Subgroups — C₂×C₂₉×#3861 #22555352

Order 8526.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3861	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇²×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×ΓL(1,𝔽₈)×C₂₉	—	7	8	no	maximal
5	ΓL(1,𝔽₈)×C₂₉	—	7	8	no	—
6	C₂×C₇×C₂₉	ΓL(1,𝔽₈)	1	8	yes	complemented
7	C₂×#3861	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₂₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
9	C₂×C₃×C₂₉	—	49	1	no	Hall
10	#3861	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇²	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
12	C₃×C₂₉	—	49	1	no	Hall
13	C₂×C₂₉	#3861	1	1	yes	characteristic, direct product factor, Hall
14	C₇²	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
15	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
16	C₂₉	C₂×#3861	1	1	yes	characteristic, direct product factor, Sylow
17	ΓL(1,𝔽₈)	—	7	8	no	—
18	C₂×C₇	ΓL(1,𝔽₈)×C₂₉	1	8	yes	complemented
19	C₇	C₂×ΓL(1,𝔽₈)×C₂₉	1	8	yes	complemented
20	C₂×C₃	—	49	1	no	Hall
21	C₃	—	49	1	no	Sylow
22	C₂	C₂₉×#3861	1	1	yes	characteristic, direct product factor, Sylow

Splittings G = N ⋊ H with N normal; H ≅ G/N.