Subgroups — D₁₅×D₄₁₇ #38736282

Order 25020.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₀₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₄₁₇	—	3	1	no	maximal
5	D₁₅×D₁₃₉	—	3	1	no	maximal
6	C₃²×C₅×C₁₃₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₄₁₇	—	5	1	no	maximal, Hall
8	D₂₀₈₅	—	3	1	no	—
9	D₂₀₈₅	—	3	1	no	—
10	D₂₀₈₅	—	6	1	no	—
11	D₁₅×C₁₃₉	D₃	1	1	yes	characteristic, complemented
12	C₅×D₄₁₇	D₃	1	1	yes	characteristic, complemented
13	C₃×D₅×C₁₃₉	—	3	1	no	—
14	C₃×C₅×D₁₃₉	—	3	1	no	—
15	D₅×D₁₃₉	—	9	1	no	Hall
16	C₃⋊D₄₁₇	—	5	1	no	—
17	C₃×D₄₁₇	D₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₁₃₉	—	5	1	no	—
19	C₃×C₅×C₁₃₉	—	2	1	no	—
20	C₃×C₅×C₁₃₉	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₁₃₉	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₄₁₇	—	15	1	no	—
23	D₃×D₁₃₉	—	15	1	no	—
24	D₆₉₅	—	9	1	no	—
25	C₅×D₁₃₉	—	3	1	no	—
26	D₅×C₁₃₉	—	3	1	no	—
27	C₃²×C₁₃₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃₉	—	15	1	no	—
29	D₄₁₇	—	15	1	no	—
30	D₄₁₇	—	15	1	no	—
31	D₄₁₇	—	30	1	no	—
32	D₄₁₇	D₁₅	1	1	yes	characteristic, direct product factor
33	C₃×D₁₃₉	—	3	1	no	—
34	D₃×C₁₃₉	—	5	1	no	—
35	C₅×C₁₃₉	D₃²	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₃₉	—	45	1	no	Hall
37	C₃×C₁₃₉	—	2	1	no	—
38	C₃×C₁₃₉	D₃×D₅	1	1	yes	characteristic, complemented
39	C₃×C₁₃₉	C₂×D₁₅	1	1	yes	characteristic, complemented
40	C₂×C₁₃₉	—	15	1	no	—
41	D₁₃₉	—	3	1	no	—
42	D₁₃₉	—	45	1	no	—
43	D₃×D₁₅	—	139	1	no	maximal, Hall
44	C₁₃₉	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
45	C₃⋊D₁₅	—	139	1	no	—
46	C₃×D₁₅	D₁₃₉	1	1	yes	characteristic, complemented
47	C₃×C₅×D₃	—	139	1	no	—
48	C₂×D₁₅	—	417	1	no	—
49	D₃×D₅	—	417	1	no	—
50	C₃²×C₅	C₂×D₁₃₉	1	1	yes	characteristic, complemented, Hall
51	D₃²	—	695	1	no	Hall
52	C₂×C₃×C₅	—	417	1	no	—
53	D₁₅	—	834	1	no	—
54	D₁₅	—	417	1	no	—
55	D₁₅	—	417	1	no	—
56	D₁₅	D₄₁₇	1	1	yes	characteristic, direct product factor
57	C₃×D₅	—	3	1	no	—
58	C₅×D₃	—	139	1	no	—
59	C₂×D₅	—	1251	1	no	Hall
60	C₃⋊D₃	—	695	1	no	—
61	C₃×D₃	—	5	1	no	—
62	C₃×D₃	—	139	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₁₃₉	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₄₁₇	1	1	yes	characteristic, complemented
66	C₂×D₃	—	2085	1	no	—
67	C₂×D₃	—	2085	1	no	—
68	C₂×C₅	—	417	1	no	—
69	D₅	—	3	1	no	—
70	D₅	—	1251	1	no	—
71	C₃²	D₅×D₁₃₉	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	15	1	no	—
73	C₂×C₃	—	417	1	no	—
74	D₃	—	5	1	no	—
75	D₃	—	2085	1	no	—
76	D₃	—	2085	1	no	—
77	D₃	—	4170	1	no	—
78	D₃	—	139	1	no	—
79	C₅	D₃×D₄₁₇	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	6255	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₅×D₁₃₉	1	1	yes	characteristic, complemented
83	C₃	D₅×D₄₁₇	1	1	yes	characteristic, complemented
84	C₂	—	15	1	no	—
85	C₂	—	6255	1	no	—
86	C₂	—	417	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₃₉	C₂²
LCS	G ▷ C₃²×C₅×C₁₃₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₄₁₇	C₂	semidirect
2. C₃×D₁₅×C₁₃₉	C₂	semidirect
3. C₃⋊D₂₀₈₅	C₂	semidirect
6. C₃²×C₅×C₁₃₉	C₂²	semidirect
11. D₁₅×C₁₃₉	D₃	semidirect
12. C₅×D₄₁₇	D₃	semidirect
17. C₃×D₄₁₇	D₅	semidirect
20. C₃×C₅×C₁₃₉	C₂×D₃	semidirect
21. C₃×C₅×C₁₃₉	C₂×D₃	semidirect
27. C₃²×C₁₃₉	C₂×D₅	semidirect
32. D₄₁₇	D₁₅	direct (N × H)
35. C₅×C₁₃₉	D₃²	semidirect
38. C₃×C₁₃₉	D₃×D₅	semidirect
39. C₃×C₁₃₉	C₂×D₁₅	semidirect
44. C₁₃₉	D₃×D₁₅	semidirect
46. C₃×D₁₅	D₁₃₉	semidirect
50. C₃²×C₅	C₂×D₁₃₉	semidirect
56. D₁₅	D₄₁₇	direct (N × H)
64. C₃×C₅	D₃×D₁₃₉	semidirect
65. C₃×C₅	C₂×D₄₁₇	semidirect
71. C₃²	D₅×D₁₃₉	semidirect
79. C₅	D₃×D₄₁₇	semidirect
82. C₃	D₁₅×D₁₃₉	semidirect
83. C₃	D₅×D₄₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₄₁₇	2
C₃×D₁₅×C₁₃₉	2
C₃⋊D₂₀₈₅	2
D₅×D₄₁₇	3
D₁₅×D₁₃₉	3
D₃×D₄₁₇	5
D₃×D₁₅	139

Subgroups — D15×D417 #38736282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×D₄₁₇ #38736282