Subgroups — C₃×Dic₃×C₁₃ #90849

Order 468.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₃	—	3	1	no	maximal
3	Dic₃×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃	—	2	1	no	—
6	C₂×C₃×C₁₃	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₄×C₁₃	—	3	1	no	Hall
9	C₃×C₁₃	—	2	1	no	—
10	C₃×C₁₃	Dic₃	1	1	yes	characteristic, direct product factor
11	C₃×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×Dic₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃²	C₂×C₁₃	1	1	yes	characteristic
15	C₁₃	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₃×C₄	—	3	1	no	—
17	Dic₃	C₃×C₁₃	1	1	yes	characteristic, direct product factor
18	C₃²	C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	2	1	no	—
20	C₂×C₃	D₃×C₁₃	1	1	yes	characteristic
21	C₂×C₃	C₂×C₃×C₁₃	1	1	yes	characteristic
22	C₄	—	3	1	no	Sylow
23	C₃	—	2	1	no	—
24	C₃	Dic₃×C₁₃	1	1	yes	characteristic, direct product factor
25	C₃	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented
26	C₂	C₃×D₃×C₁₃	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.