Subgroups — C₂×C₃×C₅⋊(C₅⋊(D₃₇⋊C₃)) #45686341

Order 33300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅²×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₅⋊D₁₈₅	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅⋊(C₅⋊(D₃₇⋊C₃))	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₅²×C₃₇⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₅⋊(D₃₇⋊C₃)	—	5	6	no	maximal
7	C₃×C₅⋊D₁₈₅	C₂×C₃	1	2	yes	complemented
8	C₂×C₅²×C₃₇⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₃×C₅²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₅⋊D₁₈₅	C₃²	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₃₇⋊C₃	D₅	1	6	yes	complemented
13	C₃×C₅⋊(D₃₇⋊C₃)	—	5	12	no	—
14	C₅²×C₃₇⋊C₃	C₂²×C₃	1	3	yes	complemented
15	C₃×C₅²×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×D₁₈₅	—	5	6	no	—
17	C₂×C₅⋊(D₃₇⋊C₃)	—	5	18	no	—
18	C₂×C₅²×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₅⋊D₁₈₅	C₂×C₃²	1	2	yes	complemented
20	C₃×C₅×C₃₇⋊C₃	C₂×D₅	1	6	yes	complemented
21	C₂×C₃×D₃₇⋊C₃	—	25	1	no	Hall
22	C₂×C₃×C₅×C₃₇	C₃×D₅	1	6	yes	complemented
23	C₃×D₁₈₅	—	5	12	no	—
24	C₂×C₅×C₃₇⋊C₃	C₃×D₅	1	18	yes	complemented
25	C₅⋊(D₃₇⋊C₃)	—	5	36	no	—
26	C₅²×C₃₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃²×C₅⋊D₅	—	37	1	no	maximal, Hall
28	C₂×D₁₈₅	—	5	6	no	—
29	C₂×C₃×C₃₇⋊C₃	C₅⋊D₅	1	1	yes	characteristic, complemented
30	C₃×D₃₇⋊C₃	—	25	2	no	—
31	C₃×C₅×C₃₇	C₂×C₃×D₅	1	6	yes	complemented
32	C₅×C₃₇⋊C₃	C₂×C₃×D₅	1	18	yes	complemented
33	C₂×C₃²×C₅²	—	37	1	no	—
34	C₃²×C₅⋊D₅	—	37	2	no	—
35	C₂×C₃×D₃₇	—	25	1	no	—
36	C₂×D₃₇⋊C₃	—	25	3	no	—
37	C₂×C₅×C₃₇	C₃²×D₅	1	6	yes	complemented
38	D₁₈₅	—	5	12	no	—
39	C₃×C₃₇⋊C₃	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×C₅⋊D₅	—	37	3	no	—
41	C₂×C₃×C₅⋊D₅	—	37	1	no	—
42	C₃²×C₅²	—	37	1	no	Hall
43	C₂×C₃×C₃₇	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
44	C₃×D₃₇	—	25	2	no	—
45	C₂×C₃₇⋊C₃	C₃×C₅⋊D₅	1	3	yes	complemented
46	D₃₇⋊C₃	—	25	6	no	—
47	C₅×C₃₇	C₂×C₃²×D₅	1	6	yes	complemented
48	C₂×C₃²×D₅	—	185	6	no	—
49	C₂×C₃×C₅²	—	37	3	no	—
50	C₂×C₃×C₅²	D₃₇⋊C₃	1	1	yes	characteristic, complemented
51	C₃×C₅⋊D₅	—	37	6	no	—
52	C₃×C₅⋊D₅	—	37	2	no	—
53	C₂×D₃₇	—	25	1	no	Hall
54	C₃×C₃₇	C₂×C₃×C₅⋊D₅	1	1	yes	characteristic, complemented
55	C₃₇⋊C₃	C₂×C₃×C₅⋊D₅	1	3	yes	complemented
56	C₂×C₅⋊D₅	—	37	1	no	Hall
57	C₂×C₃²×C₅	—	37	6	no	—
58	C₃²×D₅	—	185	12	no	—
59	C₃×C₅²	—	37	3	no	—
60	C₃×C₅²	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented
61	C₂×C₃₇	C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented
62	D₃₇	—	25	2	no	—
63	C₂×C₃×D₅	—	185	18	no	—
64	C₂×C₃×D₅	—	185	6	no	—
65	C₂×C₅²	C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented
66	C₅⋊D₅	—	37	2	no	—
67	C₃²×C₅	—	37	6	no	—
68	C₃₇	C₂×C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₃²	—	925	1	no	Hall
70	C₂×C₃×C₅	—	37	18	no	—
