Subgroups — (C₂×D₇₉)⋊C₆₄ #34176077

Order 20224.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇₉⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₆×D₇₉	C₄	1	1	yes	characteristic
5	C₂×C₇₉⋊C₃₂	C₄	1	1	yes	characteristic
6	C₃₂×D₇₉	—	2	1	no	—
7	C₃₂×D₇₉	—	2	1	no	—
8	C₇₉⋊C₆₄	—	2	1	no	—
9	C₂×C₃₂×C₇₉	C₂²	1	1	yes	characteristic
10	C₆₄×C₇₉	—	2	1	no	—
11	C₂×C₈×D₇₉	C₈	1	1	yes	characteristic
12	C₂×C₇₉⋊C₁₆	C₈	1	1	yes	characteristic
13	C₁₆×D₇₉	—	2	1	no	—
14	C₁₆×D₇₉	—	2	1	no	—
15	C₇₉⋊C₃₂	—	2	1	no	—
16	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
17	C₃₂×C₇₉	D₄	1	1	yes	characteristic
18	C₃₂×C₇₉	D₄	1	1	yes	characteristic
19	C₂×C₄×D₇₉	C₁₆	1	1	yes	characteristic
20	C₂×C₇₉⋊C₈	C₁₆	1	1	yes	characteristic
21	C₈×D₇₉	—	2	1	no	—
22	C₈×D₇₉	—	2	1	no	—
23	C₇₉⋊C₁₆	—	2	1	no	—
24	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
25	C₁₆×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₇₉	M₁₆	1	1	yes	characteristic
27	C₂²×D₇₉	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
29	C₂×Dic₇₉	C₃₂	1	1	yes	characteristic
30	C₄×D₇₉	—	2	1	no	—
31	C₄×D₇₉	—	2	1	no	—
32	C₈×C₇₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₈×C₇₉	M₃₂	1	1	yes	characteristic
34	C₇₉⋊C₈	—	2	1	no	—
35	C₂²×C₇₉	C₂×C₃₂	1	1	yes	characteristic
36	C₂×D₇₉	—	2	1	no	—
37	C₂×D₇₉	—	2	1	no	—
38	C₂×D₇₉	C₆₄	1	2	yes	complemented
39	C₄×C₇₉	C₂²⋊C₁₆	1	1	yes	characteristic
40	C₄×C₇₉	M₆₄	1	1	yes	characteristic
41	Dic₇₉	—	2	1	no	—
42	C₂²⋊C₆₄	—	79	1	no	maximal, Sylow
43	C₂×C₇₉	C₂²⋊C₃₂	1	1	yes	characteristic
44	C₂×C₇₉	C₂×C₆₄	1	1	yes	characteristic
45	C₂×C₇₉	M₁₂₈	1	1	yes	characteristic
46	D₇₉	—	2	2	no	—
47	C₂²×C₃₂	—	79	1	no	—
48	C₂×C₆₄	—	79	1	no	—
49	C₂×C₆₄	D₇₉	1	1	yes	characteristic, complemented
50	C₇₉	C₂²⋊C₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₁₆	—	79	1	no	—
52	C₂×C₃₂	—	79	1	no	—
53	C₂×C₃₂	—	158	1	no	—
54	C₂×C₃₂	—	158	1	no	—
55	C₂×C₃₂	C₂×D₇₉	1	1	yes	characteristic
56	C₆₄	—	2	1	no	—
57	C₆₄	—	158	1	no	—
58	C₂²×C₈	—	79	1	no	—
59	C₂×C₁₆	—	79	1	no	—
60	C₂×C₁₆	—	158	1	no	—
61	C₂×C₁₆	—	158	1	no	—
62	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
63	C₃₂	—	158	1	no	—
64	C₃₂	D₃₁₆	1	1	yes	characteristic
65	C₃₂	C₂²⋊D₇₉	1	1	yes	characteristic
66	C₂²×C₄	—	79	1	no	—
67	C₂×C₈	—	79	1	no	—
68	C₂×C₈	—	158	1	no	—
69	C₂×C₈	—	158	1	no	—
70	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
71	C₁₆	—	158	1	no	—
72	C₁₆	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
73	C₁₆	#11929607	1	1	yes	characteristic
74	C₂³	—	79	1	no	—
75	C₂×C₄	—	79	1	no	—
76	C₂×C₄	—	158	1	no	—
77	C₂×C₄	—	158	1	no	—
78	C₂×C₄	C₁₆×D₇₉	1	1	yes	characteristic
79	C₈	—	158	1	no	—
80	C₈	(C₂×D₇₉)⋊C₈	1	1	yes	characteristic
81	C₈	#14579100	1	1	yes	characteristic
82	C₂²	—	79	2	no	—
83	C₂²	—	158	1	no	—
84	C₂²	—	158	1	no	—
85	C₂²	C₃₂×D₇₉	1	1	yes	characteristic
86	C₄	—	158	1	no	—
87	C₄	(C₂×D₇₉)⋊C₁₆	1	1	yes	characteristic
88	C₄	#19098396	1	1	yes	characteristic
89	C₂	—	158	2	no	—
90	C₂	(C₂×D₇₉)⋊C₃₂	1	1	yes	characteristic
91	C₂	C₆₄×D₇₉	1	1	yes	characteristic
92	C₂	#23761610	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₃₂	C₂×D₇₉
commutator	C₂×C₇₉	C₂×C₆₄
Fitting	C₂×C₆₄×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₃₂
prime radical	C₂²×D₇₉	C₃₂
cosocle	C₂×C₃₂×C₇₉	C₂²
hypercenter	C₂×C₆₄	D₇₉
hypocenter	C₇₉	C₂²⋊C₆₄
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₇₉⋊C₆₄	C₂	semidirect
3. C₂×C₆₄×C₇₉	C₂	semidirect
38. C₂×D₇₉	C₆₄	semidirect
49. C₂×C₆₄	D₇₉	semidirect
50. C₇₉	C₂²⋊C₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₂×D₇₉	2
C₂×C₇₉⋊C₆₄	2
C₂×C₆₄×C₇₉	2
C₂²⋊C₆₄	79

Subgroups — (C2×D79)⋊C64 #34176077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×D₇₉)⋊C₆₄ #34176077