Group #19099113 — subgroups

Subgroups — #19099113

Order 5056.

310 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11929624	C₂	1	2	yes	maximal, complemented
2	#14579161	C₂	1	1	yes	maximal, characteristic, complemented
3	#14579158	C₂	1	1	yes	maximal, characteristic, complemented
4	#14579149	C₂	1	2	yes	maximal, complemented
5	#14579135	C₂	1	4	yes	maximal, complemented
6	C₄×D₃₁₆	C₂	1	4	yes	maximal, complemented
7	C₂×C₄²×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#11929624	—	2	8	no	—
9	C₂×Dic₁₅₈	C₂²	1	2	yes	—
10	C₂×D₃₁₆	C₂²	1	2	yes	—
11	C₂×D₃₁₆	C₂²	1	4	yes	—
12	C₂×C₂²⋊D₇₉	C₂²	1	4	yes	—
13	C₂×C₄×D₇₉	C₂²	1	4	yes	—
14	C₄⋊Dic₇₉	C₂²	1	4	yes	—
15	(C₂×D₇₉)⋊C₄	C₂²	1	8	yes	—
16	C₂²×C₄×C₇₉	C₂²	1	2	yes	—
17	C₂²×C₄×C₇₉	C₂²	1	1	yes	characteristic
18	C₄²×C₇₉	C₂²	1	2	yes	—
19	C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	C₂³×C₇₉	C₂³	1	1	yes	characteristic
22	C₂²×D₇₉	C₂³	1	4	yes	—
23	C₂×C₄×C₇₉	—	2	4	no	—
24	C₂×C₄×C₇₉	D₄	1	4	yes	complemented
25	C₂×C₄×C₇₉	C₂³	1	2	yes	—
26	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₇₉	C₂³	1	2	yes	—
28	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
29	C₂²⋊D₇₉	—	2	8	no	—
30	C₂×Dic₇₉	C₂³	1	4	yes	—
31	D₃₁₆	—	2	4	no	—
32	D₃₁₆	—	2	8	no	—
33	C₄×D₇₉	—	2	8	no	—
34	Dic₁₅₈	—	2	4	no	—
35	C₂²×C₇₉	—	2	2	no	—
36	C₂²×C₇₉	C₂×D₄	1	2	yes	—
37	C₂²×C₇₉	C₂⁴	1	1	yes	characteristic
38	C₂×D₇₉	—	2	4	no	—
39	C₂×D₇₉	—	2	8	no	—
40	C₄×C₇₉	—	2	2	no	—
41	C₄×C₇₉	C₂×D₄	1	2	yes	—
42	C₄×C₇₉	C₂×D₄	1	2	yes	—
43	C₄×C₇₉	#41	1	4	yes	complemented
44	Dic₇₉	—	2	4	no	—
45	C₂×C₇₉	—	2	2	no	—
46	C₂×C₇₉	C₂²×D₄	1	1	yes	characteristic
47	C₂×C₇₉	C₂×#41	1	2	yes	—
48	D₇₉	—	4	4	no	—
49	C₇₉	#532	1	1	yes	characteristic, complemented, Sylow
50	#532	—	79	1	no	maximal, Sylow
51	C₂×#41	—	79	2	no	—
52	C₄⋊Q₈	—	79	1	no	—
53	#127	—	79	1	no	—
54	#124	—	79	2	no	—
55	#121	—	79	4	no	—
56	C₄×D₄	—	79	4	no	—
57	C₂×C₄²	D₇₉	1	1	yes	characteristic, complemented
58	#41	—	158	8	no	—
59	C₂×Q₈	—	79	2	no	—
60	C₂×D₄	—	79	4	no	—
61	C₂×D₄	—	79	4	no	—
62	C₂×D₄	—	79	2	no	—
63	C₂²×C₄	—	79	4	no	—
64	C₂²×C₄	C₂×D₇₉	1	2	yes	—
65	C₂²×C₄	C₂×D₇₉	1	1	yes	characteristic
66	C₄⋊C₄	—	79	4	no	—
67	C₂²⋊C₄	—	79	8	no	—
68	C₄²	C₂×D₇₉	1	1	yes	characteristic
69	C₄²	C₂×D₇₉	1	1	yes	characteristic
70	C₄²	C₂×D₇₉	1	2	yes	—
71	C₂³	—	79	4	no	—
72	C₂³	C₂²×D₇₉	1	1	yes	characteristic
73	Q₈	—	158	4	no	—
74	D₄	—	158	8	no	—
75	D₄	—	158	4	no	—
76	D₄	—	158	8	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	79	4	no	—
79	C₂×C₄	—	158	8	no	—
80	C₂×C₄	D₃₁₆	1	4	yes	complemented
81	C₂×C₄	C₂²×D₇₉	1	2	yes	—
82	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
83	C₂×C₄	C₂²×D₇₉	1	2	yes	—
84	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
85	C₂²	—	2	2	no	—
86	C₂²	—	158	8	no	—
87	C₂²	—	158	4	no	—
88	C₂²	C₂×D₃₁₆	1	2	yes	—
89	C₂²	C₂³×D₇₉	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	158	4	no	—
92	C₄	C₂×D₃₁₆	1	2	yes	—
93	C₄	C₂×D₃₁₆	1	2	yes	—
94	C₄	#11929624	1	4	yes	complemented
95	C₂	—	2	2	no	—
96	C₂	—	316	4	no	—
97	C₂	C₂²×D₃₁₆	1	1	yes	characteristic
98	C₂	C₂×#11929624	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11929624

