Subgroups — C₃×C₅₃×#5997 #44528441

Order 31164.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#5997	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇²×C₅₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
5	C₇²×C₅₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×D₇×C₅₃	—	14	4	no	—
7	C₃×C₇×C₅₃	—	2	4	no	—
8	D₇×C₅₃	—	14	4	no	—
9	C₃×C₄×C₅₃	—	49	1	no	maximal, Hall
10	C₃×#5997	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₅₃	—	2	4	no	—
12	C₂×C₃×C₅₃	—	49	1	no	—
13	C₃×C₇⋊D₇	C₂×C₅₃	1	1	yes	characteristic
14	C₄×C₅₃	—	49	1	no	Hall
15	#5997	C₃×C₅₃	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₅₃	#5997	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₇²	C₄×C₅₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅₃	—	49	1	no	—
19	C₇⋊D₇	C₂×C₃×C₅₃	1	1	yes	characteristic
20	C₅₃	C₃×#5997	1	1	yes	characteristic, direct product factor, Sylow
21	C₇²	C₃×C₄×C₅₃	1	1	yes	characteristic, complemented, Sylow
22	C₃×D₇	—	14	4	no	—
23	C₃×C₇	—	2	4	no	—
24	D₇	—	14	4	no	—
25	C₃×C₄	—	49	1	no	Hall
26	C₇	—	2	4	no	—
27	C₂×C₃	—	49	1	no	—
28	C₄	—	49	1	no	Sylow
29	C₃	C₅₃×#5997	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	49	1	no	—

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.