Group #34178703 — subgroups

Subgroups — #34178703

Order 20224.

382 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 167 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	#23763145	C₂	1	3	yes	maximal
2	C₇₉⋊#1273	C₂	1	3	yes	maximal
3	C₇₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₇₉⋊C₈	C₂²	1	3	yes	—
5	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
6	#19098317	C₄	1	6	yes	—
7	#19098317	C₄	1	6	yes	—
8	C₂×C₄×C₈×C₇₉	C₂²	1	3	yes	—
9	C₂²×C₇₉⋊C₈	C₂×C₄	1	6	yes	—
10	C₂×C₄×Dic₇₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×Dic₇₉	C₂×C₄	1	3	yes	—
12	C₄×C₇₉⋊C₈	—	2	3	no	—
13	C₄×C₇₉⋊C₈	—	2	3	no	—
14	C₂²×C₈×C₇₉	C₂×C₄	1	6	yes	—
15	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₇₉	—	2	6	no	—
17	C₂²×Dic₇₉	C₄²	1	1	yes	characteristic
18	C₂²×Dic₇₉	C₄²	1	3	yes	—
19	C₂×C₇₉⋊C₈	—	2	6	no	—
20	C₂×C₇₉⋊C₈	—	2	6	no	—
21	C₂×C₇₉⋊C₈	—	2	6	no	—
22	C₄×Dic₇₉	—	2	6	no	—
23	C₄×Dic₇₉	—	2	6	no	—
24	C₂²×C₄×C₇₉	C₂²×C₄	1	3	yes	—
25	C₂×C₈×C₇₉	—	2	6	no	—
26	C₂×C₈×C₇₉	—	2	6	no	—
27	C₂×C₈×C₇₉	—	2	6	no	—
28	C₄²×C₇₉	#41	1	3	yes	—
29	C₄²×C₇₉	#41	1	1	yes	characteristic
30	C₂³×C₇₉	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄×C₇₉	#117	1	3	yes	—
32	C₂×C₄×C₇₉	#117	1	3	yes	—
33	C₂×C₄×C₇₉	#131	1	6	yes	—
34	C₂×C₄×C₇₉	#131	1	6	yes	—
35	C₂×Dic₇₉	—	2	3	no	—
36	C₂×Dic₇₉	—	2	3	no	—
37	C₂×Dic₇₉	—	2	6	no	—
38	C₈×C₇₉	—	4	6	no	—
39	C₇₉⋊C₈	—	4	6	no	—
40	C₂²×C₇₉	#376	1	1	yes	characteristic
41	C₂²×C₇₉	#405	1	3	yes	—
42	C₂²×C₇₉	#405	1	3	yes	—
43	C₄×C₇₉	#433	1	6	yes	—
44	C₄×C₇₉	#433	1	6	yes	—
45	Dic₇₉	—	4	1	no	—
46	Dic₇₉	—	4	3	no	—
47	#8135	—	79	1	no	maximal, Sylow
48	C₂×C₇₉	#1454	1	1	yes	characteristic
49	C₂×C₇₉	#1454	1	3	yes	—
50	C₂×C₇₉	#1746	1	3	yes	—
51	#1744	—	79	3	no	—
52	#1273	—	79	3	no	—
53	#1273	D₇₉	1	1	yes	characteristic
54	C₇₉	#8135	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₄×C₈	—	79	3	no	—
56	C₂×C₄×C₈	C₂×D₇₉	1	3	yes	—
57	C₄³	—	79	1	no	—
58	#336	—	79	6	no	—
59	#336	—	79	6	no	—
60	C₂²×C₈	—	79	6	no	—
61	C₂²×C₈	C₄×D₇₉	1	6	yes	—
62	C₂×C₄²	—	79	3	no	—
63	C₂×C₄²	—	79	3	no	—
64	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
65	C₄×C₈	—	2	6	no	—
66	C₄×C₈	—	158	3	no	—
67	C₄×C₈	—	158	3	no	—
68	C₂²×C₄	—	79	1	no	—
69	C₂²×C₄	—	79	3	no	—
70	C₂²×C₄	C₂×C₄×D₇₉	1	3	yes	—
71	C₂×C₈	—	2	6	no	—
72	C₂×C₈	—	2	6	no	—
73	C₂×C₈	—	2	6	no	—
74	C₂×C₈	—	158	6	no	—
75	C₂×C₈	—	158	6	no	—
76	C₂×C₈	—	158	6	no	—
77	C₄²	—	158	6	no	—
78	C₄²	—	158	6	no	—
79	C₄²	#11929623	1	3	yes	—
80	C₄²	#11929625	1	1	yes	characteristic
81	C₂³	C₄²×D₇₉	1	1	yes	characteristic
82	C₂×C₄	—	158	3	no	—
83	C₂×C₄	—	158	3	no	—
84	C₂×C₄	—	158	6	no	—
85	C₂×C₄	#14579117	1	3	yes	—
86	C₂×C₄	#14579119	1	3	yes	—
87	C₂×C₄	#14579167	1	6	yes	—
88	C₂×C₄	#14579169	1	6	yes	—
89	C₈	—	4	6	no	—
90	C₈	—	316	6	no	—
91	C₂²	#19098408	1	1	yes	characteristic
92	C₂²	#19098517	1	3	yes	—
93	C₂²	#19098520	1	3	yes	—
94	C₄	—	316	1	no	—
95	C₄	—	316	3	no	—
96	C₄	#19098621	1	6	yes	—
97	C₄	#19098623	1	6	yes	—
98	C₂	#23761699	1	1	yes	characteristic
99	C₂	#23761701	1	3	yes	—
100	C₂	#23763150	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#23763145

