Subgroups — C₅×C₄⋊#1044 #14522798

Order 2000.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1044	C₂	1	2	yes	maximal
2	C₄×C₅×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₅⋊D₅	C₂²	1	1	yes	characteristic
4	C₅×#1044	—	2	2	no	—
5	C₄×C₅³	C₄	1	1	yes	characteristic, complemented
6	C₅×#1039	C₄	1	1	yes	characteristic, complemented
7	C₄⋊#1044	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×C₄⋊AGL(1,𝔽₅)	—	5	2	no	maximal
9	C₂×C₅³	C₂×C₄	1	1	yes	characteristic
10	C₅×C₅⋊D₅	D₄	1	1	yes	characteristic
11	C₅×C₅⋊D₅	Q₈	1	1	yes	characteristic
12	C₂×#1044	C₂×C₅	1	2	yes	—
13	C₂×C₅×AGL(1,𝔽₅)	—	5	4	no	—
14	C₄×C₅⋊D₅	C₂×C₅	1	1	yes	characteristic
15	C₄×C₅×D₅	—	5	2	no	—
16	C₄×C₅×D₅	—	10	2	no	—
17	C₅³	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₅⋊D₅	C₂²×C₅	1	1	yes	characteristic
19	C₂×C₅×D₅	—	5	2	no	—
20	C₂×C₅×D₅	—	10	2	no	—
21	#1044	—	2	2	no	—
22	C₅×AGL(1,𝔽₅)	—	10	4	no	—
23	C₄×C₅²	—	2	2	no	—
24	C₄×C₅²	—	4	4	no	—
25	C₄×C₅²	—	4	2	no	—
26	C₄×C₅²	C₄×C₅	1	1	yes	characteristic, complemented
27	C₄×C₅²	AGL(1,𝔽₅)	1	2	yes	complemented
28	#1039	C₄×C₅	1	1	yes	characteristic, complemented
29	C₅×Dic₅	—	5	2	no	—
30	C₅×Dic₅	—	10	2	no	—
31	C₄⋊AGL(1,𝔽₅)	—	5	2	no	—
32	C₅×C₄⋊C₄	—	25	1	no	—
33	C₂×C₅²	—	2	2	no	—
34	C₂×C₅²	—	4	4	no	—
35	C₂×C₅²	—	4	2	no	—
36	C₂×C₅²	C₂×C₄×C₅	1	1	yes	characteristic
37	C₂×C₅²	C₂×AGL(1,𝔽₅)	1	2	yes	—
38	C₅⋊D₅	C₅×D₄	1	1	yes	characteristic
39	C₅⋊D₅	C₅×Q₈	1	1	yes	characteristic
40	C₅×D₅	—	5	2	no	—
41	C₅×D₅	—	5	2	no	—
42	C₅×D₅	—	10	2	no	—
43	C₅×D₅	—	10	2	no	—
44	C₂×AGL(1,𝔽₅)	—	5	4	no	—
45	C₂×C₄×C₅	—	25	1	no	—
46	C₂×C₄×C₅	—	25	2	no	—
47	C₄×D₅	—	5	2	no	—
48	C₄×D₅	—	10	2	no	—
49	C₅²	—	2	2	no	—
50	C₅²	—	4	4	no	—
51	C₅²	—	4	2	no	—
52	C₅²	C₅×C₄⋊C₄	1	1	yes	characteristic, complemented
53	C₅²	C₄⋊AGL(1,𝔽₅)	1	2	yes	complemented
54	C₂²×C₅	—	25	1	no	—
55	C₂×D₅	—	5	2	no	—
56	C₂×D₅	—	10	2	no	—
57	AGL(1,𝔽₅)	—	10	4	no	—
58	C₄×C₅	—	2	2	no	—
59	C₄×C₅	—	4	4	no	—
60	C₄×C₅	—	4	2	no	—
61	C₄×C₅	—	25	1	no	—
62	C₄×C₅	—	50	2	no	—
63	C₄×C₅	C₅×AGL(1,𝔽₅)	1	2	yes	complemented
64	C₄×C₅	#1044	1	1	yes	characteristic, complemented
65	Dic₅	—	5	2	no	—
66	Dic₅	—	10	2	no	—
67	C₄⋊C₄	—	25	1	no	Sylow
68	C₂×C₅	—	2	2	no	—
69	C₂×C₅	—	4	4	no	—
70	C₂×C₅	—	4	2	no	—
71	C₂×C₅	—	25	1	no	—
72	C₂×C₅	—	25	1	no	—
73	C₂×C₅	C₂×C₅×AGL(1,𝔽₅)	1	2	yes	—
74	C₂×C₅	C₂×#1044	1	1	yes	characteristic
75	D₅	—	5	2	no	—
76	D₅	—	5	2	no	—
77	D₅	—	10	2	no	—
78	D₅	—	10	2	no	—
79	C₂×C₄	—	25	1	no	—
80	C₂×C₄	—	25	2	no	—
81	C₅	—	2	2	no	—
82	C₅	—	4	4	no	—
83	C₅	—	4	2	no	—
84	C₅	C₅×C₄⋊AGL(1,𝔽₅)	1	2	yes	complemented
85	C₅	C₄⋊#1044	1	1	yes	characteristic, direct product factor
86	C₂²	—	25	1	no	—
87	C₄	—	25	1	no	—
88	C₄	—	50	2	no	—
89	C₄	C₅×#1044	1	1	yes	characteristic, complemented
90	C₂	—	25	1	no	—
91	C₂	—	25	1	no	—
92	C₂	C₂×C₅×#1044	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#1044
commutator	C₂×C₅²	C₂×C₄×C₅
Frattini	C₂	C₂×C₅×#1044
Fitting	C₄×C₅³	C₄
socle	C₂×C₅³	C₂×C₄
prime radical	C₂×C₅×C₅⋊D₅	C₂²
cosocle	C₂×C₅⋊D₅	C₂²×C₅
hypercenter	C₄×C₅	#1044
hypocenter	C₅²	C₅×C₄⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
5. C₄×C₅³	C₄	semidirect
6. C₅×#1039	C₄	semidirect
7. C₄⋊#1044	C₅	direct (N × H)
17. C₅³	C₄⋊C₄	semidirect
26. C₄×C₅²	C₄×C₅	semidirect
27. C₄×C₅²	AGL(1,𝔽₅)	semidirect
28. #1039	C₄×C₅	semidirect
52. C₅²	C₅×C₄⋊C₄	semidirect
53. C₅²	C₄⋊AGL(1,𝔽₅)	semidirect
63. C₄×C₅	C₅×AGL(1,𝔽₅)	semidirect
64. C₄×C₅	#1044	semidirect
84. C₅	C₅×C₄⋊AGL(1,𝔽₅)	semidirect
85. C₅	C₄⋊#1044	direct (N × H)
89. C₄	C₅×#1044	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1044	2
C₄×C₅×C₅⋊D₅	2
C₄⋊#1044	5
C₅×C₄⋊AGL(1,𝔽₅)	5

Subgroups — C5×C4⋊#1044 #14522798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₄⋊#1044 #14522798