Subgroups — C₅×C₁₁⋊(D₄₃⋊C₃) #28382012

Order 14190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₄₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁⋊(D₄₃⋊C₃)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₄₃⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₄₃⋊C₃	—	11	1	no	maximal, Hall
7	D₄₇₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₄₃⋊C₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×D₄₃	—	11	1	no	Hall
11	C₃×C₅×D₁₁	—	43	1	no	maximal, Hall
12	D₄₃⋊C₃	—	11	1	no	Hall
13	C₅×C₄₃	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₁	—	43	1	no	Hall
15	C₄₃⋊C₃	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
16	C₅×D₁₁	—	43	1	no	Hall
17	D₄₃	—	11	1	no	Hall
18	C₃×D₁₁	—	43	1	no	Hall
19	C₅×C₁₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₄₃	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₁	—	43	1	no	Hall
22	C₂×C₃×C₅	—	473	1	no	Hall
23	D₁₁	—	43	1	no	Hall
24	C₃×C₅	—	43	1	no	Hall
25	C₁₁	C₅×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	473	1	no	Hall
27	C₂×C₃	—	473	1	no	Hall
28	C₅	C₁₁⋊(D₄₃⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	43	1	no	Sylow
30	C₂	—	473	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊(D₄₃⋊C₃)
commutator, cosocle, hypocenter	C₁₁×C₄₃	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₄₃	C₂×C₃
LCS	G ▷ C₁₁×C₄₃
UCS	C₁ ◁ C₅

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.