1	32	yes	complemented
142	C₃₁×#123	C₂³	1	32	yes	complemented
143	C₃₁×#123	C₂³	1	32	yes	complemented
144	C₃₁×#123	C₂³	1	32	yes	complemented
145	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
146	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
147	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
148	C₃₁×C₂²⋊Q₈	C₂³	1	32	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	8	yes	complemented
152	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
155	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
156	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	complemented
158	C₃₁×#121	C₂³	1	16	yes	—
159	C₃₁×#121	C₂³	1	16	yes	—
160	C₃₁×#121	C₂³	1	16	yes	—
161	C₃₁×#121	C₂³	1	16	yes	—
162	C₃₁×#121	C₂³	1	8	yes	—
163	C₃₁×#121	C₂³	1	8	yes	complemented
164	C₃₁×#121	C₂³	1	32	yes	complemented
165	C₃₁×#121	C₂³	1	16	yes	complemented
166	C₃₁×#121	C₂³	1	32	yes	complemented
167	C₃₁×#121	C₂³	1	32	yes	complemented
168	C₃₁×#121	C₂³	1	32	yes	complemented
169	C₃₁×#121	C₂³	1	32	yes	complemented
170	C₃₁×#120	C₂³	1	16	yes	—
171	C₃₁×#120	C₂³	1	32	yes	—
172	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
173	C₄×D₄×C₃₁	C₂³	1	16	yes	—
174	C₄×D₄×C₃₁	C₂³	1	32	yes	—
175	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
176	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
177	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
178	C₃₁×#117	C₂³	1	8	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	8	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	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	4	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
195	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
196	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	complemented
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	16	yes	—
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	—
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	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	2	yes	—
211	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
214	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
215	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
216	C₂⁴×C₃₁	—	2	4	no	—
217	C₂⁴×C₃₁	—	2	4	no	—
218	C₂⁴×C₃₁	—	2	8	no	—
219	C₂⁴×C₃₁	—	4	2	no	—
220	C₂⁴×C₃₁	—	4	4	no	—
221	C₂⁴×C₃₁	—	4	4	no	—
222	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
224	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
225	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
226	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
227	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
229	#41×C₃₁	—	4	16	no	—
230	#41×C₃₁	—	4	64	no	—
231	#41×C₃₁	—	4	32	no	—
232	C₂×Q₈×C₃₁	—	2	8	no	—
233	C₂×Q₈×C₃₁	—	4	4	no	—
234	C₂×Q₈×C₃₁	—	4	2	no	—
235	C₂×Q₈×C₃₁	—	4	8	no	—
236	C₂×Q₈×C₃₁	—	4	16	no	—
237	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
238	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
240	C₂×Q₈×C₃₁	C₂⁴	1	16	yes	—
241	C₂×D₄×C₃₁	—	2	16	no	—
242	C₂×D₄×C₃₁	—	2	8	no	—
243	C₂×D₄×C₃₁	—	2	8	no	—
244	C₂×D₄×C₃₁	—	2	8	no	—
245	C₂×D₄×C₃₁	—	4	16	no	—
246	C₂×D₄×C₃₁	—	4	4	no	—
247	C₂×D₄×C₃₁	—	4	8	no	—
248	C₂×D₄×C₃₁	—	4	4	no	—
249	C₂×D₄×C₃₁	—	4	2	no	—
250	C₂×D₄×C₃₁	—	4	8	no	—
251	C₂×D₄×C₃₁	—	4	8	no	—
252	C₂×D₄×C₃₁	—	4	32	no	—
253	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
254	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
255	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
256	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
259	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
260	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
261	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
262	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₃₁	—	2	8	no	—
264	C₂²×C₄×C₃₁	—	2	4	no	—
265	C₂²×C₄×C₃₁	—	2	4	no	—
266	C₂²×C₄×C₃₁	—	2	4	no	—
267	C₂²×C₄×C₃₁	—	2	8	no	—
268	C₂²×C₄×C₃₁	—	4	16	no	—
269	C₂²×C₄×C₃₁	—	4	2	no	—
270	C₂²×C₄×C₃₁	—	4	2	no	—
271	C₂²×C₄×C₃₁	—	4	2	no	—
272	C₂²×C₄×C₃₁	—	4	4	no	—
273	C₂²×C₄×C₃₁	—	4	4	no	—
274	C₂²×C₄×C₃₁	—	4	8	no	—
275	C₂²×C₄×C₃₁	—	4	8	no	—
276	C₂²×C₄×C₃₁	—	4	8	no	—
277	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
