Group #23766705 — subgroups

Subgroups — #23766705

Order 10112.

400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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	#19098505	C₂	1	4	yes	maximal
2	#19098497	C₂	1	4	yes	maximal
3	C₄×Dic₇₉⋊C₄	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₇₉	C₂	1	2	yes	maximal
5	#376×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₉	C₂²	1	4	yes	—
7	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
8	C₂×Dic₇₉⋊C₄	C₂²	1	4	yes	—
9	C₂×C₄×Dic₇₉	C₂²	1	4	yes	—
10	C₇₉⋊#95	C₂²	1	2	yes	—
11	C₇₉⋊#95	C₂²	1	2	yes	—
12	C₇₉⋊#95	C₂²	1	4	yes	—
13	C₇₉⋊#95	C₂²	1	4	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
16	#95×C₇₉	C₂²	1	4	yes	—
17	C₂²×Dic₇₉	C₂³	1	4	yes	—
18	C₂²×Dic₇₉	C₂³	1	4	yes	—
19	C₄⋊Dic₇₉	—	2	8	no	—
20	Dic₇₉⋊C₄	—	2	8	no	—
21	Dic₇₉⋊C₄	—	2	8	no	—
22	C₄×Dic₇₉	—	2	8	no	—
23	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
24	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
26	C₄²×C₇₉	—	2	4	no	—
27	C₄²×C₇₉	Q₈	1	4	yes	—
28	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₇₉	—	2	4	no	—
30	C₂×C₄×C₇₉	—	2	4	no	—
31	C₂×C₄×C₇₉	—	2	4	no	—
32	C₂×C₄×C₇₉	—	2	4	no	—
33	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₇₉	#41	1	4	yes	—
36	C₂×Dic₇₉	—	2	4	no	—
37	C₂×Dic₇₉	—	2	4	no	—
38	C₂×Dic₇₉	—	2	4	no	—
39	C₂×Dic₇₉	—	2	4	no	—
40	C₂×Dic₇₉	—	2	4	no	—
41	C₂×Dic₇₉	#41	1	8	yes	—
42	C₂²×C₇₉	C₂²×Q₈	1	1	yes	characteristic
43	C₂²×C₇₉	C₂×#41	1	4	yes	—
44	C₂²×C₇₉	C₂×#41	1	2	yes	—
45	C₄×C₇₉	—	2	4	no	—
46	C₄×C₇₉	—	4	4	no	—
47	C₄×C₇₉	#125	1	4	yes	—
48	Dic₇₉	—	2	8	no	—
49	Dic₇₉	—	4	4	no	—
50	C₂×C₇₉	C₂×#125	1	1	yes	characteristic
51	C₂×C₇₉	#529	1	4	yes	—
52	C₂×C₇₉	#533	1	2	yes	—
53	#2402	—	79	1	no	maximal, Sylow
54	C₇₉	#2402	1	1	yes	characteristic, complemented, Sylow
55	#400	—	79	4	no	—
56	#398	—	79	4	no	—
57	C₄×C₄⋊C₄	—	79	2	no	—
58	C₄×C₄⋊C₄	—	79	4	no	—
59	#376	D₇₉	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	79	4	no	—
61	C₂×C₄⋊C₄	—	79	4	no	—
62	C₂×C₄⋊C₄	—	79	4	no	—
63	C₂×C₄²	—	79	4	no	—
64	C₂×C₄²	C₂×D₇₉	1	2	yes	—
65	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
66	#95	—	79	2	no	—
67	#95	—	79	4	no	—
68	#95	—	79	4	no	—
69	#95	—	79	2	no	—
70	#95	C₂×D₇₉	1	4	yes	—
71	C₂²×C₄	—	79	4	no	—
72	C₂²×C₄	—	79	4	no	—
73	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
74	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
75	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
76	C₄⋊C₄	—	158	8	no	—
77	C₄⋊C₄	—	158	8	no	—
78	C₄⋊C₄	—	158	8	no	—
79	C₄²	—	2	4	no	—
80	C₄²	—	158	8	no	—
81	C₄²	Dic₁₅₈	1	4	yes	—
82	C₂³	C₂³×D₇₉	1	1	yes	characteristic
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	79	8	no	—
88	C₂×C₄	—	158	4	no	—
89	C₂×C₄	—	158	4	no	—
90	C₂×C₄	—	158	4	no	—
91	C₂×C₄	—	158	4	no	—
92	C₂×C₄	—	158	4	no	—
93	C₂×C₄	C₂×Dic₁₅₈	1	4	yes	—
94	C₂×C₄	C₂×Dic₁₅₈	1	2	yes	—
95	C₂×C₄	#11929624	1	4	yes	—
96	C₂²	C₂²×Dic₁₅₈	1	1	yes	characteristic
97	C₂²	#41×D₇₉	1	4	yes	—
98	C₂²	C₂×#11929624	1	2	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	4	4	no	—
101	C₄	—	316	4	no	—
102	C₄	—	158	8	no	—
103	C₄	#14579153	1	4	yes	—
104	C₂	C₂×#14579153	1	1	yes	characteristic
105	C₂	#19099091	1	4	yes	—
106	C₂	#19099116	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19098505

C₂

yes

maximal

#19098497

C₂

yes

maximal

C₄×Dic₇₉⋊C₄

C₂

yes

maximal

C₄×C₄⋊Dic₇₉

C₂

yes

maximal

#376×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#95×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

Q₈

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

#41

yes

—

C₂²×C₇₉

C₂²×Q₈

yes

characteristic

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#125

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₂×#125

yes

characteristic

C₂×C₇₉

#529

yes

—

C₂×C₇₉

#533

yes

—

#2402

—

maximal, Sylow

C₇₉

#2402

yes

characteristic, complemented, Sylow

#400

—

#398

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

#376

D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

—

C₂×C₄²

C₂×D₇₉

yes

—

—

—

—

C₂×D₇₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₄²

—

158

—

C₄²

Dic₁₅₈

yes

—

C₂³

C₂³×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

—

158

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

C₂×Dic₁₅₈

yes

—

C₂×C₄

#11929624

yes

—

C₂²

C₂²×Dic₁₅₈

yes

characteristic

C₂²

#41×D₇₉

yes

—

C₂²

C₂×#11929624

yes

—

C₄

—

100

C₄

—

101

C₄

—

316

—

102

C₄

—

158

—

103

C₄

#14579153

yes

—

104

C₂

C₂×#14579153

yes

characteristic

105

C₂

#19099091

yes

—

106

C₂

#19099116

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Frattini	C₂³	C₂³×D₇₉
Fitting	#376×C₇₉	C₂
hypercenter	#376	D₇₉
hypocenter	C₇₉	#2402
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Frattini

C₂³

C₂³×D₇₉

Fitting

#376×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
54. C₇₉	#2402	semidirect

H ≅ G/N

type

54. C₇₉

#2402

semidirect

Subgroups — #23766705

Conjugacy classes of subgroups

Complements