Subgroups — #13086381

Order 1440.

136 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	C₄×C₃⋊Dic₁₅	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃²×C₄×C₅	C₄	1	1	yes	characteristic
4	C₂×C₃⋊Dic₁₅	C₄	1	1	yes	characteristic
5	C₂×C₃⋊Dic₁₅	C₂²	1	1	yes	characteristic
6	#67127	—	2	2	no	—
7	#63779	—	5	1	no	maximal, Hall
8	C₄×Dic₁₅	—	6	2	no	—
9	C₂²×C₃²×C₅	C₂×C₄	1	1	yes	characteristic
10	C₃²×C₄×C₅	—	2	1	no	—
11	C₃⋊Dic₁₅	C₈	1	2	yes	complemented
12	C₃⋊Dic₁₅	D₄	1	1	yes	characteristic
13	C₃⋊Dic₁₅	Q₈	1	1	yes	characteristic
14	#4004	—	9	1	no	maximal, Hall
15	C₂×#622	—	5	2	no	—
16	C₄×C₃⋊Dic₃	—	5	1	no	—
17	C₂×C₃×C₄×C₅	—	2	2	no	—
18	C₂×Dic₁₅	—	6	2	no	—
19	C₂×Dic₁₅	—	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	C₂×#170	—	9	2	no	—
24	C₄×Dic₅	—	9	1	no	—
25	C₂×C₃²×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
26	C₂×C₃⋊Dic₃	—	5	1	no	—
27	C₂×C₃⋊Dic₃	—	5	1	no	—
28	#622	—	10	2	no	—
29	C₂²×C₃×C₅	—	2	2	no	—
30	C₃×C₄×C₅	—	2	4	no	—
31	Dic₁₅	—	6	4	no	—
32	Dic₁₅	—	6	2	no	—
33	Dic₁₅	—	6	2	no	—
34	C₄×Dic₃	—	30	2	no	—
35	C₃²×C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
36	C₂×C₄×C₅	#157	1	1	yes	characteristic
37	C₂×Dic₅	—	9	1	no	—
38	C₂×Dic₅	—	9	1	no	—
39	#170	—	18	2	no	—
40	C₂²×C₃²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
41	C₃²×C₄	—	2	1	no	—
42	C₃⋊Dic₃	—	5	2	no	—
43	C₃⋊Dic₃	—	5	1	no	—
44	C₃⋊Dic₃	—	5	1	no	—
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	—	30	2	no	—
51	C₂×Dic₃	—	30	2	no	—
52	C₂²×C₅	C₂×#157	1	1	yes	characteristic
53	C₄×C₅	—	2	1	no	—
54	Dic₅	—	9	2	no	—
55	Dic₅	—	9	1	no	—
56	Dic₅	—	9	1	no	—
57	C₂×C₃²	D₅⋊C₈	1	1	yes	characteristic
58	C₂×C₃²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
59	C₂×C₃²	#704	1	1	yes	characteristic
60	C₂×C₈	—	45	2	no	—
61	C₄²	—	45	1	no	—
62	C₃×C₅	—	2	2	no	—
63	C₂²×C₃	—	2	2	no	—
64	C₃×C₄	—	2	4	no	—
65	Dic₃	—	30	4	no	—
66	Dic₃	—	30	2	no	—
67	Dic₃	—	30	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	#4004	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₄	—	45	1	no	—
73	C₂×C₄	—	45	1	no	—
74	C₂×C₄	#4380	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×#4380	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	45	2	no	—
83	C₄	—	45	1	no	—
84	C₄	—	45	1	no	—
85	C₃	—	2	2	no	—
86	C₂	#10624113	1	1	yes	characteristic
87	C₂	C₄⋊#4380	1	1	yes	characteristic
88	C₂	#10624118	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#4380
commutator	C₂×C₃²×C₅	C₂×C₈
Fitting	C₂×C₃²×C₄×C₅	C₄
socle, prime radical	C₂²×C₃²×C₅	C₂×C₄
cosocle	C₂×C₃⋊Dic₁₅	C₂²
hypercenter	C₂×C₄	#4380
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. C₃⋊Dic₁₅	C₈	semidirect
35. C₃²×C₅	C₄⋊C₈	semidirect
71. C₃²	#4004	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×#67127	2
C₄×C₃⋊Dic₁₅	2
#63779	5
#4004	9