Subgroups — C₃×C₁₉₃⋊C₂₇ #30627645

Order 15633.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉₃⋊C₂₇	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₉×C₁₉₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₁₉₃	C₉	1	1	yes	characteristic
4	C₉×C₁₉₃	C₉	1	2	yes	—
5	C₉×C₁₉₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₉₃	C₂₇	1	3	yes	complemented
7	C₃×C₁₉₃	C₃×C₉	1	1	yes	characteristic
8	C₁₉₃	C₃×C₂₇	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₂₇	—	193	1	no	maximal, Sylow
10	C₃×C₉	C₁₉₃⋊C₃	1	1	yes	characteristic
11	C₂₇	—	193	3	no	—
12	C₃²	C₁₉₃⋊C₉	1	1	yes	characteristic
13	C₉	C₁₉₃⋊C₉	1	2	yes	—
14	C₉	C₃×C₁₉₃⋊C₃	1	1	yes	characteristic
15	C₃	C₁₉₃⋊C₂₇	1	3	yes	direct product factor
16	C₃	C₃×C₁₉₃⋊C₉	1	1	yes	characteristic

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.