Subgroups — C₂×C₃₁×#3540 #21519487

Order 7936.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3540	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×H(3,𝔽₄)	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#560	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#559	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#556	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#555	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#551	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#548	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#546	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#542	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#542	C₂	1	4	yes	maximal, complemented
12	C₂×C₃₁×#538	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₁×#536	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#525	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃₁×#525	C₂	1	2	yes	maximal, complemented
17	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₃₁	C₂²	1	2	yes	—
19	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₃₁×H(3,𝔽₄)	C₂²	1	32	yes	complemented
23	C₃₁×#560	C₂²	1	32	yes	complemented
24	C₃₁×#559	C₂²	1	32	yes	complemented
25	C₃₁×#556	C₂²	1	32	yes	complemented
26	C₃₁×#555	C₂²	1	32	yes	complemented
27	C₃₁×#551	C₂²	1	32	yes	complemented
28	C₃₁×#548	C₂²	1	32	yes	complemented
29	C₃₁×#546	C₂²	1	32	yes	complemented
30	C₃₁×#542	C₂²	1	32	yes	complemented
31	C₃₁×#542	C₂²	1	64	yes	complemented
32	C₃₁×#538	C₂²	1	64	yes	complemented
33	C₃₁×#536	C₂²	1	16	yes	complemented
34	C₃₁×#535	C₂²	1	16	yes	complemented
35	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×C₃₁×#127	C₂²	1	2	yes	—
38	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
39	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
40	C₂×C₃₁×#126	C₂²	1	4	yes	complemented
41	C₂×C₃₁×#124	C₂²	1	2	yes	—
42	C₂×C₃₁×#124	C₂²	1	4	yes	—
43	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
44	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
45	C₂×C₃₁×#124	C₂²	1	2	yes	complemented
46	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
47	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
48	C₂×C₃₁×#124	C₂²	1	4	yes	complemented
49	C₃₁×#525	C₂²	1	16	yes	complemented
50	C₃₁×#525	C₂²	1	32	yes	complemented
51	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic
52	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
53	C₂×C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
55	C₂×C₃₁×#123	C₂²	1	2	yes	complemented
56	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
57	C₂×C₃₁×#123	C₂²	1	4	yes	complemented
58	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
63	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
64	C₂×C₃₁×#121	C₂²	1	2	yes	—
65	C₂×C₃₁×#121	C₂²	1	2	yes	—
66	C₂×C₃₁×#121	C₂²	1	2	yes	—
67	C₂×C₃₁×#121	C₂²	1	4	yes	—
68	C₂×C₃₁×#121	C₂²	1	2	yes	complemented
69	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
70	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
71	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic
72	C₂×C₃₁×#120	C₂²	1	2	yes	—
73	C₂×C₃₁×#120	C₂²	1	4	yes	—
74	C₂×C₃₁×#120	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₃₁×#120	C₂²	1	4	yes	complemented
76	C₂×C₃₁×#120	C₂²	1	2	yes	complemented
77	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
78	C₂×C₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
82	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
83	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
84	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
85	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₃₁×#117	C₂²	1	2	yes	complemented
87	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₃₁×#117	C₂²	1	4	yes	complemented
90	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
91	C₂⁵×C₃₁	C₂³	1	2	yes	—
92	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
93	C₂×#41×C₃₁	—	4	4	no	—
94	C₂×#41×C₃₁	—	4	8	no	—
95	C₂×#41×C₃₁	C₂³	1	8	yes	—
96	C₂×#41×C₃₁	C₂³	1	16	yes	—
97	C₂²×Q₈×C₃₁	—	4	4	no	—
98	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
99	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
100	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
101	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₃₁	C₂³	1	8	yes	complemented
103	C₂²×D₄×C₃₁	—	4	4	no	—
104	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
105	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
106	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
107	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
108	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
109	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
110	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
112	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
115	C₂²×D₄×C₃₁	C₂³	1	8	yes	complemented
116	C₂³×C₄×C₃₁	—	4	4	no	—
