Subgroups — C₃×C₅²⋊C₃×#1181 #39908022

Order 26100.

96 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	C₃×C₅²×#1181	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²⋊C₃×#1181	C₃	1	3	yes	maximal, direct product factor
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	C₂×C₃	1	3	yes	—
7	C₅²×#1181	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂₉×C₅²⋊C₃	C₃×C₄	1	3	yes	complemented
9	C₃×C₅²×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#1181	—	3	2	no	—
11	C₅²×D₂₉	C₂×C₃²	1	1	yes	characteristic
12	C₃²×#1181	—	25	1	no	maximal, Hall
13	C₃×C₄×C₅²⋊C₃	—	29	1	no	maximal, Hall
14	C₃×C₅×D₂₉	—	3	2	no	—
15	C₅²×C₂₉	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
16	C₅×#1181	—	3	2	no	—
17	C₃²×D₂₉	—	25	1	no	—
18	C₂×C₃×C₅²⋊C₃	—	29	1	no	—
19	C₃×C₅×C₂₉	—	3	2	no	—
20	C₃×#1181	—	25	3	no	—
21	C₃×#1181	C₅²⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃×C₄×C₅²	—	29	1	no	—
23	C₄×C₅²⋊C₃	—	29	3	no	—
24	C₅×D₂₉	—	3	2	no	—
25	C₃²×C₂₉	—	25	1	no	Hall
26	C₃×C₅²⋊C₃	#1181	1	1	yes	characteristic, direct product factor, Hall
27	C₃×D₂₉	—	25	3	no	—
28	C₃×D₂₉	C₂×C₅²⋊C₃	1	1	yes	characteristic
29	C₂×C₃×C₅²	—	29	1	no	—
30	C₂×C₅²⋊C₃	—	29	3	no	—
31	C₅×C₂₉	—	3	2	no	—
32	#1181	C₃×C₅²⋊C₃	1	1	yes	characteristic, direct product factor, Hall
33	C₄×C₅²	—	29	1	no	Hall
34	C₃×C₂₉	—	25	3	no	—
35	C₃×C₂₉	C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented
36	C₃×C₅²	C₃×#1181	1	1	yes	characteristic, complemented
37	C₅²⋊C₃	C₃×#1181	1	3	yes	direct product factor
38	C₃×C₄×C₅	—	87	2	no	—
39	D₂₉	C₂×C₃×C₅²⋊C₃	1	1	yes	characteristic
40	C₂×C₅²	—	29	1	no	—
41	C₃²×C₄	—	725	1	no	Hall
42	C₂×C₃×C₅	—	87	2	no	—
43	C₂₉	C₃×C₄×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₅²	C₃²×#1181	1	1	yes	characteristic, complemented, Sylow
45	C₄×C₅	—	87	2	no	—
46	C₂×C₃²	—	725	1	no	—
47	C₃×C₅	—	3	2	no	—
48	C₃×C₄	—	29	1	no	—
49	C₃×C₄	—	725	3	no	—
50	C₂×C₅	—	87	2	no	—
51	C₃²	—	25	1	no	Sylow
52	C₂×C₃	—	29	1	no	—
53	C₂×C₃	—	725	3	no	—
54	C₅	—	3	2	no	—
55	C₄	—	29	1	no	Sylow
56	C₃	—	25	3	no	—
57	C₃	C₅²⋊C₃×#1181	1	1	yes	characteristic, direct product factor
58	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₅²⋊C₃×#1181
commutator, hypocenter	C₅²×C₂₉	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₃×C₄
prime radical	C₃×D₂₉×C₅²⋊C₃	C₂
cosocle	C₅²×D₂₉	C₂×C₃²
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₅²×#1181	C₃	semidirect
3. C₅²⋊C₃×#1181	C₃	direct (N × H)
4. C₃×C₂₉×C₅²⋊C₃	C₄	semidirect
7. C₅²×#1181	C₃²	semidirect
8. C₂₉×C₅²⋊C₃	C₃×C₄	semidirect
9. C₃×C₅²×C₂₉	C₃×C₄	semidirect
15. C₅²×C₂₉	C₃²×C₄	semidirect
21. C₃×#1181	C₅²⋊C₃	direct (N × H)
26. C₃×C₅²⋊C₃	#1181	direct (N × H)
32. #1181	C₃×C₅²⋊C₃	direct (N × H)
35. C₃×C₂₉	C₄×C₅²⋊C₃	semidirect
36. C₃×C₅²	C₃×#1181	semidirect
37. C₅²⋊C₃	C₃×#1181	direct (N × H)
43. C₂₉	C₃×C₄×C₅²⋊C₃	semidirect
44. C₅²	C₃²×#1181	semidirect
57. C₃	C₅²⋊C₃×#1181	direct (N × H)

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
C₃×C₅²×#1181	3
C₅²⋊C₃×#1181	3
C₃²×#1181	25
C₃×C₄×C₅²⋊C₃	29

Subgroups — C3×C52⋊C3×#1181 #39908022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²⋊C₃×#1181 #39908022