Subgroups — D₆₄×D₇₉ #34209310

Order 20224.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₂×D₇₉	C₂	1	2	yes	maximal, complemented
2	D₅₀₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761612	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₆×D₇₉	—	2	2	no	—
7	D₂₅₂₈	C₂²	1	2	yes	complemented
8	#19098398	—	2	2	no	—
9	C₃₂×D₇₉	C₂²	1	1	yes	characteristic
10	C₇₉⋊C₆₄	C₂²	1	1	yes	characteristic, complemented
11	D₃₂×C₇₉	C₂²	1	2	yes	complemented
12	C₆₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
13	D₈×D₇₉	—	4	2	no	—
14	D₁₂₆₄	—	2	2	no	—
15	#14579102	—	4	2	no	—
16	C₁₆×D₇₉	D₄	1	1	yes	characteristic
17	C₇₉⋊C₃₂	D₄	1	1	yes	characteristic
18	D₁₆×C₇₉	—	2	2	no	—
19	C₃₂×C₇₉	C₂³	1	1	yes	characteristic
20	D₄×D₇₉	—	8	2	no	—
21	D₆₃₂	—	4	2	no	—
22	#11929609	—	8	2	no	—
23	C₈×D₇₉	D₈	1	1	yes	characteristic
24	C₇₉⋊C₁₆	D₈	1	1	yes	characteristic
25	D₈×C₇₉	—	4	2	no	—
26	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×D₇₉	—	16	2	no	—
28	D₄×C₇₉	—	8	2	no	—
29	C₂²⋊D₇₉	—	16	2	no	—
30	D₃₁₆	—	8	2	no	—
31	C₄×D₇₉	D₁₆	1	1	yes	characteristic
32	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
33	C₇₉⋊C₈	D₁₆	1	1	yes	characteristic
34	C₂²×C₇₉	—	16	2	no	—
35	C₂×D₇₉	—	16	2	no	—
36	C₂×D₇₉	—	32	4	no	—
37	C₂×D₇₉	D₃₂	1	1	yes	characteristic
38	C₄×C₇₉	C₂×D₁₆	1	1	yes	characteristic
39	Dic₇₉	D₃₂	1	1	yes	characteristic
40	C₂×D₆₄	—	79	1	no	maximal, Sylow
41	C₂×C₇₉	—	32	2	no	—
42	C₂×C₇₉	C₂×D₃₂	1	1	yes	characteristic
43	D₇₉	—	32	2	no	—
44	D₇₉	D₆₄	1	2	yes	direct product factor
45	C₂×D₃₂	—	79	2	no	—
46	D₆₄	—	79	2	no	—
47	D₆₄	—	79	1	no	—
48	D₆₄	D₇₉	1	1	yes	characteristic, direct product factor
49	C₂×C₆₄	—	79	1	no	—
50	C₇₉	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂×D₁₆	—	158	2	no	—
52	D₃₂	—	79	2	no	—
53	D₃₂	—	158	2	no	—
54	D₃₂	C₂×D₇₉	1	2	yes	complemented
55	C₂×C₃₂	—	79	1	no	—
56	C₆₄	—	79	1	no	—
57	C₆₄	C₂×D₇₉	1	1	yes	characteristic, complemented
58	C₂×D₈	—	316	2	no	—
59	D₁₆	—	2	2	no	—
60	D₁₆	—	316	2	no	—
61	D₁₆	—	158	2	no	—
62	C₂×C₁₆	—	79	1	no	—
63	C₃₂	—	79	1	no	—
64	C₃₂	C₂²×D₇₉	1	1	yes	characteristic
65	C₂×D₄	—	632	2	no	—
66	D₈	—	4	2	no	—
67	D₈	—	316	2	no	—
68	D₈	—	632	2	no	—
69	C₂×C₈	—	79	1	no	—
70	C₁₆	—	79	1	no	—
71	C₁₆	D₄×D₇₉	1	1	yes	characteristic
72	C₂³	—	1264	2	no	—
73	D₄	—	8	2	no	—
74	D₄	—	632	2	no	—
75	D₄	—	1264	2	no	—
76	C₂×C₄	—	79	1	no	—
77	C₈	—	79	1	no	—
78	C₈	D₈×D₇₉	1	1	yes	characteristic
79	C₂²	—	16	2	no	—
80	C₂²	—	79	1	no	—
81	C₂²	—	2528	4	no	—
82	C₂²	—	1264	2	no	—
83	C₄	—	79	1	no	—
84	C₄	D₁₆×D₇₉	1	1	yes	characteristic
85	C₂	—	32	2	no	—
86	C₂	—	79	2	no	—
87	C₂	—	2528	2	no	—
88	C₂	D₃₂×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₇₉
commutator, cosocle	C₃₂×C₇₉	C₂³
Frattini	C₃₂	C₂²×D₇₉
Fitting	C₇₉×D₆₄	C₂
socle	C₂×C₇₉	C₂×D₃₂
hypercenter	D₆₄	D₇₉
hypocenter	C₇₉	C₂×D₆₄
LCS	G ▷ C₃₂×C₇₉ ▷ C₁₆×C₇₉ ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. D₃₂×D₇₉	C₂	semidirect
2. D₅₀₅₆	C₂	semidirect
3. #23761612	C₂	semidirect
4. C₆₄×D₇₉	C₂	semidirect
5. C₇₉×D₆₄	C₂	semidirect
7. D₂₅₂₈	C₂²	semidirect
10. C₇₉⋊C₆₄	C₂²	semidirect
11. D₃₂×C₇₉	C₂²	semidirect
12. C₆₄×C₇₉	C₂²	semidirect
44. D₇₉	D₆₄	direct (N × H)
48. D₆₄	D₇₉	direct (N × H)
50. C₇₉	C₂×D₆₄	semidirect
54. D₃₂	C₂×D₇₉	semidirect
57. C₆₄	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
D₃₂×D₇₉	2
D₅₀₅₆	2
#23761612	2
C₆₄×D₇₉	2
C₇₉×D₆₄	2
C₂×D₆₄	79

Subgroups — D64×D79 #34209310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₄×D₇₉ #34209310