Subgroups — C₅₃×#10596868 #44528367

Order 31164.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#3862	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₇×C₅₃	—	3	1	no	maximal, Hall
3	C₅₃×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₅₃	D₃	1	1	yes	characteristic
5	C₇²×C₅₃	Dic₃	1	1	yes	characteristic, complemented, Hall
6	C₂×ΓL(1,𝔽₈)×C₅₃	—	14	1	no	—
7	C₄×C₇×C₅₃	—	21	1	no	—
8	Dic₇×C₅₃	—	3	1	no	—
9	ΓL(1,𝔽₈)×C₅₃	—	14	1	no	—
10	C₂×C₇×C₅₃	—	2	1	no	—
11	C₂×C₇×C₅₃	—	3	1	no	—
12	C₂×C₇×C₅₃	—	3	1	no	—
13	Dic₃×C₅₃	—	49	1	no	maximal, Hall
14	#10596868	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₇×C₅₃	—	2	1	no	—
16	C₇×C₅₃	—	3	1	no	—
17	C₇×C₅₃	—	3	1	no	—
18	C₂×C₃×C₅₃	—	49	1	no	—
19	C₂×#3862	C₂×C₅₃	1	1	yes	characteristic
20	C₄×C₅₃	—	21	1	no	Hall
21	C₇×Dic₇	—	3	1	no	Hall
22	C₃×C₅₃	—	49	1	no	Hall
23	#3862	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₅₃	#64418	1	1	yes	characteristic
25	C₂×C₇²	D₃×C₅₃	1	1	yes	characteristic
26	C₅₃	#10596868	1	1	yes	characteristic, direct product factor, Sylow
27	C₇²	Dic₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
29	C₄×C₇	—	21	1	no	—
30	Dic₇	—	3	1	no	—
31	ΓL(1,𝔽₈)	—	14	1	no	—
32	C₂×C₇	—	2	1	no	—
33	C₂×C₇	—	3	1	no	—
34	C₂×C₇	—	3	1	no	—
35	Dic₃	—	49	1	no	Hall
36	C₇	—	2	1	no	—
37	C₇	—	3	1	no	—
38	C₇	—	3	1	no	—
39	C₂×C₃	—	49	1	no	—
40	C₄	—	21	1	no	Sylow
41	C₃	—	49	1	no	Sylow
42	C₂	C₅₃×#64418	1	1	yes	characteristic

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.