117	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
119	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
122	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
123	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
125	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
126	C₂³×C₄×C₃₁	C₂³	1	8	yes	complemented
127	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
128	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	complemented
129	C₃₁×#127	C₂³	1	16	yes	—
130	C₃₁×#126	C₂³	1	32	yes	complemented
131	C₃₁×#126	C₂³	1	32	yes	complemented
132	C₃₁×#126	C₂³	1	32	yes	complemented
133	C₃₁×#124	C₂³	1	16	yes	—
134	C₃₁×#124	C₂³	1	32	yes	—
135	C₃₁×#124	C₂³	1	16	yes	complemented
136	C₃₁×#124	C₂³	1	32	yes	complemented
137	C₃₁×#124	C₂³	1	16	yes	complemented
138	C₃₁×#124	C₂³	1	32	yes	complemented
139	C₃₁×#124	C₂³	1	32	yes	complemented
140	C₃₁×#124	C₂³	1	32	yes	complemented
141	C₃₁×#123	C₂³	1	8	yes	—
142	C₃₁×#123	C₂³	1	32	yes	complemented
143	C₃₁×#123	C₂³	1	8	yes	complemented
144	C₃₁×#123	C₂³	1	16	yes	complemented
145	C₃₁×#123	C₂³	1	16	yes	complemented
146	C₃₁×#123	C₂³	1	32	yes	complemented
147	C₃₁×#123	C₂³	1	32	yes	complemented
148	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	complemented
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×C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₃₁×#121	C₂³	1	16	yes	—
155	C₃₁×#121	C₂³	1	16	yes	—
156	C₃₁×#121	C₂³	1	16	yes	—
157	C₃₁×#121	C₂³	1	32	yes	—
158	C₃₁×#121	C₂³	1	16	yes	complemented
159	C₃₁×#121	C₂³	1	32	yes	complemented
160	C₃₁×#121	C₂³	1	32	yes	complemented
161	C₃₁×#120	C₂³	1	8	yes	—
162	C₃₁×#120	C₂³	1	16	yes	—
163	C₃₁×#120	C₂³	1	32	yes	—
164	C₃₁×#120	C₂³	1	8	yes	complemented
165	C₃₁×#120	C₂³	1	32	yes	complemented
166	C₃₁×#120	C₂³	1	16	yes	complemented
167	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
168	C₄×Q₈×C₃₁	C₂³	1	32	yes	complemented
169	C₄×D₄×C₃₁	C₂³	1	16	yes	—
170	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
171	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
172	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
173	C₄×D₄×C₃₁	C₂³	1	32	yes	complemented
174	C₄×D₄×C₃₁	C₂³	1	16	yes	complemented
175	C₃₁×#117	C₂³	1	8	yes	complemented
176	C₃₁×#117	C₂³	1	16	yes	complemented
177	C₃₁×#117	C₂³	1	8	yes	complemented
178	C₃₁×#117	C₂³	1	8	yes	complemented
179	C₃₁×#117	C₂³	1	32	yes	complemented
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
190	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
205	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
206	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
207	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₃₁	C₂³	1	32	yes	complemented
209	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
211	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
212	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
213	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
214	C₂⁴×C₃₁	—	4	2	no	—
215	C₂⁴×C₃₁	—	4	4	no	—
216	C₂⁴×C₃₁	—	4	4	no	—
217	C₂⁴×C₃₁	—	4	8	no	—
218	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
221	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
222	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₃₁	C₂⁴	1	8	yes	—
224	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
225	#41×C₃₁	—	4	16	no	—
226	#41×C₃₁	—	4	32	no	—
227	C₂×Q₈×C₃₁	—	2	8	no	—
228	C₂×Q₈×C₃₁	—	4	4	no	—
229	C₂×Q₈×C₃₁	—	4	8	no	—
230	C₂×Q₈×C₃₁	—	4	2	no	—
231	C₂×Q₈×C₃₁	—	4	16	no	—
232	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₃₁	C₂⁴	1	16	yes	—
234	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
235	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
236	C₂×D₄×C₃₁	—	2	8	no	—
237	C₂×D₄×C₃₁	—	4	16	no	—
238	C₂×D₄×C₃₁	—	4	4	no	—
239	C₂×D₄×C₃₁	—	4	4	no	—
240	C₂×D₄×C₃₁	—	4	8	no	—
241	C₂×D₄×C₃₁	—	4	8	no	—
242	C₂×D₄×C₃₁	—	4	8	no	—
243	C₂×D₄×C₃₁	—	4	4	no	—
244	C₂×D₄×C₃₁	—	4	2	no	—
245	C₂×D₄×C₃₁	—	4	2	no	—
246	C₂×D₄×C₃₁	—	4	2	no	—
247	C₂×D₄×C₃₁	—	4	8	no	—
248	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
249	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
250	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
251	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
252	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
253	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
254	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
255	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
256	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
257	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
258	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
259	C₂²×C₄×C₃₁	—	2	8	no	—
260	C₂²×C₄×C₃₁	—	2	4	no	—
261	C₂²×C₄×C₃₁	—	2	4	no	—
262	C₂²×C₄×C₃₁	—	2	4	no	—
263	C₂²×C₄×C₃₁	—	4	16	no	—
264	C₂²×C₄×C₃₁	—	4	2	no	—
265	C₂²×C₄×C₃₁	—	4	4	no	—
266	C₂²×C₄×C₃₁	—	4	8	no	—
