Subgroups — C₅⋊D₅×D₃₆₃ #49136993

Order 36300.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₅⋊D₆₀₅)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅⋊D₅×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅×D₁₂₁	—	3	1	no	maximal, Hall
5	C₃×C₅²×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₅×D₃₆₃	—	5	6	no	maximal
7	C₅⋊D₆₀₅	—	3	1	no	—
8	C₅⋊D₅×C₁₂₁	D₃	1	1	yes	characteristic, complemented
9	C₅²×D₁₂₁	—	3	1	no	—
10	D₁₈₁₅	—	5	6	no	—
11	C₅×D₃₆₃	D₅	1	6	yes	complemented
12	C₃×D₅×C₁₂₁	—	5	6	no	—
13	C₅⋊D₅×D₃₃	—	11	1	no	maximal
14	C₅²×C₁₂₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	D₅×D₁₂₁	—	15	6	no	—
16	C₃×C₅×C₁₂₁	C₂×D₅	1	6	yes	complemented
17	C₃⋊(C₅⋊D₅₅)	—	11	1	no	—
18	C₅²×D₃₃	—	11	1	no	—
19	C₃×C₁₁×C₅⋊D₅	D₁₁	1	1	yes	characteristic
20	C₂×D₃₆₃	—	25	1	no	Hall
21	D₆₀₅	—	15	6	no	—
22	C₅×D₁₂₁	—	3	6	no	—
23	D₅×C₁₂₁	—	5	6	no	—
24	D₁₁×C₅⋊D₅	—	33	1	no	—
25	C₃×C₅²×C₁₁	C₂×D₁₁	1	1	yes	characteristic
26	C₂×C₃×C₁₂₁	—	25	1	no	—
27	D₃₆₃	—	25	1	no	—
28	D₃₆₃	C₅⋊D₅	1	1	yes	characteristic, direct product factor
29	D₅×D₃₃	—	55	6	no	—
30	C₅×C₁₂₁	D₃×D₅	1	6	yes	complemented
31	C₅⋊D₅₅	—	33	1	no	—
32	C₁₁×C₅⋊D₅	D₃₃	1	1	yes	characteristic
33	C₅²×D₁₁	—	33	1	no	—
34	C₂×D₁₂₁	—	75	1	no	Hall
35	C₃×C₁₂₁	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
36	D₁₆₅	—	55	6	no	—
37	C₅×D₃₃	—	11	6	no	—
38	C₃×D₅×C₁₁	—	5	6	no	—
39	D₃×C₅⋊D₅	—	121	1	no	Hall
40	C₅²×C₁₁	C₂×D₃₃	1	1	yes	characteristic
41	C₂×C₁₂₁	—	25	1	no	—
42	D₁₂₁	—	3	1	no	—
43	D₁₂₁	—	75	1	no	—
44	D₅×D₁₁	—	165	6	no	—
45	C₃×C₅×C₁₁	D₅×D₁₁	1	6	yes	—
46	C₃⋊(C₅⋊D₅)	—	121	1	no	—
47	C₅²×D₃	—	121	1	no	—
48	C₃×C₅⋊D₅	D₁₂₁	1	1	yes	characteristic, complemented
49	C₂×D₃₃	—	275	1	no	—
50	C₁₂₁	D₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
51	D₅₅	—	165	6	no	—
52	C₅×D₁₁	—	33	6	no	—
53	D₅×C₁₁	—	5	6	no	—
54	C₂×C₅⋊D₅	—	363	1	no	Hall
55	C₃×C₅²	C₂×D₁₂₁	1	1	yes	characteristic, complemented, Hall
56	C₂×C₃×C₁₁	—	25	1	no	—
57	D₃₃	—	11	1	no	—
58	D₃₃	—	275	1	no	—
59	D₃×D₅	—	605	6	no	—
60	C₅×C₁₁	D₅×D₃₃	1	6	yes	—
61	C₂×C₅²	—	363	1	no	—
62	C₅⋊D₅	—	363	1	no	—
63	C₅⋊D₅	D₃₆₃	1	1	yes	characteristic, direct product factor
64	C₂×D₁₁	—	825	1	no	—
65	C₃×C₁₁	D₁₁×C₅⋊D₅	1	1	yes	characteristic
66	D₁₅	—	605	6	no	—
67	C₃×D₅	—	5	6	no	—
68	C₅×D₃	—	121	6	no	—
69	C₅²	C₂×D₃₆₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₁₁	—	25	1	no	—
71	D₁₁	—	33	1	no	—
72	D₁₁	—	825	1	no	—
73	C₂×D₅	—	1815	6	no	—
74	C₃×C₅	D₅×D₁₂₁	1	6	yes	complemented
75	C₂×D₃	—	3025	1	no	Hall
76	C₁₁	C₅⋊D₅×D₃₃	1	1	yes	characteristic
77	C₂×C₅	—	363	6	no	—
78	D₅	—	5	6	no	—
79	D₅	—	1815	6	no	—
80	C₂×C₃	—	25	1	no	—
81	D₃	—	121	1	no	—
82	D₃	—	3025	1	no	—
83	C₅	D₅×D₃₆₃	1	6	yes	complemented
84	C₂²	—	9075	1	no	Sylow
85	C₃	C₅⋊D₅×D₁₂₁	1	1	yes	characteristic, complemented, Sylow
86	C₂	—	25	1	no	—
87	C₂	—	363	1	no	—
88	C₂	—	9075	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₅²×C₁₂₁	C₂²
Frattini	C₁₁	C₅⋊D₅×D₃₃
socle	C₃×C₅²×C₁₁	C₂×D₁₁
LCS	G ▷ C₃×C₅²×C₁₂₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₅⋊D₆₀₅)	C₂	semidirect
2. C₅²×D₃₆₃	C₂	semidirect
3. C₃×C₅⋊D₅×C₁₂₁	C₂	semidirect
5. C₃×C₅²×C₁₂₁	C₂²	semidirect
8. C₅⋊D₅×C₁₂₁	D₃	semidirect
11. C₅×D₃₆₃	D₅	semidirect
14. C₅²×C₁₂₁	C₂×D₃	semidirect
16. C₃×C₅×C₁₂₁	C₂×D₅	semidirect
28. D₃₆₃	C₅⋊D₅	direct (N × H)
30. C₅×C₁₂₁	D₃×D₅	semidirect
35. C₃×C₁₂₁	C₂×C₅⋊D₅	semidirect
48. C₃×C₅⋊D₅	D₁₂₁	semidirect
50. C₁₂₁	D₃×C₅⋊D₅	semidirect
55. C₃×C₅²	C₂×D₁₂₁	semidirect
63. C₅⋊D₅	D₃₆₃	direct (N × H)
69. C₅²	C₂×D₃₆₃	semidirect
74. C₃×C₅	D₅×D₁₂₁	semidirect
83. C₅	D₅×D₃₆₃	semidirect
85. C₃	C₅⋊D₅×D₁₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₅⋊D₆₀₅)	2
C₅²×D₃₆₃	2
C₃×C₅⋊D₅×C₁₂₁	2
C₅⋊D₅×D₁₂₁	3
D₅×D₃₆₃	5
C₅⋊D₅×D₃₃	11

Subgroups — C5⋊D5×D363 #49136993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊D₅×D₃₆₃ #49136993