Subgroups — C₄×D₅×D₁₇ #13062801

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₄×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#10621753	C₂	1	1	yes	maximal, characteristic, complemented
6	D₅×Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₅×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₈₅	C₂²	1	1	yes	characteristic
9	C₂×D₅×C₁₇	C₂²	1	1	yes	characteristic
10	C₂×C₅×D₁₇	C₂²	1	1	yes	characteristic
11	D₅×D₁₇	C₄	1	4	yes	direct product factor
12	C₄×C₅×C₁₇	C₂²	1	1	yes	characteristic, complemented
13	Dic₈₅	C₂²	1	1	yes	characteristic, complemented
14	C₅×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
15	C₁₇×Dic₅	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₄×D₁₇	—	5	1	no	maximal, Hall
17	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
18	D₈₅	C₂×C₄	1	2	yes	complemented
19	C₅×D₁₇	C₂×C₄	1	2	yes	complemented
20	D₅×C₁₇	C₂×C₄	1	2	yes	complemented
21	C₂²×D₁₇	—	5	1	no	—
22	C₂×C₄×C₁₇	—	5	1	no	—
23	C₂×Dic₁₇	—	5	1	no	—
24	C₄×D₁₇	—	5	1	no	—
25	C₄×D₁₇	—	5	1	no	—
26	C₄×D₁₇	—	5	1	no	—
27	C₄×D₁₇	D₅	1	1	yes	characteristic, direct product factor
28	C₅×C₁₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
29	C₂×C₄×D₅	—	17	1	no	maximal, Hall
30	C₂²×C₁₇	—	5	1	no	—
31	C₂×D₁₇	—	5	1	no	—
32	C₂×D₁₇	—	5	4	no	—
33	C₂×D₁₇	C₂×D₅	1	1	yes	characteristic
34	C₄×C₁₇	—	5	1	no	—
35	C₄×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented
36	Dic₁₇	—	5	1	no	—
37	Dic₁₇	C₂×D₅	1	1	yes	characteristic, complemented
38	C₂²×D₅	—	17	1	no	—
39	C₂×C₄×C₅	—	17	1	no	—
40	C₂×Dic₅	—	17	1	no	—
41	C₄×D₅	—	17	1	no	—
42	C₄×D₅	—	17	1	no	—
43	C₄×D₅	—	17	1	no	—
44	C₄×D₅	D₁₇	1	1	yes	characteristic, direct product factor
45	C₂×C₁₇	—	5	2	no	—
46	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
47	D₁₇	—	5	2	no	—
48	D₁₇	C₄×D₅	1	2	yes	direct product factor
49	C₂²×C₅	—	17	1	no	—
50	C₂×D₅	—	17	1	no	—
51	C₂×D₅	—	17	4	no	—
52	C₂×D₅	C₂×D₁₇	1	1	yes	characteristic
53	C₄×C₅	—	17	1	no	—
54	C₄×C₅	C₂×D₁₇	1	1	yes	characteristic, complemented
55	Dic₅	—	17	1	no	—
56	Dic₅	C₂×D₁₇	1	1	yes	characteristic, complemented
57	C₁₇	C₂×C₄×D₅	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₄	—	85	1	no	Sylow
59	C₂×C₅	—	17	2	no	—
60	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
61	D₅	—	17	2	no	—
62	D₅	C₄×D₁₇	1	2	yes	direct product factor
63	C₂³	—	85	1	no	—
64	C₂×C₄	—	5	1	no	—
65	C₂×C₄	—	17	1	no	—
66	C₂×C₄	—	85	1	no	—
67	C₂×C₄	—	85	1	no	—
68	C₂×C₄	—	85	1	no	—
69	C₂×C₄	—	85	1	no	—
70	C₅	C₂×C₄×D₁₇	1	1	yes	characteristic, complemented, Sylow
71	C₂²	—	5	1	no	—
72	C₂²	—	17	1	no	—
73	C₂²	—	85	4	no	—
74	C₂²	—	85	1	no	—
75	C₄	—	5	1	no	—
76	C₄	—	17	1	no	—
77	C₄	—	85	1	no	—
78	C₄	D₅×D₁₇	1	1	yes	characteristic, direct product factor
79	C₂	—	5	2	no	—
80	C₂	—	17	2	no	—
81	C₂	—	85	2	no	—
82	C₂	C₂×D₅×D₁₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₅×D₁₇
commutator, hypocenter	C₅×C₁₇	C₂²×C₄
Frattini	C₂	C₂×D₅×D₁₇
Fitting	C₄×C₅×C₁₇	C₂²
socle, cosocle	C₂×C₅×C₁₇	C₂³
prime radical	C₂×D₅×D₁₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₄×D₈₅	C₂	semidirect
3. C₄×D₅×C₁₇	C₂	semidirect
4. C₄×C₅×D₁₇	C₂	semidirect
5. #10621753	C₂	semidirect
6. D₅×Dic₁₇	C₂	semidirect
7. Dic₅×D₁₇	C₂	semidirect
11. D₅×D₁₇	C₄	direct (N × H)
12. C₄×C₅×C₁₇	C₂²	semidirect
13. Dic₈₅	C₂²	semidirect
14. C₅×Dic₁₇	C₂²	semidirect
15. C₁₇×Dic₅	C₂²	semidirect
18. D₈₅	C₂×C₄	semidirect
19. C₅×D₁₇	C₂×C₄	semidirect
20. D₅×C₁₇	C₂×C₄	semidirect
27. C₄×D₁₇	D₅	direct (N × H)
28. C₅×C₁₇	C₂²×C₄	semidirect
35. C₄×C₁₇	C₂×D₅	semidirect
37. Dic₁₇	C₂×D₅	semidirect
44. C₄×D₅	D₁₇	direct (N × H)
48. D₁₇	C₄×D₅	direct (N × H)
54. C₄×C₅	C₂×D₁₇	semidirect
56. Dic₅	C₂×D₁₇	semidirect
57. C₁₇	C₂×C₄×D₅	semidirect
62. D₅	C₄×D₁₇	direct (N × H)
70. C₅	C₂×C₄×D₁₇	semidirect
78. C₄	D₅×D₁₇	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×D₅×D₁₇	2
C₄×D₈₅	2
C₄×D₅×C₁₇	2
C₄×C₅×D₁₇	2
#10621753	2
D₅×Dic₁₇	2
Dic₅×D₁₇	2
C₂×C₄×D₁₇	5
C₂×C₄×D₅	17

Subgroups — C4×D5×D17 #13062801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₅×D₁₇ #13062801