Subgroups — C₂×C₃×#683 #91640

Order 480.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₃×#683	C₂	1	4	yes	maximal, direct product factor
5	C₂×#683	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₅	—	2	2	no	—
8	C₂×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂×C₃×Dic₅	—	2	2	no	—
10	C₂×C₃×Dic₅	C₄	1	4	yes	complemented
11	C₂×C₃×Dic₅	C₂²	1	2	yes	—
12	C₂×C₃×Dic₅	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊C₄	—	5	1	no	maximal, Hall
14	C₂²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
15	C₂²×Dic₅	C₂×C₃	1	1	yes	characteristic
16	C₂²×Dic₅	C₂×C₃	1	1	yes	characteristic
17	#683	C₂×C₃	1	4	yes	direct product factor
18	C₂²×C₃×C₅	C₂×C₄	1	2	yes	—
19	C₂²×C₃×C₅	D₄	1	2	yes	—
20	C₂²×C₃×C₅	Q₈	1	2	yes	—
21	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
22	C₃×C₄×C₅	—	2	2	no	—
23	C₃×Dic₅	—	2	2	no	—
24	C₃×Dic₅	C₂×C₄	1	4	yes	complemented
25	C₂²×C₃×C₄	—	5	1	no	—
26	C₂²×C₃×C₄	—	5	1	no	—
27	C₂²×C₃×C₄	D₅	1	1	yes	characteristic
28	C₃×C₄⋊C₄	—	5	4	no	—
29	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
30	C₂×C₄×C₅	—	2	2	no	—
31	C₂×C₄×C₅	C₂²×C₃	1	2	yes	—
32	C₂×Dic₅	—	2	2	no	—
33	C₂×Dic₅	C₃×C₄	1	4	yes	complemented
34	C₂×Dic₅	C₂²×C₃	1	2	yes	—
35	C₂×Dic₅	C₂²×C₃	1	2	yes	—
36	C₂×C₄⋊C₄	—	5	1	no	Sylow
37	C₂×C₃×C₅	C₄⋊C₄	1	4	yes	complemented
38	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
40	C₂×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
41	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
42	C₂×C₃×C₄	—	2	2	no	—
43	C₂×C₃×C₄	—	5	4	no	—
44	C₂×C₃×C₄	—	5	2	no	—
45	C₂×C₃×C₄	—	5	2	no	—
46	C₂×C₃×C₄	—	10	2	no	—
47	C₂×C₃×C₄	C₂×D₅	1	2	yes	—
48	C₂²×C₅	C₂×C₃×C₄	1	2	yes	—
49	C₂²×C₅	C₃×D₄	1	2	yes	—
50	C₂²×C₅	C₃×Q₈	1	2	yes	—
51	C₂²×C₅	C₂³×C₃	1	1	yes	characteristic
52	C₄×C₅	—	2	2	no	—
53	Dic₅	—	2	2	no	—
54	Dic₅	C₂×C₃×C₄	1	4	yes	complemented
55	C₂²×C₄	—	5	1	no	—
56	C₂²×C₄	—	5	1	no	—
57	C₂²×C₄	C₃×D₅	1	1	yes	characteristic
58	C₄⋊C₄	—	5	4	no	—
59	C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	Dic₁₀	1	2	yes	—
61	C₂²×C₃	C₄×D₅	1	2	yes	—
62	C₂²×C₃	C₂²⋊D₅	1	2	yes	—
63	C₂²×C₃	C₂²×D₅	1	1	yes	characteristic
64	C₃×C₄	—	2	2	no	—
65	C₃×C₄	—	5	4	no	—
66	C₃×C₄	—	10	2	no	—
67	C₂×C₅	C₃×C₄⋊C₄	1	4	yes	complemented
68	C₂×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
69	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
70	C₂×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
71	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	5	4	no	—
74	C₂×C₄	—	5	2	no	—
75	C₂×C₄	—	5	2	no	—
76	C₂×C₄	—	10	2	no	—
77	C₂×C₄	C₂×C₃×D₅	1	2	yes	—
78	C₂×C₃	#683	1	4	yes	direct product factor
79	C₂×C₃	C₂×Dic₁₀	1	1	yes	characteristic
80	C₂×C₃	C₂×C₄×D₅	1	1	yes	characteristic
81	C₂×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
82	C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
83	C₂²	C₃×Dic₁₀	1	2	yes	—
84	C₂²	C₃×C₄×D₅	1	2	yes	—
85	C₂²	C₃×C₂²⋊D₅	1	2	yes	—
86	C₂²	C₂²×C₃×D₅	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	—	5	4	no	—
89	C₄	—	10	2	no	—
90	C₃	C₂×#683	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	C₃×#683	1	4	yes	direct product factor
92	C₂	C₂×C₃×Dic₁₀	1	1	yes	characteristic
93	C₂	C₂×C₃×C₄×D₅	1	1	yes	characteristic
94	C₂	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₅
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂²	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₄×C₅	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²
cosocle	C₂²×C₅	C₂³×C₃
hypercenter	C₂²×C₃×C₄	D₅
hypocenter	C₅	C₂×C₃×C₄⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
4. C₃×#683	C₂	direct (N × H)
5. C₂×#683	C₃	direct (N × H)
10. C₂×C₃×Dic₅	C₄	semidirect
17. #683	C₂×C₃	direct (N × H)
24. C₃×Dic₅	C₂×C₄	semidirect
33. C₂×Dic₅	C₃×C₄	semidirect
37. C₂×C₃×C₅	C₄⋊C₄	semidirect
54. Dic₅	C₂×C₃×C₄	semidirect
59. C₃×C₅	C₂×C₄⋊C₄	semidirect
67. C₂×C₅	C₃×C₄⋊C₄	semidirect
78. C₂×C₃	#683	direct (N × H)
82. C₅	C₂×C₃×C₄⋊C₄	semidirect
90. C₃	C₂×#683	direct (N × H)
91. C₂	C₃×#683	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₅	2
C₂²×C₃×Dic₅	2
C₃×#683	2
C₂×#683	3
C₂×C₃×C₄⋊C₄	5

Subgroups — C2×C3×#683 #91640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#683 #91640