Subgroups — C₂×C₁₇×C₃⋊((C₅⋊D₅)⋊C₃) #29505921

Order 15300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₇×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×C₃⋊((C₅⋊D₅)⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₇×C₃⋊(C₅⋊D₅)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×(C₅⋊D₅)⋊C₃	—	3	1	no	maximal
5	C₃×C₁₇×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₃⋊(C₅⋊D₅)	C₂×C₃	1	2	yes	complemented
7	C₂×C₁₇×C₅²⋊C₃	—	2	1	no	—
8	C₂×C₁₇×C₅²⋊C₃	D₃	1	1	yes	characteristic, complemented
9	C₁₇×(C₅⋊D₅)⋊C₃	—	3	2	no	—
10	C₂×C₃×C₅²×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₁₇×C₅⋊D₅	—	3	1	no	Hall
12	C₃×C₅²×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₇×C₅²⋊C₃	—	2	1	no	—
14	C₁₇×C₅²⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₁₇×D₁₅	—	15	2	no	—
16	C₂×C₃⋊((C₅⋊D₅)⋊C₃)	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₅²×C₁₇	C₃×D₃	1	1	yes	characteristic, complemented
18	C₁₇×C₅⋊D₅	—	3	2	no	—
19	C₂×C₃×D₃×C₁₇	—	25	1	no	maximal, Hall
20	C₂×C₃×C₅×C₁₇	—	3	2	no	—
21	C₁₇×D₁₅	—	15	4	no	—
22	C₂×C₃×C₅²⋊C₃	C₂×C₁₇	1	1	yes	characteristic, complemented
23	C₃⋊((C₅⋊D₅)⋊C₃)	C₂×C₁₇	1	2	yes	direct product factor
24	C₅²×C₁₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
25	C₂×D₅×C₁₇	—	45	2	no	—
26	C₂×C₃²×C₁₇	—	25	1	no	—
27	C₃×D₃×C₁₇	—	25	2	no	—
28	C₂×C₃⋊(C₅⋊D₅)	C₃×C₁₇	1	1	yes	characteristic, complemented
29	C₂×(C₅⋊D₅)⋊C₃	—	3	1	no	—
30	C₃×C₅×C₁₇	—	3	2	no	—
31	C₃×C₅²⋊C₃	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₃×C₁₇	—	75	1	no	—
33	C₂×D₃×C₁₇	—	25	1	no	—
34	C₂×C₅×C₁₇	—	3	2	no	—
35	D₅×C₁₇	—	45	4	no	—
36	C₃²×C₁₇	—	25	1	no	Hall
37	C₂×C₃×C₅²	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
38	C₃⋊(C₅⋊D₅)	C₂×C₃×C₁₇	1	2	yes	complemented
39	C₂×C₅²⋊C₃	—	2	1	no	—
40	C₂×C₅²⋊C₃	D₃×C₁₇	1	1	yes	characteristic, complemented
41	(C₅⋊D₅)⋊C₃	—	3	2	no	—
42	C₂×C₃×C₁₇	—	25	1	no	—
43	C₂×C₃×C₁₇	—	50	1	no	—
44	C₂×C₃×C₁₇	—	75	2	no	—
45	C₂×C₃×C₁₇	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
46	D₃×C₁₇	—	25	2	no	—
47	C₂×C₅⋊D₅	—	3	1	no	Hall
48	C₅×C₁₇	—	3	2	no	—
49	C₃×C₅²	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented
50	C₅²⋊C₃	—	2	1	no	—
51	C₅²⋊C₃	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
52	C₂²×C₁₇	—	75	1	no	Hall
53	C₂×D₁₅	—	15	2	no	—
54	C₃×C₁₇	—	25	1	no	—
55	C₃×C₁₇	—	50	1	no	—
56	C₃×C₁₇	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
57	C₂×C₅²	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented
58	C₅⋊D₅	—	3	2	no	—
