Subgroups — C₁₆×#1042 #13100127

Order 1600.

121 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#1042	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#672	C₂	1	1	yes	maximal, characteristic
3	C₅×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₄×#1042	C₄	1	1	yes	characteristic
5	D₅⋊#168	C₄	1	1	yes	characteristic
6	C₅×C₈×D₅	C₂²	1	1	yes	characteristic
7	#87763	C₄	1	2	yes	complemented
8	C₅²×C₁₆	C₄	1	1	yes	characteristic, complemented
9	C₅×#672	C₄	1	1	yes	characteristic, complemented
10	C₁₆×AGL(1,𝔽₅)	—	5	1	no	maximal
11	C₁₆×Dic₅	—	5	1	no	maximal
12	C₂×#1042	C₈	1	2	yes	—
13	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic
14	#6032	C₈	1	2	yes	—
15	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
16	C₅×#168	C₂×C₄	1	1	yes	characteristic
17	C₈×AGL(1,𝔽₅)	—	5	1	no	—
18	D₅⋊C₁₆	—	5	1	no	—
19	C₂×C₅×C₁₆	—	5	1	no	—
20	C₈×Dic₅	—	5	1	no	—
21	C₂×#672	—	5	1	no	—
22	D₅×C₁₆	D₅	1	1	yes	characteristic
23	C₂×C₅×D₅	C₂×C₈	1	1	yes	characteristic
24	#1042	C₁₆	1	4	yes	direct product factor
25	C₄×C₅²	C₄²	1	1	yes	characteristic
26	C₅×Dic₅	C₂×C₈	1	1	yes	characteristic
27	C₄×AGL(1,𝔽₅)	—	5	1	no	—
28	D₅⋊C₈	—	5	1	no	—
29	C₂×C₅×C₈	—	5	1	no	—
30	C₄×Dic₅	—	5	1	no	—
31	C₂×#168	—	5	1	no	—
32	C₈×D₅	C₂×D₅	1	1	yes	characteristic
33	#674	—	5	2	no	—
34	C₅×C₁₆	—	4	1	no	—
35	C₅×C₁₆	—	5	1	no	—
36	C₅×C₁₆	Dic₅	1	1	yes	characteristic, complemented
37	C₅×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
38	#672	—	5	2	no	—
39	#672	Dic₅	1	1	yes	characteristic, complemented
40	C₄×C₁₆	—	25	1	no	Sylow
41	C₂×C₅²	C₄×C₈	1	1	yes	characteristic
42	C₅×D₅	C₂×C₁₆	1	2	yes	—
43	C₂×AGL(1,𝔽₅)	—	5	2	no	—
44	C₂×C₄×C₅	—	5	1	no	—
45	C₂×Dic₅	—	5	2	no	—
46	C₄×D₅	C₄×D₅	1	1	yes	characteristic
47	#170	—	5	2	no	—
48	C₅×C₈	—	4	1	no	—
49	C₅×C₈	—	5	1	no	—
50	C₅×C₈	C₂×Dic₅	1	1	yes	characteristic
51	C₅×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
52	#168	—	5	2	no	—
53	#168	C₄×D₅	1	1	yes	characteristic
54	C₂×C₁₆	—	5	1	no	—
55	C₂×C₁₆	—	25	1	no	—
56	C₄×C₈	—	25	1	no	—
57	C₅²	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₅	—	5	1	no	—
59	C₂×D₅	C₈×D₅	1	1	yes	characteristic
60	AGL(1,𝔽₅)	—	5	4	no	—
61	C₄×C₅	—	4	1	no	—
62	C₄×C₅	—	5	1	no	—
63	C₄×C₅	C₄×Dic₅	1	1	yes	characteristic
64	C₄×C₅	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
65	Dic₅	—	5	4	no	—
66	Dic₅	C₈×D₅	1	1	yes	characteristic
67	C₂×C₈	—	5	1	no	—
68	C₂×C₈	—	25	1	no	—
69	C₄²	—	25	1	no	—
70	C₁₆	—	5	1	no	—
71	C₁₆	—	25	2	no	—
72	C₁₆	#1042	1	1	yes	characteristic, direct product factor
73	C₂×C₅	—	4	1	no	—
74	C₂×C₅	—	5	2	no	—
75	C₂×C₅	C₈×Dic₅	1	1	yes	characteristic
76	C₂×C₅	C₈×AGL(1,𝔽₅)	1	1	yes	characteristic
77	D₅	D₅×C₁₆	1	2	yes	—
78	C₂×C₄	—	5	1	no	—
79	C₂×C₄	—	25	2	no	—
80	C₈	—	5	1	no	—
81	C₈	—	25	2	no	—
82	C₈	C₂×#1042	1	1	yes	characteristic
83	C₅	—	4	1	no	—
84	C₅	C₁₆×Dic₅	1	1	yes	characteristic, complemented
85	C₅	C₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
86	C₂²	—	5	1	no	—
87	C₄	—	5	1	no	—
88	C₄	—	25	4	no	—
89	C₄	C₄×#1042	1	1	yes	characteristic
90	C₂	—	5	2	no	—
91	C₂	C₈×#1042	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₁₆	#1042
commutator, hypocenter	C₅²	C₄×C₁₆
Frattini	C₈	C₂×#1042
Fitting	C₅²×C₁₆	C₄
socle	C₂×C₅²	C₄×C₈
prime radical	C₂×C₅×D₅	C₂×C₈
cosocle	C₅×C₈×D₅	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
7. #87763	C₄	semidirect
8. C₅²×C₁₆	C₄	semidirect
9. C₅×#672	C₄	semidirect
24. #1042	C₁₆	direct (N × H)
36. C₅×C₁₆	Dic₅	semidirect
37. C₅×C₁₆	AGL(1,𝔽₅)	semidirect
39. #672	Dic₅	semidirect
57. C₅²	C₄×C₁₆	semidirect
72. C₁₆	#1042	direct (N × H)
84. C₅	C₁₆×Dic₅	semidirect
85. C₅	C₁₆×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₈×#1042	2
D₅⋊#672	2
C₅×D₅×C₁₆	2
C₁₆×AGL(1,𝔽₅)	5
C₁₆×Dic₅	5

Subgroups — C16×#1042 #13100127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#1042 #13100127