Subgroups — C₂²×#1202 #92043

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×C₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#1202	C₂	1	12	yes	maximal, direct product factor
5	C₂²×D₂₀	—	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×C₃×D₅	—	2	4	no	—
10	C₂²×C₃×D₅	C₂²	1	6	yes	complemented
11	C₂×C₅×Dic₃	C₂²	1	6	yes	complemented
12	#1202	C₂²	1	16	yes	direct product factor
13	C₂²×#67	—	5	1	no	maximal, Hall
14	C₂³×D₅	—	3	1	no	—
15	C₂³×D₅	D₃	1	1	yes	characteristic, complemented
16	C₂²×C₄×C₅	—	3	1	no	—
17	C₂×D₂₀	—	3	12	no	—
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×C₃×D₅	—	2	12	no	—
23	C₂×C₃×D₅	C₂³	1	4	yes	complemented
24	C₅×Dic₃	C₂³	1	4	yes	complemented
25	C₂⁴×C₃	—	5	1	no	—
26	C₂³×D₃	—	5	1	no	—
27	C₂×#67	—	5	12	no	—
28	C₂²×Dic₃	D₅	1	1	yes	characteristic, complemented
29	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
30	C₂²×D₅	—	2	4	no	—
31	C₂²×D₅	—	3	6	no	—
32	C₂²×D₅	—	6	4	no	—
33	C₂²×D₅	C₂×D₃	1	6	yes	complemented
34	C₂×C₄×C₅	—	3	6	no	—
35	D₂₀	—	3	16	no	—
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	C₃×D₅	—	2	4	no	—
41	C₂³×C₃	—	5	6	no	—
42	C₂³×C₃	—	10	4	no	—
43	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
44	C₂²×D₃	—	5	6	no	—
45	C₂²×D₃	—	10	4	no	—
46	#67	—	5	16	no	—
47	C₂×Dic₃	C₂×D₅	1	6	yes	complemented
48	C₂²×C₅	#67	1	4	yes	complemented
49	C₂²×C₅	C₂²×D₃	1	3	yes	—
50	C₂×D₅	—	2	12	no	—
51	C₂×D₅	—	3	4	no	—
52	C₂×D₅	—	6	12	no	—
53	C₂×D₅	C₂²×D₃	1	4	yes	complemented
54	C₄×C₅	—	3	4	no	—
55	C₂⁴	—	5	1	no	—
56	C₂⁴	—	15	1	no	—
57	C₂×D₄	—	15	12	no	—
58	C₂²×C₄	—	3	1	no	—
59	C₃×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	—	5	4	no	—
61	C₂²×C₃	—	10	12	no	—
62	C₂²×C₃	D₂₀	1	4	yes	complemented
63	C₂²×C₃	C₂²×D₅	1	3	yes	—
64	C₂×D₃	—	5	4	no	—
65	C₂×D₃	—	10	12	no	—
66	Dic₃	C₂²×D₅	1	4	yes	complemented
67	C₂×C₅	C₂×#67	1	6	yes	complemented
68	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
69	D₅	—	2	4	no	—
70	D₅	—	6	4	no	—
71	C₂³	—	5	6	no	—
72	C₂³	—	10	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	—	3	6	no	—
78	C₂×C₃	—	10	4	no	—
79	C₂×C₃	C₂×D₂₀	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	—	5	4	no	—
84	C₂²	—	10	12	no	—
85	C₂²	—	15	4	no	—
86	C₂²	—	30	12	no	—
87	C₂²	#1202	1	4	yes	direct product factor
88	C₂²	C₂×D₃×D₅	1	3	yes	—
89	C₄	—	3	4	no	—
90	C₃	C₂²×D₂₀	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	10	4	no	—
92	C₂	—	30	4	no	—
93	C₂	C₂×#1202	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×C₃×D₅	C₂	semidirect
3. C₂²×C₅×Dic₃	C₂	semidirect
4. C₂×#1202	C₂	direct (N × H)
8. C₂²×D₁₅	C₂²	semidirect
10. C₂²×C₃×D₅	C₂²	semidirect
11. C₂×C₅×Dic₃	C₂²	semidirect
12. #1202	C₂²	direct (N × H)
15. C₂³×D₅	D₃	semidirect
18. C₂²×C₃×C₅	D₄	semidirect
21. C₂×D₁₅	C₂³	semidirect
23. C₂×C₃×D₅	C₂³	semidirect
24. C₅×Dic₃	C₂³	semidirect
28. C₂²×Dic₃	D₅	semidirect
33. C₂²×D₅	C₂×D₃	semidirect
37. C₂×C₃×C₅	C₂×D₄	semidirect
47. C₂×Dic₃	C₂×D₅	semidirect
48. C₂²×C₅	#67	semidirect
53. C₂×D₅	C₂²×D₃	semidirect
59. C₃×C₅	C₂²×D₄	semidirect
62. C₂²×C₃	D₂₀	semidirect
66. Dic₃	C₂²×D₅	semidirect
67. C₂×C₅	C₂×#67	semidirect
79. C₂×C₃	C₂×D₂₀	semidirect
82. C₅	C₂²×#67	semidirect
87. C₂²	#1202	direct (N × H)
90. C₃	C₂²×D₂₀	semidirect
93. C₂	C₂×#1202	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×C₃×D₅	2
C₂²×C₅×Dic₃	2
C₂×#1202	2
C₂²×D₂₀	3
C₂²×#67	5

Subgroups — C22×#1202 #92043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#1202 #92043