Subgroups — C₅×#14559102 #27130973

Order 12100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	#14559102	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×#92150	—	5	1	no	maximal
5	C₅×C₁₁⋊D₁₁	—	2	2	no	—
6	C₅×C₁₁⋊D₁₁	D₅	1	1	yes	characteristic
7	C₅×C₁₁⋊D₁₁	C₂×C₅	1	1	yes	characteristic
8	C₅×C₁₁²	—	2	2	no	—
9	C₅×C₁₁²	Dic₅	1	1	yes	characteristic, complemented
10	C₅×C₁₁²	C₄×C₅	1	1	yes	characteristic, complemented
11	C₅²×D₁₁	—	22	6	no	—
12	#92150	—	5	1	no	Hall
13	C₅²×C₁₁	—	2	6	no	—
14	C₁₁⋊D₁₁	C₅×D₅	1	1	yes	characteristic
15	C₁₁²	C₅×Dic₅	1	1	yes	characteristic, complemented, Sylow
16	C₅×D₁₁	—	22	6	no	—
17	C₅×D₁₁	—	22	6	no	—
18	C₅×D₁₁	—	22	24	no	—
19	C₅×Dic₅	—	121	1	no	maximal, Hall
20	C₅×C₁₁	—	2	24	no	—
21	C₅×C₁₁	—	2	6	no	—
22	C₅×C₁₁	—	2	6	no	—
23	C₂×C₅²	—	121	1	no	—
24	C₅²	#92150	1	1	yes	characteristic, complemented, Sylow
25	D₁₁	—	22	6	no	—
26	C₄×C₅	—	605	1	no	—
27	Dic₅	—	121	1	no	—
28	C₁₁	—	2	6	no	—
29	C₂×C₅	—	121	1	no	—
30	C₂×C₅	—	121	1	no	—
31	C₂×C₅	—	242	2	no	—
32	C₅	—	2	2	no	—
33	C₅	C₅×#92150	1	1	yes	characteristic, complemented
34	C₅	#14559102	1	1	yes	characteristic, direct product factor
35	C₄	—	605	1	no	Sylow
36	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.