Group #23765787 — subgroups

Subgroups — C₂×#19098429 #23765787

Order 10112.

712 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 389 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	C₂²×C₄⋊Dic₇₉	C₂	1	2	yes	maximal
2	#19098429	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₇₉⋊#95	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₇₉	C₂²	1	4	yes	—
6	C₂×C₄⋊Dic₇₉	—	2	8	no	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	8	yes	—
8	C₇₉⋊#95	C₂²	1	16	yes	—
9	C₂³×C₄×C₇₉	C₂²	1	2	yes	—
10	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₇₉	C₄	1	8	yes	complemented
12	C₂×C₄²×C₇₉	C₂²	1	4	yes	—
13	C₂²×Dic₇₉	—	2	8	no	—
14	C₂²×Dic₇₉	—	2	16	no	—
15	C₂²×Dic₇₉	C₂³	1	8	yes	—
16	C₄⋊Dic₇₉	—	2	16	no	—
17	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₇₉	—	2	8	no	—
19	C₂²×C₄×C₇₉	C₂×C₄	1	8	yes	—
20	C₂²×C₄×C₇₉	C₂×C₄	1	4	yes	—
21	C₂²×C₄×C₇₉	D₄	1	4	yes	—
22	C₂²×C₄×C₇₉	Q₈	1	4	yes	—
23	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
24	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
25	C₄²×C₇₉	C₂×C₄	1	16	yes	complemented
26	C₂³×C₇₉	C₂²×C₄	1	2	yes	—
27	C₂³×C₇₉	C₂×D₄	1	2	yes	—
28	C₂³×C₇₉	C₂×Q₈	1	2	yes	—
29	C₂³×C₇₉	#41	1	8	yes	—
30	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₇₉	—	2	16	no	—
32	C₂×C₄×C₇₉	—	2	8	no	—
33	C₂×C₄×C₇₉	C₄⋊C₄	1	16	yes	—
34	C₂×C₄×C₇₉	C₂²×C₄	1	8	yes	—
35	C₂×C₄×C₇₉	C₂²×C₄	1	4	yes	—
36	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
37	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
38	C₂×Dic₇₉	—	2	8	no	—
39	C₂×Dic₇₉	—	2	16	no	—
40	C₂×Dic₇₉	—	4	16	no	—
41	C₂²×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
42	C₂²×C₇₉	#117	1	8	yes	—
43	C₂²×C₇₉	#124	1	8	yes	—
44	C₂²×C₇₉	#125	1	8	yes	—
45	C₂²×C₇₉	C₂³×C₄	1	1	yes	characteristic
46	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
47	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
48	C₂²×C₇₉	C₂×#41	1	4	yes	—
49	C₄×C₇₉	—	2	8	no	—
50	C₄×C₇₉	C₂×C₄⋊C₄	1	8	yes	—
51	Dic₇₉	—	4	8	no	—
52	C₂×C₇₉	#382	1	8	yes	complemented
53	C₂×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₇₉	C₂×#117	1	2	yes	—
55	C₂×C₇₉	C₂×#124	1	2	yes	—
56	C₂×C₇₉	C₂×#125	1	2	yes	—
57	C₂×#382	—	79	1	no	maximal, Sylow
58	C₇₉	C₂×#382	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₄⋊C₄	—	79	2	no	—
60	C₂²×C₄²	D₇₉	1	1	yes	characteristic
61	#382	—	79	8	no	—
62	C₂×#95	—	79	4	no	—
63	C₂³×C₄	—	79	4	no	—
64	C₂³×C₄	C₂×D₇₉	1	2	yes	—
65	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic
66	C₂×C₄⋊C₄	—	79	8	no	—
67	C₂×C₄⋊C₄	—	158	8	no	—
68	C₂×C₄²	Dic₇₉	1	8	yes	complemented
69	C₂×C₄²	C₂×D₇₉	1	4	yes	—
70	#95	—	79	16	no	—
71	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
72	C₂²×C₄	—	2	8	no	—
73	C₂²×C₄	—	79	8	no	—
74	C₂²×C₄	—	158	8	no	—
75	C₂²×C₄	—	158	16	no	—
76	C₂²×C₄	Dic₁₅₈	1	4	yes	—
77	C₂²×C₄	D₃₁₆	1	4	yes	—
78	C₂²×C₄	C₂×Dic₇₉	1	8	yes	—
79	C₂²×C₄	C₂×Dic₇₉	1	4	yes	—
80	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
81	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
82	C₄⋊C₄	—	158	16	no	—
83	C₄²	C₂×Dic₇₉	1	16	yes	complemented
84	C₂³	C₂²×Dic₇₉	1	2	yes	—
85	C₂³	C₂×D₃₁₆	1	2	yes	—
86	C₂³	C₂×Dic₁₅₈	1	2	yes	—
87	C₂³	#11929624	1	8	yes	—
88	C₂³	C₂³×D₇₉	1	1	yes	characteristic
89	C₂×C₄	—	2	8	no	—
90	C₂×C₄	—	2	16	no	—
91	C₂×C₄	—	316	16	no	—
92	C₂×C₄	—	158	16	no	—
93	C₂×C₄	—	158	8	no	—
94	C₂×C₄	C₄⋊Dic₇₉	1	16	yes	—
95	C₂×C₄	C₂²×Dic₇₉	1	8	yes	—
96	C₂×C₄	C₂²×Dic₇₉	1	4	yes	—
97	C₂×C₄	C₂×D₃₁₆	1	4	yes	—
98	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
99	C₂²	C₂×C₄⋊Dic₇₉	1	4	yes	—
100	C₂²	#14579120	1	8	yes	—
101	C₂²	#14579149	1	8	yes	—
102	C₂²	#14579153	1	8	yes	—
103	C₂²	C₂³×Dic₇₉	1	1	yes	characteristic
104	C₂²	C₂²×D₃₁₆	1	1	yes	characteristic
105	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
106	C₂²	C₂×#11929624	1	4	yes	—
107	C₄	—	2	8	no	—
108	C₄	—	316	8	no	—
109	C₄	C₂×C₄⋊Dic₇₉	1	8	yes	—
110	C₂	#19098429	1	8	yes	direct product factor
111	C₂	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
112	C₂	C₂×#14579120	1	2	yes	—
113	C₂	C₂×#14579149	1	2	yes	—
114	C₂	C₂×#14579153	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₇₉

