Subgroups — #13085544

Order 1440.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67127	C₂	1	2	yes	maximal
2	Dic₅×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊Dic₁₅	C₂²	1	1	yes	characteristic
4	C₂×C₅×C₃⋊Dic₃	C₄	1	1	yes	characteristic
5	C₂×C₃²×Dic₅	C₄	1	1	yes	characteristic
6	#67127	C₄	1	4	yes	complemented
7	C₄×#622	—	5	1	no	maximal, Hall
8	Dic₃×Dic₅	—	6	2	no	—
9	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₃⋊Dic₁₅	C₂×C₄	1	2	yes	—
11	C₅×C₃⋊Dic₃	C₈	1	2	yes	complemented
12	C₃²×Dic₅	C₈	1	2	yes	complemented
13	C₄×#170	—	9	1	no	maximal, Hall
14	C₂×#622	—	5	2	no	—
15	C₄×C₃⋊Dic₃	—	5	1	no	—
16	C₂×Dic₁₅	—	6	2	no	—
17	C₂×C₅×Dic₃	—	6	2	no	—
18	C₂×C₃×Dic₅	—	2	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×#170	—	9	2	no	—
23	C₄×Dic₅	—	9	1	no	—
24	C₂×C₃²×C₄	—	5	1	no	—
25	C₂×C₃⋊Dic₃	—	5	1	no	—
26	C₂×C₃⋊Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic
27	#622	—	5	4	no	—
28	C₂²×C₃×C₅	—	2	2	no	—
29	Dic₁₅	—	6	4	no	—
30	C₃×Dic₅	—	2	4	no	—
31	C₅×Dic₃	—	6	4	no	—
32	C₄×Dic₃	—	30	2	no	—
33	C₃²×C₅	C₄×C₈	1	1	yes	characteristic, complemented, Hall
34	C₂×C₄×C₅	—	9	1	no	—
35	C₂×Dic₅	—	9	1	no	—
36	C₂×Dic₅	#157	1	1	yes	characteristic
37	#170	—	9	4	no	—
38	C₂²×C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
39	C₃²×C₄	—	5	2	no	—
40	C₃⋊Dic₃	—	5	2	no	—
41	C₃⋊Dic₃	#170	1	2	yes	complemented
42	C₄×C₈	—	45	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	—	10	2	no	—
47	C₂×Dic₃	—	6	2	no	—
48	C₂×Dic₃	—	30	2	no	—
49	C₂²×C₅	C₂×#157	1	1	yes	characteristic
50	C₄×C₅	—	9	2	no	—
51	Dic₅	—	9	2	no	—
52	Dic₅	#622	1	2	yes	complemented
53	C₂×C₃²	D₅⋊C₈	1	1	yes	characteristic
54	C₂×C₃²	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂×C₃²	C₂×#170	1	1	yes	characteristic
56	C₂×C₈	—	45	2	no	—
57	C₄²	—	45	1	no	—
58	C₃×C₅	—	2	2	no	—
59	C₂²×C₃	—	2	2	no	—
60	C₃×C₄	—	10	4	no	—
61	Dic₃	—	6	4	no	—
62	Dic₃	—	30	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×#170	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄	—	5	1	no	—
68	C₂×C₄	—	9	1	no	—
69	C₂×C₄	—	45	1	no	—
70	C₈	—	45	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, complemented, Sylow
75	C₂²	D₅⋊#157	1	1	yes	characteristic
76	C₄	—	5	2	no	—
77	C₄	—	9	2	no	—
78	C₄	—	45	2	no	—
79	C₃	—	2	2	no	—
80	C₂	#10623991	1	1	yes	characteristic
81	C₂	#10623994	1	1	yes	characteristic
82	C₂	D₅⋊#622	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₅⋊#157
commutator, hypocenter	C₃²×C₅	C₄×C₈
Fitting, socle, prime radical	C₂²×C₃²×C₅	C₂×C₄
cosocle	C₂×C₃⋊Dic₁₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
6. #67127	C₄	semidirect
11. C₅×C₃⋊Dic₃	C₈	semidirect
12. C₃²×Dic₅	C₈	semidirect
33. C₃²×C₅	C₄×C₈	semidirect
41. C₃⋊Dic₃	#170	semidirect
52. Dic₅	#622	semidirect
66. C₃²	C₄×#170	semidirect
74. C₅	C₄×#622	semidirect

Maximal subgroups

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

subgroup	index
C₂×#67127	2
Dic₅×C₃⋊Dic₃	2
C₄×#622	5
C₄×#170	9