Subgroups — C₂₉×#24325 #20319225

Order 7424.

960 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3504	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉×#137	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2565	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2061	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2060	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2028	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1882	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1882	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#1860	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1859	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1806	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
17	C₂₉×#557	—	2	1	no	—
18	C₂₉×#557	—	2	1	no	—
19	C₂₉×#554	—	2	1	no	—
20	C₂₉×#554	—	2	1	no	—
21	C₂₉×#554	—	2	2	no	—
22	C₂₉×#554	—	2	2	no	—
23	C₂₉×#544	—	2	1	no	—
24	C₂₉×#544	—	2	1	no	—
25	C₂₉×#544	C₂²	1	1	yes	characteristic
26	C₂₉×#544	C₂²	1	1	yes	characteristic
27	C₂₉×#533	—	2	1	no	—
28	C₂₉×#533	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#125	—	2	1	no	—
30	C₂×C₂₉×#125	C₂²	1	1	yes	characteristic
31	C₂₉×#520	C₂²	1	1	yes	characteristic
32	C₂₉×#520	C₂²	1	1	yes	characteristic
33	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#479	—	2	1	no	—
36	C₂₉×#479	—	2	1	no	—
37	C₂₉×#477	—	2	1	no	—
38	C₂₉×#475	—	2	1	no	—
39	C₂₉×#441	—	2	1	no	—
40	C₂₉×#440	—	2	1	no	—
41	C₄×Q₁₆×C₂₉	—	2	1	no	—
42	C₄×SD₁₆×C₂₉	—	2	1	no	—
43	C₂₉×#428	C₂²	1	1	yes	characteristic
44	C₂₉×#428	C₂²	1	1	yes	characteristic
45	C₂₉×#428	C₂²	1	1	yes	characteristic
46	C₂₉×#423	C₂²	1	1	yes	characteristic
47	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
48	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
49	C₂₉×#419	C₂²	1	1	yes	characteristic
50	C₂₉×#419	C₂²	1	1	yes	characteristic
51	C₂₉×#419	C₂²	1	1	yes	characteristic
52	C₂₉×#417	C₂²	1	1	yes	characteristic
53	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
54	C₂₉×#398	—	2	2	no	—
55	C₂₉×#391	C₂²	1	1	yes	characteristic
56	C₂₉×#391	C₂²	1	1	yes	characteristic
57	C₂₉×#387	—	2	2	no	—
58	C₂₉×#384	C₂²	1	1	yes	characteristic
59	C₂₉×#382	C₂²	1	1	yes	characteristic
60	C₄×C₄⋊C₄×C₂₉	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×#339	C₂²	1	1	yes	characteristic
66	C₂₉×#339	C₂²	1	1	yes	characteristic
67	C₂₉×#339	C₂²	1	1	yes	characteristic
68	C₂₉×#339	C₂²	1	1	yes	characteristic
69	C₂₉×#339	C₂²	1	1	yes	characteristic
70	C₂₉×#339	C₂²	1	1	yes	characteristic
71	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂₉×#137	—	2	2	no	—
74	C₂₉×#137	Q₈	1	4	yes	complemented
75	C₂×Q₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	—	2	2	no	—
82	C₂₉×C₄⋊Q₈	—	2	2	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	—	2	1	no	—
87	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
