Subgroups — C₃×(C₆₁⋊C₃)⋊D₁₃ #28384459

Order 14274.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₆₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₆₁⋊C₃)⋊D₁₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₇₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
5	C₁₃×C₆₁⋊C₃	C₂×C₃	1	3	yes	complemented
6	D₇₉₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₆₁⋊C₃	—	13	1	no	maximal, Hall
8	C₁₃×C₆₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₆₁⋊C₃	D₁₃	1	1	yes	characteristic, complemented, Hall
10	C₃×D₆₁	—	13	1	no	—
11	D₆₁⋊C₃	—	13	3	no	—
12	C₃²×D₁₃	—	61	1	no	maximal, Hall
13	C₃×C₆₁	C₃×D₁₃	1	1	yes	characteristic, complemented
14	C₆₁⋊C₃	C₃×D₁₃	1	3	yes	complemented
15	D₆₁	—	13	1	no	Hall
16	C₃²×C₁₃	—	61	1	no	Hall
17	C₃×D₁₃	—	61	3	no	—
18	C₃×D₁₃	—	183	1	no	—
19	C₆₁	C₃²×D₁₃	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₁₃	—	61	3	no	—
21	C₃×C₁₃	D₆₁⋊C₃	1	1	yes	characteristic, complemented
22	D₁₃	—	183	1	no	Hall
23	C₂×C₃²	—	793	1	no	Hall
24	C₁₃	C₃×D₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	61	1	no	Sylow
26	C₂×C₃	—	793	3	no	—
27	C₂×C₃	—	2379	1	no	—
28	C₃	—	61	3	no	—
29	C₃	(C₆₁⋊C₃)⋊D₁₃	1	1	yes	characteristic, direct product factor
30	C₂	—	2379	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	(C₆₁⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃×C₆₁	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₆₁	C₂×C₃
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₃

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.