Subgroups — C₃×C₇₉⋊C₈₁ #34063196

Order 19197.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉⋊C₈₁	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₂₇×C₇₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₉×C₇₉	C₉	1	1	yes	characteristic
4	C₂₇×C₇₉	C₉	1	2	yes	—
5	C₂₇×C₇₉	C₃²	1	1	yes	characteristic
6	C₃²×C₇₉	C₂₇	1	1	yes	characteristic
7	C₉×C₇₉	C₂₇	1	2	yes	—
8	C₉×C₇₉	C₃×C₉	1	1	yes	characteristic
9	C₃×C₈₁	—	79	1	no	maximal, Sylow
10	C₃×C₇₉	C₈₁	1	3	yes	complemented
11	C₃×C₇₉	C₃×C₂₇	1	1	yes	characteristic
12	C₃×C₂₇	C₇₉⋊C₃	1	1	yes	characteristic
13	C₈₁	—	79	3	no	—
14	C₇₉	C₃×C₈₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₉	C₇₉⋊C₉	1	1	yes	characteristic
16	C₂₇	C₇₉⋊C₉	1	2	yes	—
17	C₂₇	C₃×C₇₉⋊C₃	1	1	yes	characteristic
18	C₃²	C₇₉⋊C₂₇	1	1	yes	characteristic
19	C₉	C₇₉⋊C₂₇	1	2	yes	—
20	C₉	C₃×C₇₉⋊C₉	1	1	yes	characteristic
21	C₃	C₇₉⋊C₈₁	1	3	yes	direct product factor
22	C₃	C₃×C₇₉⋊C₂₇	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.