88	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
89	C₂₉×#125	—	2	2	no	—
90	C₂₉×#125	—	2	2	no	—
91	C₂₉×#125	—	2	2	no	—
92	C₂₉×#125	—	2	2	no	—
93	C₂₉×#125	—	2	1	no	—
94	C₂₉×#125	—	2	1	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	—	2	1	no	—
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×#125	D₄	1	1	yes	characteristic
102	C₂₉×#125	D₄	1	1	yes	characteristic
103	C₂₉×C₂²⋊Q₈	—	2	2	no	—
104	C₂₉×C₂²⋊Q₈	—	2	2	no	—
105	C₂₉×C₂²⋊Q₈	—	2	2	no	—
106	C₂₉×C₂²⋊Q₈	—	2	2	no	—
107	C₂₉×C₂²⋊Q₈	—	2	2	no	—
108	C₂₉×C₂²⋊Q₈	—	2	2	no	—
109	C₂₉×C₂²⋊Q₈	—	2	1	no	—
110	C₂₉×C₂²⋊Q₈	—	2	1	no	—
111	C₂₉×C₂²⋊Q₈	—	2	2	no	—
112	C₂₉×C₂²⋊Q₈	—	2	2	no	—
113	C₄×Q₈×C₂₉	—	2	2	no	—
114	C₄×Q₈×C₂₉	—	2	2	no	—
115	C₄×Q₈×C₂₉	—	2	1	no	—
116	C₄×Q₈×C₂₉	—	2	1	no	—
117	C₄×Q₈×C₂₉	—	2	1	no	—
118	C₄×Q₈×C₂₉	—	2	1	no	—
119	C₄×Q₈×C₂₉	—	2	1	no	—
120	C₄×Q₈×C₂₉	—	2	1	no	—
121	C₄×Q₈×C₂₉	—	2	1	no	—
122	C₄×Q₈×C₂₉	—	2	1	no	—
123	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
125	C₄×D₄×C₂₉	—	2	1	no	—
126	C₄×D₄×C₂₉	—	2	1	no	—
127	C₄×D₄×C₂₉	—	2	1	no	—
128	C₄×D₄×C₂₉	—	2	1	no	—
129	C₄×D₄×C₂₉	—	2	2	no	—
130	C₄×D₄×C₂₉	—	2	2	no	—
131	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
132	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
133	C₂₉×#117	—	2	1	no	—
134	C₂₉×#117	—	2	1	no	—
135	C₂₉×#117	—	2	1	no	—
136	C₂₉×#117	C₂³	1	1	yes	characteristic
137	C₂₉×#117	C₂³	1	1	yes	characteristic
138	C₂₉×#117	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
140	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
141	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
146	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₂₉	—	2	1	no	—
152	C₂×C₄²×C₂₉	—	2	1	no	—
153	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
156	C₂₉×#107	—	2	1	no	—
157	C₂₉×#107	—	2	1	no	—
158	C₂₉×#107	—	2	1	no	—
159	C₂₉×#106	—	2	1	no	—
160	C₂₉×#106	—	2	1	no	—
161	C₂₉×#106	—	2	1	no	—
162	C₂₉×C₄⋊C₈	—	2	1	no	—
163	C₂₉×C₄⋊C₈	—	2	1	no	—
164	C₂₉×#104	—	2	2	no	—
165	C₂₉×#104	—	2	2	no	—
166	C₂₉×#103	—	2	1	no	—
167	C₂₉×#103	—	2	1	no	—
168	C₂₉×#103	—	2	1	no	—
169	C₂₉×#103	—	2	1	no	—
170	C₂₉×#103	—	2	1	no	—
171	C₂₉×#103	—	2	1	no	—
172	C₂₉×#103	—	2	1	no	—
173	C₂₉×#102	—	2	1	no	—
174	C₂₉×#97	—	2	1	no	—
175	C₄×C₈×C₂₉	—	2	1	no	—
176	C₂₉×#95	—	2	1	no	—
177	C₂₉×#95	—	2	2	no	—
178	C₂₉×#95	—	2	2	no	—
179	C₂₉×#95	—	2	2	no	—
180	#41×C₂₉	—	2	1	no	—
181	#41×C₂₉	—	2	1	no	—
182	#41×C₂₉	C₂×Q₈	1	2	yes	—
183	#41×C₂₉	#41	1	2	yes	—
184	C₂×Q₈×C₂₉	—	2	2	no	—
185	C₂×Q₈×C₂₉	—	2	2	no	—
186	C₂×Q₈×C₂₉	—	2	1	no	—
187	C₂×Q₈×C₂₉	—	2	1	no	—
188	C₂×Q₈×C₂₉	—	2	1	no	—
189	C₂×Q₈×C₂₉	—	2	1	no	—
190	C₂×Q₈×C₂₉	—	2	1	no	—
191	C₂×Q₈×C₂₉	—	2	1	no	—
192	C₂×Q₈×C₂₉	—	2	1	no	—
193	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
194	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	—	2	1	no	—
198	C₂²×C₄×C₂₉	—	2	1	no	—
199	C₂²×C₄×C₂₉	—	2	1	no	—
