Subgroups — C₁₂₇×#1039⋊C₃ #49185366

Order 38100.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²⋊C₃×C₁₂₇	C₂	1	1	yes	maximal, characteristic
2	#1039×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²⋊C₃×C₁₂₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₅²×C₁₂₇	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₁₂₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	Dic₅×C₁₂₇	—	15	2	no	—
7	C₃×C₄×C₁₂₇	—	25	1	no	maximal, Hall
8	C₂×C₅×C₁₂₇	—	3	2	no	—
9	C₂×C₃×C₁₂₇	—	25	1	no	—
10	C₅×C₁₂₇	—	3	2	no	—
11	C₄×C₁₂₇	—	25	1	no	Hall
12	C₃×C₁₂₇	—	25	1	no	Hall
13	#1039⋊C₃	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₂₇	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
15	C₂×C₅²⋊C₃	C₂×C₁₂₇	1	1	yes	characteristic
16	C₁₂₇	#1039⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	#1039	C₃×C₁₂₇	1	1	yes	characteristic, complemented, Hall
18	C₅²⋊C₃	C₄×C₁₂₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅²	C₂×C₃×C₁₂₇	1	1	yes	characteristic
20	C₅²	C₃×C₄×C₁₂₇	1	1	yes	characteristic, complemented, Sylow
21	Dic₅	—	15	2	no	—
22	C₃×C₄	—	25	1	no	Hall
23	C₂×C₅	—	3	2	no	—
24	C₂×C₃	—	25	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	25	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	C₁₂₇×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic

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.