267	C₂²×C₄×C₃₁	—	4	4	no	—
268	C₂²×C₄×C₃₁	—	4	8	no	—
269	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
275	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
276	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
283	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
284	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
285	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
286	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
287	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
289	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
290	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
291	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
292	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
293	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
294	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
295	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
296	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
297	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
298	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
299	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
300	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
301	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
302	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
303	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
304	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
305	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
306	C₂²⋊C₄×C₃₁	C₂⁴	1	4	yes	—
307	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
308	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
309	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
310	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
311	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
313	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
315	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
316	C₄²×C₃₁	C₂⁴	1	8	yes	—
317	C₄²×C₃₁	C₂⁴	1	16	yes	—
318	C₄²×C₃₁	C₂⁴	1	8	yes	—
319	C₄²×C₃₁	C₂⁴	1	8	yes	—
320	C₄²×C₃₁	C₂⁴	1	16	yes	—
321	C₂×#3540	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
322	C₂³×C₃₁	—	2	2	no	—
323	C₂³×C₃₁	—	2	4	no	—
324	C₂³×C₃₁	—	2	2	no	—
325	C₂³×C₃₁	—	2	2	no	—
326	C₂³×C₃₁	—	2	8	no	—
327	C₂³×C₃₁	—	2	8	no	—
328	C₂³×C₃₁	—	2	4	no	—
329	C₂³×C₃₁	—	2	4	no	—
330	C₂³×C₃₁	—	2	4	no	—
331	C₂³×C₃₁	—	2	4	no	—
332	C₂³×C₃₁	—	2	8	no	—
333	C₂³×C₃₁	—	2	4	no	—
334	C₂³×C₃₁	—	4	4	no	—
335	C₂³×C₃₁	—	4	8	no	—
336	C₂³×C₃₁	—	4	8	no	—
337	C₂³×C₃₁	—	4	16	no	—
338	C₂³×C₃₁	—	4	16	no	—
339	C₂³×C₃₁	—	8	16	no	—
340	C₂³×C₃₁	C₂⁵	1	2	yes	—
341	C₂³×C₃₁	C₂⁵	1	2	yes	—
342	C₂³×C₃₁	C₂⁵	1	4	yes	—
343	C₂³×C₃₁	C₂⁵	1	8	yes	—
344	C₂³×C₃₁	C₂⁵	1	2	yes	—
345	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
346	Q₈×C₃₁	—	2	16	no	—
347	Q₈×C₃₁	—	4	8	no	—
348	Q₈×C₃₁	—	4	16	no	—
349	Q₈×C₃₁	—	4	4	no	—
350	D₄×C₃₁	—	2	16	no	—
351	D₄×C₃₁	—	4	8	no	—
352	D₄×C₃₁	—	4	8	no	—
353	D₄×C₃₁	—	4	16	no	—
354	D₄×C₃₁	—	4	16	no	—
355	D₄×C₃₁	—	4	16	no	—
356	D₄×C₃₁	—	4	8	no	—
357	D₄×C₃₁	—	4	4	no	—
358	D₄×C₃₁	—	4	4	no	—
359	D₄×C₃₁	—	4	4	no	—
360	D₄×C₃₁	—	4	16	no	—
361	C₂×C₄×C₃₁	—	2	4	no	—
362	C₂×C₄×C₃₁	—	2	2	no	—
363	C₂×C₄×C₃₁	—	2	2	no	—
364	C₂×C₄×C₃₁	—	2	2	no	—
365	C₂×C₄×C₃₁	—	2	8	no	—
366	C₂×C₄×C₃₁	—	2	4	no	—
367	C₂×C₄×C₃₁	—	2	8	no	—
368	C₂×C₄×C₃₁	—	2	8	no	—
369	C₂×C₄×C₃₁	—	2	4	no	—
370	C₂×C₄×C₃₁	—	2	16	no	—
371	C₂×C₄×C₃₁	—	2	8	no	—
372	C₂×C₄×C₃₁	—	2	8	no	—
373	C₂×C₄×C₃₁	—	2	8	no	—
374	C₂×C₄×C₃₁	—	4	4	no	—
375	C₂×C₄×C₃₁	—	4	8	no	—
376	C₂×C₄×C₃₁	—	4	16	no	—
377	C₂×C₄×C₃₁	—	4	8	no	—
378	C₂×C₄×C₃₁	—	4	16	no	—
379	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
380	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
381	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
382	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
383	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
384	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
385	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
386	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
387	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
388	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
389	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
390	#3540	C₂×C₃₁	1	32	yes	direct product factor
391	C₂×H(3,𝔽₄)	C₂×C₃₁	1	2	yes	complemented
392	C₂×#560	C₂×C₃₁	1	2	yes	complemented
393	C₂×#559	C₂×C₃₁	1	2	yes	complemented
394	C₂×#556	C₂×C₃₁	1	2	yes	complemented
395	C₂×#555	C₂×C₃₁	1	2	yes	complemented
396	C₂×#551	C₂×C₃₁	1	2	yes	complemented
397	C₂×#548	C₂×C₃₁	1	2	yes	complemented
398	C₂×#546	C₂×C₃₁	1	2	yes	complemented
399	C₂×#542	C₂×C₃₁	1	2	yes	complemented
400	C₂×#542	C₂×C₃₁	1	4	yes	complemented
401	C₂×#538	C₂×C₃₁	1	4	yes	complemented
402	C₂×#536	C₂×C₃₁	1	1	yes	characteristic, complemented
403	C₂×#535	C₂×C₃₁	1	1	yes	characteristic, complemented
