Subgroups — C₂₉×#25362 #20320262

Order 7424.

748 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3142	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3036	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1815	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
20	C₂₉×#532	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#491	—	2	1	no	—
24	C₂₉×#490	—	2	1	no	—
25	C₂₉×#488	—	2	1	no	—
26	C₂₉×#488	—	2	1	no	—
27	C₂₉×#478	—	2	1	no	—
28	C₂₉×#478	—	2	1	no	—
29	C₂₉×#478	—	2	1	no	—
30	C₂₉×#478	—	2	1	no	—
31	C₂₉×#463	—	2	1	no	—
32	C₂₉×#463	—	2	1	no	—
33	C₂₉×#461	—	2	1	no	—
34	C₂₉×#459	—	2	1	no	—
35	C₂₉×#436	—	2	1	no	—
36	C₂₉×#435	—	2	1	no	—
37	C₂₉×#435	—	2	1	no	—
38	C₈×D₄×C₂₉	—	2	1	no	—
39	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
43	C₂₉×#423	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₂₉×#417	C₂²	1	1	yes	characteristic
46	C₂₉×#417	C₂²	1	1	yes	characteristic
47	C₂₉×#417	C₂²	1	1	yes	characteristic
48	C₂₉×#417	C₂²	1	1	yes	characteristic
49	C₂₉×#417	C₂²	1	1	yes	characteristic
50	C₂₉×#417	C₂²	1	1	yes	characteristic
51	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
53	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
55	C₂₉×#408	C₂²	1	1	yes	characteristic
56	C₂₉×#408	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#343	C₂²	1	1	yes	characteristic
60	C₂₉×#343	C₂²	1	1	yes	characteristic
61	C₂₉×#343	C₂²	1	1	yes	characteristic
62	C₂₉×#343	C₂²	1	1	yes	characteristic
63	C₂₉×#343	C₂²	1	1	yes	characteristic
64	C₂₉×#343	C₂²	1	1	yes	characteristic
65	C₂₉×#341	C₂²	1	1	yes	characteristic
66	C₂₉×#341	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
68	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₉	—	2	1	no	—
71	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
72	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
73	C₂₉×AGL(1,ℤ/8)	—	4	1	no	—
74	C₂₉×AGL(1,ℤ/8)	—	4	1	no	—
75	C₂×SD₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×D₈×C₂₉	—	2	1	no	—
78	C₂×D₈×C₂₉	—	2	1	no	—
79	C₂₉×#131	—	2	2	no	—
80	C₂₉×#131	—	2	2	no	—
81	C₂₉×#131	—	4	1	no	—
82	C₂₉×#131	—	4	1	no	—
83	C₂×M₁₆×C₂₉	—	2	1	no	—
84	C₂×M₁₆×C₂₉	—	2	1	no	—
85	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₉	—	2	1	no	—
92	C₂²×C₈×C₂₉	—	2	1	no	—
93	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
95	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
96	C₂₉×#127	D₄	1	1	yes	characteristic
97	C₂₉×#125	—	2	1	no	—
98	C₂₉×#125	—	2	1	no	—
99	C₂₉×#125	—	2	1	no	—
100	C₂₉×#125	—	2	1	no	—
101	C₂₉×#124	D₄	1	1	yes	characteristic
102	C₂₉×#124	D₄	1	1	yes	characteristic
103	C₂₉×#121	—	2	1	no	—
104	C₂₉×#121	—	2	1	no	—
105	C₄×D₄×C₂₉	—	2	1	no	—
106	C₄×D₄×C₂₉	—	2	1	no	—
107	C₄×D₄×C₂₉	—	2	1	no	—
108	C₄×D₄×C₂₉	—	2	1	no	—
109	C₄×D₄×C₂₉	—	2	1	no	—
110	C₄×D₄×C₂₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
117	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
118	C₂₉×#108	—	4	1	no	—
119	C₂₉×#108	—	4	1	no	—
120	C₂₉×#107	—	2	1	no	—
121	C₂₉×#107	—	2	1	no	—
122	C₂₉×#106	—	2	1	no	—
123	C₂₉×#106	—	2	1	no	—
124	C₂₉×C₄⋊C₈	—	2	1	no	—
125	C₂₉×C₄⋊C₈	—	2	1	no	—
126	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
