Subgroups — C₃×C₅⋊D₅×#3862 #36347988

Order 22050.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊D₅×#3862	C₃	1	3	yes	maximal, direct product factor
4	C₃×D₅×#3862	—	5	6	no	maximal
5	C₅²×#3862	C₂×C₃	1	3	yes	complemented
6	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×ΓL(1,𝔽₈)×C₅⋊D₅	—	7	2	no	maximal
8	C₇²×C₅⋊D₅	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×#3862	D₅	1	6	yes	complemented
10	C₃×C₅²×ΓL(1,𝔽₈)	—	7	2	no	—
11	C₃×C₇²×D₅	—	5	6	no	—
12	D₅×#3862	—	5	18	no	—
13	C₅²×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
14	C₃×C₇×C₅⋊D₅	—	3	2	no	—
15	C₃×C₇×C₅⋊D₅	ΓL(1,𝔽₈)	1	2	yes	complemented
16	ΓL(1,𝔽₈)×C₅⋊D₅	—	7	6	no	—
17	C₂×C₃×#3862	—	25	1	no	Hall
18	C₃×C₅×C₇²	C₃×D₅	1	6	yes	complemented
19	C₅×#3862	C₃×D₅	1	18	yes	complemented
20	C₃×D₅×ΓL(1,𝔽₈)	—	35	12	no	—
21	C₃×C₅²×C₇	—	3	2	no	—
22	C₃×C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
23	C₅²×ΓL(1,𝔽₈)	—	7	6	no	—
24	C₇²×D₅	—	5	6	no	—
25	C₃²×C₅⋊D₅	—	49	1	no	Hall
26	C₃×#3862	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
27	C₇×C₅⋊D₅	—	3	2	no	—
28	C₇×C₅⋊D₅	C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
29	C₃×C₅×ΓL(1,𝔽₈)	—	7	12	no	—
30	C₂×C₃×C₇²	—	25	1	no	—
31	C₂×#3862	—	25	3	no	—
32	C₅×C₇²	C₃²×D₅	1	6	yes	complemented
33	C₃²×C₅²	—	49	1	no	Hall
34	C₃×C₇×D₅	—	5	12	no	—
35	C₃×C₇×D₅	—	15	12	no	—
36	D₅×ΓL(1,𝔽₈)	—	35	36	no	—
37	C₅²×C₇	—	3	2	no	—
38	C₅²×C₇	C₂×C₃×ΓL(1,𝔽₈)	1	2	yes	complemented
39	C₃×C₅⋊D₅	—	49	3	no	—
40	C₃×C₅⋊D₅	#3862	1	1	yes	characteristic, direct product factor
41	C₃×C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
42	#3862	C₃×C₅⋊D₅	1	3	yes	direct product factor
43	C₂×C₃×ΓL(1,𝔽₈)	—	175	2	no	—
44	C₃×C₅×C₇	—	3	12	no	—
45	C₃×C₅×C₇	D₅×ΓL(1,𝔽₈)	1	12	yes	complemented
46	C₅×ΓL(1,𝔽₈)	—	7	36	no	—
47	C₂×C₇²	—	25	1	no	Hall
48	C₃²×D₅	—	245	6	no	—
49	C₃×C₅²	—	49	3	no	—
50	C₃×C₅²	C₂×#3862	1	1	yes	characteristic, complemented
51	C₇×D₅	—	5	12	no	—
52	C₇×D₅	—	15	12	no	—
53	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
54	C₅⋊D₅	C₃×#3862	1	1	yes	characteristic, direct product factor, Hall
55	C₇²	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
56	C₃²×C₅	—	49	6	no	—
