Subgroups — C₂×C₄×D₅×C₁₇ #13062829

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₅×C₁₇	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×D₅×C₁₇	C₄	1	4	yes	direct product factor
7	C₂×D₅×C₁₇	C₂²	1	2	yes	—
8	C₄×C₅×C₁₇	C₂²	1	2	yes	complemented
9	C₁₇×Dic₅	C₂²	1	2	yes	complemented
10	C₂²×C₄×C₁₇	—	5	1	no	maximal, Hall
11	C₂×C₅×C₁₇	C₂×C₄	1	2	yes	complemented
12	C₂×C₅×C₁₇	C₂³	1	1	yes	characteristic
13	D₅×C₁₇	C₂×C₄	1	4	yes	direct product factor
14	C₂³×C₁₇	—	5	1	no	—
15	C₂×C₄×C₁₇	—	5	1	no	—
16	C₂×C₄×C₁₇	—	5	4	no	—
17	C₂×C₄×C₁₇	D₅	1	1	yes	characteristic, direct product factor
18	C₅×C₁₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₂×C₄×D₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₁₇	—	5	4	no	—
21	C₂²×C₁₇	—	5	2	no	—
22	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
23	C₄×C₁₇	—	5	2	no	—
24	C₄×C₁₇	C₂×D₅	1	2	yes	direct product factor
25	C₂²×D₅	C₂×C₁₇	1	1	yes	characteristic
26	C₂×C₄×C₅	C₂×C₁₇	1	1	yes	characteristic, complemented
27	C₂×Dic₅	C₂×C₁₇	1	1	yes	characteristic, complemented
28	C₄×D₅	C₂×C₁₇	1	4	yes	direct product factor
29	C₂×C₁₇	—	5	4	no	—
30	C₂×C₁₇	C₄×D₅	1	2	yes	direct product factor
31	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
32	C₂²×C₅	C₂²×C₁₇	1	1	yes	characteristic
33	C₂×D₅	C₄×C₁₇	1	4	yes	direct product factor
34	C₂×D₅	C₂²×C₁₇	1	2	yes	—
35	C₄×C₅	C₂²×C₁₇	1	2	yes	complemented
36	Dic₅	C₂²×C₁₇	1	2	yes	complemented
37	C₁₇	C₂×C₄×D₅	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²×C₄	—	5	1	no	Sylow
39	C₂×C₅	C₂×C₄×C₁₇	1	2	yes	complemented
40	C₂×C₅	C₂³×C₁₇	1	1	yes	characteristic
41	D₅	C₂×C₄×C₁₇	1	4	yes	direct product factor
42	C₂³	—	5	1	no	—
43	C₂×C₄	—	5	1	no	—
44	C₂×C₄	—	5	4	no	—
45	C₂×C₄	D₅×C₁₇	1	1	yes	characteristic, direct product factor
46	C₅	C₂²×C₄×C₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	5	4	no	—
48	C₂²	—	5	2	no	—
49	C₂²	C₂×D₅×C₁₇	1	1	yes	characteristic
50	C₄	—	5	2	no	—
51	C₄	C₂×D₅×C₁₇	1	2	yes	direct product factor
52	C₂	—	5	4	no	—
53	C₂	C₄×D₅×C₁₇	1	2	yes	direct product factor
54	C₂	C₂²×D₅×C₁₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×C₁₇	C₂	semidirect
3. C₂×C₁₇×Dic₅	C₂	semidirect
4. C₄×D₅×C₁₇	C₂	direct (N × H)
6. C₂×D₅×C₁₇	C₄	direct (N × H)
8. C₄×C₅×C₁₇	C₂²	semidirect
9. C₁₇×Dic₅	C₂²	semidirect
11. C₂×C₅×C₁₇	C₂×C₄	semidirect
13. D₅×C₁₇	C₂×C₄	direct (N × H)
17. C₂×C₄×C₁₇	D₅	direct (N × H)
18. C₅×C₁₇	C₂²×C₄	semidirect
19. C₂×C₄×D₅	C₁₇	direct (N × H)
24. C₄×C₁₇	C₂×D₅	direct (N × H)
26. C₂×C₄×C₅	C₂×C₁₇	semidirect
27. C₂×Dic₅	C₂×C₁₇	semidirect
28. C₄×D₅	C₂×C₁₇	direct (N × H)
30. C₂×C₁₇	C₄×D₅	direct (N × H)
33. C₂×D₅	C₄×C₁₇	direct (N × H)
35. C₄×C₅	C₂²×C₁₇	semidirect
36. Dic₅	C₂²×C₁₇	semidirect
37. C₁₇	C₂×C₄×D₅	direct (N × H)
39. C₂×C₅	C₂×C₄×C₁₇	semidirect
41. D₅	C₂×C₄×C₁₇	direct (N × H)
45. C₂×C₄	D₅×C₁₇	direct (N × H)
46. C₅	C₂²×C₄×C₁₇	semidirect
51. C₄	C₂×D₅×C₁₇	direct (N × H)
53. C₂	C₄×D₅×C₁₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₅×C₁₇	2
C₂×C₄×C₅×C₁₇	2
C₂×C₁₇×Dic₅	2
C₄×D₅×C₁₇	2
C₂²×C₄×C₁₇	5
C₂×C₄×D₅	17

Subgroups — C2×C4×D5×C17 #13062829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₅×C₁₇ #13062829