Subgroups — C₂₉×#33493 #20328393

Order 7424.

572 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2931	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2169	C₂	1	4	yes	maximal, complemented
3	D₄×C₁₆×C₂₉	C₂	1	4	yes	maximal, complemented
4	C₂₉×#2162	C₂	1	2	yes	maximal, complemented
5	C₂₉×#2113	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₉×#131	C₂²	1	2	yes	—
7	C₂₉×#532	C₄	1	1	yes	characteristic
8	C₂×C₂₉×M₃₂	C₂²	1	4	yes	—
9	C₂²×C₁₆×C₂₉	C₂²	1	4	yes	—
10	C₂₉×#436	C₄	1	4	yes	—
11	C₈×D₄×C₂₉	C₂²	1	4	yes	—
12	C₂₉×#423	C₄	1	1	yes	characteristic
13	C₂₉×#408	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
15	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	—
16	C₂₉×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₂₉×C₂²⋊C₁₆	C₂²	1	4	yes	—
18	C₂₉×C₂²⋊C₁₆	C₂²	1	8	yes	—
19	C₄×C₁₆×C₂₉	C₂²	1	4	yes	—
20	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
21	C₂₉×#131	—	4	2	no	—
22	C₂₉×#131	—	4	2	no	—
23	C₂×M₁₆×C₂₉	C₂×C₄	1	4	yes	—
24	C₂×M₁₆×C₂₉	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₂₉	C₂³	1	4	yes	—
27	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
28	C₂₉×C₄⋊Q₈	C₈	1	1	yes	characteristic
29	C₂₉×#127	C₈	1	1	yes	characteristic
30	C₂₉×#124	C₈	1	2	yes	—
31	C₂₉×#121	C₈	1	4	yes	—
32	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
33	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
34	C₂₉×M₃₂	—	4	4	no	—
35	C₂×C₁₆×C₂₉	—	4	4	no	—
36	C₂×C₁₆×C₂₉	C₂³	1	4	yes	—
37	C₂×C₁₆×C₂₉	C₂³	1	4	yes	—
38	C₂₉×C₄⋊C₈	C₂×C₄	1	4	yes	—
39	C₂₉×C₂²⋊C₈	C₂×C₄	1	8	yes	—
40	C₄×C₈×C₂₉	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₂₉	C₂³	1	2	yes	—
42	#41×C₂₉	—	4	2	no	—
43	#41×C₂₉	—	4	2	no	—
44	C₂×Q₈×C₂₉	C₂×C₈	1	2	yes	—
45	C₂×D₄×C₂₉	C₂×C₈	1	4	yes	—
46	C₂×D₄×C₂₉	C₂×C₈	1	4	yes	—
47	C₂×D₄×C₂₉	C₂×C₈	1	2	yes	—
48	C₂²×C₄×C₂₉	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
51	M₁₆×C₂₉	—	4	2	no	—
52	M₁₆×C₂₉	—	4	4	no	—
53	C₂×C₈×C₂₉	—	2	1	no	—
54	C₂×C₈×C₂₉	—	2	1	no	—
55	C₂×C₈×C₂₉	—	2	4	no	—
56	C₂×C₈×C₂₉	—	2	4	no	—
57	C₂×C₈×C₂₉	—	4	1	no	—
58	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
59	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₈×C₂₉	C₂²×C₄	1	4	yes	—
61	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
62	C₄⋊C₄×C₂₉	C₂×C₈	1	4	yes	—
63	C₂²⋊C₄×C₂₉	C₂×C₈	1	8	yes	—
64	C₄²×C₂₉	C₂×C₈	1	1	yes	characteristic
65	C₄²×C₂₉	C₂×C₈	1	1	yes	characteristic
66	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
67	C₁₆×C₂₉	—	2	4	no	—
68	C₁₆×C₂₉	—	2	4	no	—
