Group #19099366 — subgroups

Subgroups — #19099366

Order 5056.

268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14579207	C₂	1	1	yes	maximal, characteristic, complemented
2	#14579187	C₂	1	3	yes	maximal, complemented
3	#14579186	C₂	1	3	yes	maximal, complemented
4	#14579181	C₂	1	3	yes	maximal, complemented
5	C₂×#11929609	C₂	1	3	yes	maximal, complemented
6	#14579168	C₂	1	1	yes	maximal, characteristic, complemented
7	H(5,𝔽₂)×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11929625	—	2	1	no	—
9	#11929624	C₂²	1	3	yes	complemented
10	C₂×D₃₁₆	C₂²	1	3	yes	complemented
11	D₄×D₇₉	—	2	3	no	—
12	#11929614	C₂²	1	1	yes	characteristic, complemented
13	#11929612	C₂²	1	3	yes	complemented
14	#11929611	C₂²	1	3	yes	complemented
15	#11929609	C₂²	1	3	yes	complemented
16	#11929609	C₂²	1	6	yes	complemented
17	#11929608	C₂²	1	3	yes	complemented
18	C₂×C₇₉⋊C₈	C₂²	1	3	yes	complemented
19	#41×C₇₉	—	2	1	no	—
20	#41×C₇₉	C₂²	1	1	yes	characteristic
21	#41×C₇₉	C₂²	1	3	yes	complemented
22	C₂×D₄×C₇₉	—	2	3	no	—
23	C₂×D₄×C₇₉	C₂²	1	3	yes	complemented
24	C₂³×C₇₉	—	2	3	no	—
25	C₂²×D₇₉	—	2	3	no	—
26	Q₈×C₇₉	D₄	1	1	yes	characteristic
27	Q₈×C₇₉	C₂³	1	1	yes	characteristic
28	D₄×C₇₉	—	2	3	no	—
29	D₄×C₇₉	—	2	3	no	—
30	D₄×C₇₉	D₄	1	3	yes	—
31	D₄×C₇₉	C₂³	1	3	yes	—
32	C₂×C₄×C₇₉	—	2	3	no	—
33	C₂×C₄×C₇₉	C₂³	1	3	yes	—
34	C₂²⋊D₇₉	—	2	3	no	—
35	D₃₁₆	—	2	3	no	—
36	D₃₁₆	C₂³	1	3	yes	—
37	C₄×D₇₉	—	2	3	no	—
38	Dic₁₅₈	C₂³	1	1	yes	characteristic
39	C₇₉⋊C₈	C₂³	1	1	yes	characteristic
40	C₇₉⋊C₈	C₂³	1	3	yes	—
41	C₂²×C₇₉	—	2	3	no	—
42	C₂²×C₇₉	—	8	3	no	—
43	C₂²×C₇₉	C₂×D₄	1	3	yes	—
44	C₂×D₇₉	—	2	3	no	—
45	C₂×D₇₉	—	8	3	no	—
46	C₄×C₇₉	—	2	1	no	—
47	C₄×C₇₉	C₂×D₄	1	3	yes	—
48	C₄×C₇₉	C₂⁴	1	1	yes	characteristic
49	Dic₇₉	—	2	1	no	—
50	C₂×C₇₉	—	2	3	no	—
51	C₂×C₇₉	—	4	3	no	—
52	C₂×C₇₉	C₂²×D₄	1	1	yes	characteristic
53	D₇₉	—	4	3	no	—
54	C₇₉	#576	1	1	yes	characteristic, complemented, Sylow
55	#576	—	79	1	no	maximal, Sylow
56	H(5,𝔽₂)	—	79	1	no	—
57	H(5,𝔽₂)	D₇₉	1	1	yes	characteristic, complemented
58	AGL(1,ℤ/8)	—	79	3	no	—
59	AGL(1,ℤ/8)	—	79	3	no	—
60	#135	—	79	3	no	—
61	C₂×D₈	—	79	3	no	—
62	#131	—	79	1	no	—
63	#41	—	2	1	no	—
64	#41	—	79	3	no	—
65	#41	—	158	1	no	—
66	#41	C₂×D₇₉	1	1	yes	characteristic
67	#41	C₂×D₇₉	1	3	yes	complemented
68	C₂×D₄	—	2	3	no	—
69	C₂×D₄	—	79	3	no	—
70	C₂×D₄	—	158	3	no	—
71	C₂×D₄	C₂×D₇₉	1	3	yes	complemented
72	Q₁₆	—	79	1	no	—
73	SD₁₆	—	79	3	no	—
74	SD₁₆	—	79	3	no	—
75	D₈	—	79	3	no	—
76	D₈	—	79	6	no	—
77	M₁₆	—	79	3	no	—
78	C₂×C₈	—	79	3	no	—
79	C₂³	—	2	3	no	—
80	C₂³	—	158	3	no	—
81	Q₈	—	79	1	no	—
82	Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
83	Q₈	C₂²×D₇₉	1	1	yes	characteristic
84	D₄	—	2	3	no	—
85	D₄	—	2	3	no	—
86	D₄	—	79	3	no	—
87	D₄	—	158	3	no	—
88	D₄	—	158	3	no	—
89	D₄	C₂²⋊D₇₉	1	3	yes	—
90	D₄	C₂²×D₇₉	1	3	yes	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	158	3	no	—
93	C₂×C₄	C₂²×D₇₉	1	3	yes	—
94	C₈	—	79	1	no	—
95	C₈	—	79	3	no	—
96	C₂²	—	2	3	no	—
97	C₂²	—	8	3	no	—
98	C₂²	—	632	3	no	—
99	C₂²	—	158	3	no	—
100	C₂²	C₂×C₂²⋊D₇₉	1	3	yes	—
101	C₄	—	2	1	no	—
102	C₄	—	158	1	no	—
103	C₄	C₂×C₂²⋊D₇₉	1	3	yes	—
104	C₄	C₂³×D₇₉	1	1	yes	characteristic
105	C₂	—	2	3	no	—
106	C₂	—	4	3	no	—
107	C₂	—	316	3	no	—
108	C₂	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14579207

