Subgroups — D₇₀₉₅ #28382002

Order 14190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₂₃₆₅	—	3	1	no	maximal, Hall
3	D₁₄₁₉	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₄₃	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₁×C₄₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₆₄₅	—	11	1	no	maximal, Hall
7	D₄₇₃	—	15	1	no	Hall
8	C₃×C₅×C₄₃	D₁₁	1	1	yes	characteristic, complemented, Hall
9	C₁₁×C₄₃	D₁₅	1	1	yes	characteristic, complemented, Hall
10	D₂₁₅	—	33	1	no	Hall
11	D₁₆₅	—	43	1	no	maximal, Hall
12	D₁₂₉	—	55	1	no	Hall
13	C₅×C₄₃	D₃₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₁	D₄₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄₃	D₅₅	1	1	yes	characteristic, complemented, Hall
16	D₅₅	—	129	1	no	Hall
17	D₄₃	—	165	1	no	Hall
18	D₃₃	—	215	1	no	Hall
19	C₅×C₁₁	D₁₂₉	1	1	yes	characteristic, complemented, Hall
20	C₄₃	D₁₆₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₁	D₂₁₅	1	1	yes	characteristic, complemented, Hall
22	D₁₅	—	473	1	no	Hall
23	D₁₁	—	645	1	no	Hall
24	C₃×C₅	D₄₇₃	1	1	yes	characteristic, complemented, Hall
25	C₁₁	D₆₄₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	1419	1	no	Hall
27	D₃	—	2365	1	no	Hall
28	C₅	D₁₄₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₂₃₆₅	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	7095	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₁×C₄₃	C₂
LCS	G ▷ C₃×C₅×C₁₁×C₄₃
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.