Subgroups — C₃²×C₅×C₅⋊(C₇⋊D₇) #36348064

Order 22050.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×C₅⋊(C₇⋊D₇)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅⋊(C₇⋊D₇)	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₃²×C₅×C₇⋊D₇	—	5	1	no	maximal
5	C₃×C₅²×C₇²	C₂×C₃	1	4	yes	complemented
6	C₃²×C₅×D₃₅	—	7	8	no	maximal
7	C₅×C₅⋊(C₇⋊D₇)	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₅×C₇²	—	2	2	no	—
9	C₃²×C₅×C₇²	D₅	1	1	yes	characteristic, complemented
10	C₃²×C₅×C₇²	C₂×C₅	1	1	yes	characteristic, complemented
11	C₃²×C₅²×C₇	D₇	1	8	yes	complemented
12	C₃×C₅⋊(C₇⋊D₇)	C₃×C₅	1	4	yes	direct product factor
13	C₃×C₅×C₇⋊D₇	—	5	4	no	—
14	C₅²×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×D₃₅	—	7	32	no	—
16	C₃²×C₇⋊D₇	—	5	1	no	Hall
17	C₃×C₅×C₇²	—	2	8	no	—
18	C₃×C₅×C₇²	C₃×D₅	1	4	yes	complemented
19	C₃×C₅×C₇²	C₂×C₃×C₅	1	4	yes	complemented
20	C₃²×D₃₅	—	7	8	no	—
21	C₃²×C₅×D₇	—	35	8	no	—
22	C₃×C₅²×C₇	C₃×D₇	1	32	yes	complemented
23	C₅⋊(C₇⋊D₇)	C₃²×C₅	1	1	yes	characteristic, direct product factor
24	C₅×C₇⋊D₇	—	5	1	no	—
25	C₃²×C₅×D₅	—	49	1	no	Hall
26	C₃²×C₇²	C₅×D₅	1	1	yes	characteristic, complemented, Hall
27	C₅×D₃₅	—	7	8	no	—
28	C₃²×C₅×C₇	—	2	16	no	—
29	C₃²×C₅×C₇	C₅×D₇	1	8	yes	complemented
30	C₃²×C₅×C₇	D₃₅	1	8	yes	complemented
31	C₃×C₇⋊D₇	—	5	4	no	—
32	C₅×C₇²	—	2	2	no	—
33	C₅×C₇²	C₃²×D₅	1	1	yes	characteristic, complemented
34	C₅×C₇²	C₂×C₃²×C₅	1	1	yes	characteristic, complemented
35	C₃²×C₅²	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
36	C₃×D₃₅	—	7	32	no	—
37	C₃×C₅×D₇	—	35	32	no	—
38	C₅²×C₇	C₃²×D₇	1	8	yes	complemented
39	C₃×C₅×D₅	—	49	4	no	—
40	C₃×C₇²	C₃×C₅×D₅	1	4	yes	complemented
41	C₃²×D₇	—	35	8	no	—
42	C₃×C₅×C₇	—	2	64	no	—
43	C₃×C₅×C₇	C₃×C₅×D₇	1	32	yes	complemented
44	C₃×C₅×C₇	C₃×D₃₅	1	32	yes	complemented
45	C₇⋊D₇	—	5	1	no	Hall
46	C₂×C₃²×C₅	—	245	1	no	—
47	C₃²×D₅	—	49	1	no	—
48	C₃×C₅²	C₃×C₇⋊D₇	1	4	yes	complemented
49	D₃₅	—	7	8	no	—
50	C₅×D₇	—	35	8	no	—
51	C₃²×C₇	C₅×D₃₅	1	8	yes	complemented
52	C₅×D₅	—	49	1	no	Hall
53	C₇²	C₃²×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
54	C₃²×C₅	—	2	2	no	—
55	C₃²×C₅	C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
56	C₃²×C₅	C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
57	C₃×D₇	—	35	32	no	—
58	C₅×C₇	—	2	16	no	—
59	C₅×C₇	C₃²×C₅×D₇	1	8	yes	complemented
60	C₅×C₇	C₃²×D₃₅	1	8	yes	complemented
61	C₂×C₃×C₅	—	245	4	no	—
62	C₃×D₅	—	49	4	no	—