C₂

yes

maximal, characteristic, complemented

#14579187

C₂

yes

maximal, complemented

#14579186

C₂

yes

maximal, complemented

#14579181

C₂

yes

maximal, complemented

C₂×#11929609

C₂

yes

maximal, complemented

#14579168

C₂

yes

maximal, characteristic, complemented

H(5,𝔽₂)×C₇₉

C₂

yes

maximal, characteristic, complemented

#11929625

—

#11929624

C₂²

yes

complemented

C₂×D₃₁₆

C₂²

yes

complemented

D₄×D₇₉

—

#11929614

C₂²

yes

characteristic, complemented

#11929612

C₂²

yes

complemented

#11929611

C₂²

yes

complemented

#11929609

C₂²

yes

complemented

#11929609

C₂²

yes

complemented

#11929608

C₂²

yes

complemented

C₂×C₇₉⋊C₈

C₂²

yes

complemented

#41×C₇₉

—

#41×C₇₉

C₂²

yes

characteristic

#41×C₇₉

C₂²

yes

complemented

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

C₂²

yes

complemented

C₂³×C₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

D₄

yes

characteristic

Q₈×C₇₉

C₂³

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

D₄

yes

—

D₄×C₇₉

C₂³

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂³

yes

—

C₂²⋊D₇₉

—

D₃₁₆

—

D₃₁₆

C₂³

yes

—

C₄×D₇₉

—

Dic₁₅₈

C₂³

yes

characteristic

C₇₉⋊C₈

C₂³

yes

characteristic

C₇₉⋊C₈

C₂³

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₄

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₄

yes

—

C₄×C₇₉

C₂⁴

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂²×D₄

yes

characteristic

D₇₉

—

C₇₉

#576

yes

characteristic, complemented, Sylow

—

—

D₇₉

yes

characteristic, complemented

AGL(1,ℤ/8)

—

AGL(1,ℤ/8)

