Subgroups — C₈×Dic₅₅ #13182425

Order 1760.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₅₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁⋊#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×Dic₅₅	C₄	1	2	yes	—
6	C₅×C₈×C₁₁	C₄	1	2	yes	complemented
7	C₁₁⋊#168	C₄	1	2	yes	complemented
8	C₈×Dic₁₁	—	5	1	no	maximal, Hall
9	C₂²×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₄×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
12	Dic₅₅	C₈	1	4	yes	direct product factor
13	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic
14	C₄×Dic₁₁	—	5	1	no	—
15	C₂×C₁₁⋊C₈	—	5	1	no	—
16	C₈×Dic₅	—	11	1	no	maximal, Hall
17	C₂×C₅×C₁₁	C₄²	1	1	yes	characteristic
18	C₂×C₅×C₁₁	C₂×C₈	1	2	yes	—
19	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
20	C₂×Dic₁₁	—	5	2	no	—
21	C₈×C₁₁	Dic₅	1	2	yes	complemented
22	C₁₁⋊C₈	—	5	2	no	—
23	C₂×C₅×C₈	D₁₁	1	1	yes	characteristic
24	C₄×Dic₅	—	11	1	no	—
25	C₂×#168	—	11	1	no	—
26	C₅×C₁₁	C₄×C₈	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₁₁	C₄×D₅	1	1	yes	characteristic
28	C₄×C₁₁	C₄×D₅	1	1	yes	characteristic
29	C₄×C₁₁	C₂×Dic₅	1	1	yes	characteristic
30	Dic₁₁	—	5	4	no	—
31	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
32	C₂×Dic₅	—	11	2	no	—
33	C₅×C₈	Dic₁₁	1	2	yes	complemented
34	#168	—	11	2	no	—
35	C₄×C₈	—	55	1	no	Sylow
36	C₂×C₁₁	C₈×D₅	1	2	yes	—
37	C₂×C₁₁	C₄×Dic₅	1	1	yes	characteristic
38	C₂²×C₅	C₄×D₁₁	1	1	yes	characteristic
39	C₄×C₅	C₄×D₁₁	1	1	yes	characteristic
40	C₄×C₅	C₂×Dic₁₁	1	1	yes	characteristic
41	Dic₅	—	11	4	no	—
42	C₂×C₈	—	55	1	no	—
43	C₂×C₈	D₅₅	1	1	yes	characteristic
44	C₄²	—	55	1	no	—
45	C₁₁	C₈×Dic₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₅	C₈×D₁₁	1	2	yes	—
47	C₂×C₅	C₄×Dic₁₁	1	1	yes	characteristic
48	C₂×C₄	—	55	2	no	—
49	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
50	C₈	—	55	2	no	—
51	C₈	Dic₅₅	1	2	yes	direct product factor
52	C₅	C₈×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
53	C₂²	C₄×D₅₅	1	1	yes	characteristic
54	C₄	—	55	4	no	—
55	C₄	C₄×D₅₅	1	1	yes	characteristic
56	C₄	C₂×Dic₅₅	1	1	yes	characteristic
57	C₂	C₈×D₅₅	1	2	yes	—
58	C₂	C₄×Dic₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	D₅₅
commutator, hypocenter	C₅×C₁₁	C₄×C₈
Frattini	C₂×C₄	C₂×D₅₅
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	C₂×C₄
cosocle	C₂×C₄×C₅×C₁₁	C₂²
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
6. C₅×C₈×C₁₁	C₄	semidirect
7. C₁₁⋊#168	C₄	semidirect
12. Dic₅₅	C₈	direct (N × H)
21. C₈×C₁₁	Dic₅	semidirect
26. C₅×C₁₁	C₄×C₈	semidirect
33. C₅×C₈	Dic₁₁	semidirect
45. C₁₁	C₈×Dic₅	semidirect
51. C₈	Dic₅₅	direct (N × H)
52. C₅	C₈×Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₈×C₁₁	2
C₄×Dic₅₅	2
C₂×C₁₁⋊#168	2
C₈×Dic₁₁	5
C₈×Dic₅	11

Subgroups — C8×Dic55 #13182425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×Dic₅₅ #13182425