Group #23765690 — subgroups

Subgroups — M₆₄×D₇₉ #23765690

Order 10112.

112 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic
2	#19098397	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098396	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₇₉	C₂	1	2	yes	maximal, complemented
5	M₆₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₇₉	C₄	1	1	yes	characteristic
7	C₂×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
8	C₁₆×D₇₉	C₄	1	1	yes	characteristic
9	C₁₆×D₇₉	C₄	1	1	yes	characteristic
10	C₁₆×D₇₉	C₂²	1	1	yes	characteristic
11	C₁₆×D₇₉	C₂²	1	1	yes	characteristic
12	C₇₉⋊C₃₂	C₂²	1	2	yes	complemented
13	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
14	C₃₂×C₇₉	C₂²	1	2	yes	complemented
15	C₂×C₄×D₇₉	C₈	1	1	yes	characteristic
16	C₂×C₇₉⋊C₈	C₈	1	1	yes	characteristic
17	C₈×D₇₉	C₈	1	1	yes	characteristic
18	C₈×D₇₉	C₈	1	1	yes	characteristic
19	C₈×D₇₉	C₂×C₄	1	1	yes	characteristic
20	C₈×D₇₉	C₂×C₄	1	1	yes	characteristic
21	C₇₉⋊C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₇₉⋊C₁₆	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₁₆×C₇₉	C₂³	1	1	yes	characteristic
26	C₂²×D₇₉	C₁₆	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₇₉	C₁₆	1	1	yes	characteristic
29	C₄×D₇₉	C₁₆	1	1	yes	characteristic
30	C₄×D₇₉	C₁₆	1	1	yes	characteristic
31	C₄×D₇₉	C₂×C₈	1	1	yes	characteristic
32	C₄×D₇₉	C₂×C₈	1	1	yes	characteristic
33	C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
34	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
35	C₇₉⋊C₈	C₂×C₈	1	1	yes	characteristic
36	C₇₉⋊C₈	C₂×C₈	1	1	yes	characteristic
37	C₂²×C₇₉	C₂×C₁₆	1	1	yes	characteristic
38	C₂×D₇₉	—	2	2	no	—
39	C₂×D₇₉	C₂×C₁₆	1	1	yes	characteristic
40	C₂×D₇₉	C₂×C₁₆	1	1	yes	characteristic
41	C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
42	C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
43	Dic₇₉	C₂×C₁₆	1	1	yes	characteristic
44	Dic₇₉	C₂×C₁₆	1	1	yes	characteristic
45	C₂×C₇₉	—	2	1	no	—
46	C₂×C₇₉	C₂²×C₁₆	1	1	yes	characteristic
47	D₇₉	—	2	1	no	—
48	D₇₉	M₆₄	1	2	yes	direct product factor
49	C₂×M₆₄	—	79	1	no	maximal, Sylow
50	C₇₉	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₁₆	—	79	1	no	—
52	M₆₄	—	79	1	no	—
53	M₆₄	—	79	2	no	—
54	M₆₄	D₇₉	1	1	yes	characteristic, direct product factor
55	C₂×C₃₂	—	79	2	no	—
56	C₂²×C₈	—	79	1	no	—
57	C₂×C₁₆	—	79	1	no	—
58	C₂×C₁₆	—	79	1	no	—
59	C₂×C₁₆	—	79	1	no	—
60	C₂×C₁₆	—	79	1	no	—
61	C₂×C₁₆	—	79	1	no	—
62	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
63	C₃₂	—	79	2	no	—
64	C₃₂	C₂×D₇₉	1	2	yes	complemented
65	C₂²×C₄	—	79	1	no	—
66	C₂×C₈	—	79	1	no	—
67	C₂×C₈	—	79	1	no	—
68	C₂×C₈	—	79	1	no	—
69	C₂×C₈	—	79	1	no	—
70	C₂×C₈	—	79	1	no	—
71	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
72	C₁₆	—	79	1	no	—
73	C₁₆	—	79	1	no	—
74	C₁₆	C₄×D₇₉	1	1	yes	characteristic
75	C₁₆	C₂²×D₇₉	1	1	yes	characteristic
76	C₂³	—	79	1	no	—
77	C₂×C₄	—	79	1	no	—
78	C₂×C₄	—	79	1	no	—
79	C₂×C₄	—	79	1	no	—
80	C₂×C₄	—	79	1	no	—
81	C₂×C₄	—	79	1	no	—
82	C₂×C₄	C₈×D₇₉	1	1	yes	characteristic
83	C₈	—	79	1	no	—
84	C₈	—	79	1	no	—
85	C₈	C₈×D₇₉	1	1	yes	characteristic
86	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
87	C₂²	—	79	1	no	—
88	C₂²	—	79	1	no	—
89	C₂²	—	158	2	no	—
90	C₂²	C₁₆×D₇₉	1	1	yes	characteristic
91	C₄	—	79	1	no	—
92	C₄	—	79	1	no	—
93	C₄	C₁₆×D₇₉	1	1	yes	characteristic
94	C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	—	79	2	no	—
97	C₂	—	158	1	no	—
98	C₂	C₂×C₁₆×D₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₆×D₇₉

