Subgroups — C₅²⋊C₃×C₃⋊#1181 #39908037

Order 26100.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₉×C₅²⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₃⋊#1181	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²⋊C₃×#1181	—	3	1	no	maximal
4	C₃×C₂₉×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅²×D₂₉	C₂×C₃	1	1	yes	characteristic
6	D₂₉×C₅²⋊C₃	—	2	1	no	—
7	D₂₉×C₅²⋊C₃	D₃	1	1	yes	characteristic
8	C₅²×#1181	—	3	1	no	Hall
9	C₂₉×C₅²⋊C₃	—	2	1	no	—
10	C₂₉×C₅²⋊C₃	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₅²×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
12	C₅×C₃⋊#1181	—	3	2	no	—
13	C₅²×D₂₉	C₃×D₃	1	1	yes	characteristic
14	C₃×C₃⋊#1181	—	25	1	no	maximal, Hall
15	Dic₃×C₅²⋊C₃	—	29	1	no	maximal, Hall
16	C₃×C₅×D₂₉	—	3	2	no	—
17	C₅²×C₂₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₅×#1181	—	9	2	no	—
19	C₃²×D₂₉	—	25	1	no	—
20	C₂×C₃×C₅²⋊C₃	—	29	1	no	—
21	C₃×C₅×C₂₉	—	3	2	no	—
22	C₃⋊#1181	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
23	C₃×#1181	—	75	1	no	—
24	C₅²×Dic₃	—	29	1	no	—
25	C₄×C₅²⋊C₃	—	87	1	no	—
26	C₅×D₂₉	—	3	2	no	—
27	C₃²×C₂₉	—	25	1	no	Hall
28	C₃×C₅²⋊C₃	#1181	1	1	yes	characteristic, complemented, Hall
29	C₃×D₂₉	—	25	1	no	—
30	C₃×D₂₉	—	50	1	no	—
31	C₃×D₂₉	C₂×C₅²⋊C₃	1	1	yes	characteristic
32	C₂×C₃×C₅²	—	29	1	no	—
33	C₂×C₅²⋊C₃	—	29	1	no	—
34	C₂×C₅²⋊C₃	—	58	1	no	—
35	C₅×C₂₉	—	3	2	no	—
36	#1181	—	3	1	no	Hall
37	C₄×C₅²	—	87	1	no	Hall
38	C₃×C₂₉	—	25	1	no	—
39	C₃×C₂₉	—	50	1	no	—
40	C₃×C₂₉	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented
41	C₃×C₅²	C₃×#1181	1	1	yes	characteristic, complemented
42	C₅²⋊C₃	—	2	1	no	—
43	C₅²⋊C₃	C₃⋊#1181	1	1	yes	characteristic, direct product factor
44	C₅×Dic₃	—	87	2	no	—
45	D₂₉	D₃×C₅²⋊C₃	1	1	yes	characteristic
46	C₂×C₅²	—	29	1	no	—
47	C₃×Dic₃	—	725	1	no	Hall
48	C₂×C₃×C₅	—	87	2	no	—
49	C₂₉	Dic₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₅²	C₃×C₃⋊#1181	1	1	yes	characteristic, complemented, Sylow
51	C₄×C₅	—	261	2	no	—
52	C₂×C₃²	—	725	1	no	—
53	C₃×C₅	—	3	2	no	—
54	C₃×C₄	—	2175	1	no	—
55	Dic₃	—	29	1	no	—
56	C₂×C₅	—	87	2	no	—
57	C₃²	—	25	1	no	Sylow
58	C₂×C₃	—	29	1	no	—
59	C₂×C₃	—	1450	1	no	—
60	C₂×C₃	—	725	1	no	—
61	C₅	—	3	2	no	—
62	C₄	—	87	1	no	Sylow
63	C₃	—	25	1	no	—
64	C₃	—	50	1	no	—
65	C₃	C₅²⋊C₃×#1181	1	1	yes	characteristic, complemented
66	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₂₉	C₃×C₄
prime radical	C₃×D₂₉×C₅²⋊C₃	C₂
cosocle	C₃×C₅²×D₂₉	C₂×C₃
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅²×C₃⋊#1181	C₃	semidirect
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
10. C₂₉×C₅²⋊C₃	Dic₃	semidirect
11. C₃×C₅²×C₂₉	C₃×C₄	semidirect
17. C₅²×C₂₉	C₃×Dic₃	semidirect
22. C₃⋊#1181	C₅²⋊C₃	direct (N × H)
28. C₃×C₅²⋊C₃	#1181	semidirect
40. C₃×C₂₉	C₄×C₅²⋊C₃	semidirect
41. C₃×C₅²	C₃×#1181	semidirect
43. C₅²⋊C₃	C₃⋊#1181	direct (N × H)
49. C₂₉	Dic₃×C₅²⋊C₃	semidirect
50. C₅²	C₃×C₃⋊#1181	semidirect
65. C₃	C₅²⋊C₃×#1181	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₂₉×C₅²⋊C₃	2
C₅²×C₃⋊#1181	3
C₅²⋊C₃×#1181	3
C₃×C₃⋊#1181	25
Dic₃×C₅²⋊C₃	29

Subgroups — C52⋊C3×C3⋊#1181 #39908037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²⋊C₃×C₃⋊#1181 #39908037