404	C₂×#525	C₂×C₃₁	1	1	yes	characteristic, complemented
405	C₂×#525	C₂×C₃₁	1	2	yes	complemented
406	C₂²×C₃₁	—	2	2	no	—
407	C₂²×C₃₁	—	2	4	no	—
408	C₂²×C₃₁	—	2	2	no	—
409	C₂²×C₃₁	—	2	2	no	—
410	C₂²×C₃₁	—	2	8	no	—
411	C₂²×C₃₁	—	2	8	no	—
412	C₂²×C₃₁	—	2	4	no	—
413	C₂²×C₃₁	—	2	4	no	—
414	C₂²×C₃₁	—	2	4	no	—
415	C₂²×C₃₁	—	2	4	no	—
416	C₂²×C₃₁	—	2	8	no	—
417	C₂²×C₃₁	—	2	4	no	—
418	C₂²×C₃₁	—	4	16	no	—
419	C₂²×C₃₁	—	4	4	no	—
420	C₂²×C₃₁	—	4	8	no	—
421	C₂²×C₃₁	—	4	4	no	—
422	C₂²×C₃₁	—	4	16	no	—
423	C₂²×C₃₁	—	4	4	no	—
424	C₂²×C₃₁	—	8	16	no	—
425	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
426	C₂²×C₃₁	#585	1	4	yes	—
427	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
428	C₄×C₃₁	—	2	4	no	—
429	C₄×C₃₁	—	2	2	no	—
430	C₄×C₃₁	—	2	2	no	—
431	C₄×C₃₁	—	2	2	no	—
432	C₄×C₃₁	—	2	8	no	—
433	C₄×C₃₁	—	2	4	no	—
434	C₄×C₃₁	—	2	8	no	—
435	C₄×C₃₁	—	2	8	no	—
436	C₄×C₃₁	—	2	4	no	—
437	C₄×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
438	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
439	C₂²×#41	C₂²×C₃₁	1	2	yes	—
440	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
441	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
442	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
443	H(3,𝔽₄)	C₂²×C₃₁	1	32	yes	complemented
444	#560	C₂²×C₃₁	1	32	yes	complemented
445	#559	C₂²×C₃₁	1	32	yes	complemented
446	#556	C₂²×C₃₁	1	32	yes	complemented
447	#555	C₂²×C₃₁	1	32	yes	complemented
448	#551	C₂²×C₃₁	1	32	yes	complemented
449	#548	C₂²×C₃₁	1	32	yes	complemented
450	#546	C₂²×C₃₁	1	32	yes	complemented
451	#542	C₂²×C₃₁	1	32	yes	complemented
452	#542	C₂²×C₃₁	1	64	yes	complemented
453	#538	C₂²×C₃₁	1	64	yes	complemented
454	#536	C₂²×C₃₁	1	16	yes	complemented
455	#535	C₂²×C₃₁	1	16	yes	complemented
456	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
457	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
458	C₂×#127	C₂²×C₃₁	1	2	yes	—
459	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
460	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
461	C₂×#126	C₂²×C₃₁	1	4	yes	complemented
462	C₂×#124	C₂²×C₃₁	1	2	yes	—
463	C₂×#124	C₂²×C₃₁	1	4	yes	—
464	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
465	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
466	C₂×#124	C₂²×C₃₁	1	2	yes	complemented
467	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
468	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
469	C₂×#124	C₂²×C₃₁	1	4	yes	complemented
470	#525	C₂²×C₃₁	1	16	yes	complemented
471	#525	C₂²×C₃₁	1	32	yes	complemented
472	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic
473	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
474	C₂×#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
475	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
476	C₂×#123	C₂²×C₃₁	1	2	yes	complemented
477	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
478	C₂×#123	C₂²×C₃₁	1	4	yes	complemented
479	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
480	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
481	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
482	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
483	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
484	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
485	C₂×#121	C₂²×C₃₁	1	2	yes	—
486	C₂×#121	C₂²×C₃₁	1	2	yes	—
487	C₂×#121	C₂²×C₃₁	1	2	yes	—
488	C₂×#121	C₂²×C₃₁	1	4	yes	—
489	C₂×#121	C₂²×C₃₁	1	2	yes	complemented
490	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
491	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
492	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic
493	C₂×#120	C₂²×C₃₁	1	2	yes	—
494	C₂×#120	C₂²×C₃₁	1	4	yes	—
495	C₂×#120	C₂²×C₃₁	1	1	yes	characteristic, complemented
496	C₂×#120	C₂²×C₃₁	1	4	yes	complemented
497	C₂×#120	C₂²×C₃₁	1	2	yes	complemented
498	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
499	C₂×C₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
500	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
501	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
502	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
503	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
504	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
505	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
506	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
507	C₂×#117	C₂²×C₃₁	1	2	yes	complemented
508	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
509	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
510	C₂×#117	C₂²×C₃₁	1	4	yes	complemented
511	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
512	C₂×C₃₁	—	4	2	no	—
513	C₂×C₃₁	—	4	4	no	—
514	C₂×C₃₁	—	4	2	no	—
515	C₂×C₃₁	—	4	8	no	—
516	C₂×C₃₁	—	4	2	no	—
517	C₂×C₃₁	#3540	1	4	yes	direct product factor
518	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₃₁	C₂×#585	1	2	yes	—
