Subgroups — C₅×C₃⋊Dic₅₅₅ #45686124

Order 33300.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅²×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₅×Dic₅₅₅	—	3	4	no	maximal
3	C₃²×C₅²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊Dic₅₅₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₃⋊Dic₁₁₁	—	5	1	no	maximal
6	C₂×C₃×C₅²×C₃₇	D₃	1	4	yes	—
7	C₅×Dic₁₈₅	—	9	1	no	Hall
8	C₂×C₃²×C₅×C₃₇	—	2	2	no	—
9	C₂×C₃²×C₅×C₃₇	D₅	1	1	yes	characteristic
10	C₂×C₃²×C₅×C₃₇	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅²×C₃₇	Dic₃	1	4	yes	complemented
12	Dic₅₅₅	—	3	4	no	—
13	C₅×Dic₁₁₁	—	15	4	no	—
14	C₂×C₅²×C₃₇	C₃⋊D₃	1	1	yes	characteristic
15	C₃²×C₅×C₃₇	—	2	2	no	—
16	C₃²×C₅×C₃₇	Dic₅	1	1	yes	characteristic, complemented
17	C₃²×C₅×C₃₇	C₄×C₅	1	1	yes	characteristic, complemented
18	C₃⋊Dic₁₁₁	—	5	1	no	Hall
19	C₂×C₃×C₅×C₃₇	—	2	8	no	—
20	C₂×C₃×C₅×C₃₇	C₅×D₃	1	4	yes	—
21	C₂×C₃×C₅×C₃₇	D₁₅	1	4	yes	—
22	C₅²×C₃₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
23	C₅×C₃⋊Dic₁₅	—	37	1	no	maximal, Hall
24	Dic₁₈₅	—	9	1	no	—
25	C₅×Dic₃₇	—	45	1	no	—
26	C₂×C₃²×C₃₇	C₅×D₅	1	1	yes	characteristic
27	C₃×C₅×C₃₇	—	2	8	no	—
28	C₃×C₅×C₃₇	C₅×Dic₃	1	4	yes	complemented
29	C₃×C₅×C₃₇	Dic₁₅	1	4	yes	complemented
30	C₂×C₃²×C₅²	D₃₇	1	1	yes	characteristic
31	Dic₁₁₁	—	15	4	no	—
32	C₂×C₅×C₃₇	—	2	2	no	—
33	C₂×C₅×C₃₇	C₅×C₃⋊D₃	1	1	yes	characteristic
34	C₂×C₅×C₃₇	C₃⋊D₁₅	1	1	yes	characteristic
35	C₃²×C₃₇	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
36	C₅×Dic₁₅	—	111	4	no	—
37	C₃²×C₅²	Dic₃₇	1	1	yes	characteristic, complemented, Hall
38	C₂×C₃×C₃₇	C₅×D₁₅	1	4	yes	—
39	C₅×C₃₇	—	2	2	no	—
40	C₅×C₃₇	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented
41	C₅×C₃₇	C₃⋊Dic₁₅	1	1	yes	characteristic, complemented
42	C₃⋊Dic₁₅	—	37	1	no	—
43	C₅×C₃⋊Dic₃	—	185	1	no	—
44	C₂×C₃×C₅²	D₁₁₁	1	4	yes	—
45	Dic₃₇	—	45	1	no	Hall
46	C₃×C₃₇	C₅×Dic₁₅	1	4	yes	complemented
47	C₅×Dic₅	—	333	1	no	Hall
48	C₂×C₃²×C₅	—	2	2	no	—
49	C₂×C₃²×C₅	C₅×D₃₇	1	1	yes	characteristic
50	C₂×C₃²×C₅	D₁₈₅	1	1	yes	characteristic
51	C₃×C₅²	Dic₁₁₁	1	4	yes	complemented
52	C₂×C₃₇	C₅×C₃⋊D₁₅	1	1	yes	characteristic
53	Dic₁₅	—	111	4	no	—
54	C₅×Dic₃	—	555	4	no	—
55	C₂×C₅²	C₃⋊D₁₁₁	1	1	yes	characteristic
56	C₃²×C₅	—	2	2	no	—
