Subgroups — #37555432

Order 23548.

25 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26044461	C₂	1	1	yes	maximal, characteristic
2	#19154635	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₉×#1181	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂₉×D₂₉	C₂×C₇	1	1	yes	characteristic
5	C₂₉²	C₄×C₇	1	1	yes	characteristic, complemented, Sylow
6	AGL(1,𝔽₂₉)	—	29	1	no	maximal
7	C₄×C₂₉⋊C₇	—	29	1	no	maximal
8	C₂×C₂₉⋊C₇	—	29	1	no	—
9	D₂₉⋊C₇	—	29	1	no	—
10	C₂₉⋊C₇	—	29	1	no	—
11	C₂₉⋊C₇	—	29	1	no	—
12	#1181	C₂₉⋊C₇	1	1	yes	characteristic, complemented
13	C₄×C₂₉	—	203	1	no	—
14	C₂×C₂₉	—	203	1	no	—
15	D₂₉	C₂×C₂₉⋊C₇	1	1	yes	characteristic
16	C₂₉	—	28	1	no	—
17	C₂₉	C₄×C₂₉⋊C₇	1	1	yes	characteristic, complemented
18	C₂₉	AGL(1,𝔽₂₉)	1	1	yes	characteristic, complemented
19	C₄×C₇	—	841	1	no	Hall
20	C₂×C₇	—	841	1	no	—
21	C₇	—	841	1	no	Sylow
22	C₄	—	203	1	no	Sylow
23	C₂	—	203	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₉²	C₄×C₇
prime radical	#26044461	C₂
cosocle	C₂₉×D₂₉	C₂×C₇
LCS	G ▷ C₂₉²
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.