Subgroups — C₅×C₇×C₈×C₁₉ #72184635

Order 5320.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₇×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₇×C₁₉	C₄	1	1	yes	characteristic
3	C₇×C₈×C₁₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₈×C₁₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₇×C₁₉	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₇×C₁₉	C₂×C₅	1	1	yes	characteristic
7	C₄×C₅×C₁₉	C₂×C₇	1	1	yes	characteristic
8	C₅×C₇×C₈	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₇×C₁₉	C₄×C₅	1	1	yes	characteristic
10	C₂×C₅×C₁₉	C₄×C₇	1	1	yes	characteristic
11	C₈×C₁₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₄×C₅×C₇	C₂×C₁₉	1	1	yes	characteristic
13	C₇×C₁₉	C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₉	C₇×C₈	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₉	C₂×C₅×C₇	1	1	yes	characteristic
16	C₂×C₅×C₇	C₄×C₁₉	1	1	yes	characteristic
17	C₇×C₈	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₈	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₁₉	C₄×C₅×C₇	1	1	yes	characteristic
20	C₅×C₇	C₈×C₁₉	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₇	C₂×C₅×C₁₉	1	1	yes	characteristic
22	C₄×C₅	C₂×C₇×C₁₉	1	1	yes	characteristic
23	C₁₉	C₅×C₇×C₈	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₇	C₄×C₅×C₁₉	1	1	yes	characteristic
25	C₂×C₅	C₄×C₇×C₁₉	1	1	yes	characteristic
26	C₈	C₅×C₇×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₇	C₅×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₅	C₇×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₄	C₂×C₅×C₇×C₁₉	1	1	yes	characteristic
30	C₂	C₄×C₅×C₇×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₅×C₇×C₁₉
socle, prime radical	C₂×C₅×C₇×C₁₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×C₈×C₁₉	C₅	direct (N × H)
4. C₅×C₈×C₁₉	C₇	direct (N × H)
5. C₅×C₇×C₁₉	C₈	direct (N × H)
8. C₅×C₇×C₈	C₁₉	direct (N × H)
11. C₈×C₁₉	C₅×C₇	direct (N × H)
13. C₇×C₁₉	C₅×C₈	direct (N × H)
14. C₅×C₁₉	C₇×C₈	direct (N × H)
17. C₇×C₈	C₅×C₁₉	direct (N × H)
18. C₅×C₈	C₇×C₁₉	direct (N × H)
20. C₅×C₇	C₈×C₁₉	direct (N × H)
23. C₁₉	C₅×C₇×C₈	direct (N × H)
26. C₈	C₅×C₇×C₁₉	direct (N × H)
27. C₇	C₅×C₈×C₁₉	direct (N × H)
28. C₅	C₇×C₈×C₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₇×C₁₉	2
C₇×C₈×C₁₉	5
C₅×C₈×C₁₉	7
C₅×C₇×C₈	19

Subgroups — C5×C7×C8×C19 #72184635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₈×C₁₉ #72184635