Subgroups — C₂×C₃×C₅×#41 #92107

Order 480.

328 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#41	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₄	C₂	1	3	yes	maximal, complemented
4	C₂²×C₃×C₄×C₅	C₂	1	3	yes	maximal, complemented
5	C₂×C₅×#41	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₅	C₂²	1	3	yes	—
7	C₃×C₅×Q₈	C₂²	1	4	yes	complemented
8	C₃×C₅×D₄	C₂²	1	12	yes	complemented
9	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
10	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄×C₅	C₂²	1	12	yes	complemented
12	C₂×C₃×#41	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅×#41	C₂×C₃	1	8	yes	direct product factor
14	C₂×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₅×D₄	C₂×C₃	1	3	yes	complemented
16	C₂²×C₄×C₅	C₂×C₃	1	3	yes	complemented
17	C₂²×C₃×C₅	—	2	6	no	—
18	C₂²×C₃×C₅	C₂³	1	6	yes	—
19	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
20	C₃×C₄×C₅	C₂³	1	6	yes	—
21	C₃×C₄×C₅	C₂³	1	2	yes	—
22	C₃×#41	C₂×C₅	1	8	yes	direct product factor
23	C₂×C₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
24	C₂×C₃×D₄	C₂×C₅	1	3	yes	complemented
25	C₂²×C₃×C₄	C₂×C₅	1	3	yes	complemented
26	C₂³×C₅	C₂²×C₃	1	3	yes	—
27	C₅×Q₈	C₂²×C₃	1	4	yes	complemented
28	C₅×D₄	C₂²×C₃	1	12	yes	complemented
29	C₂×C₄×C₅	C₂²×C₃	1	3	yes	—
30	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₄×C₅	C₂²×C₃	1	12	yes	complemented
32	C₂×#41	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₃×C₅	—	2	6	no	—
34	C₂×C₃×C₅	#41	1	2	yes	direct product factor
35	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
36	C₂³×C₃	C₂²×C₅	1	3	yes	—
37	C₃×Q₈	C₂²×C₅	1	4	yes	complemented
38	C₃×D₄	C₂²×C₅	1	12	yes	complemented
39	C₂×C₃×C₄	C₂²×C₅	1	3	yes	—
40	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
41	C₂×C₃×C₄	C₂²×C₅	1	12	yes	complemented
42	C₂²×C₅	—	2	6	no	—
43	C₂²×C₅	C₂³×C₃	1	6	yes	—
44	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
45	C₄×C₅	C₂³×C₃	1	2	yes	—
46	C₄×C₅	C₂³×C₃	1	6	yes	—
47	#41	C₂×C₃×C₅	1	8	yes	direct product factor
48	C₂×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
49	C₂×D₄	C₂×C₃×C₅	1	3	yes	complemented
50	C₂²×C₄	C₂×C₃×C₅	1	3	yes	complemented
51	C₃×C₅	C₂×#41	1	1	yes	characteristic, direct product factor, Hall
52	C₂²×C₃	—	2	6	no	—
53	C₂²×C₃	C₂³×C₅	1	6	yes	—
54	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
55	C₃×C₄	C₂³×C₅	1	2	yes	—
56	C₃×C₄	C₂³×C₅	1	6	yes	—
57	C₂×C₅	—	2	6	no	—
58	C₂×C₅	C₃×#41	1	2	yes	direct product factor
59	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
60	C₂³	C₂²×C₃×C₅	1	3	yes	—
61	Q₈	C₂²×C₃×C₅	1	4	yes	complemented
62	D₄	C₂²×C₃×C₅	1	12	yes	complemented
63	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
64	C₂×C₄	C₂²×C₃×C₅	1	3	yes	—
65	C₂×C₄	C₂²×C₃×C₅	1	12	yes	complemented
66	C₂×C₃	—	2	6	no	—
67	C₂×C₃	C₅×#41	1	2	yes	direct product factor
68	C₂×C₃	C₂⁴×C₅	1	1	yes	characteristic
69	C₅	C₂×C₃×#41	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²	—	2	6	no	—
71	C₂²	C₂³×C₃×C₅	1	6	yes	—
72	C₂²	C₂³×C₃×C₅	1	1	yes	characteristic
73	C₄	C₂³×C₃×C₅	1	2	yes	—
74	C₄	C₂³×C₃×C₅	1	6	yes	—
75	C₃	C₂×C₅×#41	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	2	6	no	—
77	C₂	C₃×C₅×#41	1	2	yes	direct product factor
78	C₂	C₂⁴×C₃×C₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂²
commutator, Frattini, cosocle	C₂	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#41	C₂	direct (N × H)
2. C₂×C₃×C₅×Q₈	C₂	semidirect
3. C₂×C₃×C₅×D₄	C₂	semidirect
4. C₂²×C₃×C₄×C₅	C₂	semidirect
5. C₂×C₅×#41	C₃	direct (N × H)
7. C₃×C₅×Q₈	C₂²	semidirect
8. C₃×C₅×D₄	C₂²	semidirect
11. C₂×C₃×C₄×C₅	C₂²	semidirect
12. C₂×C₃×#41	C₅	direct (N × H)
13. C₅×#41	C₂×C₃	direct (N × H)
14. C₂×C₅×Q₈	C₂×C₃	semidirect
15. C₂×C₅×D₄	C₂×C₃	semidirect
16. C₂²×C₄×C₅	C₂×C₃	semidirect
22. C₃×#41	C₂×C₅	direct (N × H)
23. C₂×C₃×Q₈	C₂×C₅	semidirect
24. C₂×C₃×D₄	C₂×C₅	semidirect
25. C₂²×C₃×C₄	C₂×C₅	semidirect
27. C₅×Q₈	C₂²×C₃	semidirect
28. C₅×D₄	C₂²×C₃	semidirect
31. C₂×C₄×C₅	C₂²×C₃	semidirect
32. C₂×#41	C₃×C₅	direct (N × H)
34. C₂×C₃×C₅	#41	direct (N × H)
37. C₃×Q₈	C₂²×C₅	semidirect
38. C₃×D₄	C₂²×C₅	semidirect
41. C₂×C₃×C₄	C₂²×C₅	semidirect
47. #41	C₂×C₃×C₅	direct (N × H)
48. C₂×Q₈	C₂×C₃×C₅	semidirect
49. C₂×D₄	C₂×C₃×C₅	semidirect
50. C₂²×C₄	C₂×C₃×C₅	semidirect
51. C₃×C₅	C₂×#41	direct (N × H)
58. C₂×C₅	C₃×#41	direct (N × H)
61. Q₈	C₂²×C₃×C₅	semidirect
62. D₄	C₂²×C₃×C₅	semidirect
65. C₂×C₄	C₂²×C₃×C₅	semidirect
67. C₂×C₃	C₅×#41	direct (N × H)
69. C₅	C₂×C₃×#41	direct (N × H)
75. C₃	C₂×C₅×#41	direct (N × H)
77. C₂	C₃×C₅×#41	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×C₅×#41	2
C₂×C₃×C₅×Q₈	2
C₂×C₃×C₅×D₄	2
C₂²×C₃×C₄×C₅	2
C₂×C₅×#41	3
C₂×C₃×#41	5

Subgroups — C2×C3×C5×#41 #92107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#41 #92107