Subgroups — C₄×C₅×#622 #13086327

Order 1440.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#622	C₂	1	2	yes	maximal
2	C₄×C₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄×C₅	C₄	1	1	yes	characteristic
4	C₂×C₅×C₃⋊Dic₃	C₄	1	1	yes	characteristic
5	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
6	C₅×#622	C₄	1	4	yes	direct product factor
7	C₄×#622	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₄×C₅×Dic₃	—	6	2	no	—
9	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₃²×C₄×C₅	C₈	1	2	yes	complemented
11	C₅×C₃⋊Dic₃	C₈	1	2	yes	complemented
12	C₅×C₃⋊Dic₃	C₂×C₄	1	2	yes	—
13	C₄×C₅×C₈	—	9	1	no	maximal, Hall
14	C₂×#622	C₂×C₅	1	2	yes	—
15	C₄×C₃⋊Dic₃	C₂×C₅	1	1	yes	characteristic
16	C₂×C₃×C₄×C₅	—	2	2	no	—
17	C₂×C₅×Dic₃	—	6	2	no	—
18	C₂×C₅×Dic₃	—	6	2	no	—
19	C₂×C₃²×C₅	C₄²	1	1	yes	characteristic
20	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
21	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
22	C₂×C₅×C₈	—	9	2	no	—
23	C₄²×C₅	—	9	1	no	—
24	C₂×C₃²×C₄	C₄×C₅	1	1	yes	characteristic
25	C₂×C₃⋊Dic₃	C₄×C₅	1	1	yes	characteristic
26	C₂×C₃⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
27	#622	C₄×C₅	1	4	yes	direct product factor
28	C₂²×C₃×C₅	—	2	2	no	—
29	C₃×C₄×C₅	—	2	4	no	—
30	C₅×Dic₃	—	6	4	no	—
31	C₅×Dic₃	—	6	4	no	—
32	C₄×Dic₃	—	6	2	no	—
33	C₃²×C₅	C₄×C₈	1	1	yes	characteristic, complemented, Hall
34	C₂×C₄×C₅	—	9	1	no	—
35	C₂×C₄×C₅	—	9	1	no	—
36	C₂×C₄×C₅	#157	1	1	yes	characteristic
37	C₅×C₈	—	9	4	no	—
38	C₂²×C₃²	C₂×C₄×C₅	1	1	yes	characteristic
39	C₃²×C₄	C₅×C₈	1	2	yes	complemented
40	C₃⋊Dic₃	C₅×C₈	1	2	yes	complemented
41	C₃⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
42	C₄×C₈	—	9	1	no	Sylow
43	C₂×C₃×C₅	—	2	2	no	—
44	C₂×C₃×C₅	—	2	2	no	—
45	C₂×C₃×C₅	—	2	2	no	—
46	C₂×C₃×C₄	—	2	2	no	—
47	C₂×Dic₃	—	6	2	no	—
48	C₂×Dic₃	—	6	2	no	—
49	C₂²×C₅	C₂×#157	1	1	yes	characteristic
50	C₄×C₅	—	9	2	no	—
51	C₄×C₅	—	9	2	no	—
52	C₄×C₅	#622	1	2	yes	direct product factor
53	C₂×C₃²	C₄²×C₅	1	1	yes	characteristic
54	C₂×C₃²	C₂×C₅×C₈	1	1	yes	characteristic
55	C₂×C₃²	C₂×C₅×C₈	1	1	yes	characteristic
56	C₂×C₈	—	9	2	no	—
57	C₄²	—	9	1	no	—
58	C₃×C₅	—	2	2	no	—
59	C₂²×C₃	—	2	2	no	—
60	C₃×C₄	—	2	4	no	—
61	Dic₃	—	6	4	no	—
62	Dic₃	—	6	4	no	—
63	C₂×C₅	#3787	1	1	yes	characteristic
64	C₂×C₅	C₄×#157	1	1	yes	characteristic
65	C₂×C₅	C₂×#622	1	1	yes	characteristic
66	C₃²	C₄×C₅×C₈	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄	—	9	1	no	—
68	C₂×C₄	—	9	1	no	—
69	C₂×C₄	C₅×#157	1	1	yes	characteristic
70	C₈	—	9	4	no	—
71	C₂×C₃	—	2	2	no	—
72	C₂×C₃	—	2	2	no	—
73	C₂×C₃	—	2	2	no	—
74	C₅	C₄×#622	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	C₂×C₅×#157	1	1	yes	characteristic
76	C₄	—	9	2	no	—
77	C₄	—	9	2	no	—
78	C₄	C₅×#622	1	2	yes	direct product factor
79	C₃	—	2	2	no	—
80	C₂	C₅×#3787	1	1	yes	characteristic
81	C₂	C₄×C₅×#157	1	1	yes	characteristic
82	C₂	C₂×C₅×#622	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄×C₅	#157
commutator, hypocenter	C₃²	C₄×C₅×C₈
Frattini	C₂²	C₂×C₅×#157
Fitting	C₂×C₃²×C₄×C₅	C₄
socle, prime radical	C₂²×C₃²×C₅	C₂×C₄
cosocle	C₂×C₃⋊Dic₃	C₂²×C₅
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
6. C₅×#622	C₄	direct (N × H)
7. C₄×#622	C₅	direct (N × H)
10. C₃²×C₄×C₅	C₈	semidirect
11. C₅×C₃⋊Dic₃	C₈	semidirect
27. #622	C₄×C₅	direct (N × H)
33. C₃²×C₅	C₄×C₈	semidirect
39. C₃²×C₄	C₅×C₈	semidirect
40. C₃⋊Dic₃	C₅×C₈	semidirect
52. C₄×C₅	#622	direct (N × H)
66. C₃²	C₄×C₅×C₈	semidirect
74. C₅	C₄×#622	direct (N × H)
78. C₄	C₅×#622	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
C₄×C₅×C₃⋊Dic₃	2
C₄×#622	5
C₄×C₅×C₈	9

Subgroups — C4×C5×#622 #13086327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#622 #13086327