Subgroups — C₂×D₃₃₃₅ #27211124

Order 13340.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₃₃₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₃×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₃×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₆₆₇	—	5	1	no	maximal, Hall
5	C₂×C₂₃×C₂₉	D₅	1	1	yes	characteristic, complemented
6	D₆₆₇	—	5	2	no	—
7	C₂₃×C₂₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₁₄₅	—	23	1	no	maximal, Hall
9	C₂×D₁₁₅	—	29	1	no	maximal, Hall
10	C₂×C₅×C₂₉	D₂₃	1	1	yes	characteristic, complemented
11	D₁₄₅	—	23	2	no	—
12	C₂×C₅×C₂₃	D₂₉	1	1	yes	characteristic, complemented
13	D₁₁₅	—	29	2	no	—
14	C₅×C₂₉	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
15	C₂×D₂₉	—	115	1	no	Hall
16	C₅×C₂₃	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
17	C₂×D₂₃	—	145	1	no	Hall
18	C₂×C₂₉	D₁₁₅	1	1	yes	characteristic, complemented
19	D₂₉	—	115	2	no	—
20	C₂×C₂₃	D₁₄₅	1	1	yes	characteristic, complemented
21	D₂₃	—	145	2	no	—
22	C₂₉	C₂×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
23	C₂₃	C₂×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₅	—	667	1	no	Hall
25	C₂×C₅	D₆₆₇	1	1	yes	characteristic, complemented
26	D₅	—	667	2	no	—
27	C₅	C₂×D₆₆₇	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	3335	1	no	Sylow
29	C₂	—	3335	2	no	—
30	C₂	D₃₃₃₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃₃₃₅
commutator, cosocle, hypocenter	C₅×C₂₃×C₂₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₃×C₂₉	C₂
LCS	G ▷ C₅×C₂₃×C₂₉
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.