Group #23765205 — subgroups

Subgroups — #23765205

Order 10112.

138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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	#19098517	C₂	1	1	yes	maximal, characteristic
2	Dic₇₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
3	(C₂×D₇₉)⋊C₁₆	C₂	1	2	yes	maximal
4	#19098339	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929607	C₄	1	1	yes	characteristic
7	C₂×C₈×D₇₉	C₂²	1	1	yes	characteristic
8	#14579118	C₄	1	1	yes	characteristic
9	C₂×C₇₉⋊C₁₆	C₂²	1	2	yes	—
10	#14579072	C₄	1	1	yes	characteristic
11	#14579071	C₄	1	1	yes	characteristic
12	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×C₇₉	C₂²	1	2	yes	—
14	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
16	#11929607	—	2	2	no	—
17	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₂×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₈×D₇₉	—	2	2	no	—
20	Dic₇₉⋊C₄	C₈	1	2	yes	—
21	(C₂×D₇₉)⋊C₄	C₈	1	2	yes	—
22	C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
23	C₇₉⋊C₁₆	—	2	2	no	—
24	C₂×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
26	C₄²×C₇₉	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₇₉	—	2	2	no	—
28	C₂²×D₇₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₇₉	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₇₉	C₂×C₈	1	2	yes	—
32	C₂×Dic₇₉	C₂×C₈	1	1	yes	characteristic
33	C₄×D₇₉	—	2	1	no	—
34	C₄×D₇₉	—	2	1	no	—
35	C₈×C₇₉	M₁₆	1	2	yes	—
36	C₈×C₇₉	#41	1	2	yes	—
37	C₇₉⋊C₈	—	2	1	no	—
38	C₇₉⋊C₈	—	2	1	no	—
39	C₂²×C₇₉	C₂²×C₈	1	1	yes	characteristic
40	C₂×D₇₉	—	2	1	no	—
41	C₂×D₇₉	—	2	2	no	—
42	C₄×C₇₉	—	2	2	no	—
43	C₄×C₇₉	#117	1	1	yes	characteristic
44	C₄×C₇₉	C₂×M₁₆	1	1	yes	characteristic
45	Dic₇₉	—	2	1	no	—
46	Dic₇₉	—	2	2	no	—
47	C₂×C₇₉	#431	1	1	yes	characteristic
48	C₂×C₇₉	#504	1	2	yes	—
49	D₇₉	—	4	1	no	—
50	#2164	—	79	1	no	maximal, Sylow
51	C₇₉	#2164	1	1	yes	characteristic, complemented, Sylow
52	#405	—	79	1	no	—
53	C₄⋊C₁₆	—	79	2	no	—
54	C₂²⋊C₁₆	—	79	2	no	—
55	#346	—	79	1	no	—
56	C₄×C₁₆	D₇₉	1	1	yes	characteristic, complemented
57	C₂×M₁₆	—	79	1	no	—
58	C₂²×C₈	—	79	1	no	—
59	#117	—	79	1	no	—
60	C₂×C₁₆	—	79	2	no	—
61	C₂×C₁₆	C₂×D₇₉	1	2	yes	—
62	#97	—	79	1	no	—
63	#97	—	79	1	no	—
64	C₄×C₈	—	79	1	no	—
65	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
66	C₂²×C₄	—	79	1	no	—
67	M₁₆	—	158	2	no	—
68	C₂×C₈	—	79	1	no	—
69	C₂×C₈	—	79	1	no	—
70	C₂×C₈	—	158	2	no	—
71	C₂×C₈	C₄×D₇₉	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
73	C₄⋊C₄	—	79	2	no	—
74	C₂²⋊C₄	—	79	2	no	—
75	C₄²	—	79	1	no	—
76	C₄²	C₄×D₇₉	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	158	2	no	—
79	C₂³	—	79	1	no	—
80	C₂×C₄	—	79	2	no	—
81	C₂×C₄	—	79	1	no	—
82	C₂×C₄	—	158	1	no	—
83	C₂×C₄	—	158	1	no	—
84	C₂×C₄	C₈×D₇₉	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
86	C₈	—	158	1	no	—
87	C₈	—	158	1	no	—
88	C₈	#11929607	1	2	yes	—
89	C₈	#11929624	1	2	yes	—
90	C₂²	—	158	2	no	—
91	C₂²	—	158	1	no	—
92	C₂²	C₂×C₈×D₇₉	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	158	2	no	—
95	C₄	—	158	1	no	—
96	C₄	#14579118	1	1	yes	characteristic
97	C₄	C₂×#11929607	1	1	yes	characteristic
98	C₂	—	316	1	no	—
99	C₂	#19098614	1	1	yes	characteristic
100	C₂	#19098979	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098517

