Subgroups — D₃₉×C₆₁⋊C₅ #37558186

Order 23790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₆₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₃×C₆₁⋊C₅	—	3	1	no	maximal, Hall
3	C₆₁×D₃₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₃×C₆₁⋊C₅	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₃×C₆₁⋊C₅	—	13	1	no	maximal, Hall
7	D₁₃×C₆₁	—	3	1	no	Hall
8	C₃×C₆₁⋊C₅	D₁₃	1	1	yes	characteristic, complemented, Hall
9	C₁₃×C₆₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₆₁⋊C₅	—	39	1	no	Hall
11	C₅×D₃₉	—	61	1	no	maximal, Hall
12	D₃×C₆₁	—	13	1	no	Hall
13	C₆₁⋊C₅	D₃₉	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₁₃	—	61	1	no	Hall
15	C₃×C₆₁	C₅×D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₅×D₁₃	—	183	1	no	Hall
17	C₂×C₆₁	—	39	1	no	Hall
18	D₃₉	C₆₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₃	—	61	1	no	Hall
20	C₆₁	C₅×D₃₉	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₃	C₂×C₆₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	793	1	no	Hall
23	D₁₃	—	3	1	no	Hall
24	C₃×C₅	—	61	1	no	Hall
25	C₁₃	D₃×C₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	2379	1	no	Hall
27	D₃	—	13	1	no	Hall
28	C₅	—	61	1	no	Sylow
29	C₃	D₁₃×C₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	39	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₃×C₆₁	C₂×C₅
LCS	G ▷ C₃×C₁₃×C₆₁
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.