Subgroups — C₂×C₄×D₈₅ #13062839

Order 1360.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₈₅	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₅×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×D₈₅	C₄	1	4	yes	direct product factor
7	C₂×D₈₅	C₂²	1	2	yes	—
8	C₄×C₅×C₁₇	C₂²	1	2	yes	complemented
9	Dic₈₅	C₂²	1	2	yes	complemented
10	C₂×C₄×D₁₇	—	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	D₈₅	C₂×C₄	1	4	yes	direct product factor
14	C₂²×D₁₇	—	5	1	no	—
15	C₂×C₄×C₁₇	D₅	1	1	yes	characteristic, complemented
16	C₂×Dic₁₇	—	5	1	no	—
17	C₄×D₁₇	—	5	4	no	—
18	C₅×C₁₇	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
19	C₂×C₄×D₅	—	17	1	no	maximal, Hall
20	C₂²×C₁₇	C₂×D₅	1	1	yes	characteristic
21	C₂×D₁₇	—	5	4	no	—
22	C₂×D₁₇	—	5	2	no	—
23	C₄×C₁₇	C₂×D₅	1	2	yes	complemented
24	Dic₁₇	—	5	2	no	—
25	C₂²×D₅	—	17	1	no	—
26	C₂×C₄×C₅	D₁₇	1	1	yes	characteristic, complemented
27	C₂×Dic₅	—	17	1	no	—
28	C₄×D₅	—	17	4	no	—
29	C₂×C₁₇	C₄×D₅	1	2	yes	complemented
30	C₂×C₁₇	C₂²×D₅	1	1	yes	characteristic
31	D₁₇	—	5	4	no	—
32	C₂²×C₅	C₂×D₁₇	1	1	yes	characteristic
33	C₂×D₅	—	17	4	no	—
34	C₂×D₅	—	17	2	no	—
35	C₄×C₅	C₂×D₁₇	1	2	yes	complemented
36	Dic₅	—	17	2	no	—
37	C₁₇	C₂×C₄×D₅	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	—	85	1	no	Sylow
39	C₂×C₅	C₄×D₁₇	1	2	yes	complemented
40	C₂×C₅	C₂²×D₁₇	1	1	yes	characteristic
41	D₅	—	17	4	no	—
42	C₂³	—	85	1	no	—
43	C₂×C₄	—	85	1	no	—
44	C₂×C₄	—	85	4	no	—
45	C₂×C₄	D₈₅	1	1	yes	characteristic, direct product factor
46	C₅	C₂×C₄×D₁₇	1	1	yes	characteristic, complemented, Sylow
47	C₂²	—	85	4	no	—
48	C₂²	—	85	2	no	—
49	C₂²	C₂×D₈₅	1	1	yes	characteristic
50	C₄	—	85	2	no	—
51	C₄	C₂×D₈₅	1	2	yes	direct product factor
52	C₂	—	85	4	no	—
53	C₂	C₄×D₈₅	1	2	yes	direct product factor
54	C₂	C₂²×D₈₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₈₅
commutator, hypocenter	C₅×C₁₇	C₂²×C₄
Frattini	C₂	C₂²×D₈₅
Fitting	C₂×C₄×C₅×C₁₇	C₂
socle	C₂²×C₅×C₁₇	C₂²
prime radical	C₂²×D₈₅	C₂
cosocle	C₂×C₅×C₁₇	C₂³
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂×C₄

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×Dic₈₅	C₂	semidirect
4. C₄×D₈₅	C₂	direct (N × H)
6. C₂×D₈₅	C₄	direct (N × H)
8. C₄×C₅×C₁₇	C₂²	semidirect
9. Dic₈₅	C₂²	semidirect
11. C₂×C₅×C₁₇	C₂×C₄	semidirect
13. D₈₅	C₂×C₄	direct (N × H)
15. C₂×C₄×C₁₇	D₅	semidirect
18. C₅×C₁₇	C₂²×C₄	semidirect
23. C₄×C₁₇	C₂×D₅	semidirect
26. C₂×C₄×C₅	D₁₇	semidirect
29. C₂×C₁₇	C₄×D₅	semidirect
35. C₄×C₅	C₂×D₁₇	semidirect
37. C₁₇	C₂×C₄×D₅	semidirect
39. C₂×C₅	C₄×D₁₇	semidirect
45. C₂×C₄	D₈₅	direct (N × H)
46. C₅	C₂×C₄×D₁₇	semidirect
51. C₄	C₂×D₈₅	direct (N × H)
53. C₂	C₄×D₈₅	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×D₈₅	2
C₂×C₄×C₅×C₁₇	2
C₂×Dic₈₅	2
C₄×D₈₅	2
C₂×C₄×D₁₇	5
C₂×C₄×D₅	17

Subgroups — C2×C4×D85 #13062839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₈₅ #13062839