Subgroups — C₃⋊#22576425 #39908053

Order 26100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668530	—	3	1	no	maximal
3	#22576425	—	3	3	no	maximal
4	C₃×C₂₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₅⋊D₅	D₃	1	1	yes	characteristic
6	C₂₉×(C₅⋊D₅)⋊C₃	D₃	1	3	yes	—
7	#15668530	—	9	1	no	Hall
8	C₂₉×C₅²⋊C₃	Dic₃	1	3	yes	complemented
9	C₃×C₅²×C₂₉	Dic₃	1	1	yes	characteristic, complemented
10	C₃⋊#10596816	—	15	1	no	—
11	C₃⋊#10596816	—	15	1	no	—
12	C₂₉×C₅⋊D₅	C₃⋊D₃	1	1	yes	characteristic
13	C₃⋊Dic₈₇	—	25	1	no	maximal, Hall
14	C₃⋊#64480	—	29	1	no	maximal, Hall
15	C₃×D₅×C₂₉	—	15	1	no	—
16	C₃×D₅×C₂₉	—	30	1	no	—
17	C₅²×C₂₉	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
18	#10596816	—	45	1	no	—
19	#10596816	—	45	1	no	—
20	C₂×C₃²×C₂₉	—	25	1	no	—
21	C₃×(C₅⋊D₅)⋊C₃	D₂₉	1	1	yes	characteristic
22	C₃×C₅×C₂₉	—	3	1	no	—
23	C₃×C₅×C₂₉	—	6	1	no	—
24	Dic₈₇	—	75	1	no	—
25	Dic₈₇	—	75	3	no	—
26	C₃⋊#1044	—	87	1	no	—
27	#64480	—	87	3	no	—
28	D₅×C₂₉	—	30	1	no	—
29	D₅×C₂₉	—	30	1	no	—
30	C₃²×C₂₉	—	100	1	no	Hall
31	C₃×C₅²⋊C₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
32	C₂×C₃×C₂₉	—	25	3	no	—
33	C₂×C₃×C₂₉	—	25	1	no	—
34	C₃×C₅⋊D₅	D₈₇	1	1	yes	characteristic
35	(C₅⋊D₅)⋊C₃	D₈₇	1	3	yes	—
36	C₅×C₂₉	—	6	1	no	—
37	C₅×C₂₉	—	6	1	no	—
38	Dic₂₉	—	225	1	no	Hall
39	#1044	—	261	1	no	Hall
40	C₃×C₂₉	—	100	3	no	—
41	C₃×C₂₉	#64480	1	1	yes	characteristic, complemented
42	C₃×C₅²	Dic₈₇	1	1	yes	characteristic, complemented
43	C₅²⋊C₃	Dic₈₇	1	3	yes	complemented
44	ΓL(1,𝔽₁₆)	—	435	1	no	—
45	ΓL(1,𝔽₁₆)	—	435	1	no	—
46	C₂×C₂₉	—	25	1	no	—
47	C₅⋊D₅	C₃⋊D₈₇	1	1	yes	characteristic
48	C₃⋊Dic₃	—	725	1	no	Hall
49	C₃×D₅	—	30	1	no	—
50	C₃×D₅	—	30	1	no	—
51	C₂₉	C₃⋊#64480	1	1	yes	characteristic, complemented, Sylow
52	C₅²	C₃⋊Dic₈₇	1	1	yes	characteristic, complemented, Sylow
53	AGL(1,𝔽₅)	—	1305	1	no	—
54	AGL(1,𝔽₅)	—	1305	1	no	—
55	C₂×C₃²	—	25	1	no	—
56	C₃×C₅	—	6	1	no	—
57	C₃×C₅	—	6	1	no	—
58	Dic₃	—	2175	1	no	—
59	Dic₃	—	2175	3	no	—
60	D₅	—	30	1	no	—
61	D₅	—	30	1	no	—
62	C₃²	—	100	1	no	Sylow
63	C₂×C₃	—	25	3	no	—
64	C₂×C₃	—	25	1	no	—
65	C₅	—	6	1	no	—
66	C₅	—	6	1	no	—
67	C₄	—	6525	1	no	Sylow
68	C₃	—	100	3	no	—
69	C₃	#22576425	1	1	yes	characteristic, complemented
70	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃×C₂₉×C₅²⋊C₃	C₄
Fitting, socle	C₃×C₅²×C₂₉	Dic₃
prime radical, cosocle	C₃×C₂₉×(C₅⋊D₅)⋊C₃	C₂
LCS	G ▷ C₃×C₂₉×C₅²⋊C₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
8. C₂₉×C₅²⋊C₃	Dic₃	semidirect
9. C₃×C₅²×C₂₉	Dic₃	semidirect
17. C₅²×C₂₉	C₃⋊Dic₃	semidirect
31. C₃×C₅²⋊C₃	Dic₂₉	semidirect
41. C₃×C₂₉	#64480	semidirect
42. C₃×C₅²	Dic₈₇	semidirect
43. C₅²⋊C₃	Dic₈₇	semidirect
51. C₂₉	C₃⋊#64480	semidirect
52. C₅²	C₃⋊Dic₈₇	semidirect
69. C₃	#22576425	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₂₉×(C₅⋊D₅)⋊C₃	2
C₃⋊#15668530	3
#22576425	3
C₃⋊Dic₈₇	25
C₃⋊#64480	29

Subgroups — C3⋊#22576425 #39908053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#22576425 #39908053