127	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
128	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
129	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
130	C₂₉×#103	—	2	1	no	—
131	C₂₉×#103	—	2	1	no	—
132	C₂₉×#103	—	2	1	no	—
133	C₂₉×#103	—	2	1	no	—
134	C₂₉×#103	—	2	1	no	—
135	C₂₉×#103	—	2	1	no	—
136	C₂₉×#102	—	2	1	no	—
137	C₂₉×#102	—	2	1	no	—
138	C₂₉×#102	—	2	1	no	—
139	C₂₉×#102	—	2	1	no	—
140	C₂₉×#102	—	2	1	no	—
141	C₂₉×#102	—	2	1	no	—
142	C₂₉×#102	—	2	1	no	—
143	C₂₉×#102	—	2	1	no	—
144	C₂₉×#102	—	2	1	no	—
145	C₂₉×#102	—	2	1	no	—
146	C₂₉×#100	—	2	2	no	—
147	C₂₉×#100	—	2	2	no	—
148	C₂₉×C₂²⋊C₈	—	2	1	no	—
149	C₂₉×C₂²⋊C₈	—	2	1	no	—
150	C₂₉×C₂²⋊C₈	—	2	1	no	—
151	C₂₉×C₂²⋊C₈	—	2	1	no	—
152	C₂₉×#97	—	2	1	no	—
153	C₂₉×#97	—	2	1	no	—
154	C₄×C₈×C₂₉	—	2	1	no	—
155	C₄×C₈×C₂₉	—	2	1	no	—
156	C₂⁴×C₂₉	—	2	1	no	—
157	#41×C₂₉	—	2	1	no	—
158	#41×C₂₉	—	2	1	no	—
159	#41×C₂₉	—	2	1	no	—
160	#41×C₂₉	—	2	1	no	—
161	#41×C₂₉	—	2	1	no	—
162	#41×C₂₉	—	2	1	no	—
163	#41×C₂₉	—	2	1	no	—
164	#41×C₂₉	—	2	1	no	—
165	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₂₉	—	2	1	no	—
168	C₂×D₄×C₂₉	—	2	1	no	—
169	C₂×D₄×C₂₉	—	2	1	no	—
170	C₂×D₄×C₂₉	—	2	1	no	—
171	C₂×D₄×C₂₉	—	2	1	no	—
172	C₂×D₄×C₂₉	—	2	1	no	—
173	C₂×D₄×C₂₉	—	2	1	no	—
174	C₂×D₄×C₂₉	—	2	1	no	—
175	C₂×D₄×C₂₉	—	2	1	no	—
176	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₂₉	#41	1	2	yes	—
179	C₂²×C₄×C₂₉	—	2	1	no	—
180	C₂²×C₄×C₂₉	—	2	1	no	—
181	C₂²×C₄×C₂₉	—	2	1	no	—
182	C₂²×C₄×C₂₉	—	2	1	no	—
183	C₂²×C₄×C₂₉	—	2	1	no	—
184	C₂²×C₄×C₂₉	—	4	1	no	—
185	C₂²×C₄×C₂₉	—	4	1	no	—
186	C₂²×C₄×C₂₉	—	8	2	no	—
187	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
188	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
189	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
190	SD₁₆×C₂₉	—	4	2	no	—
191	SD₁₆×C₂₉	—	4	2	no	—
192	D₈×C₂₉	—	4	2	no	—
193	D₈×C₂₉	—	4	2	no	—
194	M₁₆×C₂₉	—	2	1	no	—
195	M₁₆×C₂₉	—	2	1	no	—
196	M₁₆×C₂₉	—	2	1	no	—
197	M₁₆×C₂₉	—	2	1	no	—
198	M₁₆×C₂₉	—	2	1	no	—
199	M₁₆×C₂₉	—	2	1	no	—
200	M₁₆×C₂₉	—	2	1	no	—
201	M₁₆×C₂₉	—	2	1	no	—
202	M₁₆×C₂₉	—	2	1	no	—
203	M₁₆×C₂₉	—	2	1	no	—
204	M₁₆×C₂₉	—	2	1	no	—
205	M₁₆×C₂₉	—	4	2	no	—
206	M₁₆×C₂₉	—	4	2	no	—
207	M₁₆×C₂₉	#41	1	2	yes	—
208	C₂×C₈×C₂₉	—	2	1	no	—
209	C₂×C₈×C₂₉	—	2	1	no	—
210	C₂×C₈×C₂₉	—	2	1	no	—
211	C₂×C₈×C₂₉	—	2	1	no	—
212	C₂×C₈×C₂₉	—	2	1	no	—
213	C₂×C₈×C₂₉	—	2	1	no	—
214	C₂×C₈×C₂₉	—	2	1	no	—
215	C₂×C₈×C₂₉	—	2	1	no	—
216	C₂×C₈×C₂₉	—	2	1	no	—
217	C₂×C₈×C₂₉	—	2	1	no	—
218	C₂×C₈×C₂₉	—	4	2	no	—
219	C₂×C₈×C₂₉	—	4	2	no	—
220	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
221	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
222	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
223	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
224	C₄⋊C₄×C₂₉	—	2	1	no	—
225	C₄⋊C₄×C₂₉	—	2	1	no	—
226	C₄⋊C₄×C₂₉	—	2	1	no	—
227	C₄⋊C₄×C₂₉	—	2	1	no	—
228	C₄⋊C₄×C₂₉	—	2	1	no	—
229	C₄⋊C₄×C₂₉	—	2	1	no	—
230	C₄⋊C₄×C₂₉	—	2	1	no	—
231	C₄⋊C₄×C₂₉	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	4	1	no	—
233	C₄⋊C₄×C₂₉	—	4	1	no	—
234	C₄⋊C₄×C₂₉	—	4	1	no	—
235	C₄⋊C₄×C₂₉	—	4	1	no	—
236	C₂²⋊C₄×C₂₉	—	2	1	no	—
237	C₂²⋊C₄×C₂₉	—	2	1	no	—
238	C₂²⋊C₄×C₂₉	—	2	1	no	—
239	C₂²⋊C₄×C₂₉	—	2	1	no	—