200	C₂²×C₄×C₂₉	—	2	2	no	—
201	C₂²×C₄×C₂₉	—	2	2	no	—
202	C₂²×C₄×C₂₉	—	2	1	no	—
203	C₂²×C₄×C₂₉	—	2	1	no	—
204	C₂²×C₄×C₂₉	—	2	1	no	—
205	C₂²×C₄×C₂₉	—	2	1	no	—
206	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
211	Q₁₆×C₂₉	—	2	4	no	—
212	SD₁₆×C₂₉	—	2	4	no	—
213	M₁₆×C₂₉	—	2	1	no	—
214	M₁₆×C₂₉	—	2	1	no	—
215	M₁₆×C₂₉	—	2	1	no	—
216	M₁₆×C₂₉	—	2	1	no	—
217	M₁₆×C₂₉	—	2	1	no	—
218	M₁₆×C₂₉	—	2	1	no	—
219	M₁₆×C₂₉	—	2	1	no	—
220	M₁₆×C₂₉	C₂×Q₈	1	2	yes	—
221	C₂×C₈×C₂₉	—	2	1	no	—
222	C₂×C₈×C₂₉	—	2	1	no	—
223	C₂×C₈×C₂₉	—	2	1	no	—
224	C₂×C₈×C₂₉	—	2	1	no	—
225	C₄⋊C₄×C₂₉	—	2	2	no	—
226	C₄⋊C₄×C₂₉	—	2	2	no	—
227	C₄⋊C₄×C₂₉	—	2	2	no	—
228	C₄⋊C₄×C₂₉	—	2	2	no	—
229	C₄⋊C₄×C₂₉	—	2	2	no	—
230	C₄⋊C₄×C₂₉	—	2	2	no	—
231	C₄⋊C₄×C₂₉	—	2	2	no	—
232	C₄⋊C₄×C₂₉	—	2	2	no	—
233	C₄⋊C₄×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	2	1	no	—
235	C₄⋊C₄×C₂₉	—	2	2	no	—
236	C₄⋊C₄×C₂₉	—	2	2	no	—
237	C₄⋊C₄×C₂₉	—	2	2	no	—
238	C₄⋊C₄×C₂₉	—	2	2	no	—
239	C₄⋊C₄×C₂₉	—	2	1	no	—
240	C₄⋊C₄×C₂₉	—	2	1	no	—
241	C₄⋊C₄×C₂₉	—	2	1	no	—
242	C₄⋊C₄×C₂₉	—	2	1	no	—
243	C₄⋊C₄×C₂₉	—	2	1	no	—
244	C₄⋊C₄×C₂₉	—	2	1	no	—
245	C₄⋊C₄×C₂₉	—	2	1	no	—
246	C₄⋊C₄×C₂₉	—	2	1	no	—
247	C₄⋊C₄×C₂₉	—	2	1	no	—
248	C₄⋊C₄×C₂₉	—	2	1	no	—
249	C₄⋊C₄×C₂₉	—	2	1	no	—
250	C₄⋊C₄×C₂₉	—	2	1	no	—
251	C₄⋊C₄×C₂₉	—	4	2	no	—
252	C₄⋊C₄×C₂₉	—	4	4	no	—
253	C₄⋊C₄×C₂₉	—	4	1	no	—
254	C₄⋊C₄×C₂₉	—	4	1	no	—
255	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
260	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
261	C₂²⋊C₄×C₂₉	—	2	2	no	—
262	C₂²⋊C₄×C₂₉	—	2	2	no	—
263	C₂²⋊C₄×C₂₉	—	2	1	no	—
264	C₂²⋊C₄×C₂₉	—	2	1	no	—
265	C₂²⋊C₄×C₂₉	—	2	1	no	—
266	C₂²⋊C₄×C₂₉	—	2	1	no	—
267	C₂²⋊C₄×C₂₉	—	2	1	no	—
268	C₄²×C₂₉	—	2	2	no	—
269	C₄²×C₂₉	—	2	2	no	—
270	C₄²×C₂₉	—	2	1	no	—
271	C₄²×C₂₉	—	2	1	no	—
272	C₄²×C₂₉	—	2	1	no	—
273	C₄²×C₂₉	—	2	1	no	—
274	C₄²×C₂₉	—	2	1	no	—
275	C₄²×C₂₉	—	2	1	no	—
276	C₄²×C₂₉	—	2	1	no	—
277	C₄²×C₂₉	—	2	1	no	—
278	C₄²×C₂₉	—	2	1	no	—
279	C₄²×C₂₉	—	4	1	no	—
280	C₄²×C₂₉	—	4	1	no	—
281	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
285	#24325	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂³×C₂₉	—	2	1	no	—
287	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
288	Q₈×C₂₉	—	2	1	no	—
289	Q₈×C₂₉	—	2	2	no	—
290	Q₈×C₂₉	—	2	2	no	—
291	Q₈×C₂₉	—	4	1	no	—
292	Q₈×C₂₉	—	4	1	no	—
293	Q₈×C₂₉	—	8	1	no	—
294	Q₈×C₂₉	—	8	1	no	—
295	Q₈×C₂₉	—	8	2	no	—
296	Q₈×C₂₉	—	8	2	no	—
297	Q₈×C₂₉	C₂²⋊Q₈	1	2	yes	—
298	D₄×C₂₉	—	2	2	no	—
299	D₄×C₂₉	—	2	2	no	—
300	D₄×C₂₉	—	2	1	no	—
301	D₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
302	C₂×C₄×C₂₉	—	2	1	no	—
303	C₂×C₄×C₂₉	—	2	2	no	—
304	C₂×C₄×C₂₉	—	2	2	no	—
305	C₂×C₄×C₂₉	—	2	2	no	—
306	C₂×C₄×C₂₉	—	2	1	no	—
307	C₂×C₄×C₂₉	—	2	1	no	—
308	C₂×C₄×C₂₉	—	2	1	no	—
309	C₂×C₄×C₂₉	—	2	1	no	—
310	C₂×C₄×C₂₉	—	2	2	no	—
311	C₂×C₄×C₂₉	—	2	2	no	—
312	C₂×C₄×C₂₉	—	2	1	no	—
313	C₂×C₄×C₂₉	—	2	1	no	—
