Subgroups — D₈₅⋊D₇₉ #41001718

Order 26860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×D₈₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×D₃₉₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₃₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₇×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₇×D₇₉	—	5	1	no	maximal, Hall
6	D₁₃₄₃	D₅	1	1	yes	characteristic, complemented
7	C₁₇×D₇₉	—	5	1	no	—
8	D₁₇×C₇₉	—	5	1	no	—
9	D₅×D₇₉	—	17	1	no	maximal, Hall
10	C₁₇×C₇₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₃₉₅	D₁₇	1	1	yes	characteristic, complemented
12	C₅×D₇₉	—	17	1	no	—
13	D₅×C₇₉	—	17	1	no	—
14	C₅×C₇₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
15	D₅×D₁₇	—	79	1	no	maximal, Hall
16	C₂×D₇₉	—	85	1	no	Hall
17	D₈₅	D₇₉	1	1	yes	characteristic, complemented
18	C₅×D₁₇	—	79	1	no	—
19	D₅×C₁₇	—	79	1	no	—
20	C₂×C₇₉	—	85	1	no	—
21	D₇₉	—	5	1	no	—
22	D₇₉	—	17	1	no	—
23	C₅×C₁₇	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
24	C₇₉	D₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₁₇	—	395	1	no	Hall
26	C₂×C₁₇	—	395	1	no	—
27	D₁₇	—	5	1	no	—
28	D₁₇	—	79	1	no	—
29	C₂×D₅	—	1343	1	no	Hall
30	C₁₇	D₅×D₇₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	1343	1	no	—
32	D₅	—	17	1	no	—
33	D₅	—	79	1	no	—
34	C₅	D₁₇×D₇₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	6715	1	no	Sylow
36	C₂	—	1343	1	no	—
37	C₂	—	85	1	no	—
38	C₂	—	395	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇×C₇₉	C₂²
LCS	G ▷ C₅×C₁₇×C₇₉
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.