Subgroups — #91913

Order 480.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6772	C₂	1	1	yes	maximal, characteristic
2	D₅⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#700	C₂	1	1	yes	maximal, characteristic, complemented
4	#6739	C₂	1	2	yes	maximal, complemented
5	D₃×#170	C₂	1	2	yes	maximal, complemented
6	#4131	—	3	1	no	maximal, Hall
7	Dic₃₀	C₄	1	1	yes	characteristic
8	C₅×D₁₂	C₄	1	1	yes	characteristic
9	C₃×C₄×D₅	C₂²	1	1	yes	characteristic
10	#1201	C₄	1	2	yes	—
11	D₃×Dic₅	C₂²	1	2	yes	—
12	C₃⋊#170	C₂²	1	1	yes	characteristic
13	C₃⋊#170	C₂²	1	1	yes	characteristic
14	C₃×#170	C₂²	1	2	yes	—
15	#907	—	5	1	no	maximal, Hall
16	#711	—	3	1	no	—
17	#704	—	3	2	no	—
18	C₂×#170	—	3	2	no	—
19	#700	D₃	1	1	yes	characteristic, complemented
20	D₅⋊C₈	—	3	1	no	—
21	C₂×C₅×D₃	C₂×C₄	1	2	yes	—
22	C₂×C₃×D₅	C₂×C₄	1	1	yes	characteristic
23	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
24	Dic₁₅	C₂×C₄	1	2	yes	—
25	C₃×Dic₅	C₂³	1	1	yes	characteristic
26	#235	—	5	1	no	—
27	C₃×M₁₆	—	5	1	no	—
28	C₂×C₃⋊C₈	—	5	1	no	—
29	ΓL(1,𝔽₂₅)	—	5	2	no	—
30	D₃×C₈	—	5	2	no	—
31	C₅×D₄	—	3	1	no	—
32	C₂²⋊D₅	—	3	2	no	—
33	C₂×Dic₅	—	3	2	no	—
34	C₄×D₅	C₂×D₃	1	1	yes	characteristic
35	Dic₁₀	—	3	1	no	—
36	#170	—	3	1	no	—
37	#170	—	3	1	no	—
38	#170	C₂×D₃	1	2	yes	—
39	#131	—	15	1	no	Sylow
40	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
41	C₃×D₅	—	2	1	no	—
42	C₅×D₃	—	2	2	no	—
43	C₂×C₃×C₄	—	5	1	no	—
44	#67	—	5	2	no	—
45	D₁₂	AGL(1,𝔽₅)	1	1	yes	characteristic
46	C₄×D₃	—	5	2	no	—
47	Dic₆	—	5	1	no	—
48	C₃×C₈	—	5	2	no	—
49	C₃⋊C₈	—	5	1	no	—
50	C₃⋊C₈	—	5	1	no	—
51	C₂²×C₅	—	3	2	no	—
52	C₂×D₅	C₄×D₃	1	1	yes	characteristic
53	C₄×C₅	C₄×D₃	1	1	yes	characteristic
54	Dic₅	—	3	2	no	—
55	Dic₅	C₂²×D₃	1	1	yes	characteristic
56	#41	—	15	1	no	—
57	M₁₆	—	5	1	no	—
58	M₁₆	—	15	2	no	—
59	C₂×C₈	—	15	2	no	—
60	C₂×C₈	—	15	1	no	—
61	C₃×C₅	#131	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	—	5	1	no	—
63	C₂×D₃	C₂×AGL(1,𝔽₅)	1	2	yes	—
64	C₃×C₄	—	5	1	no	—
65	C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
66	Dic₃	—	5	2	no	—
67	C₂×C₅	—	6	2	no	—
68	C₂×C₅	C₂×C₄×D₃	1	1	yes	characteristic
69	D₅	—	2	1	no	—
70	Q₈	—	15	1	no	—
71	D₄	—	3	1	no	—
72	D₄	—	15	2	no	—
73	C₂×C₄	—	5	1	no	—
74	C₂×C₄	—	15	2	no	—
75	C₈	—	5	2	no	—
76	C₈	—	15	1	no	—
77	C₈	—	15	1	no	—
78	C₂×C₃	—	10	1	no	—
79	C₂×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
80	D₃	—	2	2	no	—
81	C₅	#907	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	3	2	no	—
83	C₂²	—	5	1	no	—
84	C₄	—	5	1	no	—
85	C₄	—	15	2	no	—
86	C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
87	C₃	#4131	1	1	yes	characteristic, complemented, Sylow
88	C₂	—	6	2	no	—
89	C₂	—	10	1	no	—
90	C₂	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂²×C₄
Fitting	C₃×C₄×C₅	C₂×C₄
prime radical	#6772	C₂
cosocle	C₃×Dic₅	C₂³
hypercenter	C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#131
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. D₅⋊(C₃⋊C₈)	C₂	semidirect
3. C₃×#700	C₂	semidirect
4. #6739	C₂	semidirect
5. D₃×#170	C₂	semidirect
19. #700	D₃	semidirect
61. C₃×C₅	#131	semidirect
81. C₅	#907	semidirect
87. C₃	#4131	semidirect

Maximal subgroups

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

subgroup	index
#6772	2
D₅⋊(C₃⋊C₈)	2
C₃×#700	2
#6739	2
D₃×#170	2
#4131	3
#907	5