Subgroups — C₃⋊D₁₅×D₁₇₃ #44528206

Order 31140.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₁₅×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₅₉₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅×D₁₇₃	—	3	4	no	maximal
5	C₃²×C₅×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃⋊D₃×D₁₇₃	—	5	1	no	maximal, Hall
7	D₂₅₉₅	—	3	4	no	—
8	D₁₅×C₁₇₃	—	3	4	no	—
9	C₃×C₅×D₁₇₃	D₃	1	4	yes	complemented
10	D₅×D₁₇₃	—	9	1	no	Hall
11	C₃⋊D₅₁₉	—	5	1	no	—
12	C₃⋊D₃×C₁₇₃	—	5	1	no	—
13	C₃²×D₁₇₃	D₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₁₇₃	C₂×D₃	1	4	yes	complemented
15	D₃×D₁₇₃	—	15	4	no	—
16	D₈₆₅	—	9	1	no	—
17	C₅×D₁₇₃	C₃⋊D₃	1	1	yes	characteristic, complemented
18	D₅×C₁₇₃	—	9	1	no	—
19	C₃²×C₁₇₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₅₁₉	—	15	4	no	—
21	C₃×D₁₇₃	D₁₅	1	4	yes	complemented
22	D₃×C₁₇₃	—	15	4	no	—
23	C₅×C₁₇₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₇₃	—	45	1	no	Hall
25	C₃×C₁₇₃	C₂×D₁₅	1	4	yes	complemented
26	C₂×C₁₇₃	—	45	1	no	—
27	D₁₇₃	—	45	1	no	—
28	D₁₇₃	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
29	C₂×C₃⋊D₁₅	—	173	1	no	maximal, Hall
30	C₁₇₃	C₂×C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃²×C₅	—	173	1	no	—
32	C₃⋊D₁₅	—	173	1	no	—
33	C₃⋊D₁₅	D₁₇₃	1	1	yes	characteristic, direct product factor
34	C₂×D₁₅	—	519	4	no	—
35	C₃²×C₅	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃⋊D₃	—	865	1	no	Hall
37	C₂×C₃×C₅	—	173	4	no	—
38	D₁₅	—	3	4	no	—
39	D₁₅	—	519	4	no	—
40	C₂×D₅	—	1557	1	no	Hall
41	C₂×C₃²	—	173	1	no	—
42	C₃⋊D₃	—	5	1	no	—
43	C₃⋊D₃	—	865	1	no	—
44	C₃×C₅	D₃×D₁₇₃	1	4	yes	complemented
45	C₂×D₃	—	2595	4	no	—
46	C₂×C₅	—	173	1	no	—
47	D₅	—	9	1	no	—
48	D₅	—	1557	1	no	—
49	C₃²	D₅×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	173	4	no	—
51	D₃	—	15	4	no	—
52	D₃	—	2595	4	no	—
53	C₅	C₃⋊D₃×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	7785	1	no	Sylow
55	C₃	D₁₅×D₁₇₃	1	4	yes	complemented
56	C₂	—	45	1	no	—
57	C₂	—	7785	1	no	—
58	C₂	—	173	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×D₁₇₃	C₂	semidirect
2. C₃⋊D₁₅×C₁₇₃	C₂	semidirect
3. C₃⋊D₂₅₉₅	C₂	semidirect
5. C₃²×C₅×C₁₇₃	C₂²	semidirect
9. C₃×C₅×D₁₇₃	D₃	semidirect
13. C₃²×D₁₇₃	D₅	semidirect
14. C₃×C₅×C₁₇₃	C₂×D₃	semidirect
17. C₅×D₁₇₃	C₃⋊D₃	semidirect
19. C₃²×C₁₇₃	C₂×D₅	semidirect
21. C₃×D₁₇₃	D₁₅	semidirect
23. C₅×C₁₇₃	C₂×C₃⋊D₃	semidirect
25. C₃×C₁₇₃	C₂×D₁₅	semidirect
28. D₁₇₃	C₃⋊D₁₅	direct (N × H)
30. C₁₇₃	C₂×C₃⋊D₁₅	semidirect
33. C₃⋊D₁₅	D₁₇₃	direct (N × H)
35. C₃²×C₅	C₂×D₁₇₃	semidirect
44. C₃×C₅	D₃×D₁₇₃	semidirect
49. C₃²	D₅×D₁₇₃	semidirect
53. C₅	C₃⋊D₃×D₁₇₃	semidirect
55. C₃	D₁₅×D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×D₁₇₃	2
C₃⋊D₁₅×C₁₇₃	2
C₃⋊D₂₅₉₅	2
D₁₅×D₁₇₃	3
C₃⋊D₃×D₁₇₃	5
C₂×C₃⋊D₁₅	173

Subgroups — C3⋊D15×D173 #44528206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₁₅×D₁₇₃ #44528206