Subgroups — C₂₉×#12904 #20307804

Order 7424.

318 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#365	C₂	1	4	yes	maximal
2	C₄×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1848	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1846	C₂	1	1	yes	maximal, characteristic
5	C₂×C₂₉×M₃₂	C₂²	1	2	yes	—
6	C₂×C₂₉×#108	—	2	1	no	—
7	C₂×C₂₉×#108	C₂²	1	2	yes	—
8	C₂×C₂₉×#107	—	2	1	no	—
9	C₂×C₂₉×#106	C₂²	1	2	yes	—
10	C₂₉×#423	—	2	1	no	—
11	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
12	C₂₉×#382	—	2	1	no	—
13	C₂₉×#365	—	2	8	no	—
14	C₂₉×#346	C₄	1	2	yes	complemented
15	C₄×C₁₆×C₂₉	C₄	1	2	yes	complemented
16	C₂×M₁₆×C₂₉	—	2	2	no	—
17	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
20	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
21	C₂₉×M₃₂	D₄	1	4	yes	—
22	C₂₉×M₃₂	Q₈	1	4	yes	—
23	C₂×C₁₆×C₂₉	C₂×C₄	1	4	yes	—
24	C₂₉×#108	—	2	4	no	—
25	C₂₉×#108	—	4	2	no	—
26	C₂₉×#107	—	4	2	no	—
27	C₂₉×#106	—	2	4	no	—
28	C₂₉×C₄⋊C₈	—	4	2	no	—
29	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₂₉	Q₈	1	1	yes	characteristic
32	C₄×C₈×C₂₉	Q₈	1	1	yes	characteristic
33	C₂₉×#95	—	4	2	no	—
34	C₂²×C₄×C₂₉	—	4	2	no	—
35	C₂²×C₄×C₂₉	SD₁₆	1	2	yes	—
36	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
37	M₁₆×C₂₉	—	4	2	no	—
38	M₁₆×C₂₉	—	4	2	no	—
39	C₂×C₈×C₂₉	—	4	2	no	—
40	C₂×C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₂₉	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
43	C₂×C₈×C₂₉	SD₁₆	1	2	yes	—
44	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
46	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
47	C₂×C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
48	C₄⋊C₄×C₂₉	—	4	2	no	—
49	C₄⋊C₄×C₂₉	—	4	2	no	—
50	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₂₉	SD₁₆	1	2	yes	—
53	C₁₆×C₂₉	C₄⋊C₄	1	8	yes	—
54	#12904	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂³×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
56	C₂×C₄×C₂₉	—	4	2	no	—
57	C₂×C₄×C₂₉	—	8	4	no	—
58	C₂×C₄×C₂₉	—	8	2	no	—
59	C₂×C₄×C₂₉	#106	1	2	yes	—
60	C₂×C₄×C₂₉	#106	1	2	yes	—
61	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
63	C₂×C₄×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
64	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
65	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
66	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
67	C₈×C₂₉	—	8	2	no	—
68	C₈×C₂₉	#106	1	2	yes	—
69	C₈×C₂₉	#106	1	2	yes	—
70	C₈×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
71	C₈×C₂₉	C₄⋊Q₈	1	2	yes	—
72	C₂×#365	C₂×C₂₉	1	4	yes	—
73	C₄×M₃₂	C₂×C₂₉	1	1	yes	characteristic
74	#1848	C₂×C₂₉	1	1	yes	characteristic
75	#1846	C₂×C₂₉	1	1	yes	characteristic
76	C₂²×C₂₉	—	2	2	no	—
77	C₂²×C₂₉	C₂×#106	1	1	yes	characteristic
78	C₂²×C₂₉	#492	1	1	yes	characteristic
79	C₂²×C₂₉	#498	1	1	yes	characteristic
80	C₄×C₂₉	—	2	2	no	—
81	C₄×C₂₉	—	2	2	no	—
82	C₄×C₂₉	—	16	2	no	—
83	C₄×C₂₉	#384	1	1	yes	characteristic
84	C₄×C₂₉	C₂×#106	1	1	yes	characteristic
85	C₄×C₂₉	#492	1	1	yes	characteristic
86	C₄×C₂₉	#498	1	1	yes	characteristic
87	C₂×M₃₂	C₂²×C₂₉	1	2	yes	—
88	C₂×#108	—	2	1	no	—
89	C₂×#108	C₂²×C₂₉	1	2	yes	—
90	C₂×#107	—	2	1	no	—
91	C₂×#106	C₂²×C₂₉	1	2	yes	—
92	#423	—	2	1	no	—
93	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
94	#382	—	2	1	no	—
95	#365	—	2	8	no	—