C₂

yes

maximal

#19098429

C₂

yes

maximal, direct product factor

C₂×C₇₉⋊#95

C₂

yes

maximal

C₂²×C₄²×C₇₉

C₂

yes

maximal, characteristic

C₂³×Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂³×C₄×C₇₉

C₂²

yes

—

C₂³×C₄×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₄

yes

complemented

C₂×C₄²×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₂⁴×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

C₂²×C₄

yes

—

C₂³×C₇₉

C₂×D₄

yes

—

C₂³×C₇₉

C₂×Q₈

yes

—

C₂³×C₇₉

#41

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₄⋊C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

—

C₂²×C₇₉

#117

yes

—

C₂²×C₇₉

#124

yes

—

C₂²×C₇₉

#125

yes

—

C₂²×C₇₉

C₂³×C₄

yes

characteristic

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄⋊C₄

yes

—

Dic₇₉

—

C₂×C₇₉

#382

yes

complemented

C₂×C₇₉

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₇₉

C₂×#117

yes

—

C₂×C₇₉

C₂×#124

yes

—

C₂×C₇₉

C₂×#125

yes

—

C₂×#382

—

maximal, Sylow

C₇₉

C₂×#382

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂²×C₄²

D₇₉

yes

characteristic

#382

—

C₂×#95

—

C₂³×C₄

—

C₂³×C₄

C₂×D₇₉

yes

—

C₂³×C₄

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

Dic₇₉

yes

complemented

C₂×C₄²

C₂×D₇₉

yes

—

#95

—

C₂⁴

C₂²×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

Dic₁₅₈

yes

—

C₂²×C₄

D₃₁₆

yes

—

C₂²×C₄

C₂×Dic₇₉

yes

—

C₂²×C₄

C₂×Dic₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

158

—

C₄²

C₂×Dic₇₉

yes

complemented

C₂³

C₂²×Dic₇₉

yes

—

C₂³

C₂×D₃₁₆

yes

—

C₂³

C₂×Dic₁₅₈

yes

—

C₂³

#11929624

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₄⋊Dic₇₉

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

—

C₂×C₄

C₂²×Dic₇₉

yes

—

C₂×C₄

C₂×D₃₁₆

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂²

C₂×C₄⋊Dic₇₉

yes

—

100

C₂²

#14579120

yes

—

101

C₂²

#14579149

yes

—

102

C₂²

#14579153

yes

—

103

C₂²

C₂³×Dic₇₉

yes

characteristic

104

C₂²

C₂²×D₃₁₆

yes

characteristic

105

C₂²

C₂²×Dic₁₅₈

yes

characteristic

106

C₂²

C₂×#11929624

yes

—

107

C₄

—

108

C₄

—

316

—

109

C₄

C₂×C₄⋊Dic₇₉

yes

—

110

C₂

#19098429

yes

direct product factor

111

C₂

C₂²×C₄⋊Dic₇₉

yes

characteristic

112

C₂

C₂×#14579120

yes

—

113

C₂

C₂×#14579149

yes

—

114

C₂

C₂×#14579153

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₇₉
commutator	C₂²×C₇₉	C₂³×C₄
Frattini	C₂³	C₂³×D₇₉
Fitting	C₂²×C₄²×C₇₉	C₂
socle, prime radical	C₂⁴×C₇₉	C₂³
cosocle	C₂³×C₇₉	C₂⁴
hypercenter	C₂²×C₄²	D₇₉
hypocenter	C₇₉	C₂×#382
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

subgroup

G/H

center

C₂⁴

C₂²×D₇₉

commutator

C₂²×C₇₉

C₂³×C₄

Frattini

C₂³

C₂³×D₇₉

Fitting

C₂²×C₄²×C₇₉

C₂

socle, prime radical

C₂⁴×C₇₉

C₂³

cosocle

C₂³×C₇₉

C₂⁴

hypercenter

C₂²×C₄²

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂⁴ ◁ C₂²×C₄²

N	H ≅ G/N	type
2. #19098429	C₂	direct (N × H)
11. C₂×C₄²×C₇₉	C₄	semidirect
25. C₄²×C₇₉	C₂×C₄	semidirect
52. C₂×C₇₉	#382	semidirect
58. C₇₉	C₂×#382	semidirect
68. C₂×C₄²	Dic₇₉	semidirect
83. C₄²	C₂×Dic₇₉	semidirect
110. C₂	#19098429	direct (N × H)

H ≅ G/N

type

2. #19098429

C₂

direct (N × H)

11. C₂×C₄²×C₇₉

C₄

semidirect

25. C₄²×C₇₉

C₂×C₄

semidirect

52. C₂×C₇₉

#382

semidirect

58. C₇₉

C₂×#382

semidirect

68. C₂×C₄²

Dic₇₉

semidirect

83. C₄²

C₂×Dic₇₉

semidirect

110. C₂

#19098429

direct (N × H)

Subgroups — C₂×#19098429 #23765787

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19098429 #23765787

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098429 #23765787