Subgroups — #34118564

Order 20202.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23758836	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15668359	—	7	1	no	maximal, Hall
5	#13095538	—	13	1	no	maximal, Hall
6	#13089650	—	7	1	no	Hall
7	C₁₃×D₃₇	—	7	1	no	Hall
8	#11715912	—	13	1	no	Hall
9	#10587721	—	37	1	no	maximal, Hall
10	D₂₅₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₁₃×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
12	#63271	—	37	1	no	Hall
13	C₇×C₃₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	D₃₇⋊C₃	—	91	1	no	Hall
15	C₁₃×D₇	—	37	1	no	Hall
16	C₃₇⋊C₃	—	91	1	no	Hall
17	C₇×C₁₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃⋊C₃	—	259	1	no	Hall
19	D₃₇	—	7	1	no	Hall
20	AGL(1,𝔽₇)	—	481	1	no	Hall
21	C₁₃⋊C₃	—	259	1	no	Hall
22	C₃₇	#10587721	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₃	—	259	1	no	Hall
24	ΓL(1,𝔽₈)	—	481	1	no	Hall
25	D₇	—	37	1	no	Hall
26	C₁₃	#13095538	1	1	yes	characteristic, complemented, Sylow
27	C₇	#15668359	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3367	1	no	Hall
29	C₃	—	3367	1	no	Sylow
30	C₂	—	259	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₃₇
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.