240	C₂²⋊C₄×C₂₉	—	4	1	no	—
241	C₂²⋊C₄×C₂₉	—	4	1	no	—
242	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
243	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
244	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
245	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
246	#25362	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂³×C₂₉	—	2	1	no	—
248	C₂³×C₂₉	—	2	1	no	—
249	C₂³×C₂₉	—	2	2	no	—
250	C₂³×C₂₉	—	4	1	no	—
251	C₂³×C₂₉	—	4	1	no	—
252	C₂³×C₂₉	—	8	1	no	—
253	C₂³×C₂₉	—	8	1	no	—
254	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
255	Q₈×C₂₉	—	2	1	no	—
256	Q₈×C₂₉	—	2	1	no	—
257	Q₈×C₂₉	—	2	1	no	—
258	Q₈×C₂₉	—	2	1	no	—
259	D₄×C₂₉	—	2	2	no	—
260	D₄×C₂₉	—	2	1	no	—
261	D₄×C₂₉	—	2	1	no	—
262	D₄×C₂₉	—	2	1	no	—
263	D₄×C₂₉	—	2	1	no	—
264	D₄×C₂₉	—	2	2	no	—
265	D₄×C₂₉	—	4	2	no	—
266	D₄×C₂₉	—	4	1	no	—
267	D₄×C₂₉	—	4	1	no	—
268	D₄×C₂₉	—	4	1	no	—
269	D₄×C₂₉	—	4	1	no	—
270	D₄×C₂₉	—	4	1	no	—
271	D₄×C₂₉	—	4	1	no	—
272	D₄×C₂₉	—	8	1	no	—
273	C₂×C₄×C₂₉	—	2	1	no	—
274	C₂×C₄×C₂₉	—	2	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	4	1	no	—
279	C₂×C₄×C₂₉	—	4	1	no	—
280	C₂×C₄×C₂₉	—	4	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	8	2	no	—
285	C₂×C₄×C₂₉	—	8	2	no	—
286	C₂×C₄×C₂₉	—	8	1	no	—
287	C₂×C₄×C₂₉	—	8	1	no	—
288	C₂×C₄×C₂₉	—	8	1	no	—
289	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
290	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
291	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
292	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
293	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
299	C₈×C₂₉	—	2	1	no	—
300	C₈×C₂₉	—	2	1	no	—
301	C₈×C₂₉	—	2	1	no	—
302	C₈×C₂₉	—	2	1	no	—
303	C₈×C₂₉	—	2	2	no	—
304	C₈×C₂₉	—	4	1	no	—
305	C₈×C₂₉	—	4	1	no	—
306	C₈×C₂₉	—	4	1	no	—
307	C₈×C₂₉	—	4	1	no	—
308	C₈×C₂₉	—	4	1	no	—
309	#3142	C₂×C₂₉	1	1	yes	characteristic, complemented
310	C₂×#478	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#3036	C₂×C₂₉	1	1	yes	characteristic
312	#2935	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#2079	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#2078	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#2051	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#2051	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#1998	C₂×C₂₉	1	1	yes	characteristic, complemented
318	#1950	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#1907	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#1907	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#1816	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#1815	C₂×C₂₉	1	1	yes	characteristic, complemented
323	C₄×#100	C₂×C₂₉	1	1	yes	characteristic, complemented
324	C₂²×C₂₉	—	2	1	no	—
325	C₂²×C₂₉	—	2	1	no	—
326	C₂²×C₂₉	—	4	1	no	—
327	C₂²×C₂₉	—	4	1	no	—
328	C₂²×C₂₉	—	4	2	no	—
329	C₂²×C₂₉	—	4	1	no	—
330	C₂²×C₂₉	—	4	1	no	—
331	C₂²×C₂₉	—	4	1	no	—
332	C₂²×C₂₉	—	4	1	no	—
333	C₂²×C₂₉	—	8	2	no	—
334	C₂²×C₂₉	—	8	2	no	—
335	C₂²×C₂₉	—	8	1	no	—
336	C₂²×C₂₉	—	8	1	no	—
337	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
338	C₂²×C₂₉	#529	1	1	yes	characteristic
339	C₂²×C₂₉	#542	1	1	yes	characteristic
340	C₄×C₂₉	—	2	1	no	—
