Subgroups — D₃₀₈₂₅ #72296554

Order 61650.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₅×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₀₂₇₅	—	3	1	no	maximal
3	D₆₁₆₅	—	5	1	no	maximal
4	C₃×C₂₅×C₁₃₇	D₃	1	1	yes	characteristic
5	D₃₄₂₅	—	9	1	no	Hall
6	C₅×C₉×C₁₃₇	D₅	1	1	yes	characteristic
7	D₂₀₅₅	—	15	1	no	—
8	C₂₅×C₁₃₇	D₉	1	1	yes	characteristic, complemented, Hall
9	D₁₂₃₃	—	25	1	no	Hall
10	C₃×C₅×C₁₃₇	D₁₅	1	1	yes	characteristic
11	D₆₈₅	—	45	1	no	—
12	C₉×C₁₃₇	D₂₅	1	1	yes	characteristic, complemented, Hall
13	D₄₁₁	—	75	1	no	—
14	C₅×C₁₃₇	D₄₅	1	1	yes	characteristic
15	D₂₂₅	—	137	1	no	maximal, Hall
16	C₃×C₁₃₇	D₇₅	1	1	yes	characteristic
17	D₁₃₇	—	225	1	no	Hall
18	C₉×C₂₅	D₁₃₇	1	1	yes	characteristic, complemented, Hall
19	D₇₅	—	411	1	no	—
20	C₁₃₇	D₂₂₅	1	1	yes	characteristic, complemented, Sylow
21	D₄₅	—	685	1	no	—
22	C₃×C₂₅	D₄₁₁	1	1	yes	characteristic
23	D₂₅	—	1233	1	no	Hall
24	C₅×C₉	D₆₈₅	1	1	yes	characteristic
25	D₁₅	—	2055	1	no	—
26	C₂₅	D₁₂₃₃	1	1	yes	characteristic, complemented, Sylow
27	D₉	—	3425	1	no	Hall
28	C₃×C₅	D₂₀₅₅	1	1	yes	characteristic
29	D₅	—	6165	1	no	—
30	C₉	D₃₄₂₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	10275	1	no	—
32	C₅	D₆₁₆₅	1	1	yes	characteristic
33	C₃	D₁₀₂₇₅	1	1	yes	characteristic
34	C₂	—	30825	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₅×C₁₃₇	C₂
Frattini	C₃×C₅	D₂₀₅₅
socle	C₃×C₅×C₁₃₇	D₁₅
LCS	G ▷ C₉×C₂₅×C₁₃₇
UCS	C₁

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.