Subgroups — C₂×C₂₉×#1273 #20302747

Order 7424.

982 conjugacy classes of subgroups.

The subgroup lattice has 124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₂₉	C₂	1	3	yes	maximal
2	C₂₉×#1273	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₈×C₂₉	C₄	1	6	yes	—
4	C₂²×C₄²×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈×C₂₉	—	2	12	no	—
6	C₂×C₄×C₈×C₂₉	C₄	1	6	yes	—
7	C₂×C₄×C₈×C₂₉	C₂²	1	6	yes	—
8	C₂³×C₄×C₂₉	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₂₉	—	2	12	no	—
10	C₂²×C₈×C₂₉	—	2	12	no	—
11	C₂²×C₈×C₂₉	C₈	1	24	yes	complemented
12	C₂²×C₈×C₂₉	C₂×C₄	1	12	yes	—
13	C₂×C₄²×C₂₉	C₂×C₄	1	3	yes	—
14	C₂×C₄²×C₂₉	D₄	1	6	yes	—
15	C₂×C₄²×C₂₉	Q₈	1	2	yes	—
16	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
17	C₄×C₈×C₂₉	—	2	12	no	—
18	C₄×C₈×C₂₉	—	2	12	no	—
19	C₂⁴×C₂₉	C₄²	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	C₄²	1	3	yes	—
21	C₂²×C₄×C₂₉	C₂²⋊C₄	1	6	yes	—
22	C₂²×C₄×C₂₉	C₄⋊C₄	1	6	yes	—
23	C₂²×C₄×C₂₉	C₂×C₈	1	12	yes	—
24	C₂²×C₄×C₂₉	M₁₆	1	12	yes	—
25	C₂²×C₄×C₂₉	C₂²×C₄	1	3	yes	—
26	C₂×C₈×C₂₉	—	2	48	no	—
27	C₂×C₈×C₂₉	—	2	12	no	—
28	C₂×C₈×C₂₉	—	2	12	no	—
29	C₂×C₈×C₂₉	C₂×C₈	1	24	yes	complemented
30	C₄²×C₂₉	C₂²⋊C₄	1	6	yes	—
31	C₄²×C₂₉	C₄⋊C₄	1	6	yes	—
32	C₄²×C₂₉	C₂×D₄	1	3	yes	—
33	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
34	C₂×#1273	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂³×C₂₉	#95	1	2	yes	—
36	C₂³×C₂₉	C₄×C₈	1	6	yes	—
37	C₂³×C₂₉	#97	1	6	yes	—
38	C₂³×C₂₉	C₂×C₄²	1	1	yes	characteristic
39	C₂×C₄×C₂₉	#95	1	6	yes	—
40	C₂×C₄×C₂₉	C₄×C₈	1	6	yes	—
41	C₂×C₄×C₂₉	#97	1	6	yes	—
42	C₂×C₄×C₂₉	C₂²⋊C₈	1	24	yes	—
43	C₂×C₄×C₂₉	C₄⋊C₈	1	24	yes	—
44	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	3	yes	—
45	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	3	yes	—
46	C₂×C₄×C₂₉	C₂²×C₈	1	6	yes	—
47	C₂×C₄×C₂₉	C₂×M₁₆	1	6	yes	—
48	C₈×C₂₉	—	2	24	no	—
49	C₂²×C₄×C₈	C₂×C₂₉	1	3	yes	—
50	#1273	C₂×C₂₉	1	4	yes	direct product factor
51	C₂²×C₂₉	C₈²	1	4	yes	—
52	C₂²×C₂₉	#322	1	12	yes	—
53	C₂²×C₂₉	#336	1	12	yes	—
54	C₂²×C₂₉	C₂×#95	1	1	yes	characteristic
55	C₂²×C₂₉	C₂×C₄×C₈	1	3	yes	—
56	C₂²×C₂₉	C₂×#97	1	3	yes	—
57	C₄×C₂₉	#336	1	12	yes	—
58	C₄×C₂₉	C₂×C₂²⋊C₈	1	6	yes	—
59	C₄×C₂₉	C₂×C₄⋊C₈	1	6	yes	—
60	C₂³×C₈	C₄×C₂₉	1	6	yes	—
61	C₂²×C₄²	C₂²×C₂₉	1	1	yes	characteristic
62	C₂×C₄×C₈	—	2	12	no	—
63	C₂×C₄×C₈	C₄×C₂₉	1	6	yes	—
64	C₂×C₄×C₈	C₂²×C₂₉	1	6	yes	—
65	C₂×C₂₉	#1273	1	8	yes	direct product factor
66	C₂×C₂₉	C₂×C₈²	1	1	yes	characteristic
67	C₂×C₂₉	C₂×#322	1	3	yes	—
68	C₂×C₂₉	C₂×#336	1	3	yes	—
