Finite Group Databasebeta

← C₅×C₉×C₂₃² #37558362

Subgroups — C₅×C₉×C₂₃² #37558362

Order 23805.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃²	C₃	1	1	yes	maximal, characteristic
2	C₉×C₂₃²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₂₃²	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₂₃²	C₃×C₅	1	1	yes	characteristic
5	C₅×C₉×C₂₃	C₂₃	1	24	yes	maximal, direct product factor
6	C₂₃²	C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₅×C₂₃	C₃×C₂₃	1	24	yes	—
8	C₉×C₂₃	C₅×C₂₃	1	24	yes	direct product factor
9	C₅×C₂₃	C₉×C₂₃	1	24	yes	direct product factor
10	C₃×C₂₃	C₃×C₅×C₂₃	1	24	yes	—
11	C₅×C₉	C₂₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₂₃	C₅×C₉×C₂₃	1	24	yes	direct product factor
13	C₃×C₅	C₃×C₂₃²	1	1	yes	characteristic
14	C₉	C₅×C₂₃²	1	1	yes	characteristic, direct product factor, Sylow
15	C₅	C₉×C₂₃²	1	1	yes	characteristic, direct product factor, Sylow
16	C₃	C₃×C₅×C₂₃²	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₃×C₅×C₂₃²
socle, prime radical	C₃×C₅×C₂₃²	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₉×C₂₃²	C₅	direct (N × H)
3. C₅×C₂₃²	C₉	direct (N × H)
5. C₅×C₉×C₂₃	C₂₃	direct (N × H)
6. C₂₃²	C₅×C₉	direct (N × H)
8. C₉×C₂₃	C₅×C₂₃	direct (N × H)
9. C₅×C₂₃	C₉×C₂₃	direct (N × H)
11. C₅×C₉	C₂₃²	direct (N × H)
12. C₂₃	C₅×C₉×C₂₃	direct (N × H)
14. C₉	C₅×C₂₃²	direct (N × H)
15. C₅	C₉×C₂₃²	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₂₃²	3
C₉×C₂₃²	5
C₅×C₉×C₂₃	23