Subgroups — C₁₇⋊((C₁₉⋊C₃)⋊D₁₃) #38738113

Order 25194.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₁₉₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₇⋊(D₁₉⋊C₃)	—	13	1	no	maximal, Hall
5	(C₁₉⋊C₃)⋊D₁₃	—	17	1	no	maximal, Hall
6	C₃×D₂₂₁	—	19	1	no	maximal, Hall
7	C₁₇×C₁₉⋊C₃	D₁₃	1	1	yes	characteristic, complemented, Hall
8	C₁₃×C₁₉⋊C₃	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₃×C₁₇	—	19	1	no	Hall
10	D₃₂₃	—	13	1	no	Hall
11	D₂₄₇	—	17	1	no	Hall
12	D₂₂₁	—	19	1	no	Hall
13	C₁₇×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
14	C₁₃×C₁₉	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₁₃×C₁₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
16	D₁₉⋊C₃	—	221	1	no	Hall
17	C₃×D₁₇	—	247	1	no	Hall
18	C₃×D₁₃	—	323	1	no	Hall
19	C₁₉⋊C₃	D₂₂₁	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₇	—	19	1	no	Hall
21	C₃×C₁₃	—	19	1	no	Hall
22	D₁₉	—	221	1	no	Hall
23	D₁₇	—	247	1	no	Hall
24	D₁₃	—	323	1	no	Hall
25	C₁₉	C₃×D₂₂₁	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	(C₁₉⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
27	C₁₃	C₁₇⋊(D₁₉⋊C₃)	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	4199	1	no	Hall
29	C₃	—	19	1	no	Sylow
30	C₂	—	4199	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₇×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₇×C₁₉
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.