Subgroups — C₃×(C₇₁⋊C₅)⋊D₁₁ #37552886

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₇₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₇₁⋊C₅)⋊D₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₇₈₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×C₇₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇₁⋊C₅	—	11	1	no	maximal, Hall
7	D₇₈₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇₁⋊C₅	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	D₇₁⋊C₅	—	11	1	no	Hall
11	C₃×D₇₁	—	11	1	no	Hall
12	C₇₁⋊C₅	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅×D₁₁	—	71	1	no	maximal, Hall
14	C₃×C₇₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	—	71	1	no	Hall
16	D₇₁	—	11	1	no	Hall
17	C₅×D₁₁	—	71	1	no	Hall
18	C₇₁	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₁₁	—	355	1	no	Hall
20	C₅×C₁₁	—	71	1	no	Hall
21	C₃×C₁₁	D₇₁⋊C₅	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅	—	781	1	no	Hall
23	D₁₁	—	355	1	no	Hall
24	C₃×C₅	—	71	1	no	Hall
25	C₁₁	C₃×D₇₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	781	1	no	Hall
27	C₂×C₃	—	3905	1	no	Hall
28	C₅	—	71	1	no	Sylow
29	C₃	(C₇₁⋊C₅)⋊D₁₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3905	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	(C₇₁⋊C₅)⋊D₁₁
commutator, cosocle, hypocenter	C₁₁×C₇₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₇₁	C₂×C₅
LCS	G ▷ C₁₁×C₇₁
UCS	C₁ ◁ C₃

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.