Subgroups — #91175

Order 480.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1204	C₂	1	1	yes	maximal, characteristic
2	#6762	C₂	1	1	yes	maximal, characteristic
3	C₃×#704	C₂	1	1	yes	maximal, characteristic
4	#4005	—	3	1	no	maximal, Hall
5	C₂×Dic₁₅	C₄	1	1	yes	characteristic
6	C₂×C₅×Dic₃	C₄	1	1	yes	characteristic
7	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
8	#1204	—	2	1	no	—
9	#1204	—	2	1	no	—
10	C₃⋊#170	—	2	1	no	—
11	C₃×#170	—	2	1	no	—
12	#824	—	5	1	no	maximal, Hall
13	C₂×Dic₁₀	—	3	1	no	—
14	#704	—	3	1	no	—
15	#704	D₃	1	1	yes	characteristic
16	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
17	Dic₁₅	—	2	1	no	—
18	C₃×Dic₅	D₄	1	1	yes	characteristic
19	C₃×Dic₅	D₄	1	1	yes	characteristic
20	C₅×Dic₃	—	2	1	no	—
21	C₂×Dic₆	—	5	1	no	—
22	C₃×M₁₆	—	5	1	no	—
23	#208	—	5	1	no	—
24	C₂×C₄×C₅	—	3	1	no	—
25	C₂×Dic₅	—	3	1	no	—
26	C₂×Dic₅	C₂×D₃	1	1	yes	characteristic
27	Dic₁₀	—	6	1	no	—
28	Dic₁₀	—	6	1	no	—
29	#170	—	2	1	no	—
30	#170	—	6	1	no	—
31	#101	—	15	1	no	Sylow
32	C₂×C₃×C₅	—	2	1	no	—
33	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₃×C₄	—	5	1	no	—
35	C₂×Dic₃	—	5	1	no	—
36	C₂×Dic₃	AGL(1,𝔽₅)	1	1	yes	characteristic
37	Dic₆	—	10	1	no	—
38	Dic₆	—	10	1	no	—
39	C₃×C₈	—	10	1	no	—
40	C₃⋊C₈	—	10	1	no	—
41	C₂²×C₅	C₄×D₃	1	1	yes	characteristic
42	C₄×C₅	—	6	1	no	—
43	Dic₅	—	6	1	no	—
44	Dic₅	D₁₂	1	1	yes	characteristic
45	Dic₅	#67	1	1	yes	characteristic
46	C₂×Q₈	—	15	1	no	—
47	M₁₆	—	5	1	no	—
48	M₁₆	—	15	1	no	—
49	C₃×C₅	#101	1	1	yes	characteristic, complemented, Hall
50	C₂²×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
51	C₃×C₄	—	5	1	no	—
52	C₃×C₄	—	5	1	no	—
53	Dic₃	—	2	1	no	—
54	Dic₃	—	10	1	no	—
55	C₂×C₅	—	2	1	no	—
56	C₂×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
57	Q₈	—	30	1	no	—
58	Q₈	—	30	1	no	—
59	C₂×C₄	—	3	1	no	—
60	C₂×C₄	—	5	1	no	—
61	C₂×C₄	—	15	1	no	—
62	C₈	—	10	1	no	—
63	C₈	—	30	1	no	—
64	C₂×C₃	—	2	1	no	—
65	C₂×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
66	C₅	#824	1	1	yes	characteristic, complemented, Sylow
67	C₂²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
68	C₄	—	5	1	no	—
69	C₄	—	5	1	no	—
70	C₄	—	6	1	no	—
71	C₄	—	30	1	no	—
72	C₃	#4005	1	1	yes	characteristic, complemented, Sylow
73	C₂	—	2	1	no	—
74	C₂	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×D₃)⋊AGL(1,𝔽₅)
commutator, Fitting, prime radical	C₂²×C₃×C₅	C₂×C₄
Frattini, hypercenter	C₂²	D₃×AGL(1,𝔽₅)
socle	C₂×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₃×Dic₅	C₂²
hypocenter	C₃×C₅	#101
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
49. C₃×C₅	#101	semidirect
66. C₅	#824	semidirect
72. C₃	#4005	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1204	2
#6762	2
C₃×#704	2
#4005	3
#824	5