Subgroups — C₃₁×C₂²⋊(C₅²⋊C₃) #22604929

Order 9300.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×C₅²⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₅²×C₃₁	—	3	1	no	—
4	C₅²×C₃₁	A₄	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₅×C₃₁	—	3	2	no	—
6	A₄×C₃₁	—	25	1	no	maximal, Hall
7	C₂×C₅×C₃₁	—	3	6	no	—
8	C₂²⋊(C₅²⋊C₃)	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₅×C₃₁	—	3	2	no	—
10	C₂²×C₃₁	C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₅²	C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₃₁	—	100	1	no	Hall
13	C₅²⋊C₃	—	4	1	no	Hall
14	C₂×C₃₁	—	3	1	no	—
15	C₂×C₅²	—	3	1	no	—
16	C₃₁	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
17	C₅²	A₄×C₃₁	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₅	—	3	2	no	—
19	A₄	—	25	1	no	Hall
20	C₂×C₅	—	3	6	no	—
21	C₅	—	3	2	no	—
22	C₂²	C₃₁×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃	—	100	1	no	Sylow
24	C₂	—	3	1	no	—

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