Subgroups — C₃×C₅×#14559102 #49137708

Order 36300.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅×#14559102	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14559102	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×#92150	—	5	1	no	maximal
6	C₅²×C₁₁⋊D₁₁	C₂×C₃	1	1	yes	characteristic
7	C₃×C₅×C₁₁⋊D₁₁	—	2	2	no	—
8	C₃×C₅×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic
9	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic
10	C₅²×C₁₁²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
11	#14559102	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₅×#92150	—	5	1	no	—
13	C₃×C₅×C₁₁²	—	2	2	no	—
14	C₃×C₅×C₁₁²	Dic₅	1	1	yes	characteristic, complemented
15	C₃×C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
16	C₃×C₅²×D₁₁	—	22	6	no	—
17	C₃×#92150	—	5	1	no	Hall
18	C₅×C₁₁⋊D₁₁	—	2	2	no	—
19	C₅×C₁₁⋊D₁₁	C₃×D₅	1	1	yes	characteristic
20	C₅×C₁₁⋊D₁₁	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₅²×C₁₁	—	2	6	no	—
22	C₃×C₁₁⋊D₁₁	C₅×D₅	1	1	yes	characteristic
23	C₅×C₁₁²	—	2	2	no	—
24	C₅×C₁₁²	C₃×Dic₅	1	1	yes	characteristic, complemented
25	C₅×C₁₁²	C₃×C₄×C₅	1	1	yes	characteristic, complemented
26	C₅²×D₁₁	—	22	6	no	—
27	#92150	—	5	1	no	Hall
28	C₃×C₁₁²	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅×D₁₁	—	22	6	no	—
30	C₃×C₅×D₁₁	—	22	6	no	—
31	C₃×C₅×D₁₁	—	22	24	no	—
32	C₃×C₅×Dic₅	—	121	1	no	maximal, Hall
33	C₅²×C₁₁	—	2	6	no	—
34	C₁₁⋊D₁₁	C₃×C₅×D₅	1	1	yes	characteristic
35	C₃×C₅×C₁₁	—	2	24	no	—
36	C₃×C₅×C₁₁	—	2	6	no	—
37	C₃×C₅×C₁₁	—	2	6	no	—
38	C₂×C₃×C₅²	—	121	1	no	—
39	C₁₁²	C₃×C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
40	C₅×D₁₁	—	22	6	no	—
41	C₅×D₁₁	—	22	6	no	—
42	C₅×D₁₁	—	22	24	no	—
43	C₅×Dic₅	—	121	1	no	Hall
44	C₃×C₅²	#92150	1	1	yes	characteristic, complemented, Hall
45	C₃×D₁₁	—	22	6	no	—
46	C₃×C₄×C₅	—	605	1	no	—
47	C₃×Dic₅	—	121	1	no	—
48	C₅×C₁₁	—	2	24	no	—
49	C₅×C₁₁	—	2	6	no	—
50	C₅×C₁₁	—	2	6	no	—
51	C₂×C₅²	—	121	1	no	—
52	C₃×C₁₁	—	2	6	no	—
53	C₂×C₃×C₅	—	121	1	no	—
54	C₂×C₃×C₅	—	121	1	no	—
55	C₂×C₃×C₅	—	242	2	no	—
56	C₅²	C₃×#92150	1	1	yes	characteristic, complemented, Sylow
57	D₁₁	—	22	6	no	—
58	C₄×C₅	—	605	1	no	—
59	Dic₅	—	121	1	no	—
60	C₃×C₅	—	2	2	no	—
61	C₃×C₅	C₅×#92150	1	1	yes	characteristic, complemented
62	C₃×C₅	#14559102	1	1	yes	characteristic, direct product factor
63	C₃×C₄	—	605	1	no	Hall
64	C₁₁	—	2	6	no	—
65	C₂×C₅	—	121	1	no	—
66	C₂×C₅	—	121	1	no	—
67	C₂×C₅	—	242	2	no	—
68	C₂×C₃	—	121	1	no	—
69	C₅	—	2	2	no	—
70	C₅	C₃×C₅×#92150	1	1	yes	characteristic, complemented
71	C₅	C₃×#14559102	1	1	yes	characteristic, direct product factor
72	C₄	—	605	1	no	Sylow
73	C₃	C₅×#14559102	1	1	yes	characteristic, direct product factor, Sylow
74	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	#14559102
commutator, hypocenter	C₅×C₁₁²	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁²	C₄
prime radical	C₃×C₅²×C₁₁⋊D₁₁	C₂
cosocle	C₅×C₁₁⋊D₁₁	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₁²
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×#14559102	C₃	direct (N × H)
3. C₃×C₅²×C₁₁²	C₄	semidirect
4. C₃×#14559102	C₅	direct (N × H)
10. C₅²×C₁₁²	C₃×C₄	semidirect
11. #14559102	C₃×C₅	direct (N × H)
14. C₃×C₅×C₁₁²	Dic₅	semidirect
15. C₃×C₅×C₁₁²	C₄×C₅	semidirect
24. C₅×C₁₁²	C₃×Dic₅	semidirect
25. C₅×C₁₁²	C₃×C₄×C₅	semidirect
28. C₃×C₁₁²	C₅×Dic₅	semidirect
39. C₁₁²	C₃×C₅×Dic₅	semidirect
44. C₃×C₅²	#92150	semidirect
56. C₅²	C₃×#92150	semidirect
61. C₃×C₅	C₅×#92150	semidirect
62. C₃×C₅	#14559102	direct (N × H)
70. C₅	C₃×C₅×#92150	semidirect
71. C₅	C₃×#14559102	direct (N × H)
73. C₃	C₅×#14559102	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×C₅²×C₁₁⋊D₁₁	2
C₅×#14559102	3
C₃×#14559102	5
C₃×C₅×#92150	5
C₃×C₅×Dic₅	121

Subgroups — C3×C5×#14559102 #49137708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#14559102 #49137708