Subgroups — #157×#10597245 #36345075

Order 21780.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×#10597245	C₂	1	1	yes	maximal, characteristic
2	C₃²×#10597245	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁²×#157	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	D₃×#10597245	—	6	2	no	—
5	C₄×#10597245	—	9	1	no	maximal, Hall
6	C₁₁²×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic
7	#157×C₁₁⋊C₅	—	11	2	no	maximal
8	C₃×#10597245	—	2	2	no	—
9	C₂×#10597245	—	9	1	no	—
10	C₃²×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃⋊D₃×C₁₁⋊C₅	—	11	2	no	—
12	D₃×C₁₁²	—	6	2	no	—
13	#10597245	#157	1	1	yes	characteristic, direct product factor, Hall
14	C₃²×C₁₁⋊C₅	—	11	2	no	—
15	C₄×C₁₁²	—	9	1	no	Hall
16	C₁₁×#157	—	5	2	no	—
17	C₁₁×#157	C₁₁⋊C₅	1	2	yes	complemented
18	C₃×C₁₁²	—	2	2	no	—
19	D₃×C₁₁⋊C₅	—	66	4	no	—
20	C₂×C₁₁²	—	9	1	no	—
21	C₄×C₁₁⋊C₅	—	99	2	no	—
22	C₁₁×C₃⋊D₃	—	5	2	no	—
23	C₁₁×C₃⋊D₃	C₂×C₁₁⋊C₅	1	2	yes	—
24	C₅×#157	—	121	1	no	Hall
25	C₃×C₁₁⋊C₅	—	22	4	no	—
26	C₁₁²	C₅×#157	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₁⋊C₅	—	99	2	no	—
28	C₃²×C₁₁	—	5	2	no	—
29	C₃²×C₁₁	C₄×C₁₁⋊C₅	1	2	yes	complemented
30	C₅×C₃⋊D₃	—	121	1	no	—
31	D₃×C₁₁	—	6	4	no	—
32	D₃×C₁₁	—	30	4	no	—
33	C₁₁⋊C₅	—	11	2	no	—
34	C₃²×C₅	—	121	1	no	Hall
35	C₄×C₁₁	—	9	2	no	—
36	C₄×C₁₁	—	45	2	no	—
37	#157	#10597245	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₁₁	—	2	4	no	—
39	C₃×C₁₁	—	10	4	no	—
40	C₅×D₃	—	726	2	no	—
41	C₂×C₁₁	—	9	2	no	—
42	C₂×C₁₁	—	45	2	no	—
43	C₄×C₅	—	1089	1	no	Hall
44	C₃⋊D₃	C₂×#10597245	1	1	yes	characteristic
45	C₃×C₅	—	242	2	no	—
46	C₁₁	—	5	2	no	—
47	C₁₁	#157×C₁₁⋊C₅	1	2	yes	complemented
48	C₂×C₅	—	1089	1	no	—
49	C₃²	C₄×#10597245	1	1	yes	characteristic, complemented, Sylow
50	D₃	—	6	2	no	—
51	C₅	—	121	1	no	Sylow
52	C₄	—	9	1	no	Sylow
53	C₃	—	2	2	no	—
54	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₁²	C₄×C₅
prime radical	C₃⋊D₃×#10597245	C₂
cosocle	C₁₁²×C₃⋊D₃	C₂×C₅
LCS	G ▷ C₃²×C₁₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×#10597245	C₄	semidirect
3. C₁₁²×#157	C₅	semidirect
10. C₃²×C₁₁²	C₄×C₅	semidirect
13. #10597245	#157	direct (N × H)
17. C₁₁×#157	C₁₁⋊C₅	semidirect
26. C₁₁²	C₅×#157	semidirect
29. C₃²×C₁₁	C₄×C₁₁⋊C₅	semidirect
37. #157	#10597245	direct (N × H)
47. C₁₁	#157×C₁₁⋊C₅	semidirect
49. C₃²	C₄×#10597245	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×#10597245	2
C₁₁²×#157	5
C₄×#10597245	9
#157×C₁₁⋊C₅	11