341	C₄×C₂₉	—	2	1	no	—
342	C₄×C₂₉	—	2	1	no	—
343	C₄×C₂₉	—	2	1	no	—
344	C₄×C₂₉	—	4	1	no	—
345	C₄×C₂₉	—	4	1	no	—
346	C₄×C₂₉	—	8	1	no	—
347	C₄×C₂₉	—	8	1	no	—
348	C₄×C₂₉	—	8	1	no	—
349	C₄×C₂₉	#546	1	1	yes	characteristic
350	C₄×C₂₉	#546	1	1	yes	characteristic
351	C₄×C₂₉	#547	1	1	yes	characteristic
352	C₄×C₂₉	#548	1	1	yes	characteristic
353	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
357	#532	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
360	#491	—	2	1	no	—
361	#490	—	2	1	no	—
362	#488	—	2	1	no	—
363	#488	—	2	1	no	—
364	#478	—	2	1	no	—
365	#478	—	2	1	no	—
366	#478	—	2	1	no	—
367	#478	—	2	1	no	—
368	#463	—	2	1	no	—
369	#463	—	2	1	no	—
370	#461	—	2	1	no	—
371	#459	—	2	1	no	—
372	#436	—	2	1	no	—
373	#435	—	2	1	no	—
374	#435	—	2	1	no	—
375	C₈×D₄	—	2	1	no	—
376	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
380	#423	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
382	#417	C₂²×C₂₉	1	1	yes	characteristic
383	#417	C₂²×C₂₉	1	1	yes	characteristic
384	#417	C₂²×C₂₉	1	1	yes	characteristic
385	#417	C₂²×C₂₉	1	1	yes	characteristic
386	#417	C₂²×C₂₉	1	1	yes	characteristic
387	#417	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
390	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
391	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
392	#408	C₂²×C₂₉	1	1	yes	characteristic
393	#408	C₂²×C₂₉	1	1	yes	characteristic
394	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
395	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
396	#343	C₂²×C₂₉	1	1	yes	characteristic
397	#343	C₂²×C₂₉	1	1	yes	characteristic
398	#343	C₂²×C₂₉	1	1	yes	characteristic
399	#343	C₂²×C₂₉	1	1	yes	characteristic
400	#343	C₂²×C₂₉	1	1	yes	characteristic
401	#343	C₂²×C₂₉	1	1	yes	characteristic
402	#341	C₂²×C₂₉	1	1	yes	characteristic
403	#341	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×C₂₉	—	2	1	no	—
405	C₂×C₂₉	—	2	1	no	—
406	C₂×C₂₉	—	8	1	no	—
407	C₂×C₂₉	—	8	1	no	—
408	C₂×C₂₉	—	8	2	no	—
409	C₂×C₂₉	#2427	1	1	yes	characteristic
410	C₂×C₂₉	#3067	1	1	yes	characteristic
411	C₂×C₂₉	#3068	1	1	yes	characteristic
412	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
413	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
414	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
415	C₂³×C₄	—	2	1	no	—
416	AGL(1,ℤ/8)	—	2	2	no	—
417	AGL(1,ℤ/8)	—	2	2	no	—
418	AGL(1,ℤ/8)	—	4	1	no	—
419	AGL(1,ℤ/8)	—	4	1	no	—
420	C₂×SD₁₆	—	2	1	no	—
421	C₂×SD₁₆	—	2	1	no	—
422	C₂×D₈	—	2	1	no	—
423	C₂×D₈	—	2	1	no	—
424	#131	—	2	2	no	—
425	#131	—	2	2	no	—
426	#131	—	4	1	no	—
427	#131	—	4	1	no	—
428	C₂×M₁₆	—	2	1	no	—
429	C₂×M₁₆	—	2	1	no	—
430	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
431	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
432	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
433	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
434	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
435	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
436	C₂²×C₈	—	2	1	no	—
437	C₂²×C₈	—	2	1	no	—
438	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
440	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
441	#127	D₄×C₂₉	1	1	yes	characteristic
