Subgroups — C₂×#6651 #91295

Order 480.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	#6651	C₂	1	4	yes	maximal, direct product factor
5	C₂×#676	—	3	1	no	maximal, Hall
6	C₂²×D₁₅	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₅	C₄	1	1	yes	characteristic
9	C₄×D₁₅	C₄	1	2	yes	—
10	C₄×D₁₅	C₂²	1	2	yes	—
11	C₃×#168	C₂²	1	2	yes	complemented
12	C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	maximal, Hall
14	C₂×C₄×D₅	—	3	1	no	—
15	C₂×C₅×C₈	—	3	1	no	—
16	C₂×#168	D₃	1	1	yes	characteristic, complemented
17	#676	—	3	4	no	—
18	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂×D₁₅	—	2	2	no	—
20	C₂×D₁₅	C₂×C₄	1	2	yes	—
21	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
22	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
23	Dic₁₅	C₂×C₄	1	2	yes	—
24	C₂×C₄×D₃	—	5	1	no	—
25	C₂×C₃×C₈	—	5	1	no	—
26	C₂×C₃⋊C₈	D₅	1	1	yes	characteristic, complemented
27	ΓL(1,𝔽₂₅)	—	5	4	no	—
28	C₂²×D₅	—	3	1	no	—
29	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
30	C₂×Dic₅	—	3	1	no	—
31	C₄×D₅	—	3	2	no	—
32	C₄×D₅	—	3	2	no	—
33	C₅×C₈	—	3	2	no	—
34	#168	C₂×D₃	1	2	yes	complemented
35	C₂×M₁₆	—	15	1	no	Sylow
36	C₂×C₃×C₅	M₁₆	1	2	yes	complemented
37	C₂×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
38	D₁₅	—	2	2	no	—
39	C₂²×D₃	—	5	1	no	—
40	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
41	C₂×Dic₃	—	5	1	no	—
42	C₄×D₃	—	5	2	no	—
43	C₄×D₃	—	5	2	no	—
44	C₃×C₈	—	5	2	no	—
45	C₃⋊C₈	C₂×D₅	1	2	yes	complemented
46	C₂²×C₅	C₄×D₃	1	1	yes	characteristic
47	C₂×D₅	—	3	2	no	—
48	C₂×D₅	—	6	2	no	—
49	C₄×C₅	C₄×D₃	1	1	yes	characteristic
50	C₄×C₅	C₂²×D₃	1	1	yes	characteristic
51	Dic₅	—	3	2	no	—
52	C₂²×C₄	—	15	1	no	—
53	M₁₆	—	15	4	no	—
54	C₂×C₈	—	3	1	no	—
55	C₂×C₈	—	5	1	no	—
56	C₃×C₅	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
57	C₂²×C₃	C₄×D₅	1	1	yes	characteristic
58	C₂×D₃	—	5	2	no	—
59	C₂×D₃	—	10	2	no	—
60	C₃×C₄	C₄×D₅	1	1	yes	characteristic
61	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
62	Dic₃	—	5	2	no	—
63	C₂×C₅	ΓL(1,𝔽₂₅)	1	2	yes	complemented
64	C₂×C₅	C₂×C₄×D₃	1	1	yes	characteristic
65	D₅	—	6	2	no	—
66	C₂³	—	15	1	no	—
67	C₂×C₄	—	15	1	no	—
68	C₂×C₄	—	15	2	no	—
69	C₂×C₄	—	15	2	no	—
70	C₂×C₄	D₃×D₅	1	1	yes	characteristic
71	C₈	—	3	2	no	—
72	C₈	—	5	2	no	—
73	C₂×C₃	#676	1	2	yes	complemented
74	C₂×C₃	C₂×C₄×D₅	1	1	yes	characteristic
75	D₃	—	10	2	no	—
76	C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic, complemented, Sylow
77	C₂²	—	15	2	no	—
78	C₂²	—	30	2	no	—
79	C₂²	#1200	1	1	yes	characteristic
80	C₄	—	15	2	no	—
81	C₄	#1200	1	1	yes	characteristic
82	C₄	C₂×D₃×D₅	1	1	yes	characteristic
83	C₃	C₂×#676	1	1	yes	characteristic, complemented, Sylow
84	C₂	—	30	2	no	—
85	C₂	#6651	1	2	yes	direct product factor
86	C₂	C₂×#1200	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄
Frattini	C₄	C₂×D₃×D₅
Fitting	C₂×C₃×C₄×C₅	C₂²
socle	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×D₁₅	C₄
cosocle	C₃×C₄×C₅	C₂³
hypocenter	C₃×C₅	C₂×M₁₆
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₃⋊C₈	C₂	semidirect
3. C₂×C₃×#168	C₂	semidirect
4. #6651	C₂	direct (N × H)
11. C₃×#168	C₂²	semidirect
12. C₅×C₃⋊C₈	C₂²	semidirect
16. C₂×#168	D₃	semidirect
26. C₂×C₃⋊C₈	D₅	semidirect
34. #168	C₂×D₃	semidirect
36. C₂×C₃×C₅	M₁₆	semidirect
45. C₃⋊C₈	C₂×D₅	semidirect
56. C₃×C₅	C₂×M₁₆	semidirect
63. C₂×C₅	ΓL(1,𝔽₂₅)	semidirect
73. C₂×C₃	#676	semidirect
76. C₅	C₂×ΓL(1,𝔽₂₅)	semidirect
83. C₃	C₂×#676	semidirect
85. C₂	#6651	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₁₅	2
C₂×C₅×C₃⋊C₈	2
C₂×C₃×#168	2
#6651	2
C₂×#676	3
C₂×ΓL(1,𝔽₂₅)	5

Subgroups — C2×#6651 #91295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6651 #91295