Subgroups — C₄×C₇²×C₈×C₁₃ #72197949

Order 20384.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇²×C₈×C₁₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₇²×C₁₃	C₄	1	2	yes	—
4	C₂×C₄×C₇²×C₁₃	C₂²	1	1	yes	characteristic
5	C₇²×C₈×C₁₃	C₄	1	4	yes	direct product factor
6	C₄×C₇×C₈×C₁₃	C₇	1	8	yes	maximal, direct product factor
7	C₂²×C₇²×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₇²×C₁₃	C₈	1	4	yes	direct product factor
9	C₄×C₇²×C₁₃	C₂×C₄	1	2	yes	—
10	C₄×C₇²×C₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₇×C₈×C₁₃	C₂×C₇	1	16	yes	—
12	C₄²×C₇×C₁₃	C₂×C₇	1	8	yes	—
13	C₂×C₇²×C₁₃	C₄²	1	1	yes	characteristic
14	C₂×C₇²×C₁₃	C₂×C₈	1	2	yes	—
15	C₂×C₇²×C₈	C₂×C₁₃	1	2	yes	—
16	C₄²×C₇²	C₂×C₁₃	1	1	yes	characteristic
17	C₂×C₄×C₇×C₁₃	C₄×C₇	1	16	yes	—
18	C₂×C₄×C₇×C₁₃	C₂²×C₇	1	8	yes	—
19	C₇×C₈×C₁₃	C₄×C₇	1	32	yes	direct product factor
20	C₇²×C₁₃	C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₈×C₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₄×C₇²	C₄×C₁₃	1	2	yes	—
23	C₂×C₄×C₇²	C₂²×C₁₃	1	1	yes	characteristic
24	C₇²×C₈	C₄×C₁₃	1	4	yes	direct product factor
25	C₂²×C₇×C₁₃	C₂×C₄×C₇	1	8	yes	—
26	C₄×C₇×C₁₃	C₇×C₈	1	32	yes	direct product factor
27	C₄×C₇×C₁₃	C₂×C₄×C₇	1	16	yes	—
28	C₄×C₇×C₈	C₇×C₁₃	1	8	yes	direct product factor
29	C₂×C₈×C₁₃	C₂×C₇²	1	2	yes	—
30	C₄²×C₁₃	C₂×C₇²	1	1	yes	characteristic
31	C₂²×C₇²	C₂×C₄×C₁₃	1	1	yes	characteristic
32	C₄×C₇²	C₈×C₁₃	1	4	yes	direct product factor
33	C₄×C₇²	C₂×C₄×C₁₃	1	2	yes	—
34	C₂×C₇×C₁₃	C₄²×C₇	1	8	yes	—
35	C₂×C₇×C₁₃	C₂×C₇×C₈	1	16	yes	—
36	C₂×C₇×C₈	C₂×C₇×C₁₃	1	16	yes	—
37	C₄²×C₇	C₂×C₇×C₁₃	1	8	yes	—
38	C₂×C₄×C₁₃	C₄×C₇²	1	2	yes	—
39	C₂×C₄×C₁₃	C₂²×C₇²	1	1	yes	characteristic
40	C₈×C₁₃	C₄×C₇²	1	4	yes	direct product factor
41	C₂×C₇²	C₄²×C₁₃	1	1	yes	characteristic
42	C₂×C₇²	C₂×C₈×C₁₃	1	2	yes	—
43	C₇×C₁₃	C₄×C₇×C₈	1	8	yes	direct product factor
44	C₂×C₄×C₇	C₄×C₇×C₁₃	1	16	yes	—
45	C₂×C₄×C₇	C₂²×C₇×C₁₃	1	8	yes	—
46	C₇×C₈	C₄×C₇×C₁₃	1	32	yes	direct product factor
47	C₂²×C₁₃	C₂×C₄×C₇²	1	1	yes	characteristic
48	C₄×C₁₃	C₇²×C₈	1	4	yes	direct product factor
49	C₄×C₁₃	C₂×C₄×C₇²	1	2	yes	—
50	C₇²	C₄×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₄×C₈	C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₇	C₂×C₄×C₇×C₁₃	1	8	yes	—
53	C₄×C₇	C₇×C₈×C₁₃	1	32	yes	direct product factor
54	C₄×C₇	C₂×C₄×C₇×C₁₃	1	16	yes	—
55	C₂×C₁₃	C₄²×C₇²	1	1	yes	characteristic
56	C₂×C₁₃	C₂×C₇²×C₈	1	2	yes	—
57	C₂×C₈	C₂×C₇²×C₁₃	1	2	yes	—
58	C₄²	C₂×C₇²×C₁₃	1	1	yes	characteristic
59	C₂×C₇	C₄²×C₇×C₁₃	1	8	yes	—
60	C₂×C₇	C₂×C₇×C₈×C₁₃	1	16	yes	—
61	C₁₃	C₄×C₇²×C₈	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₄	C₄×C₇²×C₁₃	1	2	yes	—
63	C₂×C₄	C₂²×C₇²×C₁₃	1	1	yes	characteristic
64	C₈	C₄×C₇²×C₁₃	1	4	yes	direct product factor
65	C₇	C₄×C₇×C₈×C₁₃	1	8	yes	direct product factor
66	C₂²	C₂×C₄×C₇²×C₁₃	1	1	yes	characteristic
67	C₄	C₇²×C₈×C₁₃	1	4	yes	direct product factor
68	C₄	C₂×C₄×C₇²×C₁₃	1	2	yes	—
69	C₂	C₂×C₇²×C₈×C₁₃	1	2	yes	—
70	C₂	C₄²×C₇²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₇²×C₁₃
socle, prime radical	C₂²×C₇²×C₁₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇²×C₈×C₁₃	C₄	direct (N × H)
6. C₄×C₇×C₈×C₁₃	C₇	direct (N × H)
8. C₄×C₇²×C₁₃	C₈	direct (N × H)
10. C₄×C₇²×C₈	C₁₃	direct (N × H)
19. C₇×C₈×C₁₃	C₄×C₇	direct (N × H)
20. C₇²×C₁₃	C₄×C₈	direct (N × H)
21. C₄×C₈×C₁₃	C₇²	direct (N × H)
24. C₇²×C₈	C₄×C₁₃	direct (N × H)
26. C₄×C₇×C₁₃	C₇×C₈	direct (N × H)
28. C₄×C₇×C₈	C₇×C₁₃	direct (N × H)
32. C₄×C₇²	C₈×C₁₃	direct (N × H)
40. C₈×C₁₃	C₄×C₇²	direct (N × H)
43. C₇×C₁₃	C₄×C₇×C₈	direct (N × H)
46. C₇×C₈	C₄×C₇×C₁₃	direct (N × H)
48. C₄×C₁₃	C₇²×C₈	direct (N × H)
50. C₇²	C₄×C₈×C₁₃	direct (N × H)
51. C₄×C₈	C₇²×C₁₃	direct (N × H)
53. C₄×C₇	C₇×C₈×C₁₃	direct (N × H)
61. C₁₃	C₄×C₇²×C₈	direct (N × H)
64. C₈	C₄×C₇²×C₁₃	direct (N × H)
65. C₇	C₄×C₇×C₈×C₁₃	direct (N × H)
67. C₄	C₇²×C₈×C₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₇²×C₁₃	2
C₂×C₇²×C₈×C₁₃	2
C₄×C₇×C₈×C₁₃	7
C₄×C₇²×C₈	13

Subgroups — C4×C72×C8×C13 #72197949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇²×C₈×C₁₃ #72197949