57	C₃²×C₅	C₅×Dic₃₇	1	1	yes	characteristic, complemented
58	C₃²×C₅	Dic₁₈₅	1	1	yes	characteristic, complemented
59	C₃₇	C₅×C₃⋊Dic₁₅	1	1	yes	characteristic, complemented, Sylow
60	C₃⋊Dic₃	—	185	1	no	Hall
61	C₂×C₃×C₅	—	2	8	no	—
62	C₂×C₃×C₅	C₅×D₁₁₁	1	4	yes	—
63	C₂×C₃×C₅	D₅₅₅	1	4	yes	—
64	C₅²	C₃⋊Dic₁₁₁	1	1	yes	characteristic, complemented, Sylow
65	C₄×C₅	—	1665	1	no	—
66	Dic₅	—	333	1	no	—
67	C₂×C₃²	C₅×D₁₈₅	1	1	yes	characteristic
68	C₃×C₅	—	2	8	no	—
69	C₃×C₅	C₅×Dic₁₁₁	1	4	yes	complemented
70	C₃×C₅	Dic₅₅₅	1	4	yes	complemented
71	Dic₃	—	555	4	no	—
72	C₂×C₅	—	2	2	no	—
73	C₂×C₅	C₅×C₃⋊D₁₁₁	1	1	yes	characteristic
74	C₂×C₅	C₃⋊D₅₅₅	1	1	yes	characteristic
75	C₃²	C₅×Dic₁₈₅	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	C₅×D₅₅₅	1	4	yes	—
77	C₅	—	2	2	no	—
78	C₅	C₅×C₃⋊Dic₁₁₁	1	1	yes	characteristic, complemented
79	C₅	C₃⋊Dic₅₅₅	1	1	yes	characteristic, direct product factor
80	C₄	—	1665	1	no	Sylow
81	C₃	C₅×Dic₅₅₅	1	4	yes	complemented
82	C₂	C₅×C₃⋊D₅₅₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₅₅₅
commutator, hypocenter	C₃²×C₅×C₃₇	C₄×C₅
Frattini	C₂	C₅×C₃⋊D₅₅₅
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₃₇	C₂
cosocle	C₂×C₃²×C₅×C₃₇	C₂×C₅
LCS	G ▷ C₃²×C₅×C₃₇
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅²×C₃₇	C₄	semidirect
4. C₃⋊Dic₅₅₅	C₅	direct (N × H)
11. C₃×C₅²×C₃₇	Dic₃	semidirect
16. C₃²×C₅×C₃₇	Dic₅	semidirect
17. C₃²×C₅×C₃₇	C₄×C₅	semidirect
22. C₅²×C₃₇	C₃⋊Dic₃	semidirect
28. C₃×C₅×C₃₇	C₅×Dic₃	semidirect
29. C₃×C₅×C₃₇	Dic₁₅	semidirect
35. C₃²×C₃₇	C₅×Dic₅	semidirect
37. C₃²×C₅²	Dic₃₇	semidirect
40. C₅×C₃₇	C₅×C₃⋊Dic₃	semidirect
41. C₅×C₃₇	C₃⋊Dic₁₅	semidirect
46. C₃×C₃₇	C₅×Dic₁₅	semidirect
51. C₃×C₅²	Dic₁₁₁	semidirect
57. C₃²×C₅	C₅×Dic₃₇	semidirect
58. C₃²×C₅	Dic₁₈₅	semidirect
59. C₃₇	C₅×C₃⋊Dic₁₅	semidirect
64. C₅²	C₃⋊Dic₁₁₁	semidirect
69. C₃×C₅	C₅×Dic₁₁₁	semidirect
70. C₃×C₅	Dic₅₅₅	semidirect
75. C₃²	C₅×Dic₁₈₅	semidirect
78. C₅	C₅×C₃⋊Dic₁₁₁	semidirect
79. C₅	C₃⋊Dic₅₅₅	direct (N × H)
81. C₃	C₅×Dic₅₅₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₅²×C₃₇	2
C₅×Dic₅₅₅	3
C₃⋊Dic₅₅₅	5
C₅×C₃⋊Dic₁₁₁	5
C₅×C₃⋊Dic₁₅	37

Subgroups — C5×C3⋊Dic555 #45686124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊Dic₅₅₅ #45686124