520	C₂⁵	C₂³×C₃₁	1	2	yes	—
521	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
522	C₂×#41	—	4	4	no	—
523	C₂×#41	—	4	8	no	—
524	C₂×#41	C₂³×C₃₁	1	8	yes	—
525	C₂×#41	C₂³×C₃₁	1	16	yes	—
526	C₂²×Q₈	—	4	4	no	—
527	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
528	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
529	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
530	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₃₁	1	8	yes	complemented
532	C₂²×D₄	—	4	4	no	—
533	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
534	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
535	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
536	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
537	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
538	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
539	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
540	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
541	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
542	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
544	C₂²×D₄	C₂³×C₃₁	1	8	yes	complemented
545	C₂³×C₄	—	4	4	no	—
546	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
548	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
551	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
552	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
554	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
555	C₂³×C₄	C₂³×C₃₁	1	8	yes	complemented
556	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
557	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
558	#127	C₂³×C₃₁	1	16	yes	—
559	#126	C₂³×C₃₁	1	32	yes	complemented
560	#126	C₂³×C₃₁	1	32	yes	complemented
561	#126	C₂³×C₃₁	1	32	yes	complemented
562	#124	C₂³×C₃₁	1	16	yes	—
563	#124	C₂³×C₃₁	1	32	yes	—
564	#124	C₂³×C₃₁	1	16	yes	complemented
565	#124	C₂³×C₃₁	1	32	yes	complemented
566	#124	C₂³×C₃₁	1	16	yes	complemented
567	#124	C₂³×C₃₁	1	32	yes	complemented
568	#124	C₂³×C₃₁	1	32	yes	complemented
569	#124	C₂³×C₃₁	1	32	yes	complemented
570	#123	C₂³×C₃₁	1	8	yes	—
571	#123	C₂³×C₃₁	1	32	yes	complemented
572	#123	C₂³×C₃₁	1	8	yes	complemented
573	#123	C₂³×C₃₁	1	16	yes	complemented
574	#123	C₂³×C₃₁	1	16	yes	complemented
575	#123	C₂³×C₃₁	1	32	yes	complemented
576	#123	C₂³×C₃₁	1	32	yes	complemented
577	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
578	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
579	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
580	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	complemented
581	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
582	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	complemented
583	#121	C₂³×C₃₁	1	16	yes	—
584	#121	C₂³×C₃₁	1	16	yes	—
585	#121	C₂³×C₃₁	1	16	yes	—
586	#121	C₂³×C₃₁	1	32	yes	—
587	#121	C₂³×C₃₁	1	16	yes	complemented
588	#121	C₂³×C₃₁	1	32	yes	complemented
589	#121	C₂³×C₃₁	1	32	yes	complemented
590	#120	C₂³×C₃₁	1	8	yes	—
591	#120	C₂³×C₃₁	1	16	yes	—
592	#120	C₂³×C₃₁	1	32	yes	—
593	#120	C₂³×C₃₁	1	8	yes	complemented
594	#120	C₂³×C₃₁	1	32	yes	complemented
595	#120	C₂³×C₃₁	1	16	yes	complemented
596	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
597	C₄×Q₈	C₂³×C₃₁	1	32	yes	complemented
598	C₄×D₄	C₂³×C₃₁	1	16	yes	—
599	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
600	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
601	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
602	C₄×D₄	C₂³×C₃₁	1	32	yes	complemented
603	C₄×D₄	C₂³×C₃₁	1	16	yes	complemented
604	#117	C₂³×C₃₁	1	8	yes	complemented
605	#117	C₂³×C₃₁	1	16	yes	complemented
606	#117	C₂³×C₃₁	1	8	yes	complemented
607	#117	C₂³×C₃₁	1	8	yes	complemented
608	#117	C₂³×C₃₁	1	32	yes	complemented
609	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
614	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
616	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
617	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
618	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₃₁	1	32	yes	complemented
638	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
639	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
640	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
641	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
642	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
643	C₃₁	C₂×#3540	1	1	yes	characteristic, direct product factor, Sylow
644	C₂⁴	—	4	2	no	—
645	C₂⁴	—	4	4	no	—
646	C₂⁴	—	4	4	no	—
647	C₂⁴	—	4	8	no	—
648	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
649	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
650	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
651	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
652	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂⁴	C₂⁴×C₃₁	1	8	yes	—
654	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