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	2	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
293	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
294	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
295	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
296	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
297	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
298	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
299	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
301	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
303	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
305	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
306	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
308	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
311	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
312	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
315	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₃₁	C₂⁴	1	16	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	16	yes	—
321	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
326	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
328	C₄²×C₃₁	C₂⁴	1	8	yes	—
329	C₄²×C₃₁	C₂⁴	1	16	yes	—
330	C₂×#3536	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
331	C₂³×C₃₁	—	2	2	no	—
332	C₂³×C₃₁	—	2	2	no	—
333	C₂³×C₃₁	—	2	2	no	—
334	C₂³×C₃₁	—	2	2	no	—
335	C₂³×C₃₁	—	2	2	no	—
336	C₂³×C₃₁	—	2	4	no	—
337	C₂³×C₃₁	—	2	4	no	—
338	C₂³×C₃₁	—	2	8	no	—
339	C₂³×C₃₁	—	2	8	no	—
340	C₂³×C₃₁	—	2	8	no	—
341	C₂³×C₃₁	—	2	2	no	—
342	C₂³×C₃₁	—	2	4	no	—
343	C₂³×C₃₁	—	2	8	no	—
344	C₂³×C₃₁	—	2	2	no	—
345	C₂³×C₃₁	—	2	8	no	—
346	C₂³×C₃₁	—	2	16	no	—
347	C₂³×C₃₁	—	4	4	no	—
348	C₂³×C₃₁	—	4	8	no	—
349	C₂³×C₃₁	—	4	8	no	—
350	C₂³×C₃₁	—	4	16	no	—
351	C₂³×C₃₁	—	8	16	no	—
352	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
353	C₂³×C₃₁	2₋¹⁺⁴	1	4	yes	—
354	C₂³×C₃₁	C₂⁵	1	2	yes	—
355	C₂³×C₃₁	C₂⁵	1	8	yes	—
356	C₂³×C₃₁	C₂⁵	1	4	yes	—
357	C₂³×C₃₁	C₂⁵	1	2	yes	—
358	C₂³×C₃₁	C₂⁵	1	2	yes	—
359	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
360	Q₈×C₃₁	—	2	16	no	—
361	Q₈×C₃₁	—	4	8	no	—
362	Q₈×C₃₁	—	4	4	no	—
363	Q₈×C₃₁	—	4	16	no	—
364	D₄×C₃₁	—	2	32	no	—
365	D₄×C₃₁	—	2	16	no	—
366	D₄×C₃₁	—	2	16	no	—
367	D₄×C₃₁	—	2	16	no	—
368	D₄×C₃₁	—	4	8	no	—
369	D₄×C₃₁	—	4	16	no	—
370	D₄×C₃₁	—	4	8	no	—
371	D₄×C₃₁	—	4	4	no	—
372	D₄×C₃₁	—	4	16	no	—
373	D₄×C₃₁	—	4	16	no	—
374	C₂×C₄×C₃₁	—	2	2	no	—
375	C₂×C₄×C₃₁	—	2	8	no	—
376	C₂×C₄×C₃₁	—	2	2	no	—
377	C₂×C₄×C₃₁	—	2	4	no	—
378	C₂×C₄×C₃₁	—	2	2	no	—
379	C₂×C₄×C₃₁	—	2	16	no	—
380	C₂×C₄×C₃₁	—	2	8	no	—
381	C₂×C₄×C₃₁	—	2	4	no	—
382	C₂×C₄×C₃₁	—	2	8	no	—
383	C₂×C₄×C₃₁	—	2	4	no	—
384	C₂×C₄×C₃₁	—	2	8	no	—
385	C₂×C₄×C₃₁	—	2	8	no	—
386	C₂×C₄×C₃₁	—	2	8	no	—
387	C₂×C₄×C₃₁	—	2	16	no	—
388	C₂×C₄×C₃₁	—	4	4	no	—
389	C₂×C₄×C₃₁	—	4	4	no	—
390	C₂×C₄×C₃₁	—	4	4	no	—
391	C₂×C₄×C₃₁	—	4	8	no	—
392	C₂×C₄×C₃₁	—	4	8	no	—
393	C₂×C₄×C₃₁	—	4	16	no	—
394	C₂×C₄×C₃₁	—	4	16	no	—
395	C₂×C₄×C₃₁	—	4	16	no	—
396	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
397	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
398	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
399	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
400	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
401	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
402	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
403	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
404	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
405	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
406	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
407	#3536	C₂×C₃₁	1	32	yes	direct product factor
408	C₂×#562	C₂×C₃₁	1	4	yes	complemented
409	C₂×#554	C₂×C₃₁	1	2	yes	complemented
410	C₂×#548	C₂×C₃₁	1	2	yes	complemented
411	C₂×#547	C₂×C₃₁	1	2	yes	complemented
412	C₂×#546	C₂×C₃₁	1	4	yes	complemented
413	C₂×#546	C₂×C₃₁	1	2	yes	complemented
414	C₂×#543	C₂×C₃₁	1	2	yes	complemented
415	C₂×#542	C₂×C₃₁	1	2	yes	complemented
416	C₂×#539	C₂×C₃₁	1	2	yes	complemented
417	C₂×#538	C₂×C₃₁	1	2	yes	complemented
418	C₂×#537	C₂×C₃₁	1	2	yes	complemented
419	C₂×#537	C₂×C₃₁	1	2	yes	complemented
420	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
