Subgroups — C₂×C₅×C₉⋊(D₃₁⋊C₅) #42124518

Order 27900.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₉⋊(D₃₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×C₃⋊(D₃₁⋊C₅)	—	3	1	no	maximal
4	C₅×C₉×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₂₇₉	C₅	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉⋊(D₃₁⋊C₅)	C₅	1	5	yes	maximal, direct product factor
7	C₂×C₃×C₅×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic
8	C₅×C₃⋊(D₃₁⋊C₅)	—	3	2	no	—
9	C₂×C₅×D₃₁⋊C₅	—	9	1	no	Hall
10	C₅×D₂₇₉	C₂×C₅	1	2	yes	complemented
11	C₂×C₉×ΓL(1,𝔽₃₂)	C₂×C₅	1	5	yes	complemented
12	C₉⋊(D₃₁⋊C₅)	C₂×C₅	1	10	yes	direct product factor
13	C₂×C₅×C₉×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×ΓL(1,𝔽₃₂)	C₂×D₃	1	1	yes	characteristic
15	C₂×C₅×D₉₃	—	3	1	no	—
16	C₂×C₃⋊(D₃₁⋊C₅)	—	3	5	no	—
17	C₂×C₅×ΓL(1,𝔽₃₂)	D₉	1	1	yes	characteristic, complemented
18	C₅×D₃₁⋊C₅	—	9	2	no	—
19	C₅×C₉×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented
20	C₉×ΓL(1,𝔽₃₂)	C₂²×C₅	1	5	yes	complemented
21	C₂×D₂₇₉	C₅²	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₅×C₃₁	C₅×D₃	1	1	yes	characteristic
23	C₅×D₉₃	—	3	2	no	—
24	C₂×C₃×ΓL(1,𝔽₃₂)	C₅×D₃	1	5	yes	—
25	C₃⋊(D₃₁⋊C₅)	—	3	10	no	—
26	C₂×C₅²×D₉	—	31	1	no	maximal, Hall
27	C₅×ΓL(1,𝔽₃₂)	C₂×D₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×D₃₁	—	9	1	no	—
29	C₂×D₃₁⋊C₅	—	9	5	no	—
30	C₂×C₉×C₃₁	C₂×C₅²	1	1	yes	characteristic, complemented
31	D₂₇₉	C₂×C₅²	1	2	yes	complemented
32	C₃×C₅×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic
33	C₃×ΓL(1,𝔽₃₂)	C₂×C₅×D₃	1	5	yes	—
34	C₂×C₅²×C₉	—	31	1	no	—
35	C₅²×D₉	—	31	2	no	—
36	C₂×D₉₃	—	3	1	no	—
37	C₂×C₅×C₃₁	C₅×D₉	1	1	yes	characteristic, complemented
38	C₅×D₃₁	—	9	2	no	—
39	C₂×ΓL(1,𝔽₃₂)	C₅×D₉	1	5	yes	complemented
40	D₃₁⋊C₅	—	9	10	no	—
41	C₂×C₅²×D₃	—	93	1	no	—
42	C₉×C₃₁	C₂²×C₅²	1	1	yes	characteristic, complemented, Hall
43	C₅²×C₉	—	31	1	no	Hall
44	C₂×C₃×C₃₁	C₅²×D₃	1	1	yes	characteristic
45	D₉₃	—	3	2	no	—
46	C₂×C₅×D₉	—	31	5	no	—
47	C₂×C₅×D₉	—	31	1	no	—
48	C₅×C₃₁	C₂×C₅×D₉	1	1	yes	characteristic, complemented
49	ΓL(1,𝔽₃₂)	C₂×C₅×D₉	1	5	yes	complemented
50	C₂×C₃×C₅²	—	31	1	no	—
51	C₅²×D₃	—	93	2	no	—
52	C₂×D₃₁	—	9	1	no	Hall
53	C₂²×C₅²	—	279	1	no	Hall
54	C₃×C₃₁	C₂×C₅²×D₃	1	1	yes	characteristic
55	C₂×C₅×C₉	—	31	5	no	—
56	C₂×C₅×C₉	D₃₁⋊C₅	1	1	yes	characteristic, complemented
57	C₅×D₉	—	31	10	no	—
58	C₅×D₉	—	31	2	no	—
59	C₃×C₅²	—	31	1	no	—
60	C₂×C₃₁	C₅²×D₉	1	1	yes	characteristic, complemented
61	D₃₁	—	9	2	no	—
62	C₂×C₅×D₃	—	93	5	no	—
63	C₂×C₅×D₃	—	93	1	no	—
64	C₂×C₅²	—	279	2	no	—
65	C₂×C₅²	—	31	1	no	—
66	C₅×C₉	—	31	5	no	—
