Subgroups — #43249353

Order 28420.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₉×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	D₅	1	1	yes	characteristic
5	C₅×D₇×C₂₉	—	14	4	no	—
6	C₇²×C₂₉	Dic₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₇×C₂₉	—	2	4	no	—
8	#11758267	—	29	1	no	maximal, Hall
9	Dic₁₄₅	—	49	1	no	maximal, Hall
10	C₅×C₇⋊D₇	D₂₉	1	1	yes	characteristic
11	D₇×C₂₉	—	14	4	no	—
12	C₂×C₅×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	D₁₄₅	1	1	yes	characteristic
19	C₅×D₇	—	14	4	no	—
20	C₂×C₂₉	—	49	1	no	—
21	C₇²	Dic₁₄₅	1	1	yes	characteristic, complemented, Sylow
22	C₅×C₇	—	2	4	no	—
23	C₂₉	#11758267	1	1	yes	characteristic, complemented, Sylow
24	Dic₅	—	1421	1	no	Hall
25	D₇	—	14	4	no	—
26	C₂×C₅	—	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	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇²×C₂₉	C₄
prime radical, cosocle	C₅×C₂₉×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.