Subgroups — C₇²×C₁₃×A₅ #50304534

Order 38220.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×A₄×C₁₃	—	5	1	no	maximal, Hall
2	C₇²×D₅×C₁₃	—	6	1	no	maximal
3	C₇×C₁₃×A₅	C₇	1	8	yes	maximal, direct product factor
4	D₃×C₇²×C₁₃	—	10	1	no	maximal
5	C₅×C₇²×C₁₃	—	6	1	no	Hall
6	C₇²×A₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₇²×C₁₃	—	5	1	no	Hall
8	C₃×C₇²×C₁₃	—	10	1	no	Hall
9	C₂×C₇²×C₁₃	—	15	1	no	—
10	C₇×A₄×C₁₃	—	5	8	no	—
11	C₇×D₅×C₁₃	—	6	8	no	—
12	C₁₃×A₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	C₇²×C₁₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor, Hall
14	C₇²×A₄	—	5	1	no	Hall
15	D₃×C₇×C₁₃	—	10	8	no	—
16	C₇²×D₅	—	6	1	no	—
17	C₅×C₇×C₁₃	—	6	8	no	—
18	C₇×A₅	C₇×C₁₃	1	8	yes	direct product factor
19	C₂²×C₇×C₁₃	—	5	8	no	—
20	D₃×C₇²	—	10	1	no	—
21	C₃×C₇×C₁₃	—	10	8	no	—
22	C₅×C₇²	—	6	1	no	Hall
23	C₂²×C₇²	—	5	1	no	Hall
24	C₂×C₇×C₁₃	—	15	8	no	—
25	A₄×C₁₃	—	5	1	no	Hall
26	C₃×C₇²	—	10	1	no	Hall
27	D₅×C₁₃	—	6	1	no	—
28	C₂×C₇²	—	15	1	no	—
29	C₇×C₁₃	C₇×A₅	1	8	yes	direct product factor
30	C₇×A₄	—	5	8	no	—
31	D₃×C₁₃	—	10	1	no	—
32	C₇×D₅	—	6	8	no	—
33	C₅×C₁₃	—	6	1	no	Hall
34	A₅	C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
35	C₂²×C₁₃	—	5	1	no	Hall
36	C₇²	C₁₃×A₅	1	1	yes	characteristic, direct product factor, Sylow
37	D₃×C₇	—	10	8	no	—
38	C₃×C₁₃	—	10	1	no	Hall
39	C₅×C₇	—	6	8	no	—
40	C₂²×C₇	—	5	8	no	—
41	C₂×C₁₃	—	15	1	no	—
42	C₃×C₇	—	10	8	no	—
43	C₂×C₇	—	15	8	no	—
44	C₁₃	C₇²×A₅	1	1	yes	characteristic, direct product factor, Sylow
45	A₄	—	5	1	no	Hall
46	D₅	—	6	1	no	—
47	C₇	C₇×C₁₃×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×C₁₃	A₅
commutator, hypocenter	A₅	C₇²×C₁₃
Frattini	C₁	G
LCS	G ▷ A₅
UCS	C₁ ◁ C₇²×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₇×C₁₃×A₅	C₇	direct (N × H)
6. C₇²×A₅	C₁₃	direct (N × H)
12. C₁₃×A₅	C₇²	direct (N × H)
13. C₇²×C₁₃	A₅	direct (N × H)
18. C₇×A₅	C₇×C₁₃	direct (N × H)
29. C₇×C₁₃	C₇×A₅	direct (N × H)
34. A₅	C₇²×C₁₃	direct (N × H)
36. C₇²	C₁₃×A₅	direct (N × H)
44. C₁₃	C₇²×A₅	direct (N × H)
47. C₇	C₇×C₁₃×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×A₄×C₁₃	5
C₇²×D₅×C₁₃	6
C₇×C₁₃×A₅	7
D₃×C₇²×C₁₃	10
C₇²×A₅	13

Subgroups — C72×C13×A5 #50304534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×C₁₃×A₅ #50304534