Subgroups — C₃⋊(C₅⋊D₅)×D₁₀₇ #44545694

Order 32100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₇×C₃⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₅⋊D₅₃₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₁₀₇	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₅×D₁₀₇	—	5	6	no	maximal
7	C₅⋊D₅₃₅	—	3	1	no	—
8	C₅⋊D₅×C₁₀₇	—	3	1	no	—
9	C₅²×D₁₀₇	D₃	1	1	yes	characteristic, complemented
10	D₁₆₀₅	—	5	6	no	—
11	D₁₅×C₁₀₇	—	5	6	no	—
12	C₃×C₅×D₁₀₇	D₅	1	6	yes	complemented
13	C₅²×C₁₀₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₁₀₇	—	15	6	no	—
15	C₃×C₅×C₁₀₇	C₂×D₅	1	6	yes	complemented
16	D₃×D₁₀₇	—	25	1	no	Hall
17	D₅₃₅	—	15	6	no	—
18	C₅×D₁₀₇	D₁₅	1	6	yes	complemented
19	D₅×C₁₀₇	—	15	6	no	—
20	D₃₂₁	—	25	1	no	—
21	C₃×D₁₀₇	C₅⋊D₅	1	1	yes	characteristic, complemented
22	D₃×C₁₀₇	—	25	1	no	—
23	C₅×C₁₀₇	C₂×D₁₅	1	6	yes	complemented
24	C₂×D₁₀₇	—	75	1	no	Hall
25	C₃×C₁₀₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃⋊(C₅⋊D₅)	—	107	1	no	maximal, Hall
27	C₂×C₁₀₇	—	75	1	no	—
28	D₁₀₇	—	75	1	no	—
29	D₁₀₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₅²	—	107	1	no	—
31	C₃⋊(C₅⋊D₅)	—	107	1	no	—
32	C₃⋊(C₅⋊D₅)	D₁₀₇	1	1	yes	characteristic, direct product factor
33	C₁₀₇	C₂×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₅⋊D₅	—	321	1	no	Hall
35	C₃×C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₅	—	535	6	no	—
37	C₂×C₅²	—	107	1	no	—
38	C₅⋊D₅	—	3	1	no	—
39	C₅⋊D₅	—	321	1	no	—
40	C₂×C₃×C₅	—	107	6	no	—
41	D₁₅	—	5	6	no	—
42	D₁₅	—	535	6	no	—
43	C₅²	D₃×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
44	C₂×D₅	—	1605	6	no	—
45	C₃×C₅	D₅×D₁₀₇	1	6	yes	complemented
46	C₂×D₃	—	2675	1	no	Hall
47	C₂×C₅	—	107	6	no	—
48	D₅	—	15	6	no	—
49	D₅	—	1605	6	no	—
50	C₂×C₃	—	107	1	no	—
51	D₃	—	25	1	no	—
52	D₃	—	2675	1	no	—
53	C₅	D₁₅×D₁₀₇	1	6	yes	complemented
54	C₂²	—	8025	1	no	Sylow
55	C₃	C₅⋊D₅×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	75	1	no	—
57	C₂	—	8025	1	no	—
58	C₂	—	107	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²×C₁₀₇	C₂²
LCS	G ▷ C₃×C₅²×C₁₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×D₁₀₇	C₂	semidirect
2. C₁₀₇×C₃⋊(C₅⋊D₅)	C₂	semidirect
3. C₃⋊(C₅⋊D₅₃₅)	C₂	semidirect
5. C₃×C₅²×C₁₀₇	C₂²	semidirect
9. C₅²×D₁₀₇	D₃	semidirect
12. C₃×C₅×D₁₀₇	D₅	semidirect
13. C₅²×C₁₀₇	C₂×D₃	semidirect
15. C₃×C₅×C₁₀₇	C₂×D₅	semidirect
18. C₅×D₁₀₇	D₁₅	semidirect
21. C₃×D₁₀₇	C₅⋊D₅	semidirect
23. C₅×C₁₀₇	C₂×D₁₅	semidirect
25. C₃×C₁₀₇	C₂×C₅⋊D₅	semidirect
29. D₁₀₇	C₃⋊(C₅⋊D₅)	direct (N × H)
32. C₃⋊(C₅⋊D₅)	D₁₀₇	direct (N × H)
33. C₁₀₇	C₂×C₃⋊(C₅⋊D₅)	semidirect
35. C₃×C₅²	C₂×D₁₀₇	semidirect
43. C₅²	D₃×D₁₀₇	semidirect
45. C₃×C₅	D₅×D₁₀₇	semidirect
53. C₅	D₁₅×D₁₀₇	semidirect
55. C₃	C₅⋊D₅×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×D₁₀₇	2
C₁₀₇×C₃⋊(C₅⋊D₅)	2
C₃⋊(C₅⋊D₅₃₅)	2
C₅⋊D₅×D₁₀₇	3
D₁₅×D₁₀₇	5
C₂×C₃⋊(C₅⋊D₅)	107

Subgroups — C3⋊(C5⋊D5)×D107 #44545694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊D₅)×D₁₀₇ #44545694