Subgroups — C₂×#26044455 #37555443

Order 23548.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19154634	C₂	1	1	yes	maximal, characteristic, complemented
2	#26044455	C₂	1	2	yes	maximal, direct product factor
3	#19154634	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₉⋊D₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₂₉²	C₂×C₇	1	1	yes	characteristic, complemented
6	C₂₉⋊D₂₉	C₂×C₇	1	2	yes	complemented
7	C₂₉²	C₂²×C₇	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₂₉⋊C₇	—	29	30	no	maximal
9	C₂×C₂₉⋊C₇	—	29	30	no	—
10	D₂₉⋊C₇	—	29	60	no	—
11	C₂₉⋊C₇	—	29	30	no	—
12	C₂×D₂₉	—	29	30	no	—
13	C₂×C₂₉	D₂₉⋊C₇	1	30	yes	complemented
14	D₂₉	—	29	60	no	—
15	C₂₉	C₂×D₂₉⋊C₇	1	30	yes	complemented
16	C₂²×C₇	—	841	1	no	Hall
17	C₂×C₇	—	841	2	no	—
18	C₂×C₇	—	841	1	no	—
19	C₇	—	841	1	no	Sylow
20	C₂²	—	841	1	no	Sylow
21	C₂	—	841	2	no	—
22	C₂	#26044455	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#26044455
commutator, cosocle, hypocenter	C₂₉²	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₂₉²	C₂×C₇
LCS	G ▷ C₂₉²
UCS	C₁ ◁ C₂

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.