Subgroups — C₅×#3674 #10623593

Order 720.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₁₈	C₂	1	1	yes	maximal, characteristic
3	C₅×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#216	—	3	1	no	maximal
5	C₄×C₅×C₉	—	2	1	no	—
6	C₄×C₅×C₉	C₂²	1	1	yes	characteristic
7	C₅×Dic₉	—	2	1	no	—
8	#3674	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×Q₈	D₃	1	1	yes	characteristic
10	C₅×Dic₆	—	3	1	no	—
11	C₅×C₃⋊C₈	—	3	1	no	—
12	C₂×C₅×C₉	D₄	1	1	yes	characteristic
13	C₅×Q₁₆	—	9	1	no	Hall
14	Q₈×C₉	C₂×C₅	1	1	yes	characteristic
15	Dic₁₈	C₂×C₅	1	1	yes	characteristic
16	C₉⋊C₈	C₂×C₅	1	1	yes	characteristic
17	C₃×C₄×C₅	—	2	1	no	—
18	C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
19	C₅×Dic₃	—	6	1	no	—
20	#216	—	3	1	no	—
21	C₅×C₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
22	C₅×Q₈	—	9	1	no	—
23	C₅×Q₈	D₉	1	1	yes	characteristic
24	C₅×C₈	—	9	1	no	—
25	C₄×C₉	—	2	1	no	—
26	C₄×C₉	C₂²×C₅	1	1	yes	characteristic
27	Dic₉	—	2	1	no	—
28	C₂×C₃×C₅	#67	1	1	yes	characteristic
29	C₃×Q₈	C₅×D₃	1	1	yes	characteristic
30	Dic₆	—	3	1	no	—
31	C₃⋊C₈	—	3	1	no	—
32	C₄×C₅	—	2	1	no	—
33	C₄×C₅	—	18	1	no	—
34	C₄×C₅	C₂×D₉	1	1	yes	characteristic
35	C₂×C₉	C₅×D₄	1	1	yes	characteristic
36	Q₁₆	—	9	1	no	Sylow
37	C₃×C₅	#216	1	1	yes	characteristic
38	C₃×C₄	—	2	1	no	—
39	C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic
40	Dic₃	—	6	1	no	—
41	C₂×C₅	#611	1	1	yes	characteristic
42	C₉	C₅×Q₁₆	1	1	yes	characteristic, complemented, Sylow
43	Q₈	—	9	1	no	—
44	Q₈	C₅×D₉	1	1	yes	characteristic
45	C₈	—	9	1	no	—
46	C₂×C₃	C₅×#67	1	1	yes	characteristic
47	C₅	#3674	1	1	yes	characteristic, direct product factor, Sylow
48	C₄	—	2	1	no	—
49	C₄	—	18	1	no	—
50	C₄	C₂×C₅×D₉	1	1	yes	characteristic
51	C₃	C₅×#216	1	1	yes	characteristic
52	C₂	C₅×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#611
commutator, cosocle	C₄×C₉	C₂²×C₅
Frattini	C₃×C₄	C₂×C₅×D₃
Fitting	C₅×Q₈×C₉	C₂
socle, prime radical	C₂×C₃×C₅	#67
hypercenter	C₅×Q₈	D₉
hypocenter	C₉	C₅×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×Q₈

Complements

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

N	H ≅ G/N	type
8. #3674	C₅	direct (N × H)
21. C₅×C₉	Q₁₆	semidirect
42. C₉	C₅×Q₁₆	semidirect
47. C₅	#3674	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×Q₈×C₉	2
C₅×Dic₁₈	2
C₅×C₉⋊C₈	2
C₅×#216	3
#3674	5

Subgroups — C5×#3674 #10623593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3674 #10623593