Subgroups — C₅×#985 #91944

Order 480.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×GL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#226	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#135	—	3	1	no	maximal, Hall
5	C₄×C₅×D₃	—	4	1	no	maximal
6	C₅×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	#985	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×#41	—	3	1	no	—
9	C₅×#41	D₃	1	1	yes	characteristic, complemented
10	C₅×Q₁₆	—	3	1	no	—
11	C₅×SD₁₆	—	3	1	no	—
12	C₅×SD₁₆	—	3	1	no	—
13	C₅×D₈	—	3	1	no	—
14	C₂×C₅×C₈	—	3	1	no	—
15	C₂×C₅×D₃	—	4	1	no	—
16	C₃×C₄×C₅	—	4	1	no	—
17	C₅×Dic₃	—	4	1	no	—
18	#41⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
19	GL(2,𝔽₃)	C₂×C₅	1	1	yes	characteristic, complemented
20	#226	C₂×C₅	1	1	yes	characteristic, complemented
21	C₅×Q₈	—	3	1	no	—
22	C₅×Q₈	C₂×D₃	1	1	yes	characteristic
23	C₅×D₄	—	3	1	no	—
24	C₅×D₄	—	3	1	no	—
25	C₅×D₄	—	6	1	no	—
26	C₂×C₄×C₅	—	3	1	no	—
27	C₂×C₄×C₅	—	6	1	no	—
28	C₅×C₈	—	3	1	no	—
29	C₅×C₈	—	3	1	no	—
30	#135	—	3	1	no	Sylow
31	C₂×C₃×C₅	—	4	1	no	—
32	C₅×D₃	—	4	2	no	—
33	C₄×D₃	—	4	1	no	—
34	SL(2,𝔽₃)	C₂²×C₅	1	1	yes	characteristic
35	C₂²×C₅	—	3	1	no	—
36	C₂²×C₅	—	6	1	no	—
37	C₄×C₅	—	3	1	no	—
38	C₄×C₅	—	6	1	no	—
39	C₄×C₅	S₄	1	1	yes	characteristic
40	#41	—	3	1	no	—
41	#41	C₅×D₃	1	1	yes	characteristic, complemented
42	Q₁₆	—	3	1	no	—
43	SD₁₆	—	3	1	no	—
44	SD₁₆	—	3	1	no	—
45	D₈	—	3	1	no	—
46	C₂×C₈	—	3	1	no	—
47	C₃×C₅	—	4	1	no	Hall
48	C₂×D₃	—	4	1	no	—
49	C₃×C₄	—	4	1	no	—
50	Dic₃	—	4	1	no	—
51	C₂×C₅	—	6	1	no	—
52	C₂×C₅	—	12	1	no	—
53	C₂×C₅	C₂×S₄	1	1	yes	characteristic
54	Q₈	—	3	1	no	—
55	Q₈	C₂×C₅×D₃	1	1	yes	characteristic
56	D₄	—	3	1	no	—
57	D₄	—	3	1	no	—
58	D₄	—	6	1	no	—
59	C₂×C₄	—	3	1	no	—
60	C₂×C₄	—	6	1	no	—
61	C₈	—	3	1	no	—
62	C₈	—	3	1	no	—
63	C₂×C₃	—	4	1	no	—
64	D₃	—	4	2	no	—
65	C₅	#985	1	1	yes	characteristic, direct product factor, Sylow
66	C₂²	—	3	1	no	—
67	C₂²	—	6	1	no	—
68	C₄	—	3	1	no	—
69	C₄	—	6	1	no	—
70	C₄	C₅×S₄	1	1	yes	characteristic
71	C₃	—	4	1	no	Sylow
72	C₂	—	6	1	no	—
73	C₂	—	12	1	no	—
74	C₂	C₂×C₅×S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₅	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂²×C₅
Frattini	C₂	C₂×C₅×S₄
Fitting	C₅×#41	D₃
socle	C₂×C₅	C₂×S₄
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#41⋊C₃	C₂	semidirect
2. C₅×GL(2,𝔽₃)	C₂	semidirect
3. C₅×#226	C₂	semidirect
7. #985	C₅	direct (N × H)
9. C₅×#41	D₃	semidirect
18. #41⋊C₃	C₂×C₅	semidirect
19. GL(2,𝔽₃)	C₂×C₅	semidirect
20. #226	C₂×C₅	semidirect
41. #41	C₅×D₃	semidirect
65. C₅	#985	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#41⋊C₃	2
C₅×GL(2,𝔽₃)	2
C₅×#226	2
C₅×#135	3
C₄×C₅×D₃	4
#985	5

Subgroups — C5×#985 #91944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#985 #91944