Subgroups — C₄×C₅×Dic₂₂ #13182995

Order 1760.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	C₄²×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	C₅×Dic₁₁⋊C₄	C₂	1	2	yes	maximal
5	C₄×C₅×Dic₁₁	C₂	1	2	yes	maximal
6	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₁₁	C₂²	1	2	yes	—
10	C₂×C₅×Dic₁₁	C₂²	1	2	yes	—
11	C₅×Dic₂₂	C₄	1	4	yes	direct product factor
12	C₄×Dic₂₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₅×C₁₁	C₂³	1	1	yes	characteristic
14	C₄×C₅×C₁₁	—	2	1	no	—
15	C₄×C₅×C₁₁	C₂×C₄	1	2	yes	—
16	C₄×C₅×C₁₁	Q₈	1	2	yes	complemented
17	C₅×Dic₁₁	—	2	2	no	—
18	C₅×Dic₁₁	C₂×C₄	1	4	yes	—
19	C₂×Dic₂₂	C₂×C₅	1	1	yes	characteristic
20	C₄²×C₁₁	C₂×C₅	1	1	yes	characteristic
21	C₄⋊Dic₁₁	C₂×C₅	1	1	yes	characteristic
22	Dic₁₁⋊C₄	C₂×C₅	1	2	yes	—
23	C₄×Dic₁₁	C₂×C₅	1	2	yes	—
24	C₄×C₅×Q₈	—	11	1	no	maximal, Hall
25	C₂×C₅×C₁₁	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₅×C₁₁	C₂×Q₈	1	1	yes	characteristic
27	C₂×C₅×C₁₁	#41	1	1	yes	characteristic
28	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
29	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
30	C₂×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
31	C₂×Dic₁₁	C₂²×C₅	1	2	yes	—
32	C₂×Dic₁₁	C₂²×C₅	1	2	yes	—
33	Dic₂₂	C₄×C₅	1	4	yes	direct product factor
34	C₂×C₅×Q₈	—	11	1	no	—
35	C₅×C₄⋊C₄	—	11	2	no	—
36	C₅×C₄⋊C₄	—	11	1	no	—
37	C₄²×C₅	—	11	2	no	—
38	C₄²×C₅	D₁₁	1	1	yes	characteristic
39	C₅×C₁₁	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
41	C₄×C₁₁	—	2	1	no	—
42	C₄×C₁₁	C₂×C₄×C₅	1	2	yes	—
43	C₄×C₁₁	C₅×Q₈	1	2	yes	complemented
44	Dic₁₁	—	2	2	no	—
45	Dic₁₁	C₂×C₄×C₅	1	4	yes	—
46	C₅×Q₈	—	11	4	no	—
47	C₂×C₄×C₅	—	11	2	no	—
48	C₂×C₄×C₅	—	11	2	no	—
49	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
50	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
51	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
52	C₄×Q₈	—	11	1	no	Sylow
53	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
54	C₂×C₁₁	C₂×C₅×Q₈	1	1	yes	characteristic
55	C₂×C₁₁	C₅×#41	1	1	yes	characteristic
56	C₂²×C₅	C₂²×D₁₁	1	1	yes	characteristic
57	C₄×C₅	—	2	1	no	—
58	C₄×C₅	—	11	4	no	—
59	C₄×C₅	—	22	2	no	—
60	C₄×C₅	Dic₂₂	1	2	yes	direct product factor
61	C₄×C₅	C₄×D₁₁	1	2	yes	—
62	C₂×Q₈	—	11	1	no	—
63	C₄⋊C₄	—	11	2	no	—
64	C₄⋊C₄	—	11	1	no	—
65	C₄²	—	11	2	no	—
66	C₄²	C₅×D₁₁	1	1	yes	characteristic
67	C₁₁	C₄×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₅	C₂×Dic₂₂	1	1	yes	characteristic
69	C₂×C₅	C₂×C₄×D₁₁	1	1	yes	characteristic
70	C₂×C₅	#4339	1	1	yes	characteristic
71	Q₈	—	11	4	no	—
72	C₂×C₄	—	11	2	no	—
73	C₂×C₄	—	11	2	no	—
74	C₂×C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
75	C₂×C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
76	C₂×C₄	C₂×C₅×D₁₁	1	1	yes	characteristic
77	C₅	C₄×Dic₂₂	1	1	yes	characteristic, direct product factor, Sylow
78	C₂²	C₂²×C₅×D₁₁	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	11	4	no	—
81	C₄	—	22	2	no	—
82	C₄	C₅×Dic₂₂	1	2	yes	direct product factor
83	C₄	C₄×C₅×D₁₁	1	2	yes	—
84	C₂	C₂×C₅×Dic₂₂	1	1	yes	characteristic
85	C₂	C₂×C₄×C₅×D₁₁	1	1	yes	characteristic
86	C₂	C₅×#4339	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₅
Frattini	C₂²	C₂²×C₅×D₁₁
Fitting	C₄²×C₅×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	C₂³
cosocle	C₂²×C₁₁	C₂³×C₅
hypercenter	C₄²×C₅	D₁₁
hypocenter	C₁₁	C₄×C₅×Q₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
11. C₅×Dic₂₂	C₄	direct (N × H)
12. C₄×Dic₂₂	C₅	direct (N × H)
16. C₄×C₅×C₁₁	Q₈	semidirect
33. Dic₂₂	C₄×C₅	direct (N × H)
39. C₅×C₁₁	C₄×Q₈	semidirect
43. C₄×C₁₁	C₅×Q₈	semidirect
60. C₄×C₅	Dic₂₂	direct (N × H)
67. C₁₁	C₄×C₅×Q₈	semidirect
77. C₅	C₄×Dic₂₂	direct (N × H)
82. C₄	C₅×Dic₂₂	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×C₅×Dic₂₂	2
C₄²×C₅×C₁₁	2
C₅×C₄⋊Dic₁₁	2
C₅×Dic₁₁⋊C₄	2
C₄×C₅×Dic₁₁	2
C₄×Dic₂₂	5
C₄×C₅×Q₈	11

Subgroups — C4×C5×Dic22 #13182995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×Dic₂₂ #13182995