Subgroups — C₂×C₃×D₁₅×C₁₇₉ #44567396

Order 32220.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₁₅×C₁₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅×C₁₇₉	—	3	1	no	maximal
4	C₂×D₁₅×C₁₇₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₅×C₁₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃×C₁₇₉	—	5	1	no	maximal, Hall
7	D₁₅×C₁₇₉	C₂×C₃	1	2	yes	direct product factor
8	C₃×D₅×C₁₇₉	—	3	2	no	—
9	C₂×C₃×C₅×C₁₇₉	—	2	1	no	—
10	C₂×C₃×C₅×C₁₇₉	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×C₁₇₉	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×D₅×C₁₇₉	—	3	1	no	Hall
13	C₃×D₃×C₁₇₉	—	5	2	no	—
14	C₂×C₃²×C₁₇₉	D₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₁₇₉	—	2	1	no	—
16	C₃×C₅×C₁₇₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅×C₁₇₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×D₃×C₁₇₉	—	5	1	no	—
19	C₂²×C₃×C₁₇₉	—	15	1	no	—
20	C₂×C₅×C₁₇₉	C₃×D₃	1	1	yes	characteristic, complemented
21	D₅×C₁₇₉	—	3	2	no	—
22	C₃²×C₁₇₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₁₇₉	—	2	1	no	—
24	C₂×C₃×C₁₇₉	—	15	2	no	—
25	C₂×C₃×C₁₇₉	C₃×D₅	1	1	yes	characteristic, complemented
26	C₂×C₃×C₁₇₉	D₁₅	1	1	yes	characteristic, direct product factor
27	D₃×C₁₇₉	—	5	2	no	—
28	C₅×C₁₇₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₁₇₉	—	15	1	no	Hall
30	C₃×C₁₇₉	—	2	1	no	—
31	C₃×C₁₇₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented
32	C₃×C₁₇₉	C₂×D₁₅	1	1	yes	characteristic, direct product factor
33	C₂×C₁₇₉	—	15	2	no	—
34	C₂×C₁₇₉	C₃×D₁₅	1	1	yes	characteristic, direct product factor
35	C₂×C₃×D₁₅	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₁₇₉	C₂×C₃×D₁₅	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₃²×C₅	C₂×C₁₇₉	1	1	yes	characteristic, complemented
38	C₃×D₁₅	C₂×C₁₇₉	1	2	yes	direct product factor
39	C₂×D₁₅	C₃×C₁₇₉	1	1	yes	characteristic, direct product factor
40	C₂×C₃×D₅	—	3	1	no	—
41	C₃²×C₅	C₂²×C₁₇₉	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₃	—	5	1	no	Hall
43	C₂×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅	D₃×C₁₇₉	1	1	yes	characteristic, complemented
45	C₂×C₃×C₅	C₂×C₃×C₁₇₉	1	1	yes	characteristic, complemented
46	D₁₅	C₂×C₃×C₁₇₉	1	2	yes	direct product factor
47	C₃×D₅	—	3	2	no	—
48	C₂×D₅	—	3	1	no	Hall
49	C₂×C₃²	D₅×C₁₇₉	1	1	yes	characteristic, complemented
50	C₃×D₃	—	5	2	no	—
51	C₃×C₅	—	2	1	no	—
52	C₃×C₅	C₂²×C₃×C₁₇₉	1	1	yes	characteristic, complemented
53	C₃×C₅	C₂×D₃×C₁₇₉	1	1	yes	characteristic, complemented
54	C₂²×C₃	—	15	1	no	—
55	C₂×D₃	—	5	1	no	—
56	C₂×C₅	C₃×D₃×C₁₇₉	1	1	yes	characteristic, complemented
57	D₅	—	3	2	no	—
58	C₃²	C₂×D₅×C₁₇₉	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	15	2	no	—
61	C₂×C₃	C₃×D₅×C₁₇₉	1	1	yes	characteristic, complemented
62	C₂×C₃	D₁₅×C₁₇₉	1	1	yes	characteristic, direct product factor
63	D₃	—	5	2	no	—
64	C₅	C₂×C₃×D₃×C₁₇₉	1	1	yes	characteristic, complemented, Sylow
65	C₂²	—	15	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×D₁₅×C₁₇₉	1	1	yes	characteristic, direct product factor
68	C₃	C₂×C₃×D₅×C₁₇₉	1	1	yes	characteristic, complemented
69	C₂	—	15	2	no	—
70	C₂	C₃×D₁₅×C₁₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇₉	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₃×C₁₇₉
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₇₉	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃×C₁₇₉

