Subgroups — #13064008

Order 1404.

44 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
2	C₂²⋊(C₁₃⋊C₉)	C₃	1	3	yes	maximal, complemented
3	#66851	—	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	C₃²×C₁₃	A₄	1	1	yes	characteristic
8	C₁₃⋊C₉	—	4	3	no	—
9	#1094	—	13	1	no	maximal, Hall
10	C₂×C₃×C₁₃	—	3	3	no	—
11	C₂×C₃×C₁₃	—	3	1	no	—
12	C₂²×C₁₃	3₋¹⁺²	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₃	—	3	1	no	—
14	C₃×C₁₃	C₃×A₄	1	1	yes	characteristic
15	C₂²×C₃²	C₁₃⋊C₃	1	1	yes	characteristic
16	C₂²⋊C₉	—	13	3	no	—
17	3₋¹⁺²	—	52	1	no	Sylow
18	C₂×C₁₃	—	3	1	no	—
19	C₂×C₃²	—	3	1	no	—
20	C₁₃	#1094	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₃	—	3	1	no	—
22	C₂²×C₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic
23	C₃²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
24	C₉	—	52	3	no	—
25	C₂×C₃	—	3	3	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂²	#66851	1	1	yes	characteristic, complemented, Sylow
28	C₃	—	3	1	no	—
29	C₃	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic
30	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.