Subgroups — C₃×D₅₄₁₅ #44570448

Order 32490.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₃₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₄₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₈₀₅	—	3	1	no	maximal
4	C₃×D₁₀₈₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₃₆₁	—	2	1	no	—
6	C₃×C₅×C₃₆₁	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₃₆₁	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₈₀₅	—	3	1	no	Hall
9	C₃²×C₃₆₁	D₅	1	1	yes	characteristic, complemented, Hall
10	D₁₀₈₃	—	5	1	no	—
11	C₃×D₃₆₁	—	15	1	no	—
12	C₅×C₃₆₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₂₈₅	—	19	1	no	maximal
14	C₃×C₃₆₁	—	2	1	no	—
15	C₃×C₃₆₁	C₃×D₅	1	1	yes	characteristic, complemented
16	C₃×C₃₆₁	D₁₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₁₉	D₁₉	1	1	yes	characteristic
18	D₃₆₁	—	15	1	no	Hall
19	D₂₈₅	—	19	1	no	—
20	C₃×D₉₅	—	57	1	no	—
21	C₃₆₁	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
22	C₃×D₅₇	—	95	1	no	—
23	C₃×C₅×C₁₉	—	2	1	no	—
24	C₃×C₅×C₁₉	C₃×D₁₉	1	1	yes	characteristic
25	C₃×C₅×C₁₉	D₅₇	1	1	yes	characteristic
26	D₉₅	—	57	1	no	—
27	C₃²×C₁₉	D₉₅	1	1	yes	characteristic
28	D₅₇	—	95	1	no	—
29	C₃×D₁₉	—	285	1	no	—
30	C₅×C₁₉	C₃×D₅₇	1	1	yes	characteristic
31	C₃×D₁₅	—	361	1	no	Hall
32	C₃×C₁₉	—	2	1	no	—
33	C₃×C₁₉	C₃×D₉₅	1	1	yes	characteristic
34	C₃×C₁₉	D₂₈₅	1	1	yes	characteristic
35	C₃²×C₅	D₃₆₁	1	1	yes	characteristic, complemented, Hall
36	D₁₉	—	285	1	no	—
37	D₁₅	—	361	1	no	—
38	C₃×D₅	—	1083	1	no	—
39	C₁₉	C₃×D₂₈₅	1	1	yes	characteristic
40	C₃×D₃	—	1805	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×D₃₆₁	1	1	yes	characteristic, complemented
43	C₃×C₅	D₁₀₈₃	1	1	yes	characteristic, complemented
44	D₅	—	1083	1	no	Hall
45	C₃²	D₁₈₀₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	5415	1	no	—
47	D₃	—	1805	1	no	—
48	C₅	C₃×D₁₀₈₃	1	1	yes	characteristic, complemented, Sylow
49	C₃	—	2	1	no	—
50	C₃	C₃×D₁₈₀₅	1	1	yes	characteristic, complemented
51	C₃	D₅₄₁₅	1	1	yes	characteristic, direct product factor
52	C₂	—	5415	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₄₁₅
commutator, cosocle, hypocenter	C₃×C₅×C₃₆₁	C₂×C₃
Frattini	C₁₉	C₃×D₂₈₅
Fitting	C₃²×C₅×C₃₆₁	C₂
socle	C₃²×C₅×C₁₉	D₁₉
LCS	G ▷ C₃×C₅×C₃₆₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₃₆₁	C₂	semidirect
2. D₅₄₁₅	C₃	direct (N × H)
6. C₃×C₅×C₃₆₁	D₃	semidirect
7. C₃×C₅×C₃₆₁	C₂×C₃	semidirect
9. C₃²×C₃₆₁	D₅	semidirect
12. C₅×C₃₆₁	C₃×D₃	semidirect
15. C₃×C₃₆₁	C₃×D₅	semidirect
16. C₃×C₃₆₁	D₁₅	semidirect
21. C₃₆₁	C₃×D₁₅	semidirect
35. C₃²×C₅	D₃₆₁	semidirect
42. C₃×C₅	C₃×D₃₆₁	semidirect
43. C₃×C₅	D₁₀₈₃	semidirect
45. C₃²	D₁₈₀₅	semidirect
48. C₅	C₃×D₁₀₈₃	semidirect
50. C₃	C₃×D₁₈₀₅	semidirect
51. C₃	D₅₄₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₃₆₁	2
D₅₄₁₅	3
C₃×D₁₈₀₅	3
C₃×D₁₀₈₃	5
C₃×D₂₈₅	19

Subgroups — C3×D5415 #44570448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₄₁₅ #44570448