Subgroups — ((C₅⋊D₅)⋊C₃)⋊D₉₃ #42124794

Order 27900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃₁⋊#3874)	C₂	1	2	yes	maximal, complemented
2	C₃×C₃₁×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#22604926	—	3	1	no	maximal
4	((C₅⋊D₅)⋊C₃)⋊D₃₁	—	3	3	no	maximal
5	C₃×C₃₁×C₅²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₅×D₄₆₅	—	3	2	no	—
7	C₃×C₃₁×C₅⋊D₅	D₃	1	1	yes	characteristic, complemented
8	C₃₁×(C₅⋊D₅)⋊C₃	D₃	1	3	yes	complemented
9	C₃₁⋊#3874	—	3	6	no	—
10	(C₅⋊D₅)⋊D₃₁	—	9	1	no	Hall
11	C₃₁×C₅²⋊C₃	C₂×D₃	1	3	yes	complemented
12	C₃×C₅²×C₃₁	C₂×D₃	1	1	yes	characteristic, complemented
13	D₅×D₉₃	—	15	2	no	—
14	C₃₁×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic, complemented
15	C₅×D₁₅₅	—	9	2	no	—
16	C₂×C₃⋊D₉₃	—	25	1	no	maximal, Hall
17	D₄₆₅	—	3	2	no	—
18	C₅×D₉₃	—	15	2	no	—
19	C₃×D₅×C₃₁	—	15	2	no	—
20	((C₅⋊D₅)⋊C₃)⋊D₃	—	31	1	no	maximal, Hall
21	C₅²×C₃₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
22	D₅×D₃₁	—	45	2	no	—
23	C₂×C₃²×C₃₁	—	25	1	no	—
24	C₃⋊D₉₃	—	25	2	no	—
25	C₃×C₅×C₃₁	—	3	2	no	—
26	C₃×(C₅⋊D₅)⋊C₃	D₃₁	1	1	yes	characteristic, complemented
27	C₃⋊#3874	—	31	2	no	—
28	C₂×D₉₃	—	75	1	no	—
29	C₂×D₉₃	—	75	3	no	—
30	D₁₅₅	—	9	2	no	—
31	C₅×D₃₁	—	45	2	no	—
32	D₅×C₃₁	—	15	2	no	—
33	D₁₅⋊D₅	—	93	1	no	—
34	#3874⋊C₂	—	93	3	no	—
35	C₃²×C₃₁	—	25	1	no	Hall
36	C₃×C₅²⋊C₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₃₁	—	25	3	no	—
38	C₂×C₃×C₃₁	—	25	1	no	—
39	D₉₃	—	15	2	no	—
40	D₉₃	—	75	6	no	—
41	C₅×C₃₁	—	3	2	no	—
42	C₅×D₁₅	—	93	2	no	—
43	C₃×C₅⋊D₅	D₉₃	1	1	yes	characteristic, complemented
44	(C₅⋊D₅)⋊C₃	D₉₃	1	3	yes	complemented
45	#3874	—	93	6	no	—
46	C₂×D₃₁	—	225	1	no	Hall
47	D₅²	—	279	1	no	Hall
48	C₃×C₃₁	—	25	3	no	—
49	C₃×C₃₁	#3874⋊C₂	1	1	yes	characteristic, complemented
50	C₃×C₅²	C₂×D₉₃	1	1	yes	characteristic, complemented
51	C₅²⋊C₃	C₂×D₉₃	1	3	yes	complemented
52	C₂×C₃₁	—	25	1	no	—
53	D₃₁	—	45	2	no	—
54	D₃×D₅	—	465	2	no	—
55	C₅⋊D₅	C₃⋊D₉₃	1	1	yes	characteristic, complemented
56	C₅×D₅	—	279	2	no	—
57	C₂×C₃⋊D₃	—	775	1	no	Hall
58	C₃₁	((C₅⋊D₅)⋊C₃)⋊D₃	1	1	yes	characteristic, complemented, Sylow
59	D₁₅	—	93	2	no	—
60	C₃×D₅	—	15	2	no	—
61	C₅×D₃	—	465	2	no	—
62	C₅²	C₂×C₃⋊D₉₃	1	1	yes	characteristic, complemented, Sylow
63	C₂×D₅	—	1395	2	no	—
64	C₂×C₃²	—	25	1	no	—
65	C₃⋊D₃	—	775	2	no	—
66	C₃×C₅	—	3	2	no	—
67	C₂×D₃	—	2325	3	no	—
68	C₂×D₃	—	2325	1	no	—
69	C₂×C₅	—	1395	2	no	—
70	D₅	—	15	2	no	—
71	D₅	—	279	2	no	—
72	C₃²	—	25	1	no	Sylow
73	C₂×C₃	—	25	3	no	—
74	C₂×C₃	—	25	1	no	—
75	D₃	—	2325	6	no	—
76	D₃	—	465	2	no	—
77	C₅	—	3	2	no	—
78	C₂²	—	6975	1	no	Sylow
79	C₃	—	25	3	no	—
80	C₃	((C₅⋊D₅)⋊C₃)⋊D₃₁	1	1	yes	characteristic, complemented
81	C₂	—	25	1	no	—
82	C₂	—	1395	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₃₁×C₅²⋊C₃	C₂²
Fitting, socle	C₃×C₅²×C₃₁	C₂×D₃
LCS	G ▷ C₃×C₃₁×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃₁⋊#3874)	C₂	semidirect
2. C₃×C₃₁×(C₅⋊D₅)⋊C₃	C₂	semidirect
5. C₃×C₃₁×C₅²⋊C₃	C₂²	semidirect
7. C₃×C₃₁×C₅⋊D₅	D₃	semidirect
8. C₃₁×(C₅⋊D₅)⋊C₃	D₃	semidirect
11. C₃₁×C₅²⋊C₃	C₂×D₃	semidirect
12. C₃×C₅²×C₃₁	C₂×D₃	semidirect
14. C₃₁×C₅⋊D₅	C₃⋊D₃	semidirect
21. C₅²×C₃₁	C₂×C₃⋊D₃	semidirect
26. C₃×(C₅⋊D₅)⋊C₃	D₃₁	semidirect
36. C₃×C₅²⋊C₃	C₂×D₃₁	semidirect
43. C₃×C₅⋊D₅	D₉₃	semidirect
44. (C₅⋊D₅)⋊C₃	D₉₃	semidirect
49. C₃×C₃₁	#3874⋊C₂	semidirect
50. C₃×C₅²	C₂×D₉₃	semidirect
51. C₅²⋊C₃	C₂×D₉₃	semidirect
55. C₅⋊D₅	C₃⋊D₉₃	semidirect
58. C₃₁	((C₅⋊D₅)⋊C₃)⋊D₃	semidirect
62. C₅²	C₂×C₃⋊D₉₃	semidirect
80. C₃	((C₅⋊D₅)⋊C₃)⋊D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃₁⋊#3874)	2
C₃×C₃₁×(C₅⋊D₅)⋊C₃	2
#22604926	3
((C₅⋊D₅)⋊C₃)⋊D₃₁	3
C₂×C₃⋊D₉₃	25
((C₅⋊D₅)⋊C₃)⋊D₃	31

Subgroups — ((C5⋊D5)⋊C3)⋊D93 #42124794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — ((C₅⋊D₅)⋊C₃)⋊D₉₃ #42124794