Subgroups — C₂₉×#12545 #20307445

Order 7424.

614 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#405	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1374	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₂₉	C₄	1	1	yes	characteristic
6	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
7	C₂×C₂₉×#117	C₄	1	1	yes	characteristic
8	C₂×C₂₉×M₃₂	—	2	2	no	—
9	C₂×C₂₉×M₃₂	—	2	2	no	—
10	C₂×C₂₉×M₃₂	C₄	1	4	yes	complemented
11	C₂²×C₁₆×C₂₉	—	2	2	no	—
12	C₂²×C₁₆×C₂₉	—	2	2	no	—
13	C₂²×C₁₆×C₂₉	C₄	1	4	yes	complemented
14	C₂²×C₁₆×C₂₉	C₂²	1	2	yes	—
15	C₂²×C₁₆×C₂₉	C₂²	1	2	yes	—
16	C₂₉×#405	—	2	2	no	—
17	C₂₉×#405	—	2	2	no	—
18	C₂×C₂₉×#97	C₄	1	2	yes	—
19	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
20	C₂³×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×M₁₆×C₂₉	—	2	2	no	—
22	C₂×M₁₆×C₂₉	—	2	2	no	—
23	C₂×M₁₆×C₂₉	C₈	1	4	yes	—
24	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₂₉	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₂₉	D₄	1	2	yes	—
29	C₂²×C₈×C₂₉	D₄	1	2	yes	—
30	C₂²×C₈×C₂₉	D₄	1	2	yes	—
31	C₂²×C₈×C₂₉	Q₈	1	2	yes	—
32	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
33	C₂₉×#117	—	2	2	no	—
34	C₂₉×#117	—	2	2	no	—
35	C₂×C₄⋊C₄×C₂₉	C₈	1	2	yes	—
36	C₂×C₂²⋊C₄×C₂₉	C₈	1	2	yes	—
37	C₂×C₄²×C₂₉	C₂×C₄	1	2	yes	—
38	C₂₉×M₃₂	—	2	8	no	—
39	C₂×C₁₆×C₂₉	—	2	8	no	—
40	C₂×C₁₆×C₂₉	—	2	2	no	—
41	C₂×C₁₆×C₂₉	—	2	2	no	—
42	C₂×C₁₆×C₂₉	—	2	2	no	—
43	C₂×C₁₆×C₂₉	—	2	2	no	—
44	C₂×C₁₆×C₂₉	C₂×C₄	1	4	yes	—
45	C₂×C₁₆×C₂₉	C₂×C₄	1	4	yes	—
46	C₂₉×#97	—	2	4	no	—
47	C₄×C₈×C₂₉	—	2	2	no	—
48	C₄×C₈×C₂₉	—	2	2	no	—
49	C₂⁴×C₂₉	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₂₉	C₄²	1	2	yes	—
51	C₂²×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₂₉	C₂×C₈	1	4	yes	—
54	C₂²×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₂₉	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₂₉	M₁₆	1	2	yes	—
57	C₂²×C₄×C₂₉	M₁₆	1	2	yes	—
58	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
59	M₁₆×C₂₉	—	2	8	no	—
60	C₂×C₈×C₂₉	—	2	2	no	—
61	C₂×C₈×C₂₉	—	2	2	no	—
62	C₂×C₈×C₂₉	C₄²	1	2	yes	—
63	C₂×C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
64	C₂×C₈×C₂₉	C₂²⋊C₄	1	4	yes	—
65	C₂×C₈×C₂₉	C₂²⋊C₄	1	4	yes	—
66	C₂×C₈×C₂₉	C₄⋊C₄	1	2	yes	—
67	C₂×C₈×C₂₉	C₄⋊C₄	1	4	yes	—
68	C₂×C₈×C₂₉	C₄⋊C₄	1	4	yes	—
69	C₂×C₈×C₂₉	C₂×C₈	1	4	yes	—
70	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
72	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₂₉	C₂×Q₈	1	1	yes	characteristic
76	C₄⋊C₄×C₂₉	—	2	4	no	—
77	C₂²⋊C₄×C₂₉	—	2	4	no	—
78	C₄²×C₂₉	—	2	2	no	—
79	C₄²×C₂₉	—	2	2	no	—
80	C₁₆×C₂₉	—	2	4	no	—
81	C₁₆×C₂₉	—	2	4	no	—
82	#12545	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂³×C₂₉	—	2	4	no	—
84	C₂³×C₂₉	C₄×C₈	1	2	yes	—
85	C₂³×C₂₉	C₂²⋊C₈	1	2	yes	—
86	C₂³×C₂₉	C₄⋊C₈	1	2	yes	—
87	C₂³×C₂₉	C₂²×C₈	1	1	yes	characteristic
88	C₂×C₄×C₂₉	—	2	4	no	—
89	C₂×C₄×C₂₉	—	2	8	no	—
90	C₂×C₄×C₂₉	#95	1	4	yes	—
91	C₂×C₄×C₂₉	C₄×C₈	1	2	yes	—
92	C₂×C₄×C₂₉	#97	1	4	yes	—
93	C₂×C₄×C₂₉	C₂²⋊C₈	1	2	yes	—
94	C₂×C₄×C₂₉	C₂²⋊C₈	1	4	yes	—
95	C₂×C₄×C₂₉	C₄⋊C₈	1	2	yes	—
96	C₂×C₄×C₂₉	C₄⋊C₈	1	4	yes	—
