Subgroups — C₅×#92150⋊C₅ #27130890

Order 12100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#11925892	C₂	1	1	yes	maximal, characteristic
2	C₅×#10597243	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×#92150	C₅	1	1	yes	maximal, characteristic, complemented
4	#92150⋊C₅	C₅	1	5	yes	maximal, direct product factor
5	C₅×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic
6	#11925892	C₂×C₅	1	5	yes	—
7	C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
8	#10597243	C₄×C₅	1	5	yes	complemented
9	C₅×AGL(1,𝔽₁₁)	—	22	6	no	—
10	#92150	C₅²	1	1	yes	characteristic, complemented, Hall
11	C₅×C₁₁⋊C₅	—	22	6	no	—
12	C₁₁⋊D₁₁	C₂×C₅²	1	1	yes	characteristic
13	C₁₁²	C₄×C₅²	1	1	yes	characteristic, complemented, Sylow
14	C₅×D₁₁	—	22	6	no	—
15	AGL(1,𝔽₁₁)	—	22	30	no	—
16	C₄×C₅²	—	121	1	no	maximal, Hall
17	C₅×C₁₁	—	2	6	no	—
18	C₁₁⋊C₅	—	22	30	no	—
19	C₂×C₅²	—	121	1	no	—
20	C₅²	—	121	1	no	Sylow
21	D₁₁	—	22	6	no	—
22	C₄×C₅	—	121	5	no	—
23	C₄×C₅	—	121	1	no	—
24	C₁₁	—	2	6	no	—
25	C₂×C₅	—	121	5	no	—
26	C₂×C₅	—	121	1	no	—
27	C₅	—	121	5	no	—
28	C₅	#92150⋊C₅	1	1	yes	characteristic, direct product factor
29	C₄	—	121	1	no	Sylow
30	C₂	—	121	1	no	—

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.