Subgroups — C₅×#65429 #13102401

Order 1600.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×#131	C₂	1	1	yes	maximal, characteristic
2	C₅×#3944	C₂	1	3	yes	maximal, complemented
3	C₂×C₅×#672	C₂	1	3	yes	maximal, complemented
4	C₅²×#41	C₄	1	1	yes	characteristic
5	C₅²×M₁₆	C₄	1	3	yes	—
6	C₂×C₅²×C₈	C₂²	1	3	yes	—
7	C₅×#672	C₂²	1	1	yes	characteristic
8	C₅×#672	C₂²	1	3	yes	—
9	C₅×#504	—	5	1	no	maximal
10	#65429	C₅	1	1	yes	maximal, characteristic, direct product factor
11	C₅²×Q₈	C₈	1	1	yes	characteristic
12	C₅²×D₄	C₈	1	3	yes	—
13	C₂×C₄×C₅²	C₂×C₄	1	3	yes	—
14	C₅²×C₈	C₂×C₄	1	3	yes	—
15	C₅²×C₈	C₂³	1	1	yes	characteristic
16	C₅×#131	—	2	2	no	—
17	C₅×#131	D₅	1	1	yes	characteristic
18	C₅×#131	C₂×C₅	1	1	yes	characteristic
19	C₅×M₃₂	—	5	3	no	—
20	C₂×C₅×C₁₆	—	5	3	no	—
21	#3944	C₂×C₅	1	3	yes	complemented
22	C₂×#672	C₂×C₅	1	3	yes	complemented
23	C₂²×C₅²	C₂×C₈	1	3	yes	—
24	C₄×C₅²	C₂×C₈	1	3	yes	—
25	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
26	C₅×#41	—	2	2	no	—
27	C₅×#41	Dic₅	1	1	yes	characteristic
28	C₅×#41	C₄×C₅	1	1	yes	characteristic
29	C₅×M₁₆	—	2	6	no	—
30	C₅×M₁₆	Dic₅	1	3	yes	—
31	C₅×M₁₆	C₄×C₅	1	3	yes	—
32	C₂×C₅×C₈	—	2	6	no	—
33	C₂×C₅×C₈	C₂×D₅	1	3	yes	—
34	C₂×C₅×C₈	C₂²×C₅	1	3	yes	—
35	C₅×C₁₆	—	5	1	no	—
36	C₅×C₁₆	—	5	3	no	—
37	#672	C₂²×C₅	1	1	yes	characteristic
38	#672	C₂²×C₅	1	3	yes	—
39	#504	—	5	1	no	Sylow
40	C₂×C₅²	—	2	3	no	—
41	C₂×C₅²	C₂²×C₈	1	1	yes	characteristic
42	C₅×Q₈	—	2	2	no	—
43	C₅×Q₈	#168	1	1	yes	characteristic
44	C₅×Q₈	C₅×C₈	1	1	yes	characteristic
45	C₅×D₄	—	2	6	no	—
46	C₅×D₄	#168	1	3	yes	—
47	C₅×D₄	C₅×C₈	1	3	yes	—
48	C₂×C₄×C₅	—	2	6	no	—
49	C₂×C₄×C₅	C₂×Dic₅	1	3	yes	—
50	C₂×C₄×C₅	C₂×C₄×C₅	1	3	yes	—
51	C₅×C₈	—	2	6	no	—
52	C₅×C₈	—	2	2	no	—
53	C₅×C₈	C₂×Dic₅	1	3	yes	—
54	C₅×C₈	C₂×C₄×C₅	1	3	yes	—
55	C₅×C₈	C₂²×D₅	1	1	yes	characteristic
56	C₅×C₈	C₂³×C₅	1	1	yes	characteristic
57	#131	C₅×D₅	1	1	yes	characteristic
58	M₃₂	—	5	3	no	—
59	C₂×C₁₆	—	5	3	no	—
60	C₅²	#504	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₅	—	2	6	no	—
62	C₂²×C₅	C₂×#168	1	3	yes	—
63	C₂²×C₅	C₂×C₅×C₈	1	3	yes	—
64	C₄×C₅	—	2	2	no	—
65	C₄×C₅	—	2	6	no	—
66	C₄×C₅	C₂×#168	1	3	yes	—
67	C₄×C₅	C₂×C₅×C₈	1	3	yes	—
68	C₄×C₅	C₂²×Dic₅	1	1	yes	characteristic
69	C₄×C₅	C₂²×C₄×C₅	1	1	yes	characteristic
70	#41	C₅×Dic₅	1	1	yes	characteristic
71	M₁₆	C₅×Dic₅	1	3	yes	—
72	C₂×C₈	C₂×C₅×D₅	1	3	yes	—
73	C₁₆	—	5	1	no	—
74	C₁₆	—	5	3	no	—
75	C₂×C₅	—	2	3	no	—
76	C₂×C₅	—	2	3	no	—
77	C₂×C₅	—	2	2	no	—
78	C₂×C₅	—	4	6	no	—
79	C₂×C₅	C₂²×#168	1	1	yes	characteristic
80	C₂×C₅	C₂²×C₅×C₈	1	1	yes	characteristic
81	Q₈	C₅×#168	1	1	yes	characteristic
82	D₄	C₅×#168	1	3	yes	—
83	C₂×C₄	C₂×C₅×Dic₅	1	3	yes	—
84	C₈	C₂×C₅×Dic₅	1	3	yes	—
85	C₈	C₂²×C₅×D₅	1	1	yes	characteristic
86	C₅	—	2	2	no	—
87	C₅	#65429	1	1	yes	characteristic, direct product factor
88	C₅	C₅×#504	1	1	yes	characteristic, complemented
89	C₂²	C₂×C₅×#168	1	3	yes	—
90	C₄	C₂×C₅×#168	1	3	yes	—
91	C₄	C₂²×C₅×Dic₅	1	1	yes	characteristic
92	C₂	—	2	3	no	—
93	C₂	C₂²×C₅×#168	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₈	C₂²×D₅
commutator	C₂×C₅	C₂²×C₅×C₈
Frattini	C₈	C₂²×C₅×D₅
Fitting	C₅²×#131	C₂
socle	C₂×C₅²	C₂²×C₈
prime radical	C₅²×#41	C₄
cosocle	C₅×C₈	C₂³×C₅
hypercenter	C₅×#131	D₅
hypocenter	C₅	C₅×#504
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₅×C₈ ◁ C₅×#131

Complements

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

N	H ≅ G/N	type
2. C₅×#3944	C₂	semidirect
3. C₂×C₅×#672	C₂	semidirect
10. #65429	C₅	direct (N × H)
21. #3944	C₂×C₅	semidirect
22. C₂×#672	C₂×C₅	semidirect
60. C₅²	#504	semidirect
87. C₅	#65429	direct (N × H)
88. C₅	C₅×#504	semidirect

Maximal subgroups

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

subgroup	index
C₅²×#131	2
C₅×#3944	2
C₂×C₅×#672	2
C₅×#504	5
#65429	5

Subgroups — C5×#65429 #13102401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#65429 #13102401