442	#125	—	2	1	no	—
443	#125	—	2	1	no	—
444	#125	—	2	1	no	—
445	#125	—	2	1	no	—
446	#124	D₄×C₂₉	1	1	yes	characteristic
447	#124	D₄×C₂₉	1	1	yes	characteristic
448	#121	—	2	1	no	—
449	#121	—	2	1	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	—	2	1	no	—
456	C₂×C₄⋊C₄	—	2	1	no	—
457	C₂×C₄⋊C₄	—	2	1	no	—
458	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
463	#108	—	4	1	no	—
464	#108	—	4	1	no	—
465	#107	—	2	1	no	—
466	#107	—	2	1	no	—
467	#106	—	2	1	no	—
468	#106	—	2	1	no	—
469	C₄⋊C₈	—	2	1	no	—
470	C₄⋊C₈	—	2	1	no	—
471	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
472	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
473	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
474	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
475	#103	—	2	1	no	—
476	#103	—	2	1	no	—
477	#103	—	2	1	no	—
478	#103	—	2	1	no	—
479	#103	—	2	1	no	—
480	#103	—	2	1	no	—
481	#102	—	2	1	no	—
482	#102	—	2	1	no	—
483	#102	—	2	1	no	—
484	#102	—	2	1	no	—
485	#102	—	2	1	no	—
486	#102	—	2	1	no	—
487	#102	—	2	1	no	—
488	#102	—	2	1	no	—
489	#102	—	2	1	no	—
490	#102	—	2	1	no	—
491	#100	—	2	2	no	—
492	#100	—	2	2	no	—
493	C₂²⋊C₈	—	2	1	no	—
494	C₂²⋊C₈	—	2	1	no	—
495	C₂²⋊C₈	—	2	1	no	—
496	C₂²⋊C₈	—	2	1	no	—
497	#97	—	2	1	no	—
498	#97	—	2	1	no	—
499	C₄×C₈	—	2	1	no	—
500	C₄×C₈	—	2	1	no	—
501	C₂₉	#25362	1	1	yes	characteristic, direct product factor, Sylow
502	C₂⁴	—	2	1	no	—
503	#41	—	2	1	no	—
504	#41	—	2	1	no	—
505	#41	—	2	1	no	—
506	#41	—	2	1	no	—
507	#41	—	2	1	no	—
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	#41	—	2	1	no	—
511	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
512	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	1	no	—
522	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
523	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
524	C₂×D₄	#41×C₂₉	1	2	yes	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	8	2	no	—
533	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
534	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
536	SD₁₆	—	4	2	no	—
537	SD₁₆	—	4	2	no	—
538	D₈	—	4	2	no	—
539	D₈	—	4	2	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	—	2	1	no	—
544	M₁₆	—	2	1	no	—
545	M₁₆	—	2	1	no	—
546	M₁₆	—	2	1	no	—
547	M₁₆	—	2	1	no	—
548	M₁₆	—	2	1	no	—
549	M₁₆	—	2	1	no	—
550	M₁₆	—	2	1	no	—
551	M₁₆	—	4	2	no	—
552	M₁₆	—	4	2	no	—
553	M₁₆	#41×C₂₉	1	2	yes	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	4	2	no	—
565	C₂×C₈	—	4	2	no	—
566	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
567	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
568	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
569	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	4	1	no	—
579	C₄⋊C₄	—	4	1	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₂²⋊C₄	—	2	1	no	—
583	C₂²⋊C₄	—	2	1	no	—
584	C₂²⋊C₄	—	2	1	no	—
585	C₂²⋊C₄	—	2	1	no	—
586	C₂²⋊C₄	—	4	1	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
589	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
590	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
591	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	8	1	no	—
598	C₂³	—	8	1	no	—
