Subgroups — D₁₅×C₃₁×D₁₇ #44539374

Order 31620.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₂₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₁₅×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₃₁×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×C₃₁×D₁₇	—	3	1	no	maximal, Hall
5	C₃×C₅×C₁₇×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×C₃₁×D₁₇	—	5	1	no	maximal, Hall
7	C₃₁×D₈₅	—	3	1	no	—
8	D₅×C₁₇×C₃₁	—	3	1	no	—
9	C₅×C₃₁×D₁₇	D₃	1	1	yes	characteristic, complemented
10	C₃₁×D₅₁	—	5	1	no	—
11	D₃×C₁₇×C₃₁	—	5	1	no	—
12	C₃×C₃₁×D₁₇	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₇×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃₁×D₁₇	—	15	1	no	Hall
15	C₂×D₁₅×C₃₁	—	17	1	no	maximal, Hall
16	C₃×C₁₇×C₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₁₇×C₃₁	—	15	1	no	—
18	C₃₁×D₁₇	—	15	1	no	—
19	C₃₁×D₁₇	D₁₅	1	1	yes	characteristic, direct product factor
20	D₁₅×D₁₇	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₅×C₃₁	—	17	1	no	—
22	D₁₅×C₃₁	—	17	1	no	—
23	D₁₅×C₃₁	D₁₇	1	1	yes	characteristic, direct product factor
24	C₂×D₅×C₃₁	—	51	1	no	Hall
25	C₁₇×C₃₁	C₂×D₁₅	1	1	yes	characteristic, complemented, Hall
26	D₂₅₅	C₂×C₃₁	1	1	yes	characteristic, complemented
27	C₁₇×D₁₅	C₂×C₃₁	1	1	yes	characteristic, complemented
28	C₃×C₅×D₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented
29	C₃×C₅×C₃₁	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
30	C₂×D₃×C₃₁	—	85	1	no	Hall
31	D₅×D₁₇	—	3	1	no	Hall
32	C₂×C₅×C₃₁	—	17	1	no	—
33	D₅×C₃₁	—	3	1	no	—
34	D₅×C₃₁	—	51	1	no	—
35	C₃×C₅×C₁₇	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₇	—	5	1	no	Hall
37	C₂×C₃×C₃₁	—	17	1	no	—
38	D₃×C₃₁	—	5	1	no	—
39	D₃×C₃₁	—	85	1	no	—
40	D₈₅	—	3	1	no	—
41	C₅×D₁₇	D₃×C₃₁	1	1	yes	characteristic, complemented
42	D₅×C₁₇	—	3	1	no	—
43	C₅×C₃₁	D₃×D₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂²×C₃₁	—	255	1	no	Hall
45	D₅₁	—	5	1	no	—
46	C₃×D₁₇	D₅×C₃₁	1	1	yes	characteristic, complemented
47	D₃×C₁₇	—	5	1	no	—
48	C₃×C₃₁	D₅×D₁₇	1	1	yes	characteristic, complemented, Hall
49	C₅×C₁₇	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Hall
50	C₂×D₁₇	—	15	1	no	Hall
51	C₂×C₃₁	—	15	1	no	—
52	C₂×C₃₁	—	17	1	no	—
53	C₂×C₃₁	—	255	1	no	—
54	C₂×D₁₅	—	17	1	no	Hall
55	C₃×C₁₇	C₂×D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
56	C₂×C₁₇	—	15	1	no	—
57	D₁₇	—	15	1	no	—
58	D₁₇	D₁₅×C₃₁	1	1	yes	characteristic, direct product factor
59	C₃₁	D₁₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
60	C₂×C₃×C₅	—	17	1	no	—
61	D₁₅	—	17	1	no	—
62	D₁₅	C₃₁×D₁₇	1	1	yes	characteristic, direct product factor
63	C₂×D₅	—	51	1	no	Hall
64	C₁₇	C₂×D₁₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
65	C₃×C₅	C₂×C₃₁×D₁₇	1	1	yes	characteristic, complemented, Hall
66	C₂×D₃	—	85	1	no	Hall
67	C₂×C₅	—	17	1	no	—
68	D₅	—	3	1	no	—
69	D₅	—	51	1	no	—
70	C₂×C₃	—	17	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	85	1	no	—
73	C₅	D₃×C₃₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	255	1	no	Sylow
75	C₃	D₅×C₃₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	17	1	no	—
78	C₂	—	255	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₁₅×D₁₇
commutator, cosocle, hypocenter	C₃×C₅×C₁₇	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₁	C₂²
LCS	G ▷ C₃×C₅×C₁₇
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃₁×D₂₅₅	C₂	semidirect
2. C₁₇×D₁₅×C₃₁	C₂	semidirect
3. C₃×C₅×C₃₁×D₁₇	C₂	semidirect
5. C₃×C₅×C₁₇×C₃₁	C₂²	semidirect
9. C₅×C₃₁×D₁₇	D₃	semidirect
12. C₃×C₃₁×D₁₇	D₅	semidirect
13. C₅×C₁₇×C₃₁	C₂×D₃	semidirect
16. C₃×C₁₇×C₃₁	C₂×D₅	semidirect
19. C₃₁×D₁₇	D₁₅	direct (N × H)
20. D₁₅×D₁₇	C₃₁	direct (N × H)
23. D₁₅×C₃₁	D₁₇	direct (N × H)
25. C₁₇×C₃₁	C₂×D₁₅	semidirect
26. D₂₅₅	C₂×C₃₁	semidirect
27. C₁₇×D₁₅	C₂×C₃₁	semidirect
28. C₃×C₅×D₁₇	C₂×C₃₁	semidirect
29. C₃×C₅×C₃₁	C₂×D₁₇	semidirect
35. C₃×C₅×C₁₇	C₂²×C₃₁	semidirect
41. C₅×D₁₇	D₃×C₃₁	semidirect
43. C₅×C₃₁	D₃×D₁₇	semidirect
46. C₃×D₁₇	D₅×C₃₁	semidirect
48. C₃×C₃₁	D₅×D₁₇	semidirect
49. C₅×C₁₇	C₂×D₃×C₃₁	semidirect
55. C₃×C₁₇	C₂×D₅×C₃₁	semidirect
58. D₁₇	D₁₅×C₃₁	direct (N × H)
59. C₃₁	D₁₅×D₁₇	direct (N × H)
62. D₁₅	C₃₁×D₁₇	direct (N × H)
64. C₁₇	C₂×D₁₅×C₃₁	semidirect
65. C₃×C₅	C₂×C₃₁×D₁₇	semidirect
73. C₅	D₃×C₃₁×D₁₇	semidirect
75. C₃	D₅×C₃₁×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×D₂₅₅	2
C₁₇×D₁₅×C₃₁	2
C₃×C₅×C₃₁×D₁₇	2
D₅×C₃₁×D₁₇	3
D₃×C₃₁×D₁₇	5
C₂×D₁₅×C₃₁	17
D₁₅×D₁₇	31

Subgroups — D15×C31×D17 #44539374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×C₃₁×D₁₇ #44539374