Subgroups — #13086356

Order 1440.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#67126	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	#67126	—	2	2	no	—
7	#63779	—	5	1	no	maximal, Hall
8	C₄×C₅×Dic₃	—	6	2	no	—
9	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₃²×C₄×C₅	—	2	1	no	—
11	C₅×C₃⋊Dic₃	C₈	1	2	yes	complemented
12	C₅×C₃⋊Dic₃	D₄	1	1	yes	characteristic
13	C₅×C₃⋊Dic₃	Q₈	1	1	yes	characteristic
14	C₄⋊#168	—	9	1	no	maximal, Hall
15	C₂×#622	—	5	2	no	—
16	C₄×C₃⋊Dic₃	D₅	1	1	yes	characteristic
17	C₂×C₃×C₄×C₅	—	2	2	no	—
18	C₂×C₅×Dic₃	—	6	2	no	—
19	C₂×C₅×Dic₃	—	6	2	no	—
20	C₂×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃²×C₅	C₂×C₈	1	1	yes	characteristic
22	C₂×C₃²×C₅	M₁₆	1	1	yes	characteristic
23	C₄²×C₅	—	9	1	no	—
24	C₂×#168	—	9	2	no	—
25	C₂×C₃²×C₄	Dic₅	1	1	yes	characteristic
26	C₂×C₃⋊Dic₃	Dic₅	1	1	yes	characteristic
27	C₂×C₃⋊Dic₃	C₂×D₅	1	1	yes	characteristic
28	#622	—	10	2	no	—
29	C₂²×C₃×C₅	—	2	2	no	—
30	C₃×C₄×C₅	—	2	4	no	—
31	C₅×Dic₃	—	6	4	no	—
32	C₅×Dic₃	—	6	2	no	—
33	C₅×Dic₃	—	6	2	no	—
34	C₄×Dic₃	—	6	2	no	—
35	C₃²×C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
36	C₂×C₄×C₅	—	9	1	no	—
37	C₂×C₄×C₅	—	9	1	no	—
38	C₂×C₄×C₅	#157	1	1	yes	characteristic
39	#168	—	18	2	no	—
40	C₂²×C₃²	C₂×Dic₅	1	1	yes	characteristic
41	C₃²×C₄	—	2	1	no	—
42	C₃⋊Dic₃	#168	1	2	yes	complemented
43	C₃⋊Dic₃	Dic₁₀	1	1	yes	characteristic
44	C₃⋊Dic₃	D₂₀	1	1	yes	characteristic
45	C₄⋊C₈	—	45	1	no	Sylow
46	C₂×C₃×C₅	—	2	2	no	—
47	C₂×C₃×C₅	—	2	2	no	—
48	C₂×C₃×C₅	—	2	2	no	—
49	C₂×C₃×C₄	—	2	2	no	—
50	C₂×Dic₃	—	6	2	no	—
51	C₂×Dic₃	—	6	2	no	—
52	C₂²×C₅	C₂×#157	1	1	yes	characteristic
53	C₄×C₅	—	2	1	no	—
54	C₄×C₅	—	9	2	no	—
55	C₄×C₅	—	9	1	no	—
56	C₄×C₅	—	9	1	no	—
57	C₂×C₃²	C₂×#168	1	1	yes	characteristic
58	C₂×C₃²	#681	1	1	yes	characteristic
59	C₂×C₃²	C₄⋊Dic₅	1	1	yes	characteristic
60	C₂×C₈	—	45	2	no	—
61	C₄²	—	9	1	no	—
62	C₃×C₅	—	2	2	no	—
63	C₂²×C₃	—	2	2	no	—
64	C₃×C₄	—	2	4	no	—
65	Dic₃	—	6	4	no	—
66	Dic₃	—	6	2	no	—
67	Dic₃	—	6	2	no	—
68	C₂×C₅	#3787	1	1	yes	characteristic
69	C₂×C₅	C₄⋊#157	1	1	yes	characteristic
70	C₂×C₅	#3792	1	1	yes	characteristic
71	C₃²	C₄⋊#168	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₄	—	9	1	no	—
73	C₂×C₄	—	9	1	no	—
74	C₂×C₄	#4379	1	1	yes	characteristic
75	C₈	—	90	2	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	—	2	2	no	—
79	C₅	#63779	1	1	yes	characteristic, complemented, Sylow
80	C₂²	C₂×#4379	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	9	2	no	—
83	C₄	—	9	1	no	—
84	C₄	—	9	1	no	—
85	C₃	—	2	2	no	—
86	C₂	#10624106	1	1	yes	characteristic
87	C₂	C₄⋊#4379	1	1	yes	characteristic
88	C₂	#10624111	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#4379
commutator	C₂×C₃²×C₅	C₂×C₈
Fitting	C₂×C₃²×C₄×C₅	C₄
socle, prime radical	C₂²×C₃²×C₅	C₂×C₄
cosocle	C₂×C₅×C₃⋊Dic₃	C₂²
hypercenter	C₂×C₄	#4379
hypocenter	C₃²×C₅	C₄⋊C₈
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
11. C₅×C₃⋊Dic₃	C₈	semidirect
35. C₃²×C₅	C₄⋊C₈	semidirect
42. C₃⋊Dic₃	#168	semidirect
71. C₃²	C₄⋊#168	semidirect
79. C₅	#63779	semidirect

Maximal subgroups

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

subgroup	index
C₂×#67126	2
C₄×C₅×C₃⋊Dic₃	2
#63779	5
C₄⋊#168	9