314	C₂×C₄×C₂₉	—	2	2	no	—
315	C₂×C₄×C₂₉	—	4	1	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	4	1	no	—
318	C₂×C₄×C₂₉	—	4	1	no	—
319	C₂×C₄×C₂₉	—	4	1	no	—
320	C₂×C₄×C₂₉	—	4	1	no	—
321	C₂×C₄×C₂₉	—	4	2	no	—
322	C₂×C₄×C₂₉	—	4	2	no	—
323	C₂×C₄×C₂₉	—	4	1	no	—
324	C₂×C₄×C₂₉	—	4	2	no	—
325	C₂×C₄×C₂₉	—	4	1	no	—
326	C₂×C₄×C₂₉	—	4	1	no	—
327	C₂×C₄×C₂₉	—	4	1	no	—
328	C₂×C₄×C₂₉	—	8	1	no	—
329	C₂×C₄×C₂₉	—	8	1	no	—
330	C₂×C₄×C₂₉	—	8	2	no	—
331	C₂×C₄×C₂₉	—	8	2	no	—
332	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
333	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
334	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
335	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
336	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
339	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
340	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
341	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
342	C₈×C₂₉	—	2	2	no	—
343	C₈×C₂₉	—	4	1	no	—
344	C₈×C₂₉	—	4	1	no	—
345	C₈×C₂₉	—	4	1	no	—
346	#3504	C₂×C₂₉	1	1	yes	characteristic
347	#3078	C₂×C₂₉	1	1	yes	characteristic, complemented
348	C₄×#137	C₂×C₂₉	1	1	yes	characteristic
349	#2565	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#2061	C₂×C₂₉	1	1	yes	characteristic, complemented
351	#2060	C₂×C₂₉	1	1	yes	characteristic, complemented
352	#2028	C₂×C₂₉	1	1	yes	characteristic, complemented
353	#2028	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#1998	C₂×C₂₉	1	1	yes	characteristic, complemented
355	#1986	C₂×C₂₉	1	1	yes	characteristic, complemented
356	#1882	C₂×C₂₉	1	1	yes	characteristic
357	#1882	C₂×C₂₉	1	1	yes	characteristic
358	#1860	C₂×C₂₉	1	1	yes	characteristic
359	#1859	C₂×C₂₉	1	1	yes	characteristic
360	#1806	C₂×C₂₉	1	1	yes	characteristic
361	C₂²×C₂₉	—	2	1	no	—
362	C₂²×C₂₉	—	2	1	no	—
363	C₂²×C₂₉	—	2	2	no	—
364	C₂²×C₂₉	—	4	1	no	—
365	C₂²×C₂₉	—	4	1	no	—
366	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
367	C₂²×C₂₉	#548	1	1	yes	characteristic
368	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
369	C₄×C₂₉	—	2	2	no	—
370	C₄×C₂₉	—	2	1	no	—
371	C₄×C₂₉	—	2	1	no	—
372	C₄×C₂₉	—	2	1	no	—
373	C₄×C₂₉	—	2	1	no	—
374	C₄×C₂₉	—	4	2	no	—
375	C₄×C₂₉	—	4	2	no	—
376	C₄×C₂₉	—	4	2	no	—
377	C₄×C₂₉	—	4	1	no	—
378	C₄×C₂₉	—	4	1	no	—
379	C₄×C₂₉	—	4	1	no	—
380	C₄×C₂₉	—	4	2	no	—
381	C₄×C₂₉	—	4	1	no	—
382	C₄×C₂₉	—	4	1	no	—
383	C₄×C₂₉	—	4	1	no	—
384	C₄×C₂₉	—	8	1	no	—
385	C₄×C₂₉	—	8	1	no	—
386	C₄×C₂₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
387	C₄×C₂₉	#536	1	1	yes	characteristic
388	C₄×C₂₉	#548	1	1	yes	characteristic
389	C₄×C₂₉	D₄×Q₈	1	1	yes	characteristic
390	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
391	#557	—	2	1	no	—
392	#557	—	2	1	no	—
393	#554	—	2	1	no	—
394	#554	—	2	1	no	—
395	#554	—	2	2	no	—
396	#554	—	2	2	no	—
397	#544	—	2	1	no	—
398	#544	—	2	1	no	—
