Subgroups — #91256

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6777	C₂	1	2	yes	maximal, complemented
2	C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
5	#6652	C₂	1	2	yes	maximal, complemented
6	D₅×D₈	—	3	1	no	maximal, Hall
7	C₂×D₃×D₅	—	2	2	no	—
8	C₄×D₁₅	C₂²	1	1	yes	characteristic
9	C₅×D₁₂	C₂²	1	2	yes	complemented
10	C₃×D₂₀	C₂²	1	2	yes	complemented
11	#1201	—	2	2	no	—
12	C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
13	C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
14	D₃×D₈	—	5	1	no	maximal, Hall
15	D₄×D₅	—	3	2	no	—
16	C₅×D₈	—	3	1	no	—
17	#686	—	3	2	no	—
18	D₄₀	D₃	1	1	yes	characteristic, complemented
19	C₈×D₅	—	3	1	no	—
20	C₂×D₁₅	D₄	1	1	yes	characteristic
21	C₂×C₅×D₃	—	2	2	no	—
22	C₂×C₃×D₅	—	2	2	no	—
23	D₃×D₅	—	4	4	no	—
24	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	Dic₁₅	D₄	1	1	yes	characteristic
26	D₃×D₄	—	5	2	no	—
27	C₃×D₈	—	5	1	no	—
28	#213	—	5	2	no	—
29	D₂₄	D₅	1	1	yes	characteristic, complemented
30	D₃×C₈	—	5	1	no	—
31	C₂²×D₅	—	6	2	no	—
32	C₅×D₄	—	3	2	no	—
33	C₂²⋊D₅	—	6	2	no	—
34	D₂₀	C₂×D₃	1	2	yes	complemented
35	C₄×D₅	—	3	1	no	—
36	C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
37	#168	—	3	1	no	—
38	C₂×D₈	—	15	1	no	Sylow
39	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
40	D₁₅	D₈	1	2	yes	complemented
41	C₃×D₅	—	4	2	no	—
42	C₅×D₃	—	4	2	no	—
43	C₂²×D₃	—	10	2	no	—
44	C₃×D₄	—	5	2	no	—
45	#67	—	10	2	no	—
46	D₁₂	C₂×D₅	1	2	yes	complemented
47	C₄×D₃	—	5	1	no	—
48	C₃×C₈	C₂×D₅	1	1	yes	characteristic, complemented
49	C₃⋊C₈	—	5	1	no	—
50	C₂²×C₅	—	6	2	no	—
51	C₂×D₅	—	2	2	no	—
52	C₂×D₅	—	3	1	no	—
53	C₂×D₅	—	12	4	no	—
54	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
55	Dic₅	—	3	1	no	—
56	C₂×D₄	—	15	2	no	—
57	D₈	—	3	1	no	—
58	D₈	—	5	1	no	—
59	D₈	—	15	2	no	—
60	C₂×C₈	—	15	1	no	—
61	C₃×C₅	C₂×D₈	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₃	—	10	2	no	—
63	C₂×D₃	—	2	2	no	—
64	C₂×D₃	—	5	1	no	—
65	C₂×D₃	—	20	4	no	—
66	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
67	Dic₃	—	5	1	no	—
68	C₂×C₅	—	12	2	no	—
69	C₂×C₅	D₃×D₄	1	1	yes	characteristic
70	D₅	—	3	2	no	—
71	D₅	—	4	2	no	—
72	C₂³	—	30	2	no	—
73	D₄	—	3	2	no	—
74	D₄	—	5	2	no	—
75	D₄	—	30	2	no	—
76	C₂×C₄	—	15	1	no	—
77	C₈	—	15	1	no	—
78	C₈	D₃×D₅	1	1	yes	characteristic, complemented
79	C₂×C₃	—	20	2	no	—
80	C₂×C₃	D₄×D₅	1	1	yes	characteristic
81	D₃	—	4	2	no	—
82	D₃	—	5	2	no	—
83	C₅	D₃×D₈	1	1	yes	characteristic, complemented, Sylow
84	C₂²	—	6	2	no	—
85	C₂²	—	10	2	no	—
86	C₂²	—	15	1	no	—
87	C₂²	—	60	4	no	—
88	C₄	—	15	1	no	—
89	C₄	C₂×D₃×D₅	1	1	yes	characteristic
90	C₃	D₅×D₈	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	12	2	no	—
92	C₂	—	15	2	no	—
93	C₂	—	20	2	no	—
94	C₂	#6777	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#6777
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂×D₃×D₅
Fitting	C₃×C₅×C₈	C₂²
socle	C₂×C₃×C₅	C₂×D₄
hypercenter	C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×D₈
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
1. #6777	C₂	semidirect
2. C₈×D₁₅	C₂	semidirect
3. C₅×D₂₄	C₂	semidirect
4. C₃×D₄₀	C₂	semidirect
5. #6652	C₂	semidirect
9. C₅×D₁₂	C₂²	semidirect
10. C₃×D₂₀	C₂²	semidirect
12. C₃×C₅×C₈	C₂²	semidirect
13. C₃⋊#168	C₂²	semidirect
18. D₄₀	D₃	semidirect
29. D₂₄	D₅	semidirect
34. D₂₀	C₂×D₃	semidirect
36. C₅×C₈	C₂×D₃	semidirect
40. D₁₅	D₈	semidirect
46. D₁₂	C₂×D₅	semidirect
48. C₃×C₈	C₂×D₅	semidirect
61. C₃×C₅	C₂×D₈	semidirect
78. C₈	D₃×D₅	semidirect
83. C₅	D₃×D₈	semidirect
90. C₃	D₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
#6777	2
C₈×D₁₅	2
C₅×D₂₄	2
C₃×D₄₀	2
#6652	2
D₅×D₈	3
D₃×D₈	5