Subgroups — #35229696

Order 20896.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₆₅₃	C₂	1	3	yes	maximal, complemented
2	C₂²⋊Dic₆₅₃	C₂	1	3	yes	maximal, complemented
3	C₂⁴×C₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₆₅₃	C₂²	1	1	yes	characteristic, complemented
5	C₂²⋊D₆₅₃	—	2	6	no	—
6	C₂×Dic₆₅₃	C₂²	1	3	yes	complemented
7	C₂³×C₆₅₃	—	2	6	no	—
8	C₂³×C₆₅₃	C₂²	1	3	yes	—
9	C₂²×C₆₅₃	—	2	8	no	—
10	C₂²×C₆₅₃	—	2	6	no	—
11	C₂²×C₆₅₃	D₄	1	6	yes	complemented
12	C₂²×C₆₅₃	C₂³	1	1	yes	characteristic
13	C₂×D₆₅₃	—	2	3	no	—
14	Dic₆₅₃	—	2	3	no	—
15	C₂×C₆₅₃	—	2	6	no	—
16	C₂×C₆₅₃	C₂×D₄	1	3	yes	—
17	D₆₅₃	—	4	1	no	—
18	C₆₅₃	#120	1	1	yes	characteristic, complemented, Sylow
19	#120	—	653	1	no	maximal, Sylow
20	C₂⁴	D₆₅₃	1	1	yes	characteristic, complemented
21	C₂×D₄	—	653	3	no	—
22	C₂²⋊C₄	—	653	3	no	—
23	C₂³	—	2	6	no	—
24	C₂³	—	653	1	no	—
25	C₂³	C₂×D₆₅₃	1	3	yes	—
26	D₄	—	1306	6	no	—
27	C₂×C₄	—	653	3	no	—
28	C₂²	—	2	8	no	—
29	C₂²	—	2	6	no	—
30	C₂²	—	1306	3	no	—
31	C₂²	C₂²⋊D₆₅₃	1	6	yes	complemented
32	C₂²	C₂²×D₆₅₃	1	1	yes	characteristic
33	C₄	—	1306	3	no	—
34	C₂	—	2	6	no	—
35	C₂	—	2612	1	no	—
36	C₂	C₂×C₂²⋊D₆₅₃	1	3	yes	—

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.