Subgroups — C₂²⋊#66772 #13062790

Order 1360.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#66772	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×C₁₇	C₄	1	1	yes	characteristic, complemented
4	C₂×C₅×D₁₇	—	2	2	no	—
5	C₂×C₅×D₁₇	C₄	1	1	yes	characteristic, complemented
6	C₂×C₅×D₁₇	C₂²	1	1	yes	characteristic
7	#66772	—	2	2	no	—
8	C₂²⋊#595	—	5	1	no	maximal, Hall
9	C₂×C₅×C₁₇	—	2	1	no	—
10	C₂×C₅×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₅×D₁₇	—	2	1	no	—
12	C₅×D₁₇	D₄	1	2	yes	—
13	C₂²×D₁₇	D₅	1	1	yes	characteristic
14	C₂×#595	—	5	2	no	—
15	C₅×C₁₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
16	C₂²⋊Dic₅	—	17	1	no	maximal, Hall
17	C₂²×C₁₇	Dic₅	1	1	yes	characteristic, complemented
18	C₂×D₁₇	—	2	2	no	—
19	C₂×D₁₇	Dic₅	1	1	yes	characteristic, complemented
20	C₂×D₁₇	C₂×D₅	1	1	yes	characteristic
21	#595	—	10	2	no	—
22	C₂³×C₅	—	17	1	no	—
23	C₂×Dic₅	—	17	2	no	—
24	C₂×C₁₇	—	2	1	no	—
25	C₂×C₁₇	C₂×Dic₅	1	1	yes	characteristic
26	D₁₇	—	2	1	no	—
27	D₁₇	C₂²⋊D₅	1	2	yes	—
28	C₂²×C₅	—	17	1	no	—
29	C₂²×C₅	—	17	1	no	—
30	C₂²×C₅	—	34	2	no	—
31	C₂²×C₅	#595	1	1	yes	characteristic, complemented
32	Dic₅	—	34	2	no	—
33	C₁₇	C₂²⋊Dic₅	1	1	yes	characteristic, complemented, Sylow
34	C₂²⋊C₄	—	85	1	no	Sylow
35	C₂×C₅	—	2	1	no	—
36	C₂×C₅	—	17	2	no	—
37	C₂×C₅	—	34	1	no	—
38	C₂×C₅	C₂×#595	1	1	yes	characteristic
39	C₂³	—	17	1	no	—
40	C₂×C₄	—	85	2	no	—
41	C₅	C₂²⋊#595	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	17	1	no	—
43	C₂²	—	17	1	no	—
44	C₂²	—	34	2	no	—
45	C₂²	#66772	1	1	yes	characteristic, complemented
46	C₄	—	170	2	no	—
47	C₂	—	2	1	no	—
48	C₂	—	17	2	no	—
49	C₂	—	34	1	no	—
50	C₂	C₂×#66772	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#66772
commutator, socle	C₂×C₅×C₁₇	C₂×C₄
Fitting	C₂²×C₅×C₁₇	C₄
prime radical	C₂²×C₅×D₁₇	C₂
cosocle	C₂×C₅×D₁₇	C₂²
hypercenter	C₂²	#66772
hypocenter	C₅×C₁₇	C₂²⋊C₄
LCS	G ▷ C₂×C₅×C₁₇ ▷ C₅×C₁₇
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. C₂×#66772	C₂	semidirect
3. C₂²×C₅×C₁₇	C₄	semidirect
5. C₂×C₅×D₁₇	C₄	semidirect
15. C₅×C₁₇	C₂²⋊C₄	semidirect
17. C₂²×C₁₇	Dic₅	semidirect
19. C₂×D₁₇	Dic₅	semidirect
31. C₂²×C₅	#595	semidirect
33. C₁₇	C₂²⋊Dic₅	semidirect
41. C₅	C₂²⋊#595	semidirect
45. C₂²	#66772	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₁₇	2
C₂×#66772	2
C₂²⋊#595	5
C₂²⋊Dic₅	17

Subgroups — C22⋊#66772 #13062790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#66772 #13062790