Finite Group Databasebeta

← C₅×C₁₆×C₃₀₇ #72201798

Subgroups — C₅×C₁₆×C₃₀₇ #72201798

Order 24560.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₃₀₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₃₀₇	C₄	1	1	yes	characteristic
3	C₁₆×C₃₀₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₃₀₇	C₈	1	1	yes	characteristic
5	C₈×C₃₀₇	C₂×C₅	1	1	yes	characteristic
6	C₅×C₃₀₇	C₁₆	1	1	yes	characteristic, direct product factor, Hall
7	C₄×C₃₀₇	C₄×C₅	1	1	yes	characteristic
8	C₂×C₃₀₇	C₅×C₈	1	1	yes	characteristic
9	C₃₀₇	C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
10	C₅×C₁₆	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₈	C₂×C₃₀₇	1	1	yes	characteristic
12	C₄×C₅	C₄×C₃₀₇	1	1	yes	characteristic
13	C₁₆	C₅×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₅	C₈×C₃₀₇	1	1	yes	characteristic
15	C₈	C₂×C₅×C₃₀₇	1	1	yes	characteristic
16	C₅	C₁₆×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₄	C₄×C₅×C₃₀₇	1	1	yes	characteristic
18	C₂	C₅×C₈×C₃₀₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₃₀₇
socle, prime radical	C₂×C₅×C₃₀₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₆×C₃₀₇	C₅	direct (N × H)
6. C₅×C₃₀₇	C₁₆	direct (N × H)
9. C₃₀₇	C₅×C₁₆	direct (N × H)
10. C₅×C₁₆	C₃₀₇	direct (N × H)
13. C₁₆	C₅×C₃₀₇	direct (N × H)
16. C₅	C₁₆×C₃₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×C₃₀₇	2
C₁₆×C₃₀₇	5
C₅×C₁₆	307