Subgroups — C₃×C₂₅×C₇₃⋊C₃ #30656019

Order 16425.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₇₃⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₂₅×C₇₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₇₃⋊C₃	C₅	1	1	yes	maximal, characteristic
4	C₂₅×C₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₇₃	C₃×C₅	1	1	yes	characteristic
6	C₅×C₇₃⋊C₃	C₃×C₅	1	3	yes	—
7	C₃×C₇₃⋊C₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇₃	C₃²×C₅	1	1	yes	characteristic
9	C₃²×C₂₅	—	73	1	no	maximal, Hall
10	C₃×C₇₃	C₃×C₂₅	1	1	yes	characteristic, complemented
11	C₇₃⋊C₃	C₃×C₂₅	1	3	yes	direct product factor
12	C₃×C₂₅	—	73	3	no	—
13	C₃×C₂₅	C₇₃⋊C₃	1	1	yes	characteristic, direct product factor
14	C₇₃	C₃²×C₂₅	1	1	yes	characteristic, complemented, Sylow
15	C₃²×C₅	—	73	1	no	—
16	C₂₅	C₃×C₇₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅	—	73	3	no	—
18	C₃×C₅	C₅×C₇₃⋊C₃	1	1	yes	characteristic
19	C₃²	—	73	1	no	Sylow
20	C₅	C₃×C₅×C₇₃⋊C₃	1	1	yes	characteristic
21	C₃	—	73	3	no	—
22	C₃	C₂₅×C₇₃⋊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.