Subgroups — C₅×#62624 #11985344

Order 1280.

2038 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3573	C₂	1	1	yes	maximal, characteristic
2	C₅×#3407	C₂	1	15	yes	maximal, complemented
3	C₂×C₅×#504	C₂	1	15	yes	maximal, complemented
4	C₅×#585	C₄	1	1	yes	characteristic
5	C₅×#568	C₄	1	15	yes	—
6	C₂×C₅×#131	C₂²	1	15	yes	—
7	C₅×#504	C₂²	1	20	yes	complemented
8	C₅×#504	C₂²	1	60	yes	complemented
9	C₂×C₅×M₃₂	C₂²	1	45	yes	complemented
10	C₂²×C₅×C₁₆	C₂²	1	15	yes	complemented
11	#62624	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₅×2₋¹⁺⁴	C₈	1	6	yes	—
13	C₅×H(5,𝔽₂)	C₈	1	10	yes	—
14	C₂×C₅×#41	C₂×C₄	1	15	yes	—
15	C₅×#131	C₂×C₄	1	60	yes	—
16	C₅×#131	C₂³	1	20	yes	—
17	C₂×C₅×M₁₆	C₂×C₄	1	45	yes	—
18	C₂²×C₅×C₈	C₂³	1	15	yes	—
19	C₅×M₃₂	C₂³	1	60	yes	—
20	C₂×C₅×C₁₆	C₂³	1	45	yes	—
21	C₂×C₅×C₁₆	C₂³	1	15	yes	—
22	#3573	C₂×C₅	1	1	yes	characteristic
23	#3407	C₂×C₅	1	15	yes	complemented
24	C₂×#504	C₂×C₅	1	15	yes	complemented
25	C₅×#41	C₂×C₈	1	60	yes	—
26	C₅×#41	C₂²×C₄	1	20	yes	—
27	C₂×C₅×Q₈	C₂×C₈	1	15	yes	—
28	C₂×C₅×D₄	C₂×C₈	1	45	yes	—
29	C₂²×C₄×C₅	C₂²×C₄	1	15	yes	—
30	C₅×M₁₆	C₂²×C₄	1	60	yes	—
31	C₂×C₅×C₈	C₂²×C₄	1	45	yes	—
32	C₂×C₅×C₈	C₂⁴	1	15	yes	—
33	C₅×C₁₆	C₂⁴	1	15	yes	—
34	C₅×C₁₆	C₂⁴	1	1	yes	characteristic
35	#585	C₄×C₅	1	1	yes	characteristic
36	#568	C₄×C₅	1	15	yes	—
37	C₂×#131	C₂²×C₅	1	15	yes	—
38	#504	C₂²×C₅	1	20	yes	complemented
39	#504	C₂²×C₅	1	60	yes	complemented
40	C₂×M₃₂	C₂²×C₅	1	45	yes	complemented
41	C₂²×C₁₆	C₂²×C₅	1	15	yes	complemented
42	C₂³×C₅	C₂²×C₈	1	15	yes	—
43	C₅×Q₈	C₂²×C₈	1	20	yes	—
44	C₅×D₄	C₂²×C₈	1	60	yes	—
45	C₂×C₄×C₅	C₂²×C₈	1	45	yes	—
46	C₂×C₄×C₅	C₂³×C₄	1	15	yes	—
47	C₅×C₈	C₂³×C₄	1	15	yes	—
48	C₅×C₈	C₂⁵	1	1	yes	characteristic
49	2₋¹⁺⁴	C₅×C₈	1	6	yes	—
50	H(5,𝔽₂)	C₅×C₈	1	10	yes	—
51	C₂×#41	C₂×C₄×C₅	1	15	yes	—
52	#131	C₂×C₄×C₅	1	60	yes	—
53	#131	C₂³×C₅	1	20	yes	—
54	C₂×M₁₆	C₂×C₄×C₅	1	45	yes	—
55	C₂²×C₈	C₂³×C₅	1	15	yes	—
56	M₃₂	C₂³×C₅	1	60	yes	—
57	C₂×C₁₆	C₂³×C₅	1	15	yes	—
58	C₂×C₁₆	C₂³×C₅	1	45	yes	—
59	C₂²×C₅	—	4	15	no	—
60	C₂²×C₅	C₂³×C₈	1	15	yes	—
61	C₄×C₅	C₂³×C₈	1	15	yes	—
62	C₄×C₅	C₂⁴×C₄	1	1	yes	characteristic
63	#41	C₂×C₅×C₈	1	60	yes	—
64	#41	C₂²×C₄×C₅	1	20	yes	—
65	C₂×Q₈	C₂×C₅×C₈	1	15	yes	—
66	C₂×D₄	C₂×C₅×C₈	1	45	yes	—
67	C₂²×C₄	C₂²×C₄×C₅	1	15	yes	—
68	M₁₆	C₂²×C₄×C₅	1	60	yes	—
69	C₂×C₈	C₂²×C₄×C₅	1	45	yes	—
70	C₂×C₈	C₂⁴×C₅	1	15	yes	—
71	C₁₆	C₂⁴×C₅	1	1	yes	characteristic
72	C₁₆	C₂⁴×C₅	1	15	yes	—
73	C₂×C₅	—	2	15	no	—
74	C₂×C₅	C₂⁴×C₈	1	1	yes	characteristic
75	C₂³	C₂²×C₅×C₈	1	15	yes	—
76	Q₈	C₂²×C₅×C₈	1	20	yes	—
77	D₄	C₂²×C₅×C₈	1	60	yes	—
78	C₂×C₄	C₂²×C₅×C₈	1	45	yes	—
79	C₂×C₄	C₂³×C₄×C₅	1	15	yes	—
80	C₈	C₂³×C₄×C₅	1	15	yes	—
81	C₈	C₂⁵×C₅	1	1	yes	characteristic
82	C₅	#62624	1	1	yes	characteristic, direct product factor, Sylow
83	C₂²	—	4	15	no	—
84	C₂²	C₂³×C₅×C₈	1	15	yes	—
85	C₄	C₂³×C₅×C₈	1	15	yes	—
86	C₄	C₂⁴×C₄×C₅	1	1	yes	characteristic
87	C₂	—	2	15	no	—
88	C₂	C₂⁴×C₅×C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₅×C₁₆	C₂⁴
commutator	C₂	C₂⁴×C₅×C₈
Frattini, cosocle	C₈	C₂⁵×C₅
socle	C₂×C₅	C₂⁴×C₈
prime radical	C₅×#585	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₅×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3407	C₂	semidirect
3. C₂×C₅×#504	C₂	semidirect
7. C₅×#504	C₂²	semidirect
8. C₅×#504	C₂²	semidirect
9. C₂×C₅×M₃₂	C₂²	semidirect
10. C₂²×C₅×C₁₆	C₂²	semidirect
11. #62624	C₅	direct (N × H)
23. #3407	C₂×C₅	semidirect
24. C₂×#504	C₂×C₅	semidirect
38. #504	C₂²×C₅	semidirect
39. #504	C₂²×C₅	semidirect
40. C₂×M₃₂	C₂²×C₅	semidirect
41. C₂²×C₁₆	C₂²×C₅	semidirect
82. C₅	#62624	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3573	2
C₅×#3407	2
C₂×C₅×#504	2
#62624	5

Subgroups — C5×#62624 #11985344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#62624 #11985344