Subgroups — C₂×#64605 #10597753

Order 624.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#64605	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₂₆	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	Dic₃₉	C₂²	1	2	yes	—
8	C₃×Dic₁₃	C₂²	1	2	yes	—
9	Dic₃×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×C₁₃	—	3	1	no	—
11	C₂×Dic₁₃	—	3	1	no	—
12	C₂×Dic₁₃	D₃	1	1	yes	characteristic
13	Dic₂₆	—	3	4	no	—
14	C₂×C₃×C₁₃	Q₈	1	2	yes	complemented
15	C₂×C₃×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×C₁₃	C₂×D₃	1	1	yes	characteristic
17	C₄×C₁₃	—	3	2	no	—
18	Dic₁₃	—	3	2	no	—
19	Dic₁₃	C₂×D₃	1	2	yes	—
20	C₂×Dic₆	—	13	1	no	maximal, Hall
21	C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₃	Dic₆	1	2	yes	complemented
23	C₂×C₁₃	C₂²×D₃	1	1	yes	characteristic
24	C₂×C₃×C₄	—	13	1	no	—
25	C₂×Dic₃	—	13	1	no	—
26	C₂×Dic₃	D₁₃	1	1	yes	characteristic
27	Dic₆	—	13	4	no	—
28	C₂×Q₈	—	39	1	no	Sylow
29	C₁₃	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₃	C₂×D₁₃	1	1	yes	characteristic
31	C₃×C₄	—	13	2	no	—
32	Dic₃	—	13	2	no	—
33	Dic₃	C₂×D₁₃	1	2	yes	—
34	Q₈	—	39	4	no	—
35	C₂×C₄	—	3	1	no	—
36	C₂×C₄	—	13	1	no	—
37	C₂×C₄	—	39	1	no	—
38	C₂×C₃	Dic₂₆	1	2	yes	complemented
39	C₂×C₃	C₂²×D₁₃	1	1	yes	characteristic
40	C₂²	D₃×D₁₃	1	1	yes	characteristic
41	C₄	—	3	2	no	—
42	C₄	—	13	2	no	—
43	C₄	—	39	2	no	—
44	C₃	C₂×Dic₂₆	1	1	yes	characteristic, complemented, Sylow
45	C₂	#64605	1	2	yes	direct product factor
46	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, prime radical	C₂²×C₃×C₁₃	C₂²
hypocenter	C₃×C₁₃	C₂×Q₈
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
4. #64605	C₂	direct (N × H)
14. C₂×C₃×C₁₃	Q₈	semidirect
21. C₃×C₁₃	C₂×Q₈	semidirect
22. C₂×C₁₃	Dic₆	semidirect
29. C₁₃	C₂×Dic₆	semidirect
38. C₂×C₃	Dic₂₆	semidirect
44. C₃	C₂×Dic₂₆	semidirect
45. C₂	#64605	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×Dic₃₉	2
C₂×Dic₃×C₁₃	2
C₂×C₃×Dic₁₃	2
#64605	2
C₂×Dic₂₆	3
C₂×Dic₆	13

Subgroups — C2×#64605 #10597753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#64605 #10597753