Subgroups — C₇×C₈×C₁₉×C₂₃ #72201738

Order 24472.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₉×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₄×C₇×C₁₉×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×C₁₉×C₂₃	C₄	1	1	yes	characteristic
4	C₇×C₁₉×C₂₃	C₈	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₁₉×C₂₃	C₂×C₇	1	1	yes	characteristic
6	C₇×C₈×C₂₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₈×C₁₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₁₉×C₂₃	C₄×C₇	1	1	yes	characteristic
9	C₄×C₇×C₂₃	C₂×C₁₉	1	1	yes	characteristic
10	C₄×C₇×C₁₉	C₂×C₂₃	1	1	yes	characteristic
11	C₁₉×C₂₃	C₇×C₈	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₂₃	C₄×C₁₉	1	1	yes	characteristic
13	C₂×C₇×C₁₉	C₄×C₂₃	1	1	yes	characteristic
14	C₈×C₂₃	C₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
15	C₇×C₂₃	C₈×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₈×C₁₉	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
17	C₇×C₁₉	C₈×C₂₃	1	1	yes	characteristic, direct product factor, Hall
18	C₄×C₂₃	C₂×C₇×C₁₉	1	1	yes	characteristic
19	C₄×C₁₉	C₂×C₇×C₂₃	1	1	yes	characteristic
20	C₇×C₈	C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₂₃	C₄×C₇×C₁₉	1	1	yes	characteristic
22	C₂×C₁₉	C₄×C₇×C₂₃	1	1	yes	characteristic
23	C₄×C₇	C₂×C₁₉×C₂₃	1	1	yes	characteristic
24	C₂₃	C₇×C₈×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₁₉	C₇×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	C₄×C₁₉×C₂₃	1	1	yes	characteristic
27	C₈	C₇×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
28	C₇	C₈×C₁₉×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₄	C₂×C₇×C₁₉×C₂₃	1	1	yes	characteristic
30	C₂	C₄×C₇×C₁₉×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₇×C₁₉×C₂₃
socle, prime radical	C₂×C₇×C₁₉×C₂₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×C₁₉×C₂₃	C₇	direct (N × H)
4. C₇×C₁₉×C₂₃	C₈	direct (N × H)
6. C₇×C₈×C₂₃	C₁₉	direct (N × H)
7. C₇×C₈×C₁₉	C₂₃	direct (N × H)
11. C₁₉×C₂₃	C₇×C₈	direct (N × H)
14. C₈×C₂₃	C₇×C₁₉	direct (N × H)
15. C₇×C₂₃	C₈×C₁₉	direct (N × H)
16. C₈×C₁₉	C₇×C₂₃	direct (N × H)
17. C₇×C₁₉	C₈×C₂₃	direct (N × H)
20. C₇×C₈	C₁₉×C₂₃	direct (N × H)
24. C₂₃	C₇×C₈×C₁₉	direct (N × H)
25. C₁₉	C₇×C₈×C₂₃	direct (N × H)
27. C₈	C₇×C₁₉×C₂₃	direct (N × H)
28. C₇	C₈×C₁₉×C₂₃	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×C₁₉×C₂₃	7
C₄×C₇×C₁₉×C₂₃	2
C₇×C₈×C₂₃	19
C₇×C₈×C₁₉	23

Subgroups — C7×C8×C19×C23 #72201738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₈×C₁₉×C₂₃ #72201738