Subgroups — #43249338

Order 28420.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₅⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19150998	—	5	1	no	maximal, Hall
4	C₂₉×C₇⋊D₇	—	5	1	no	—
5	C₂₉×D₃₅	—	14	4	no	—
6	C₇²×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₂₉	—	2	4	no	—
8	#11758266	—	29	1	no	maximal, Hall
9	#10596816	—	49	1	no	maximal, Hall
10	C₅⋊(C₇⋊D₇)	D₂₉	1	1	yes	characteristic
11	D₇×C₂₉	—	70	4	no	—
12	D₅×C₂₉	—	49	1	no	—
13	C₅×C₇²	Dic₂₉	1	1	yes	characteristic, complemented, Hall
14	C₇×C₂₉	—	2	4	no	—
15	#5997	—	145	1	no	Hall
16	C₅×C₂₉	#5997	1	1	yes	characteristic, complemented, Hall
17	Dic₂₉	—	245	1	no	Hall
18	C₇⋊D₇	—	5	1	no	—
19	D₃₅	—	14	4	no	—
20	C₂×C₂₉	—	245	1	no	—
21	C₇²	#10596816	1	1	yes	characteristic, complemented, Sylow
22	C₅×C₇	—	2	4	no	—
23	C₂₉	#11758266	1	1	yes	characteristic, complemented, Sylow
24	AGL(1,𝔽₅)	—	1421	1	no	Hall
25	D₇	—	70	4	no	—
26	D₅	—	49	1	no	—
27	C₇	—	2	4	no	—
28	C₅	#19150998	1	1	yes	characteristic, complemented, Sylow
29	C₄	—	7105	1	no	Sylow
30	C₂	—	245	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇²×C₂₉	C₄
prime radical, cosocle	C₂₉×C₅⋊(C₇⋊D₇)	C₂
LCS	G ▷ C₅×C₇²×C₂₉
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.