Subgroups — C₅×#875 #91678

Order 480.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₅×#124	—	3	1	no	maximal, Hall
6	C₂²×C₅×D₃	C₂²	1	2	yes	—
7	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂×C₅×Dic₃	C₂²	1	2	yes	—
10	C₅×D₁₂	—	2	2	no	—
11	C₅×Dic₆	—	2	2	no	—
12	#875	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×Q₈	—	3	1	no	—
14	C₂×C₅×D₄	—	3	1	no	—
15	C₅×C₂²⋊C₄	—	3	4	no	—
16	C₄²×C₅	D₃	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
18	C₂×C₅×D₃	—	2	2	no	—
19	C₂×C₅×D₃	—	2	4	no	—
20	C₃×C₄×C₅	—	2	2	no	—
21	C₃×C₄×C₅	D₄	1	2	yes	—
22	C₅×Dic₃	—	2	2	no	—
23	C₂×D₁₂	C₂×C₅	1	1	yes	characteristic
24	C₂×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
25	C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
26	(C₂×D₃)⋊C₄	C₂×C₅	1	4	yes	complemented
27	C₂³×C₅	—	3	2	no	—
28	C₅×Q₈	—	6	2	no	—
29	C₅×D₄	—	6	2	no	—
30	C₂×C₄×C₅	—	3	2	no	—
31	C₂×C₄×C₅	C₂×D₃	1	2	yes	—
32	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
33	#124	—	3	1	no	Sylow
34	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃×C₅	#41	1	2	yes	—
36	C₅×D₃	—	4	2	no	—
37	C₂²×D₃	C₂²×C₅	1	2	yes	—
38	C₂×C₃×C₄	C₂²×C₅	1	2	yes	—
39	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
40	C₂×Dic₃	C₂²×C₅	1	2	yes	—
41	D₁₂	—	2	2	no	—
42	Dic₆	—	2	2	no	—
43	C₂²×C₅	—	6	2	no	—
44	C₂²×C₅	—	6	4	no	—
45	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
46	C₄×C₅	—	2	2	no	—
47	C₄×C₅	—	6	2	no	—
48	C₄×C₅	D₁₂	1	2	yes	—
49	C₂×Q₈	—	3	1	no	—
50	C₂×D₄	—	3	1	no	—
51	C₂²⋊C₄	—	3	4	no	—
52	C₄²	C₅×D₃	1	1	yes	characteristic, complemented
53	C₃×C₅	#124	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
55	C₂×D₃	—	2	2	no	—
56	C₂×D₃	—	2	4	no	—
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	C₅×D₄	1	2	yes	—
59	Dic₃	—	2	2	no	—
60	C₂×C₅	—	12	2	no	—
61	C₂×C₅	C₂×D₁₂	1	1	yes	characteristic
62	C₂×C₅	#235	1	2	yes	—
63	C₂³	—	3	2	no	—
64	Q₈	—	6	2	no	—
65	D₄	—	6	2	no	—
66	C₂×C₄	—	3	2	no	—
67	C₂×C₄	C₂×C₅×D₃	1	2	yes	—
68	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
69	C₂×C₃	C₂×C₅×D₄	1	1	yes	characteristic
70	C₂×C₃	C₅×#41	1	2	yes	—
71	D₃	—	4	2	no	—
72	C₅	#875	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²	—	6	2	no	—
74	C₂²	—	6	4	no	—
75	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	6	2	no	—
78	C₄	C₅×D₁₂	1	2	yes	—
79	C₃	C₅×#124	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	12	2	no	—
81	C₂	C₂×C₅×D₁₂	1	1	yes	characteristic
82	C₂	C₅×#235	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₅
Frattini	C₂²	C₂²×C₅×D₃
Fitting	C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂³
prime radical	C₂×C₅×D₁₂	C₂
hypercenter	C₄²×C₅	D₃
hypocenter	C₃	C₅×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×Dic₆	C₂	semidirect
3. C₃×C₄²×C₅	C₂	semidirect
4. C₅×(C₂×D₃)⋊C₄	C₂	semidirect
12. #875	C₅	direct (N × H)
16. C₄²×C₅	D₃	semidirect
24. C₂×Dic₆	C₂×C₅	semidirect
25. C₃×C₄²	C₂×C₅	semidirect
26. (C₂×D₃)⋊C₄	C₂×C₅	semidirect
52. C₄²	C₅×D₃	semidirect
53. C₃×C₅	#124	semidirect
72. C₅	#875	direct (N × H)
79. C₃	C₅×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₁₂	2
C₂×C₅×Dic₆	2
C₃×C₄²×C₅	2
C₅×(C₂×D₃)⋊C₄	2
C₅×#124	3
#875	5

Subgroups — C5×#875 #91678

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#875 #91678