399	#544	C₂²×C₂₉	1	1	yes	characteristic
400	#544	C₂²×C₂₉	1	1	yes	characteristic
401	#533	—	2	1	no	—
402	#533	C₂²×C₂₉	1	1	yes	characteristic
403	C₂×#125	—	2	1	no	—
404	C₂×#125	C₂²×C₂₉	1	1	yes	characteristic
405	#520	C₂²×C₂₉	1	1	yes	characteristic
406	#520	C₂²×C₂₉	1	1	yes	characteristic
407	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
408	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
409	#479	—	2	1	no	—
410	#479	—	2	1	no	—
411	#477	—	2	1	no	—
412	#475	—	2	1	no	—
413	#441	—	2	1	no	—
414	#440	—	2	1	no	—
415	C₄×Q₁₆	—	2	1	no	—
416	C₄×SD₁₆	—	2	1	no	—
417	#428	C₂²×C₂₉	1	1	yes	characteristic
418	#428	C₂²×C₂₉	1	1	yes	characteristic
419	#428	C₂²×C₂₉	1	1	yes	characteristic
420	#423	C₂²×C₂₉	1	1	yes	characteristic
421	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
422	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
423	#419	C₂²×C₂₉	1	1	yes	characteristic
424	#419	C₂²×C₂₉	1	1	yes	characteristic
425	#419	C₂²×C₂₉	1	1	yes	characteristic
426	#417	C₂²×C₂₉	1	1	yes	characteristic
427	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
428	#398	—	2	2	no	—
429	#391	C₂²×C₂₉	1	1	yes	characteristic
430	#391	C₂²×C₂₉	1	1	yes	characteristic
431	#387	—	2	2	no	—
432	#384	C₂²×C₂₉	1	1	yes	characteristic
433	#382	C₂²×C₂₉	1	1	yes	characteristic
434	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
435	#343	C₂²×C₂₉	1	1	yes	characteristic
436	#343	C₂²×C₂₉	1	1	yes	characteristic
437	#343	C₂²×C₂₉	1	1	yes	characteristic
438	#343	C₂²×C₂₉	1	1	yes	characteristic
439	#339	C₂²×C₂₉	1	1	yes	characteristic
440	#339	C₂²×C₂₉	1	1	yes	characteristic
441	#339	C₂²×C₂₉	1	1	yes	characteristic
442	#339	C₂²×C₂₉	1	1	yes	characteristic
443	#339	C₂²×C₂₉	1	1	yes	characteristic
444	#339	C₂²×C₂₉	1	1	yes	characteristic
445	C₂×C₂₉	—	2	1	no	—
446	C₂×C₂₉	—	2	1	no	—
447	C₂×C₂₉	—	4	2	no	—
448	C₂×C₂₉	#2409	1	1	yes	characteristic
449	C₂×C₂₉	#3018	1	1	yes	characteristic
450	C₂×C₂₉	#3022	1	1	yes	characteristic
451	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
452	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
453	#137	—	2	2	no	—
454	#137	Q₈×C₂₉	1	4	yes	complemented
455	C₂×Q₁₆	—	2	1	no	—
456	C₂×SD₁₆	—	2	1	no	—
457	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
458	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
459	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
460	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	—	2	1	no	—
464	C₄⋊Q₈	—	2	1	no	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
468	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
469	#125	—	2	2	no	—
470	#125	—	2	2	no	—
471	#125	—	2	2	no	—
472	#125	—	2	2	no	—
473	#125	—	2	1	no	—
474	#125	—	2	1	no	—
475	#125	—	2	1	no	—
476	#125	—	2	1	no	—
477	#125	—	2	1	no	—
478	#125	—	2	1	no	—
479	#125	—	2	1	no	—
480	#125	—	2	1	no	—
481	#125	D₄×C₂₉	1	1	yes	characteristic
