Subgroups — C₂²×#1220 #92103

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#1220	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊D₅	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₅	—	2	4	no	—
7	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₅	C₂²	1	6	yes	complemented
9	C₂²×D₁₅	—	2	4	no	—
10	C₂²×D₁₅	C₂²	1	6	yes	complemented
11	#1220	C₂²	1	16	yes	direct product factor
12	C₂×Dic₁₅	C₂²	1	6	yes	complemented
13	C₂²×#67	—	5	1	no	maximal, Hall
14	C₂⁴×C₅	D₃	1	1	yes	characteristic, complemented
15	C₂³×D₅	—	3	1	no	—
16	C₂×C₂²⋊D₅	—	3	12	no	—
17	C₂²×Dic₅	—	3	1	no	—
18	C₂²×C₃×C₅	—	2	12	no	—
19	C₂²×C₃×C₅	D₄	1	4	yes	complemented
20	C₂²×C₃×C₅	C₂³	1	3	yes	—
21	C₂²×C₃×C₅	C₂³	1	4	yes	complemented
22	C₂×D₁₅	—	2	12	no	—
23	C₂×D₁₅	C₂³	1	4	yes	complemented
24	Dic₁₅	C₂³	1	4	yes	complemented
25	C₂⁴×C₃	D₅	1	1	yes	characteristic, complemented
26	C₂³×D₃	—	5	1	no	—
27	C₂×#67	—	5	12	no	—
28	C₂²×Dic₃	—	5	1	no	—
29	C₂³×C₅	—	2	4	no	—
30	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
31	C₂³×C₅	C₂×D₃	1	6	yes	complemented
32	C₂²×D₅	—	3	6	no	—
33	C₂²×D₅	—	6	4	no	—
34	C₂²⋊D₅	—	3	16	no	—
35	C₂×Dic₅	—	3	6	no	—
36	C₂²×D₄	—	15	1	no	Sylow
37	C₂×C₃×C₅	—	2	4	no	—
38	C₂×C₃×C₅	C₂×D₄	1	6	yes	complemented
39	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
40	D₁₅	—	2	4	no	—
41	C₂³×C₃	—	2	4	no	—
42	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
43	C₂³×C₃	C₂×D₅	1	6	yes	complemented
44	C₂²×D₃	—	5	6	no	—
45	C₂²×D₃	—	10	4	no	—
46	#67	—	5	16	no	—
47	C₂×Dic₃	—	5	6	no	—
48	C₂²×C₅	—	2	12	no	—
49	C₂²×C₅	#67	1	4	yes	complemented
50	C₂²×C₅	C₂²×D₃	1	3	yes	—
51	C₂²×C₅	C₂²×D₃	1	4	yes	complemented
52	C₂×D₅	—	3	4	no	—
53	C₂×D₅	—	6	12	no	—
54	Dic₅	—	3	4	no	—
55	C₂⁴	—	15	1	no	—
56	C₂⁴	D₁₅	1	1	yes	characteristic, complemented
57	C₂×D₄	—	15	12	no	—
58	C₂²×C₄	—	15	1	no	—
59	C₃×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	—	2	12	no	—
61	C₂²×C₃	C₂²⋊D₅	1	4	yes	complemented
62	C₂²×C₃	C₂²×D₅	1	3	yes	—
63	C₂²×C₃	C₂²×D₅	1	4	yes	complemented
64	C₂×D₃	—	5	4	no	—
65	C₂×D₃	—	10	12	no	—
66	Dic₃	—	5	4	no	—
67	C₂×C₅	—	2	4	no	—
68	C₂×C₅	C₂×#67	1	6	yes	complemented
69	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
70	D₅	—	6	4	no	—
71	C₂³	—	2	4	no	—
72	C₂³	—	15	6	no	—
73	C₂³	—	30	4	no	—
74	C₂³	C₂×D₁₅	1	1	yes	characteristic
75	C₂³	C₂×D₁₅	1	6	yes	complemented
76	D₄	—	15	16	no	—
77	C₂×C₄	—	15	6	no	—
78	C₂×C₃	—	2	4	no	—
79	C₂×C₃	C₂×C₂²⋊D₅	1	6	yes	complemented
80	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
81	D₃	—	10	4	no	—
82	C₅	C₂²×#67	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	2	12	no	—
84	C₂²	—	15	4	no	—
85	C₂²	—	30	12	no	—
86	C₂²	#1220	1	4	yes	direct product factor
87	C₂²	C₂²×D₁₅	1	3	yes	—
88	C₂²	C₂²×D₁₅	1	4	yes	complemented
89	C₄	—	15	4	no	—
90	C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	2	4	no	—
92	C₂	—	30	4	no	—
93	C₂	C₂×#1220	1	6	yes	direct product factor
94	C₂	C₂³×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴
Frattini	C₂	C₂³×D₁₅
Fitting	C₂⁴×C₃×C₅	C₂
socle	C₂³×C₃×C₅	C₂²
hypercenter	C₂⁴	D₁₅
hypocenter	C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₅	C₂	semidirect
2. C₂³×D₁₅	C₂	semidirect
3. C₂×#1220	C₂	direct (N × H)
4. C₂²×Dic₁₅	C₂	semidirect
8. C₂³×C₃×C₅	C₂²	semidirect
10. C₂²×D₁₅	C₂²	semidirect
11. #1220	C₂²	direct (N × H)
12. C₂×Dic₁₅	C₂²	semidirect
14. C₂⁴×C₅	D₃	semidirect
19. C₂²×C₃×C₅	D₄	semidirect
21. C₂²×C₃×C₅	C₂³	semidirect
23. C₂×D₁₅	C₂³	semidirect
24. Dic₁₅	C₂³	semidirect
25. C₂⁴×C₃	D₅	semidirect
31. C₂³×C₅	C₂×D₃	semidirect
38. C₂×C₃×C₅	C₂×D₄	semidirect
43. C₂³×C₃	C₂×D₅	semidirect
49. C₂²×C₅	#67	semidirect
51. C₂²×C₅	C₂²×D₃	semidirect
56. C₂⁴	D₁₅	semidirect
59. C₃×C₅	C₂²×D₄	semidirect
61. C₂²×C₃	C₂²⋊D₅	semidirect
63. C₂²×C₃	C₂²×D₅	semidirect
68. C₂×C₅	C₂×#67	semidirect
75. C₂³	C₂×D₁₅	semidirect
79. C₂×C₃	C₂×C₂²⋊D₅	semidirect
82. C₅	C₂²×#67	semidirect
86. C₂²	#1220	direct (N × H)
88. C₂²	C₂²×D₁₅	semidirect
90. C₃	C₂²×C₂²⋊D₅	semidirect
93. C₂	C₂×#1220	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₅	2
C₂³×D₁₅	2
C₂×#1220	2
C₂²×Dic₁₅	2
C₂²×C₂²⋊D₅	3
C₂²×#67	5

Subgroups — C22×#1220 #92103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1220 #92103