Subgroups — C₁₃⋊C₃×D₂₉₉ #37552228

Order 23322.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₉₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₂₉₉	—	13	1	no	maximal
5	C₁₃⋊C₃×D₂₃	—	13	1	no	maximal
6	D₁₃×C₁₃⋊C₃	—	23	1	no	maximal, Hall
7	C₃×C₁₃×C₂₃	—	13	1	no	—
8	C₂₃×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
9	D₂₉₉	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
10	C₁₃×D₂₃	—	13	1	no	—
11	C₁₃×C₁₃⋊C₃	D₂₃	1	1	yes	characteristic, complemented, Hall
12	C₁₃×D₁₃	—	23	1	no	Hall
13	C₁₃×C₂₃	—	6	2	no	—
14	C₁₃×C₂₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic, complemented
16	C₁₃²	C₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×D₂₃	—	169	1	no	Hall
18	C₃×D₁₃	—	299	1	no	—
19	C₂×C₁₃⋊C₃	—	299	1	no	—
20	C₃×C₂₃	—	13	1	no	Hall
21	D₂₃	—	13	1	no	Hall
22	C₃×C₁₃	—	13	1	no	—
23	C₁₃⋊C₃	D₂₉₉	1	1	yes	characteristic, direct product factor
24	C₂×C₁₃	—	299	1	no	—
25	D₁₃	—	23	1	no	—
26	C₂₃	D₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₁₃	—	6	2	no	—
28	C₁₃	C₁₃⋊C₃×D₂₃	1	1	yes	characteristic, complemented
29	C₁₃	C₃×D₂₉₉	1	1	yes	characteristic, complemented
30	C₂×C₃	—	3887	1	no	Hall
31	C₃	—	13	1	no	Sylow
32	C₂	—	299	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₂₃	C₂×C₃
LCS	G ▷ C₁₃²×C₂₃
UCS	C₁

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.