Subgroups — C₂×C₃₁×#3874 #22604880

Order 9300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3874	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₅×C₃₁	—	3	1	no	maximal, Hall
4	C₃₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅²×C₃₁	D₃	1	1	yes	characteristic, complemented
6	C₅×D₅×C₃₁	—	3	2	no	—
7	C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₅×C₃₁	—	15	1	no	—
9	C₂×D₅×C₃₁	—	3	1	no	—
10	C₂×D₃×C₃₁	—	25	1	no	maximal, Hall
11	C₂×C₅×C₃₁	—	3	1	no	—
12	C₂×C₅×C₃₁	—	3	1	no	—
13	C₂×C₅×C₃₁	—	15	2	no	—
14	D₅×C₃₁	—	3	2	no	—
15	C₂×#3874	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃×C₃₁	—	25	1	no	—
17	D₃×C₃₁	—	25	2	no	—
18	C₅×C₃₁	—	3	1	no	—
19	C₅×C₃₁	—	3	1	no	—
20	C₂×C₅²⋊C₃	C₂×C₃₁	1	1	yes	characteristic, complemented
21	#3874	C₂×C₃₁	1	2	yes	direct product factor
22	C₂²×C₃₁	—	15	1	no	Hall
23	C₂×C₅×D₅	—	3	1	no	Hall
24	C₃×C₃₁	—	25	1	no	Hall
25	C₅²⋊C₃	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃₁	—	15	2	no	—
27	C₂×C₃₁	#3874	1	1	yes	characteristic, direct product factor
28	C₂×C₅²	D₃×C₃₁	1	1	yes	characteristic, complemented
29	C₅×D₅	—	3	2	no	—
30	C₃₁	C₂×#3874	1	1	yes	characteristic, direct product factor, Sylow
31	C₅²	C₂×D₃×C₃₁	1	1	yes	characteristic, complemented, Sylow
32	C₂²×C₅	—	15	1	no	—
33	C₂×D₅	—	3	1	no	—
34	C₂×D₃	—	25	1	no	Hall
35	C₂×C₅	—	3	1	no	—
36	C₂×C₅	—	3	1	no	—
37	C₂×C₅	—	15	2	no	—
38	D₅	—	3	2	no	—
39	C₂×C₃	—	25	1	no	—
40	D₃	—	25	2	no	—
41	C₅	—	3	1	no	—
42	C₅	—	3	1	no	—
43	C₂²	—	15	1	no	Sylow
44	C₃	—	25	1	no	Sylow
45	C₂	—	15	2	no	—
46	C₂	C₃₁×#3874	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃₁	#3874
commutator, hypocenter	C₅²⋊C₃	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₃₁	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×C₅²⋊C₃	C₂	semidirect
2. C₃₁×#3874	C₂	direct (N × H)
4. C₃₁×C₅²⋊C₃	C₂²	semidirect
5. C₂×C₅²×C₃₁	D₃	semidirect
7. C₅²×C₃₁	C₂×D₃	semidirect
15. C₂×#3874	C₃₁	direct (N × H)
20. C₂×C₅²⋊C₃	C₂×C₃₁	semidirect
21. #3874	C₂×C₃₁	direct (N × H)
25. C₅²⋊C₃	C₂²×C₃₁	semidirect
27. C₂×C₃₁	#3874	direct (N × H)
28. C₂×C₅²	D₃×C₃₁	semidirect
30. C₃₁	C₂×#3874	direct (N × H)
31. C₅²	C₂×D₃×C₃₁	semidirect
46. C₂	C₃₁×#3874	direct (N × H)

Subgroups — C2×C31×#3874 #22604880

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃₁×#3874 #22604880