Subgroups — C₂×D₆₇₁₅ #41001725

Order 26860.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₁₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₇×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₇×C₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₃₄₃	—	5	1	no	maximal, Hall
5	C₂×C₁₇×C₇₉	D₅	1	1	yes	characteristic, complemented
6	D₁₃₄₃	—	5	2	no	—
7	C₂×D₃₉₅	—	17	1	no	maximal, Hall
8	C₁₇×C₇₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₅×C₇₉	D₁₇	1	1	yes	characteristic, complemented
10	D₃₉₅	—	17	2	no	—
11	C₅×C₇₉	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
12	C₂×D₈₅	—	79	1	no	maximal, Hall
13	C₂×D₇₉	—	85	1	no	Hall
14	C₂×C₅×C₁₇	D₇₉	1	1	yes	characteristic, complemented
15	D₈₅	—	79	2	no	—
16	C₂×C₇₉	D₈₅	1	1	yes	characteristic, complemented
17	D₇₉	—	85	2	no	—
18	C₅×C₁₇	C₂×D₇₉	1	1	yes	characteristic, complemented, Hall
19	C₇₉	C₂×D₈₅	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₁₇	—	395	1	no	Hall
21	C₂×C₁₇	D₃₉₅	1	1	yes	characteristic, complemented
22	D₁₇	—	395	2	no	—
23	C₂×D₅	—	1343	1	no	Hall
24	C₁₇	C₂×D₃₉₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	D₁₃₄₃	1	1	yes	characteristic, complemented
26	D₅	—	1343	2	no	—
27	C₅	C₂×D₁₃₄₃	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	6715	1	no	Sylow
29	C₂	—	6715	2	no	—
30	C₂	D₆₇₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₆₇₁₅
commutator, cosocle, hypocenter	C₅×C₁₇×C₇₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₇×C₇₉	C₂
LCS	G ▷ C₅×C₁₇×C₇₉
UCS	C₁ ◁ C₂

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.