421	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
422	C₂²×#121	C₂×C₃₁	1	1	yes	characteristic, complemented
423	C₂²×C₃₁	—	2	2	no	—
424	C₂²×C₃₁	—	2	2	no	—
425	C₂²×C₃₁	—	2	2	no	—
426	C₂²×C₃₁	—	2	2	no	—
427	C₂²×C₃₁	—	2	8	no	—
428	C₂²×C₃₁	—	2	8	no	—
429	C₂²×C₃₁	—	2	2	no	—
430	C₂²×C₃₁	—	2	4	no	—
431	C₂²×C₃₁	—	2	4	no	—
432	C₂²×C₃₁	—	2	8	no	—
433	C₂²×C₃₁	—	2	8	no	—
434	C₂²×C₃₁	—	2	2	no	—
435	C₂²×C₃₁	—	2	4	no	—
436	C₂²×C₃₁	—	2	2	no	—
437	C₂²×C₃₁	—	2	8	no	—
438	C₂²×C₃₁	—	4	16	no	—
439	C₂²×C₃₁	—	4	8	no	—
440	C₂²×C₃₁	—	4	4	no	—
441	C₂²×C₃₁	—	4	16	no	—
442	C₂²×C₃₁	—	8	16	no	—
443	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
444	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
445	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
446	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	—
447	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
448	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
449	C₄×C₃₁	—	2	2	no	—
450	C₄×C₃₁	—	2	8	no	—
451	C₄×C₃₁	—	2	2	no	—
452	C₄×C₃₁	—	2	4	no	—
453	C₄×C₃₁	—	2	2	no	—
454	C₄×C₃₁	—	2	8	no	—
455	C₄×C₃₁	—	2	4	no	—
456	C₄×C₃₁	—	2	8	no	—
457	C₄×C₃₁	—	2	4	no	—
458	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
459	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
460	C₂²×#41	C₂²×C₃₁	1	4	yes	complemented
461	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
462	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
463	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
464	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
465	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
466	#562	C₂²×C₃₁	1	64	yes	complemented
467	#554	C₂²×C₃₁	1	32	yes	complemented
468	#548	C₂²×C₃₁	1	32	yes	complemented
469	#547	C₂²×C₃₁	1	32	yes	complemented
470	#546	C₂²×C₃₁	1	64	yes	complemented
471	#546	C₂²×C₃₁	1	32	yes	complemented
472	#543	C₂²×C₃₁	1	32	yes	complemented
473	#542	C₂²×C₃₁	1	32	yes	complemented
474	#539	C₂²×C₃₁	1	32	yes	complemented
475	#538	C₂²×C₃₁	1	32	yes	complemented
476	#537	C₂²×C₃₁	1	32	yes	complemented
477	#537	C₂²×C₃₁	1	32	yes	complemented
478	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
479	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
480	C₂×#125	C₂²×C₃₁	1	4	yes	complemented
481	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
482	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
483	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
484	#525	C₂²×C₃₁	1	16	yes	complemented
485	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
486	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
487	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
488	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
489	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
490	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
491	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	—
492	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
494	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
495	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
496	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
497	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
498	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
499	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
500	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
501	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
502	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
503	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	16	yes	complemented
504	C₂×#121	C₂²×C₃₁	1	2	yes	—
505	C₂×#121	C₂²×C₃₁	1	2	yes	—
506	C₂×#121	C₂²×C₃₁	1	2	yes	—
507	C₂×#121	C₂²×C₃₁	1	2	yes	—
508	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
509	C₂×#121	C₂²×C₃₁	1	16	yes	complemented
510	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic, complemented
511	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
512	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
513	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
514	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
515	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
516	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
517	C₂×#120	C₂²×C₃₁	1	2	yes	—
