Subgroups — C₃×C₂₅×D₈₇ #27189382

Order 13050.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₅×D₈₇	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₂₅×D₂₉	—	3	1	no	maximal
4	C₃×C₅×D₈₇	C₅	1	1	yes	maximal, characteristic
5	C₃×C₂₅×C₂₉	—	2	1	no	—
6	C₃×C₂₅×C₂₉	D₃	1	1	yes	characteristic, complemented
7	C₃×C₂₅×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂₅×D₂₉	—	3	1	no	Hall
9	C₃²×C₅×C₂₉	C₂×C₅	1	1	yes	characteristic
10	C₅×D₈₇	C₃×C₅	1	1	yes	characteristic
11	C₃×C₅×D₂₉	—	3	1	no	—
12	C₂₅×C₂₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
13	C₃×D₈₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×D₃×C₂₅	—	29	1	no	maximal, Hall
15	C₃×C₅×C₂₉	—	2	1	no	—
16	C₃×C₅×C₂₉	C₅×D₃	1	1	yes	characteristic
17	C₃×C₅×C₂₉	C₂×C₃×C₅	1	1	yes	characteristic
18	C₅×D₂₉	—	3	1	no	—
19	C₃²×C₂₉	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₅	D₂₉	1	1	yes	characteristic, complemented, Hall
21	D₈₇	C₃×C₂₅	1	1	yes	characteristic, direct product factor
22	C₃×D₂₉	—	3	1	no	—
23	C₂×C₃×C₂₅	—	87	1	no	—
24	D₃×C₂₅	—	29	1	no	—
25	C₅×C₂₉	C₃×C₅×D₃	1	1	yes	characteristic
26	C₃×C₅×D₃	—	29	1	no	—
27	C₃×C₂₉	—	2	1	no	—
28	C₃×C₂₉	D₃×C₂₅	1	1	yes	characteristic, complemented
29	C₃×C₂₉	C₂×C₃×C₂₅	1	1	yes	characteristic, complemented
30	C₃×C₂₅	—	2	1	no	—
31	C₃×C₂₅	C₃×D₂₉	1	1	yes	characteristic, complemented
32	C₃×C₂₅	D₈₇	1	1	yes	characteristic, direct product factor
33	D₂₉	—	3	1	no	Hall
34	C₂×C₂₅	—	87	1	no	Hall
35	C₃²×C₅	C₅×D₂₉	1	1	yes	characteristic
36	C₂×C₃×C₅	—	87	1	no	—
37	C₅×D₃	—	29	1	no	—
38	C₂₉	C₃×D₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
39	C₂₅	C₃×D₈₇	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×D₃	—	29	1	no	Hall
41	C₃×C₅	—	2	1	no	—
42	C₃×C₅	C₃×C₅×D₂₉	1	1	yes	characteristic
43	C₃×C₅	C₅×D₈₇	1	1	yes	characteristic
44	C₂×C₅	—	87	1	no	—
45	C₃²	C₂₅×D₂₉	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	87	1	no	—
47	D₃	—	29	1	no	—
48	C₅	C₃×C₅×D₈₇	1	1	yes	characteristic
49	C₃	—	2	1	no	—
50	C₃	C₃×C₂₅×D₂₉	1	1	yes	characteristic, complemented
51	C₃	C₂₅×D₈₇	1	1	yes	characteristic, direct product factor
52	C₂	—	87	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₅	D₈₇
commutator, hypocenter	C₃×C₂₉	C₂×C₃×C₂₅
Frattini	C₅	C₃×C₅×D₈₇
Fitting	C₃²×C₂₅×C₂₉	C₂
socle	C₃²×C₅×C₂₉	C₂×C₅
prime radical	C₃×C₅×D₈₇	C₅
cosocle	C₃×C₅×C₂₉	C₂×C₃×C₅
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₃×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂₅×C₂₉	C₂	semidirect
2. C₂₅×D₈₇	C₃	direct (N × H)
6. C₃×C₂₅×C₂₉	D₃	semidirect
7. C₃×C₂₅×C₂₉	C₂×C₃	semidirect
12. C₂₅×C₂₉	C₃×D₃	semidirect
13. C₃×D₈₇	C₂₅	direct (N × H)
19. C₃²×C₂₉	C₂×C₂₅	semidirect
20. C₃²×C₂₅	D₂₉	semidirect
21. D₈₇	C₃×C₂₅	direct (N × H)
28. C₃×C₂₉	D₃×C₂₅	semidirect
29. C₃×C₂₉	C₂×C₃×C₂₅	semidirect
31. C₃×C₂₅	C₃×D₂₉	semidirect
32. C₃×C₂₅	D₈₇	direct (N × H)
38. C₂₉	C₃×D₃×C₂₅	semidirect
39. C₂₅	C₃×D₈₇	direct (N × H)
45. C₃²	C₂₅×D₂₉	semidirect
50. C₃	C₃×C₂₅×D₂₉	semidirect
51. C₃	C₂₅×D₈₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₅×C₂₉	2
C₂₅×D₈₇	3
C₃×C₂₅×D₂₉	3
C₃×C₅×D₈₇	5
C₃×D₃×C₂₅	29

Subgroups — C3×C25×D87 #27189382

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₅×D₈₇ #27189382