Subgroups — C₅²×C₈×C₁₂₁ #72201499

Order 24200.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₁₂₁	C₅	1	6	yes	maximal, direct product factor
2	C₅²×C₈×C₁₁	C₁₁	1	1	yes	maximal, characteristic
3	C₄×C₅²×C₁₂₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅²×C₁₂₁	C₄	1	1	yes	characteristic
5	C₅²×C₁₂₁	C₈	1	1	yes	characteristic, direct product factor, Hall
6	C₄×C₅×C₁₂₁	C₂×C₅	1	6	yes	—
7	C₂×C₅×C₁₂₁	C₄×C₅	1	6	yes	—
8	C₄×C₅²×C₁₁	C₂×C₁₁	1	1	yes	characteristic
9	C₈×C₁₂₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₁₂₁	C₅×C₈	1	6	yes	direct product factor
11	C₂×C₅²×C₁₁	C₄×C₁₁	1	1	yes	characteristic
12	C₄×C₁₂₁	C₂×C₅²	1	1	yes	characteristic
13	C₅×C₈×C₁₁	C₅×C₁₁	1	6	yes	—
14	C₅²×C₁₁	C₈×C₁₁	1	1	yes	characteristic
15	C₂×C₁₂₁	C₄×C₅²	1	1	yes	characteristic
16	C₄×C₅×C₁₁	C₂×C₅×C₁₁	1	6	yes	—
17	C₅²×C₈	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
18	C₁₂₁	C₅²×C₈	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅×C₁₁	C₄×C₅×C₁₁	1	6	yes	—
20	C₄×C₅²	C₂×C₁₂₁	1	1	yes	characteristic
21	C₈×C₁₁	C₅²×C₁₁	1	1	yes	characteristic
22	C₅×C₁₁	C₅×C₈×C₁₁	1	6	yes	—
23	C₂×C₅²	C₄×C₁₂₁	1	1	yes	characteristic
24	C₄×C₁₁	C₂×C₅²×C₁₁	1	1	yes	characteristic
25	C₅×C₈	C₅×C₁₂₁	1	6	yes	direct product factor
26	C₅²	C₈×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	C₄×C₅²×C₁₁	1	1	yes	characteristic
28	C₄×C₅	C₂×C₅×C₁₂₁	1	6	yes	—
29	C₁₁	C₅²×C₈×C₁₁	1	1	yes	characteristic
30	C₂×C₅	C₄×C₅×C₁₂₁	1	6	yes	—
31	C₈	C₅²×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
32	C₅	C₅×C₈×C₁₂₁	1	6	yes	direct product factor
33	C₄	C₂×C₅²×C₁₂₁	1	1	yes	characteristic
34	C₂	C₄×C₅²×C₁₂₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₁₁	C₂×C₅²×C₁₁
socle, prime radical	C₂×C₅²×C₁₁	C₄×C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₈×C₁₂₁	C₅	direct (N × H)
5. C₅²×C₁₂₁	C₈	direct (N × H)
9. C₈×C₁₂₁	C₅²	direct (N × H)
10. C₅×C₁₂₁	C₅×C₈	direct (N × H)
17. C₅²×C₈	C₁₂₁	direct (N × H)
18. C₁₂₁	C₅²×C₈	direct (N × H)
25. C₅×C₈	C₅×C₁₂₁	direct (N × H)
26. C₅²	C₈×C₁₂₁	direct (N × H)
31. C₈	C₅²×C₁₂₁	direct (N × H)
32. C₅	C₅×C₈×C₁₂₁	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×C₁₂₁	5
C₅²×C₈×C₁₁	11
C₄×C₅²×C₁₂₁	2

Subgroups — C52×C8×C121 #72201499

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×C₈×C₁₂₁ #72201499