Finite Group Databasebeta

← C₂×C₂₃²×C₂₉ #44501599

Subgroups — C₂×C₂₃²×C₂₉ #44501599

Order 30682.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃²×C₂₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₂₃×C₂₉	C₂₃	1	24	yes	maximal, direct product factor
3	C₂×C₂₃²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂₃×C₂₉	C₂×C₂₃	1	24	yes	direct product factor
5	C₂₃²	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
6	C₂×C₂₉	C₂₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₂₃	C₂₃×C₂₉	1	24	yes	direct product factor
8	C₂₉	C₂×C₂₃²	1	1	yes	characteristic, direct product factor, Sylow
9	C₂₃	C₂×C₂₃×C₂₉	1	24	yes	direct product factor
10	C₂	C₂₃²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃²×C₂₉	C₂	direct (N × H)
2. C₂×C₂₃×C₂₉	C₂₃	direct (N × H)
3. C₂×C₂₃²	C₂₉	direct (N × H)
4. C₂₃×C₂₉	C₂×C₂₃	direct (N × H)
5. C₂₃²	C₂×C₂₉	direct (N × H)
6. C₂×C₂₉	C₂₃²	direct (N × H)
7. C₂×C₂₃	C₂₃×C₂₉	direct (N × H)
8. C₂₉	C₂×C₂₃²	direct (N × H)
9. C₂₃	C₂×C₂₃×C₂₉	direct (N × H)
10. C₂	C₂₃²×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃²×C₂₉	2
C₂×C₂₃×C₂₉	23
C₂×C₂₃²	29