Group #16815804 — subgroups

Subgroups — C₂₉×#2090 #16815804

Order 3712.

176 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 84 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	C₂₉×#428	C₂	1	2	yes	maximal
2	C₂×C₂₉×#106	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#424	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#343	C₂	1	2	yes	maximal
5	C₂₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₂₉	C₂²	1	2	yes	—
8	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
9	C₂₉×#117	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
11	C₂₉×#107	—	2	2	no	—
12	C₂₉×#106	—	2	2	no	—
13	C₂₉×#106	—	2	2	no	—
14	C₂₉×C₄⋊C₈	—	2	2	no	—
15	C₂²×C₄×C₂₉	—	2	2	no	—
16	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	M₁₆×C₂₉	—	2	2	no	—
18	M₁₆×C₂₉	—	2	2	no	—
19	M₁₆×C₂₉	Q₈	1	4	yes	—
20	C₂×C₈×C₂₉	—	2	2	no	—
21	C₂×C₈×C₂₉	—	2	2	no	—
22	C₂×C₈×C₂₉	—	2	1	no	—
23	C₂×C₈×C₂₉	D₄	1	2	yes	—
24	C₄⋊C₄×C₂₉	—	2	2	no	—
25	C₄⋊C₄×C₂₉	—	2	2	no	—
26	C₄⋊C₄×C₂₉	D₄	1	2	yes	—
27	C₂²⋊C₄×C₂₉	—	2	1	no	—
28	C₄²×C₂₉	—	2	1	no	—
29	C₂³×C₂₉	#41	1	1	yes	characteristic
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	4	2	no	—
32	C₂×C₄×C₂₉	—	8	2	no	—
33	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₂₉	#41	1	2	yes	—
37	C₈×C₂₉	—	2	4	no	—
38	C₈×C₂₉	—	2	2	no	—
39	C₈×C₂₉	—	4	1	no	—
40	#2090	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₂₉	—	2	2	no	—
42	C₂²×C₂₉	#121	1	1	yes	characteristic
43	C₂²×C₂₉	#125	1	2	yes	—
44	C₄×C₂₉	—	4	2	no	—
45	C₄×C₂₉	—	8	2	no	—
46	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₂₉	#123	1	1	yes	characteristic
48	C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
49	#428	C₂×C₂₉	1	2	yes	—
50	C₂×#106	C₂×C₂₉	1	1	yes	characteristic
51	#424	C₂×C₂₉	1	1	yes	characteristic
52	#343	C₂×C₂₉	1	2	yes	—
53	#341	C₂×C₂₉	1	1	yes	characteristic
54	C₂×C₂₉	—	2	2	no	—
55	C₂×C₂₉	#398	1	1	yes	characteristic
56	C₂×C₂₉	#471	1	2	yes	—
57	C₂×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
58	C₂×M₁₆	C₂²×C₂₉	1	2	yes	—
59	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic
60	#117	C₂²×C₂₉	1	1	yes	characteristic
61	C₂×C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
62	#107	—	2	2	no	—
63	#106	—	2	2	no	—
64	#106	—	2	2	no	—
65	C₄⋊C₈	—	2	2	no	—
66	C₂₉	#2090	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²×C₄	—	2	2	no	—
68	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
69	M₁₆	—	2	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	Q₈×C₂₉	1	4	yes	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	2	2	no	—
74	C₂×C₈	—	2	1	no	—
75	C₂×C₈	D₄×C₂₉	1	2	yes	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	D₄×C₂₉	1	2	yes	—
79	C₂²⋊C₄	—	2	1	no	—
80	C₄²	—	2	1	no	—
81	C₂³	#41×C₂₉	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	—	8	2	no	—
85	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
86	C₂×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
87	C₂×C₄	C₂×Q₈×C₂₉	1	2	yes	—
88	C₂×C₄	#41×C₂₉	1	2	yes	—
89	C₈	—	2	4	no	—
90	C₈	—	2	2	no	—
91	C₈	—	4	1	no	—
92	C₂²	—	2	2	no	—
93	C₂²	C₂₉×#121	1	1	yes	characteristic
94	C₂²	C₂₉×#125	1	2	yes	—
95	C₄	—	4	2	no	—
96	C₄	—	8	2	no	—
97	C₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
98	C₄	C₂₉×#123	1	1	yes	characteristic
99	C₄	C₂₉×C₄⋊Q₈	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	C₂₉×#398	1	1	yes	characteristic
102	C₂	C₂₉×#471	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₉×#428

