Subgroups — C₁₃⋊C₃×#10621924 #41008763

Order 26988.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#10621924	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₇₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₁₇₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₇₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×#10621924	—	13	1	no	maximal, Hall
7	C₃×D₁₇₃	—	13	1	no	—
8	#10621924	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₇₃	—	13	1	no	Hall
10	D₁₇₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
11	C₁₇₃	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₄×C₁₃⋊C₃	—	173	1	no	maximal, Hall
13	C₂×C₁₃⋊C₃	—	173	1	no	—
14	C₄×C₁₃	—	173	1	no	Hall
15	C₁₃⋊C₃	#10621924	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	—	173	1	no	—
17	C₁₃	C₃×#10621924	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2249	1	no	Hall
19	C₂×C₃	—	2249	1	no	—
20	C₄	—	173	1	no	Sylow
21	C₃	—	13	1	no	Sylow
22	C₂	—	173	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₁₇₃	C₃×C₄
prime radical	C₁₃⋊C₃×D₁₇₃	C₂
cosocle	C₁₃×D₁₇₃	C₂×C₃
LCS	G ▷ C₁₃×C₁₇₃
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.