Subgroups — C₂×C₂₉×#1726 #20315227

Order 7424.

1614 conjugacy classes of subgroups.

The subgroup lattice has 140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×#97	C₂	1	3	yes	maximal
2	C₂²×C₄×C₈×C₂₉	C₂	1	3	yes	maximal
3	C₂×C₂₉×#376	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1726	C₂	1	8	yes	maximal, direct product factor
5	C₂³×C₈×C₂₉	C₂²	1	3	yes	—
6	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄²×C₂₉	C₂²	1	3	yes	—
8	C₂×C₂₉×#97	C₄	1	24	yes	complemented
9	C₂×C₂₉×#97	C₂²	1	12	yes	—
10	C₂×C₄×C₈×C₂₉	C₄	1	24	yes	complemented
11	C₂×C₄×C₈×C₂₉	C₂²	1	12	yes	—
12	C₂₉×#376	C₄	1	4	yes	—
13	C₂₉×#376	C₂²	1	4	yes	—
14	C₂×C₂₉×#95	C₄	1	4	yes	—
15	C₂³×C₄×C₂₉	C₂×C₄	1	6	yes	—
16	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
17	C₂²×C₈×C₂₉	C₂×C₄	1	12	yes	—
18	C₂²×C₈×C₂₉	C₂×C₄	1	24	yes	—
19	C₂²×C₈×C₂₉	C₂×C₄	1	12	yes	—
20	C₂²×C₈×C₂₉	C₂³	1	6	yes	—
21	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
22	C₂×C₄²×C₂₉	C₂×C₄	1	6	yes	—
23	C₂×C₄²×C₂₉	C₂×C₄	1	12	yes	—
24	C₂×C₄²×C₂₉	C₂×C₄	1	12	yes	—
25	C₂×C₄²×C₂₉	C₂³	1	6	yes	—
26	C₂₉×#97	C₂×C₄	1	48	yes	complemented
27	C₄×C₈×C₂₉	C₂×C₄	1	48	yes	complemented
28	C₂₉×#95	C₂×C₄	1	16	yes	—
29	C₂⁴×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₂₉	—	2	24	no	—
31	C₂²×C₄×C₂₉	C₄²	1	24	yes	—
32	C₂²×C₄×C₂₉	C₂²×C₄	1	12	yes	—
33	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₂₉	C₂²×C₄	1	6	yes	—
35	C₂²×C₄×C₂₉	C₂²×C₄	1	6	yes	—
36	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
37	C₂×C₈×C₂₉	C₄²	1	48	yes	—
38	C₂×C₈×C₂₉	C₄²	1	16	yes	—
39	C₂×C₈×C₂₉	C₂²×C₄	1	12	yes	—
40	C₂×C₈×C₂₉	C₂²×C₄	1	12	yes	—
41	C₂×C₈×C₂₉	C₂²×C₄	1	24	yes	—
42	C₄²×C₂₉	C₄²	1	24	yes	—
43	C₄²×C₂₉	C₂²×C₄	1	12	yes	—
44	C₄²×C₂₉	C₂²×C₄	1	12	yes	—
45	C₂×#1726	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂³×C₂₉	C₂×C₄²	1	6	yes	—
47	C₂³×C₂₉	#131	1	8	yes	—
48	C₂³×C₂₉	C₂³×C₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	—	2	24	no	—
50	C₂×C₄×C₂₉	—	2	48	no	—
51	C₂×C₄×C₂₉	C₂×C₄²	1	24	yes	—
52	C₂×C₄×C₂₉	C₂×C₄²	1	6	yes	—
53	C₂×C₄×C₂₉	C₂×C₄²	1	12	yes	—
54	C₂×C₄×C₂₉	C₂×C₄²	1	4	yes	—
55	C₂×C₄×C₂₉	C₂³×C₄	1	3	yes	—
56	C₂×C₄×C₂₉	C₂³×C₄	1	3	yes	—
57	C₈×C₂₉	C₂×C₄²	1	8	yes	—
58	C₈×C₂₉	C₂×C₄²	1	24	yes	—
59	C₂²×#97	C₂×C₂₉	1	3	yes	—
60	C₂²×C₄×C₈	C₂×C₂₉	1	3	yes	—
61	C₂×#376	C₂×C₂₉	1	1	yes	characteristic
62	#1726	C₂×C₂₉	1	8	yes	direct product factor
63	C₂²×C₂₉	C₄³	1	4	yes	—
64	C₂²×C₂₉	#405	1	24	yes	—
65	C₂²×C₂₉	C₂²×C₄²	1	3	yes	—
66	C₂²×C₂₉	C₂×#131	1	4	yes	—
67	C₄×C₂₉	—	2	24	no	—
68	C₄×C₂₉	C₄³	1	4	yes	—
69	C₄×C₂₉	C₂²×C₄²	1	1	yes	characteristic
70	C₄×C₂₉	C₂²×C₄²	1	3	yes	—
71	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
72	C₂³×C₈	C₂²×C₂₉	1	3	yes	—
73	C₂²×C₄²	C₂²×C₂₉	1	3	yes	—
74	C₂×#97	C₄×C₂₉	1	24	yes	complemented
75	C₂×#97	C₂²×C₂₉	1	12	yes	—
76	C₂×C₄×C₈	C₄×C₂₉	1	24	yes	complemented
77	C₂×C₄×C₈	C₂²×C₂₉	1	12	yes	—
78	#376	C₄×C₂₉	1	4	yes	—
79	#376	C₂²×C₂₉	1	4	yes	—
