Finite Group Databasebeta

← C₁₆×C₁₇×C₅₃ #72192587

Subgroups — C₁₆×C₁₇×C₅₃ #72192587

Order 14416.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₇×C₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×C₅₃	C₄	1	1	yes	characteristic
3	C₂×C₁₇×C₅₃	C₈	1	1	yes	characteristic
4	C₁₇×C₅₃	C₁₆	1	1	yes	characteristic, direct product factor, Hall
5	C₁₆×C₅₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₈×C₅₃	C₂×C₁₇	1	1	yes	characteristic
7	C₁₆×C₁₇	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₄×C₅₃	C₄×C₁₇	1	1	yes	characteristic
9	C₈×C₁₇	C₂×C₅₃	1	1	yes	characteristic
10	C₂×C₅₃	C₈×C₁₇	1	1	yes	characteristic
11	C₄×C₁₇	C₄×C₅₃	1	1	yes	characteristic
12	C₅₃	C₁₆×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₁₇	C₈×C₅₃	1	1	yes	characteristic
14	C₁₇	C₁₆×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
15	C₁₆	C₁₇×C₅₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₈	C₂×C₁₇×C₅₃	1	1	yes	characteristic
17	C₄	C₄×C₁₇×C₅₃	1	1	yes	characteristic
18	C₂	C₈×C₁₇×C₅₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₁₇×C₅₃
socle, prime radical	C₂×C₁₇×C₅₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₇×C₅₃	C₁₆	direct (N × H)
5. C₁₆×C₅₃	C₁₇	direct (N × H)
7. C₁₆×C₁₇	C₅₃	direct (N × H)
12. C₅₃	C₁₆×C₁₇	direct (N × H)
14. C₁₇	C₁₆×C₅₃	direct (N × H)
15. C₁₆	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
C₈×C₁₇×C₅₃	2
C₁₆×C₅₃	17
C₁₆×C₁₇	53