C₂

yes

maximal, characteristic

Dic₇₉⋊C₁₆

C₂

yes

maximal, complemented

(C₂×D₇₉)⋊C₁₆

C₂

yes

maximal

#19098339

C₂

yes

maximal, characteristic, complemented

C₄×C₁₆×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929607

C₄

yes

characteristic

C₂×C₈×D₇₉

C₂²

yes

characteristic

#14579118

C₄

yes

characteristic

C₂×C₇₉⋊C₁₆

C₂²

yes

—

#14579072

C₄

yes

characteristic

#14579071

C₄

yes

characteristic

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄×D₇₉

C₂×C₄

yes

characteristic

#11929607

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₂×C₇₉⋊C₈

C₂×C₄

yes

characteristic

C₈×D₇₉

—

Dic₇₉⋊C₄

C₈

yes

—

(C₂×D₇₉)⋊C₄

C₈

yes

—

C₄×Dic₇₉

C₂×C₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂×C₄

yes

characteristic

C₁₆×C₇₉

—

C₂²×D₇₉

C₂×C₈

yes

characteristic

C₂×C₄×C₇₉

C₂×C₈

yes

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×Dic₇₉

C₂×C₈

yes

—

C₂×Dic₇₉

C₂×C₈

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₈×C₇₉

M₁₆

yes

—

C₈×C₇₉

#41

yes

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂²×C₈

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#117

yes

characteristic

C₄×C₇₉

C₂×M₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#431

yes

characteristic

C₂×C₇₉

#504

yes

—

D₇₉

—

#2164

—

maximal, Sylow

C₇₉

#2164

yes

characteristic, complemented, Sylow

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

—

C₄×C₁₆

D₇₉

yes

characteristic, complemented

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂²×C₄

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₇₉

yes

characteristic

C₁₆

—

C₁₆

—

158

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₈×D₇₉

yes

—

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

C₈

—

158

—

C₈

—

158

—

C₈

#11929607

yes

—

C₈

#11929624

yes

—

C₂²

—

158

—

C₂²

—

158

—

C₂²

C₂×C₈×D₇₉

yes

characteristic

C₄

—

C₄

—

158

—

C₄

—

158

—

C₄

yes

C₄

yes

C₂

—

316

—

C₂

#19098614

yes

characteristic

100

C₂

#19098979

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₇₉
commutator, socle	C₂²×C₇₉	C₂²×C₈
Fitting	C₄×C₁₆×C₇₉	C₂
prime radical	C₂²×D₇₉	C₂×C₈
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×C₁₆	D₇₉
hypocenter	C₇₉	#2164
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₇₉

commutator, socle

C₂²×C₇₉

C₂²×C₈

Fitting

C₄×C₁₆×C₇₉

C₂

prime radical

C₂²×D₇₉

C₂×C₈

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₄×C₁₆

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. Dic₇₉⋊C₁₆	C₂	semidirect
4. #19098339	C₂	semidirect
5. C₄×C₁₆×C₇₉	C₂	semidirect
51. C₇₉	#2164	semidirect
56. C₄×C₁₆	D₇₉	semidirect

H ≅ G/N

type

2. Dic₇₉⋊C₁₆

C₂

semidirect

4. #19098339

C₂

semidirect

5. C₄×C₁₆×C₇₉

C₂

semidirect

51. C₇₉

#2164

semidirect

56. C₄×C₁₆

D₇₉

semidirect

Subgroups — #23765205

Conjugacy classes of subgroups

Complements