Subgroups — #44545692

Order 32100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₆₀₅	C₂	1	2	yes	maximal, complemented
3	(C₅⋊D₅)⋊D₁₀₇	—	3	1	no	maximal, Hall
4	C₃×C₅²×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅×D₃₂₁	—	5	2	no	maximal
6	C₅⋊D₅×C₁₀₇	D₃	1	1	yes	characteristic, complemented
7	C₅×D₅₃₅	—	3	2	no	—
8	D₁₆₀₅	D₅	1	2	yes	complemented
9	C₅×D₃₂₁	—	5	2	no	—
10	C₃×D₅×C₁₀₇	—	5	2	no	—
11	C₃×D₅×C₁₀₇	—	10	2	no	—
12	C₅²×C₁₀₇	C₂×D₃	1	1	yes	characteristic, complemented, Hall
13	D₅×D₁₀₇	—	15	2	no	—
14	C₃×C₅×C₁₀₇	—	2	2	no	—
15	C₃×C₅×C₁₀₇	C₂×D₅	1	2	yes	complemented
16	C₂×D₃₂₁	—	25	1	no	Hall
17	D₅₃₅	—	3	2	no	—
18	C₅×D₁₀₇	—	15	2	no	—
19	D₅×C₁₀₇	—	5	2	no	—
20	D₅×C₁₀₇	—	10	2	no	—
21	C₂×C₃×C₁₀₇	—	25	1	no	—
22	D₃₂₁	—	5	2	no	—
23	C₅×C₁₀₇	—	2	2	no	—
24	C₅×C₁₀₇	D₃×D₅	1	2	yes	complemented
25	C₂×D₁₀₇	—	75	1	no	Hall
26	C₃×C₁₀₇	D₅²	1	1	yes	characteristic, complemented, Hall
27	D₁₅⋊D₅	—	107	1	no	maximal, Hall
28	C₂×C₁₀₇	—	25	1	no	—
29	D₁₀₇	—	15	2	no	—
30	C₅×D₁₅	—	107	2	no	—
31	C₃×C₅⋊D₅	D₁₀₇	1	1	yes	characteristic, complemented
32	C₁₀₇	D₁₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
33	D₅²	—	321	1	no	Hall
34	C₃×C₅²	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
35	D₃×D₅	—	535	2	no	—
36	C₅⋊D₅	D₃₂₁	1	1	yes	characteristic, complemented
37	C₅×D₅	—	321	2	no	—
38	D₁₅	—	107	2	no	—
39	C₃×D₅	—	5	2	no	—
40	C₃×D₅	—	10	2	no	—
41	C₅×D₃	—	535	2	no	—
42	C₅²	C₂×D₃₂₁	1	1	yes	characteristic, complemented, Sylow
43	C₂×D₅	—	1605	2	no	—
44	C₃×C₅	—	2	2	no	—
45	C₃×C₅	D₅×D₁₀₇	1	2	yes	complemented
46	C₂×D₃	—	2675	1	no	Hall
47	C₂×C₅	—	1605	2	no	—
48	D₅	—	5	2	no	—
49	D₅	—	10	2	no	—
50	D₅	—	321	2	no	—
51	C₂×C₃	—	25	1	no	—
52	D₃	—	535	2	no	—
53	C₅	—	2	2	no	—
54	C₅	D₅×D₃₂₁	1	2	yes	complemented
55	C₂²	—	8025	1	no	Sylow
56	C₃	(C₅⋊D₅)⋊D₁₀₇	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	25	1	no	—
58	C₂	—	1605	2	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×C₅⋊D₅×C₁₀₇	C₂	semidirect
2. C₅×D₁₆₀₅	C₂	semidirect
4. C₃×C₅²×C₁₀₇	C₂²	semidirect
6. C₅⋊D₅×C₁₀₇	D₃	semidirect
8. D₁₆₀₅	D₅	semidirect
12. C₅²×C₁₀₇	C₂×D₃	semidirect
15. C₃×C₅×C₁₀₇	C₂×D₅	semidirect
24. C₅×C₁₀₇	D₃×D₅	semidirect
26. C₃×C₁₀₇	D₅²	semidirect
31. C₃×C₅⋊D₅	D₁₀₇	semidirect
32. C₁₀₇	D₁₅⋊D₅	semidirect
34. C₃×C₅²	C₂×D₁₀₇	semidirect
36. C₅⋊D₅	D₃₂₁	semidirect
42. C₅²	C₂×D₃₂₁	semidirect
45. C₃×C₅	D₅×D₁₀₇	semidirect
54. C₅	D₅×D₃₂₁	semidirect
56. 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×C₅⋊D₅×C₁₀₇	2
C₅×D₁₆₀₅	2
(C₅⋊D₅)⋊D₁₀₇	3
D₅×D₃₂₁	5
D₁₅⋊D₅	107