Complements

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

N	H ≅ G/N	type
1. C₃×D₁₅×C₁₇₉	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₇₉	C₂	semidirect
4. C₂×D₁₅×C₁₇₉	C₃	direct (N × H)
5. C₃²×C₅×C₁₇₉	C₂²	semidirect
7. D₁₅×C₁₇₉	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅×C₁₇₉	D₃	semidirect
11. C₂×C₃×C₅×C₁₇₉	C₂×C₃	semidirect
14. C₂×C₃²×C₁₇₉	D₅	semidirect
16. C₃×C₅×C₁₇₉	C₂×D₃	semidirect
17. C₃×C₅×C₁₇₉	C₂²×C₃	semidirect
20. C₂×C₅×C₁₇₉	C₃×D₃	semidirect
22. C₃²×C₁₇₉	C₂×D₅	semidirect
25. C₂×C₃×C₁₇₉	C₃×D₅	semidirect
26. C₂×C₃×C₁₇₉	D₁₅	direct (N × H)
28. C₅×C₁₇₉	C₂×C₃×D₃	semidirect
31. C₃×C₁₇₉	C₂×C₃×D₅	semidirect
32. C₃×C₁₇₉	C₂×D₁₅	direct (N × H)
34. C₂×C₁₇₉	C₃×D₁₅	direct (N × H)
35. C₂×C₃×D₁₅	C₁₇₉	direct (N × H)
36. C₁₇₉	C₂×C₃×D₁₅	direct (N × H)
37. C₂×C₃²×C₅	C₂×C₁₇₉	semidirect
38. C₃×D₁₅	C₂×C₁₇₉	direct (N × H)
39. C₂×D₁₅	C₃×C₁₇₉	direct (N × H)
41. C₃²×C₅	C₂²×C₁₇₉	semidirect
44. C₂×C₃×C₅	D₃×C₁₇₉	semidirect
45. C₂×C₃×C₅	C₂×C₃×C₁₇₉	semidirect
46. D₁₅	C₂×C₃×C₁₇₉	direct (N × H)
49. C₂×C₃²	D₅×C₁₇₉	semidirect
52. C₃×C₅	C₂²×C₃×C₁₇₉	semidirect
53. C₃×C₅	C₂×D₃×C₁₇₉	semidirect
56. C₂×C₅	C₃×D₃×C₁₇₉	semidirect
58. C₃²	C₂×D₅×C₁₇₉	semidirect
61. C₂×C₃	C₃×D₅×C₁₇₉	semidirect
62. C₂×C₃	D₁₅×C₁₇₉	direct (N × H)
64. C₅	C₂×C₃×D₃×C₁₇₉	semidirect
67. C₃	C₂×D₁₅×C₁₇₉	direct (N × H)
68. C₃	C₂×C₃×D₅×C₁₇₉	semidirect
70. C₂	C₃×D₁₅×C₁₇₉	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×C₁₇₉	2
C₂×C₃²×C₅×C₁₇₉	2
C₂×C₃×D₅×C₁₇₉	3
C₂×D₁₅×C₁₇₉	3
C₂×C₃×D₃×C₁₇₉	5
C₂×C₃×D₁₅	179

Subgroups — C2×C3×D15×C179 #44567396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₅×C₁₇₉ #44567396