69	#33493	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂³×C₂₉	C₂²×C₈	1	4	yes	—
71	C₂³×C₂₉	C₂²×C₈	1	1	yes	characteristic
72	Q₈×C₂₉	—	4	2	no	—
73	D₄×C₂₉	—	2	8	no	—
74	D₄×C₂₉	—	4	2	no	—
75	D₄×C₂₉	—	4	4	no	—
76	C₂×C₄×C₂₉	—	2	1	no	—
77	C₂×C₄×C₂₉	—	2	4	no	—
78	C₂×C₄×C₂₉	—	2	1	no	—
79	C₂×C₄×C₂₉	—	2	4	no	—
80	C₂×C₄×C₂₉	—	2	4	no	—
81	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
83	C₂×C₄×C₂₉	C₂²×C₈	1	4	yes	—
84	C₂×C₄×C₂₉	C₂²×C₈	1	2	yes	—
85	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
86	C₈×C₂₉	—	2	4	no	—
87	C₈×C₂₉	—	2	1	no	—
88	C₈×C₂₉	—	2	2	no	—
89	C₈×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
90	C₈×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
91	#2931	C₂×C₂₉	1	1	yes	characteristic
92	#2169	C₂×C₂₉	1	4	yes	complemented
93	D₄×C₁₆	C₂×C₂₉	1	4	yes	complemented
94	#2162	C₂×C₂₉	1	2	yes	complemented
95	#2113	C₂×C₂₉	1	4	yes	complemented
96	C₂²×C₂₉	—	2	2	no	—
97	C₂²×C₂₉	—	2	8	no	—
98	C₂²×C₂₉	—	2	1	no	—
99	C₂²×C₂₉	—	2	4	no	—
100	C₂²×C₂₉	C₂³×C₈	1	1	yes	characteristic
101	C₄×C₂₉	—	2	2	no	—
102	C₄×C₂₉	—	2	1	no	—
103	C₄×C₂₉	—	2	4	no	—
104	C₄×C₂₉	#504	1	4	yes	—
105	C₄×C₂₉	#518	1	1	yes	characteristic
106	C₄×C₂₉	#568	1	1	yes	characteristic
107	C₂×#131	C₂²×C₂₉	1	2	yes	—
108	#532	C₄×C₂₉	1	1	yes	characteristic
109	C₂×M₃₂	C₂²×C₂₉	1	4	yes	—
110	C₂²×C₁₆	C₂²×C₂₉	1	4	yes	—
111	#436	C₄×C₂₉	1	4	yes	—
112	C₈×D₄	C₂²×C₂₉	1	4	yes	—
113	#423	C₄×C₂₉	1	1	yes	characteristic
114	#408	C₄×C₂₉	1	2	yes	—
115	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
116	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	—
117	C₄⋊C₁₆	C₂²×C₂₉	1	2	yes	—
118	C₂²⋊C₁₆	C₂²×C₂₉	1	4	yes	—
119	C₂²⋊C₁₆	C₂²×C₂₉	1	8	yes	—
120	C₄×C₁₆	C₂²×C₂₉	1	4	yes	—
121	C₂×C₂₉	—	4	1	no	—
122	C₂×C₂₉	—	4	4	no	—
123	C₂×C₂₉	#2972	1	1	yes	characteristic
124	C₂×C₂₉	C₂×#504	1	2	yes	—
125	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
126	#131	—	4	2	no	—
127	#131	—	4	2	no	—
128	C₂×M₁₆	C₂×C₄×C₂₉	1	2	yes	—
129	C₂×M₁₆	C₂×C₄×C₂₉	1	4	yes	—
130	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
132	C₂²×C₈	C₂³×C₂₉	1	4	yes	—
133	C₄⋊Q₈	C₈×C₂₉	1	1	yes	characteristic
134	#127	C₈×C₂₉	1	1	yes	characteristic
135	#124	C₈×C₂₉	1	2	yes	—
136	#121	C₈×C₂₉	1	4	yes	—
137	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
138	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
139	M₃₂	—	4	4	no	—
140	C₂×C₁₆	—	4	4	no	—
141	C₂×C₁₆	C₂³×C₂₉	1	4	yes	—
142	C₂×C₁₆	C₂³×C₂₉	1	4	yes	—
143	C₄⋊C₈	C₂×C₄×C₂₉	1	4	yes	—
144	C₂²⋊C₈	C₂×C₄×C₂₉	1	8	yes	—
145	C₄×C₈	C₂×C₄×C₂₉	1	2	yes	—
146	C₄×C₈	C₂³×C₂₉	1	2	yes	—
