Subgroups — #30660367

Order 16736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₅₂₃⋊C₄	C₂	1	3	yes	maximal, complemented
2	(C₂×D₅₂₃)⋊C₄	C₂	1	3	yes	maximal
3	C₄²×C₅₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₅₂₃	C₂²	1	1	yes	characteristic
5	C₂×Dic₅₂₃	C₂²	1	3	yes	—
6	C₂×C₄×C₅₂₃	C₂²	1	3	yes	—
7	C₂²×C₅₂₃	C₂³	1	1	yes	characteristic
8	C₂×D₅₂₃	—	2	3	no	—
9	C₄×C₅₂₃	—	2	3	no	—
10	Dic₅₂₃	—	2	3	no	—
11	C₂×C₅₂₃	#41	1	3	yes	—
12	D₅₂₃	—	4	1	no	—
13	C₅₂₃	#126	1	1	yes	characteristic, complemented, Sylow
14	#126	—	523	1	no	maximal, Sylow
15	C₄⋊C₄	—	523	3	no	—
16	C₂²⋊C₄	—	523	3	no	—
17	C₄²	D₅₂₃	1	1	yes	characteristic, complemented
18	C₂³	—	523	1	no	—
19	C₂×C₄	—	523	3	no	—
20	C₂×C₄	C₂×D₅₂₃	1	3	yes	—
21	C₂²	—	1046	3	no	—
22	C₂²	C₂²×D₅₂₃	1	1	yes	characteristic
23	C₄	—	2	3	no	—
24	C₄	—	1046	3	no	—
25	C₂	—	2092	1	no	—
26	C₂	#22552641	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.