Subgroups — #21419258

Order 7533.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁⋊C₈₁	C₃	1	3	yes	maximal, complemented
2	C₃×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₃₁	C₉	1	1	yes	characteristic
4	C₂₇×C₃₁	C₉	1	2	yes	—
5	C₂₇×C₃₁	C₃²	1	1	yes	characteristic
6	C₃²×C₃₁	C₂₇	1	1	yes	characteristic
7	C₉×C₃₁	C₂₇	1	2	yes	—
8	C₉×C₃₁	C₃×C₉	1	1	yes	characteristic
9	C₈₁⋊C₃	—	31	1	no	maximal, Sylow
10	C₃×C₃₁	—	3	1	no	—
11	C₃×C₃₁	C₃×C₂₇	1	1	yes	characteristic
12	C₃×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic
13	C₈₁	—	31	3	no	—
14	C₃₁	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₉	C₃₁⋊C₉	1	1	yes	characteristic
16	C₂₇	C₃₁⋊C₉	1	2	yes	—
17	C₂₇	C₃×C₃₁⋊C₃	1	1	yes	characteristic
18	C₃²	C₃₁⋊C₂₇	1	1	yes	characteristic
19	C₉	C₃₁⋊C₂₇	1	2	yes	—
20	C₉	C₃×C₃₁⋊C₉	1	1	yes	characteristic
21	C₃	—	3	1	no	—
22	C₃	C₃×C₃₁⋊C₂₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₃₁⋊C₈₁	C₃	semidirect
14. C₃₁	C₈₁⋊C₃	semidirect