Subgroups — C₇₃×C₃⋊D₃₉ #30685213

Order 17082.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₃×D₃₉	—	3	4	no	maximal
3	C₃×C₁₃×C₇₃	D₃	1	4	yes	complemented
4	D₁₃×C₇₃	—	9	1	no	Hall
5	C₃⋊D₃×C₇₃	—	13	1	no	maximal, Hall
6	C₁₃×C₇₃	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
7	C₃²×C₇₃	D₁₃	1	1	yes	characteristic, complemented, Hall
8	D₃×C₇₃	—	39	4	no	—
9	C₃⋊D₃₉	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇₃	D₃₉	1	4	yes	complemented
11	C₂×C₇₃	—	117	1	no	Hall
12	C₃²×C₁₃	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
13	D₃₉	—	3	4	no	—
14	C₇₃	C₃⋊D₃₉	1	1	yes	characteristic, direct product factor, Sylow
15	C₃×C₁₃	D₃×C₇₃	1	4	yes	complemented
16	D₁₃	—	9	1	no	Hall
17	C₃⋊D₃	—	13	1	no	Hall
18	C₁₃	C₃⋊D₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
19	C₃²	D₁₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
20	D₃	—	39	4	no	—
21	C₃	C₇₃×D₃₉	1	4	yes	complemented
22	C₂	—	117	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₃	C₃⋊D₃₉
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂×C₇₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₇₃	C₂
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₇₃

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.