Subgroups — C₃²×C₂₅×C₇⋊D₇ #36347768

Order 22050.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₂₅×C₇⋊D₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₇⋊D₇	C₅	1	1	yes	maximal, characteristic
4	C₃×C₇²×C₂₅	C₂×C₃	1	4	yes	complemented
5	C₃²×D₇×C₂₅	—	7	8	no	maximal
6	C₂₅×C₇⋊D₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic
8	C₃²×C₇×C₂₅	D₇	1	8	yes	complemented
9	C₃×C₅×C₇⋊D₇	C₃×C₅	1	4	yes	—
10	C₇²×C₂₅	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×D₇×C₂₅	—	7	32	no	—
12	C₃²×C₇⋊D₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅×C₇²	C₂×C₃×C₅	1	4	yes	—
14	C₃²×C₅×D₇	—	7	8	no	—
15	C₃×C₇×C₂₅	C₃×D₇	1	32	yes	complemented
16	C₅×C₇⋊D₇	C₃²×C₅	1	1	yes	characteristic
17	C₂×C₃²×C₂₅	—	49	1	no	Hall
18	C₃²×C₇²	C₂×C₂₅	1	1	yes	characteristic, complemented, Hall
19	D₇×C₂₅	—	7	8	no	—
20	C₃²×C₅×C₇	C₅×D₇	1	8	yes	—
21	C₃×C₇⋊D₇	C₃×C₂₅	1	4	yes	direct product factor
22	C₅×C₇²	C₂×C₃²×C₅	1	1	yes	characteristic
23	C₃²×C₂₅	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₅×D₇	—	7	32	no	—
25	C₇×C₂₅	C₃²×D₇	1	8	yes	complemented
26	C₂×C₃×C₂₅	—	49	4	no	—
27	C₃×C₇²	C₂×C₃×C₂₅	1	4	yes	complemented
28	C₃²×D₇	—	7	8	no	—
29	C₃×C₅×C₇	C₃×C₅×D₇	1	32	yes	—
30	C₇⋊D₇	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²×C₅	—	49	1	no	—
32	C₃×C₂₅	C₃×C₇⋊D₇	1	4	yes	direct product factor
33	C₅×D₇	—	7	8	no	—
34	C₃²×C₇	D₇×C₂₅	1	8	yes	complemented
35	C₂×C₂₅	—	49	1	no	Hall
36	C₇²	C₂×C₃²×C₂₅	1	1	yes	characteristic, complemented, Sylow
37	C₃²×C₅	C₅×C₇⋊D₇	1	1	yes	characteristic
38	C₃×D₇	—	7	32	no	—
39	C₅×C₇	C₃²×C₅×D₇	1	8	yes	—
40	C₂×C₃×C₅	—	49	4	no	—
41	C₂₅	C₃²×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₃×C₇	C₃×D₇×C₂₅	1	32	yes	complemented
43	C₂×C₃²	—	49	1	no	Hall
44	C₃×C₅	C₃×C₅×C₇⋊D₇	1	4	yes	—
45	D₇	—	7	8	no	—
46	C₂×C₅	—	49	1	no	—
47	C₃²	C₂₅×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
48	C₇	C₃²×D₇×C₂₅	1	8	yes	complemented
49	C₂×C₃	—	49	4	no	—
50	C₅	C₃²×C₅×C₇⋊D₇	1	1	yes	characteristic
51	C₃	C₃×C₂₅×C₇⋊D₇	1	4	yes	direct product factor
52	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₂₅	C₇⋊D₇
commutator, hypocenter	C₇²	C₂×C₃²×C₂₅
Frattini	C₅	C₃²×C₅×C₇⋊D₇
Fitting	C₃²×C₇²×C₂₅	C₂
socle	C₃²×C₅×C₇²	C₂×C₅
prime radical	C₃²×C₅×C₇⋊D₇	C₅
cosocle	C₅×C₇²	C₂×C₃²×C₅
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃²×C₂₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇²×C₂₅	C₂	semidirect
2. C₃×C₂₅×C₇⋊D₇	C₃	direct (N × H)
4. C₃×C₇²×C₂₅	C₂×C₃	semidirect
6. C₂₅×C₇⋊D₇	C₃²	direct (N × H)
8. C₃²×C₇×C₂₅	D₇	semidirect
10. C₇²×C₂₅	C₂×C₃²	semidirect
12. C₃²×C₇⋊D₇	C₂₅	direct (N × H)
15. C₃×C₇×C₂₅	C₃×D₇	semidirect
18. C₃²×C₇²	C₂×C₂₅	semidirect
21. C₃×C₇⋊D₇	C₃×C₂₅	direct (N × H)
23. C₃²×C₂₅	C₇⋊D₇	direct (N × H)
25. C₇×C₂₅	C₃²×D₇	semidirect
27. C₃×C₇²	C₂×C₃×C₂₅	semidirect
30. C₇⋊D₇	C₃²×C₂₅	direct (N × H)
32. C₃×C₂₅	C₃×C₇⋊D₇	direct (N × H)
34. C₃²×C₇	D₇×C₂₅	semidirect
36. C₇²	C₂×C₃²×C₂₅	semidirect
41. C₂₅	C₃²×C₇⋊D₇	direct (N × H)
42. C₃×C₇	C₃×D₇×C₂₅	semidirect
47. C₃²	C₂₅×C₇⋊D₇	direct (N × H)
48. C₇	C₃²×D₇×C₂₅	semidirect
51. C₃	C₃×C₂₅×C₇⋊D₇	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×C₇²×C₂₅	2
C₃×C₂₅×C₇⋊D₇	3
C₃²×C₅×C₇⋊D₇	5
C₃²×D₇×C₂₅	7

Subgroups — C32×C25×C7⋊D7 #36347768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₂₅×C₇⋊D₇ #36347768