C₂

yes

maximal, characteristic

#19098397

C₂

yes

maximal, characteristic, complemented

#19098396

C₂

yes

maximal, complemented

C₃₂×D₇₉

C₂

yes

maximal, complemented

M₆₄×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₇₉

C₄

yes

characteristic

C₂×C₇₉⋊C₁₆

C₄

yes

characteristic

C₁₆×D₇₉

C₄

yes

characteristic

C₁₆×D₇₉

C₄

yes

characteristic

C₁₆×D₇₉

C₂²

yes

characteristic

C₁₆×D₇₉

C₂²

yes

characteristic

C₇₉⋊C₃₂

C₂²

yes

complemented

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

C₃₂×C₇₉

C₂²

yes

complemented

C₂×C₄×D₇₉

C₈

yes

characteristic

C₂×C₇₉⋊C₈

C₈

yes

characteristic

C₈×D₇₉

C₈

yes

characteristic

C₈×D₇₉

C₈

yes

characteristic

C₈×D₇₉

C₂×C₄

yes

characteristic

C₈×D₇₉

C₂×C₄

yes

characteristic

C₇₉⋊C₁₆

C₂×C₄

yes

characteristic

C₇₉⋊C₁₆

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×Dic₇₉

C₁₆

yes

characteristic

C₄×D₇₉

C₁₆

yes

characteristic

C₄×D₇₉

C₁₆

yes

characteristic

C₄×D₇₉

C₂×C₈

yes

characteristic

C₄×D₇₉

C₂×C₈

yes

characteristic

C₈×C₇₉

C₂×C₈

yes

characteristic

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₇₉⋊C₈

C₂×C₈

yes

characteristic

C₇₉⋊C₈

C₂×C₈

yes

characteristic

C₂²×C₇₉

C₂×C₁₆

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

C₂×C₁₆

yes

characteristic

C₂×D₇₉

C₂×C₁₆

yes

characteristic

C₄×C₇₉

C₂×C₁₆

yes

characteristic

C₄×C₇₉

C₂²×C₈

yes

characteristic

Dic₇₉

C₂×C₁₆

yes

characteristic

Dic₇₉

C₂×C₁₆

yes

characteristic

C₂×C₇₉

—

C₂×C₇₉

C₂²×C₁₆

yes

characteristic

D₇₉

—

D₇₉

M₆₄

yes

direct product factor

C₂×M₆₄

—

maximal, Sylow

C₇₉

C₂×M₆₄

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

M₆₄

—

M₆₄

—

M₆₄

D₇₉

yes

characteristic, direct product factor

C₂×C₃₂

—

C₂²×C₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

C₃₂

—

C₃₂

C₂×D₇₉

yes

complemented

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

C₄×D₇₉

yes

characteristic

C₁₆

C₂²×D₇₉

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₇₉

yes

characteristic

C₈

—

C₈

—

C₈

C₈×D₇₉

yes

characteristic

C₈

C₂×C₄×D₇₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

158

—

C₂²

C₁₆×D₇₉

yes

characteristic

C₄

—

C₄

—

C₄

C₁₆×D₇₉

yes

characteristic

C₄

C₂×C₈×D₇₉

yes

characteristic

C₂

—

C₂

—

C₂

—

158

—

C₂

C₂×C₁₆×D₇₉

yes

characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₇₉
commutator, socle	C₂×C₇₉	C₂²×C₁₆
Fitting	M₆₄×C₇₉	C₂
prime radical	C₂²×D₇₉	C₁₆
cosocle	C₁₆×C₇₉	C₂³
hypercenter	M₆₄	D₇₉
hypocenter	C₇₉	C₂×M₆₄
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₁₆ ◁ M₆₄

subgroup

G/H

center, Frattini

C₁₆

C₂²×D₇₉

commutator, socle

C₂×C₇₉

C₂²×C₁₆

Fitting

M₆₄×C₇₉

C₂

prime radical

C₂²×D₇₉

C₁₆

cosocle

C₁₆×C₇₉

C₂³

hypercenter

M₆₄

D₇₉

hypocenter

C₇₉

C₂×M₆₄

LCS

G ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₁₆ ◁ M₆₄

N	H ≅ G/N	type
2. #19098397	C₂	semidirect
3. #19098396	C₂	semidirect
4. C₃₂×D₇₉	C₂	semidirect
5. M₆₄×C₇₉	C₂	semidirect
12. C₇₉⋊C₃₂	C₂²	semidirect
14. C₃₂×C₇₉	C₂²	semidirect
48. D₇₉	M₆₄	direct (N × H)
50. C₇₉	C₂×M₆₄	semidirect
54. M₆₄	D₇₉	direct (N × H)
64. C₃₂	C₂×D₇₉	semidirect

H ≅ G/N

type

2. #19098397

C₂

semidirect

3. #19098396

C₂

semidirect

4. C₃₂×D₇₉

C₂

semidirect

5. M₆₄×C₇₉

C₂

semidirect

12. C₇₉⋊C₃₂

C₂²

semidirect

14. C₃₂×C₇₉

C₂²

semidirect

48. D₇₉

M₆₄

direct (N × H)

50. C₇₉

C₂×M₆₄

semidirect

54. M₆₄

D₇₉

direct (N × H)

64. C₃₂

C₂×D₇₉

semidirect

Subgroups — M₆₄×D₇₉ #23765690

Conjugacy classes of subgroups

Complements

Subgroups — M64×D79 #23765690

Conjugacy classes of subgroups

Complements

Subgroups — M₆₄×D₇₉ #23765690