Subgroups — C₂×C₃×C₇₁⋊C₂₅ #24922425

Order 10650.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇₁⋊C₂₅	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₅×C₇₁	C₅	1	1	yes	maximal, characteristic
4	C₇₁⋊C₂₅	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₅×C₇₁	C₂×C₅	1	1	yes	characteristic
6	C₂×C₅×C₇₁	C₃×C₅	1	1	yes	characteristic
7	C₂×C₃×C₇₁	C₂₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic
9	C₃×C₇₁	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₂₅	—	71	1	no	maximal, Hall
11	C₂×C₇₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₂₅	—	71	1	no	Hall
13	C₇₁	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₂₅	—	71	1	no	Hall
15	C₂×C₃×C₅	C₇₁⋊C₅	1	1	yes	characteristic
16	C₂₅	—	71	1	no	Sylow
17	C₃×C₅	C₂×C₇₁⋊C₅	1	1	yes	characteristic
18	C₂×C₅	C₃×C₇₁⋊C₅	1	1	yes	characteristic
19	C₂×C₃	C₇₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Hall
20	C₅	C₂×C₃×C₇₁⋊C₅	1	1	yes	characteristic
21	C₃	C₂×C₇₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×C₇₁⋊C₂₅	1	1	yes	characteristic, direct product factor, Sylow

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