Subgroups — C₃²⋊(C₂²⋊(C₁₃⋊C₃)) #13064009

Order 1404.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂²⋊(C₁₃⋊C₃)	C₃	1	3	yes	maximal, complemented
3	C₃²⋊(C₁₃⋊C₃)	—	4	1	no	maximal, Hall
4	C₂×C₃²×C₁₃	—	3	1	no	—
5	C₂²×C₃×C₁₃	—	3	1	no	—
6	C₂²×C₃×C₁₃	C₃²	1	1	yes	characteristic
7	C₂²⋊(C₁₃⋊C₃)	—	3	3	no	—
8	C₃²×C₁₃	A₄	1	1	yes	characteristic, complemented
9	C₃×C₁₃⋊C₃	—	4	3	no	—
10	C₂²⋊H(3,𝔽₃)	—	13	1	no	maximal, Hall
11	C₂×C₃×C₁₃	—	3	3	no	—
12	C₂×C₃×C₁₃	—	3	1	no	—
13	C₂²×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₃	—	3	1	no	—
15	C₃×C₁₃	C₃×A₄	1	1	yes	characteristic
16	C₁₃⋊C₃	—	12	3	no	—
17	C₂²×C₃²	C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₃×A₄	—	13	3	no	—
19	H(3,𝔽₃)	—	52	1	no	Sylow
20	C₂×C₁₃	—	3	1	no	—
21	C₂×C₃²	—	3	1	no	—
22	C₁₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₃	—	3	1	no	—
24	C₂²×C₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic
25	A₄	—	39	3	no	—
26	C₃²	—	52	3	no	—
27	C₃²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented
28	C₂×C₃	—	3	3	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂²	C₃²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
31	C₃	—	3	1	no	—
32	C₃	—	156	3	no	—
33	C₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
34	C₂	—	3	1	no	—

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.