Subgroups — C₃⋊(#92150⋊C₂₅) #49137105

Order 36300.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#20258402	C₂	1	1	yes	maximal, characteristic
2	#92150⋊C₂₅	—	3	1	no	maximal, Hall
3	C₃×#15690027	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅×C₃⋊#92150	C₅	1	1	yes	maximal, characteristic
5	#20258402	D₃	1	1	yes	characteristic
6	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic
7	#15690027	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₅×#92150	—	3	1	no	—
9	C₃×C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic
10	C₃×D₁₁⋊C₂₅	—	22	1	no	—
11	C₃×D₁₁⋊C₂₅	—	22	5	no	—
12	C₃⋊#92150	C₂₅	1	1	yes	characteristic, complemented, Hall
13	C₅×C₁₁⋊D₁₁	C₅×D₃	1	1	yes	characteristic
14	C₃×C₁₁⋊C₂₅	—	22	1	no	—
15	C₃×C₁₁⋊C₂₅	—	22	5	no	—
16	C₃×C₁₁⋊D₁₁	C₂×C₂₅	1	1	yes	characteristic
17	C₅×C₁₁²	C₅×Dic₃	1	1	yes	characteristic
18	D₁₁⋊C₂₅	—	22	1	no	—
19	D₁₁⋊C₂₅	—	22	5	no	—
20	#92150	—	3	1	no	Hall
21	C₃×C₁₁²	C₄×C₂₅	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅×D₁₁	—	110	1	no	—
23	C₃×C₅×D₁₁	—	110	5	no	—
24	Dic₃×C₂₅	—	121	1	no	maximal, Hall
25	C₁₁⋊C₂₅	—	22	1	no	—
26	C₁₁⋊C₂₅	—	22	5	no	—
27	C₁₁⋊D₁₁	D₃×C₂₅	1	1	yes	characteristic
28	C₃×C₅×C₁₁	—	2	1	no	—
29	C₃×C₅×C₁₁	—	2	5	no	—
30	C₂×C₃×C₂₅	—	121	1	no	—
31	C₁₁²	Dic₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
32	C₅×D₁₁	—	22	1	no	—
33	C₅×D₁₁	—	110	5	no	—
34	C₄×C₂₅	—	363	1	no	Hall
35	C₃×C₂₅	—	121	1	no	Hall
36	C₃×D₁₁	—	110	1	no	—
37	C₃×D₁₁	—	110	5	no	—
38	C₅×Dic₃	—	605	1	no	—
39	C₅×C₁₁	—	2	1	no	—
40	C₅×C₁₁	—	2	5	no	—
41	C₂×C₂₅	—	121	1	no	—
42	C₃×C₁₁	—	2	1	no	—
43	C₃×C₁₁	—	2	5	no	—
44	C₂×C₃×C₅	—	605	1	no	—
45	C₂₅	—	121	1	no	Sylow
46	D₁₁	—	22	1	no	—
47	D₁₁	—	110	5	no	—
48	C₄×C₅	—	1815	1	no	—
49	C₃×C₅	#92150⋊C₅	1	1	yes	characteristic
50	Dic₃	—	605	1	no	Hall
51	C₁₁	—	2	1	no	—
52	C₁₁	—	2	5	no	—
53	C₂×C₅	—	605	1	no	—
54	C₂×C₃	—	605	1	no	—
55	C₅	C₃⋊(#92150⋊C₅)	1	1	yes	characteristic
56	C₄	—	1815	1	no	Sylow
57	C₃	#92150⋊C₂₅	1	1	yes	characteristic, complemented, Sylow
58	C₂	—	605	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₅	C₃⋊(#92150⋊C₅)
commutator, hypocenter	C₃×C₁₁²	C₄×C₂₅
Fitting, socle	C₃×C₅×C₁₁²	C₄×C₅
prime radical, cosocle	C₃×C₅×C₁₁⋊D₁₁	C₂×C₅
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×#15690027	C₄	semidirect
7. #15690027	Dic₃	semidirect
12. C₃⋊#92150	C₂₅	semidirect
21. C₃×C₁₁²	C₄×C₂₅	semidirect
31. C₁₁²	Dic₃×C₂₅	semidirect
57. C₃	#92150⋊C₂₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×#20258402	2
#92150⋊C₂₅	3
C₅×C₃⋊#92150	5
Dic₃×C₂₅	121

Subgroups — C3⋊(#92150⋊C25) #49137105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(#92150⋊C₂₅) #49137105