Finite Group Databasebeta

← C₃²×C₅₃×C₆₇ #44544179

Subgroups — C₃²×C₅₃×C₆₇ #44544179

Order 31959.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₆₇	C₃	1	4	yes	maximal, direct product factor
2	C₅₃×C₆₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
3	C₃²×C₆₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃²×C₅₃	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₆₇	C₃×C₅₃	1	4	yes	direct product factor
6	C₃×C₅₃	C₃×C₆₇	1	4	yes	direct product factor
7	C₆₇	C₃²×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
8	C₅₃	C₃²×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
9	C₃²	C₅₃×C₆₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₅₃×C₆₇	1	4	yes	direct product factor

	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. C₃×C₅₃×C₆₇	C₃	direct (N × H)
2. C₅₃×C₆₇	C₃²	direct (N × H)
3. C₃²×C₆₇	C₅₃	direct (N × H)
4. C₃²×C₅₃	C₆₇	direct (N × H)
5. C₃×C₆₇	C₃×C₅₃	direct (N × H)
6. C₃×C₅₃	C₃×C₆₇	direct (N × H)
7. C₆₇	C₃²×C₅₃	direct (N × H)
8. C₅₃	C₃²×C₆₇	direct (N × H)
9. C₃²	C₅₃×C₆₇	direct (N × H)
10. C₃	C₃×C₅₃×C₆₇	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×C₅₃×C₆₇	3
C₃²×C₆₇	53
C₃²×C₅₃	67