Group #23765763 — subgroups

Subgroups — #23765763

Order 10112.

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

normal subgroups only

This group has 628 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×Dic₁₅₈	C₂	1	3	yes	maximal
2	C₄×C₄⋊Dic₇₉	C₂	1	3	yes	maximal
3	#19098414	C₂	1	6	yes	maximal
4	#19098408	C₂	1	2	yes	maximal
5	#376×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	C₄×Dic₁₅₈	C₄	1	24	yes	complemented
8	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
9	C₂×Dic₇₉⋊C₄	C₂²	1	6	yes	—
10	C₂×C₄×Dic₇₉	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	C₂×Dic₁₅₈	C₂×C₄	1	12	yes	—
17	C₂²×Dic₇₉	C₂³	1	6	yes	—
18	C₂²×Dic₇₉	C₂³	1	2	yes	—
19	C₄⋊Dic₇₉	C₂×C₄	1	12	yes	—
20	Dic₇₉⋊C₄	C₂×C₄	1	24	yes	—
21	C₄×Dic₇₉	—	4	6	no	—
22	C₄×Dic₇₉	C₂×C₄	1	24	yes	—
23	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
24	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
26	C₄²×C₇₉	C₂×C₄	1	12	yes	—
27	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₇₉	—	2	3	no	—
29	C₂×C₄×C₇₉	—	2	6	no	—
30	C₂×C₄×C₇₉	—	2	3	no	—
31	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
32	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
33	C₂×C₄×C₇₉	C₂²×C₄	1	6	yes	—
34	C₂×Dic₇₉	—	2	6	no	—
35	C₂×Dic₇₉	—	2	6	no	—
36	C₂×Dic₇₉	C₂²×C₄	1	12	yes	—
37	C₂×Dic₇₉	C₂²×C₄	1	12	yes	—
38	Dic₁₅₈	C₄²	1	16	yes	complemented
39	C₂²×C₇₉	C₂³×C₄	1	3	yes	—
40	C₂²×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
41	C₂²×C₇₉	2₋¹⁺⁴	1	3	yes	—
42	C₄×C₇₉	—	2	6	no	—
43	C₄×C₇₉	—	2	6	no	—
44	C₄×C₇₉	C₂×C₄²	1	4	yes	—
45	Dic₇₉	—	2	12	no	—
46	Dic₇₉	C₂×C₄²	1	8	yes	—
47	C₂×C₇₉	C₂²×C₄²	1	1	yes	characteristic
48	C₂×C₇₉	#519	1	3	yes	—
49	C₂×C₇₉	#520	1	3	yes	—
50	#2276	—	79	1	no	maximal, Sylow
51	C₇₉	#2276	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₄×Q₈	—	79	3	no	—
53	C₄×C₄⋊C₄	—	79	3	no	—
54	C₄×C₄⋊C₄	—	79	6	no	—
55	#376	—	79	2	no	—
56	#376	D₇₉	1	1	yes	characteristic
57	C₂²×Q₈	—	79	1	no	—
58	C₄×Q₈	—	79	24	no	—
59	C₂×C₄⋊C₄	—	79	6	no	—
60	C₂×C₄⋊C₄	—	79	3	no	—
61	C₂×C₄²	—	79	6	no	—
62	C₂×C₄²	—	79	6	no	—
63	C₂×C₄²	C₂×D₇₉	1	3	yes	—
64	#95	—	79	6	no	—
65	#95	C₂×D₇₉	1	1	yes	characteristic
66	#95	C₂×D₇₉	1	3	yes	—
67	C₂×Q₈	—	79	12	no	—
68	C₂²×C₄	—	79	2	no	—
69	C₂²×C₄	—	79	6	no	—
70	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
71	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
72	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
73	C₄⋊C₄	—	79	24	no	—
74	C₄⋊C₄	—	79	12	no	—
75	C₄²	—	316	6	no	—
76	C₄²	—	79	24	no	—
77	C₄²	C₄×D₇₉	1	12	yes	—
78	C₂³	C₂³×D₇₉	1	1	yes	characteristic
79	Q₈	—	79	16	no	—
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	6	no	—
82	C₂×C₄	—	2	3	no	—
83	C₂×C₄	—	79	12	no	—
84	C₂×C₄	—	79	12	no	—
85	C₂×C₄	—	158	6	no	—
86	C₂×C₄	—	158	6	no	—
87	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
88	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
89	C₂×C₄	C₂×C₄×D₇₉	1	6	yes	—
90	C₂²	C₂²×C₄×D₇₉	1	3	yes	—
91	C₂²	#14579207	1	1	yes	characteristic
92	C₂²	#14579208	1	3	yes	—
93	C₄	—	2	6	no	—
94	C₄	—	2	6	no	—
95	C₄	—	79	8	no	—
96	C₄	—	158	12	no	—
97	C₄	C₄²×D₇₉	1	4	yes	—
98	C₂	C₂×C₄²×D₇₉	1	1	yes	characteristic
99	C₂	#19099040	1	3	yes	—
100	C₂	#19099043	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₁₅₈

C₂

yes

maximal

C₄×C₄⋊Dic₇₉

C₂

yes

maximal

#19098414

C₂

yes

maximal

#19098408

C₂

yes

maximal

#376×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

C₄×Dic₁₅₈

C₄

yes

complemented

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

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

—

C₂×Dic₁₅₈

C₂×C₄

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

C₂×C₄

yes

—

Dic₇₉⋊C₄

C₂×C₄

yes

—

C₄×Dic₇₉

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

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

—

C₂×Dic₇₉

C₂²×C₄

yes

—

C₂×Dic₇₉

C₂²×C₄

yes

—

Dic₁₅₈

C₄²

yes

complemented

C₂²×C₇₉

C₂³×C₄

yes

—

C₂²×C₇₉

H(5,𝔽₂)

yes

characteristic

C₂²×C₇₉

2₋¹⁺⁴

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×C₄²

yes

—

Dic₇₉

—

Dic₇₉

C₂×C₄²

yes

—

C₂×C₇₉

C₂²×C₄²

yes

characteristic

C₂×C₇₉

#519

yes

—

C₂×C₇₉

#520

yes

—

#2276

—

maximal, Sylow

C₇₉

#2276

yes

characteristic, complemented, Sylow

C₂×C₄×Q₈

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

#376

—

#376

D₇₉

yes

characteristic

C₂²×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

#95

—

#95

C₂×D₇₉

yes

characteristic

#95

C₂×D₇₉

yes

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

316

—

C₄²

—

C₄²

C₄×D₇₉

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

—

C₂²

C₂²×C₄×D₇₉

yes

—

C₂²

#14579207

yes

characteristic

C₂²

#14579208

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

158

—

C₄

C₄²×D₇₉

yes

—

C₂

C₂×C₄²×D₇₉

yes

characteristic

C₂

#19099040

yes

—

100

C₂

#19099043

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator	C₂×C₇₉	C₂²×C₄²
Fitting	#376×C₇₉	C₂
socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
hypercenter	#376	D₇₉
hypocenter	C₇₉	#2276
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, prime radical, cosocle

C₂³×C₇₉

C₂⁴

D₇₉

C₇₉

G ▷ C₂×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
7. C₄×Dic₁₅₈	C₄	semidirect
38. Dic₁₅₈	C₄²	semidirect
51. C₇₉	#2276	semidirect

H ≅ G/N

type

7. C₄×Dic₁₅₈

C₄

semidirect

38. Dic₁₅₈

C₄²

semidirect

51. C₇₉

#2276

semidirect

Subgroups — #23765763

Conjugacy classes of subgroups

Complements