63	C₅²	C₃²×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	C₃×C₅×D₃₅	1	32	yes	complemented
65	C₂×C₃²	—	245	1	no	Hall
66	C₃×C₅	—	2	8	no	—
67	C₃×C₅	C₃×C₅×C₇⋊D₇	1	4	yes	complemented
68	C₃×C₅	C₃×C₅⋊(C₇⋊D₇)	1	4	yes	direct product factor
69	D₇	—	35	8	no	—
70	C₂×C₅	—	245	1	no	—
71	D₅	—	49	1	no	—
72	C₃²	C₅×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
73	C₇	C₃²×C₅×D₃₅	1	8	yes	complemented
74	C₂×C₃	—	245	4	no	—
75	C₅	—	2	2	no	—
76	C₅	C₃²×C₅×C₇⋊D₇	1	1	yes	characteristic, complemented
77	C₅	C₃²×C₅⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor
78	C₃	C₃×C₅×C₅⋊(C₇⋊D₇)	1	4	yes	direct product factor
79	C₂	—	245	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₅	C₅⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₅×C₇²	C₂×C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇²	C₂
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₃²×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇²	C₂	semidirect
2. C₃×C₅×C₅⋊(C₇⋊D₇)	C₃	direct (N × H)
3. C₃²×C₅⋊(C₇⋊D₇)	C₅	direct (N × H)
5. C₃×C₅²×C₇²	C₂×C₃	semidirect
7. C₅×C₅⋊(C₇⋊D₇)	C₃²	direct (N × H)
9. C₃²×C₅×C₇²	D₅	semidirect
10. C₃²×C₅×C₇²	C₂×C₅	semidirect
11. C₃²×C₅²×C₇	D₇	semidirect
12. C₃×C₅⋊(C₇⋊D₇)	C₃×C₅	direct (N × H)
14. C₅²×C₇²	C₂×C₃²	semidirect
18. C₃×C₅×C₇²	C₃×D₅	semidirect
19. C₃×C₅×C₇²	C₂×C₃×C₅	semidirect
22. C₃×C₅²×C₇	C₃×D₇	semidirect
23. C₅⋊(C₇⋊D₇)	C₃²×C₅	direct (N × H)
26. C₃²×C₇²	C₅×D₅	semidirect
29. C₃²×C₅×C₇	C₅×D₇	semidirect
30. C₃²×C₅×C₇	D₃₅	semidirect
33. C₅×C₇²	C₃²×D₅	semidirect
34. C₅×C₇²	C₂×C₃²×C₅	semidirect
35. C₃²×C₅²	C₇⋊D₇	semidirect
38. C₅²×C₇	C₃²×D₇	semidirect
40. C₃×C₇²	C₃×C₅×D₅	semidirect
43. C₃×C₅×C₇	C₃×C₅×D₇	semidirect
44. C₃×C₅×C₇	C₃×D₃₅	semidirect
48. C₃×C₅²	C₃×C₇⋊D₇	semidirect
51. C₃²×C₇	C₅×D₃₅	semidirect
53. C₇²	C₃²×C₅×D₅	semidirect
55. C₃²×C₅	C₅×C₇⋊D₇	semidirect
56. C₃²×C₅	C₅⋊(C₇⋊D₇)	direct (N × H)
59. C₅×C₇	C₃²×C₅×D₇	semidirect
60. C₅×C₇	C₃²×D₃₅	semidirect
63. C₅²	C₃²×C₇⋊D₇	semidirect
64. C₃×C₇	C₃×C₅×D₃₅	semidirect
67. C₃×C₅	C₃×C₅×C₇⋊D₇	semidirect
68. C₃×C₅	C₃×C₅⋊(C₇⋊D₇)	direct (N × H)
72. C₃²	C₅×C₅⋊(C₇⋊D₇)	direct (N × H)
73. C₇	C₃²×C₅×D₃₅	semidirect
76. C₅	C₃²×C₅×C₇⋊D₇	semidirect
77. C₅	C₃²×C₅⋊(C₇⋊D₇)	direct (N × H)
78. C₃	C₃×C₅×C₅⋊(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×C₅²×C₇²	2
C₃×C₅×C₅⋊(C₇⋊D₇)	3
C₃²×C₅⋊(C₇⋊D₇)	5
C₃²×C₅×C₇⋊D₇	5
C₃²×C₅×D₃₅	7

Subgroups — C32×C5×C5⋊(C7⋊D7) #36348064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅×C₅⋊(C₇⋊D₇) #36348064