Group #23765762 — subgroups

Subgroups — #23765762

Order 10112.

780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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×C₄×D₃₁₆	C₂	1	3	yes	maximal
2	C₄×C₄⋊Dic₇₉	C₂	1	3	yes	maximal, complemented
3	#19098410	C₂	1	6	yes	maximal, complemented
4	#95×D₇₉	C₂	1	2	yes	maximal, complemented
5	#376×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₄×D₇₉	C₂²	1	6	yes	—
8	C₄×D₃₁₆	C₄	1	24	yes	complemented
9	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
10	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	6	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	6	yes	—
12	C₇₉⋊#95	C₂²	1	6	yes	—
13	C₂×C₄²×C₇₉	C₂²	1	3	yes	—
14	#95×C₇₉	C₂²	1	1	yes	characteristic
15	#95×C₇₉	C₂²	1	3	yes	—
16	C₂³×D₇₉	C₂³	1	2	yes	—
17	C₂×D₃₁₆	C₂×C₄	1	12	yes	—
18	C₂²×Dic₇₉	C₂³	1	6	yes	—
19	C₂×C₄×D₇₉	—	4	12	no	—
20	C₂×C₄×D₇₉	C₂×C₄	1	24	yes	complemented
21	C₄⋊Dic₇₉	C₂×C₄	1	12	yes	complemented
22	(C₂×D₇₉)⋊C₄	C₂×C₄	1	24	yes	complemented
23	C₄×Dic₇₉	—	4	6	no	—
24	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
26	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
27	C₄²×C₇₉	C₂×C₄	1	12	yes	complemented
28	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
29	C₂²×D₇₉	—	2	6	no	—
30	C₂²×D₇₉	—	2	2	no	—
31	C₂²×D₇₉	C₂²×C₄	1	12	yes	—
32	C₂×C₄×C₇₉	—	2	3	no	—
33	C₂×C₄×C₇₉	—	2	6	no	—
34	C₂×C₄×C₇₉	—	2	3	no	—
35	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
36	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
37	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
38	C₂×Dic₇₉	—	2	12	no	—
39	C₂×Dic₇₉	C₂²×C₄	1	12	yes	—
40	D₃₁₆	C₄²	1	16	yes	complemented
41	C₄×D₇₉	—	4	24	no	—
42	C₂²×C₇₉	C₂³×C₄	1	3	yes	—
43	C₂²×C₇₉	H(5,𝔽₂)	1	3	yes	—
44	C₂²×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
45	C₂×D₇₉	—	2	12	no	—
46	C₂×D₇₉	—	2	12	no	—
47	C₂×D₇₉	C₂×C₄²	1	8	yes	—
48	C₄×C₇₉	—	2	6	no	—
49	C₄×C₇₉	—	2	6	no	—
50	C₄×C₇₉	C₂×C₄²	1	4	yes	—
51	Dic₇₉	—	2	12	no	—
52	C₂×C₇₉	C₂²×C₄²	1	1	yes	characteristic
53	C₂×C₇₉	#518	1	3	yes	—
54	C₂×C₇₉	#520	1	3	yes	—
55	D₇₉	—	2	8	no	—
56	#2275	—	79	1	no	maximal, Sylow
57	C₇₉	#2275	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₄×D₄	—	79	3	no	—
59	C₄×C₄⋊C₄	—	79	3	no	—
60	C₄×C₂²⋊C₄	—	79	6	no	—
61	#376	D₇₉	1	1	yes	characteristic, complemented
62	C₂×#95	—	79	2	no	—
63	C₂²×D₄	—	79	1	no	—
64	C₂³×C₄	—	79	6	no	—
65	C₄×D₄	—	79	24	no	—
66	C₂×C₄⋊C₄	—	79	3	no	—
67	C₂×C₂²⋊C₄	—	79	6	no	—
68	C₂×C₄²	—	79	6	no	—
69	C₂×C₄²	C₂×D₇₉	1	3	yes	—
70	#95	—	79	6	no	—
71	#95	C₂×D₇₉	1	1	yes	characteristic
72	#95	C₂×D₇₉	1	3	yes	—
73	C₂⁴	—	79	2	no	—
74	C₂×D₄	—	79	12	no	—
75	C₂²×C₄	—	316	12	no	—
76	C₂²×C₄	—	79	24	no	—
77	C₂²×C₄	—	79	6	no	—
78	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
79	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
80	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
81	C₄⋊C₄	—	79	12	no	—
82	C₂²⋊C₄	—	79	24	no	—
83	C₄²	—	316	6	no	—
84	C₄²	C₄×D₇₉	1	12	yes	complemented
85	C₂³	—	79	12	no	—
86	C₂³	—	158	6	no	—
87	C₂³	—	158	2	no	—
88	C₂³	C₂³×D₇₉	1	1	yes	characteristic
89	D₄	—	79	16	no	—
90	C₂×C₄	—	2	3	no	—
91	C₂×C₄	—	2	6	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	316	24	no	—
94	C₂×C₄	—	79	12	no	—
95	C₂×C₄	—	158	12	no	—
96	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
97	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
98	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
99	C₂²	—	79	8	no	—
100	C₂²	—	158	12	no	—
101	C₂²	—	158	12	no	—
102	C₂²	C₂²×C₄×D₇₉	1	3	yes	—
103	C₂²	#14579207	1	3	yes	—
104	C₂²	#14579208	1	1	yes	characteristic
105	C₄	—	2	6	no	—
106	C₄	—	2	6	no	—
107	C₄	—	158	12	no	—
108	C₄	C₄²×D₇₉	1	4	yes	—
109	C₂	—	158	8	no	—
110	C₂	C₂×C₄²×D₇₉	1	1	yes	characteristic
111	C₂	#19099037	1	3	yes	—
112	C₂	#19099043	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×D₃₁₆