80	C₂×#95	C₄×C₂₉	1	4	yes	—
81	C₂×C₂₉	#1726	1	8	yes	direct product factor
82	C₂×C₂₉	C₂×C₄³	1	1	yes	characteristic
83	C₂×C₂₉	C₂×#405	1	6	yes	—
84	C₂³×C₄	C₂×C₄×C₂₉	1	6	yes	—
85	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
86	C₂²×C₈	C₂×C₄×C₂₉	1	12	yes	—
87	C₂²×C₈	C₂×C₄×C₂₉	1	12	yes	—
88	C₂²×C₈	C₂×C₄×C₂₉	1	24	yes	—
89	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
90	C₂²×C₈	C₂³×C₂₉	1	6	yes	—
91	C₂×C₄²	C₂×C₄×C₂₉	1	6	yes	—
92	C₂×C₄²	C₂×C₄×C₂₉	1	12	yes	—
93	C₂×C₄²	C₂×C₄×C₂₉	1	12	yes	—
94	C₂×C₄²	C₂³×C₂₉	1	6	yes	—
95	#97	C₂×C₄×C₂₉	1	48	yes	complemented
96	C₄×C₈	C₂×C₄×C₂₉	1	48	yes	complemented
97	#95	C₂×C₄×C₂₉	1	16	yes	—
98	C₂₉	C₂×#1726	1	1	yes	characteristic, direct product factor, Sylow
99	C₂⁴	C₂²×C₄×C₂₉	1	1	yes	characteristic
100	C₂²×C₄	—	2	24	no	—
101	C₂²×C₄	C₄²×C₂₉	1	24	yes	—
102	C₂²×C₄	C₂²×C₄×C₂₉	1	12	yes	—
103	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
104	C₂²×C₄	C₂²×C₄×C₂₉	1	6	yes	—
105	C₂²×C₄	C₂²×C₄×C₂₉	1	6	yes	—
106	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
107	C₂×C₈	C₄²×C₂₉	1	16	yes	—
108	C₂×C₈	C₄²×C₂₉	1	48	yes	—
109	C₂×C₈	C₂²×C₄×C₂₉	1	12	yes	—
110	C₂×C₈	C₂²×C₄×C₂₉	1	12	yes	—
111	C₂×C₈	C₂²×C₄×C₂₉	1	24	yes	—
112	C₄²	C₄²×C₂₉	1	24	yes	—
113	C₄²	C₂²×C₄×C₂₉	1	12	yes	—
114	C₄²	C₂²×C₄×C₂₉	1	12	yes	—
115	C₂³	C₂×C₄²×C₂₉	1	6	yes	—
116	C₂³	C₂₉×#131	1	8	yes	—
117	C₂³	C₂³×C₄×C₂₉	1	1	yes	characteristic
118	C₂×C₄	—	2	24	no	—
119	C₂×C₄	—	2	48	no	—
120	C₂×C₄	C₂×C₄²×C₂₉	1	24	yes	—
121	C₂×C₄	C₂×C₄²×C₂₉	1	4	yes	—
122	C₂×C₄	C₂×C₄²×C₂₉	1	12	yes	—
123	C₂×C₄	C₂×C₄²×C₂₉	1	6	yes	—
124	C₂×C₄	C₂³×C₄×C₂₉	1	3	yes	—
125	C₂×C₄	C₂³×C₄×C₂₉	1	3	yes	—
126	C₈	C₂×C₄²×C₂₉	1	8	yes	—
127	C₈	C₂×C₄²×C₂₉	1	24	yes	—
128	C₂²	C₄³×C₂₉	1	4	yes	—
129	C₂²	C₂₉×#405	1	24	yes	—
130	C₂²	C₂²×C₄²×C₂₉	1	3	yes	—
131	C₂²	C₂×C₂₉×#131	1	4	yes	—
132	C₄	—	2	24	no	—
133	C₄	C₄³×C₂₉	1	4	yes	—
134	C₄	C₂²×C₄²×C₂₉	1	1	yes	characteristic
135	C₄	C₂²×C₄²×C₂₉	1	3	yes	—
136	C₂	C₂₉×#1726	1	8	yes	direct product factor
137	C₂	C₂×C₄³×C₂₉	1	1	yes	characteristic
138	C₂	C₂×C₂₉×#405	1	6	yes	—

	subgroup	G/H
center	C₂³×C₈×C₂₉	C₂²
commutator	C₂	C₂×C₄³×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle, prime radical	C₂⁴×C₂₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂₉×#1726	C₂	direct (N × H)
8. C₂×C₂₉×#97	C₄	semidirect
10. C₂×C₄×C₈×C₂₉	C₄	semidirect
26. C₂₉×#97	C₂×C₄	semidirect
27. C₄×C₈×C₂₉	C₂×C₄	semidirect
45. C₂×#1726	C₂₉	direct (N × H)
62. #1726	C₂×C₂₉	direct (N × H)
74. C₂×#97	C₄×C₂₉	semidirect
76. C₂×C₄×C₈	C₄×C₂₉	semidirect
81. C₂×C₂₉	#1726	direct (N × H)
95. #97	C₂×C₄×C₂₉	semidirect
96. C₄×C₈	C₂×C₄×C₂₉	semidirect
98. C₂₉	C₂×#1726	direct (N × H)
136. C₂	C₂₉×#1726	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×#97	2
C₂²×C₄×C₈×C₂₉	2
C₂×C₂₉×#376	2
C₂₉×#1726	2
C₂×#1726	29

Subgroups — C2×C29×#1726 #20315227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1726 #20315227