Subgroups — C₁₃⋊C₃×D₃₃₅ #39908424

Order 26130.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃⋊C₃×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×D₆₇	—	5	1	no	maximal, Hall
4	C₅×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃⋊C₃×C₆₇	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃×D₃₃₅	—	13	1	no	maximal, Hall
7	C₁₃×D₆₇	—	5	1	no	Hall
8	C₃×C₅×C₆₇	—	13	1	no	Hall
9	C₁₃×C₆₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
10	D₃₃₅	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₆₇	—	65	1	no	Hall
12	D₅×C₁₃⋊C₃	—	67	1	no	maximal, Hall
13	C₅×C₆₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₃×C₆₇	—	13	1	no	Hall
15	C₅×C₁₃⋊C₃	D₆₇	1	1	yes	characteristic, complemented, Hall
16	D₆₇	—	5	1	no	Hall
17	D₅×C₁₃	—	67	1	no	Hall
18	C₂×C₁₃⋊C₃	—	335	1	no	Hall
19	C₆₇	D₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₅×C₁₃	C₃×D₆₇	1	1	yes	characteristic, complemented, Hall
21	C₁₃⋊C₃	D₃₃₅	1	1	yes	characteristic, direct product factor, Hall
22	C₃×D₅	—	871	1	no	Hall
23	C₂×C₁₃	—	335	1	no	Hall
24	C₃×C₅	—	13	1	no	Hall
25	C₁₃	C₃×D₃₃₅	1	1	yes	characteristic, complemented, Sylow
26	D₅	—	67	1	no	Hall
27	C₂×C₃	—	4355	1	no	Hall
28	C₅	C₁₃⋊C₃×D₆₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	13	1	no	Sylow
30	C₂	—	335	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₃×C₆₇	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₆₇
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.