Subgroups — #120×C₆₅₃ #35229608

Order 20896.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₆₅₃	C₂	1	3	yes	maximal, complemented
3	C₂²⋊C₄×C₆₅₃	C₂	1	3	yes	maximal, complemented
4	C₂³×C₆₅₃	—	2	6	no	—
5	C₂³×C₆₅₃	C₂²	1	3	yes	—
6	C₂³×C₆₅₃	C₂²	1	1	yes	characteristic, complemented
7	D₄×C₆₅₃	—	2	6	no	—
8	C₂×C₄×C₆₅₃	C₂²	1	3	yes	complemented
9	C₂²×C₆₅₃	—	2	8	no	—
10	C₂²×C₆₅₃	—	2	6	no	—
11	C₂²×C₆₅₃	—	2	3	no	—
12	C₂²×C₆₅₃	D₄	1	6	yes	complemented
13	C₂²×C₆₅₃	C₂³	1	1	yes	characteristic
14	C₄×C₆₅₃	—	2	3	no	—
15	C₂×C₆₅₃	—	2	6	no	—
16	C₂×C₆₅₃	—	4	1	no	—
17	C₂×C₆₅₃	C₂×D₄	1	3	yes	—
18	C₆₅₃	#120	1	1	yes	characteristic, direct product factor, Sylow
19	#120	C₆₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂⁴	C₂×C₆₅₃	1	1	yes	characteristic, complemented
21	C₂×D₄	C₂×C₆₅₃	1	3	yes	complemented
22	C₂²⋊C₄	C₂×C₆₅₃	1	3	yes	complemented
23	C₂³	—	2	6	no	—
24	C₂³	C₂²×C₆₅₃	1	3	yes	—
25	C₂³	C₂²×C₆₅₃	1	1	yes	characteristic, complemented
26	D₄	—	2	6	no	—
27	C₂×C₄	C₂²×C₆₅₃	1	3	yes	complemented
28	C₂²	—	2	8	no	—
29	C₂²	—	2	6	no	—
30	C₂²	—	2	3	no	—
31	C₂²	D₄×C₆₅₃	1	6	yes	complemented
32	C₂²	C₂³×C₆₅₃	1	1	yes	characteristic
33	C₄	—	2	3	no	—
34	C₂	—	2	6	no	—
35	C₂	—	4	1	no	—
36	C₂	C₂×D₄×C₆₅₃	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₅₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₆₅₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₅₃ ◁ G

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.