Subgroups — C₅×#63742 #13085570

Order 1440.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#622	C₂	1	1	yes	maximal, characteristic
2	C₅×#3724	C₂	1	2	yes	maximal
3	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
4	C₂×C₃×C₅×Dic₃	—	2	2	no	—
5	C₅×#622	C₄	1	2	yes	complemented
6	#63742	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×Dic₃⋊C₄	—	6	2	no	—
8	C₂²×C₃²×C₅	D₄	1	1	yes	characteristic
9	C₅×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
10	C₅×C₃⋊Dic₃	Q₈	1	1	yes	characteristic
11	C₃×C₅×Dic₃	—	4	2	no	—
12	C₅×#106	—	9	1	no	maximal, Hall
13	C₂×#622	C₂×C₅	1	1	yes	characteristic
14	#3724	C₂×C₅	1	2	yes	—
15	C₂×C₃×C₄×C₅	—	6	2	no	—
16	C₂×C₅×Dic₃	—	2	2	no	—
17	C₂×C₅×Dic₃	—	6	2	no	—
18	C₂×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₃²×C₅	SD₁₆	1	2	yes	—
20	C₂×C₅×C₈	—	9	1	no	—
21	C₅×C₄⋊C₄	—	9	2	no	—
22	C₂×C₃⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
23	C₂×C₃×Dic₃	—	2	2	no	—
24	#622	C₄×C₅	1	2	yes	complemented
25	C₂²×C₃×C₅	—	2	2	no	—
26	C₃×C₄×C₅	—	12	2	no	—
27	C₅×Dic₃	—	4	2	no	—
28	C₅×Dic₃	—	6	2	no	—
29	C₅×Dic₃	—	6	2	no	—
30	Dic₃⋊C₄	—	6	2	no	—
31	C₃²×C₅	#106	1	1	yes	characteristic, complemented, Hall
32	C₂×C₄×C₅	—	6	2	no	—
33	C₂×C₄×C₅	—	9	1	no	—
34	C₅×C₈	—	9	2	no	—
35	C₂²×C₃²	C₅×D₄	1	1	yes	characteristic
36	C₃⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
37	C₃⋊Dic₃	C₅×Q₈	1	1	yes	characteristic
38	C₃×Dic₃	—	4	2	no	—
39	#106	—	9	1	no	Sylow
40	C₂×C₃×C₅	—	2	2	no	—
41	C₂×C₃×C₅	—	2	2	no	—
42	C₂×C₃×C₅	—	2	2	no	—
43	C₂×C₃×C₄	—	6	2	no	—
44	C₂×Dic₃	—	2	2	no	—
45	C₂×Dic₃	—	6	2	no	—
46	C₂²×C₅	GO⁺(4,𝔽₂)	1	1	yes	characteristic
47	C₄×C₅	—	9	1	no	—
48	C₄×C₅	—	9	1	no	—
49	C₄×C₅	—	12	2	no	—
50	C₂×C₃²	C₅×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₃²	C₅×SD₁₆	1	2	yes	—
52	C₂×C₈	—	9	1	no	—
53	C₄⋊C₄	—	9	2	no	—
54	C₃×C₅	—	2	2	no	—
55	C₂²×C₃	—	2	2	no	—
56	C₃×C₄	—	12	2	no	—
57	Dic₃	—	4	2	no	—
58	Dic₃	—	6	2	no	—
59	Dic₃	—	6	2	no	—
60	C₂×C₅	#3773	1	1	yes	characteristic
61	C₂×C₅	#3775	1	2	yes	—
62	C₃²	C₅×#106	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₄	—	6	2	no	—
64	C₂×C₄	—	9	1	no	—
65	C₈	—	9	2	no	—
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	—	2	2	no	—
68	C₂×C₃	—	2	2	no	—
69	C₅	#63742	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²	C₅×GO⁺(4,𝔽₂)	1	1	yes	characteristic
71	C₄	—	9	1	no	—
72	C₄	—	9	1	no	—
73	C₄	—	12	2	no	—
74	C₃	—	2	2	no	—
75	C₂	C₅×#3773	1	1	yes	characteristic
76	C₂	C₅×#3775	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₅	GO⁺(4,𝔽₂)
commutator	C₃⋊Dic₃	C₂×C₄×C₅
Frattini	C₂²	C₅×GO⁺(4,𝔽₂)
Fitting, socle, prime radical	C₂²×C₃²×C₅	D₄
cosocle	C₂×C₃⋊Dic₃	C₂²×C₅
hypocenter	C₃²	C₅×#106
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
5. C₅×#622	C₄	semidirect
6. #63742	C₅	direct (N × H)
24. #622	C₄×C₅	semidirect
31. C₃²×C₅	#106	semidirect
62. C₃²	C₅×#106	semidirect
69. C₅	#63742	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#622	2
C₅×#3724	2
#63742	5
C₅×#106	9

Subgroups — C5×#63742 #13085570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63742 #13085570