Subgroups — #3874×C₁₇₉ #41001618

Order 26850.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊C₃×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₅×C₁₇₉	—	3	1	no	maximal, Hall
3	C₅²×C₁₇₉	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅×C₁₇₉	—	15	1	no	—
5	D₅×C₁₇₉	—	3	1	no	—
6	D₃×C₁₇₉	—	25	1	no	maximal, Hall
7	C₅×C₁₇₉	—	3	1	no	—
8	C₅×C₁₇₉	—	3	1	no	—
9	C₃×C₁₇₉	—	25	1	no	Hall
10	C₂×C₁₇₉	—	15	1	no	Hall
11	C₁₇₉	#3874	1	1	yes	characteristic, direct product factor, Sylow
12	#3874	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₅²⋊C₃	C₂×C₁₇₉	1	1	yes	characteristic, complemented, Hall
14	C₅×D₅	—	3	1	no	Hall
15	C₅²	D₃×C₁₇₉	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₅	—	15	1	no	—
17	D₅	—	3	1	no	—
18	D₃	—	25	1	no	Hall
19	C₅	—	3	1	no	—
20	C₅	—	3	1	no	—
21	C₃	—	25	1	no	Sylow
22	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇₉	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂×C₁₇₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇₉	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₁₇₉

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.