Subgroups — C₅×C₃₁×#4379 #42124872

Order 27900.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₃₁×#4379	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×C₃₁×#157	—	5	1	no	maximal
5	C₅²×D₃×C₃₁	—	6	2	no	—
6	C₅×Dic₅×C₃₁	—	9	1	no	maximal, Hall
7	C₅×C₃⋊D₃×C₃₁	—	2	2	no	—
8	C₅×C₃⋊D₃×C₃₁	D₅	1	1	yes	characteristic
9	C₅×C₃⋊D₃×C₃₁	C₂×C₅	1	1	yes	characteristic
10	C₃×C₅²×C₃₁	—	2	2	no	—
11	C₂×C₅²×C₃₁	—	9	1	no	—
12	C₃²×C₅×C₃₁	—	2	2	no	—
13	C₃²×C₅×C₃₁	Dic₅	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₃₁	C₄×C₅	1	1	yes	characteristic, complemented
15	C₃₁×#157	—	5	1	no	Hall
16	C₅×D₃×C₃₁	—	6	2	no	—
17	C₅×D₃×C₃₁	—	6	2	no	—
18	C₅×D₃×C₃₁	—	6	8	no	—
19	C₅×#4379	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₅²×C₃₁	#157	1	1	yes	characteristic, complemented, Hall
21	C₄×C₅×C₃₁	—	45	1	no	—
22	Dic₅×C₃₁	—	9	1	no	—
23	C₃⋊D₃×C₃₁	C₅×D₅	1	1	yes	characteristic
24	C₃×C₅×C₃₁	—	2	8	no	—
25	C₃×C₅×C₃₁	—	2	2	no	—
26	C₃×C₅×C₃₁	—	2	2	no	—
27	C₅²×C₃⋊D₃	C₂×C₃₁	1	1	yes	characteristic
28	C₂×C₅×C₃₁	—	9	1	no	—
29	C₂×C₅×C₃₁	—	9	1	no	—
30	C₂×C₅×C₃₁	—	18	2	no	—
31	C₃²×C₃₁	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
33	D₃×C₃₁	—	6	2	no	—
34	#4379	C₅×C₃₁	1	1	yes	characteristic, direct product factor
35	C₅×#157	—	5	1	no	—
36	C₅×C₃₁	—	2	2	no	—
37	C₅×C₃₁	C₅×#157	1	1	yes	characteristic, complemented
38	C₅×C₃₁	#4379	1	1	yes	characteristic, direct product factor
39	C₅²×D₃	—	6	2	no	—
40	C₄×C₃₁	—	45	1	no	Hall
41	C₅×Dic₅	—	9	1	no	Hall
42	C₃×C₃₁	—	2	2	no	—
43	C₅×C₃⋊D₃	—	2	2	no	—
44	C₅×C₃⋊D₃	D₅×C₃₁	1	1	yes	characteristic
45	C₅×C₃⋊D₃	C₂×C₅×C₃₁	1	1	yes	characteristic
46	C₃×C₅²	—	2	2	no	—
47	C₂×C₃₁	—	9	1	no	—
48	C₂×C₅²	—	9	1	no	—
49	C₃²×C₅	—	2	2	no	—
50	C₃²×C₅	Dic₅×C₃₁	1	1	yes	characteristic, complemented
51	C₃²×C₅	C₄×C₅×C₃₁	1	1	yes	characteristic, complemented
52	#157	—	5	1	no	Hall
53	C₃₁	C₅×#4379	1	1	yes	characteristic, direct product factor, Sylow
54	C₅×D₃	—	6	2	no	—
55	C₅×D₃	—	6	2	no	—
56	C₅×D₃	—	6	8	no	—
57	C₅²	C₃₁×#157	1	1	yes	characteristic, complemented, Sylow
58	C₄×C₅	—	45	1	no	—
59	Dic₅	—	9	1	no	—
60	C₃⋊D₃	C₅×D₅×C₃₁	1	1	yes	characteristic
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	C₂×C₅	—	9	1	no	—
65	C₂×C₅	—	9	1	no	—
66	C₂×C₅	—	18	2	no	—
67	C₃²	C₅×Dic₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	6	2	no	—
69	C₅	—	2	2	no	—
70	C₅	C₅×C₃₁×#157	1	1	yes	characteristic, complemented
71	C₅	C₃₁×#4379	1	1	yes	characteristic, direct product factor
72	C₄	—	45	1	no	Sylow
73	C₃	—	2	2	no	—
74	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₃₁	#4379
commutator, hypocenter	C₃²×C₅	C₄×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₃₁	C₄
prime radical	C₅²×C₃⋊D₃×C₃₁	C₂
cosocle	C₅×C₃⋊D₃	C₂×C₅×C₃₁
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₃₁	C₄	semidirect
3. C₃₁×#4379	C₅	direct (N × H)
13. C₃²×C₅×C₃₁	Dic₅	semidirect
14. C₃²×C₅×C₃₁	C₄×C₅	semidirect
19. C₅×#4379	C₃₁	direct (N × H)
20. C₅²×C₃₁	#157	semidirect
31. C₃²×C₃₁	C₅×Dic₅	semidirect
32. C₃²×C₅²	C₄×C₃₁	semidirect
34. #4379	C₅×C₃₁	direct (N × H)
37. C₅×C₃₁	C₅×#157	semidirect
38. C₅×C₃₁	#4379	direct (N × H)
50. C₃²×C₅	Dic₅×C₃₁	semidirect
51. C₃²×C₅	C₄×C₅×C₃₁	semidirect
53. C₃₁	C₅×#4379	direct (N × H)
57. C₅²	C₃₁×#157	semidirect
67. C₃²	C₅×Dic₅×C₃₁	semidirect
70. C₅	C₅×C₃₁×#157	semidirect
71. C₅	C₃₁×#4379	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₃⋊D₃×C₃₁	2
C₃₁×#4379	5
C₅×C₃₁×#157	5
C₅×Dic₅×C₃₁	9
C₅×#4379	31

Subgroups — C5×C31×#4379 #42124872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃₁×#4379 #42124872