Subgroups — C₅×D₁₅×C₃₁⋊C₃ #28358488

Order 13950.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₅×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅×D₅×C₃₁⋊C₃	—	3	1	no	maximal
4	D₁₅×C₃₁⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×D₃×C₃₁⋊C₃	—	5	1	no	maximal
6	C₅²×C₃₁⋊C₃	—	2	1	no	—
7	C₅²×C₃₁⋊C₃	D₃	1	1	yes	characteristic, complemented
8	C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅×C₃₁	—	3	1	no	Hall
10	C₃×C₅×C₃₁⋊C₃	—	2	2	no	—
11	C₃×C₅×C₃₁⋊C₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₃₁⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented
13	D₁₅×C₃₁	C₃×C₅	1	1	yes	characteristic, complemented
14	C₅×D₃×C₃₁	—	5	1	no	—
15	C₂×C₅×C₃₁⋊C₃	—	15	1	no	—
16	D₅×C₃₁⋊C₃	—	3	1	no	—
17	C₅²×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
18	D₃×C₃₁⋊C₃	—	5	1	no	Hall
19	C₃×C₅×C₃₁	—	2	2	no	—
20	C₃×C₅×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
21	C₃×C₅×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
22	C₅×C₃₁⋊C₃	—	2	4	no	—
23	C₅×C₃₁⋊C₃	—	2	1	no	—
24	C₅×C₃₁⋊C₃	—	2	1	no	—
25	C₅×C₃₁⋊C₃	—	2	2	no	—
26	C₅×C₃₁⋊C₃	C₅×D₃	1	1	yes	characteristic, complemented
27	C₅×C₃₁⋊C₃	D₁₅	1	1	yes	characteristic, direct product factor
28	C₃×C₅×D₁₅	—	31	1	no	maximal, Hall
29	C₂×C₅×C₃₁	—	15	1	no	—
30	D₅×C₃₁	—	3	1	no	—
31	C₃×C₃₁⋊C₃	C₅×D₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	—	31	1	no	Hall
33	D₃×C₃₁	—	5	1	no	—
34	C₂×C₃₁⋊C₃	—	15	1	no	—
35	C₅×C₃₁	—	2	2	no	—
36	C₅×C₃₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented
37	C₅×C₃₁	C₃×D₁₅	1	1	yes	characteristic, complemented
38	C₅×D₁₅	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃×C₅×D₅	—	93	1	no	—
40	C₃×C₃₁	C₃×C₅×D₅	1	1	yes	characteristic, complemented
41	C₃₁⋊C₃	—	2	1	no	—
42	C₃₁⋊C₃	C₅×D₁₅	1	1	yes	characteristic, direct product factor
43	C₃×D₁₅	—	31	1	no	—
44	C₃×C₅×D₃	—	155	1	no	—
45	C₃×C₅²	—	31	1	no	—
46	C₃×C₅²	—	62	1	no	—
47	C₃×C₅²	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
48	C₂×C₃₁	—	15	1	no	Hall
49	C₅×D₅	—	3	1	no	Hall
50	C₃²×C₅	—	31	1	no	—
51	C₃²×C₅	—	31	1	no	—
52	C₃²×C₅	—	62	2	no	—
53	C₃₁	C₃×C₅×D₁₅	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃×C₅	—	465	1	no	—
55	D₁₅	C₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
56	C₃×D₅	—	93	1	no	—
57	C₅×D₃	—	5	1	no	—
58	C₅²	D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₃×D₃	—	155	1	no	Hall
60	C₃×C₅	—	2	2	no	—
61	C₃×C₅	—	31	1	no	—
62	C₃×C₅	—	31	1	no	—
63	C₃×C₅	—	62	2	no	—
64	C₃×C₅	—	62	4	no	—
65	C₃×C₅	—	62	1	no	—
66	C₃×C₅	—	62	1	no	—
67	C₃×C₅	D₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented
68	C₃×C₅	C₂×C₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented
69	C₂×C₅	—	15	1	no	—
70	D₅	—	3	1	no	—
71	C₃²	—	31	1	no	Sylow
72	C₂×C₃	—	465	1	no	—
73	D₃	—	5	1	no	—
74	C₅	—	2	2	no	—
75	C₅	C₅×D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented
76	C₅	D₁₅×C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
77	C₃	—	31	1	no	—
78	C₃	—	62	1	no	—
79	C₃	C₅×D₅×C₃₁⋊C₃	1	1	yes	characteristic, complemented
80	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₅×C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃×C₅×C₃₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₂×C₃
LCS	G ▷ C₃×C₅×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₃₁⋊C₃	C₂	semidirect
2. C₅×D₁₅×C₃₁	C₃	semidirect
4. D₁₅×C₃₁⋊C₃	C₅	direct (N × H)
7. C₅²×C₃₁⋊C₃	D₃	semidirect
8. C₃×C₅²×C₃₁	C₂×C₃	semidirect
11. C₃×C₅×C₃₁⋊C₃	D₅	semidirect
12. C₃×C₅×C₃₁⋊C₃	C₂×C₅	semidirect
13. D₁₅×C₃₁	C₃×C₅	semidirect
17. C₅²×C₃₁	C₃×D₃	semidirect
20. C₃×C₅×C₃₁	C₃×D₅	semidirect
21. C₃×C₅×C₃₁	C₂×C₃×C₅	semidirect
26. C₅×C₃₁⋊C₃	C₅×D₃	semidirect
27. C₅×C₃₁⋊C₃	D₁₅	direct (N × H)
31. C₃×C₃₁⋊C₃	C₅×D₅	semidirect
36. C₅×C₃₁	C₃×C₅×D₃	semidirect
37. C₅×C₃₁	C₃×D₁₅	semidirect
38. C₅×D₁₅	C₃₁⋊C₃	direct (N × H)
40. C₃×C₃₁	C₃×C₅×D₅	semidirect
42. C₃₁⋊C₃	C₅×D₁₅	direct (N × H)
47. C₃×C₅²	C₂×C₃₁⋊C₃	semidirect
53. C₃₁	C₃×C₅×D₁₅	semidirect
55. D₁₅	C₅×C₃₁⋊C₃	direct (N × H)
58. C₅²	D₃×C₃₁⋊C₃	semidirect
67. C₃×C₅	D₅×C₃₁⋊C₃	semidirect
68. C₃×C₅	C₂×C₅×C₃₁⋊C₃	semidirect
75. C₅	C₅×D₃×C₃₁⋊C₃	semidirect
76. C₅	D₁₅×C₃₁⋊C₃	direct (N × H)
79. C₃	C₅×D₅×C₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₃₁⋊C₃	2
C₅×D₁₅×C₃₁	3
C₅×D₅×C₃₁⋊C₃	3
D₁₅×C₃₁⋊C₃	5
C₅×D₃×C₃₁⋊C₃	5
C₃×C₅×D₁₅	31

Subgroups — C5×D15×C31⋊C3 #28358488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₅×C₃₁⋊C₃ #28358488