Subgroups — C₂×D₈₆₉₅ #46852016

Order 34780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₆₉₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₃₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃₇×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₇₃₉	—	5	1	no	maximal, Hall
5	C₂×C₃₇×C₄₇	D₅	1	1	yes	characteristic, complemented
6	D₁₇₃₉	—	5	2	no	—
7	C₃₇×C₄₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₂₃₅	—	37	1	no	maximal, Hall
9	C₂×D₁₈₅	—	47	1	no	maximal, Hall
10	C₂×C₅×C₄₇	D₃₇	1	1	yes	characteristic, complemented
11	D₂₃₅	—	37	2	no	—
12	C₂×C₅×C₃₇	D₄₇	1	1	yes	characteristic, complemented
13	D₁₈₅	—	47	2	no	—
14	C₅×C₄₇	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
15	C₂×D₄₇	—	185	1	no	Hall
16	C₅×C₃₇	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃₇	—	235	1	no	Hall
18	C₂×C₄₇	D₁₈₅	1	1	yes	characteristic, complemented
19	D₄₇	—	185	2	no	—
20	C₂×C₃₇	D₂₃₅	1	1	yes	characteristic, complemented
21	D₃₇	—	235	2	no	—
22	C₄₇	C₂×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
23	C₃₇	C₂×D₂₃₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₅	—	1739	1	no	Hall
25	C₂×C₅	D₁₇₃₉	1	1	yes	characteristic, complemented
26	D₅	—	1739	2	no	—
27	C₅	C₂×D₁₇₃₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	8695	1	no	Sylow
29	C₂	—	8695	2	no	—
30	C₂	D₈₆₉₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₈₆₉₅
commutator, cosocle, hypocenter	C₅×C₃₇×C₄₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₃₇×C₄₇	C₂
LCS	G ▷ C₅×C₃₇×C₄₇
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.