Subgroups — C₂×D₁₅₁₁₁ #72295539

Order 60444.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅₁₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₂₃×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅₀₃₇	—	3	1	no	maximal
4	C₉×C₂₃×C₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₀₃₇	—	3	2	no	—
6	C₂×C₃×C₂₃×C₇₃	D₃	1	1	yes	characteristic
7	C₂×D₁₆₇₉	—	9	1	no	Hall
8	C₃×C₂₃×C₇₃	C₂×D₃	1	1	yes	characteristic
9	C₂×C₂₃×C₇₃	D₉	1	1	yes	characteristic, complemented
10	D₁₆₇₉	—	9	2	no	—
11	C₂×D₆₅₇	—	23	1	no	maximal, Hall
12	C₂₃×C₇₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₉×C₇₃	D₂₃	1	1	yes	characteristic, complemented
14	D₆₅₇	—	23	2	no	—
15	C₂×D₂₁₉	—	69	1	no	—
16	C₂×D₂₀₇	—	73	1	no	maximal, Hall
17	C₉×C₇₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇₃	D₆₉	1	1	yes	characteristic
19	D₂₁₉	—	69	2	no	—
20	C₂×C₉×C₂₃	D₇₃	1	1	yes	characteristic, complemented
21	D₂₀₇	—	73	2	no	—
22	C₂×D₇₃	—	207	1	no	Hall
23	C₂×D₆₉	—	219	1	no	—
24	C₃×C₇₃	C₂×D₆₉	1	1	yes	characteristic
25	C₉×C₂₃	C₂×D₇₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇₃	D₂₀₇	1	1	yes	characteristic, complemented
27	D₇₃	—	207	2	no	—
28	C₂×C₃×C₂₃	D₂₁₉	1	1	yes	characteristic
29	D₆₉	—	219	2	no	—
30	C₂×D₂₃	—	657	1	no	Hall
31	C₇₃	C₂×D₂₀₇	1	1	yes	characteristic, complemented, Sylow
32	C₃×C₂₃	C₂×D₂₁₉	1	1	yes	characteristic
33	C₂×C₂₃	D₆₅₇	1	1	yes	characteristic, complemented
34	D₂₃	—	657	2	no	—
35	C₂×D₉	—	1679	1	no	Hall
36	C₂₃	C₂×D₆₅₇	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	D₁₆₇₉	1	1	yes	characteristic, complemented
38	D₉	—	1679	2	no	—
39	C₂×D₃	—	5037	1	no	—
40	C₉	C₂×D₁₆₇₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	D₅₀₃₇	1	1	yes	characteristic
42	D₃	—	5037	2	no	—
43	C₂²	—	15111	1	no	Sylow
44	C₃	C₂×D₅₀₃₇	1	1	yes	characteristic
45	C₂	—	15111	2	no	—
46	C₂	D₁₅₁₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₁₅₁₁₁
commutator, cosocle, hypocenter	C₉×C₂₃×C₇₃	C₂²
Frattini	C₃	C₂×D₅₀₃₇
Fitting	C₂×C₉×C₂₃×C₇₃	C₂
socle	C₂×C₃×C₂₃×C₇₃	D₃
LCS	G ▷ C₉×C₂₃×C₇₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. D₁₅₁₁₁	C₂	direct (N × H)
2. C₂×C₉×C₂₃×C₇₃	C₂	semidirect
4. C₉×C₂₃×C₇₃	C₂²	semidirect
9. C₂×C₂₃×C₇₃	D₉	semidirect
12. C₂₃×C₇₃	C₂×D₉	semidirect
13. C₂×C₉×C₇₃	D₂₃	semidirect
17. C₉×C₇₃	C₂×D₂₃	semidirect
20. C₂×C₉×C₂₃	D₇₃	semidirect
25. C₉×C₂₃	C₂×D₇₃	semidirect
26. C₂×C₇₃	D₂₀₇	semidirect
31. C₇₃	C₂×D₂₀₇	semidirect
33. C₂×C₂₃	D₆₅₇	semidirect
36. C₂₃	C₂×D₆₅₇	semidirect
37. C₂×C₉	D₁₆₇₉	semidirect
40. C₉	C₂×D₁₆₇₉	semidirect
46. C₂	D₁₅₁₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
D₁₅₁₁₁	2
C₂×C₉×C₂₃×C₇₃	2
C₂×D₅₀₃₇	3
C₂×D₆₅₇	23
C₂×D₂₀₇	73

Subgroups — C2×D15111 #72295539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₅₁₁₁ #72295539