59	C₂×C₃×D₃	—	25	1	no	Hall
60	C₂×C₁₇	—	75	2	no	—
61	C₂×C₁₇	C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor
62	C₂×C₃×C₅	—	3	2	no	—
63	D₁₅	—	15	4	no	—
64	C₅²	C₂×C₃×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
65	C₂×D₅	—	45	2	no	—
66	C₂×C₃²	—	25	1	no	—
67	C₃×D₃	—	25	2	no	—
68	C₁₇	C₂×C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor, Sylow
69	C₃×C₅	—	3	2	no	—
70	C₂²×C₃	—	75	1	no	—
71	C₂×D₃	—	25	1	no	—
72	C₂×C₅	—	3	2	no	—
73	D₅	—	45	4	no	—
74	C₃²	—	25	1	no	Sylow
75	C₂×C₃	—	25	1	no	—
76	C₂×C₃	—	50	1	no	—
77	C₂×C₃	—	75	2	no	—
78	C₂×C₃	C₁₇×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
79	D₃	—	25	2	no	—
80	C₅	—	3	2	no	—
81	C₂²	—	75	1	no	Sylow
82	C₃	—	25	1	no	—
83	C₃	—	50	1	no	—
84	C₃	C₂×C₁₇×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented
85	C₂	—	75	2	no	—
86	C₂	C₁₇×C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇	C₃⋊((C₅⋊D₅)⋊C₃)
commutator, cosocle, hypocenter	C₃×C₅²	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₁₇	C₂×C₃
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₂×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₇×C₅²⋊C₃	C₂	semidirect
2. C₁₇×C₃⋊((C₅⋊D₅)⋊C₃)	C₂	direct (N × H)
3. C₂×C₁₇×C₃⋊(C₅⋊D₅)	C₃	semidirect
5. C₃×C₁₇×C₅²⋊C₃	C₂²	semidirect
6. C₁₇×C₃⋊(C₅⋊D₅)	C₂×C₃	semidirect
8. C₂×C₁₇×C₅²⋊C₃	D₃	semidirect
10. C₂×C₃×C₅²×C₁₇	C₂×C₃	semidirect
12. C₃×C₅²×C₁₇	C₂²×C₃	semidirect
14. C₁₇×C₅²⋊C₃	C₂×D₃	semidirect
16. C₂×C₃⋊((C₅⋊D₅)⋊C₃)	C₁₇	direct (N × H)
17. C₂×C₅²×C₁₇	C₃×D₃	semidirect
22. C₂×C₃×C₅²⋊C₃	C₂×C₁₇	semidirect
23. C₃⋊((C₅⋊D₅)⋊C₃)	C₂×C₁₇	direct (N × H)
24. C₅²×C₁₇	C₂×C₃×D₃	semidirect
28. C₂×C₃⋊(C₅⋊D₅)	C₃×C₁₇	semidirect
31. C₃×C₅²⋊C₃	C₂²×C₁₇	semidirect
37. C₂×C₃×C₅²	C₂×C₃×C₁₇	semidirect
38. C₃⋊(C₅⋊D₅)	C₂×C₃×C₁₇	semidirect
40. C₂×C₅²⋊C₃	D₃×C₁₇	semidirect
45. C₂×C₃×C₁₇	(C₅⋊D₅)⋊C₃	semidirect
49. C₃×C₅²	C₂²×C₃×C₁₇	semidirect
51. C₅²⋊C₃	C₂×D₃×C₁₇	semidirect
56. C₃×C₁₇	C₂×(C₅⋊D₅)⋊C₃	semidirect
57. C₂×C₅²	C₃×D₃×C₁₇	semidirect
61. C₂×C₁₇	C₃⋊((C₅⋊D₅)⋊C₃)	direct (N × H)
64. C₅²	C₂×C₃×D₃×C₁₇	semidirect
68. C₁₇	C₂×C₃⋊((C₅⋊D₅)⋊C₃)	direct (N × H)
78. C₂×C₃	C₁₇×(C₅⋊D₅)⋊C₃	semidirect
84. C₃	C₂×C₁₇×(C₅⋊D₅)⋊C₃	semidirect
86. C₂	C₁₇×C₃⋊((C₅⋊D₅)⋊C₃)	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×C₁₇×C₅²⋊C₃	2
C₁₇×C₃⋊((C₅⋊D₅)⋊C₃)	2
C₂×C₁₇×C₃⋊(C₅⋊D₅)	3
C₂×C₁₇×(C₅⋊D₅)⋊C₃	3
C₂×C₃⋊((C₅⋊D₅)⋊C₃)	17
C₂×C₃×D₃×C₁₇	25

Subgroups — C2×C17×C3⋊((C5⋊D5)⋊C3) #29505921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₃⋊((C₅⋊D₅)⋊C₃) #29505921