67	C₅×C₉	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented
68	C₂×D₉	—	31	1	no	Hall
69	C₃₁	C₂×C₅²×D₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃×C₅	—	31	5	no	—
71	C₂×C₃×C₅	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
72	C₅×D₃	—	93	10	no	—
73	C₅×D₃	—	93	2	no	—
74	C₅²	—	31	1	no	Sylow
75	C₂²×C₅	—	279	5	no	—
76	C₂²×C₅	—	279	1	no	—
77	C₂×C₉	C₅×D₃₁⋊C₅	1	1	yes	characteristic, complemented
78	D₉	—	31	2	no	—
79	C₃×C₅	—	31	5	no	—
80	C₃×C₅	C₂×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
81	C₂×D₃	—	93	1	no	—
82	C₂×C₅	—	279	10	no	—
83	C₂×C₅	—	279	2	no	—
84	C₂×C₅	—	31	5	no	—
85	C₂×C₅	C₉⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
86	C₉	C₂×C₅×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
87	C₂×C₃	C₅×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
88	D₃	—	93	2	no	—
89	C₅	—	31	5	no	—
90	C₅	C₂×C₉⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
91	C₂²	—	279	1	no	Sylow
92	C₃	C₂×C₅×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic
93	C₂	—	279	2	no	—
94	C₂	C₅×C₉⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₉⋊(D₃₁⋊C₅)
commutator, cosocle, hypocenter	C₉×C₃₁	C₂²×C₅²
Frattini	C₃	C₂×C₅×C₃⋊(D₃₁⋊C₅)
Fitting	C₂×C₅×C₉×C₃₁	C₂×C₅
socle	C₂×C₃×C₅×C₃₁	C₅×D₃
LCS	G ▷ C₉×C₃₁
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₉×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₅×C₉⋊(D₃₁⋊C₅)	C₂	direct (N × H)
4. C₅×C₉×ΓL(1,𝔽₃₂)	C₂²	semidirect
5. C₂×C₅×D₂₇₉	C₅	semidirect
6. C₂×C₉⋊(D₃₁⋊C₅)	C₅	direct (N × H)
10. C₅×D₂₇₉	C₂×C₅	semidirect
11. C₂×C₉×ΓL(1,𝔽₃₂)	C₂×C₅	semidirect
12. C₉⋊(D₃₁⋊C₅)	C₂×C₅	direct (N × H)
13. C₂×C₅×C₉×C₃₁	C₂×C₅	semidirect
17. C₂×C₅×ΓL(1,𝔽₃₂)	D₉	semidirect
19. C₅×C₉×C₃₁	C₂²×C₅	semidirect
20. C₉×ΓL(1,𝔽₃₂)	C₂²×C₅	semidirect
21. C₂×D₂₇₉	C₅²	semidirect
27. C₅×ΓL(1,𝔽₃₂)	C₂×D₉	semidirect
30. C₂×C₉×C₃₁	C₂×C₅²	semidirect
31. D₂₇₉	C₂×C₅²	semidirect
37. C₂×C₅×C₃₁	C₅×D₉	semidirect
39. C₂×ΓL(1,𝔽₃₂)	C₅×D₉	semidirect
42. C₉×C₃₁	C₂²×C₅²	semidirect
48. C₅×C₃₁	C₂×C₅×D₉	semidirect
49. ΓL(1,𝔽₃₂)	C₂×C₅×D₉	semidirect
56. C₂×C₅×C₉	D₃₁⋊C₅	semidirect
60. C₂×C₃₁	C₅²×D₉	semidirect
67. C₅×C₉	C₂×D₃₁⋊C₅	semidirect
69. C₃₁	C₂×C₅²×D₉	semidirect
77. C₂×C₉	C₅×D₃₁⋊C₅	semidirect
85. C₂×C₅	C₉⋊(D₃₁⋊C₅)	direct (N × H)
86. C₉	C₂×C₅×D₃₁⋊C₅	semidirect
90. C₅	C₂×C₉⋊(D₃₁⋊C₅)	direct (N × H)
94. C₂	C₅×C₉⋊(D₃₁⋊C₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×C₉×ΓL(1,𝔽₃₂)	2
C₅×C₉⋊(D₃₁⋊C₅)	2
C₂×C₅×C₃⋊(D₃₁⋊C₅)	3
C₂×C₅×D₂₇₉	5
C₂×C₉⋊(D₃₁⋊C₅)	5
C₂×C₅²×D₉	31

Subgroups — C2×C5×C9⋊(D31⋊C5) #42124518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉⋊(D₃₁⋊C₅) #42124518