Subgroups — C₅×D₂₃₄₃ #37552869

Order 23430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇₈₁	—	3	1	no	maximal, Hall
3	D₂₃₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₁×C₇₁	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₇₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₅×D₂₁₃	—	11	1	no	maximal, Hall
7	D₇₈₁	—	3	1	no	Hall
8	C₃×C₅×C₇₁	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₇₁	C₅×D₃	1	1	yes	characteristic, complemented, Hall
10	C₅×D₇₁	—	33	1	no	Hall
11	D₂₁₃	—	11	1	no	Hall
12	C₅×C₇₁	D₃₃	1	1	yes	characteristic, complemented, Hall
13	C₅×D₃₃	—	71	1	no	maximal, Hall
14	C₃×C₇₁	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×C₁₁	D₇₁	1	1	yes	characteristic, complemented, Hall
16	D₇₁	—	33	1	no	Hall
17	C₅×D₁₁	—	213	1	no	Hall
18	C₇₁	C₅×D₃₃	1	1	yes	characteristic, complemented, Sylow
19	D₃₃	—	71	1	no	Hall
20	C₅×C₁₁	D₂₁₃	1	1	yes	characteristic, complemented, Hall
21	C₃×C₁₁	C₅×D₇₁	1	1	yes	characteristic, complemented, Hall
22	C₅×D₃	—	781	1	no	Hall
23	D₁₁	—	213	1	no	Hall
24	C₃×C₅	D₇₈₁	1	1	yes	characteristic, complemented, Hall
25	C₁₁	C₅×D₂₁₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	2343	1	no	Hall
27	D₃	—	781	1	no	Hall
28	C₅	D₂₃₄₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₇₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	2343	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₃₄₃
commutator, cosocle, hypocenter	C₃×C₁₁×C₇₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₇₁	C₂
LCS	G ▷ C₃×C₁₁×C₇₁
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.