Subgroups — C₅²×D₃×#3862 #36348029

Order 22050.

352 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	C₅²×D₃×C₇²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅²×#3862	—	3	1	no	maximal
4	C₅×D₃×#3862	C₅	1	6	yes	maximal, direct product factor
5	C₅²×#3862	—	2	1	no	—
6	C₅²×#3862	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₃×ΓL(1,𝔽₈)	—	7	2	no	maximal
9	C₂×C₅²×C₇²	—	3	1	no	Hall
10	C₃×C₅×#3862	C₂×C₅	1	6	yes	complemented
11	C₃×C₅²×ΓL(1,𝔽₈)	—	7	2	no	—
12	C₅×D₃×C₇²	C₃×C₅	1	6	yes	complemented
13	C₂×C₅×#3862	—	3	6	no	—
14	C₅²×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅²×D₃×C₇	—	3	2	no	—
16	C₅²×D₃×C₇	ΓL(1,𝔽₈)	1	2	yes	complemented
17	C₂×C₅²×ΓL(1,𝔽₈)	—	21	2	no	—
18	D₃×#3862	C₅²	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅×C₇²	C₂×C₃×C₅	1	6	yes	complemented
20	C₅×#3862	—	2	6	no	—
21	C₅×#3862	C₅×D₃	1	6	yes	direct product factor
22	C₅×D₃×ΓL(1,𝔽₈)	—	7	12	no	—
23	C₃×C₅²×C₇	—	3	2	no	—
24	C₃×C₅²×C₇	C₂×ΓL(1,𝔽₈)	1	2	yes	complemented
25	C₅²×ΓL(1,𝔽₈)	—	7	2	no	—
26	C₅²×ΓL(1,𝔽₈)	—	14	2	no	—
27	C₂×C₅×C₇²	—	3	6	no	—
28	C₃×C₅²×D₃	—	49	1	no	Hall
29	C₃×#3862	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅²×C₇	—	3	2	no	—
31	C₂×C₅²×C₇	—	9	2	no	—
32	C₃×C₅×ΓL(1,𝔽₈)	—	7	12	no	—
33	D₃×C₇²	C₃×C₅²	1	1	yes	characteristic, complemented
34	C₂×#3862	—	3	1	no	—
35	C₅×C₇²	C₃×C₅×D₃	1	6	yes	complemented
36	C₃²×C₅²	—	49	1	no	Hall
37	C₅×D₃×C₇	—	3	12	no	—
38	C₅×D₃×C₇	C₅×ΓL(1,𝔽₈)	1	12	yes	complemented
39	C₂×C₅×ΓL(1,𝔽₈)	—	21	12	no	—
40	C₅²×C₇	—	3	2	no	—
41	C₅²×C₇	D₃×ΓL(1,𝔽₈)	1	2	yes	complemented
42	C₂×C₃×C₅²	—	147	1	no	—
43	C₅²×D₃	#3862	1	1	yes	characteristic, direct product factor
44	C₃×C₇²	C₂×C₃×C₅²	1	1	yes	characteristic, complemented
45	#3862	—	2	1	no	—
46	#3862	C₅²×D₃	1	1	yes	characteristic, direct product factor
47	D₃×ΓL(1,𝔽₈)	—	7	2	no	—
48	C₃×C₅×C₇	—	3	12	no	—
49	C₃×C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	1	12	yes	complemented
50	C₅×ΓL(1,𝔽₈)	—	7	12	no	—
51	C₅×ΓL(1,𝔽₈)	—	14	12	no	—
52	C₂×C₇²	—	3	1	no	Hall
53	C₃×C₅×D₃	—	49	6	no	—
54	C₃×C₅²	—	49	1	no	—
55	C₃×C₅²	—	98	1	no	—
56	C₃×C₅²	C₂×#3862	1	1	yes	characteristic, complemented
57	C₂×C₅×C₇	—	3	12	no	—
58	C₂×C₅×C₇	—	9	12	no	—
59	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
60	C₂×C₅²	—	3	1	no	Hall
61	C₇²	C₃×C₅²×D₃	1	1	yes	characteristic, complemented, Sylow
62	C₃²×C₅	—	49	6	no	—
63	D₃×C₇	—	3	2	no	—
64	D₃×C₇	C₅²×ΓL(1,𝔽₈)	1	2	yes	complemented
