Subgroups — C₂²×C₁₃×C₁₃⋊C₃ #14523183

Order 2028.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₃⋊C₃	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃²	C₂×C₃	1	3	yes	complemented
5	C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
6	C₂²×C₃×C₁₃	—	13	1	no	maximal
7	C₂²×C₁₃⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×C₁₃	—	13	3	no	—
9	C₂×C₁₃⋊C₃	C₂×C₁₃	1	3	yes	direct product factor
10	C₂²×C₁₃	—	3	4	no	—
11	C₂²×C₁₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
12	C₂²×C₁₃	C₃×C₁₃	1	1	yes	characteristic, complemented
13	C₃×C₁₃	—	13	1	no	—
14	C₁₃⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, direct product factor
15	C₂×C₁₃	—	3	12	no	—
16	C₂×C₁₃	C₂×C₁₃⋊C₃	1	3	yes	direct product factor
17	C₂×C₁₃	C₂×C₃×C₁₃	1	3	yes	complemented
18	C₁₃	—	3	4	no	—
19	C₁₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
20	C₁₃	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
21	C₂²×C₃	—	13	1	no	Hall
22	C₂×C₃	—	13	3	no	—
23	C₂²	C₁₃×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₃	—	13	1	no	Sylow
25	C₂	C₂×C₁₃×C₁₃⋊C₃	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₃	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃²	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₁₃

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.