Subgroups — C₅²×D₄₇₇ #37558705

Order 23850.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅²×D₁₅₉	—	3	1	no	maximal
3	C₅×D₄₇₇	C₅	1	6	yes	maximal, direct product factor
4	C₃×C₅²×C₅₃	D₃	1	1	yes	characteristic
5	C₅²×D₅₃	—	9	1	no	Hall
6	C₅×C₉×C₅₃	C₂×C₅	1	6	yes	complemented
7	C₅×D₁₅₉	—	3	6	no	—
8	C₅²×C₅₃	D₉	1	1	yes	characteristic, complemented, Hall
9	D₄₇₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₅₃	C₅×D₃	1	6	yes	—
11	C₅×D₅₃	—	9	6	no	—
12	C₉×C₅₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
13	C₅²×D₉	—	53	1	no	maximal, Hall
14	D₁₅₉	—	3	1	no	—
15	C₅×C₅₃	C₅×D₉	1	6	yes	complemented
16	C₅²×C₉	D₅₃	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅₃	C₅²×D₃	1	1	yes	characteristic
18	C₅²×D₃	—	159	1	no	—
19	D₅₃	—	9	1	no	Hall
20	C₅×D₉	—	53	6	no	—
21	C₃×C₅²	D₁₅₉	1	1	yes	characteristic
22	C₅₃	C₅²×D₉	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₅²	—	477	1	no	Hall
24	C₅×C₉	C₅×D₅₃	1	6	yes	complemented
25	C₅×D₃	—	159	6	no	—
26	C₅²	D₄₇₇	1	1	yes	characteristic, direct product factor, Sylow
27	D₉	—	53	1	no	Hall
28	C₃×C₅	C₅×D₁₅₉	1	6	yes	—
29	C₂×C₅	—	477	6	no	—
30	C₉	C₅²×D₅₃	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	159	1	no	—
32	C₅	C₅×D₄₇₇	1	6	yes	direct product factor
33	C₃	C₅²×D₁₅₉	1	1	yes	characteristic
34	C₂	—	477	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₄₇₇
commutator, cosocle, hypocenter	C₉×C₅₃	C₂×C₅²
Frattini	C₃	C₅²×D₁₅₉
Fitting	C₅²×C₉×C₅₃	C₂
socle	C₃×C₅²×C₅₃	D₃
LCS	G ▷ C₉×C₅₃
UCS	C₁ ◁ C₅²

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.