Subgroups — C₇²×C₁₁×A₅ #44568956

Order 32340.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁×A₄	—	5	1	no	maximal, Hall
2	C₇²×D₅×C₁₁	—	6	1	no	maximal
3	C₇×C₁₁×A₅	C₇	1	8	yes	maximal, direct product factor
4	D₃×C₇²×C₁₁	—	10	1	no	maximal
5	C₇²×A₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₇²×C₁₁	—	6	1	no	Hall
7	C₂²×C₇²×C₁₁	—	5	1	no	Hall
8	C₃×C₇²×C₁₁	—	10	1	no	Hall
9	C₂×C₇²×C₁₁	—	15	1	no	—
10	C₇×C₁₁×A₄	—	5	8	no	—
11	C₇×D₅×C₁₁	—	6	8	no	—
12	C₁₁×A₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	C₇²×A₄	—	5	1	no	Hall
14	C₇²×C₁₁	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
15	C₇²×D₅	—	6	1	no	—
16	D₃×C₇×C₁₁	—	10	8	no	—
17	C₇×A₅	C₇×C₁₁	1	8	yes	direct product factor
18	C₅×C₇×C₁₁	—	6	8	no	—
19	C₂²×C₇×C₁₁	—	5	8	no	—
20	D₃×C₇²	—	10	1	no	—
21	C₅×C₇²	—	6	1	no	Hall
22	C₃×C₇×C₁₁	—	10	8	no	—
23	C₂²×C₇²	—	5	1	no	Hall
24	C₂×C₇×C₁₁	—	15	8	no	—
25	C₃×C₇²	—	10	1	no	Hall
26	C₁₁×A₄	—	5	1	no	Hall
27	D₅×C₁₁	—	6	1	no	—
28	C₂×C₇²	—	15	1	no	—
29	C₇×A₄	—	5	8	no	—
30	C₇×C₁₁	C₇×A₅	1	8	yes	direct product factor
31	C₇×D₅	—	6	8	no	—
32	D₃×C₁₁	—	10	1	no	—
33	A₅	C₇²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
34	C₅×C₁₁	—	6	1	no	Hall
35	C₇²	C₁₁×A₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₁₁	—	5	1	no	Hall
37	D₃×C₇	—	10	8	no	—
38	C₅×C₇	—	6	8	no	—
39	C₃×C₁₁	—	10	1	no	Hall
40	C₂²×C₇	—	5	8	no	—
41	C₂×C₁₁	—	15	1	no	—
42	C₃×C₇	—	10	8	no	—
43	C₂×C₇	—	15	8	no	—
44	A₄	—	5	1	no	Hall
45	C₁₁	C₇²×A₅	1	1	yes	characteristic, direct product factor, Sylow
46	D₅	—	6	1	no	—
47	C₇	C₇×C₁₁×A₅	1	8	yes	direct product factor
48	D₃	—	10	1	no	—
49	C₅	—	6	1	no	Sylow
50	C₂²	—	5	1	no	Sylow
51	C₃	—	10	1	no	Sylow
52	C₂	—	15	1	no	—

	subgroup	G/H
center, Fitting, hypercenter	C₇²×C₁₁	A₅
commutator, hypocenter	A₅	C₇²×C₁₁
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₇²×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₁×A₅	C₇	direct (N × H)
5. C₇²×A₅	C₁₁	direct (N × H)
12. C₁₁×A₅	C₇²	direct (N × H)
14. C₇²×C₁₁	A₅	direct (N × H)
17. C₇×A₅	C₇×C₁₁	direct (N × H)
30. C₇×C₁₁	C₇×A₅	direct (N × H)
33. A₅	C₇²×C₁₁	direct (N × H)
35. C₇²	C₁₁×A₅	direct (N × H)
45. C₁₁	C₇²×A₅	direct (N × H)
47. C₇	C₇×C₁₁×A₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇²×C₁₁×A₄	5
C₇²×D₅×C₁₁	6
C₇×C₁₁×A₅	7
D₃×C₇²×C₁₁	10
C₇²×A₅	11

Subgroups — C72×C11×A5 #44568956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₁₁×A₅ #44568956