Subgroups — C₂×C₈×C₁₃×C₄₉ #72188809

Order 10192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₄₉	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₃×C₄₉	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₁₃×C₄₉	C₄	1	1	yes	characteristic
4	C₄×C₁₃×C₄₉	C₄	1	1	yes	characteristic
5	C₄×C₁₃×C₄₉	C₂²	1	1	yes	characteristic
6	C₂×C₇×C₈×C₁₃	C₇	1	1	yes	maximal, characteristic
7	C₂×C₁₃×C₄₉	C₈	1	2	yes	direct product factor
8	C₂×C₁₃×C₄₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈×C₄₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₄×C₇×C₁₃	C₂×C₇	1	1	yes	characteristic
11	C₇×C₈×C₁₃	C₂×C₇	1	2	yes	—
12	C₁₃×C₄₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₄×C₄₉	C₂×C₁₃	1	1	yes	characteristic
14	C₈×C₄₉	C₂×C₁₃	1	2	yes	direct product factor
15	C₂²×C₇×C₁₃	C₄×C₇	1	1	yes	characteristic
16	C₄×C₇×C₁₃	C₄×C₇	1	1	yes	characteristic
17	C₄×C₇×C₁₃	C₂²×C₇	1	1	yes	characteristic
18	C₂×C₈×C₁₃	C₄₉	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₄₉	C₄×C₁₃	1	1	yes	characteristic
20	C₄×C₄₉	C₄×C₁₃	1	1	yes	characteristic
21	C₄×C₄₉	C₂²×C₁₃	1	1	yes	characteristic
22	C₂×C₇×C₁₃	C₇×C₈	1	2	yes	—
23	C₂×C₇×C₁₃	C₂×C₄×C₇	1	1	yes	characteristic
24	C₂×C₇×C₈	C₇×C₁₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₂×C₄₉	1	1	yes	characteristic
26	C₈×C₁₃	C₂×C₄₉	1	2	yes	direct product factor
27	C₂×C₄₉	C₈×C₁₃	1	2	yes	direct product factor
28	C₂×C₄₉	C₂×C₄×C₁₃	1	1	yes	characteristic
29	C₇×C₁₃	C₂×C₇×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇	C₂×C₇×C₁₃	1	1	yes	characteristic
31	C₇×C₈	C₂×C₇×C₁₃	1	2	yes	—
32	C₂²×C₁₃	C₄×C₄₉	1	1	yes	characteristic
33	C₄×C₁₃	C₄×C₄₉	1	1	yes	characteristic
34	C₄×C₁₃	C₂²×C₄₉	1	1	yes	characteristic
35	C₄₉	C₂×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₂²×C₇	C₄×C₇×C₁₃	1	1	yes	characteristic
37	C₄×C₇	C₄×C₇×C₁₃	1	1	yes	characteristic
38	C₄×C₇	C₂²×C₇×C₁₃	1	1	yes	characteristic
39	C₂×C₁₃	C₈×C₄₉	1	2	yes	direct product factor
40	C₂×C₁₃	C₂×C₄×C₄₉	1	1	yes	characteristic
41	C₂×C₈	C₁₃×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₇	C₇×C₈×C₁₃	1	2	yes	—
43	C₂×C₇	C₂×C₄×C₇×C₁₃	1	1	yes	characteristic
44	C₁₃	C₂×C₈×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₄	C₂×C₁₃×C₄₉	1	1	yes	characteristic
46	C₈	C₂×C₁₃×C₄₉	1	2	yes	direct product factor
47	C₇	C₂×C₇×C₈×C₁₃	1	1	yes	characteristic
48	C₂²	C₄×C₁₃×C₄₉	1	1	yes	characteristic
49	C₄	C₄×C₁₃×C₄₉	1	1	yes	characteristic
50	C₄	C₂²×C₁₃×C₄₉	1	1	yes	characteristic
51	C₂	C₈×C₁₃×C₄₉	1	2	yes	direct product factor
52	C₂	C₂×C₄×C₁₃×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₇	C₂²×C₇×C₁₃
socle, prime radical	C₂²×C₇×C₁₃	C₄×C₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₁₃×C₄₉	C₂	direct (N × H)
7. C₂×C₁₃×C₄₉	C₈	direct (N × H)
9. C₂×C₈×C₄₉	C₁₃	direct (N × H)
12. C₁₃×C₄₉	C₂×C₈	direct (N × H)
14. C₈×C₄₉	C₂×C₁₃	direct (N × H)
18. C₂×C₈×C₁₃	C₄₉	direct (N × H)
26. C₈×C₁₃	C₂×C₄₉	direct (N × H)
27. C₂×C₄₉	C₈×C₁₃	direct (N × H)
35. C₄₉	C₂×C₈×C₁₃	direct (N × H)
39. C₂×C₁₃	C₈×C₄₉	direct (N × H)
41. C₂×C₈	C₁₃×C₄₉	direct (N × H)
44. C₁₃	C₂×C₈×C₄₉	direct (N × H)
46. C₈	C₂×C₁₃×C₄₉	direct (N × H)
51. C₂	C₈×C₁₃×C₄₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×C₄₉	2
C₈×C₁₃×C₄₉	2
C₂×C₇×C₈×C₁₃	7
C₂×C₈×C₄₉	13

Subgroups — C2×C8×C13×C49 #72188809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₁₃×C₄₉ #72188809