Subgroups — C₅×#14559075 #27130889

Order 12100.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#11925893	C₂	1	1	yes	maximal, characteristic
2	C₅×#10597245	C₄	1	1	yes	characteristic, complemented, Hall
3	C₅×#92150	—	5	1	no	maximal
4	#14559075	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic
6	#11925893	—	2	2	no	—
7	#11925893	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₁²	Dic₅	1	1	yes	characteristic, complemented
9	#10597245	—	2	2	no	—
10	#10597245	C₄×C₅	1	1	yes	characteristic, complemented
11	C₅×AGL(1,𝔽₁₁)	—	22	1	no	—
12	#92150	—	5	1	no	Hall
13	C₅×C₁₁⋊C₅	—	22	1	no	—
14	C₁₁⋊D₁₁	C₅×D₅	1	1	yes	characteristic
15	C₁₁²	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
16	C₅×D₁₁	—	22	1	no	—
17	C₅×D₁₁	—	110	1	no	—
18	AGL(1,𝔽₁₁)	—	22	1	no	—
19	AGL(1,𝔽₁₁)	—	22	4	no	—
20	C₅×Dic₅	—	121	1	no	maximal, Hall
21	C₅×C₁₁	—	2	1	no	—
22	C₅×C₁₁	—	10	1	no	—
23	C₁₁⋊C₅	—	22	1	no	—
24	C₁₁⋊C₅	—	22	4	no	—
25	C₂×C₅²	—	121	1	no	—
26	C₅²	—	121	1	no	Sylow
27	D₁₁	—	22	1	no	—
28	D₁₁	—	110	1	no	—
29	C₄×C₅	—	605	1	no	—
30	Dic₅	—	121	1	no	—
31	C₁₁	—	2	1	no	—
32	C₁₁	—	10	1	no	—
33	C₂×C₅	—	121	1	no	—
34	C₂×C₅	—	121	1	no	—
35	C₂×C₅	—	242	2	no	—
36	C₅	—	121	1	no	—
37	C₅	—	242	2	no	—
38	C₅	#14559075	1	1	yes	characteristic, direct product factor
39	C₄	—	605	1	no	Sylow
40	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.