Group #23771763 — subgroups

Subgroups — #23771763

Order 10112.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#14579153	C₂	1	2	yes	maximal
2	#19098461	C₂	1	8	yes	maximal
3	#19098433	C₂	1	2	yes	maximal
4	#19098429	C₂	1	2	yes	maximal
5	C₄³×C₇₉	C₂	1	1	yes	maximal, characteristic
6	#14579153	—	2	8	no	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	8	yes	—
9	C₂×Dic₇₉⋊C₄	C₂²	1	8	yes	—
10	C₇₉⋊#95	C₂²	1	8	yes	—
11	C₂×C₄²×C₇₉	C₂²	1	4	yes	—
12	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₉	C₂³	1	8	yes	—
16	C₄⋊Dic₇₉	—	2	8	no	—
17	C₄⋊Dic₇₉	—	2	16	no	—
18	Dic₇₉⋊C₄	—	2	16	no	—
19	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
20	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
21	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
23	C₄²×C₇₉	—	2	8	no	—
24	C₄²×C₇₉	D₄	1	4	yes	—
25	C₄²×C₇₉	Q₈	1	4	yes	—
26	C₄²×C₇₉	Q₈	1	4	yes	—
27	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₇₉	—	2	4	no	—
29	C₂×C₄×C₇₉	—	2	4	no	—
30	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₇₉	#41	1	8	yes	—
37	C₂×Dic₇₉	—	2	8	no	—
38	C₂×Dic₇₉	—	2	16	no	—
39	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
41	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₇₉	C₂×#41	1	4	yes	—
43	C₄×C₇₉	—	2	4	no	—
44	C₄×C₇₉	—	2	4	no	—
45	C₄×C₇₉	#125	1	8	yes	complemented
46	C₄×C₇₉	C₄⋊Q₈	1	4	yes	—
47	Dic₇₉	—	4	8	no	—
48	C₂×C₇₉	C₂×#125	1	2	yes	—
49	C₂×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₇₉	#532	1	2	yes	—
51	C₂×C₇₉	#533	1	2	yes	—
52	#2859	—	79	1	no	maximal, Sylow
53	C₇₉	#2859	1	1	yes	characteristic, complemented, Sylow
54	C₂×#125	—	79	2	no	—
55	#389	—	79	8	no	—
56	#384	—	79	2	no	—
57	#382	—	79	2	no	—
58	C₄³	D₇₉	1	1	yes	characteristic
59	#125	—	158	8	no	—
60	C₂×C₄⋊C₄	—	79	4	no	—
61	C₂×C₄⋊C₄	—	79	8	no	—
62	C₂×C₄⋊C₄	—	79	8	no	—
63	C₂×C₄²	C₂×D₇₉	1	4	yes	—
64	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
67	#95	—	79	8	no	—
68	C₂²×C₄	—	79	8	no	—
69	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
70	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
71	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
73	C₄⋊C₄	—	158	16	no	—
74	C₄⋊C₄	—	158	8	no	—
75	C₄⋊C₄	—	158	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₁₅₈	1	4	yes	—
78	C₄²	Dic₁₅₈	1	4	yes	—
79	C₄²	D₃₁₆	1	4	yes	—
80	C₂³	C₂³×D₇₉	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	158	16	no	—
84	C₂×C₄	—	158	8	no	—
85	C₂×C₄	C₂×D₃₁₆	1	4	yes	—
86	C₂×C₄	C₂×D₃₁₆	1	2	yes	—
87	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
88	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
89	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
90	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
91	C₂×C₄	#11929624	1	8	yes	—
92	C₂²	C₂²×D₃₁₆	1	1	yes	characteristic
93	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
94	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
95	C₂²	C₂×#11929624	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	316	8	no	—
99	C₄	#14579153	1	8	yes	complemented
100	C₄	#14579161	1	4	yes	—
101	C₂	C₂×#14579153	1	2	yes	—
102	C₂	C₂×#14579161	1	1	yes	characteristic
103	C₂	#19099113	1	2	yes	—
104	C₂	#19099120	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579153

C₂

yes

maximal

#19098461

C₂

yes

maximal

#19098433

C₂

yes

maximal

#19098429

C₂

yes

maximal

C₄³×C₇₉

C₂

yes

maximal, characteristic

#14579153

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

D₄

yes

—

C₄²×C₇₉

Q₈

yes

—

C₄²×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#125

yes

complemented

C₄×C₇₉

C₄⋊Q₈

yes

—

Dic₇₉

—

C₂×C₇₉

C₂×#125

yes

—

C₂×C₇₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₉

#532

yes

—

C₂×C₇₉

#533

yes

—

#2859

—

maximal, Sylow

C₇₉

#2859

yes

characteristic, complemented, Sylow

—

—

—

—

C₄³

D₇₉

yes

characteristic

#125

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₂×C₄²

C₂×D₇₉

yes

characteristic

C₂×C₄²

C₂×D₇₉

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₄²

Dic₁₅₈

yes

—

C₄²

Dic₁₅₈

yes

—

C₄²

D₃₁₆

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×D₃₁₆

yes

—

C₂×C₄

C₂×D₃₁₆

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

#11929624

yes

—

C₂²

C₂²×D₃₁₆

yes

characteristic

C₂²

C₂²×Dic₁₅₈

yes

characteristic

C₂²

C₂²×Dic₁₅₈

yes

characteristic

C₂²

C₂×#11929624

yes

—

C₄

—

C₄

—

C₄

—

316

—

C₄

#14579153

yes

complemented

100

C₄

#14579161

yes

—

101

C₂

C₂×#14579153

yes

—

102

C₂

C₂×#14579161

yes

characteristic

103

C₂

#19099113

yes

—

104

C₂

#19099120

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	C₄³×C₇₉	C₂
hypercenter	C₄³	D₇₉
hypocenter	C₇₉	#2859
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

C₄³×C₇₉

C₂

hypercenter

C₄³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
45. C₄×C₇₉	#125	semidirect
53. C₇₉	#2859	semidirect
99. C₄	#14579153	semidirect

H ≅ G/N

type

45. C₄×C₇₉

#125

semidirect

53. C₇₉

#2859

semidirect

99. C₄

#14579153

semidirect

Subgroups — #23771763

Conjugacy classes of subgroups

Complements