57	C₂×C₃×C₇	—	25	2	no	—
58	C₂×C₃×C₇	—	75	2	no	—
59	C₂×ΓL(1,𝔽₈)	—	175	6	no	—
60	C₅×C₇	—	3	12	no	—
61	C₅×C₇	C₃×D₅×ΓL(1,𝔽₈)	1	12	yes	complemented
62	C₃×D₅	—	5	6	no	—
63	C₃×D₅	—	245	18	no	—
64	C₅²	C₂×C₃×#3862	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₇	—	3	2	no	—
66	C₃×C₇	ΓL(1,𝔽₈)×C₅⋊D₅	1	2	yes	complemented
67	ΓL(1,𝔽₈)	—	7	6	no	—
68	C₂×C₃²	—	1225	1	no	Hall
69	C₃×C₅	—	49	18	no	—
70	C₃×C₅	D₅×#3862	1	6	yes	complemented
71	C₂×C₇	—	25	2	no	—
72	C₂×C₇	—	75	2	no	—
73	D₅	—	5	6	no	—
74	C₃²	—	49	1	no	Sylow
75	C₇	—	3	2	no	—
76	C₇	C₃×ΓL(1,𝔽₈)×C₅⋊D₅	1	2	yes	complemented
77	C₂×C₃	—	25	1	no	—
78	C₂×C₃	—	1225	3	no	—
79	C₅	C₃×D₅×#3862	1	6	yes	complemented
80	C₃	—	49	3	no	—
81	C₃	C₅⋊D₅×#3862	1	1	yes	characteristic, direct product factor
82	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₅⋊D₅×#3862
commutator, cosocle, hypocenter	C₅²×C₇²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×#3862	C₂	semidirect
2. C₃×C₇²×C₅⋊D₅	C₃	semidirect
3. C₅⋊D₅×#3862	C₃	direct (N × H)
5. C₅²×#3862	C₂×C₃	semidirect
6. C₃×C₅²×C₇²	C₂×C₃	semidirect
8. C₇²×C₅⋊D₅	C₃²	semidirect
9. C₃×C₅×#3862	D₅	semidirect
13. C₅²×C₇²	C₂×C₃²	semidirect
15. C₃×C₇×C₅⋊D₅	ΓL(1,𝔽₈)	semidirect
18. C₃×C₅×C₇²	C₃×D₅	semidirect
19. C₅×#3862	C₃×D₅	semidirect
22. C₃×C₅²×C₇	C₂×ΓL(1,𝔽₈)	semidirect
26. C₃×#3862	C₅⋊D₅	direct (N × H)
28. C₇×C₅⋊D₅	C₃×ΓL(1,𝔽₈)	semidirect
32. C₅×C₇²	C₃²×D₅	semidirect
38. C₅²×C₇	C₂×C₃×ΓL(1,𝔽₈)	semidirect
40. C₃×C₅⋊D₅	#3862	direct (N × H)
41. C₃×C₇²	C₃×C₅⋊D₅	semidirect
42. #3862	C₃×C₅⋊D₅	direct (N × H)
45. C₃×C₅×C₇	D₅×ΓL(1,𝔽₈)	semidirect
50. C₃×C₅²	C₂×#3862	semidirect
54. C₅⋊D₅	C₃×#3862	direct (N × H)
55. C₇²	C₃²×C₅⋊D₅	semidirect
61. C₅×C₇	C₃×D₅×ΓL(1,𝔽₈)	semidirect
64. C₅²	C₂×C₃×#3862	semidirect
66. C₃×C₇	ΓL(1,𝔽₈)×C₅⋊D₅	semidirect
70. C₃×C₅	D₅×#3862	semidirect
76. C₇	C₃×ΓL(1,𝔽₈)×C₅⋊D₅	semidirect
79. C₅	C₃×D₅×#3862	semidirect
81. C₃	C₅⋊D₅×#3862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅²×#3862	2
C₃×C₇²×C₅⋊D₅	3
C₅⋊D₅×#3862	3
C₃×D₅×#3862	5
C₃×ΓL(1,𝔽₈)×C₅⋊D₅	7

Subgroups — C3×C5⋊D5×#3862 #36347988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅⋊D₅×#3862 #36347988