Subgroups — C₅²×Dic₃×C₁₀₇ #44545643

Order 32100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅²×C₁₀₇	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×Dic₃×C₁₀₇	C₅	1	6	yes	maximal, direct product factor
5	C₂×C₅²×C₁₀₇	D₃	1	1	yes	characteristic
6	C₂×C₃×C₅×C₁₀₇	C₂×C₅	1	6	yes	—
7	C₅²×C₁₀₇	Dic₃	1	1	yes	characteristic, direct product factor, Hall
8	C₄×C₅×C₁₀₇	—	3	6	no	—
9	C₃×C₅×C₁₀₇	C₄×C₅	1	6	yes	complemented
10	Dic₃×C₁₀₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₅×C₁₀₇	C₅×D₃	1	6	yes	—
12	C₂×C₃×C₁₀₇	C₂×C₅²	1	1	yes	characteristic
13	C₅×C₁₀₇	C₅×Dic₃	1	6	yes	direct product factor
14	C₄×C₁₀₇	—	3	1	no	Hall
15	C₃×C₁₀₇	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
16	C₅²×Dic₃	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₀₇	C₅²×D₃	1	1	yes	characteristic
18	C₂×C₃×C₅²	C₂×C₁₀₇	1	1	yes	characteristic
19	C₁₀₇	C₅²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₄×C₅²	—	3	1	no	Hall
21	C₃×C₅²	C₄×C₁₀₇	1	1	yes	characteristic, complemented, Hall
22	C₅×Dic₃	C₅×C₁₀₇	1	6	yes	direct product factor
23	C₂×C₅²	D₃×C₁₀₇	1	1	yes	characteristic
24	C₂×C₃×C₅	C₂×C₅×C₁₀₇	1	6	yes	—
25	C₅²	Dic₃×C₁₀₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₄×C₅	—	3	6	no	—
27	C₃×C₅	C₄×C₅×C₁₀₇	1	6	yes	complemented
28	Dic₃	C₅²×C₁₀₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₅	C₅×D₃×C₁₀₇	1	6	yes	—
30	C₂×C₃	C₂×C₅²×C₁₀₇	1	1	yes	characteristic
31	C₅	C₅×Dic₃×C₁₀₇	1	6	yes	direct product factor
32	C₄	—	3	1	no	Sylow
33	C₃	C₄×C₅²×C₁₀₇	1	1	yes	characteristic, complemented, Sylow
34	C₂	C₅²×D₃×C₁₀₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₁₀₇	D₃
commutator, hypocenter	C₃	C₄×C₅²×C₁₀₇
Frattini	C₂	C₅²×D₃×C₁₀₇
Fitting, socle, prime radical	C₂×C₃×C₅²×C₁₀₇	C₂
cosocle	C₂×C₃	C₂×C₅²×C₁₀₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅²×C₁₀₇

Complements

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

N	H ≅ G/N	type
3. C₃×C₅²×C₁₀₇	C₄	semidirect
4. C₅×Dic₃×C₁₀₇	C₅	direct (N × H)
7. C₅²×C₁₀₇	Dic₃	direct (N × H)
9. C₃×C₅×C₁₀₇	C₄×C₅	semidirect
10. Dic₃×C₁₀₇	C₅²	direct (N × H)
13. C₅×C₁₀₇	C₅×Dic₃	direct (N × H)
15. C₃×C₁₀₇	C₄×C₅²	semidirect
16. C₅²×Dic₃	C₁₀₇	direct (N × H)
19. C₁₀₇	C₅²×Dic₃	direct (N × H)
21. C₃×C₅²	C₄×C₁₀₇	semidirect
22. C₅×Dic₃	C₅×C₁₀₇	direct (N × H)
25. C₅²	Dic₃×C₁₀₇	direct (N × H)
27. C₃×C₅	C₄×C₅×C₁₀₇	semidirect
28. Dic₃	C₅²×C₁₀₇	direct (N × H)
31. C₅	C₅×Dic₃×C₁₀₇	direct (N × H)
33. C₃	C₄×C₅²×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₁₀₇	2
C₄×C₅²×C₁₀₇	3
C₅×Dic₃×C₁₀₇	5
C₅²×Dic₃	107

Subgroups — C52×Dic3×C107 #44545643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×Dic₃×C₁₀₇ #44545643