Subgroups — C₃⋊((D₂₇₁⋊C₃)⋊C₅) #37567264

Order 24390.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₂₇₁⋊C₃)⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(D₂₇₁⋊C₃)⋊C₅	—	3	1	no	maximal
3	C₃⋊(D₂₇₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃⋊(D₂₇₁⋊C₃)	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₂₇₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
6	(C₂₇₁⋊C₃)⋊C₅	—	2	1	no	—
7	(C₂₇₁⋊C₃)⋊C₅	D₃	1	1	yes	characteristic, complemented
8	D₂₇₁⋊C₅	—	3	1	no	Hall
9	C₃×C₂₇₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	D₈₁₃	C₃×C₅	1	1	yes	characteristic, complemented
11	D₂₇₁⋊C₃	—	3	1	no	—
12	C₂₇₁⋊C₅	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×C₂₇₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
14	C₂₇₁⋊C₃	—	2	1	no	—
15	C₂₇₁⋊C₃	C₅×D₃	1	1	yes	characteristic, complemented
16	D₂₇₁	—	3	1	no	Hall
17	C₂₇₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₅×D₃	—	271	1	no	maximal, Hall
19	C₃²×C₅	—	271	1	no	Hall
20	C₂×C₃×C₅	—	813	1	no	—
21	C₅×D₃	—	271	1	no	—
22	C₃×D₃	—	1355	1	no	Hall
23	C₃×C₅	—	271	1	no	—
24	C₃×C₅	—	271	1	no	—
25	C₃×C₅	—	542	1	no	—
26	C₂×C₅	—	813	1	no	Hall
27	C₃²	—	1355	1	no	Sylow
28	C₂×C₃	—	4065	1	no	—
29	D₃	—	1355	1	no	—
30	C₅	—	271	1	no	Sylow
31	C₃	—	1355	1	no	—
32	C₃	—	2710	1	no	—
33	C₃	(D₂₇₁⋊C₃)⋊C₅	1	1	yes	characteristic, complemented
34	C₂	—	4065	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₇₁	C₂×C₃×C₅
LCS	G ▷ C₃×C₂₇₁
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.