Subgroups — D₁₅×D₁₀₉⋊C₃ #34087134

Order 19620.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(C₅⋊(D₁₀₉⋊C₃))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅×D₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented
5	D₅×D₁₀₉⋊C₃	—	3	1	no	maximal
6	C₃×C₅×C₁₀₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₁₀₉⋊C₃	—	5	1	no	maximal, Hall
8	C₅⋊(D₁₀₉⋊C₃)	—	3	1	no	—
9	D₅×C₁₀₉⋊C₃	—	3	1	no	—
10	C₅×D₁₀₉⋊C₃	—	2	1	no	—
11	C₅×D₁₀₉⋊C₃	D₃	1	1	yes	characteristic, complemented
12	D₁₆₃₅	C₂×C₃	1	1	yes	characteristic, complemented
13	D₁₅×C₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₅×D₁₀₉	C₂×C₃	1	1	yes	characteristic, complemented
15	D₅×D₁₀₉	—	3	1	no	Hall
16	C₃⋊(D₁₀₉⋊C₃)	—	5	1	no	—
17	D₃×C₁₀₉⋊C₃	—	5	1	no	—
18	C₃×D₁₀₉⋊C₃	D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₁₀₉	C₂²×C₃	1	1	yes	characteristic, complemented
20	C₅×C₁₀₉⋊C₃	—	2	1	no	—
21	C₅×C₁₀₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
22	D₃×D₁₀₉	—	5	1	no	—
23	C₂×D₁₀₉⋊C₃	—	15	1	no	—
24	D₅₄₅	—	3	1	no	—
25	C₅×D₁₀₉	C₃×D₃	1	1	yes	characteristic, complemented
26	D₅×C₁₀₉	—	3	1	no	—
27	C₃×C₁₀₉⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	D₃₂₇	—	5	1	no	—
29	C₃×D₁₀₉	C₃×D₅	1	1	yes	characteristic, complemented
30	D₃×C₁₀₉	—	5	1	no	—
31	C₂×C₁₀₉⋊C₃	—	15	1	no	—
32	D₁₀₉⋊C₃	—	2	1	no	—
33	D₁₀₉⋊C₃	—	15	1	no	—
34	D₁₀₉⋊C₃	D₁₅	1	1	yes	characteristic, direct product factor
35	C₅×C₁₀₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₀₉	—	15	1	no	Hall
37	C₃×C₁₀₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
38	C₁₀₉⋊C₃	—	2	1	no	—
39	C₁₀₉⋊C₃	C₂×D₁₅	1	1	yes	characteristic, complemented
40	C₂×C₁₀₉	—	15	1	no	—
41	D₁₀₉	—	15	1	no	—
42	D₁₀₉	C₃×D₁₅	1	1	yes	characteristic, complemented
43	C₂×C₃×D₁₅	—	109	1	no	maximal, Hall
44	C₁₀₉	C₂×C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃²×C₅	—	109	1	no	—
46	C₃×D₁₅	—	109	1	no	—
47	C₃×D₁₅	—	218	1	no	—
48	C₂×D₁₅	—	109	1	no	—
49	C₂×C₃×D₅	—	327	1	no	—
50	C₃²×C₅	—	218	1	no	Hall
51	C₂×C₃×D₃	—	545	1	no	Hall
52	C₂×C₃×C₅	—	109	1	no	—
53	C₂×C₃×C₅	—	109	1	no	—
54	C₂×C₃×C₅	—	218	1	no	—
55	D₁₅	—	109	1	no	—
56	D₁₅	D₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor
57	C₃×D₅	—	327	1	no	—
58	C₃×D₅	—	654	1	no	—
59	C₂×D₅	—	327	1	no	Hall
60	C₂×C₃²	—	109	1	no	—
61	C₃×D₃	—	545	1	no	—
62	C₃×D₃	—	1090	1	no	—
63	C₃×C₅	—	436	1	no	—
64	C₃×C₅	—	218	1	no	—
65	C₃×C₅	C₂×D₁₀₉⋊C₃	1	1	yes	characteristic, complemented
66	C₂²×C₃	—	1635	1	no	—
67	C₂×D₃	—	545	1	no	—
68	C₂×C₅	—	109	1	no	—
69	D₅	—	3	1	no	—
70	D₅	—	327	1	no	—
71	C₃²	—	218	1	no	Sylow
72	C₂×C₃	—	1635	1	no	—
73	C₂×C₃	—	109	1	no	—
74	C₂×C₃	—	109	1	no	—
75	C₂×C₃	—	3270	1	no	—
76	C₂×C₃	—	218	1	no	—
77	D₃	—	5	1	no	—
78	D₃	—	545	1	no	—
79	C₅	D₃×D₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	1635	1	no	Sylow
81	C₃	—	436	1	no	—
82	C₃	—	218	1	no	—
83	C₃	D₅×D₁₀₉⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	15	1	no	—
85	C₂	—	1635	1	no	—
86	C₂	—	109	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₀₉	C₂²×C₃
LCS	G ▷ C₃×C₅×C₁₀₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₁₅×C₁₀₉⋊C₃	C₂	semidirect
2. C₃⋊(C₅⋊(D₁₀₉⋊C₃))	C₂	semidirect
3. C₃×C₅×D₁₀₉⋊C₃	C₂	semidirect
4. D₁₅×D₁₀₉	C₃	semidirect
6. C₃×C₅×C₁₀₉⋊C₃	C₂²	semidirect
11. C₅×D₁₀₉⋊C₃	D₃	semidirect
12. D₁₆₃₅	C₂×C₃	semidirect
13. D₁₅×C₁₀₉	C₂×C₃	semidirect
14. C₃×C₅×D₁₀₉	C₂×C₃	semidirect
18. C₃×D₁₀₉⋊C₃	D₅	semidirect
19. C₃×C₅×C₁₀₉	C₂²×C₃	semidirect
21. C₅×C₁₀₉⋊C₃	C₂×D₃	semidirect
25. C₅×D₁₀₉	C₃×D₃	semidirect
27. C₃×C₁₀₉⋊C₃	C₂×D₅	semidirect
29. C₃×D₁₀₉	C₃×D₅	semidirect
34. D₁₀₉⋊C₃	D₁₅	direct (N × H)
35. C₅×C₁₀₉	C₂×C₃×D₃	semidirect
37. C₃×C₁₀₉	C₂×C₃×D₅	semidirect
39. C₁₀₉⋊C₃	C₂×D₁₅	semidirect
42. D₁₀₉	C₃×D₁₅	semidirect
44. C₁₀₉	C₂×C₃×D₁₅	semidirect
56. D₁₅	D₁₀₉⋊C₃	direct (N × H)
65. C₃×C₅	C₂×D₁₀₉⋊C₃	semidirect
79. C₅	D₃×D₁₀₉⋊C₃	semidirect
83. C₃	D₅×D₁₀₉⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×C₁₀₉⋊C₃	2
C₃⋊(C₅⋊(D₁₀₉⋊C₃))	2
C₃×C₅×D₁₀₉⋊C₃	2
D₁₅×D₁₀₉	3
D₅×D₁₀₉⋊C₃	3
D₃×D₁₀₉⋊C₃	5
C₂×C₃×D₁₅	109

Subgroups — D15×D109⋊C3 #34087134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×D₁₀₉⋊C₃ #34087134