Subgroups — C₅²⋊C₃×D₃₁⋊C₃ #28358458

Order 13950.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₁×C₅²⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	D₃₁⋊(C₅²⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₅²×D₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₅²⋊(C₃₁⋊C₃)	C₂×C₃	1	2	yes	complemented
6	C₃₁×C₅²⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅²×C₃₁⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₅²×D₃₁	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₅×D₃₁⋊C₃	—	3	2	no	—
10	C₅²×C₃₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×D₃₁⋊C₃	—	25	1	no	maximal, Hall
12	C₅×C₃₁⋊C₃	—	3	2	no	—
13	C₂×C₃×C₅²⋊C₃	—	31	1	no	maximal, Hall
14	C₅×D₃₁	—	3	2	no	—
15	C₃×C₃₁⋊C₃	—	25	1	no	Hall
16	C₃×C₅²⋊C₃	—	31	1	no	Hall
17	C₃×D₃₁	—	25	1	no	—
18	D₃₁⋊C₃	—	25	2	no	—
19	D₃₁⋊C₃	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
20	C₅×C₃₁	—	3	2	no	—
21	C₂×C₃×C₅²	—	31	1	no	—
22	C₂×C₅²⋊C₃	—	31	2	no	—
23	C₂×C₅²⋊C₃	—	31	1	no	—
24	C₃×C₃₁	—	25	1	no	—
25	C₃₁⋊C₃	—	25	2	no	—
26	C₃₁⋊C₃	C₂×C₅²⋊C₃	1	1	yes	characteristic, complemented
27	C₃×C₅²	—	31	1	no	—
28	C₅²⋊C₃	—	31	2	no	—
29	C₅²⋊C₃	D₃₁⋊C₃	1	1	yes	characteristic, direct product factor
30	D₃₁	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₅²	—	31	1	no	Hall
32	C₃₁	C₂×C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃×C₅	—	93	2	no	—
34	C₅²	C₃×D₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃²	—	775	1	no	Hall
36	C₃×C₅	—	93	2	no	—
37	C₂×C₅	—	93	2	no	—
38	C₃²	—	775	1	no	Sylow
39	C₂×C₃	—	775	2	no	—
40	C₂×C₃	—	775	1	no	—
41	C₂×C₃	—	31	1	no	—
42	C₅	—	3	2	no	—
43	C₃	—	775	2	no	—
44	C₃	—	25	1	no	—
45	C₃	—	31	1	no	—
46	C₂	—	31	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₃₁	C₂×C₃²
LCS	G ▷ C₅²×C₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²⋊C₃×C₃₁⋊C₃	C₂	semidirect
2. D₃₁×C₅²⋊C₃	C₃	semidirect
3. D₃₁⋊(C₅²⋊C₃)	C₃	semidirect
4. C₅²×D₃₁⋊C₃	C₃	semidirect
5. C₅²⋊(C₃₁⋊C₃)	C₂×C₃	semidirect
6. C₃₁×C₅²⋊C₃	C₂×C₃	semidirect
7. C₅²×C₃₁⋊C₃	C₂×C₃	semidirect
8. C₅²×D₃₁	C₃²	semidirect
10. C₅²×C₃₁	C₂×C₃²	semidirect
19. D₃₁⋊C₃	C₅²⋊C₃	direct (N × H)
26. C₃₁⋊C₃	C₂×C₅²⋊C₃	semidirect
29. C₅²⋊C₃	D₃₁⋊C₃	direct (N × H)
30. D₃₁	C₃×C₅²⋊C₃	semidirect
32. C₃₁	C₂×C₃×C₅²⋊C₃	semidirect
34. C₅²	C₃×D₃₁⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₅²⋊C₃×C₃₁⋊C₃	2
D₃₁×C₅²⋊C₃	3
D₃₁⋊(C₅²⋊C₃)	3
C₅²×D₃₁⋊C₃	3
C₃×D₃₁⋊C₃	25
C₂×C₃×C₅²⋊C₃	31

Subgroups — C52⋊C3×D31⋊C3 #28358458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²⋊C₃×D₃₁⋊C₃ #28358458