Subgroups — C₂²×C₂²⋊(C₁₃⋊C₃) #10597817

Order 624.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊(C₁₃⋊C₃)	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic, direct product factor
4	C₂²×C₁₃⋊C₃	—	4	1	no	maximal
5	C₂³×C₁₃	—	3	1	no	—
6	C₂³×C₁₃	—	3	3	no	—
7	C₂³×C₁₃	C₂×C₃	1	3	yes	complemented
8	C₂×C₁₃⋊C₃	—	4	3	no	—
9	C₂²×C₁₃	—	3	3	no	—
10	C₂²×C₁₃	—	3	2	no	—
11	C₂²×C₁₃	—	3	3	no	—
12	C₂²×C₁₃	—	3	3	no	—
13	C₂²×C₁₃	A₄	1	1	yes	characteristic, complemented
14	C₂²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂²×A₄	—	13	1	no	maximal, Hall
16	C₁₃⋊C₃	—	4	1	no	Hall
17	C₂×C₁₃	—	3	3	no	—
18	C₂×C₁₃	—	3	1	no	—
19	C₂×C₁₃	C₂×A₄	1	3	yes	complemented
20	C₂×A₄	—	13	3	no	—
21	C₂⁴	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₁₃	C₂²×A₄	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₃	—	52	1	no	—
24	A₄	—	13	1	no	—
25	C₂³	—	3	3	no	—
26	C₂³	—	3	1	no	—
27	C₂³	C₂×C₁₃⋊C₃	1	3	yes	complemented
28	C₂×C₃	—	52	3	no	—
29	C₂²	—	3	3	no	—
30	C₂²	—	3	2	no	—
31	C₂²	—	3	3	no	—
32	C₂²	—	3	3	no	—
33	C₂²	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented
34	C₂²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor
35	C₃	—	52	1	no	Sylow
36	C₂	—	3	1	no	—
37	C₂	—	3	3	no	—
38	C₂	C₂×C₂²⋊(C₁₃⋊C₃)	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₂²

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.