482	#125	D₄×C₂₉	1	1	yes	characteristic
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	C₂²⋊Q₈	—	2	2	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	1	no	—
490	C₂²⋊Q₈	—	2	1	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×Q₈	—	2	1	no	—
496	C₄×Q₈	—	2	1	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	—	2	1	no	—
499	C₄×Q₈	—	2	1	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×Q₈	—	2	1	no	—
502	C₄×Q₈	—	2	1	no	—
503	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
504	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	1	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	—	2	1	no	—
509	C₄×D₄	—	2	2	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
512	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
513	#117	—	2	1	no	—
514	#117	—	2	1	no	—
515	#117	—	2	1	no	—
516	#117	C₂³×C₂₉	1	1	yes	characteristic
517	#117	C₂³×C₂₉	1	1	yes	characteristic
518	#117	C₂³×C₂₉	1	1	yes	characteristic
519	C₂×C₄⋊C₄	—	2	2	no	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	—	2	1	no	—
522	C₂×C₄⋊C₄	—	2	1	no	—
523	C₂×C₄⋊C₄	—	2	1	no	—
524	C₂×C₄⋊C₄	—	2	1	no	—
525	C₂×C₄⋊C₄	—	2	2	no	—
526	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
527	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
531	C₂×C₄²	—	2	1	no	—
532	C₂×C₄²	—	2	1	no	—
533	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
534	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
535	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
536	#107	—	2	1	no	—
537	#107	—	2	1	no	—
538	#107	—	2	1	no	—
539	#106	—	2	1	no	—
540	#106	—	2	1	no	—
541	#106	—	2	1	no	—
542	C₄⋊C₈	—	2	1	no	—
543	C₄⋊C₈	—	2	1	no	—
544	#104	—	2	2	no	—
545	#104	—	2	2	no	—
546	#103	—	2	1	no	—
547	#103	—	2	1	no	—
548	#103	—	2	1	no	—
549	#103	—	2	1	no	—
550	#103	—	2	1	no	—
551	#103	—	2	1	no	—
552	#103	—	2	1	no	—
553	#102	—	2	1	no	—
554	#97	—	2	1	no	—
555	C₄×C₈	—	2	1	no	—
556	#95	—	2	1	no	—
557	#95	—	2	2	no	—
558	#95	—	2	2	no	—
559	#95	—	2	2	no	—
560	C₂₉	#24325	1	1	yes	characteristic, direct product factor, Sylow
561	#41	—	2	1	no	—
562	#41	—	2	1	no	—
563	#41	C₂×Q₈×C₂₉	1	2	yes	—
564	#41	#41×C₂₉	1	2	yes	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	2	1	no	—
571	C₂×Q₈	—	2	1	no	—
572	C₂×Q₈	—	2	1	no	—
573	C₂×Q₈	—	2	1	no	—
574	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
575	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
588	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
589	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
592	Q₁₆	—	2	4	no	—
593	SD₁₆	—	2	4	no	—
594	M₁₆	—	2	1	no	—
595	M₁₆	—	2	1	no	—
596	M₁₆	—	2	1	no	—
597	M₁₆	—	2	1	no	—
598	M₁₆	—	2	1	no	—
599	M₁₆	—	2	1	no	—
600	M₁₆	—	2	1	no	—
601	M₁₆	C₂×Q₈×C₂₉	1	2	yes	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	1	no	—
622	C₄⋊C₄	—	2	1	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	4	no	—