518	C₂×#120	C₂²×C₃₁	1	4	yes	—
519	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
520	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
521	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
522	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
523	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
524	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
525	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
526	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
527	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
528	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
529	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
530	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
531	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
532	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	—
533	C₂×C₃₁	—	2	4	no	—
534	C₂×C₃₁	—	2	4	no	—
535	C₂×C₃₁	—	4	4	no	—
536	C₂×C₃₁	—	4	2	no	—
537	C₂×C₃₁	—	4	8	no	—
538	C₂×C₃₁	#3536	1	4	yes	direct product factor
539	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
542	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
543	C₂⁵	C₂³×C₃₁	1	2	yes	—
544	C₂×#41	—	4	4	no	—
545	C₂×#41	—	4	16	no	—
546	C₂×#41	—	4	8	no	—
547	C₂×#41	C₂³×C₃₁	1	8	yes	complemented
548	C₂×#41	C₂³×C₃₁	1	32	yes	complemented
549	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
550	C₂²×Q₈	—	4	4	no	—
551	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
552	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
553	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
554	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
555	C₂²×Q₈	C₂³×C₃₁	1	8	yes	complemented
556	C₂²×D₄	—	4	4	no	—
557	C₂²×D₄	—	4	8	no	—
558	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
559	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
560	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
561	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
562	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
563	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
564	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
565	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
566	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
567	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₃₁	1	8	yes	—
569	C₂²×D₄	C₂³×C₃₁	1	16	yes	—
570	C₂³×C₄	—	4	4	no	—
571	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
572	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
574	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
575	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
578	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
579	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
580	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
581	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
583	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
585	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
586	#126	C₂³×C₃₁	1	32	yes	complemented
587	#125	C₂³×C₃₁	1	32	yes	complemented
588	#124	C₂³×C₃₁	1	32	yes	complemented
589	#124	C₂³×C₃₁	1	16	yes	complemented
590	#124	C₂³×C₃₁	1	32	yes	complemented
591	#123	C₂³×C₃₁	1	16	yes	complemented
592	#123	C₂³×C₃₁	1	32	yes	complemented
593	#123	C₂³×C₃₁	1	32	yes	complemented
594	#123	C₂³×C₃₁	1	32	yes	complemented
595	#123	C₂³×C₃₁	1	32	yes	complemented
596	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
597	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
598	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
599	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
600	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
601	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
602	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
603	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
604	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
605	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
606	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
607	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
608	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
609	#121	C₂³×C₃₁	1	16	yes	—
610	#121	C₂³×C₃₁	1	16	yes	—
611	#121	C₂³×C₃₁	1	16	yes	—