655	#41	—	4	16	no	—
656	#41	—	4	32	no	—
657	C₂×Q₈	—	2	8	no	—
658	C₂×Q₈	—	4	4	no	—
659	C₂×Q₈	—	4	8	no	—
660	C₂×Q₈	—	4	2	no	—
661	C₂×Q₈	—	4	16	no	—
662	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
663	C₂×Q₈	C₂⁴×C₃₁	1	16	yes	—
664	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
665	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
666	C₂×D₄	—	2	8	no	—
667	C₂×D₄	—	4	16	no	—
668	C₂×D₄	—	4	4	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	8	no	—
671	C₂×D₄	—	4	8	no	—
672	C₂×D₄	—	4	8	no	—
673	C₂×D₄	—	4	4	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	2	no	—
676	C₂×D₄	—	4	2	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
679	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
680	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
681	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
682	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
683	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
684	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
685	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
686	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
687	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
688	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
689	C₂²×C₄	—	2	8	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	16	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	4	8	no	—
697	C₂²×C₄	—	4	4	no	—
698	C₂²×C₄	—	4	8	no	—
699	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
701	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
702	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
705	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
707	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
709	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
711	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
713	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
714	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
715	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
716	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
717	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
718	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
719	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
720	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
721	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
722	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
723	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
724	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
725	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
726	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
727	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
728	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
729	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
730	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
731	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
732	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
733	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
734	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
735	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
736	C₂²⋊C₄	C₂⁴×C₃₁	1	4	yes	—
737	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
738	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
739	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
740	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
741	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
742	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
743	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
744	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
745	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
746	C₄²	C₂⁴×C₃₁	1	8	yes	—
747	C₄²	C₂⁴×C₃₁	1	16	yes	—
748	C₄²	C₂⁴×C₃₁	1	8	yes	—
749	C₄²	C₂⁴×C₃₁	1	8	yes	—
750	C₄²	C₂⁴×C₃₁	1	16	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	8	no	—
756	C₂³	—	2	8	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	2	4	no	—
761	C₂³	—	2	8	no	—
762	C₂³	—	2	4	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	8	no	—
765	C₂³	—	4	8	no	—
766	C₂³	—	4	16	no	—
767	C₂³	—	4	16	no	—
768	C₂³	—	8	16	no	—
769	C₂³	C₂⁵×C₃₁	1	2	yes	—
770	C₂³	C₂⁵×C₃₁	1	2	yes	—
771	C₂³	C₂⁵×C₃₁	1	4	yes	—
772	C₂³	C₂⁵×C₃₁	1	8	yes	—
773	C₂³	C₂⁵×C₃₁	1	2	yes	—
774	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
775	Q₈	—	2	16	no	—
776	Q₈	—	4	8	no	—
777	Q₈	—	4	16	no	—
778	Q₈	—	4	4	no	—
779	D₄	—	2	16	no	—
780	D₄	—	4	8	no	—
781	D₄	—	4	8	no	—
782	D₄	—	4	16	no	—
783	D₄	—	4	16	no	—
784	D₄	—	4	16	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	4	no	—
789	D₄	—	4	16	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	16	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	8	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	16	no	—