C₂

yes

maximal

C₇₉⋊#1273

C₂

yes

maximal

C₇₉×#1273

C₂

yes

maximal, characteristic

C₂×C₄×C₇₉⋊C₈

C₂²

yes

—

C₄²×Dic₇₉

C₂²

yes

characteristic

#19098317

C₄

yes

—

#19098317

C₄

yes

—

C₂×C₄×C₈×C₇₉

C₂²

yes

—

C₂²×C₇₉⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₇₉

C₂×C₄

yes

—

C₂×C₄×Dic₇₉

C₂×C₄

yes

—

C₄×C₇₉⋊C₈

—

C₄×C₇₉⋊C₈

—

C₂²×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₄²×C₇₉

C₂³

yes

characteristic

C₄×C₈×C₇₉

—

C₂²×Dic₇₉

C₄²

yes

characteristic

C₂²×Dic₇₉

C₄²

yes

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

#41

yes

—

C₄²×C₇₉

#41

yes

characteristic

C₂³×C₇₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₇₉

#117

yes

—

C₂×C₄×C₇₉

#117

yes

—

C₂×C₄×C₇₉

#131

yes

—

C₂×C₄×C₇₉

#131

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

#376

yes

characteristic

C₂²×C₇₉

#405

yes

—

C₂²×C₇₉

#405

yes

—

C₄×C₇₉

#433

yes

—

C₄×C₇₉

#433

yes

—

Dic₇₉

—

Dic₇₉

—

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#1746

yes

—

#1744

—

#1273

—

#1273

D₇₉

yes

characteristic

C₇₉

#8135

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₇₉

yes

—

C₄³

—

#336

—

#336

—

C₂²×C₈

—

C₂²×C₈

C₄×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₇₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

158

—

C₄×C₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₇₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₄²

—

158

—

C₄²

—

158

—

C₄²

#11929623

yes

—

C₄²

#11929625

yes

characteristic

C₂³

C₄²×D₇₉

yes

characteristic

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

#14579117

yes

—

C₂×C₄

#14579119

yes

—

C₂×C₄

#14579167

yes

—

C₂×C₄

#14579169

yes

—

C₈

—

C₈

—

316

—

C₂²

#19098408

yes

characteristic

C₂²

#19098517

yes

—

C₂²

#19098520

yes

—

C₄

—

316

—

C₄

—

316

—

C₄

#19098621

yes

—

C₄

#19098623

yes

—

C₂

#23761699

yes

characteristic

C₂

#23761701

yes

—

100

C₂

#23763150

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₇₉
commutator, socle, prime radical	C₂³×C₇₉	C₂×C₄²
Fitting	C₇₉×#1273	C₂
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1273	D₇₉
hypocenter	C₇₉	#8135
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₇₉

commutator, socle, prime radical

C₂³×C₇₉

C₂×C₄²

Fitting

C₇₉×#1273

C₂

cosocle

C₂×C₄²×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
54. C₇₉	#8135	semidirect

H ≅ G/N

type

54. C₇₉

#8135

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23763145	2
C₇₉⋊#1273	2
C₇₉×#1273	2
#8135	79

subgroup

index

#23763145

C₇₉⋊#1273

C₇₉×#1273

#8135

Subgroups — #34178703

Conjugacy classes of subgroups

Complements

Maximal subgroups