Subgroups — (C₂²⋊D₁₃)⋊C₃ #64596

Order 312.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₃⋊C₃	—	2	1	no	—
6	C₂×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
7	D₁₃⋊C₃	—	2	1	no	—
8	C₂²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
10	Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₁₃⋊C₃	D₄	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₃	—	2	1	no	—
13	C₂×C₁₃	C₂²×C₃	1	1	yes	characteristic
14	D₁₃	—	2	1	no	—
15	C₃×D₄	—	13	1	no	maximal, Hall
16	C₁₃	C₃×D₄	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃	—	13	1	no	—
18	C₂²×C₃	—	13	1	no	—
19	C₃×C₄	—	13	1	no	—
20	D₄	—	13	1	no	Sylow
21	C₂×C₃	—	13	1	no	—
22	C₂×C₃	—	26	1	no	—
23	C₂×C₃	—	26	1	no	—
24	C₂²	—	13	1	no	—
25	C₂²	D₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₄	—	13	1	no	—
27	C₃	—	13	1	no	Sylow
28	C₂	—	2	1	no	—
29	C₂	—	26	1	no	—
30	C₂	C₂×D₁₃⋊C₃	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.