Subgroups — C₂×C₃²×C₃₇×D₂₅ #45685935

Order 33300.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇×D₂₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₂₅×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₃₇×D₂₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₂₅×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₅×C₃₇	—	5	1	no	maximal
6	C₃×C₃₇×D₂₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₂₅×C₃₇	C₂×C₃	1	4	yes	complemented
8	C₂×C₃₇×D₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×D₅×C₃₇	—	5	2	no	—
10	C₂×C₃²×C₅×C₃₇	D₅	1	1	yes	characteristic
11	C₃×C₂₅×C₃₇	C₂²×C₃	1	4	yes	complemented
12	C₂×C₃×D₅×C₃₇	—	5	4	no	—
13	C₂×C₂₅×C₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₃₇×D₂₅	C₂×C₃²	1	2	yes	direct product factor
15	C₃²×C₅×C₃₇	C₂×D₅	1	1	yes	characteristic
16	C₂²×C₃²×C₃₇	—	25	1	no	Hall
17	C₂×C₃×C₅×C₃₇	C₃×D₅	1	4	yes	—
18	C₃×D₅×C₃₇	—	5	8	no	—
19	C₂₅×C₃₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×D₂₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×D₅×C₃₇	—	5	1	no	—
22	C₂×C₃²×C₃₇	—	25	2	no	—
23	C₂×C₃²×C₃₇	D₂₅	1	1	yes	characteristic, direct product factor
24	C₃×C₅×C₃₇	C₂×C₃×D₅	1	4	yes	—
25	C₂×C₃²×C₂₅	C₂×C₃₇	1	1	yes	characteristic, complemented
26	C₃²×D₂₅	C₂×C₃₇	1	2	yes	direct product factor
27	C₂²×C₃×C₃₇	—	25	4	no	—
28	C₂×C₅×C₃₇	C₃²×D₅	1	1	yes	characteristic
29	D₅×C₃₇	—	5	2	no	—
30	C₃²×C₃₇	C₂×D₂₅	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃×D₂₅	C₃×C₃₇	1	4	yes	direct product factor
32	C₃²×C₂₅	C₂²×C₃₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×C₃₇	—	25	8	no	—
34	C₂×C₃×C₃₇	C₃×D₂₅	1	4	yes	direct product factor
35	C₅×C₃₇	C₂×C₃²×D₅	1	1	yes	characteristic
36	C₂×C₃²×D₅	—	5	1	no	—
37	C₂×C₃×C₂₅	C₂×C₃×C₃₇	1	4	yes	complemented
38	C₃×D₂₅	C₂×C₃×C₃₇	1	8	yes	direct product factor
39	C₂²×C₃₇	—	25	1	no	Hall
40	C₃×C₃₇	C₂×C₃×D₂₅	1	4	yes	direct product factor
41	C₂×D₂₅	C₃²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₃²×C₅	D₅×C₃₇	1	1	yes	characteristic
43	C₃²×D₅	—	5	2	no	—
44	C₃×C₂₅	C₂²×C₃×C₃₇	1	4	yes	complemented
45	C₂×C₃₇	—	25	2	no	—
46	C₂×C₃₇	C₃²×D₂₅	1	1	yes	characteristic, direct product factor
47	C₂×C₃×D₅	—	5	4	no	—
48	C₂×C₂₅	C₂×C₃²×C₃₇	1	1	yes	characteristic, complemented
49	D₂₅	C₂×C₃²×C₃₇	1	2	yes	direct product factor
50	C₃²×C₅	C₂×D₅×C₃₇	1	1	yes	characteristic
51	C₃₇	C₂×C₃²×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₃²	—	25	1	no	Hall