634	C₄⋊C₄	—	4	1	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
641	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	4	1	no	—
661	C₄²	—	4	1	no	—
662	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
664	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
665	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
666	C₂³	—	2	1	no	—
667	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
668	Q₈	—	2	1	no	—
669	Q₈	—	2	2	no	—
670	Q₈	—	2	2	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	—	8	1	no	—
674	Q₈	—	8	1	no	—
675	Q₈	—	8	2	no	—
676	Q₈	—	8	2	no	—
677	Q₈	C₂₉×C₂²⋊Q₈	1	2	yes	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	1	no	—
681	D₄	C₂₉×C₂²⋊Q₈	1	2	yes	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	8	1	no	—
709	C₂×C₄	—	8	1	no	—
710	C₂×C₄	—	8	2	no	—
711	C₂×C₄	—	8	2	no	—
712	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
713	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
714	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
715	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
718	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
719	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
720	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
721	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
722	C₈	—	2	2	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
732	C₂²	C₂₉×#548	1	1	yes	characteristic
733	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	2	no	—
749	C₄	—	8	1	no	—
750	C₄	—	8	1	no	—
751	C₄	C₂×C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
752	C₄	C₂₉×#536	1	1	yes	characteristic
753	C₄	C₂₉×#548	1	1	yes	characteristic
754	C₄	D₄×Q₈×C₂₉	1	1	yes	characteristic
755	C₂	—	2	1	no	—
756	C₂	—	2	1	no	—
757	C₂	—	4	2	no	—
758	C₂	C₂₉×#2409	1	1	yes	characteristic
759	C₂	C₂₉×#3018	1	1	yes	characteristic
760	C₂	C₂₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	C₂³
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
2. C₂₉×#3078	C₂	semidirect
4. C₂₉×#2565	C₂	semidirect
5. C₂₉×#2061	C₂	semidirect
6. C₂₉×#2060	C₂	semidirect
7. C₂₉×#2028	C₂	semidirect
8. C₂₉×#2028	C₂	semidirect
9. C₂₉×#1998	C₂	semidirect
10. C₂₉×#1986	C₂	semidirect
74. C₂₉×#137	Q₈	semidirect
285. #24325	C₂₉	direct (N × H)
347. #3078	C₂×C₂₉	semidirect
349. #2565	C₂×C₂₉	semidirect
350. #2061	C₂×C₂₉	semidirect
351. #2060	C₂×C₂₉	semidirect
352. #2028	C₂×C₂₉	semidirect
353. #2028	C₂×C₂₉	semidirect
354. #1998	C₂×C₂₉	semidirect
355. #1986	C₂×C₂₉	semidirect
454. #137	Q₈×C₂₉	semidirect
560. C₂₉	#24325	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×#3504	2
C₂₉×#3078	2
C₄×C₂₉×#137	2
C₂₉×#2565	2
C₂₉×#2061	2
C₂₉×#2060	2
C₂₉×#2028	2
C₂₉×#1998	2
C₂₉×#1986	2
C₂₉×#1882	2
C₂₉×#1860	2
C₂₉×#1859	2
C₂₉×#1806	2
#24325	29

Subgroups — C29×#24325 #20319225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24325 #20319225