Subgroups — C₃×C₂₅×C₁₆₃⋊C₃ #49144164

Order 36675.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₁₆₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₂₅×C₁₆₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₆₃⋊C₃	C₅	1	1	yes	maximal, characteristic
4	C₂₅×C₁₆₃	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₆₃	C₃×C₅	1	1	yes	characteristic
6	C₅×C₁₆₃⋊C₃	C₃×C₅	1	3	yes	—
7	C₃×C₁₆₃⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₁₆₃	C₃²×C₅	1	1	yes	characteristic
9	C₃×C₁₆₃	C₃×C₂₅	1	1	yes	characteristic, complemented
10	C₁₆₃⋊C₃	C₃×C₂₅	1	3	yes	direct product factor
11	C₃²×C₂₅	—	163	1	no	maximal, Hall
12	C₁₆₃	C₃²×C₂₅	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₂₅	—	163	3	no	—
14	C₃×C₂₅	C₁₆₃⋊C₃	1	1	yes	characteristic, direct product factor
15	C₃²×C₅	—	163	1	no	—
16	C₂₅	C₃×C₁₆₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	—	163	3	no	—
18	C₃×C₅	C₅×C₁₆₃⋊C₃	1	1	yes	characteristic
19	C₃²	—	163	1	no	Sylow
20	C₅	C₃×C₅×C₁₆₃⋊C₃	1	1	yes	characteristic
21	C₃	—	163	3	no	—
22	C₃	C₂₅×C₁₆₃⋊C₃	1	1	yes	characteristic, direct product factor

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.