C₂

yes

maximal, complemented

#14579161

C₂

yes

maximal, characteristic, complemented

#14579158

C₂

yes

maximal, characteristic, complemented

#14579149

C₂

yes

maximal, complemented

#14579135

C₂

yes

maximal, complemented

C₄×D₃₁₆

C₂

yes

maximal, complemented

C₂×C₄²×C₇₉

C₂

yes

maximal, characteristic, complemented

#11929624

—

C₂×Dic₁₅₈

C₂²

yes

—

C₂×D₃₁₆

C₂²

yes

—

C₂×D₃₁₆

C₂²

yes

—

C₂×C₂²⋊D₇₉

C₂²

yes

—

C₂×C₄×D₇₉

C₂²

yes

—

C₄⋊Dic₇₉

C₂²

yes

—

(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₂²×C₄×C₇₉

C₂²

yes

—

C₂²×C₄×C₇₉

C₂²

yes

characteristic

C₄²×C₇₉

C₂²

yes

—

C₄²×C₇₉

C₂²

yes

characteristic

C₄²×C₇₉

C₂²

yes

characteristic

C₂³×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₂³

yes

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₄

yes

complemented

C₂×C₄×C₇₉

C₂³

yes

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂³

yes

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂²⋊D₇₉

—

C₂×Dic₇₉

C₂³

yes

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

Dic₁₅₈

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₄

yes

—

C₂²×C₇₉

C₂⁴

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×D₄

yes

—

C₄×C₇₉

C₂×D₄

yes

—

C₄×C₇₉

#41

yes

complemented

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₂²×D₄

yes

characteristic

C₂×C₇₉

C₂×#41

yes

—

D₇₉

—

C₇₉

#532

yes

characteristic, complemented, Sylow

#532

—

maximal, Sylow

C₂×#41

—

C₄⋊Q₈

—

#127

—

#124

—

#121

—

C₄×D₄

—

C₂×C₄²

D₇₉

yes

characteristic, complemented

#41

—

158

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₇₉

yes

—

C₂²×C₄

C₂×D₇₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×D₇₉

yes

characteristic

C₄²

C₂×D₇₉

yes

characteristic

C₄²

C₂×D₇₉

yes

—

C₂³

—

C₂³

C₂²×D₇₉

yes

characteristic

Q₈

—

158

—

D₄

—

158

—

D₄

—

158

—

D₄

—

158

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

158

—

C₂×C₄

D₃₁₆

yes

complemented

C₂×C₄

C₂²×D₇₉

yes

—

C₂×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₄

C₂²×D₇₉

yes

—

C₂×C₄

C₂²×D₇₉

yes

characteristic

C₂²

—

C₂²

—

158

—

C₂²

—

158

—

C₂²

C₂×D₃₁₆

yes

—

C₂²

C₂³×D₇₉

yes

characteristic

C₄

—

C₄

—

158

—

C₄

C₂×D₃₁₆

yes

—

C₄

C₂×D₃₁₆

yes

—

C₄

#11929624

yes

complemented

C₂

—

C₂

—

316

—

C₂

C₂²×D₃₁₆

yes

characteristic

C₂

C₂×#11929624

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴
Frattini	C₂²	C₂³×D₇₉
Fitting	C₂×C₄²×C₇₉	C₂
hypercenter	C₂×C₄²	D₇₉
hypocenter	C₇₉	#532
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

subgroup

G/H

center

C₂×C₄

C₂²×D₇₉

commutator, socle

C₂²×C₇₉

C₂⁴

Frattini

C₂²

C₂³×D₇₉

Fitting

C₂×C₄²×C₇₉

C₂

hypercenter

C₂×C₄²

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₄ ◁ C₂×C₄²

N	H ≅ G/N	type
1. C₂×#11929624	C₂	semidirect
2. #14579161	C₂	semidirect
3. #14579158	C₂	semidirect
4. #14579149	C₂	semidirect
5. #14579135	C₂	semidirect
6. C₄×D₃₁₆	C₂	semidirect
7. C₂×C₄²×C₇₉	C₂	semidirect
24. C₂×C₄×C₇₉	D₄	semidirect
43. C₄×C₇₉	#41	semidirect
49. C₇₉	#532	semidirect
57. C₂×C₄²	D₇₉	semidirect
80. C₂×C₄	D₃₁₆	semidirect
94. C₄	#11929624	semidirect

H ≅ G/N

type

1. C₂×#11929624

C₂

semidirect

2. #14579161

C₂

semidirect

3. #14579158

C₂

semidirect

4. #14579149

C₂

semidirect

5. #14579135

C₂

semidirect

6. C₄×D₃₁₆

C₂

semidirect

7. C₂×C₄²×C₇₉

C₂

semidirect

24. C₂×C₄×C₇₉

D₄

semidirect

43. C₄×C₇₉

#41

semidirect

49. C₇₉

#532

semidirect

57. C₂×C₄²

D₇₉

semidirect

80. C₂×C₄

D₃₁₆

semidirect

94. C₄

#11929624

semidirect

Subgroups — #19099113

Conjugacy classes of subgroups

Complements