Subgroups — C₂²×#1203 #92044

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#1203	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₂²⋊D₅	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂²×D₁₅	—	2	4	no	—
8	C₂²×D₁₅	C₂²	1	6	yes	complemented
9	C₂²×C₅×D₃	—	2	4	no	—
10	C₂²×C₅×D₃	C₂²	1	6	yes	complemented
11	C₂×C₃×Dic₅	C₂²	1	6	yes	complemented
12	#1203	C₂²	1	16	yes	direct product factor
13	C₂²×D₁₂	—	5	1	no	maximal, Hall
14	C₂⁴×C₅	—	3	1	no	—
15	C₂³×D₅	—	3	1	no	—
16	C₂×C₂²⋊D₅	—	3	12	no	—
17	C₂²×Dic₅	D₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅	D₄	1	4	yes	complemented
19	C₂²×C₃×C₅	C₂³	1	3	yes	—
20	C₂×D₁₅	—	2	12	no	—
21	C₂×D₁₅	C₂³	1	4	yes	complemented
22	C₂×C₅×D₃	—	2	12	no	—
23	C₂×C₅×D₃	C₂³	1	4	yes	complemented
24	C₃×Dic₅	C₂³	1	4	yes	complemented
25	C₂³×D₃	—	5	1	no	—
26	C₂³×D₃	D₅	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₄	—	5	1	no	—
28	C₂×D₁₂	—	5	12	no	—
29	C₂³×C₅	—	3	6	no	—
30	C₂³×C₅	—	6	4	no	—
31	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
32	C₂²×D₅	—	3	6	no	—
33	C₂²×D₅	—	6	4	no	—
34	C₂²⋊D₅	—	3	16	no	—
35	C₂×Dic₅	C₂×D₃	1	6	yes	complemented
36	C₂²×D₄	—	15	1	no	Sylow
37	C₂×C₃×C₅	C₂×D₄	1	6	yes	complemented
38	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
39	D₁₅	—	2	4	no	—
40	C₅×D₃	—	2	4	no	—
41	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
42	C₂²×D₃	—	2	4	no	—
43	C₂²×D₃	—	5	6	no	—
44	C₂²×D₃	—	10	4	no	—
45	C₂²×D₃	C₂×D₅	1	6	yes	complemented
46	C₂×C₃×C₄	—	5	6	no	—
47	D₁₂	—	5	16	no	—
48	C₂²×C₅	—	3	4	no	—
49	C₂²×C₅	—	6	12	no	—
50	C₂²×C₅	D₁₂	1	4	yes	complemented
51	C₂²×C₅	C₂²×D₃	1	3	yes	—
52	C₂×D₅	—	3	4	no	—
53	C₂×D₅	—	6	12	no	—
54	Dic₅	C₂²×D₃	1	4	yes	complemented
55	C₂⁴	—	3	1	no	—
56	C₂⁴	—	15	1	no	—
57	C₂×D₄	—	15	12	no	—
58	C₂²×C₄	—	5	1	no	—
59	C₃×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	C₂²⋊D₅	1	4	yes	complemented
61	C₂²×C₃	C₂²×D₅	1	3	yes	—
62	C₂×D₃	—	2	12	no	—
63	C₂×D₃	—	5	4	no	—
64	C₂×D₃	—	10	12	no	—
65	C₂×D₃	C₂²×D₅	1	4	yes	complemented
66	C₃×C₄	—	5	4	no	—
67	C₂×C₅	—	6	4	no	—
68	C₂×C₅	C₂×D₁₂	1	6	yes	complemented
69	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
70	D₅	—	6	4	no	—
71	C₂³	—	3	6	no	—
72	C₂³	—	6	4	no	—
73	C₂³	—	15	6	no	—
74	C₂³	—	30	4	no	—
75	C₂³	D₃×D₅	1	1	yes	characteristic
76	D₄	—	15	16	no	—
77	C₂×C₄	—	5	6	no	—
78	C₂×C₃	C₂×C₂²⋊D₅	1	6	yes	complemented
79	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
80	D₃	—	2	4	no	—
81	D₃	—	10	4	no	—
82	C₅	C₂²×D₁₂	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	3	4	no	—
84	C₂²	—	6	12	no	—
85	C₂²	—	15	4	no	—
86	C₂²	—	30	12	no	—
87	C₂²	#1203	1	4	yes	direct product factor
88	C₂²	C₂×D₃×D₅	1	3	yes	—
89	C₄	—	5	4	no	—
90	C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	6	4	no	—
92	C₂	—	30	4	no	—
93	C₂	C₂×#1203	1	6	yes	direct product factor
94	C₂	C₂²×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴
Frattini	C₂	C₂²×D₃×D₅
Fitting, socle	C₂³×C₃×C₅	C₂²
hypocenter	C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×D₁₅	C₂	semidirect
2. C₂³×C₅×D₃	C₂	semidirect
3. C₂²×C₃×Dic₅	C₂	semidirect
4. C₂×#1203	C₂	direct (N × H)
8. C₂²×D₁₅	C₂²	semidirect
10. C₂²×C₅×D₃	C₂²	semidirect
11. C₂×C₃×Dic₅	C₂²	semidirect
12. #1203	C₂²	direct (N × H)
17. C₂²×Dic₅	D₃	semidirect
18. C₂²×C₃×C₅	D₄	semidirect
21. C₂×D₁₅	C₂³	semidirect
23. C₂×C₅×D₃	C₂³	semidirect
24. C₃×Dic₅	C₂³	semidirect
26. C₂³×D₃	D₅	semidirect
35. C₂×Dic₅	C₂×D₃	semidirect
37. C₂×C₃×C₅	C₂×D₄	semidirect
45. C₂²×D₃	C₂×D₅	semidirect
50. C₂²×C₅	D₁₂	semidirect
54. Dic₅	C₂²×D₃	semidirect
59. C₃×C₅	C₂²×D₄	semidirect
60. C₂²×C₃	C₂²⋊D₅	semidirect
65. C₂×D₃	C₂²×D₅	semidirect
68. C₂×C₅	C₂×D₁₂	semidirect
78. C₂×C₃	C₂×C₂²⋊D₅	semidirect
82. C₅	C₂²×D₁₂	semidirect
87. C₂²	#1203	direct (N × H)
90. C₃	C₂²×C₂²⋊D₅	semidirect
93. C₂	C₂×#1203	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₁₅	2
C₂³×C₅×D₃	2
C₂²×C₃×Dic₅	2
C₂×#1203	2
C₂²×C₂²⋊D₅	3
C₂²×D₁₂	5

Subgroups — C22×#1203 #92044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1203 #92044