Subgroups — C₃×C₅×Dic₅₃₅ #44545646

Order 32100.

64 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	C₅×Dic₅₃₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₀₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×Dic₅₃₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×Dic₁₀₇	—	5	1	no	maximal
6	C₂×C₅²×C₁₀₇	C₂×C₃	1	1	yes	characteristic
7	C₂×C₃×C₅×C₁₀₇	—	2	2	no	—
8	C₂×C₃×C₅×C₁₀₇	D₅	1	1	yes	characteristic
9	C₂×C₃×C₅×C₁₀₇	C₂×C₅	1	1	yes	characteristic
10	C₅²×C₁₀₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
11	Dic₅₃₅	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×Dic₁₀₇	—	5	1	no	—
13	C₃×C₅×C₁₀₇	—	2	2	no	—
14	C₃×C₅×C₁₀₇	Dic₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₁₀₇	C₄×C₅	1	1	yes	characteristic, complemented
16	C₃×Dic₁₀₇	—	5	1	no	Hall
17	C₂×C₅×C₁₀₇	—	2	2	no	—
18	C₂×C₅×C₁₀₇	C₃×D₅	1	1	yes	characteristic
19	C₂×C₅×C₁₀₇	C₂×C₃×C₅	1	1	yes	characteristic
20	C₂×C₃×C₁₀₇	C₅×D₅	1	1	yes	characteristic
21	C₅×C₁₀₇	—	2	2	no	—
22	C₅×C₁₀₇	C₃×Dic₅	1	1	yes	characteristic, complemented
23	C₅×C₁₀₇	C₃×C₄×C₅	1	1	yes	characteristic, complemented
24	Dic₁₀₇	—	5	1	no	Hall
25	C₃×C₁₀₇	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
26	C₃×C₅×Dic₅	—	107	1	no	maximal, Hall
27	C₂×C₁₀₇	C₃×C₅×D₅	1	1	yes	characteristic
28	C₂×C₃×C₅²	D₁₀₇	1	1	yes	characteristic
29	C₁₀₇	C₃×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
30	C₅×Dic₅	—	107	1	no	Hall
31	C₃×C₅²	Dic₁₀₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₄×C₅	—	535	1	no	—
33	C₃×Dic₅	—	107	1	no	—
34	C₂×C₅²	C₃×D₁₀₇	1	1	yes	characteristic
35	C₂×C₃×C₅	—	2	2	no	—
36	C₂×C₃×C₅	C₅×D₁₀₇	1	1	yes	characteristic
37	C₂×C₃×C₅	D₅₃₅	1	1	yes	characteristic
38	C₅²	C₃×Dic₁₀₇	1	1	yes	characteristic, complemented, Sylow
39	C₄×C₅	—	535	1	no	—
40	Dic₅	—	107	1	no	—
41	C₃×C₅	—	2	2	no	—
42	C₃×C₅	C₅×Dic₁₀₇	1	1	yes	characteristic, complemented
43	C₃×C₅	Dic₅₃₅	1	1	yes	characteristic, direct product factor
44	C₃×C₄	—	535	1	no	Hall
45	C₂×C₅	—	2	2	no	—
46	C₂×C₅	C₃×C₅×D₁₀₇	1	1	yes	characteristic
47	C₂×C₅	C₃×D₅₃₅	1	1	yes	characteristic
48	C₂×C₃	C₅×D₅₃₅	1	1	yes	characteristic
49	C₅	—	2	2	no	—
50	C₅	C₃×C₅×Dic₁₀₇	1	1	yes	characteristic, complemented
51	C₅	C₃×Dic₅₃₅	1	1	yes	characteristic, direct product factor
52	C₄	—	535	1	no	Sylow
53	C₃	C₅×Dic₅₃₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	C₃×C₅×D₅₃₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅	D₅₃₅
commutator, hypocenter	C₅×C₁₀₇	C₃×C₄×C₅
Frattini	C₂	C₃×C₅×D₅₃₅
Fitting, socle, prime radical	C₂×C₃×C₅²×C₁₀₇	C₂
cosocle	C₂×C₅×C₁₀₇	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₀₇
UCS	C₁ ◁ C₂×C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×Dic₅₃₅	C₃	direct (N × H)
3. C₃×C₅²×C₁₀₇	C₄	semidirect
4. C₃×Dic₅₃₅	C₅	direct (N × H)
10. C₅²×C₁₀₇	C₃×C₄	semidirect
11. Dic₅₃₅	C₃×C₅	direct (N × H)
14. C₃×C₅×C₁₀₇	Dic₅	semidirect
15. C₃×C₅×C₁₀₇	C₄×C₅	semidirect
22. C₅×C₁₀₇	C₃×Dic₅	semidirect
23. C₅×C₁₀₇	C₃×C₄×C₅	semidirect
25. C₃×C₁₀₇	C₅×Dic₅	semidirect
29. C₁₀₇	C₃×C₅×Dic₅	semidirect
31. C₃×C₅²	Dic₁₀₇	semidirect
38. C₅²	C₃×Dic₁₀₇	semidirect
42. C₃×C₅	C₅×Dic₁₀₇	semidirect
43. C₃×C₅	Dic₅₃₅	direct (N × H)
50. C₅	C₃×C₅×Dic₁₀₇	semidirect
51. C₅	C₃×Dic₅₃₅	direct (N × H)
53. C₃	C₅×Dic₅₃₅	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×C₃×C₅²×C₁₀₇	2
C₅×Dic₅₃₅	3
C₃×Dic₅₃₅	5
C₃×C₅×Dic₁₀₇	5
C₃×C₅×Dic₅	107

Subgroups — C3×C5×Dic535 #44545646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×Dic₅₃₅ #44545646