97	C₂×C₄×C₂₉	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×C₂₉	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
102	C₂×C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
103	C₈×C₂₉	—	2	4	no	—
104	C₈×C₂₉	#95	1	4	yes	—
105	C₈×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₈×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
107	C₈×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₈×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂²×M₃₂	C₂×C₂₉	1	1	yes	characteristic
110	C₂³×C₁₆	C₂×C₂₉	1	1	yes	characteristic
111	C₂×#405	C₂×C₂₉	1	1	yes	characteristic
112	#1374	C₂×C₂₉	1	4	yes	complemented
113	C₂²×C₂₉	—	2	4	no	—
114	C₂²×C₂₉	—	2	4	no	—
115	C₂²×C₂₉	—	2	4	no	—
116	C₂²×C₂₉	#336	1	4	yes	—
117	C₂²×C₂₉	C₂×C₄×C₈	1	1	yes	characteristic
118	C₂²×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
119	C₂²×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
120	C₂²×C₂₉	#504	1	4	yes	—
121	C₄×C₂₉	—	4	4	no	—
122	C₄×C₂₉	#336	1	4	yes	—
123	C₄×C₂₉	C₂×#95	1	1	yes	characteristic
124	C₄×C₂₉	C₂×#97	1	1	yes	characteristic
125	C₄×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
126	C₄×C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic
127	C₂²×M₁₆	C₄×C₂₉	1	1	yes	characteristic
128	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
129	C₂×#117	C₄×C₂₉	1	1	yes	characteristic
130	C₂×M₃₂	—	2	2	no	—
131	C₂×M₃₂	—	2	2	no	—
132	C₂×M₃₂	C₄×C₂₉	1	4	yes	complemented
133	C₂²×C₁₆	—	2	2	no	—
134	C₂²×C₁₆	—	2	2	no	—
135	C₂²×C₁₆	C₄×C₂₉	1	4	yes	complemented
136	C₂²×C₁₆	C₂²×C₂₉	1	2	yes	—
137	C₂²×C₁₆	C₂²×C₂₉	1	2	yes	—
138	#405	—	2	2	no	—
139	#405	—	2	2	no	—
140	C₂×#97	C₄×C₂₉	1	2	yes	—
141	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
142	C₂×C₂₉	—	2	4	no	—
143	C₂×C₂₉	C₂×#336	1	1	yes	characteristic
144	C₂×C₂₉	#2108	1	2	yes	—
145	C₂×C₂₉	#2113	1	2	yes	—
146	C₂×C₂₉	#2151	1	2	yes	—
147	C₂³×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
148	C₂×M₁₆	—	2	2	no	—
149	C₂×M₁₆	—	2	2	no	—
150	C₂×M₁₆	C₈×C₂₉	1	4	yes	—
151	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
152	C₂²×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
153	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
154	C₂²×C₈	C₂×C₄×C₂₉	1	2	yes	—
155	C₂²×C₈	D₄×C₂₉	1	2	yes	—
156	C₂²×C₈	D₄×C₂₉	1	2	yes	—
157	C₂²×C₈	D₄×C₂₉	1	2	yes	—
158	C₂²×C₈	Q₈×C₂₉	1	2	yes	—
159	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
160	#117	—	2	2	no	—
161	#117	—	2	2	no	—
162	C₂×C₄⋊C₄	C₈×C₂₉	1	2	yes	—
163	C₂×C₂²⋊C₄	C₈×C₂₉	1	2	yes	—
164	C₂×C₄²	C₂×C₄×C₂₉	1	2	yes	—
165	M₃₂	—	2	8	no	—
166	C₂×C₁₆	—	2	8	no	—
167	C₂×C₁₆	—	2	2	no	—
168	C₂×C₁₆	—	2	2	no	—
169	C₂×C₁₆	—	2	2	no	—
170	C₂×C₁₆	—	2	2	no	—
171	C₂×C₁₆	C₂×C₄×C₂₉	1	4	yes	—
172	C₂×C₁₆	C₂×C₄×C₂₉	1	4	yes	—
173	#97	—	2	4	no	—
174	C₄×C₈	—	2	2	no	—
175	C₄×C₈	—	2	2	no	—
176	C₂₉	#12545	1	1	yes	characteristic, direct product factor, Sylow
177	C₂⁴	C₂×C₈×C₂₉	1	1	yes	characteristic
178	C₂²×C₄	C₄²×C₂₉	1	2	yes	—
179	C₂²×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
180	C₂²×C₄	C₄⋊C₄×C₂₉	1	2	yes	—
181	C₂²×C₄	C₂×C₈×C₂₉	1	4	yes	—
182	C₂²×C₄	C₂×C₈×C₂₉	1	2	yes	—
183	C₂²×C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