612	#121	C₂³×C₃₁	1	16	yes	—
613	#121	C₂³×C₃₁	1	8	yes	—
614	#121	C₂³×C₃₁	1	8	yes	complemented
615	#121	C₂³×C₃₁	1	32	yes	complemented
616	#121	C₂³×C₃₁	1	16	yes	complemented
617	#121	C₂³×C₃₁	1	32	yes	complemented
618	#121	C₂³×C₃₁	1	32	yes	complemented
619	#121	C₂³×C₃₁	1	32	yes	complemented
620	#121	C₂³×C₃₁	1	32	yes	complemented
621	#120	C₂³×C₃₁	1	16	yes	—
622	#120	C₂³×C₃₁	1	32	yes	—
623	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
624	C₄×D₄	C₂³×C₃₁	1	16	yes	—
625	C₄×D₄	C₂³×C₃₁	1	32	yes	—
626	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
627	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
628	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
629	#117	C₂³×C₃₁	1	8	yes	complemented
630	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
633	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
635	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
636	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
637	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
642	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
643	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
645	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
646	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
647	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	complemented
648	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₃₁	1	16	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
665	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
666	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
667	C₃₁	C₂×#3536	1	1	yes	characteristic, direct product factor, Sylow
668	C₂⁴	—	2	4	no	—
669	C₂⁴	—	2	4	no	—
670	C₂⁴	—	2	8	no	—
671	C₂⁴	—	4	2	no	—
672	C₂⁴	—	4	4	no	—
673	C₂⁴	—	4	4	no	—
674	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
675	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
676	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
677	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
678	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
679	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
680	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
681	#41	—	4	16	no	—
682	#41	—	4	64	no	—
683	#41	—	4	32	no	—
684	C₂×Q₈	—	2	8	no	—
685	C₂×Q₈	—	4	4	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	8	no	—
688	C₂×Q₈	—	4	16	no	—
689	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
690	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
691	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
692	C₂×Q₈	C₂⁴×C₃₁	1	16	yes	—
693	C₂×D₄	—	2	16	no	—
694	C₂×D₄	—	2	8	no	—
695	C₂×D₄	—	2	8	no	—
696	C₂×D₄	—	2	8	no	—
697	C₂×D₄	—	4	16	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	8	no	—
700	C₂×D₄	—	4	4	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	8	no	—
703	C₂×D₄	—	4	8	no	—
704	C₂×D₄	—	4	32	no	—
705	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
706	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
707	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
708	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
709	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
710	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
711	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
712	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
713	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
714	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
715	C₂²×C₄	—	2	8	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	4	16	no	—
721	C₂²×C₄	—	4	2	no	—
722	C₂²×C₄	—	4	2	no	—
723	C₂²×C₄	—	4	2	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	—	4	8	no	—
727	C₂²×C₄	—	4	8	no	—
728	C₂²×C₄	—	4	8	no	—
729	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
733	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
736	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
739	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
740	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
741	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
742	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
743	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
745	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
