Subgroups — C₅×#63419 #13083937

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#805	—	3	1	no	maximal
3	C₅×(C₂²⋊C₉)⋊C₂	—	4	1	no	maximal
4	#63419	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×#235	—	3	1	no	—
6	C₃×C₄²×C₅	D₃	1	1	yes	characteristic
7	C₅×#208	—	3	1	no	—
8	C₅×C₂²⋊C₉	—	4	1	no	—
9	C₅×#104	—	9	1	no	Hall
10	C₄²⋊C₉	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₃×C₄×C₅	—	3	1	no	—
12	C₅×#67	—	6	1	no	—
13	C₅×D₁₂	—	3	1	no	—
14	C₄×C₅×D₃	—	6	1	no	—
15	C₅×Dic₆	—	3	1	no	—
16	C₅×C₃⋊C₈	—	6	1	no	—
17	#805	—	3	1	no	—
18	C₅×D₉	—	16	1	no	—
19	C₅×#41	—	9	1	no	—
20	C₅×M₁₆	—	9	1	no	—
21	C₄²×C₅	D₉	1	1	yes	characteristic, complemented
22	(C₂²⋊C₉)⋊C₂	—	4	1	no	—
23	C₂²×C₃×C₅	S₄	1	1	yes	characteristic
24	C₂×C₅×D₃	—	6	1	no	—
25	C₃×C₄×C₅	—	3	1	no	—
26	C₃×C₄×C₅	—	3	1	no	—
27	C₅×Dic₃	—	6	1	no	—
28	#235	—	3	1	no	—
29	C₃×C₄²	C₅×D₃	1	1	yes	characteristic
30	#208	—	3	1	no	—
31	C₅×C₉	—	16	1	no	Hall
32	C₅×Q₈	—	9	1	no	—
33	C₅×D₄	—	9	1	no	—
34	C₅×D₄	—	18	1	no	—
35	C₂×C₄×C₅	—	3	1	no	—
36	C₂×C₄×C₅	—	18	1	no	—
37	C₅×C₈	—	18	1	no	—
38	C₂²⋊C₉	—	4	1	no	—
39	#104	—	9	1	no	Sylow
40	C₂×C₃×C₅	—	3	1	no	—
41	C₅×D₃	—	12	1	no	—
42	C₂×C₃×C₄	—	3	1	no	—
43	#67	—	6	1	no	—
44	D₁₂	—	3	1	no	—
45	C₄×D₃	—	6	1	no	—
46	Dic₆	—	3	1	no	—
47	C₃⋊C₈	—	6	1	no	—
48	C₂²×C₅	—	18	1	no	—
49	C₂²×C₅	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
50	C₄×C₅	—	3	1	no	—
51	C₄×C₅	—	3	1	no	—
52	C₄×C₅	—	18	1	no	—
53	D₉	—	16	1	no	—
54	#41	—	9	1	no	—
55	M₁₆	—	9	1	no	—
56	C₄²	C₅×D₉	1	1	yes	characteristic, complemented
57	C₃×C₅	#857	1	1	yes	characteristic
58	C₂²×C₃	C₅×S₄	1	1	yes	characteristic
59	C₂×D₃	—	6	1	no	—
60	C₃×C₄	—	3	1	no	—
61	C₃×C₄	—	3	1	no	—
62	Dic₃	—	6	1	no	—
63	C₂×C₅	—	3	1	no	—
64	C₂×C₅	—	36	1	no	—
65	C₉	—	16	1	no	Sylow
66	Q₈	—	9	1	no	—
67	D₄	—	9	1	no	—
68	D₄	—	18	1	no	—
69	C₂×C₄	—	3	1	no	—
70	C₂×C₄	—	18	1	no	—
71	C₈	—	18	1	no	—
72	C₂×C₃	—	3	1	no	—
73	D₃	—	12	1	no	—
74	C₅	#63419	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	—	18	1	no	—
76	C₂²	C₅×(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
77	C₄	—	3	1	no	—
78	C₄	—	3	1	no	—
79	C₄	—	18	1	no	—
80	C₃	C₅×#857	1	1	yes	characteristic
81	C₂	—	3	1	no	—
82	C₂	—	36	1	no	—

	subgroup	G/H
center, hypercenter	C₅	#63419
commutator, cosocle, hypocenter	C₄²⋊C₉	C₂×C₅
Frattini	C₂²×C₃	C₅×S₄
Fitting	C₃×C₄²×C₅	D₃
socle	C₂²×C₃×C₅	S₄
LCS	G ▷ C₄²⋊C₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₄²⋊C₉	C₂	semidirect
4. #63419	C₅	direct (N × H)
10. C₄²⋊C₉	C₂×C₅	semidirect
21. C₄²×C₅	D₉	semidirect
56. C₄²	C₅×D₉	semidirect
74. C₅	#63419	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×C₄²⋊C₉	2
C₅×#805	3
C₅×(C₂²⋊C₉)⋊C₂	4
#63419	5

Subgroups — C5×#63419 #13083937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63419 #13083937