Group #23765001 — subgroups

Subgroups — C₂×#19098340 #23765001

Order 10112.

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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×#14579101	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579071	C₂	1	1	yes	maximal, characteristic
3	#19098340	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₇₉⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₇₉	C₄	1	1	yes	characteristic
7	#14579101	C₄	1	2	yes	complemented
8	#14579101	C₂²	1	2	yes	—
9	C₂×C₇₉⋊C₁₆	C₄	1	2	yes	complemented
10	#14579071	C₄	1	2	yes	—
11	#14579071	C₂²	1	2	yes	—
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	M₃₂×C₇₉	C₄	1	2	yes	complemented
14	M₃₂×C₇₉	C₂²	1	2	yes	—
15	C₂×C₁₆×C₇₉	C₄	1	2	yes	complemented
16	C₂²×Dic₇₉	—	2	1	no	—
17	C₂×C₇₉⋊C₈	—	2	1	no	—
18	C₂×C₇₉⋊C₈	—	2	1	no	—
19	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
20	C₄×Dic₇₉	—	2	1	no	—
21	C₄×Dic₇₉	C₂×C₄	1	2	yes	—
22	C₇₉⋊C₁₆	C₂×C₄	1	4	yes	complemented
23	C₂²×C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
30	C₁₆×C₇₉	C₂×C₄	1	4	yes	complemented
31	C₂³×C₇₉	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₇₉	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₇₉	M₁₆	1	1	yes	characteristic
35	C₂×C₄×C₇₉	M₁₆	1	1	yes	characteristic
36	C₂×C₄×C₇₉	M₁₆	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₇₉	—	2	2	no	—
39	C₂×Dic₇₉	—	4	2	no	—
40	C₈×C₇₉	C₄²	1	1	yes	characteristic
41	C₈×C₇₉	C₄²	1	1	yes	characteristic
42	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
43	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
44	C₇₉⋊C₈	—	2	2	no	—
45	C₂²×C₇₉	—	2	2	no	—
46	C₂²×C₇₉	#97	1	1	yes	characteristic
47	C₂²×C₇₉	#97	1	1	yes	characteristic
48	C₂²×C₇₉	C₂×M₁₆	1	1	yes	characteristic
49	C₄×C₇₉	#97	1	1	yes	characteristic
50	C₄×C₇₉	#97	1	1	yes	characteristic
51	C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
52	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
53	Dic₇₉	—	4	2	no	—
54	C₂×C₇₉	—	2	1	no	—
55	C₂×C₇₉	—	2	1	no	—
56	C₂×C₇₉	#347	1	2	yes	complemented
57	C₂×C₇₉	C₂×#97	1	1	yes	characteristic
58	C₂×#347	—	79	1	no	maximal, Sylow
59	C₇₉	C₂×#347	1	1	yes	characteristic, complemented, Sylow
60	C₂×M₃₂	—	79	1	no	—
61	C₂×M₃₂	D₇₉	1	1	yes	characteristic
62	C₂×#97	—	79	1	no	—
63	#347	—	79	4	no	—
64	C₂²×C₈	—	79	1	no	—
65	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
66	C₂×C₄²	—	79	1	no	—
67	M₃₂	—	79	2	no	—
68	M₃₂	—	79	2	no	—
69	M₃₂	Dic₇₉	1	2	yes	complemented
70	M₃₂	C₂×D₇₉	1	2	yes	—
71	C₂×C₁₆	—	79	2	no	—
72	C₂×C₁₆	Dic₇₉	1	2	yes	complemented
73	#97	—	79	2	no	—
74	#97	—	79	2	no	—
75	C₂²×C₄	—	158	1	no	—
76	C₂²×C₄	C₄×D₇₉	1	1	yes	characteristic
77	C₂×C₈	—	79	2	no	—
78	C₂×C₈	—	158	1	no	—
79	C₂×C₈	—	158	1	no	—
80	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
81	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
82	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
83	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
84	C₂×C₈	C₂×Dic₇₉	1	1	yes	characteristic
85	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
86	C₄²	—	79	2	no	—
87	C₄²	—	158	1	no	—
88	C₁₆	—	79	4	no	—
89	C₁₆	C₂×Dic₇₉	1	4	yes	complemented
90	C₂³	#11929607	1	1	yes	characteristic
91	C₂×C₄	—	316	2	no	—
92	C₂×C₄	—	158	2	no	—
93	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
94	C₂×C₄	C₄×Dic₇₉	1	1	yes	characteristic
95	C₂×C₄	#11929607	1	1	yes	characteristic
96	C₂×C₄	#11929607	1	1	yes	characteristic
97	C₂×C₄	#11929607	1	1	yes	characteristic
98	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
99	C₈	—	158	2	no	—
100	C₈	C₄×Dic₇₉	1	1	yes	characteristic
101	C₈	C₄×Dic₇₉	1	1	yes	characteristic
102	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
103	C₈	C₂²×Dic₇₉	1	1	yes	characteristic
104	C₂²	—	2	2	no	—
105	C₂²	#14579071	1	1	yes	characteristic
106	C₂²	#14579071	1	1	yes	characteristic
107	C₂²	C₂×#11929607	1	1	yes	characteristic
108	C₄	—	316	2	no	—
109	C₄	#14579071	1	1	yes	characteristic
110	C₄	#14579071	1	1	yes	characteristic
111	C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
112	C₄	C₂×#11929607	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#19098340	1	2	yes	direct product factor
116	C₂	C₂×#14579071	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579101

