Subgroups — C₂×#64604 #10597752

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×D₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#64604	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₂²⋊D₁₃	—	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×D₃×C₁₃	—	2	2	no	—
10	C₂×D₃×C₁₃	C₂²	1	2	yes	complemented
11	C₃×Dic₁₃	C₂²	1	2	yes	complemented
12	C₂³×C₁₃	—	3	1	no	—
13	C₂²×D₁₃	—	3	1	no	—
14	C₂²⋊D₁₃	—	3	4	no	—
15	C₂×Dic₁₃	D₃	1	1	yes	characteristic, complemented
16	C₂×C₃×C₁₃	D₄	1	2	yes	complemented
17	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
18	D₃₉	—	2	2	no	—
19	D₃×C₁₃	—	2	2	no	—
20	C₂²×C₁₃	—	3	2	no	—
21	C₂²×C₁₃	—	6	2	no	—
22	C₂²×C₁₃	C₂×D₃	1	1	yes	characteristic
23	C₂×D₁₃	—	3	2	no	—
24	C₂×D₁₃	—	6	2	no	—
25	Dic₁₃	C₂×D₃	1	2	yes	complemented
26	C₂×D₁₂	—	13	1	no	maximal, Hall
27	C₃×C₁₃	C₂×D₄	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₃	—	6	2	no	—
29	C₂×C₁₃	D₁₂	1	2	yes	complemented
30	C₂×C₁₃	C₂²×D₃	1	1	yes	characteristic
31	D₁₃	—	6	2	no	—
32	C₂²×D₃	—	13	1	no	—
33	C₂²×D₃	D₁₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₄	—	13	1	no	—
35	D₁₂	—	13	4	no	—
36	C₂×D₄	—	39	1	no	Sylow
37	C₁₃	C₂×D₁₂	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	C₂×D₁₃	1	1	yes	characteristic
39	C₂×D₃	—	2	2	no	—
40	C₂×D₃	—	13	2	no	—
41	C₂×D₃	—	26	2	no	—
42	C₂×D₃	C₂×D₁₃	1	2	yes	complemented
43	C₃×C₄	—	13	2	no	—
44	C₂³	—	3	1	no	—
45	C₂³	—	39	1	no	—
46	D₄	—	39	4	no	—
47	C₂×C₄	—	13	1	no	—
48	C₂×C₃	C₂²⋊D₁₃	1	2	yes	complemented
49	C₂×C₃	C₂²×D₁₃	1	1	yes	characteristic
50	D₃	—	2	2	no	—
51	D₃	—	26	2	no	—
52	C₂²	—	3	2	no	—
53	C₂²	—	6	2	no	—
54	C₂²	—	39	2	no	—
55	C₂²	—	78	2	no	—
56	C₂²	D₃×D₁₃	1	1	yes	characteristic
57	C₄	—	13	2	no	—
58	C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	6	2	no	—
60	C₂	—	78	2	no	—
61	C₂	#64604	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×D₃×C₁₃	C₂	semidirect
3. C₂×C₃×Dic₁₃	C₂	semidirect
4. #64604	C₂	direct (N × H)
8. C₂×D₃₉	C₂²	semidirect
10. C₂×D₃×C₁₃	C₂²	semidirect
11. C₃×Dic₁₃	C₂²	semidirect
15. C₂×Dic₁₃	D₃	semidirect
16. C₂×C₃×C₁₃	D₄	semidirect
25. Dic₁₃	C₂×D₃	semidirect
27. C₃×C₁₃	C₂×D₄	semidirect
29. C₂×C₁₃	D₁₂	semidirect
33. C₂²×D₃	D₁₃	semidirect
37. C₁₃	C₂×D₁₂	semidirect
42. C₂×D₃	C₂×D₁₃	semidirect
48. C₂×C₃	C₂²⋊D₁₃	semidirect
58. C₃	C₂×C₂²⋊D₁₃	semidirect
61. C₂	#64604	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×D₃×C₁₃	2
C₂×C₃×Dic₁₃	2
#64604	2
C₂×C₂²⋊D₁₃	3
C₂×D₁₂	13

Subgroups — C2×#64604 #10597752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#64604 #10597752