806	C₂×C₄	—	4	8	no	—
807	C₂×C₄	—	4	16	no	—
808	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
809	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
810	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
811	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
812	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
813	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
814	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
815	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
816	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
817	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
818	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	8	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	4	16	no	—
832	C₂²	—	4	8	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	16	no	—
836	C₂²	—	4	4	no	—
837	C₂²	—	8	16	no	—
838	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
839	C₂²	C₃₁×#585	1	4	yes	—
840	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	8	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	8	no	—
848	C₄	—	2	8	no	—
849	C₄	—	2	4	no	—
850	C₄	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
851	C₂	—	4	4	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	8	no	—
855	C₂	—	4	2	no	—
856	C₂	C₃₁×#3540	1	4	yes	direct product factor
857	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
858	C₂	C₂×C₃₁×#585	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3540	C₂	direct (N × H)
2. C₂×C₃₁×H(3,𝔽₄)	C₂	semidirect
3. C₂×C₃₁×#560	C₂	semidirect
4. C₂×C₃₁×#559	C₂	semidirect
5. C₂×C₃₁×#556	C₂	semidirect
6. C₂×C₃₁×#555	C₂	semidirect
7. C₂×C₃₁×#551	C₂	semidirect
8. C₂×C₃₁×#548	C₂	semidirect
9. C₂×C₃₁×#546	C₂	semidirect
10. C₂×C₃₁×#542	C₂	semidirect
11. C₂×C₃₁×#542	C₂	semidirect
12. C₂×C₃₁×#538	C₂	semidirect
13. C₂×C₃₁×#536	C₂	semidirect
14. C₂×C₃₁×#535	C₂	semidirect
15. C₂×C₃₁×#525	C₂	semidirect
16. C₂×C₃₁×#525	C₂	semidirect
19. C₂³×Q₈×C₃₁	C₂²	semidirect
20. C₂³×D₄×C₃₁	C₂²	semidirect
21. C₂⁴×C₄×C₃₁	C₂²	semidirect
22. C₃₁×H(3,𝔽₄)	C₂²	semidirect
23. C₃₁×#560	C₂²	semidirect
24. C₃₁×#559	C₂²	semidirect
25. C₃₁×#556	C₂²	semidirect
26. C₃₁×#555	C₂²	semidirect
27. C₃₁×#551	C₂²	semidirect
28. C₃₁×#548	C₂²	semidirect
29. C₃₁×#546	C₂²	semidirect
30. C₃₁×#542	C₂²	semidirect
31. C₃₁×#542	C₂²	semidirect
32. C₃₁×#538	C₂²	semidirect
33. C₃₁×#536	C₂²	semidirect
34. C₃₁×#535	C₂²	semidirect
35. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
36. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
38. C₂×C₃₁×#126	C₂²	semidirect
39. C₂×C₃₁×#126	C₂²	semidirect
40. C₂×C₃₁×#126	C₂²	semidirect
43. C₂×C₃₁×#124	C₂²	semidirect
44. C₂×C₃₁×#124	C₂²	semidirect
45. C₂×C₃₁×#124	C₂²	semidirect
46. C₂×C₃₁×#124	C₂²	semidirect
47. C₂×C₃₁×#124	C₂²	semidirect
48. C₂×C₃₁×#124	C₂²	semidirect
49. C₃₁×#525	C₂²	semidirect
50. C₃₁×#525	C₂²	semidirect
52. C₂×C₃₁×#123	C₂²	semidirect
53. C₂×C₃₁×#123	C₂²	semidirect
54. C₂×C₃₁×#123	C₂²	semidirect
55. C₂×C₃₁×#123	C₂²	semidirect
56. C₂×C₃₁×#123	C₂²	semidirect
57. C₂×C₃₁×#123	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
62. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
68. C₂×C₃₁×#121	C₂²	semidirect
69. C₂×C₃₁×#121	C₂²	semidirect
70. C₂×C₃₁×#121	C₂²	semidirect
74. C₂×C₃₁×#120	C₂²	semidirect
75. C₂×C₃₁×#120	C₂²	semidirect
76. C₂×C₃₁×#120	C₂²	semidirect
77. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
78. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
80. C₂×C₄×D₄×C₃₁	C₂²	semidirect
81. C₂×C₄×D₄×C₃₁	C₂²	semidirect
82. C₂×C₄×D₄×C₃₁	C₂²	semidirect
83. C₂×C₄×D₄×C₃₁	C₂²	semidirect
84. C₂×C₄×D₄×C₃₁	C₂²	semidirect
85. C₂×C₃₁×#117	C₂²	semidirect
86. C₂×C₃₁×#117	C₂²	semidirect
87. C₂×C₃₁×#117	C₂²	semidirect
88. C₂×C₃₁×#117	C₂²	semidirect
89. C₂×C₃₁×#117	C₂²	semidirect
90. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
102. C₂²×Q₈×C₃₁	C₂³	semidirect
115. C₂²×D₄×C₃₁	C₂³	semidirect
126. C₂³×C₄×C₃₁	C₂³	semidirect
127. C₃₁×C₄⋊Q₈	C₂³	semidirect
128. C₃₁×C₄⋊Q₈	C₂³	semidirect
130. C₃₁×#126	C₂³	semidirect
131. C₃₁×#126	C₂³	semidirect
132. C₃₁×#126	C₂³	semidirect
135. C₃₁×#124	C₂³	semidirect
136. C₃₁×#124	C₂³	semidirect
137. C₃₁×#124	C₂³	semidirect
138. C₃₁×#124	C₂³	semidirect
139. C₃₁×#124	C₂³	semidirect
140. C₃₁×#124	C₂³	semidirect
142. C₃₁×#123	C₂³	semidirect
143. C₃₁×#123	C₂³	semidirect
144. C₃₁×#123	C₂³	semidirect
145. C₃₁×#123	C₂³	semidirect
146. C₃₁×#123	C₂³	semidirect
147. C₃₁×#123	C₂³	semidirect
148. C₃₁×C₂²⋊Q₈	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
158. C₃₁×#121	C₂³	semidirect
159. C₃₁×#121	C₂³	semidirect
160. C₃₁×#121	C₂³	semidirect
164. C₃₁×#120	C₂³	semidirect
165. C₃₁×#120	C₂³	semidirect
166. C₃₁×#120	C₂³	semidirect
167. C₄×Q₈×C₃₁	C₂³	semidirect
168. C₄×Q₈×C₃₁	C₂³	semidirect
170. C₄×D₄×C₃₁	C₂³	semidirect
171. C₄×D₄×C₃₁	C₂³	semidirect
