Subgroups — C₂×C₃⋊D₁₅×C₁₇₃ #44528221

Order 31140.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₅×C₁₇₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₅×C₁₇₃	—	3	4	no	maximal
4	C₃²×C₅×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₃×C₁₇₃	—	5	1	no	maximal, Hall
6	D₁₅×C₁₇₃	—	3	8	no	—
7	C₂×C₃×C₅×C₁₇₃	D₃	1	4	yes	complemented
8	C₂×D₅×C₁₇₃	—	9	1	no	Hall
9	C₃⋊D₃×C₁₇₃	—	5	2	no	—
10	C₂×C₃²×C₁₇₃	D₅	1	1	yes	characteristic, complemented
11	C₃×C₅×C₁₇₃	C₂×D₃	1	4	yes	complemented
12	C₂×D₃×C₁₇₃	—	15	4	no	—
13	C₂×C₅×C₁₇₃	C₃⋊D₃	1	1	yes	characteristic, complemented
14	D₅×C₁₇₃	—	9	2	no	—
15	C₃²×C₁₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₁₇₃	D₁₅	1	4	yes	complemented
17	D₃×C₁₇₃	—	15	8	no	—
18	C₅×C₁₇₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₁₇₃	—	45	1	no	Hall
20	C₃×C₁₇₃	C₂×D₁₅	1	4	yes	complemented
21	C₂×C₁₇₃	—	45	2	no	—
22	C₂×C₁₇₃	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
23	C₂×C₃⋊D₁₅	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₁₇₃	C₂×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₃²×C₅	C₂×C₁₇₃	1	1	yes	characteristic, complemented
26	C₃⋊D₁₅	C₂×C₁₇₃	1	2	yes	direct product factor
27	C₂×D₁₅	—	3	4	no	—
28	C₃²×C₅	C₂²×C₁₇₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃⋊D₃	—	5	1	no	Hall
30	C₂×C₃×C₅	D₃×C₁₇₃	1	4	yes	complemented
31	D₁₅	—	3	8	no	—
32	C₂×D₅	—	9	1	no	Hall
33	C₂×C₃²	D₅×C₁₇₃	1	1	yes	characteristic, complemented
34	C₃⋊D₃	—	5	2	no	—
35	C₃×C₅	C₂×D₃×C₁₇₃	1	4	yes	complemented
36	C₂×D₃	—	15	4	no	—
37	C₂×C₅	C₃⋊D₃×C₁₇₃	1	1	yes	characteristic, complemented
38	D₅	—	9	2	no	—
39	C₃²	C₂×D₅×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	D₁₅×C₁₇₃	1	4	yes	complemented
41	D₃	—	15	8	no	—
42	C₅	C₂×C₃⋊D₃×C₁₇₃	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	45	1	no	Sylow
44	C₃	C₂×D₁₅×C₁₇₃	1	4	yes	complemented
45	C₂	—	45	2	no	—
46	C₂	C₃⋊D₁₅×C₁₇₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₇₃	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂²×C₁₇₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₇₃	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂×C₁₇₃

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₁₅×C₁₇₃	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₇₃	C₂	semidirect
4. C₃²×C₅×C₁₇₃	C₂²	semidirect
7. C₂×C₃×C₅×C₁₇₃	D₃	semidirect
10. C₂×C₃²×C₁₇₃	D₅	semidirect
11. C₃×C₅×C₁₇₃	C₂×D₃	semidirect
13. C₂×C₅×C₁₇₃	C₃⋊D₃	semidirect
15. C₃²×C₁₇₃	C₂×D₅	semidirect
16. C₂×C₃×C₁₇₃	D₁₅	semidirect
18. C₅×C₁₇₃	C₂×C₃⋊D₃	semidirect
20. C₃×C₁₇₃	C₂×D₁₅	semidirect
22. C₂×C₁₇₃	C₃⋊D₁₅	direct (N × H)
23. C₂×C₃⋊D₁₅	C₁₇₃	direct (N × H)
24. C₁₇₃	C₂×C₃⋊D₁₅	direct (N × H)
25. C₂×C₃²×C₅	C₂×C₁₇₃	semidirect
26. C₃⋊D₁₅	C₂×C₁₇₃	direct (N × H)
28. C₃²×C₅	C₂²×C₁₇₃	semidirect
30. C₂×C₃×C₅	D₃×C₁₇₃	semidirect
33. C₂×C₃²	D₅×C₁₇₃	semidirect
35. C₃×C₅	C₂×D₃×C₁₇₃	semidirect
37. C₂×C₅	C₃⋊D₃×C₁₇₃	semidirect
39. C₃²	C₂×D₅×C₁₇₃	semidirect
40. C₂×C₃	D₁₅×C₁₇₃	semidirect
42. C₅	C₂×C₃⋊D₃×C₁₇₃	semidirect
44. C₃	C₂×D₁₅×C₁₇₃	semidirect
46. C₂	C₃⋊D₁₅×C₁₇₃	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⋊D₁₅×C₁₇₃	2
C₂×C₃²×C₅×C₁₇₃	2
C₂×D₁₅×C₁₇₃	3
C₂×C₃⋊D₃×C₁₇₃	5
C₂×C₃⋊D₁₅	173

Subgroups — C2×C3⋊D15×C173 #44528221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊D₁₅×C₁₇₃ #44528221