Subgroups — C₃²×D₁₇₇₅ #44544019

Order 31950.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₅×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₇₇₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₃₅₅	—	5	1	no	maximal
4	C₃×C₂₅×C₇₁	C₂×C₃	1	4	yes	complemented
5	D₁₇₇₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₃²×C₅×C₇₁	D₅	1	1	yes	characteristic
7	C₃×D₃₅₅	—	5	4	no	—
8	C₂₅×C₇₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃²×D₇₁	—	25	1	no	Hall
10	C₃×C₅×C₇₁	C₃×D₅	1	4	yes	—
11	D₃₅₅	—	5	1	no	—
12	C₃²×C₇₁	D₂₅	1	1	yes	characteristic, complemented, Hall
13	C₃²×D₂₅	—	71	1	no	maximal, Hall
14	C₃×D₇₁	—	25	4	no	—
15	C₅×C₇₁	C₃²×D₅	1	1	yes	characteristic
16	C₃²×C₂₅	D₇₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₇₁	C₃×D₂₅	1	4	yes	complemented
18	C₃×D₂₅	—	71	4	no	—
19	D₇₁	—	25	1	no	Hall
20	C₃²×D₅	—	355	1	no	—
21	C₃×C₂₅	C₃×D₇₁	1	4	yes	complemented
22	C₇₁	C₃²×D₂₅	1	1	yes	characteristic, complemented, Sylow
23	D₂₅	—	71	1	no	Hall
24	C₃²×C₅	D₃₅₅	1	1	yes	characteristic
25	C₃×D₅	—	355	4	no	—
26	C₂₅	C₃²×D₇₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃²	—	1775	1	no	Hall
28	C₃×C₅	C₃×D₃₅₅	1	4	yes	—
29	D₅	—	355	1	no	—
30	C₃²	D₁₇₇₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	—	1775	4	no	—
32	C₅	C₃²×D₃₅₅	1	1	yes	characteristic
33	C₃	C₃×D₁₇₇₅	1	4	yes	direct product factor
34	C₂	—	1775	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₇₇₅
commutator, cosocle, hypocenter	C₂₅×C₇₁	C₂×C₃²
Frattini	C₅	C₃²×D₃₅₅
Fitting	C₃²×C₂₅×C₇₁	C₂
socle	C₃²×C₅×C₇₁	D₅
LCS	G ▷ C₂₅×C₇₁
UCS	C₁ ◁ C₃²

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.