69	C₂³×C₄	C₂×C₄×C₂₉	1	3	yes	—
70	C₂²×C₈	—	2	12	no	—
71	C₂²×C₈	—	2	12	no	—
72	C₂²×C₈	C₈×C₂₉	1	24	yes	complemented
73	C₂²×C₈	C₂×C₄×C₂₉	1	12	yes	—
74	C₂×C₄²	C₂×C₄×C₂₉	1	3	yes	—
75	C₂×C₄²	D₄×C₂₉	1	6	yes	—
76	C₂×C₄²	Q₈×C₂₉	1	2	yes	—
77	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
78	C₄×C₈	—	2	12	no	—
79	C₄×C₈	—	2	12	no	—
80	C₂₉	C₂×#1273	1	1	yes	characteristic, direct product factor, Sylow
81	C₂⁴	C₄²×C₂₉	1	1	yes	characteristic
82	C₂²×C₄	C₄²×C₂₉	1	3	yes	—
83	C₂²×C₄	C₂²⋊C₄×C₂₉	1	6	yes	—
84	C₂²×C₄	C₄⋊C₄×C₂₉	1	6	yes	—
85	C₂²×C₄	C₂×C₈×C₂₉	1	12	yes	—
86	C₂²×C₄	M₁₆×C₂₉	1	12	yes	—
87	C₂²×C₄	C₂²×C₄×C₂₉	1	3	yes	—
88	C₂×C₈	—	2	12	no	—
89	C₂×C₈	—	2	12	no	—
90	C₂×C₈	—	2	48	no	—
91	C₂×C₈	C₂×C₈×C₂₉	1	24	yes	complemented
92	C₄²	C₂²⋊C₄×C₂₉	1	6	yes	—
93	C₄²	C₄⋊C₄×C₂₉	1	6	yes	—
94	C₄²	C₂×D₄×C₂₉	1	3	yes	—
95	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
96	C₂³	C₂₉×#95	1	2	yes	—
97	C₂³	C₄×C₈×C₂₉	1	6	yes	—
98	C₂³	C₂₉×#97	1	6	yes	—
99	C₂³	C₂×C₄²×C₂₉	1	1	yes	characteristic
100	C₂×C₄	C₂₉×#95	1	6	yes	—
101	C₂×C₄	C₄×C₈×C₂₉	1	6	yes	—
102	C₂×C₄	C₂₉×#97	1	6	yes	—
103	C₂×C₄	C₂₉×C₂²⋊C₈	1	24	yes	—
104	C₂×C₄	C₂₉×C₄⋊C₈	1	24	yes	—
105	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	3	yes	—
106	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	3	yes	—
107	C₂×C₄	C₂²×C₈×C₂₉	1	6	yes	—
108	C₂×C₄	C₂×M₁₆×C₂₉	1	6	yes	—
109	C₈	—	2	24	no	—
110	C₂²	C₈²×C₂₉	1	4	yes	—
111	C₂²	C₂₉×#322	1	12	yes	—
112	C₂²	C₂₉×#336	1	12	yes	—
113	C₂²	C₂×C₂₉×#95	1	1	yes	characteristic
114	C₂²	C₂×C₄×C₈×C₂₉	1	3	yes	—
115	C₂²	C₂×C₂₉×#97	1	3	yes	—
116	C₄	C₂₉×#336	1	12	yes	—
117	C₄	C₂×C₂₉×C₂²⋊C₈	1	6	yes	—
118	C₄	C₂×C₂₉×C₄⋊C₈	1	6	yes	—
119	C₂	C₂₉×#1273	1	8	yes	direct product factor
120	C₂	C₂×C₈²×C₂₉	1	1	yes	characteristic
121	C₂	C₂×C₂₉×#322	1	3	yes	—
122	C₂	C₂×C₂₉×#336	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄²×C₂₉	C₂²
commutator	C₂	C₂×C₈²×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle, prime radical	C₂⁴×C₂₉	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#1273	C₂	direct (N × H)
11. C₂²×C₈×C₂₉	C₈	semidirect
29. C₂×C₈×C₂₉	C₂×C₈	semidirect
34. C₂×#1273	C₂₉	direct (N × H)
50. #1273	C₂×C₂₉	direct (N × H)
65. C₂×C₂₉	#1273	direct (N × H)
72. C₂²×C₈	C₈×C₂₉	semidirect
80. C₂₉	C₂×#1273	direct (N × H)
91. C₂×C₈	C₂×C₈×C₂₉	semidirect
119. C₂	C₂₉×#1273	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×C₄×C₈×C₂₉	2
C₂₉×#1273	2
C₂×#1273	29

Subgroups — C2×C29×#1273 #20302747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉×#1273 #20302747