C₂

yes

maximal, characteristic

C₂×#14579071

C₂

yes

maximal, characteristic

#19098340

C₂

yes

maximal, direct product factor

C₂×M₃₂×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₇₉

C₄

yes

characteristic

#14579101

C₄

yes

complemented

#14579101

C₂²

yes

—

C₂×C₇₉⋊C₁₆

C₄

yes

complemented

#14579071

C₄

yes

—

#14579071

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₄

yes

complemented

M₃₂×C₇₉

C₂²

yes

—

C₂×C₁₆×C₇₉

C₄

yes

complemented

C₂²×Dic₇₉

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₇₉⋊C₁₆

C₂×C₄

yes

complemented

C₂²×C₄×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₁₆×C₇₉

C₂×C₄

yes

complemented

C₂³×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

C₄²

yes

characteristic

C₂×C₄×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

M₁₆

yes

characteristic

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

C₄²

yes

characteristic

C₈×C₇₉

C₄²

yes

characteristic

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

yes

C₂²×C₇₉

yes

C₂²×C₇₉

C₂×M₁₆

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

C₂×C₄²

yes

characteristic

C₄×C₇₉

C₂×M₁₆

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#347

yes

complemented

C₂×C₇₉

C₂×#97

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×M₃₂

D₇₉

yes

characteristic

C₂×#97

—

#347

—

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

Dic₇₉

yes

complemented

M₃₂

C₂×D₇₉

yes

—

C₂×C₁₆

—

C₂×C₁₆

Dic₇₉

yes

complemented

#97

—

#97

—

C₂²×C₄

—

158

—

C₂²×C₄

C₄×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂×Dic₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄²

—

C₄²

—

158

—

C₁₆

—

C₁₆

C₂×Dic₇₉

yes

complemented

C₂³

#11929607

yes

characteristic

C₂×C₄

—

316

—

C₂×C₄

—

158

—

C₂×C₄

C₄×Dic₇₉

yes

characteristic

C₂×C₄

C₄×Dic₇₉

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₈

—

158

—

100

C₈

C₄×Dic₇₉

yes

characteristic

101

C₈

C₄×Dic₇₉

yes

characteristic

102

C₈

C₂×C₄×D₇₉

yes

characteristic

103

C₈

C₂²×Dic₇₉

yes

characteristic

104

C₂²

—

105

C₂²

#14579071

yes

characteristic

106

C₂²

#14579071

yes

characteristic

107

C₂²

C₂×#11929607

yes

characteristic

108

C₄

—

316

—

109

C₄

#14579071

yes

characteristic

110

C₄

#14579071

yes

characteristic

111

C₄

C₂×C₄×Dic₇₉

yes

characteristic

112

C₄

C₂×#11929607

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#19098340

yes

direct product factor

116

C₂

C₂×#14579071

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄×Dic₇₉
commutator	C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₂×M₃₂×C₇₉	C₂
socle	C₂²×C₇₉	#97
prime radical	C₂³×C₇₉	M₁₆
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₂×M₃₂	D₇₉
hypocenter	C₇₉	C₂×#347
LCS	G ▷ C₄×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₃₂

subgroup

G/H

center

C₂×C₄

C₄×Dic₇₉

commutator

C₄×C₇₉

C₂×C₄²

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₂×M₃₂×C₇₉

C₂

socle

C₂²×C₇₉

#97

prime radical

C₂³×C₇₉

M₁₆

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₂×M₃₂

D₇₉

C₇₉

G ▷ C₄×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₄ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #19098340	C₂	direct (N × H)
7. #14579101	C₄	semidirect
9. C₂×C₇₉⋊C₁₆	C₄	semidirect
13. M₃₂×C₇₉	C₄	semidirect
15. C₂×C₁₆×C₇₉	C₄	semidirect
22. C₇₉⋊C₁₆	C₂×C₄	semidirect
30. C₁₆×C₇₉	C₂×C₄	semidirect
56. C₂×C₇₉	#347	semidirect
59. C₇₉	C₂×#347	semidirect
69. M₃₂	Dic₇₉	semidirect
72. C₂×C₁₆	Dic₇₉	semidirect
89. C₁₆	C₂×Dic₇₉	semidirect
115. C₂	#19098340	direct (N × H)

H ≅ G/N

type

3. #19098340

C₂

direct (N × H)

7. #14579101

C₄

semidirect

9. C₂×C₇₉⋊C₁₆

C₄

semidirect

13. M₃₂×C₇₉

C₄

semidirect

15. C₂×C₁₆×C₇₉

C₄

semidirect

22. C₇₉⋊C₁₆

C₂×C₄

semidirect

30. C₁₆×C₇₉

C₂×C₄

semidirect

56. C₂×C₇₉

#347

semidirect

59. C₇₉

C₂×#347

semidirect

69. M₃₂

Dic₇₉

semidirect

72. C₂×C₁₆

Dic₇₉

semidirect

89. C₁₆

C₂×Dic₇₉

semidirect

115. C₂

#19098340

direct (N × H)

Subgroups — C₂×#19098340 #23765001

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19098340 #23765001

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098340 #23765001