172. C₄×D₄×C₃₁	C₂³	semidirect
173. C₄×D₄×C₃₁	C₂³	semidirect
174. C₄×D₄×C₃₁	C₂³	semidirect
175. C₃₁×#117	C₂³	semidirect
176. C₃₁×#117	C₂³	semidirect
177. C₃₁×#117	C₂³	semidirect
178. C₃₁×#117	C₂³	semidirect
179. C₃₁×#117	C₂³	semidirect
208. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
321. C₂×#3540	C₃₁	direct (N × H)
390. #3540	C₂×C₃₁	direct (N × H)
391. C₂×H(3,𝔽₄)	C₂×C₃₁	semidirect
392. C₂×#560	C₂×C₃₁	semidirect
393. C₂×#559	C₂×C₃₁	semidirect
394. C₂×#556	C₂×C₃₁	semidirect
395. C₂×#555	C₂×C₃₁	semidirect
396. C₂×#551	C₂×C₃₁	semidirect
397. C₂×#548	C₂×C₃₁	semidirect
398. C₂×#546	C₂×C₃₁	semidirect
399. C₂×#542	C₂×C₃₁	semidirect
400. C₂×#542	C₂×C₃₁	semidirect
401. C₂×#538	C₂×C₃₁	semidirect
402. C₂×#536	C₂×C₃₁	semidirect
403. C₂×#535	C₂×C₃₁	semidirect
404. C₂×#525	C₂×C₃₁	semidirect
405. C₂×#525	C₂×C₃₁	semidirect
440. C₂³×Q₈	C₂²×C₃₁	semidirect
441. C₂³×D₄	C₂²×C₃₁	semidirect
442. C₂⁴×C₄	C₂²×C₃₁	semidirect
443. H(3,𝔽₄)	C₂²×C₃₁	semidirect
444. #560	C₂²×C₃₁	semidirect
445. #559	C₂²×C₃₁	semidirect
446. #556	C₂²×C₃₁	semidirect
447. #555	C₂²×C₃₁	semidirect
448. #551	C₂²×C₃₁	semidirect
449. #548	C₂²×C₃₁	semidirect
450. #546	C₂²×C₃₁	semidirect
451. #542	C₂²×C₃₁	semidirect
452. #542	C₂²×C₃₁	semidirect
453. #538	C₂²×C₃₁	semidirect
454. #536	C₂²×C₃₁	semidirect
455. #535	C₂²×C₃₁	semidirect
456. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
459. C₂×#126	C₂²×C₃₁	semidirect
460. C₂×#126	C₂²×C₃₁	semidirect
461. C₂×#126	C₂²×C₃₁	semidirect
464. C₂×#124	C₂²×C₃₁	semidirect
465. C₂×#124	C₂²×C₃₁	semidirect
466. C₂×#124	C₂²×C₃₁	semidirect
467. C₂×#124	C₂²×C₃₁	semidirect
468. C₂×#124	C₂²×C₃₁	semidirect
469. C₂×#124	C₂²×C₃₁	semidirect
470. #525	C₂²×C₃₁	semidirect
471. #525	C₂²×C₃₁	semidirect
473. C₂×#123	C₂²×C₃₁	semidirect
474. C₂×#123	C₂²×C₃₁	semidirect
475. C₂×#123	C₂²×C₃₁	semidirect
476. C₂×#123	C₂²×C₃₁	semidirect
477. C₂×#123	C₂²×C₃₁	semidirect
478. C₂×#123	C₂²×C₃₁	semidirect
479. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
480. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
481. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
482. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
483. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
484. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
489. C₂×#121	C₂²×C₃₁	semidirect
490. C₂×#121	C₂²×C₃₁	semidirect
491. C₂×#121	C₂²×C₃₁	semidirect
495. C₂×#120	C₂²×C₃₁	semidirect
496. C₂×#120	C₂²×C₃₁	semidirect
497. C₂×#120	C₂²×C₃₁	semidirect
498. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
499. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
501. C₂×C₄×D₄	C₂²×C₃₁	semidirect
502. C₂×C₄×D₄	C₂²×C₃₁	semidirect
503. C₂×C₄×D₄	C₂²×C₃₁	semidirect
504. C₂×C₄×D₄	C₂²×C₃₁	semidirect
505. C₂×C₄×D₄	C₂²×C₃₁	semidirect
506. C₂×#117	C₂²×C₃₁	semidirect
507. C₂×#117	C₂²×C₃₁	semidirect
508. C₂×#117	C₂²×C₃₁	semidirect
509. C₂×#117	C₂²×C₃₁	semidirect
510. C₂×#117	C₂²×C₃₁	semidirect
511. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
517. C₂×C₃₁	#3540	direct (N × H)
531. C₂²×Q₈	C₂³×C₃₁	semidirect
544. C₂²×D₄	C₂³×C₃₁	semidirect
555. C₂³×C₄	C₂³×C₃₁	semidirect
556. C₄⋊Q₈	C₂³×C₃₁	semidirect
557. C₄⋊Q₈	C₂³×C₃₁	semidirect
559. #126	C₂³×C₃₁	semidirect
560. #126	C₂³×C₃₁	semidirect
561. #126	C₂³×C₃₁	semidirect
564. #124	C₂³×C₃₁	semidirect
565. #124	C₂³×C₃₁	semidirect
566. #124	C₂³×C₃₁	semidirect
567. #124	C₂³×C₃₁	semidirect
568. #124	C₂³×C₃₁	semidirect
569. #124	C₂³×C₃₁	semidirect
571. #123	C₂³×C₃₁	semidirect
572. #123	C₂³×C₃₁	semidirect
573. #123	C₂³×C₃₁	semidirect
574. #123	C₂³×C₃₁	semidirect
575. #123	C₂³×C₃₁	semidirect
576. #123	C₂³×C₃₁	semidirect
577. C₂²⋊Q₈	C₂³×C₃₁	semidirect
578. C₂²⋊Q₈	C₂³×C₃₁	semidirect
579. C₂²⋊Q₈	C₂³×C₃₁	semidirect
580. C₂²⋊Q₈	C₂³×C₃₁	semidirect
581. C₂²⋊Q₈	C₂³×C₃₁	semidirect
582. C₂²⋊Q₈	C₂³×C₃₁	semidirect
587. #121	C₂³×C₃₁	semidirect
588. #121	C₂³×C₃₁	semidirect
589. #121	C₂³×C₃₁	semidirect
593. #120	C₂³×C₃₁	semidirect
594. #120	C₂³×C₃₁	semidirect
595. #120	C₂³×C₃₁	semidirect
596. C₄×Q₈	C₂³×C₃₁	semidirect
597. C₄×Q₈	C₂³×C₃₁	semidirect
599. C₄×D₄	C₂³×C₃₁	semidirect
600. C₄×D₄	C₂³×C₃₁	semidirect
601. C₄×D₄	C₂³×C₃₁	semidirect
602. C₄×D₄	C₂³×C₃₁	semidirect
603. C₄×D₄	C₂³×C₃₁	semidirect
604. #117	C₂³×C₃₁	semidirect
605. #117	C₂³×C₃₁	semidirect
606. #117	C₂³×C₃₁	semidirect
607. #117	C₂³×C₃₁	semidirect
608. #117	C₂³×C₃₁	semidirect
637. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
643. C₃₁	C₂×#3540	direct (N × H)
856. C₂	C₃₁×#3540	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×#3540	2
C₂×C₃₁×H(3,𝔽₄)	2
C₂×C₃₁×#560	2
C₂×C₃₁×#559	2
C₂×C₃₁×#556	2
C₂×C₃₁×#555	2
C₂×C₃₁×#551	2
C₂×C₃₁×#548	2
C₂×C₃₁×#546	2
C₂×C₃₁×#542	2
C₂×C₃₁×#538	2
C₂×C₃₁×#536	2
C₂×C₃₁×#535	2
C₂×C₃₁×#525	2
C₂×#3540	31

Subgroups — C2×C31×#3540 #21519487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3540 #21519487