Subgroups — C₁₃⋊C₃×D₃₇₇ #44440607

Order 29406.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₂₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₃₇₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₁₃⋊C₃×D₂₉	—	13	1	no	maximal
5	C₃×D₃₇₇	—	13	1	no	maximal
6	C₃×C₁₃×C₂₉	—	13	1	no	—
7	C₂₉×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
8	D₁₃×C₁₃⋊C₃	—	29	1	no	maximal, Hall
9	D₃₇₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
10	C₁₃×D₂₉	—	13	1	no	—
11	C₁₃×C₁₃⋊C₃	D₂₉	1	1	yes	characteristic, complemented, Hall
12	C₁₃×C₂₉	—	6	2	no	—
13	C₁₃×C₂₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
14	C₁₃×C₂₉	C₃×D₁₃	1	1	yes	characteristic, complemented
15	C₁₃×D₁₃	—	29	1	no	Hall
16	C₃×D₂₉	—	169	1	no	Hall
17	C₁₃²	C₃×D₂₉	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₂₉	—	13	1	no	Hall
19	C₃×D₁₃	—	377	1	no	—
20	C₂×C₁₃⋊C₃	—	377	1	no	—
21	D₂₉	—	13	1	no	Hall
22	C₃×C₁₃	—	13	1	no	—
23	C₁₃⋊C₃	D₃₇₇	1	1	yes	characteristic, direct product factor
24	C₂₉	D₁₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₁₃	—	377	1	no	—
26	D₁₃	—	29	1	no	—
27	C₁₃	—	6	2	no	—
28	C₁₃	C₃×D₃₇₇	1	1	yes	characteristic, complemented
29	C₁₃	C₁₃⋊C₃×D₂₉	1	1	yes	characteristic, complemented
30	C₂×C₃	—	4901	1	no	Hall
31	C₃	—	13	1	no	Sylow
32	C₂	—	377	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₂₉	C₂×C₃
LCS	G ▷ C₁₃²×C₂₉
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.