599	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
600	Q₈	—	2	1	no	—
601	Q₈	—	2	1	no	—
602	Q₈	—	2	1	no	—
603	Q₈	—	2	1	no	—
604	D₄	—	2	2	no	—
605	D₄	—	2	1	no	—
606	D₄	—	2	1	no	—
607	D₄	—	2	1	no	—
608	D₄	—	2	1	no	—
609	D₄	—	2	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	8	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	8	2	no	—
630	C₂×C₄	—	8	2	no	—
631	C₂×C₄	—	8	1	no	—
632	C₂×C₄	—	8	1	no	—
633	C₂×C₄	—	8	1	no	—
634	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
635	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
636	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
637	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
638	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
639	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
640	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
641	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
642	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
643	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
644	C₈	—	2	1	no	—
645	C₈	—	2	1	no	—
646	C₈	—	2	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	2	2	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₈	—	4	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	8	2	no	—
664	C₂²	—	8	2	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
668	C₂²	C₂₉×#529	1	1	yes	characteristic
669	C₂²	C₂₉×#542	1	1	yes	characteristic
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	8	1	no	—
677	C₄	—	8	1	no	—
678	C₄	—	8	1	no	—
679	C₄	C₂₉×#546	1	1	yes	characteristic
680	C₄	C₂₉×#546	1	1	yes	characteristic
681	C₄	C₂₉×#547	1	1	yes	characteristic
682	C₄	C₂₉×#548	1	1	yes	characteristic
683	C₂	—	2	1	no	—
684	C₂	—	2	1	no	—
685	C₂	—	8	1	no	—
686	C₂	—	8	1	no	—
687	C₂	—	8	2	no	—
688	C₂	C₂₉×#2427	1	1	yes	characteristic
689	C₂	C₂₉×#3067	1	1	yes	characteristic
690	C₂	C₂₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#3036	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3142	C₂	semidirect
2. C₂×C₂₉×#478	C₂	semidirect
4. C₂₉×#2935	C₂	semidirect
5. C₂₉×#2079	C₂	semidirect
6. C₂₉×#2078	C₂	semidirect
7. C₂₉×#2051	C₂	semidirect
8. C₂₉×#2051	C₂	semidirect
9. C₂₉×#1998	C₂	semidirect
10. C₂₉×#1950	C₂	semidirect
11. C₂₉×#1907	C₂	semidirect
12. C₂₉×#1907	C₂	semidirect
13. C₂₉×#1816	C₂	semidirect
14. C₂₉×#1815	C₂	semidirect
15. C₄×C₂₉×#100	C₂	semidirect
246. #25362	C₂₉	direct (N × H)
309. #3142	C₂×C₂₉	semidirect
310. C₂×#478	C₂×C₂₉	semidirect
312. #2935	C₂×C₂₉	semidirect
313. #2079	C₂×C₂₉	semidirect
314. #2078	C₂×C₂₉	semidirect
315. #2051	C₂×C₂₉	semidirect
316. #2051	C₂×C₂₉	semidirect
317. #1998	C₂×C₂₉	semidirect
318. #1950	C₂×C₂₉	semidirect
319. #1907	C₂×C₂₉	semidirect
320. #1907	C₂×C₂₉	semidirect
321. #1816	C₂×C₂₉	semidirect
322. #1815	C₂×C₂₉	semidirect
323. C₄×#100	C₂×C₂₉	semidirect
501. C₂₉	#25362	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×#3142	2
C₂×C₂₉×#478	2
C₂₉×#3036	2
C₂₉×#2935	2
C₂₉×#2079	2
C₂₉×#2078	2
C₂₉×#2051	2
C₂₉×#1998	2
C₂₉×#1950	2
C₂₉×#1907	2
C₂₉×#1816	2
C₂₉×#1815	2
C₄×C₂₉×#100	2
#25362	29

Subgroups — C29×#25362 #20320262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25362 #20320262