Subgroups — C₂×#64603 #10597751

Order 624.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#64603	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₅₂	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×D₃₉	—	2	2	no	—
8	C₂×D₃₉	C₂²	1	2	yes	complemented
9	C₂×C₃×D₁₃	—	2	2	no	—
10	C₂×C₃×D₁₃	C₂²	1	2	yes	complemented
11	Dic₃×C₁₃	C₂²	1	2	yes	complemented
12	C₂²×D₁₃	—	3	1	no	—
13	C₂²×D₁₃	D₃	1	1	yes	characteristic, complemented
14	C₂×C₄×C₁₃	—	3	1	no	—
15	D₅₂	—	3	4	no	—
16	C₂×C₃×C₁₃	D₄	1	2	yes	complemented
17	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
18	D₃₉	—	2	2	no	—
19	C₃×D₁₃	—	2	2	no	—
20	C₂²×C₁₃	C₂×D₃	1	1	yes	characteristic
21	C₂×D₁₃	—	2	2	no	—
22	C₂×D₁₃	—	3	2	no	—
23	C₂×D₁₃	—	6	2	no	—
24	C₂×D₁₃	C₂×D₃	1	2	yes	complemented
25	C₄×C₁₃	—	3	2	no	—
26	C₂×#67	—	13	1	no	maximal, Hall
27	C₃×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₃	#67	1	2	yes	complemented
29	C₂×C₁₃	C₂²×D₃	1	1	yes	characteristic
30	D₁₃	—	2	2	no	—
31	D₁₃	—	6	2	no	—
32	C₂³×C₃	—	13	1	no	—
33	C₂²×D₃	—	13	1	no	—
34	#67	—	13	4	no	—
35	C₂×Dic₃	D₁₃	1	1	yes	characteristic, complemented
36	C₂×D₄	—	39	1	no	Sylow
37	C₁₃	C₂×#67	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	—	13	2	no	—
39	C₂²×C₃	—	26	2	no	—
40	C₂²×C₃	C₂×D₁₃	1	1	yes	characteristic
41	C₂×D₃	—	13	2	no	—
42	C₂×D₃	—	26	2	no	—
43	Dic₃	C₂×D₁₃	1	2	yes	complemented
44	C₂³	—	13	1	no	—
45	C₂³	—	39	1	no	—
46	D₄	—	39	4	no	—
47	C₂×C₄	—	3	1	no	—
48	C₂×C₃	—	26	2	no	—
49	C₂×C₃	D₅₂	1	2	yes	complemented
50	C₂×C₃	C₂²×D₁₃	1	1	yes	characteristic
51	D₃	—	26	2	no	—
52	C₂²	—	13	2	no	—
53	C₂²	—	26	2	no	—
54	C₂²	—	39	2	no	—
55	C₂²	—	78	2	no	—
56	C₂²	D₃×D₁₃	1	1	yes	characteristic
57	C₄	—	3	2	no	—
58	C₃	C₂×D₅₂	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	26	2	no	—
60	C₂	—	78	2	no	—
61	C₂	#64603	1	2	yes	direct product factor
62	C₂	C₂×D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₁₃
commutator, cosocle	C₂×C₃×C₁₃	C₂³
Frattini	C₂	C₂×D₃×D₁₃
Fitting, socle	C₂²×C₃×C₁₃	C₂²
hypocenter	C₃×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×D₃₉	C₂	semidirect
2. C₂²×C₃×D₁₃	C₂	semidirect
3. C₂×Dic₃×C₁₃	C₂	semidirect
4. #64603	C₂	direct (N × H)
8. C₂×D₃₉	C₂²	semidirect
10. C₂×C₃×D₁₃	C₂²	semidirect
11. Dic₃×C₁₃	C₂²	semidirect
13. C₂²×D₁₃	D₃	semidirect
16. C₂×C₃×C₁₃	D₄	semidirect
24. C₂×D₁₃	C₂×D₃	semidirect
27. C₃×C₁₃	C₂×D₄	semidirect
28. C₂×C₁₃	#67	semidirect
35. C₂×Dic₃	D₁₃	semidirect
37. C₁₃	C₂×#67	semidirect
43. Dic₃	C₂×D₁₃	semidirect
49. C₂×C₃	D₅₂	semidirect
58. C₃	C₂×D₅₂	semidirect
61. C₂	#64603	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×D₃₉	2
C₂²×C₃×D₁₃	2
C₂×Dic₃×C₁₃	2
#64603	2
C₂×D₅₂	3
C₂×#67	13

Subgroups — C2×#64603 #10597751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#64603 #10597751