Subgroups — C₅⋊((C₁₃⋊C₃)⋊D₇₃) #43249727

Order 28470.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₇₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	(C₁₃⋊C₃)⋊D₇₃	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊C₃×C₇₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃×D₃₆₅	—	13	1	no	maximal, Hall
7	D₉₄₉	—	5	1	no	Hall
8	C₃×C₅×C₇₃	—	13	1	no	Hall
9	C₁₃×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₃₆₅	—	13	1	no	Hall
11	C₃×D₇₃	—	65	1	no	Hall
12	C₅⋊(D₁₃⋊C₃)	—	73	1	no	maximal, Hall
13	C₅×C₇₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇₃	—	13	1	no	Hall
15	C₅×C₁₃⋊C₃	D₇₃	1	1	yes	characteristic, complemented, Hall
16	D₇₃	—	65	1	no	Hall
17	D₆₅	—	73	1	no	Hall
18	D₁₃⋊C₃	—	365	1	no	Hall
19	C₇₃	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₁₃	C₃×D₇₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃⋊C₃	D₃₆₅	1	1	yes	characteristic, complemented, Hall
22	C₃×D₅	—	949	1	no	Hall
23	D₁₃	—	365	1	no	Hall
24	C₃×C₅	—	13	1	no	Hall
25	C₁₃	C₃×D₃₆₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	949	1	no	Hall
27	C₂×C₃	—	4745	1	no	Hall
28	C₅	(C₁₃⋊C₃)⋊D₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	13	1	no	Sylow
30	C₂	—	4745	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃×C₇₃	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₇₃
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.