Subgroups — C₃⋊#22604804 #42124643

Order 27900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₃₁⋊#1039)	C₃	1	1	yes	maximal, characteristic, complemented
3	#22604804	—	3	1	no	maximal
4	C₃×C₃₁×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×C₅²⋊C₃	—	2	1	no	—
6	C₂×C₃₁×C₅²⋊C₃	D₃	1	1	yes	characteristic
7	C₂×C₃×C₅²×C₃₁	C₂×C₃	1	1	yes	characteristic
8	C₃₁⋊#1039	—	3	1	no	Hall
9	C₃₁×C₅²⋊C₃	—	2	1	no	—
10	C₃₁×C₅²⋊C₃	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
12	Dic₄₆₅	—	15	2	no	—
13	C₂×C₅²×C₃₁	C₃×D₃	1	1	yes	characteristic
14	C₃×Dic₉₃	—	25	1	no	maximal, Hall
15	C₂×C₃×C₅×C₃₁	—	3	2	no	—
16	C₃⋊(#1039⋊C₃)	—	31	1	no	maximal, Hall
17	C₅²×C₃₁	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	Dic₁₅₅	—	45	2	no	—
19	C₂×C₃²×C₃₁	—	25	1	no	—
20	C₃×C₅×C₃₁	—	3	2	no	—
21	C₂×C₃×C₅²⋊C₃	D₃₁	1	1	yes	characteristic
22	Dic₉₃	—	25	1	no	—
23	C₃×Dic₃₁	—	75	1	no	—
24	C₂×C₅×C₃₁	—	3	2	no	—
25	C₃⋊#1039	—	31	1	no	—
26	#1039⋊C₃	—	93	1	no	—
27	C₃²×C₃₁	—	25	1	no	Hall
28	C₃×C₅²⋊C₃	Dic₃₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₃₁	—	25	1	no	—
30	C₂×C₃×C₃₁	—	50	1	no	—
31	C₂×C₃×C₃₁	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
32	C₅×C₃₁	—	3	2	no	—
33	C₂×C₃×C₅²	C₃×D₃₁	1	1	yes	characteristic
34	C₂×C₅²⋊C₃	—	2	1	no	—
35	C₂×C₅²⋊C₃	D₉₃	1	1	yes	characteristic
36	Dic₃₁	—	75	1	no	Hall
37	#1039	—	93	1	no	Hall
38	C₃×C₃₁	—	25	1	no	—
39	C₃×C₃₁	—	50	1	no	—
40	C₃×C₃₁	#1039⋊C₃	1	1	yes	characteristic, complemented
41	C₃×C₅²	C₃×Dic₃₁	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	2	1	no	—
43	C₅²⋊C₃	Dic₉₃	1	1	yes	characteristic, complemented
44	C₂×C₃₁	C₃⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic
45	Dic₁₅	—	465	2	no	—
46	C₂×C₅²	C₃×D₉₃	1	1	yes	characteristic
47	C₃×Dic₃	—	775	1	no	Hall
48	C₃₁	C₃⋊(#1039⋊C₃)	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₃×C₅	—	3	2	no	—
50	C₅²	C₃×Dic₉₃	1	1	yes	characteristic, complemented, Sylow
51	Dic₅	—	1395	2	no	—
52	C₂×C₃²	—	25	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	2325	1	no	—
55	Dic₃	—	775	1	no	—
56	C₂×C₅	—	3	2	no	—
57	C₃²	—	25	1	no	Sylow
58	C₂×C₃	—	25	1	no	—
59	C₂×C₃	—	50	1	no	—
60	C₂×C₃	#17987871	1	1	yes	characteristic
61	C₅	—	3	2	no	—
62	C₄	—	2325	1	no	Sylow
63	C₃	—	25	1	no	—
64	C₃	—	50	1	no	—
65	C₃	#22604804	1	1	yes	characteristic, complemented
66	C₂	C₃⋊#17987871	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#17987871
commutator, hypocenter	C₃×C₅²×C₃₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₅²×C₃₁	C₂×C₃
prime radical	C₂×C₃×C₃₁×C₅²⋊C₃	C₂
LCS	G ▷ C₃×C₅²×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₃⋊(C₃₁⋊#1039)	C₃	semidirect
4. C₃×C₃₁×C₅²⋊C₃	C₄	semidirect
10. C₃₁×C₅²⋊C₃	Dic₃	semidirect
11. C₃×C₅²×C₃₁	C₃×C₄	semidirect
17. C₅²×C₃₁	C₃×Dic₃	semidirect
28. C₃×C₅²⋊C₃	Dic₃₁	semidirect
40. C₃×C₃₁	#1039⋊C₃	semidirect
41. C₃×C₅²	C₃×Dic₃₁	semidirect
43. C₅²⋊C₃	Dic₉₃	semidirect
48. C₃₁	C₃⋊(#1039⋊C₃)	semidirect
50. C₅²	C₃×Dic₉₃	semidirect
65. C₃	#22604804	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₃₁×C₅²⋊C₃	2
C₃⋊(C₃₁⋊#1039)	3
#22604804	3
C₃×Dic₉₃	25
C₃⋊(#1039⋊C₃)	31

Subgroups — C3⋊#22604804 #42124643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#22604804 #42124643