96	#346	C₄×C₂₉	1	2	yes	complemented
97	C₄×C₁₆	C₄×C₂₉	1	2	yes	complemented
98	C₂×C₂₉	—	2	1	no	—
99	C₂×C₂₉	—	2	1	no	—
100	C₂×C₂₉	#1844	1	1	yes	characteristic
101	C₂×C₂₉	#2155	1	2	yes	—
102	C₂×M₁₆	—	2	2	no	—
103	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
104	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
107	M₃₂	D₄×C₂₉	1	4	yes	—
108	M₃₂	Q₈×C₂₉	1	4	yes	—
109	C₂×C₁₆	C₂×C₄×C₂₉	1	4	yes	—
110	#108	—	2	4	no	—
111	#108	—	4	2	no	—
112	#107	—	4	2	no	—
113	#106	—	2	4	no	—
114	C₄⋊C₈	—	4	2	no	—
115	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
116	C₄×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
117	C₄×C₈	Q₈×C₂₉	1	1	yes	characteristic
118	C₄×C₈	Q₈×C₂₉	1	1	yes	characteristic
119	#95	—	4	2	no	—
120	C₂₉	#12904	1	1	yes	characteristic, direct product factor, Sylow
121	C₂²×C₄	—	4	2	no	—
122	C₂²×C₄	SD₁₆×C₂₉	1	2	yes	—
123	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
124	M₁₆	—	4	2	no	—
125	M₁₆	—	4	2	no	—
126	C₂×C₈	—	4	2	no	—
127	C₂×C₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
128	C₂×C₈	C₄⋊C₄×C₂₉	1	1	yes	characteristic
129	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
130	C₂×C₈	SD₁₆×C₂₉	1	2	yes	—
131	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
132	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
133	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
134	C₂×C₈	C₂×Q₈×C₂₉	1	1	yes	characteristic
135	C₄⋊C₄	—	4	2	no	—
136	C₄⋊C₄	—	4	2	no	—
137	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
138	C₄²	C₄⋊C₄×C₂₉	1	1	yes	characteristic
139	C₄²	SD₁₆×C₂₉	1	2	yes	—
140	C₁₆	C₄⋊C₄×C₂₉	1	8	yes	—
141	C₂³	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
142	C₂×C₄	—	4	2	no	—
143	C₂×C₄	—	8	4	no	—
144	C₂×C₄	—	8	2	no	—
145	C₂×C₄	C₂₉×#106	1	2	yes	—
146	C₂×C₄	C₂₉×#106	1	2	yes	—
147	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
148	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
149	C₂×C₄	C₂₉×C₄⋊Q₈	1	1	yes	characteristic
150	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
151	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
152	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
153	C₈	—	8	2	no	—
154	C₈	C₂₉×#106	1	2	yes	—
155	C₈	C₂₉×#106	1	2	yes	—
156	C₈	C₂×C₄⋊C₄×C₂₉	1	2	yes	—
157	C₈	C₂₉×C₄⋊Q₈	1	2	yes	—
158	C₂²	—	2	2	no	—
159	C₂²	C₂×C₂₉×#106	1	1	yes	characteristic
160	C₂²	C₂₉×#492	1	1	yes	characteristic
161	C₂²	C₂₉×#498	1	1	yes	characteristic
162	C₄	—	2	2	no	—
163	C₄	—	2	2	no	—
164	C₄	—	16	2	no	—
165	C₄	C₂₉×#384	1	1	yes	characteristic
166	C₄	C₂×C₂₉×#106	1	1	yes	characteristic
167	C₄	C₂₉×#492	1	1	yes	characteristic
168	C₄	C₂₉×#498	1	1	yes	characteristic
169	C₂	—	2	1	no	—
170	C₂	—	2	1	no	—
171	C₂	C₂₉×#1844	1	1	yes	characteristic
172	C₂	C₂₉×#2155	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₈	C₂³×C₂₉
prime radical	C₂³×C₂₉	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ C₂×C₄×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂₉×#346	C₄	semidirect
15. C₄×C₁₆×C₂₉	C₄	semidirect
54. #12904	C₂₉	direct (N × H)
96. #346	C₄×C₂₉	semidirect
97. C₄×C₁₆	C₄×C₂₉	semidirect
120. C₂₉	#12904	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#365	2
C₄×C₂₉×M₃₂	2
C₂₉×#1848	2
C₂₉×#1846	2
#12904	29

Subgroups — C29×#12904 #20307804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#12904 #20307804