184	C₂²×C₄	M₁₆×C₂₉	1	2	yes	—
185	C₂²×C₄	M₁₆×C₂₉	1	2	yes	—
186	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
187	M₁₆	—	2	8	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	2	no	—
190	C₂×C₈	C₄²×C₂₉	1	2	yes	—
191	C₂×C₈	C₂²⋊C₄×C₂₉	1	4	yes	—
192	C₂×C₈	C₂²⋊C₄×C₂₉	1	4	yes	—
193	C₂×C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
194	C₂×C₈	C₄⋊C₄×C₂₉	1	4	yes	—
195	C₂×C₈	C₄⋊C₄×C₂₉	1	4	yes	—
196	C₂×C₈	C₄⋊C₄×C₂₉	1	2	yes	—
197	C₂×C₈	C₂×C₈×C₂₉	1	4	yes	—
198	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
199	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
200	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
201	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
202	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
203	C₂×C₈	C₂×Q₈×C₂₉	1	1	yes	characteristic
204	C₄⋊C₄	—	2	4	no	—
205	C₂²⋊C₄	—	2	4	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	2	2	no	—
208	C₁₆	—	2	4	no	—
209	C₁₆	—	2	4	no	—
210	C₂³	—	2	4	no	—
211	C₂³	C₄×C₈×C₂₉	1	2	yes	—
212	C₂³	C₂₉×C₂²⋊C₈	1	2	yes	—
213	C₂³	C₂₉×C₄⋊C₈	1	2	yes	—
214	C₂³	C₂²×C₈×C₂₉	1	1	yes	characteristic
215	C₂×C₄	—	2	8	no	—
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	C₂₉×#95	1	4	yes	—
218	C₂×C₄	C₄×C₈×C₂₉	1	2	yes	—
219	C₂×C₄	C₂₉×#97	1	4	yes	—
220	C₂×C₄	C₂₉×C₂²⋊C₈	1	2	yes	—
221	C₂×C₄	C₂₉×C₂²⋊C₈	1	4	yes	—
222	C₂×C₄	C₂₉×C₄⋊C₈	1	2	yes	—
223	C₂×C₄	C₂₉×C₄⋊C₈	1	4	yes	—
224	C₂×C₄	C₂×C₄²×C₂₉	1	1	yes	characteristic
225	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
226	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
227	C₂×C₄	C₂²×C₈×C₂₉	1	1	yes	characteristic
228	C₂×C₄	C₂×M₁₆×C₂₉	1	1	yes	characteristic
229	C₂×C₄	C₂×M₁₆×C₂₉	1	1	yes	characteristic
230	C₈	—	2	4	no	—
231	C₈	C₂₉×#95	1	4	yes	—
232	C₈	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
233	C₈	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
234	C₈	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
235	C₈	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
236	C₂²	—	2	4	no	—
237	C₂²	—	2	4	no	—
238	C₂²	—	2	4	no	—
239	C₂²	C₂₉×#336	1	4	yes	—
240	C₂²	C₂×C₄×C₈×C₂₉	1	1	yes	characteristic
241	C₂²	C₂×C₂₉×C₂²⋊C₈	1	1	yes	characteristic
242	C₂²	C₂×C₂₉×C₄⋊C₈	1	1	yes	characteristic
243	C₂²	C₂₉×#504	1	4	yes	—
244	C₄	—	4	4	no	—
245	C₄	C₂₉×#336	1	4	yes	—
246	C₄	C₂×C₂₉×#95	1	1	yes	characteristic
247	C₄	C₂×C₂₉×#97	1	1	yes	characteristic
248	C₄	C₂×C₂₉×C₂²⋊C₈	1	1	yes	characteristic
249	C₄	C₂×C₂₉×C₄⋊C₈	1	1	yes	characteristic
250	C₂	—	2	4	no	—
251	C₂	C₂×C₂₉×#336	1	1	yes	characteristic
252	C₂	C₂₉×#2108	1	2	yes	—
253	C₂	C₂₉×#2113	1	2	yes	—
254	C₂	C₂₉×#2151	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₂₉×#1374	C₂	semidirect
10. C₂×C₂₉×M₃₂	C₄	semidirect
13. C₂²×C₁₆×C₂₉	C₄	semidirect
82. #12545	C₂₉	direct (N × H)
112. #1374	C₂×C₂₉	semidirect
132. C₂×M₃₂	C₄×C₂₉	semidirect
135. C₂²×C₁₆	C₄×C₂₉	semidirect
176. C₂₉	#12545	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×M₃₂	2
C₂³×C₁₆×C₂₉	2
C₂×C₂₉×#405	2
C₂₉×#1374	2
#12545	29

Subgroups — C29×#12545 #20307445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#12545 #20307445