147	C₂₉	#33493	1	1	yes	characteristic, direct product factor, Sylow
148	#41	—	4	2	no	—
149	#41	—	4	2	no	—
150	C₂×Q₈	C₂×C₈×C₂₉	1	2	yes	—
151	C₂×D₄	C₂×C₈×C₂₉	1	4	yes	—
152	C₂×D₄	C₂×C₈×C₂₉	1	4	yes	—
153	C₂×D₄	C₂×C₈×C₂₉	1	2	yes	—
154	C₂²×C₄	C₂×C₈×C₂₉	1	2	yes	—
155	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
156	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
157	M₁₆	—	4	4	no	—
158	M₁₆	—	4	2	no	—
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	4	1	no	—
164	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
165	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
166	C₂×C₈	C₂²×C₄×C₂₉	1	4	yes	—
167	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
168	C₄⋊C₄	C₂×C₈×C₂₉	1	4	yes	—
169	C₂²⋊C₄	C₂×C₈×C₂₉	1	8	yes	—
170	C₄²	C₂×C₈×C₂₉	1	1	yes	characteristic
171	C₄²	C₂×C₈×C₂₉	1	1	yes	characteristic
172	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
173	C₁₆	—	2	4	no	—
174	C₁₆	—	2	4	no	—
175	C₂³	C₂²×C₈×C₂₉	1	4	yes	—
176	C₂³	C₂²×C₈×C₂₉	1	1	yes	characteristic
177	Q₈	—	4	2	no	—
178	D₄	—	2	8	no	—
179	D₄	—	4	2	no	—
180	D₄	—	4	4	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
187	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
188	C₂×C₄	C₂²×C₈×C₂₉	1	4	yes	—
189	C₂×C₄	C₂²×C₈×C₂₉	1	2	yes	—
190	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
191	C₈	—	2	1	no	—
192	C₈	—	2	4	no	—
193	C₈	—	2	2	no	—
194	C₈	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
195	C₈	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
196	C₂²	—	2	1	no	—
197	C₂²	—	2	4	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	8	no	—
200	C₂²	C₂³×C₈×C₂₉	1	1	yes	characteristic
201	C₄	—	2	1	no	—
202	C₄	—	2	4	no	—
203	C₄	—	2	2	no	—
204	C₄	C₂₉×#504	1	4	yes	—
205	C₄	C₂₉×#518	1	1	yes	characteristic
206	C₄	C₂₉×#568	1	1	yes	characteristic
207	C₂	—	4	1	no	—
208	C₂	—	4	4	no	—
209	C₂	C₂₉×#2972	1	1	yes	characteristic
210	C₂	C₂×C₂₉×#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₈
prime radical	C₂₉×#532	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2169	C₂	semidirect
3. D₄×C₁₆×C₂₉	C₂	semidirect
4. C₂₉×#2162	C₂	semidirect
5. C₂₉×#2113	C₂	semidirect
69. #33493	C₂₉	direct (N × H)
92. #2169	C₂×C₂₉	semidirect
93. D₄×C₁₆	C₂×C₂₉	semidirect
94. #2162	C₂×C₂₉	semidirect
95. #2113	C₂×C₂₉	semidirect
147. C₂₉	#33493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#2931	2
C₂₉×#2169	2
D₄×C₁₆×C₂₉	2
C₂₉×#2162	2
C₂₉×#2113	2
#33493	29

Subgroups — C29×#33493 #20328393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#33493 #20328393