C₂

yes

maximal

C₂×C₂₉×#106

C₂

yes

maximal, characteristic

C₂₉×#424

C₂

yes

maximal, characteristic

C₂₉×#343

C₂

yes

maximal

C₂₉×#341

C₂

yes

maximal, characteristic

C₂×M₁₆×C₂₉

C₂²

yes

characteristic

C₂×M₁₆×C₂₉

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

characteristic

C₂₉×#117

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂₉×#107

—

C₂₉×#106

—

C₂₉×#106

—

C₂₉×C₄⋊C₈

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

M₁₆×C₂₉

—

M₁₆×C₂₉

—

M₁₆×C₂₉

Q₈

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

D₄

yes

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

D₄

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₂³×C₂₉

#41

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₈×C₂₉

—

C₈×C₂₉

—

C₈×C₂₉

—

#2090

C₂₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

#121

yes

characteristic

C₂²×C₂₉

#125

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

C₄×C₂₉

#123

yes

characteristic

C₄×C₂₉

C₄⋊Q₈

yes

characteristic

#428

C₂×C₂₉

yes

—

C₂×#106

C₂×C₂₉

yes

characteristic

#424

C₂×C₂₉

yes

characteristic

#343

C₂×C₂₉

yes

—

#341

C₂×C₂₉

yes

characteristic

C₂×C₂₉

—

C₂×C₂₉

#398

yes

characteristic

C₂×C₂₉

#471

yes

—

C₂×M₁₆

C₂²×C₂₉

yes

characteristic

C₂×M₁₆

C₂²×C₂₉

yes

—

C₂²×C₈

C₂²×C₂₉

yes

characteristic

#117

C₂²×C₂₉

yes

characteristic

C₂×C₄⋊C₄

C₂²×C₂₉

yes

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂₉

#2090

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

C₂³×C₂₉

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Q₈×C₂₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₄×C₂₉

yes

—

C₂²⋊C₄

—

C₄²

—

C₂³

#41×C₂₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

C₂×C₄

C₂×D₄×C₂₉

yes

characteristic

C₂×C₄

C₂×Q₈×C₂₉

yes

—

C₂×C₄

#41×C₂₉

yes

—

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

C₂₉×#121

yes

characteristic

C₂²

C₂₉×#125

yes

—

C₄

—

C₄

—

C₄

C₂₉×C₂²⋊Q₈

yes

—

C₄

C₂₉×#123

yes

characteristic

C₄

C₂₉×C₄⋊Q₈

yes

characteristic

100

C₂

—

101

C₂

C₂₉×#398

yes

characteristic

102

C₂

C₂₉×#471

yes

—

	subgroup	G/H
center, socle	C₂²×C₂₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂³×C₂₉	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₉

#121

commutator, Frattini, cosocle

C₂²×C₄

C₂³×C₂₉

C₂³×C₂₉

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

N	H ≅ G/N	type
40. #2090	C₂₉	direct (N × H)
66. C₂₉	#2090	direct (N × H)

H ≅ G/N

type

40. #2090

C₂₉

direct (N × H)

66. C₂₉

#2090

direct (N × H)

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

subgroup	index
C₂₉×#428	2
C₂×C₂₉×#106	2
C₂₉×#424	2
C₂₉×#343	2
C₂₉×#341	2
#2090	29

subgroup

index

C₂₉×#428

C₂×C₂₉×#106

C₂₉×#424

C₂₉×#343

C₂₉×#341

#2090

Subgroups — C₂₉×#2090 #16815804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C29×#2090 #16815804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2090 #16815804