Subgroups — C₅×C₇×C₁₆×C₄₃ #72201378

Order 24080.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₆×C₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₁₆×C₄₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₈×C₄₃	C₂×C₅	1	1	yes	characteristic
5	C₄×C₅×C₇×C₄₃	C₄	1	1	yes	characteristic
6	C₂×C₅×C₇×C₄₃	C₈	1	1	yes	characteristic
7	C₅×C₈×C₄₃	C₂×C₇	1	1	yes	characteristic
8	C₅×C₇×C₄₃	C₁₆	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₇×C₄₃	C₄×C₅	1	1	yes	characteristic
10	C₄×C₅×C₄₃	C₄×C₇	1	1	yes	characteristic
11	C₁₆×C₄₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₄₃	C₅×C₈	1	1	yes	characteristic
13	C₅×C₇×C₁₆	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₅×C₄₃	C₇×C₈	1	1	yes	characteristic
15	C₈×C₄₃	C₂×C₅×C₇	1	1	yes	characteristic
16	C₇×C₄₃	C₅×C₁₆	1	1	yes	characteristic, direct product factor, Hall
17	C₅×C₇×C₈	C₂×C₄₃	1	1	yes	characteristic
18	C₅×C₄₃	C₇×C₁₆	1	1	yes	characteristic, direct product factor, Hall
19	C₄×C₄₃	C₄×C₅×C₇	1	1	yes	characteristic
20	C₄×C₅×C₇	C₄×C₄₃	1	1	yes	characteristic
21	C₇×C₁₆	C₅×C₄₃	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₄₃	C₅×C₇×C₈	1	1	yes	characteristic
23	C₅×C₁₆	C₇×C₄₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂×C₅×C₇	C₈×C₄₃	1	1	yes	characteristic
25	C₇×C₈	C₂×C₅×C₄₃	1	1	yes	characteristic
26	C₄₃	C₅×C₇×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
27	C₅×C₈	C₂×C₇×C₄₃	1	1	yes	characteristic
28	C₅×C₇	C₁₆×C₄₃	1	1	yes	characteristic, direct product factor, Hall
29	C₄×C₇	C₄×C₅×C₄₃	1	1	yes	characteristic
30	C₄×C₅	C₄×C₇×C₄₃	1	1	yes	characteristic
31	C₁₆	C₅×C₇×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₇	C₅×C₈×C₄₃	1	1	yes	characteristic
33	C₂×C₅	C₇×C₈×C₄₃	1	1	yes	characteristic
34	C₈	C₂×C₅×C₇×C₄₃	1	1	yes	characteristic
35	C₇	C₅×C₁₆×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₅	C₇×C₁₆×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₄	C₄×C₅×C₇×C₄₃	1	1	yes	characteristic
38	C₂	C₅×C₇×C₈×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₅×C₇×C₄₃
socle, prime radical	C₂×C₅×C₇×C₄₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₆×C₄₃	C₅	direct (N × H)
3. C₅×C₁₆×C₄₃	C₇	direct (N × H)
8. C₅×C₇×C₄₃	C₁₆	direct (N × H)
11. C₁₆×C₄₃	C₅×C₇	direct (N × H)
13. C₅×C₇×C₁₆	C₄₃	direct (N × H)
16. C₇×C₄₃	C₅×C₁₆	direct (N × H)
18. C₅×C₄₃	C₇×C₁₆	direct (N × H)
21. C₇×C₁₆	C₅×C₄₃	direct (N × H)
23. C₅×C₁₆	C₇×C₄₃	direct (N × H)
26. C₄₃	C₅×C₇×C₁₆	direct (N × H)
28. C₅×C₇	C₁₆×C₄₃	direct (N × H)
31. C₁₆	C₅×C₇×C₄₃	direct (N × H)
35. C₇	C₅×C₁₆×C₄₃	direct (N × H)
36. C₅	C₇×C₁₆×C₄₃	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×C₇×C₈×C₄₃	2
C₇×C₁₆×C₄₃	5
C₅×C₁₆×C₄₃	7
C₅×C₇×C₁₆	43

Subgroups — C5×C7×C16×C43 #72201378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇×C₁₆×C₄₃ #72201378