—

#135

—

C₂×D₈

—

—

—

—

—

158

—

#41

C₂×D₇₉

yes

characteristic

#41

C₂×D₇₉

yes

complemented

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂×D₄

C₂×D₇₉

yes

complemented

Q₁₆

—

SD₁₆

—

SD₁₆

—

D₈

—

D₈

—

M₁₆

—

C₂×C₈

—

C₂³

—

C₂³

—

158

—

Q₈

—

Q₈

C₂²⋊D₇₉

yes

characteristic

Q₈

C₂²×D₇₉

yes

characteristic

D₄

—

D₄

—

D₄

—

D₄

—

158

—

D₄

—

158

—

D₄

C₂²⋊D₇₉

yes

—

D₄

C₂²×D₇₉

yes

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

C₂²×D₇₉

yes

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

632

—

C₂²

—

158

—

100

C₂²

C₂×C₂²⋊D₇₉

yes

—

101

C₄

—

102

C₄

—

158

—

103

C₄

C₂×C₂²⋊D₇₉

yes

—

104

C₄

C₂³×D₇₉

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

316

—

108

C₂

C₂²×C₂²⋊D₇₉

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×C₂²⋊D₇₉
commutator	C₄×C₇₉	C₂⁴
Frattini	C₄	C₂³×D₇₉
Fitting	H(5,𝔽₂)×C₇₉	C₂
socle	C₂×C₇₉	C₂²×D₄
hypercenter	H(5,𝔽₂)	D₇₉
hypocenter	C₇₉	#576
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ H(5,𝔽₂)

subgroup

G/H

center

C₂

C₂²×C₂²⋊D₇₉

commutator

C₄×C₇₉

C₂⁴

Frattini

C₄

C₂³×D₇₉

Fitting

H(5,𝔽₂)×C₇₉

C₂

socle

C₂×C₇₉

C₂²×D₄

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ #41 ◁ H(5,𝔽₂)

N	H ≅ G/N	type
1. #14579207	C₂	semidirect
2. #14579187	C₂	semidirect
3. #14579186	C₂	semidirect
4. #14579181	C₂	semidirect
5. C₂×#11929609	C₂	semidirect
6. #14579168	C₂	semidirect
7. H(5,𝔽₂)×C₇₉	C₂	semidirect
9. #11929624	C₂²	semidirect
10. C₂×D₃₁₆	C₂²	semidirect
12. #11929614	C₂²	semidirect
13. #11929612	C₂²	semidirect
14. #11929611	C₂²	semidirect
15. #11929609	C₂²	semidirect
16. #11929609	C₂²	semidirect
17. #11929608	C₂²	semidirect
18. C₂×C₇₉⋊C₈	C₂²	semidirect
21. #41×C₇₉	C₂²	semidirect
23. C₂×D₄×C₇₉	C₂²	semidirect
54. C₇₉	#576	semidirect
57. H(5,𝔽₂)	D₇₉	semidirect
67. #41	C₂×D₇₉	semidirect
71. C₂×D₄	C₂×D₇₉	semidirect

H ≅ G/N

type

1. #14579207

C₂

semidirect

2. #14579187

C₂

semidirect

3. #14579186

C₂

semidirect

4. #14579181

C₂

semidirect

5. C₂×#11929609

C₂

semidirect

6. #14579168

C₂

semidirect

7. H(5,𝔽₂)×C₇₉

C₂

semidirect

9. #11929624

C₂²

semidirect

10. C₂×D₃₁₆

C₂²

semidirect

12. #11929614

C₂²

semidirect

13. #11929612

C₂²

semidirect

14. #11929611

C₂²

semidirect

15. #11929609

C₂²

semidirect

16. #11929609

C₂²

semidirect

17. #11929608

C₂²

semidirect

18. C₂×C₇₉⋊C₈

C₂²

semidirect

21. #41×C₇₉

C₂²

semidirect

23. C₂×D₄×C₇₉

C₂²

semidirect

54. C₇₉

#576

semidirect

57. H(5,𝔽₂)

D₇₉

semidirect

67. #41

C₂×D₇₉

semidirect

71. C₂×D₄

C₂×D₇₉

semidirect

Subgroups — #19099366

Conjugacy classes of subgroups

Complements