Subgroups — C₅×A₄×C₂₃² #44540765

Order 31740.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₂₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₂₃²	—	4	1	no	maximal, Hall
3	A₄×C₂₃²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₂₃²	—	3	1	no	—
5	C₅×C₂₃²	A₄	1	1	yes	characteristic, direct product factor, Hall
6	C₂²×C₂₃²	C₃×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₂₃²	—	4	1	no	Hall
8	C₅×A₄×C₂₃	C₂₃	1	24	yes	maximal, direct product factor
9	C₂×C₂₃²	—	3	1	no	—
10	C₂₃²	C₅×A₄	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₅×C₂₃	C₃×C₂₃	1	24	yes	complemented
12	C₃×C₅×C₂₃	—	4	24	no	—
13	A₄×C₂₃	C₅×C₂₃	1	24	yes	direct product factor
14	C₂×C₅×C₂₃	—	3	24	no	—
15	C₅×C₂₃	A₄×C₂₃	1	24	yes	direct product factor
16	C₂²×C₂₃	C₃×C₅×C₂₃	1	24	yes	complemented
17	C₃×C₂₃	—	4	24	no	—
18	C₅×A₄	C₂₃²	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₂₃	—	3	24	no	—
20	C₂₃	C₅×A₄×C₂₃	1	24	yes	direct product factor
21	C₂²×C₅	C₃×C₂₃²	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅	—	4	1	no	Hall
23	A₄	C₅×C₂₃²	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅	—	3	1	no	—
25	C₅	A₄×C₂₃²	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²	C₃×C₅×C₂₃²	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	4	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₂₃²	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₅×C₂₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₂₃²	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₂₃²

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.