Subgroups — C₃⋊#27130800 #49137104

Order 36300.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#20258403	C₂	1	1	yes	maximal, characteristic
2	#27130800	—	3	1	no	maximal, Hall
3	C₃×#15690029	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#14559102	—	5	1	no	maximal
5	#20258403	D₃	1	1	yes	characteristic
6	C₃×C₅×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic
7	#15690029	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#14559102	—	15	1	no	—
9	C₃×C₅×C₁₁²	Dic₅	1	1	yes	characteristic
10	C₃×D₁₁⋊C₂₅	—	22	1	no	—
11	C₃⋊#92150	—	25	1	no	Hall
12	C₅×C₁₁⋊D₁₁	D₁₅	1	1	yes	characteristic
13	C₃×C₁₁⋊C₂₅	—	44	1	no	—
14	C₃×C₁₁⋊D₁₁	D₂₅	1	1	yes	characteristic
15	C₅×C₁₁²	Dic₁₅	1	1	yes	characteristic
16	D₁₁⋊C₂₅	—	22	1	no	—
17	#92150	—	75	1	no	Hall
18	C₃×C₁₁²	Dic₂₅	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×D₁₁	—	22	1	no	—
20	C₃×C₅×D₁₁	—	110	1	no	—
21	Dic₇₅	—	121	1	no	maximal, Hall
22	C₁₁⋊C₂₅	—	44	1	no	—
23	C₁₁⋊D₁₁	D₇₅	1	1	yes	characteristic
24	C₃×C₅×C₁₁	—	2	1	no	—
25	C₃×C₅×C₁₁	—	10	1	no	—
26	C₂×C₃×C₂₅	—	121	1	no	—
27	C₁₁²	Dic₇₅	1	1	yes	characteristic, complemented, Sylow
28	C₅×D₁₁	—	22	1	no	—
29	C₅×D₁₁	—	110	1	no	—
30	Dic₂₅	—	363	1	no	Hall
31	C₃×C₂₅	—	484	1	no	Hall
32	C₃×D₁₁	—	22	1	no	—
33	C₃×D₁₁	—	110	1	no	—
34	Dic₁₅	—	605	1	no	—
35	C₅×C₁₁	—	2	1	no	—
36	C₅×C₁₁	—	10	1	no	—
37	C₂×C₂₅	—	121	1	no	—
38	C₃×C₁₁	—	2	1	no	—
39	C₃×C₁₁	—	10	1	no	—
40	C₂×C₃×C₅	—	121	1	no	—
41	C₂₅	—	484	1	no	Sylow
42	D₁₁	—	22	1	no	—
43	D₁₁	—	110	1	no	—
44	Dic₅	—	1815	1	no	—
45	C₃×C₅	#14559075	1	1	yes	characteristic
46	Dic₃	—	3025	1	no	Hall
47	C₁₁	—	2	1	no	—
48	C₁₁	—	10	1	no	—
49	C₂×C₅	—	121	1	no	—
50	C₂×C₃	—	121	1	no	—
51	C₅	C₃⋊#14559075	1	1	yes	characteristic
52	C₄	—	9075	1	no	Sylow
53	C₃	#27130800	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	121	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₃×#15690029	C₄
Frattini	C₅	C₃⋊#14559075
Fitting, socle	C₃×C₅×C₁₁²	Dic₅
prime radical	C₃×C₅×C₁₁⋊D₁₁	D₅
cosocle	C₃×#20258403	C₂
LCS	G ▷ C₃×#15690029
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×#15690029	C₄	semidirect
7. #15690029	Dic₃	semidirect
18. C₃×C₁₁²	Dic₂₅	semidirect
27. C₁₁²	Dic₇₅	semidirect
53. C₃	#27130800	semidirect

Maximal subgroups

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

subgroup	index
C₃×#20258403	2
#27130800	3
C₃⋊#14559102	5
Dic₇₅	121

Subgroups — C3⋊#27130800 #49137104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#27130800 #49137104