Subgroups — ((C₅⋊D₅)⋊C₃)⋊D₁₁₁ #45686281

Order 33300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃₇⋊#3874)	C₂	1	2	yes	maximal, complemented
2	C₃×C₃₇×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012924	—	3	1	no	maximal
4	((C₅⋊D₅)⋊C₃)⋊D₃₇	—	3	3	no	maximal
5	C₃×C₃₇×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₅₅₅	—	3	2	no	—
7	C₃×C₃₇×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
8	C₃₇×(C₅⋊D₅)⋊C₃	D₃	1	3	yes	complemented
9	C₃₇⋊#3874	—	3	6	no	—
10	(C₅⋊D₅)⋊D₃₇	—	9	1	no	Hall
11	C₃₇×C₅²⋊C₃	C₂×D₃	1	3	yes	complemented
12	C₃×C₅²×C₃₇	C₂×D₃	1	1	yes	characteristic, complemented
13	D₅×D₁₁₁	—	15	2	no	—
14	C₃₇×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₅×D₁₈₅	—	9	2	no	—
16	C₂×C₃⋊D₁₁₁	—	25	1	no	maximal, Hall
17	D₅₅₅	—	3	2	no	—
18	C₅×D₁₁₁	—	15	2	no	—
19	C₃×D₅×C₃₇	—	15	2	no	—
20	C₅²×C₃₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
21	((C₅⋊D₅)⋊C₃)⋊D₃	—	37	1	no	maximal, Hall
22	D₅×D₃₇	—	45	2	no	—
23	C₂×C₃²×C₃₇	—	25	1	no	—
24	C₃⋊D₁₁₁	—	25	2	no	—
25	C₃×C₅×C₃₇	—	3	2	no	—
26	C₃×(C₅⋊D₅)⋊C₃	D₃₇	1	1	yes	characteristic, complemented
27	C₃⋊#3874	—	37	2	no	—
28	C₂×D₁₁₁	—	75	1	no	—
29	C₂×D₁₁₁	—	75	3	no	—
30	D₁₈₅	—	9	2	no	—
31	C₅×D₃₇	—	45	2	no	—
32	D₅×C₃₇	—	15	2	no	—
33	C₃²×C₃₇	—	25	1	no	Hall
34	D₁₅⋊D₅	—	111	1	no	—
35	#3874⋊C₂	—	111	3	no	—
36	C₃×C₅²⋊C₃	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₃₇	—	25	3	no	—
38	C₂×C₃×C₃₇	—	25	1	no	—
39	D₁₁₁	—	15	2	no	—
40	D₁₁₁	—	75	6	no	—
41	C₅×C₃₇	—	3	2	no	—
42	C₅×D₁₅	—	111	2	no	—
43	C₃×C₅⋊D₅	D₁₁₁	1	1	yes	characteristic, complemented
44	(C₅⋊D₅)⋊C₃	D₁₁₁	1	3	yes	complemented
45	#3874	—	111	6	no	—
46	C₂×D₃₇	—	225	1	no	Hall
47	C₃×C₃₇	—	25	3	no	—
48	C₃×C₃₇	#3874⋊C₂	1	1	yes	characteristic, complemented
49	D₅²	—	333	1	no	Hall
50	C₃×C₅²	C₂×D₁₁₁	1	1	yes	characteristic, complemented
51	C₅²⋊C₃	C₂×D₁₁₁	1	3	yes	complemented
52	C₂×C₃₇	—	25	1	no	—
53	D₃₇	—	45	2	no	—
54	D₃×D₅	—	555	2	no	—
55	C₅⋊D₅	C₃⋊D₁₁₁	1	1	yes	characteristic, complemented
56	C₅×D₅	—	333	2	no	—
57	C₃₇	((C₅⋊D₅)⋊C₃)⋊D₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃⋊D₃	—	925	1	no	Hall
59	D₁₅	—	111	2	no	—
60	C₃×D₅	—	15	2	no	—
61	C₅×D₃	—	555	2	no	—
62	C₅²	C₂×C₃⋊D₁₁₁	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	1665	2	no	—
64	C₂×C₃²	—	25	1	no	—
65	C₃⋊D₃	—	925	2	no	—
66	C₃×C₅	—	3	2	no	—
67	C₂×D₃	—	2775	1	no	—
68	C₂×D₃	—	2775	3	no	—
69	C₂×C₅	—	1665	2	no	—
70	D₅	—	15	2	no	—
71	D₅	—	333	2	no	—
72	C₃²	—	25	1	no	Sylow
73	C₂×C₃	—	25	3	no	—
74	C₂×C₃	—	25	1	no	—
75	D₃	—	555	2	no	—
76	D₃	—	2775	6	no	—
77	C₅	—	3	2	no	—
78	C₂²	—	8325	1	no	Sylow
79	C₃	—	25	3	no	—
80	C₃	((C₅⋊D₅)⋊C₃)⋊D₃₇	1	1	yes	characteristic, complemented
81	C₂	—	25	1	no	—
82	C₂	—	1665	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₃₇×C₅²⋊C₃	C₂²
Fitting, socle	C₃×C₅²×C₃₇	C₂×D₃
LCS	G ▷ C₃×C₃₇×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃₇⋊#3874)	C₂	semidirect
2. C₃×C₃₇×(C₅⋊D₅)⋊C₃	C₂	semidirect
5. C₃×C₃₇×C₅²⋊C₃	C₂²	semidirect
7. C₃×C₃₇×C₅⋊D₅	D₃	semidirect
8. C₃₇×(C₅⋊D₅)⋊C₃	D₃	semidirect
11. C₃₇×C₅²⋊C₃	C₂×D₃	semidirect
12. C₃×C₅²×C₃₇	C₂×D₃	semidirect
14. C₃₇×C₅⋊D₅	C₃⋊D₃	semidirect
20. C₅²×C₃₇	C₂×C₃⋊D₃	semidirect
26. C₃×(C₅⋊D₅)⋊C₃	D₃₇	semidirect
36. C₃×C₅²⋊C₃	C₂×D₃₇	semidirect
43. C₃×C₅⋊D₅	D₁₁₁	semidirect
44. (C₅⋊D₅)⋊C₃	D₁₁₁	semidirect
48. C₃×C₃₇	#3874⋊C₂	semidirect
50. C₃×C₅²	C₂×D₁₁₁	semidirect
51. C₅²⋊C₃	C₂×D₁₁₁	semidirect
55. C₅⋊D₅	C₃⋊D₁₁₁	semidirect
57. C₃₇	((C₅⋊D₅)⋊C₃)⋊D₃	semidirect
62. C₅²	C₂×C₃⋊D₁₁₁	semidirect
80. C₃	((C₅⋊D₅)⋊C₃)⋊D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃₇⋊#3874)	2
C₃×C₃₇×(C₅⋊D₅)⋊C₃	2
#26012924	3
((C₅⋊D₅)⋊C₃)⋊D₃₇	3
C₂×C₃⋊D₁₁₁	25
((C₅⋊D₅)⋊C₃)⋊D₃	37

Subgroups — ((C5⋊D5)⋊C3)⋊D111 #45686281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₅⋊D₅)⋊C₃)⋊D₁₁₁ #45686281