71	C₂×C₃×C₅	C₅⋊(D₃₇⋊C₃)	1	6	yes	complemented
72	C₃×D₅	—	185	36	no	—
73	C₃×D₅	—	185	12	no	—
74	C₅²	C₂×C₃×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
75	C₂×D₅	—	185	6	no	—
76	C₂×C₃²	—	37	1	no	—
77	C₂×C₃²	—	925	2	no	—
78	C₃×C₅	—	37	18	no	—
79	C₃×C₅	C₂×C₅⋊(D₃₇⋊C₃)	1	6	yes	complemented
80	C₂²×C₃	—	925	3	no	—
81	C₂²×C₃	—	925	1	no	—
82	C₂×C₅	C₃×C₅⋊(D₃₇⋊C₃)	1	6	yes	complemented
83	D₅	—	185	12	no	—
84	C₃²	—	37	1	no	Sylow
85	C₂×C₃	—	37	3	no	—
86	C₂×C₃	—	925	6	no	—
87	C₂×C₃	—	925	2	no	—
88	C₂×C₃	C₅⋊(C₅⋊(D₃₇⋊C₃))	1	1	yes	characteristic, direct product factor
89	C₅	C₂×C₃×C₅⋊(D₃₇⋊C₃)	1	6	yes	complemented
90	C₂²	—	925	1	no	Sylow
91	C₃	—	37	3	no	—
92	C₃	C₂×C₅⋊(C₅⋊(D₃₇⋊C₃))	1	1	yes	characteristic, direct product factor
93	C₂	—	925	2	no	—
94	C₂	C₃×C₅⋊(C₅⋊(D₃₇⋊C₃))	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊(C₅⋊(D₃₇⋊C₃))
commutator, cosocle, hypocenter	C₅²×C₃₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₃₇	C₂×C₃
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅²×C₃₇⋊C₃	C₂	semidirect
2. C₃×C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂	direct (N × H)
3. C₂×C₃×C₅⋊D₁₈₅	C₃	semidirect
4. C₂×C₅⋊(C₅⋊(D₃₇⋊C₃))	C₃	direct (N × H)
5. C₃×C₅²×C₃₇⋊C₃	C₂²	semidirect
7. C₃×C₅⋊D₁₈₅	C₂×C₃	semidirect
8. C₂×C₅²×C₃₇⋊C₃	C₂×C₃	semidirect
9. C₅⋊(C₅⋊(D₃₇⋊C₃))	C₂×C₃	direct (N × H)
10. C₂×C₃×C₅²×C₃₇	C₂×C₃	semidirect
11. C₂×C₅⋊D₁₈₅	C₃²	semidirect
12. C₂×C₃×C₅×C₃₇⋊C₃	D₅	semidirect
14. C₅²×C₃₇⋊C₃	C₂²×C₃	semidirect
15. C₃×C₅²×C₃₇	C₂²×C₃	semidirect
18. C₂×C₅²×C₃₇	C₂×C₃²	semidirect
19. C₅⋊D₁₈₅	C₂×C₃²	semidirect
20. C₃×C₅×C₃₇⋊C₃	C₂×D₅	semidirect
22. C₂×C₃×C₅×C₃₇	C₃×D₅	semidirect
24. C₂×C₅×C₃₇⋊C₃	C₃×D₅	semidirect
26. C₅²×C₃₇	C₂²×C₃²	semidirect
29. C₂×C₃×C₃₇⋊C₃	C₅⋊D₅	semidirect
31. C₃×C₅×C₃₇	C₂×C₃×D₅	semidirect
32. C₅×C₃₇⋊C₃	C₂×C₃×D₅	semidirect
37. C₂×C₅×C₃₇	C₃²×D₅	semidirect
39. C₃×C₃₇⋊C₃	C₂×C₅⋊D₅	semidirect
43. C₂×C₃×C₃₇	C₃×C₅⋊D₅	semidirect
45. C₂×C₃₇⋊C₃	C₃×C₅⋊D₅	semidirect
47. C₅×C₃₇	C₂×C₃²×D₅	semidirect
50. C₂×C₃×C₅²	D₃₇⋊C₃	semidirect
54. C₃×C₃₇	C₂×C₃×C₅⋊D₅	semidirect
55. C₃₇⋊C₃	C₂×C₃×C₅⋊D₅	semidirect
60. C₃×C₅²	C₂×D₃₇⋊C₃	semidirect
61. C₂×C₃₇	C₃²×C₅⋊D₅	semidirect
65. C₂×C₅²	C₃×D₃₇⋊C₃	semidirect
68. C₃₇	C₂×C₃²×C₅⋊D₅	semidirect
71. C₂×C₃×C₅	C₅⋊(D₃₇⋊C₃)	semidirect
74. C₅²	C₂×C₃×D₃₇⋊C₃	semidirect
79. C₃×C₅	C₂×C₅⋊(D₃₇⋊C₃)	semidirect
82. C₂×C₅	C₃×C₅⋊(D₃₇⋊C₃)	semidirect
88. C₂×C₃	C₅⋊(C₅⋊(D₃₇⋊C₃))	direct (N × H)
89. C₅	C₂×C₃×C₅⋊(D₃₇⋊C₃)	semidirect
92. C₃	C₂×C₅⋊(C₅⋊(D₃₇⋊C₃))	direct (N × H)
94. C₂	C₃×C₅⋊(C₅⋊(D₃₇⋊C₃))	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅²×C₃₇⋊C₃	2
C₃×C₅⋊(C₅⋊(D₃₇⋊C₃))	2
C₂×C₃×C₅⋊D₁₈₅	3
C₂×C₅⋊(C₅⋊(D₃₇⋊C₃))	3
C₂×C₃×C₅⋊(D₃₇⋊C₃)	5
C₂×C₃²×C₅⋊D₅	37

Subgroups — C2×C3×C5⋊(C5⋊(D37⋊C3)) #45686341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅⋊(C₅⋊(D₃₇⋊C₃)) #45686341