Subgroups — C₂³×D₃₉ #10597822

Order 624.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₃₉	C₂	1	14	yes	maximal, direct product factor
3	C₂³×D₁₃	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₁₃	C₂²	1	7	yes	complemented
5	C₂×D₃₉	C₂²	1	28	yes	direct product factor
6	C₂³×C₁₃	D₃	1	1	yes	characteristic, complemented
7	C₂²×D₁₃	—	3	14	no	—
8	C₂×C₃×C₁₃	C₂³	1	7	yes	complemented
9	D₃₉	C₂³	1	8	yes	direct product factor
10	C₂²×C₁₃	C₂×D₃	1	7	yes	complemented
11	C₂×D₁₃	—	3	28	no	—
12	C₂³×D₃	—	13	1	no	maximal, Hall
13	C₃×C₁₃	C₂⁴	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃	C₂²×D₃	1	7	yes	complemented
15	D₁₃	—	3	8	no	—
16	C₂³×C₃	D₁₃	1	1	yes	characteristic, complemented
17	C₂²×D₃	—	13	14	no	—
18	C₂⁴	—	39	1	no	Sylow
19	C₁₃	C₂³×D₃	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₃	C₂×D₁₃	1	7	yes	complemented
21	C₂×D₃	—	13	28	no	—
22	C₂³	—	39	14	no	—
23	C₂³	D₃₉	1	1	yes	characteristic, direct product factor
24	C₂×C₃	C₂²×D₁₃	1	7	yes	complemented
25	D₃	—	13	8	no	—
26	C₂²	—	39	28	no	—
27	C₂²	C₂×D₃₉	1	7	yes	direct product factor
28	C₃	C₂³×D₁₃	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	39	8	no	—
30	C₂	C₂²×D₃₉	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₁₃	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³

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

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