Subgroups — D₁₅×C₄₇⋊C₂₃ #44569876

Order 32430.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₄₇⋊C₂₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅×C₄₇⋊C₂₃	—	3	1	no	maximal, Hall
3	D₃×C₄₇⋊C₂₃	—	5	1	no	maximal, Hall
4	C₅×C₄₇⋊C₂₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₄₇⋊C₂₃	D₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₄₇⋊C₂₃	—	15	1	no	Hall
7	D₁₅×C₄₇	C₂₃	1	1	yes	maximal, characteristic, complemented, Hall
8	C₄₇⋊C₂₃	D₁₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×C₄₇	C₂×C₂₃	1	1	yes	characteristic, complemented, Hall
10	C₂₃×D₁₅	—	47	1	no	maximal, Hall
11	D₅×C₄₇	—	3	1	no	Hall
12	C₃×C₅×C₂₃	—	47	1	no	Hall
13	D₃×C₄₇	—	5	1	no	Hall
14	C₅×C₄₇	D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
15	D₅×C₂₃	—	141	1	no	Hall
16	C₃×C₄₇	D₅×C₂₃	1	1	yes	characteristic, complemented, Hall
17	D₃×C₂₃	—	235	1	no	Hall
18	C₅×C₂₃	—	47	1	no	Hall
19	C₂×C₄₇	—	15	1	no	Hall
20	C₃×C₂₃	—	47	1	no	Hall
21	C₄₇	C₂₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₂₃	—	705	1	no	Hall
23	D₁₅	C₄₇⋊C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂₃	—	47	1	no	Sylow
25	C₃×C₅	C₂×C₄₇⋊C₂₃	1	1	yes	characteristic, complemented, Hall
26	D₅	—	3	1	no	Hall
27	D₃	—	5	1	no	Hall
28	C₅	D₃×C₄₇⋊C₂₃	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₄₇⋊C₂₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₄₇	C₂×C₂₃
LCS	G ▷ C₃×C₅×C₄₇
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.