746	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
747	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
748	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
749	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
750	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
753	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
754	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
755	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
756	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
757	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
758	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
759	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
760	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
761	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
762	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
763	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
764	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
765	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
766	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
767	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
768	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
769	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
770	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
771	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
772	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
773	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
774	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
775	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
776	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
777	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
778	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
779	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
780	C₄²	C₂⁴×C₃₁	1	8	yes	—
781	C₄²	C₂⁴×C₃₁	1	16	yes	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	4	no	—
788	C₂³	—	2	4	no	—
789	C₂³	—	2	8	no	—
790	C₂³	—	2	8	no	—
791	C₂³	—	2	8	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	4	no	—
794	C₂³	—	2	8	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	8	no	—
797	C₂³	—	2	16	no	—
798	C₂³	—	4	4	no	—
799	C₂³	—	4	8	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	16	no	—
802	C₂³	—	8	16	no	—
803	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
804	C₂³	C₃₁×2₋¹⁺⁴	1	4	yes	—
805	C₂³	C₂⁵×C₃₁	1	2	yes	—
806	C₂³	C₂⁵×C₃₁	1	8	yes	—
807	C₂³	C₂⁵×C₃₁	1	4	yes	—
808	C₂³	C₂⁵×C₃₁	1	2	yes	—
809	C₂³	C₂⁵×C₃₁	1	2	yes	—
810	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
811	Q₈	—	2	16	no	—
812	Q₈	—	4	8	no	—
813	Q₈	—	4	4	no	—
814	Q₈	—	4	16	no	—
815	D₄	—	2	32	no	—
816	D₄	—	2	16	no	—
817	D₄	—	2	16	no	—
818	D₄	—	2	16	no	—
819	D₄	—	4	8	no	—
820	D₄	—	4	16	no	—
821	D₄	—	4	8	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	16	no	—
824	D₄	—	4	16	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	8	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	16	no	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	8	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	16	no	—
839	C₂×C₄	—	4	4	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	8	no	—
843	C₂×C₄	—	4	8	no	—
844	C₂×C₄	—	4	16	no	—
845	C₂×C₄	—	4	16	no	—
846	C₂×C₄	—	4	16	no	—
847	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
848	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
849	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
850	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
851	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
852	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
853	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
854	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
855	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
856	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
857	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	8	no	—
863	C₂²	—	2	8	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	8	no	—
868	C₂²	—	2	8	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	2	no	—
872	C₂²	—	2	8	no	—
