Subgroups — C₅×C₃⋊(#92150⋊C₅) #49137416

Order 36300.

288 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#11925892	C₂	1	1	yes	maximal, characteristic
2	C₅×#92150⋊C₅	—	3	1	no	maximal, Hall
3	C₃×C₅×#10597243	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊#92150	C₅	1	1	yes	maximal, characteristic, complemented
5	C₃⋊(#92150⋊C₅)	C₅	1	5	yes	maximal, direct product factor
6	C₅×#11925892	D₃	1	1	yes	characteristic
7	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic
8	C₃×#11925892	C₂×C₅	1	5	yes	—
9	C₅×#10597243	Dic₃	1	1	yes	characteristic, complemented, Hall
10	C₅×#92150	—	3	1	no	—
11	#92150⋊C₅	—	3	5	no	—
12	C₃×C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
13	C₃×#10597243	C₄×C₅	1	5	yes	complemented
14	C₃×C₅×AGL(1,𝔽₁₁)	—	22	1	no	—
15	C₃×C₅×AGL(1,𝔽₁₁)	—	22	5	no	—
16	C₃⋊#92150	C₅²	1	1	yes	characteristic, complemented, Hall
17	C₅×C₁₁⋊D₁₁	C₅×D₃	1	1	yes	characteristic
18	#11925892	C₅×D₃	1	5	yes	—
19	C₃×C₅×C₁₁⋊C₅	—	22	1	no	—
20	C₃×C₅×C₁₁⋊C₅	—	22	5	no	—
21	C₃×C₁₁⋊D₁₁	C₂×C₅²	1	1	yes	characteristic
22	C₅×C₁₁²	C₅×Dic₃	1	1	yes	characteristic, complemented
23	#10597243	C₅×Dic₃	1	5	yes	complemented
24	C₅×AGL(1,𝔽₁₁)	—	22	1	no	—
25	C₅×AGL(1,𝔽₁₁)	—	22	5	no	—
26	#92150	—	3	1	no	Hall
27	C₃×C₁₁²	C₄×C₅²	1	1	yes	characteristic, complemented, Hall
28	C₃×C₅×D₁₁	—	22	1	no	—
29	C₃×C₅×D₁₁	—	110	5	no	—
30	C₃×AGL(1,𝔽₁₁)	—	22	5	no	—
31	C₃×AGL(1,𝔽₁₁)	—	22	25	no	—
32	C₅²×Dic₃	—	121	1	no	maximal, Hall
33	C₅×C₁₁⋊C₅	—	22	1	no	—
34	C₅×C₁₁⋊C₅	—	22	5	no	—
35	C₁₁⋊D₁₁	C₅²×D₃	1	1	yes	characteristic
36	C₃×C₅×C₁₁	—	2	1	no	—
37	C₃×C₅×C₁₁	—	2	5	no	—
38	C₃×C₁₁⋊C₅	—	22	5	no	—
39	C₃×C₁₁⋊C₅	—	22	25	no	—
40	C₂×C₃×C₅²	—	121	1	no	—
41	C₁₁²	C₅²×Dic₃	1	1	yes	characteristic, complemented, Sylow
42	C₅×D₁₁	—	110	1	no	—
43	C₅×D₁₁	—	110	5	no	—
44	AGL(1,𝔽₁₁)	—	22	5	no	—
45	AGL(1,𝔽₁₁)	—	22	25	no	—
46	C₄×C₅²	—	363	1	no	Hall
47	C₃×C₅²	—	121	1	no	Hall
48	C₃×D₁₁	—	22	1	no	—
49	C₃×D₁₁	—	110	5	no	—
50	C₅×Dic₃	—	605	1	no	—
51	C₅×Dic₃	—	121	5	no	—
52	C₅×C₁₁	—	2	1	no	—
53	C₅×C₁₁	—	2	5	no	—
54	C₁₁⋊C₅	—	22	5	no	—
55	C₁₁⋊C₅	—	22	25	no	—
56	C₂×C₅²	—	121	1	no	—
57	C₃×C₁₁	—	2	1	no	—
58	C₃×C₁₁	—	2	5	no	—
59	C₂×C₃×C₅	—	605	1	no	—
60	C₂×C₃×C₅	—	121	5	no	—
61	C₅²	—	121	1	no	Sylow
62	D₁₁	—	110	1	no	—
63	D₁₁	—	110	5	no	—
64	C₄×C₅	—	1815	1	no	—
65	C₄×C₅	—	363	5	no	—
66	C₃×C₅	—	121	5	no	—
67	C₃×C₅	#92150⋊C₅	1	1	yes	characteristic, complemented
68	Dic₃	—	605	1	no	Hall
69	C₁₁	—	2	1	no	—
70	C₁₁	—	2	5	no	—
71	C₂×C₅	—	605	1	no	—
72	C₂×C₅	—	121	5	no	—
73	C₂×C₃	—	605	1	no	—
74	C₅	—	121	5	no	—
75	C₅	C₃⋊(#92150⋊C₅)	1	1	yes	characteristic, direct product factor
76	C₄	—	1815	1	no	Sylow
77	C₃	C₅×#92150⋊C₅	1	1	yes	characteristic, complemented, Sylow
78	C₂	—	605	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₃⋊(#92150⋊C₅)
commutator, hypocenter	C₃×C₁₁²	C₄×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁²	C₄×C₅
prime radical	C₃×C₅×#11925892	C₂
cosocle	C₃×C₁₁⋊D₁₁	C₂×C₅²
LCS	G ▷ C₃×C₁₁²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#10597243	C₄	semidirect
4. C₅×C₃⋊#92150	C₅	semidirect
5. C₃⋊(#92150⋊C₅)	C₅	direct (N × H)
9. C₅×#10597243	Dic₃	semidirect
12. C₃×C₅×C₁₁²	C₄×C₅	semidirect
13. C₃×#10597243	C₄×C₅	semidirect
16. C₃⋊#92150	C₅²	semidirect
22. C₅×C₁₁²	C₅×Dic₃	semidirect
23. #10597243	C₅×Dic₃	semidirect
27. C₃×C₁₁²	C₄×C₅²	semidirect
41. C₁₁²	C₅²×Dic₃	semidirect
67. C₃×C₅	#92150⋊C₅	semidirect
75. C₅	C₃⋊(#92150⋊C₅)	direct (N × H)
77. C₃	C₅×#92150⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#11925892	2
C₅×#92150⋊C₅	3
C₅×C₃⋊#92150	5
C₃⋊(#92150⋊C₅)	5
C₅²×Dic₃	121

Subgroups — C5×C3⋊(#92150⋊C5) #49137416

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊(#92150⋊C₅) #49137416