65	C₂×ΓL(1,𝔽₈)	—	21	2	no	—
66	C₅×C₇	—	3	12	no	—
67	C₅×C₇	C₅×D₃×ΓL(1,𝔽₈)	1	12	yes	complemented
68	C₂×C₃×C₅	—	147	6	no	—
69	C₅×D₃	C₅×#3862	1	6	yes	direct product factor
70	C₅²	D₃×#3862	1	1	yes	characteristic, direct product factor, Sylow
71	C₃×C₇	—	3	2	no	—
72	C₃×C₇	C₂×C₅²×ΓL(1,𝔽₈)	1	2	yes	complemented
73	ΓL(1,𝔽₈)	—	7	2	no	—
74	ΓL(1,𝔽₈)	—	14	2	no	—
75	C₃×D₃	—	49	1	no	Hall
76	C₃×C₅	—	49	6	no	—
77	C₃×C₅	—	98	6	no	—
78	C₃×C₅	C₂×C₅×#3862	1	6	yes	complemented
79	C₂×C₇	—	3	2	no	—
80	C₂×C₇	—	9	2	no	—
81	C₂×C₅	—	3	6	no	—
82	C₃²	—	49	1	no	Sylow
83	C₇	—	3	2	no	—
84	C₇	C₅²×D₃×ΓL(1,𝔽₈)	1	2	yes	complemented
85	C₂×C₃	—	147	1	no	—
86	D₃	C₅²×#3862	1	1	yes	characteristic, direct product factor
87	C₅	C₅×D₃×#3862	1	6	yes	direct product factor
88	C₃	—	49	1	no	—
89	C₃	—	98	1	no	—
90	C₃	C₂×C₅²×#3862	1	1	yes	characteristic, complemented
91	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₃×#3862
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇²	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×#3862	C₂	semidirect
2. C₅²×D₃×C₇²	C₃	semidirect
4. C₅×D₃×#3862	C₅	direct (N × H)
6. C₅²×#3862	D₃	direct (N × H)
7. C₃×C₅²×C₇²	C₂×C₃	semidirect
10. C₃×C₅×#3862	C₂×C₅	semidirect
12. C₅×D₃×C₇²	C₃×C₅	semidirect
14. C₅²×C₇²	C₃×D₃	semidirect
16. C₅²×D₃×C₇	ΓL(1,𝔽₈)	semidirect
18. D₃×#3862	C₅²	direct (N × H)
19. C₃×C₅×C₇²	C₂×C₃×C₅	semidirect
21. C₅×#3862	C₅×D₃	direct (N × H)
24. C₃×C₅²×C₇	C₂×ΓL(1,𝔽₈)	semidirect
29. C₃×#3862	C₂×C₅²	semidirect
33. D₃×C₇²	C₃×C₅²	semidirect
35. C₅×C₇²	C₃×C₅×D₃	semidirect
38. C₅×D₃×C₇	C₅×ΓL(1,𝔽₈)	semidirect
41. C₅²×C₇	D₃×ΓL(1,𝔽₈)	semidirect
43. C₅²×D₃	#3862	direct (N × H)
44. C₃×C₇²	C₂×C₃×C₅²	semidirect
46. #3862	C₅²×D₃	direct (N × H)
49. C₃×C₅×C₇	C₂×C₅×ΓL(1,𝔽₈)	semidirect
56. C₃×C₅²	C₂×#3862	semidirect
61. C₇²	C₃×C₅²×D₃	semidirect
64. D₃×C₇	C₅²×ΓL(1,𝔽₈)	semidirect
67. C₅×C₇	C₅×D₃×ΓL(1,𝔽₈)	semidirect
69. C₅×D₃	C₅×#3862	direct (N × H)
70. C₅²	D₃×#3862	direct (N × H)
72. C₃×C₇	C₂×C₅²×ΓL(1,𝔽₈)	semidirect
78. C₃×C₅	C₂×C₅×#3862	semidirect
84. C₇	C₅²×D₃×ΓL(1,𝔽₈)	semidirect
86. D₃	C₅²×#3862	direct (N × H)
87. C₅	C₅×D₃×#3862	direct (N × H)
90. C₃	C₂×C₅²×#3862	semidirect

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
C₅²×D₃×C₇²	3
C₂×C₅²×#3862	3
C₅×D₃×#3862	5
C₅²×D₃×ΓL(1,𝔽₈)	7

Subgroups — C52×D3×#3862 #36348029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×#3862 #36348029