Subgroups — #91174

Order 480.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1203	C₂	1	1	yes	maximal, characteristic
2	#6762	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#704	C₂	1	1	yes	maximal, characteristic, complemented
4	#4013	—	3	1	no	maximal, Hall
5	C₂²×D₁₅	C₄	1	1	yes	characteristic
6	C₂²×C₅×D₃	C₄	1	1	yes	characteristic
7	C₂×C₃×Dic₅	C₂²	1	1	yes	characteristic
8	#1203	—	2	1	no	—
9	#1203	—	2	1	no	—
10	C₃⋊#170	—	2	1	no	—
11	C₃×#170	—	2	1	no	—
12	#823	—	5	1	no	maximal, Hall
13	C₂×C₂²⋊D₅	—	3	1	no	—
14	#704	—	3	1	no	—
15	#704	D₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×D₁₅	—	2	1	no	—
18	C₂×D₁₅	—	4	1	no	—
19	C₂×C₅×D₃	—	2	1	no	—
20	C₂×C₅×D₃	—	4	1	no	—
21	C₃×Dic₅	D₄	1	1	yes	characteristic
22	C₃×Dic₅	D₄	1	1	yes	characteristic
23	C₂×D₁₂	—	5	1	no	—
24	C₃×M₁₆	—	5	1	no	—
25	#208	—	5	1	no	—
26	C₂³×C₅	—	3	1	no	—
27	C₂²×D₅	—	3	1	no	—
28	C₂²⋊D₅	—	6	1	no	—
29	C₂²⋊D₅	—	6	1	no	—
30	C₂×Dic₅	C₂×D₃	1	1	yes	characteristic
31	#170	—	2	1	no	—
32	#170	—	6	1	no	—
33	#100	—	15	1	no	Sylow
34	C₂×C₃×C₅	—	2	1	no	—
35	C₂×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
36	D₁₅	—	4	1	no	—
37	C₅×D₃	—	4	1	no	—
38	C₂²×D₃	—	5	1	no	—
39	C₂²×D₃	AGL(1,𝔽₅)	1	1	yes	characteristic
40	C₂×C₃×C₄	—	5	1	no	—
41	D₁₂	—	10	1	no	—
42	D₁₂	—	10	1	no	—
43	C₃×C₈	—	10	1	no	—
44	C₃⋊C₈	—	10	1	no	—
45	C₂²×C₅	—	6	1	no	—
46	C₂²×C₅	—	12	1	no	—
47	C₂²×C₅	C₄×D₃	1	1	yes	characteristic
48	C₂×D₅	—	6	1	no	—
49	C₂×D₅	—	12	1	no	—
50	Dic₅	D₁₂	1	1	yes	characteristic
51	Dic₅	#67	1	1	yes	characteristic
52	C₂×D₄	—	15	1	no	—
53	M₁₆	—	5	1	no	—
54	M₁₆	—	15	1	no	—
55	C₃×C₅	#100	1	1	yes	characteristic, complemented, Hall
56	C₂²×C₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
57	C₂×D₃	—	2	1	no	—
58	C₂×D₃	—	4	1	no	—
59	C₂×D₃	—	10	1	no	—
60	C₂×D₃	—	20	1	no	—
61	C₃×C₄	—	5	1	no	—
62	C₃×C₄	—	5	1	no	—
63	C₂×C₅	—	2	1	no	—
64	C₂×C₅	—	12	1	no	—
65	C₂×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
66	D₅	—	12	1	no	—
67	C₂³	—	3	1	no	—
68	C₂³	—	15	1	no	—
69	D₄	—	30	1	no	—
70	D₄	—	30	1	no	—
71	C₂×C₄	—	5	1	no	—
72	C₈	—	10	1	no	—
73	C₈	—	30	1	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
76	D₃	—	4	1	no	—
77	D₃	—	20	1	no	—
78	C₅	#823	1	1	yes	characteristic, complemented, Sylow
79	C₂²	—	6	1	no	—
80	C₂²	—	12	1	no	—
81	C₂²	—	30	1	no	—
82	C₂²	—	60	1	no	—
83	C₂²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
84	C₄	—	5	1	no	—
85	C₄	—	5	1	no	—
86	C₃	#4013	1	1	yes	characteristic, complemented, Sylow
87	C₂	—	2	1	no	—
88	C₂	—	12	1	no	—
89	C₂	—	60	1	no	—
90	C₂	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×D₃)⋊AGL(1,𝔽₅)
commutator, Fitting	C₂²×C₃×C₅	C₂×C₄
Frattini, hypercenter	C₂²	D₃×AGL(1,𝔽₅)
socle	C₂×C₃×C₅	C₂²⋊C₄
prime radical	C₂×#1203	C₂
cosocle	C₂×C₃×Dic₅	C₂²
hypocenter	C₃×C₅	#100
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
2. #6762	C₂	semidirect
3. C₃×#704	C₂	semidirect
15. #704	D₃	semidirect
55. C₃×C₅	#100	semidirect
78. C₅	#823	semidirect
86. C₃	#4013	semidirect

Maximal subgroups

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

subgroup	index
C₂×#1203	2
#6762	2
C₃×#704	2
#4013	3
#823	5