Subgroups — C₄²×C₅²×C₇₉ #72208348

Order 31600.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²×C₇₉	C₂	1	3	yes	maximal
2	C₄²×C₅×C₇₉	C₅	1	6	yes	maximal, direct product factor
3	C₂×C₄×C₅×C₇₉	C₂×C₅	1	18	yes	—
4	C₂²×C₅²×C₇₉	C₂²	1	1	yes	characteristic
5	C₄×C₅²×C₇₉	C₄	1	6	yes	direct product factor
6	C₂×C₅²×C₇₉	C₂×C₄	1	3	yes	—
7	C₅²×C₇₉	C₄²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₅×C₇₉	C₂²×C₅	1	6	yes	—
9	C₄×C₅×C₇₉	C₄×C₅	1	36	yes	direct product factor
10	C₄²×C₇₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₇₉	C₂×C₄×C₅	1	18	yes	—
12	C₂×C₄×C₇₉	C₂×C₅²	1	3	yes	—
13	C₄²×C₅²	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₅×C₇₉	C₄²×C₅	1	6	yes	direct product factor
15	C₂²×C₇₉	C₂²×C₅²	1	1	yes	characteristic
16	C₄×C₇₉	C₄×C₅²	1	6	yes	direct product factor
17	C₂×C₄×C₅²	C₂×C₇₉	1	3	yes	—
18	C₂×C₇₉	C₂×C₄×C₅²	1	3	yes	—
19	C₂²×C₅²	C₂²×C₇₉	1	1	yes	characteristic
20	C₄×C₅²	C₄×C₇₉	1	6	yes	direct product factor
21	C₄²×C₅	C₅×C₇₉	1	6	yes	direct product factor
22	C₇₉	C₄²×C₅²	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₅²	C₂×C₄×C₇₉	1	3	yes	—
24	C₂×C₄×C₅	C₂×C₅×C₇₉	1	18	yes	—
25	C₅²	C₄²×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₂²×C₅×C₇₉	1	6	yes	—
27	C₄×C₅	C₄×C₅×C₇₉	1	36	yes	direct product factor
28	C₄²	C₅²×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅	C₂×C₄×C₅×C₇₉	1	18	yes	—
30	C₂×C₄	C₂×C₅²×C₇₉	1	3	yes	—
31	C₅	C₄²×C₅×C₇₉	1	6	yes	direct product factor
32	C₂²	C₂²×C₅²×C₇₉	1	1	yes	characteristic
33	C₄	C₄×C₅²×C₇₉	1	6	yes	direct product factor
34	C₂	C₂×C₄×C₅²×C₇₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₅²×C₇₉
socle, prime radical	C₂²×C₅²×C₇₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄²×C₅×C₇₉	C₅	direct (N × H)
5. C₄×C₅²×C₇₉	C₄	direct (N × H)
7. C₅²×C₇₉	C₄²	direct (N × H)
9. C₄×C₅×C₇₉	C₄×C₅	direct (N × H)
10. C₄²×C₇₉	C₅²	direct (N × H)
13. C₄²×C₅²	C₇₉	direct (N × H)
14. C₅×C₇₉	C₄²×C₅	direct (N × H)
16. C₄×C₇₉	C₄×C₅²	direct (N × H)
20. C₄×C₅²	C₄×C₇₉	direct (N × H)
21. C₄²×C₅	C₅×C₇₉	direct (N × H)
22. C₇₉	C₄²×C₅²	direct (N × H)
25. C₅²	C₄²×C₇₉	direct (N × H)
27. C₄×C₅	C₄×C₅×C₇₉	direct (N × H)
28. C₄²	C₅²×C₇₉	direct (N × H)
31. C₅	C₄²×C₅×C₇₉	direct (N × H)
33. C₄	C₄×C₅²×C₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅²×C₇₉	2
C₄²×C₅×C₇₉	5
C₄²×C₅²	79

Subgroups — C42×C52×C79 #72208348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅²×C₇₉ #72208348