Subgroups — C₂×(C₁₃⋊C₃)⋊D₁₃ #14523167

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	1	yes	maximal, characteristic, complemented
2	(C₁₃⋊C₃)⋊D₁₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₃⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₁₃⋊D₁₃	C₂×C₃	1	2	yes	complemented
7	C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×D₁₃	—	13	1	no	maximal
9	C₂×D₁₃⋊C₃	—	13	1	no	maximal
10	C₂×C₃×C₁₃	—	13	1	no	—
11	C₃×D₁₃	—	13	2	no	—
12	C₂×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
13	D₁₃⋊C₃	—	13	2	no	—
14	C₂×D₁₃	—	13	1	no	—
15	C₂×D₁₃	—	13	1	no	—
16	C₂×D₁₃	—	39	4	no	—
17	C₃×C₁₃	—	13	1	no	—
18	C₁₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented
19	C₂×C₁₃	—	3	4	no	—
20	C₂×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
21	C₂×C₁₃	C₃×D₁₃	1	1	yes	characteristic, complemented
22	D₁₃	—	13	2	no	—
23	D₁₃	—	13	2	no	—
24	D₁₃	—	39	8	no	—
25	C₁₃	—	3	4	no	—
26	C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
27	C₁₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
28	C₂²×C₃	—	169	1	no	Hall
29	C₂×C₃	—	13	1	no	—
30	C₂×C₃	—	169	2	no	—
31	C₂²	—	169	1	no	Sylow
32	C₃	—	13	1	no	Sylow
33	C₂	—	169	2	no	—
34	C₂	(C₁₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₁₃⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²	C₂×C₃
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₂

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.