Subgroups — C₅×#4065 #11717153

Order 800.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#713	C₂	1	2	yes	maximal, complemented
2	C₅²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#688	C₂	1	2	yes	maximal, complemented
4	C₅×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅²×Q₈	C₂²	1	2	yes	—
7	C₅×D₂₀	—	2	2	no	—
8	C₅×D₂₀	C₂²	1	2	yes	—
9	C₄×C₅×D₅	—	2	2	no	—
10	C₄×C₅×D₅	C₂²	1	1	yes	characteristic
11	C₅²×C₈	C₂²	1	1	yes	characteristic
12	C₅×#168	C₂²	1	1	yes	characteristic
13	C₅×#135	—	5	1	no	maximal
14	#4065	C₅	1	1	yes	maximal, characteristic, direct product factor
15	C₂×C₅×D₅	—	2	2	no	—
16	C₂×C₅×D₅	D₄	1	1	yes	characteristic
17	C₄×C₅²	—	2	2	no	—
18	C₄×C₅²	C₂³	1	1	yes	characteristic
19	C₅×Dic₅	D₄	1	1	yes	characteristic
20	C₅×#41	—	5	2	no	—
21	#713	C₂×C₅	1	2	yes	complemented
22	C₅×Q₁₆	—	2	2	no	—
23	C₅×Q₁₆	D₅	1	1	yes	characteristic, complemented
24	C₅×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
25	C₅×SD₁₆	—	5	2	no	—
26	C₅×D₈	—	5	1	no	—
27	C₂×C₅×C₈	—	5	1	no	—
28	#688	C₂×C₅	1	2	yes	complemented
29	D₄₀	C₂×C₅	1	1	yes	characteristic, complemented
30	C₈×D₅	C₂×C₅	1	1	yes	characteristic, complemented
31	C₂×C₅²	C₂×D₄	1	1	yes	characteristic
32	C₅×D₅	—	2	1	no	—
33	C₅×D₅	—	4	2	no	—
34	C₅×Q₈	—	2	4	no	—
35	C₅×Q₈	C₂×D₅	1	2	yes	—
36	C₅×Q₈	C₂²×C₅	1	2	yes	—
37	C₅×D₄	—	5	2	no	—
38	C₅×D₄	—	10	2	no	—
39	C₂×C₄×C₅	—	5	1	no	—
40	C₂×C₄×C₅	—	10	2	no	—
41	D₂₀	—	2	2	no	—
42	D₂₀	C₂²×C₅	1	2	yes	—
43	C₄×D₅	—	2	2	no	—
44	C₄×D₅	C₂²×C₅	1	1	yes	characteristic
45	C₅×C₈	—	2	2	no	—
46	C₅×C₈	—	5	1	no	—
47	C₅×C₈	C₂×D₅	1	1	yes	characteristic
48	C₅×C₈	C₂²×C₅	1	1	yes	characteristic
49	#168	C₂²×C₅	1	1	yes	characteristic
50	#135	—	5	1	no	Sylow
51	C₅²	#135	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₅	—	5	1	no	—
53	C₂²×C₅	—	10	2	no	—
54	C₂×D₅	—	2	2	no	—
55	C₂×D₅	C₅×D₄	1	1	yes	characteristic
56	C₄×C₅	—	2	2	no	—
57	C₄×C₅	—	2	2	no	—
58	C₄×C₅	—	2	2	no	—
59	C₄×C₅	—	4	4	no	—
60	C₄×C₅	—	5	1	no	—
61	C₄×C₅	C₂²×D₅	1	1	yes	characteristic
62	C₄×C₅	C₂³×C₅	1	1	yes	characteristic
63	Dic₅	C₅×D₄	1	1	yes	characteristic
64	#41	—	5	2	no	—
65	Q₁₆	C₅×D₅	1	1	yes	characteristic, complemented
66	SD₁₆	—	5	2	no	—
67	D₈	—	5	1	no	—
68	C₂×C₈	—	5	1	no	—
69	C₂×C₅	—	2	2	no	—
70	C₂×C₅	—	10	1	no	—
71	C₂×C₅	—	20	2	no	—
72	C₂×C₅	D₄×D₅	1	1	yes	characteristic
73	C₂×C₅	C₂×C₅×D₄	1	1	yes	characteristic
74	D₅	—	2	1	no	—
75	D₅	—	4	2	no	—
76	Q₈	C₂×C₅×D₅	1	2	yes	—
77	D₄	—	5	2	no	—
78	D₄	—	10	2	no	—
79	C₂×C₄	—	5	1	no	—
80	C₂×C₄	—	10	2	no	—
81	C₈	—	5	1	no	—
82	C₈	C₂×C₅×D₅	1	1	yes	characteristic
83	C₅	—	2	2	no	—
84	C₅	#4065	1	1	yes	characteristic, direct product factor
85	C₅	C₅×#135	1	1	yes	characteristic, complemented
86	C₂²	—	5	1	no	—
87	C₂²	—	10	2	no	—
88	C₄	—	2	2	no	—
89	C₄	—	5	1	no	—
90	C₄	C₂²×C₅×D₅	1	1	yes	characteristic
91	C₂	—	10	1	no	—
92	C₂	—	20	2	no	—
93	C₂	C₅×D₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₄×D₅
commutator, cosocle	C₄×C₅	C₂³×C₅
Frattini	C₄	C₂²×C₅×D₅
Fitting	C₅²×Q₁₆	C₂
socle	C₂×C₅²	C₂×D₄
hypercenter	C₅×Q₁₆	D₅
hypocenter	C₅	C₅×#135
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₅×#713	C₂	semidirect
2. C₅²×Q₁₆	C₂	semidirect
3. C₅×#688	C₂	semidirect
4. C₅×D₄₀	C₂	semidirect
5. C₅×C₈×D₅	C₂	semidirect
14. #4065	C₅	direct (N × H)
21. #713	C₂×C₅	semidirect
23. C₅×Q₁₆	D₅	semidirect
24. C₅×Q₁₆	C₂×C₅	semidirect
28. #688	C₂×C₅	semidirect
29. D₄₀	C₂×C₅	semidirect
30. C₈×D₅	C₂×C₅	semidirect
51. C₅²	#135	semidirect
65. Q₁₆	C₅×D₅	semidirect
84. C₅	#4065	direct (N × H)
85. C₅	C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
C₅×#713	2
C₅²×Q₁₆	2
C₅×#688	2
C₅×D₄₀	2
C₅×C₈×D₅	2
C₅×#135	5
#4065	5

Subgroups — C5×#4065 #11717153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#4065 #11717153