Finite Group Databasebeta

← C₃³×C₁₇×C₅₃ #72201629

Subgroups — C₃³×C₁₇×C₅₃ #72201629

Order 24327.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×C₅₃	C₃	1	13	yes	maximal, direct product factor
2	C₃×C₁₇×C₅₃	C₃²	1	13	yes	direct product factor
3	C₃³×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₇×C₅₃	C₃³	1	1	yes	characteristic, direct product factor, Hall
5	C₃²×C₅₃	C₃×C₁₇	1	13	yes	direct product factor
6	C₃³×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅₃	C₃²×C₁₇	1	13	yes	direct product factor
8	C₃²×C₁₇	C₃×C₅₃	1	13	yes	direct product factor
9	C₅₃	C₃³×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
10	C₃×C₁₇	C₃²×C₅₃	1	13	yes	direct product factor
11	C₃³	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₁₇	C₃³×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₃²	C₃×C₁₇×C₅₃	1	13	yes	direct product factor
14	C₃	C₃²×C₁₇×C₅₃	1	13	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. C₃²×C₁₇×C₅₃	C₃	direct (N × H)
2. C₃×C₁₇×C₅₃	C₃²	direct (N × H)
3. C₃³×C₅₃	C₁₇	direct (N × H)
4. C₁₇×C₅₃	C₃³	direct (N × H)
5. C₃²×C₅₃	C₃×C₁₇	direct (N × H)
6. C₃³×C₁₇	C₅₃	direct (N × H)
7. C₃×C₅₃	C₃²×C₁₇	direct (N × H)
8. C₃²×C₁₇	C₃×C₅₃	direct (N × H)
9. C₅₃	C₃³×C₁₇	direct (N × H)
10. C₃×C₁₇	C₃²×C₅₃	direct (N × H)
11. C₃³	C₁₇×C₅₃	direct (N × H)
12. C₁₇	C₃³×C₅₃	direct (N × H)
13. C₃²	C₃×C₁₇×C₅₃	direct (N × H)
14. C₃	C₃²×C₁₇×C₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×C₅₃	3
C₃³×C₅₃	17
C₃³×C₁₇	53