53	C₂×C₃×C₅	C₃×D₅×C₃₇	1	4	yes	—
54	C₃×D₅	—	5	8	no	—
55	C₂₅	C₂²×C₃²×C₃₇	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₅	—	5	1	no	—
57	C₂×C₃²	—	25	2	no	—
58	C₂×C₃²	C₃₇×D₂₅	1	1	yes	characteristic, direct product factor
59	C₃×C₅	C₂×C₃×D₅×C₃₇	1	4	yes	—
60	C₂²×C₃	—	25	4	no	—
61	C₂×C₅	C₃²×D₅×C₃₇	1	1	yes	characteristic
62	D₅	—	5	2	no	—
63	C₃²	C₂×C₃₇×D₂₅	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₃	—	25	8	no	—
65	C₂×C₃	C₃×C₃₇×D₂₅	1	4	yes	direct product factor
66	C₅	C₂×C₃²×D₅×C₃₇	1	1	yes	characteristic
67	C₂²	—	25	1	no	Sylow
68	C₃	C₂×C₃×C₃₇×D₂₅	1	4	yes	direct product factor
69	C₂	—	25	2	no	—
70	C₂	C₃²×C₃₇×D₂₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₃₇	D₂₅
commutator, cosocle, hypocenter	C₂₅	C₂²×C₃²×C₃₇
Frattini	C₅	C₂×C₃²×D₅×C₃₇
Fitting	C₂×C₃²×C₂₅×C₃₇	C₂
socle	C₂×C₃²×C₅×C₃₇	D₅
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₃²×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃₇×D₂₅	C₂	direct (N × H)
2. C₂×C₃²×C₂₅×C₃₇	C₂	semidirect
3. C₂×C₃×C₃₇×D₂₅	C₃	direct (N × H)
4. C₃²×C₂₅×C₃₇	C₂²	semidirect
6. C₃×C₃₇×D₂₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₂₅×C₃₇	C₂×C₃	semidirect
8. C₂×C₃₇×D₂₅	C₃²	direct (N × H)
11. C₃×C₂₅×C₃₇	C₂²×C₃	semidirect
13. C₂×C₂₅×C₃₇	C₂×C₃²	semidirect
14. C₃₇×D₂₅	C₂×C₃²	direct (N × H)
19. C₂₅×C₃₇	C₂²×C₃²	semidirect
20. C₂×C₃²×D₂₅	C₃₇	direct (N × H)
23. C₂×C₃²×C₃₇	D₂₅	direct (N × H)
25. C₂×C₃²×C₂₅	C₂×C₃₇	semidirect
26. C₃²×D₂₅	C₂×C₃₇	direct (N × H)
30. C₃²×C₃₇	C₂×D₂₅	direct (N × H)
31. C₂×C₃×D₂₅	C₃×C₃₇	direct (N × H)
32. C₃²×C₂₅	C₂²×C₃₇	semidirect
34. C₂×C₃×C₃₇	C₃×D₂₅	direct (N × H)
37. C₂×C₃×C₂₅	C₂×C₃×C₃₇	semidirect
38. C₃×D₂₅	C₂×C₃×C₃₇	direct (N × H)
40. C₃×C₃₇	C₂×C₃×D₂₅	direct (N × H)
41. C₂×D₂₅	C₃²×C₃₇	direct (N × H)
44. C₃×C₂₅	C₂²×C₃×C₃₇	semidirect
46. C₂×C₃₇	C₃²×D₂₅	direct (N × H)
48. C₂×C₂₅	C₂×C₃²×C₃₇	semidirect
49. D₂₅	C₂×C₃²×C₃₇	direct (N × H)
51. C₃₇	C₂×C₃²×D₂₅	direct (N × H)
55. C₂₅	C₂²×C₃²×C₃₇	semidirect
58. C₂×C₃²	C₃₇×D₂₅	direct (N × H)
63. C₃²	C₂×C₃₇×D₂₅	direct (N × H)
65. C₂×C₃	C₃×C₃₇×D₂₅	direct (N × H)
68. C₃	C₂×C₃×C₃₇×D₂₅	direct (N × H)
70. C₂	C₃²×C₃₇×D₂₅	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×C₃₇×D₂₅	2
C₂×C₃²×C₂₅×C₃₇	2
C₂×C₃×C₃₇×D₂₅	3
C₂×C₃²×D₅×C₃₇	5
C₂×C₃²×D₂₅	37

Subgroups — C2×C32×C37×D25 #45685935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₃₇×D₂₅ #45685935