873	C₂²	—	4	16	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	16	no	—
876	C₂²	—	4	8	no	—
877	C₂²	—	8	16	no	—
878	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
879	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
880	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
881	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	—
882	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
883	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	8	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	4	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	8	no	—
890	C₄	—	2	4	no	—
891	C₄	—	2	8	no	—
892	C₄	—	2	4	no	—
893	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
894	C₂	—	2	4	no	—
895	C₂	—	2	4	no	—
896	C₂	—	4	2	no	—
897	C₂	—	4	8	no	—
898	C₂	—	4	4	no	—
899	C₂	C₃₁×#3536	1	4	yes	direct product factor
900	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
901	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂	C₂²×C₃₁×2₋¹⁺⁴	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×#3536	C₂	direct (N × H)
2. C₂×C₃₁×#562	C₂	semidirect
3. C₂×C₃₁×#554	C₂	semidirect
4. C₂×C₃₁×#548	C₂	semidirect
5. C₂×C₃₁×#547	C₂	semidirect
6. C₂×C₃₁×#546	C₂	semidirect
7. C₂×C₃₁×#546	C₂	semidirect
8. C₂×C₃₁×#543	C₂	semidirect
9. C₂×C₃₁×#542	C₂	semidirect
10. C₂×C₃₁×#539	C₂	semidirect
11. C₂×C₃₁×#538	C₂	semidirect
12. C₂×C₃₁×#537	C₂	semidirect
13. C₂×C₃₁×#537	C₂	semidirect
14. C₂×C₃₁×#525	C₂	semidirect
15. C₂²×C₃₁×C₂²⋊Q₈	C₂	semidirect
16. C₂²×C₃₁×#121	C₂	semidirect
17. C₂²×#41×C₃₁	C₂²	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
19. C₂²×#41×C₃₁	C₂²	semidirect
20. C₂³×Q₈×C₃₁	C₂²	semidirect
24. C₃₁×#562	C₂²	semidirect
25. C₃₁×#554	C₂²	semidirect
26. C₃₁×#548	C₂²	semidirect
27. C₃₁×#547	C₂²	semidirect
28. C₃₁×#546	C₂²	semidirect
29. C₃₁×#546	C₂²	semidirect
30. C₃₁×#543	C₂²	semidirect
31. C₃₁×#542	C₂²	semidirect
32. C₃₁×#539	C₂²	semidirect
33. C₃₁×#538	C₂²	semidirect
34. C₃₁×#537	C₂²	semidirect
35. C₃₁×#537	C₂²	semidirect
36. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
37. C₂×C₃₁×#126	C₂²	semidirect
38. C₂×C₃₁×#125	C₂²	semidirect
39. C₂×C₃₁×#124	C₂²	semidirect
40. C₂×C₃₁×#124	C₂²	semidirect
41. C₂×C₃₁×#124	C₂²	semidirect
42. C₃₁×#525	C₂²	semidirect
43. C₂×C₃₁×#123	C₂²	semidirect
44. C₂×C₃₁×#123	C₂²	semidirect
45. C₂×C₃₁×#123	C₂²	semidirect
46. C₂×C₃₁×#123	C₂²	semidirect
47. 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
56. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
57. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
67. C₂×C₃₁×#121	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
74. 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×C₃₁×#117	C₂²	semidirect
85. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
86. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
87. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
96. C₂×#41×C₃₁	C₂³	semidirect
97. C₂×#41×C₃₁	C₂³	semidirect
98. C₂×#41×C₃₁	C₂³	semidirect
104. C₂²×Q₈×C₃₁	C₂³	semidirect
134. C₃₁×C₄⋊Q₈	C₂³	semidirect
135. C₃₁×#126	C₂³	semidirect
136. C₃₁×#125	C₂³	semidirect
137. C₃₁×#124	C₂³	semidirect
138. C₃₁×#124	C₂³	semidirect
139. C₃₁×#124	C₂³	semidirect
140. C₃₁×#123	C₂³	semidirect
141. C₃₁×#123	C₂³	semidirect
142. C₃₁×#123	C₂³	semidirect
143. C₃₁×#123	C₂³	semidirect
144. 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
153. C₃₁×C₂²⋊Q₈	C₂³	semidirect
154. C₃₁×C₂²⋊Q₈	C₂³	semidirect
155. C₃₁×C₂²⋊Q₈	C₂³	semidirect
156. C₃₁×C₂²⋊Q₈	C₂³	semidirect
157. C₃₁×C₂²⋊Q₈	C₂³	semidirect
163. C₃₁×#121	C₂³	semidirect
164. C₃₁×#121	C₂³	semidirect
165. C₃₁×#121	C₂³	semidirect
166. C₃₁×#121	C₂³	semidirect
167. C₃₁×#121	C₂³	semidirect
168. C₃₁×#121	C₂³	semidirect
169. C₃₁×#121	C₂³	semidirect
172. C₄×Q₈×C₃₁	C₂³	semidirect
175. C₄×D₄×C₃₁	C₂³	semidirect
176. C₄×D₄×C₃₁	C₂³	semidirect
177. C₄×D₄×C₃₁	C₂³	semidirect
178. C₃₁×#117	C₂³	semidirect
194. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
195. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
196. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
330. C₂×#3536	C₃₁	direct (N × H)
407. #3536	C₂×C₃₁	direct (N × H)
408. C₂×#562	C₂×C₃₁	semidirect
409. C₂×#554	C₂×C₃₁	semidirect
410. C₂×#548	C₂×C₃₁	semidirect
411. C₂×#547	C₂×C₃₁	semidirect