C₂

yes

maximal

C₄×C₄⋊Dic₇₉

C₂

yes

maximal, complemented

#19098410

C₂

yes

maximal, complemented

#95×D₇₉

C₂

yes

maximal, complemented

#376×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×D₃₁₆

C₂²

yes

characteristic

C₂²×C₄×D₇₉

C₂²

yes

—

C₄×D₃₁₆

C₄

yes

complemented

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

characteristic

#95×C₇₉

C₂²

yes

—

C₂³×D₇₉

C₂³

yes

—

C₂×D₃₁₆

C₂×C₄

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

C₂×C₄

yes

complemented

C₄⋊Dic₇₉

C₂×C₄

yes

complemented

(C₂×D₇₉)⋊C₄

C₂×C₄

yes

complemented

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

—

C₂²×D₇₉

—

C₂²×D₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂²×C₄

yes

—

D₃₁₆

C₄²

yes

complemented

C₄×D₇₉

—

C₂²×C₇₉

C₂³×C₄

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

—

C₂²×C₇₉

2₋¹⁺⁴

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

C₂×C₄²

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄²

yes

—

Dic₇₉

—

C₂×C₇₉

C₂²×C₄²

yes

characteristic

C₂×C₇₉

#518

yes

—

C₂×C₇₉

#520

yes

—

D₇₉

—

#2275

—

maximal, Sylow

C₇₉

#2275

yes

characteristic, complemented, Sylow

C₂×C₄×D₄

—

C₄×C₄⋊C₄

—

C₄×C₂²⋊C₄

—

#376

D₇₉

yes

characteristic, complemented

C₂×#95

—

C₂²×D₄

—

C₂³×C₄

—

C₄×D₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

#95

—

#95

C₂×D₇₉

yes

characteristic

#95

C₂×D₇₉

yes

—

C₂⁴

—

C₂×D₄

—

C₂²×C₄

—

316

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

316

—

C₄²

C₄×D₇₉

yes

complemented

C₂³

—

C₂³

—

158

—

C₂³

—

158

—

C₂³

C₂³×D₇₉

yes

characteristic

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂²

—

100

C₂²

—

158

—

101

C₂²

—

158

—

102

C₂²

C₂²×C₄×D₇₉

yes

—

103

C₂²

#14579207

yes

—

104

C₂²

#14579208

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

158

—

108

C₄

C₄²×D₇₉

yes

—

109

C₂

—

158

—

110

C₂

C₂×C₄²×D₇₉

yes

characteristic

111

C₂

#19099037

yes

—

112

C₂

#19099043

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂×C₇₉	C₂²×C₄²
Fitting	#376×C₇₉	C₂
socle, cosocle	C₂³×C₇₉	C₂⁴
prime radical	C₂²×D₃₁₆	C₂²
hypercenter	#376	D₇₉
hypocenter	C₇₉	#2275
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator

C₂×C₇₉

C₂²×C₄²

Fitting

#376×C₇₉

C₂

socle, cosocle

C₂³×C₇₉

C₂⁴

prime radical

C₂²×D₃₁₆

C₂²

D₇₉

C₇₉

G ▷ C₂×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
2. C₄×C₄⋊Dic₇₉	C₂	semidirect
3. #19098410	C₂	semidirect
4. #95×D₇₉	C₂	semidirect
5. #376×C₇₉	C₂	semidirect
8. C₄×D₃₁₆	C₄	semidirect
20. C₂×C₄×D₇₉	C₂×C₄	semidirect
21. C₄⋊Dic₇₉	C₂×C₄	semidirect
22. (C₂×D₇₉)⋊C₄	C₂×C₄	semidirect
27. C₄²×C₇₉	C₂×C₄	semidirect
40. D₃₁₆	C₄²	semidirect
57. C₇₉	#2275	semidirect
61. #376	D₇₉	semidirect
84. C₄²	C₄×D₇₉	semidirect

H ≅ G/N

type

2. C₄×C₄⋊Dic₇₉

C₂

semidirect

3. #19098410

C₂

semidirect

4. #95×D₇₉

C₂

semidirect

5. #376×C₇₉

C₂

semidirect

8. C₄×D₃₁₆

C₄

semidirect

20. C₂×C₄×D₇₉

C₂×C₄

semidirect

21. C₄⋊Dic₇₉

C₂×C₄

semidirect

22. (C₂×D₇₉)⋊C₄

C₂×C₄

semidirect

27. C₄²×C₇₉

C₂×C₄

semidirect

40. D₃₁₆

C₄²

semidirect

57. C₇₉

#2275

semidirect

61. #376

D₇₉

semidirect

84. C₄²

C₄×D₇₉

semidirect

Subgroups — #23765762

Conjugacy classes of subgroups

Complements