Subgroups — C₁₁⋊C₅×#5997 #24924749

Order 10780.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁⋊C₅×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₇²×C₁₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×#5997	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×C₇⋊D₇	C₂×C₅	1	1	yes	characteristic
5	C₅×#5997	—	11	1	no	maximal, Hall
6	D₇×C₁₁⋊C₅	—	14	4	no	—
7	C₇²×C₁₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇⋊D₇	—	11	1	no	—
9	C₇×C₁₁⋊C₅	—	2	4	no	—
10	C₅×C₇²	—	11	1	no	Hall
11	C₄×C₁₁⋊C₅	—	49	1	no	maximal, Hall
12	#5997	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
13	C₁₁×D₇	—	14	4	no	—
14	C₂×C₁₁⋊C₅	—	49	1	no	—
15	C₇⋊D₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic
16	C₇×C₁₁	—	2	4	no	—
17	C₅×D₇	—	154	4	no	—
18	C₁₁⋊C₅	#5997	1	1	yes	characteristic, direct product factor, Hall
19	C₇²	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
20	C₄×C₁₁	—	49	1	no	Hall
21	C₅×C₇	—	22	4	no	—
22	C₂×C₁₁	—	49	1	no	—
23	C₄×C₅	—	539	1	no	Hall
24	D₇	—	14	4	no	—
25	C₁₁	C₅×#5997	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	—	539	1	no	—
27	C₇	—	2	4	no	—
28	C₅	—	11	1	no	Sylow
29	C₄	—	49	1	no	Sylow
30	C₂	—	49	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₁	C₄×C₅
prime radical	C₁₁⋊C₅×C₇⋊D₇	C₂
cosocle	C₁₁×C₇⋊D₇	C₂×C₅
LCS	G ▷ C₇²×C₁₁
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.