412. C₂×#546	C₂×C₃₁	semidirect
413. C₂×#546	C₂×C₃₁	semidirect
414. C₂×#543	C₂×C₃₁	semidirect
415. C₂×#542	C₂×C₃₁	semidirect
416. C₂×#539	C₂×C₃₁	semidirect
417. C₂×#538	C₂×C₃₁	semidirect
418. C₂×#537	C₂×C₃₁	semidirect
419. C₂×#537	C₂×C₃₁	semidirect
420. C₂×#525	C₂×C₃₁	semidirect
421. C₂²×C₂²⋊Q₈	C₂×C₃₁	semidirect
422. C₂²×#121	C₂×C₃₁	semidirect
459. C₂²×#41	C₂²×C₃₁	semidirect
460. C₂²×#41	C₂²×C₃₁	semidirect
461. C₂²×#41	C₂²×C₃₁	semidirect
462. C₂³×Q₈	C₂²×C₃₁	semidirect
466. #562	C₂²×C₃₁	semidirect
467. #554	C₂²×C₃₁	semidirect
468. #548	C₂²×C₃₁	semidirect
469. #547	C₂²×C₃₁	semidirect
470. #546	C₂²×C₃₁	semidirect
471. #546	C₂²×C₃₁	semidirect
472. #543	C₂²×C₃₁	semidirect
473. #542	C₂²×C₃₁	semidirect
474. #539	C₂²×C₃₁	semidirect
475. #538	C₂²×C₃₁	semidirect
476. #537	C₂²×C₃₁	semidirect
477. #537	C₂²×C₃₁	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
479. C₂×#126	C₂²×C₃₁	semidirect
480. C₂×#125	C₂²×C₃₁	semidirect
481. C₂×#124	C₂²×C₃₁	semidirect
482. C₂×#124	C₂²×C₃₁	semidirect
483. C₂×#124	C₂²×C₃₁	semidirect
484. #525	C₂²×C₃₁	semidirect
485. C₂×#123	C₂²×C₃₁	semidirect
486. C₂×#123	C₂²×C₃₁	semidirect
487. C₂×#123	C₂²×C₃₁	semidirect
488. C₂×#123	C₂²×C₃₁	semidirect
489. C₂×#123	C₂²×C₃₁	semidirect
494. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
495. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
496. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
497. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
498. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
499. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
500. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
501. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
502. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
503. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
509. C₂×#121	C₂²×C₃₁	semidirect
510. C₂×#121	C₂²×C₃₁	semidirect
511. C₂×#121	C₂²×C₃₁	semidirect
512. C₂×#121	C₂²×C₃₁	semidirect
513. C₂×#121	C₂²×C₃₁	semidirect
514. C₂×#121	C₂²×C₃₁	semidirect
515. C₂×#121	C₂²×C₃₁	semidirect
516. C₂×#121	C₂²×C₃₁	semidirect
519. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
522. C₂×C₄×D₄	C₂²×C₃₁	semidirect
523. C₂×C₄×D₄	C₂²×C₃₁	semidirect
524. C₂×C₄×D₄	C₂²×C₃₁	semidirect
525. C₂×#117	C₂²×C₃₁	semidirect
527. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
528. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
529. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
538. C₂×C₃₁	#3536	direct (N × H)
547. C₂×#41	C₂³×C₃₁	semidirect
548. C₂×#41	C₂³×C₃₁	semidirect
549. C₂×#41	C₂³×C₃₁	semidirect
555. C₂²×Q₈	C₂³×C₃₁	semidirect
585. C₄⋊Q₈	C₂³×C₃₁	semidirect
586. #126	C₂³×C₃₁	semidirect
587. #125	C₂³×C₃₁	semidirect
588. #124	C₂³×C₃₁	semidirect
589. #124	C₂³×C₃₁	semidirect
590. #124	C₂³×C₃₁	semidirect
591. #123	C₂³×C₃₁	semidirect
592. #123	C₂³×C₃₁	semidirect
593. #123	C₂³×C₃₁	semidirect
594. #123	C₂³×C₃₁	semidirect
595. #123	C₂³×C₃₁	semidirect
600. C₂²⋊Q₈	C₂³×C₃₁	semidirect
601. C₂²⋊Q₈	C₂³×C₃₁	semidirect
602. C₂²⋊Q₈	C₂³×C₃₁	semidirect
603. C₂²⋊Q₈	C₂³×C₃₁	semidirect
604. C₂²⋊Q₈	C₂³×C₃₁	semidirect
605. C₂²⋊Q₈	C₂³×C₃₁	semidirect
606. C₂²⋊Q₈	C₂³×C₃₁	semidirect
607. C₂²⋊Q₈	C₂³×C₃₁	semidirect
608. C₂²⋊Q₈	C₂³×C₃₁	semidirect
614. #121	C₂³×C₃₁	semidirect
615. #121	C₂³×C₃₁	semidirect
616. #121	C₂³×C₃₁	semidirect
617. #121	C₂³×C₃₁	semidirect
618. #121	C₂³×C₃₁	semidirect
619. #121	C₂³×C₃₁	semidirect
620. #121	C₂³×C₃₁	semidirect
623. C₄×Q₈	C₂³×C₃₁	semidirect
626. C₄×D₄	C₂³×C₃₁	semidirect
627. C₄×D₄	C₂³×C₃₁	semidirect
628. C₄×D₄	C₂³×C₃₁	semidirect
629. #117	C₂³×C₃₁	semidirect
645. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
646. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
647. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
667. C₃₁	C₂×#3536	direct (N × H)
899. C₂	C₃₁×#3536	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×#3536	2
C₂×C₃₁×#562	2
C₂×C₃₁×#554	2
C₂×C₃₁×#548	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×C₃₁×#543	2
C₂×C₃₁×#542	2
C₂×C₃₁×#539	2
C₂×C₃₁×#538	2
C₂×C₃₁×#537	2
C₂×C₃₁×#525	2
C₂²×C₃₁×C₂²⋊Q₈	2
C₂²×C₃₁×#121	2
C₂×#3536	31

Subgroups — C2×C31×#3536 #21519482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3536 #21519482