Subgroups — C₅⋊#16809813 #30680819

Order 16770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#13131976	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#16809813	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#13131976	D₅	1	1	yes	characteristic, complemented, Hall
6	D₅×C₄₃⋊C₃	—	13	1	no	maximal, Hall
7	D₁₃×C₄₃	—	5	1	no	Hall
8	C₅×C₄₃⋊C₃	—	13	1	no	Hall
9	C₁₃×C₄₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₅×C₄₃	—	39	1	no	Hall
11	C₅⋊(D₁₃⋊C₃)	—	43	1	no	maximal, Hall
12	C₂×C₄₃⋊C₃	—	65	1	no	Hall
13	C₅×C₄₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₃⋊C₃	—	43	1	no	Hall
15	D₆₅	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₄₃⋊C₃	—	13	1	no	Hall
17	C₂×C₄₃	—	195	1	no	Hall
18	D₁₃⋊C₃	—	215	1	no	Hall
19	C₅×C₁₃	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₄₃	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
21	C₁₃⋊C₃	—	43	1	no	Hall
22	C₃×D₅	—	559	1	no	Hall
23	D₁₃	—	5	1	no	Hall
24	C₃×C₅	—	559	1	no	Hall
25	C₁₃	D₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	39	1	no	Hall
27	C₂×C₃	—	2795	1	no	Hall
28	C₅	#16809813	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	559	1	no	Sylow
30	C₂	—	195	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₃
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.