Subgroups — #28413367

Order 14700.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20301299	C₂	1	1	yes	maximal, characteristic
2	#19096680	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅⋊(C₅⋊(C₇⋊D₇))	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₇²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#11760384	—	14	4	no	—
7	#11758266	—	15	2	no	—
8	C₃×#5997	—	25	1	no	maximal, Hall
9	C₇×C₅²⋊C₃	—	2	4	no	—
10	C₅⋊(C₇⋊D₇)	—	15	2	no	—
11	C₅⋊D₃₅	—	14	4	no	—
12	#1043⋊C₃	—	49	1	no	maximal, Hall
13	C₃×C₇⋊D₇	—	25	1	no	—
14	C₅×C₇²	—	3	2	no	—
15	#5997	—	25	1	no	Hall
16	C₅²×C₇	—	2	4	no	—
17	(C₅⋊D₅)⋊C₃	—	49	1	no	—
18	C₃×C₇²	—	25	1	no	Hall
19	#1043	—	49	1	no	Hall
20	C₇⋊D₇	—	25	1	no	—
21	C₅²⋊C₃	#5997	1	1	yes	characteristic, complemented, Hall
22	D₃₅	—	210	8	no	—
23	C₅⋊D₅	—	49	1	no	—
24	C₇²	#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×D₇	—	350	4	no	—
26	C₅×C₇	—	6	8	no	—
27	C₅²	C₃×#5997	1	1	yes	characteristic, complemented, Sylow
28	C₃×C₇	—	50	4	no	—
29	AGL(1,𝔽₅)	—	735	2	no	—
30	D₇	—	350	4	no	—
31	C₃×C₄	—	1225	1	no	Hall
32	D₅	—	735	2	no	—
33	C₇	—	2	4	no	—
34	C₂×C₃	—	1225	1	no	—
35	C₅	—	3	2	no	—
36	C₄	—	1225	1	no	Sylow
37	C₃	—	25	1	no	Sylow
38	C₂	—	1225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇²	C₃×C₄
prime radical	#20301299	C₂
cosocle	C₅⋊(C₅⋊(C₇⋊D₇))	C₂×C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁

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.