Subgroups — C₂₉×#8581 #20303481

Order 7424.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂₉×#124	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#329	C₂	1	2	yes	maximal
5	C₂₉×#1295	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄×C₂₉	C₄	1	1	yes	characteristic
9	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
10	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
11	C₂×C₂₉×#97	C₂²	1	2	yes	—
12	C₂×C₂₉×#97	C₂²	1	2	yes	—
13	C₂₉×#391	C₄	1	1	yes	characteristic
14	C₂₉×#390	C₄	1	1	yes	characteristic
15	C₂₉×#388	—	2	1	no	—
16	C₂₉×#388	—	2	1	no	—
17	C₂₉×#382	C₂²	1	1	yes	characteristic
18	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
19	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
20	C₄³×C₂₉	C₂²	1	1	yes	characteristic
21	C₂₉×#336	—	2	1	no	—
22	C₂₉×#336	—	2	1	no	—
23	C₂₉×#329	—	2	4	no	—
24	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₂₉	—	2	1	no	—
27	C₂²×C₈×C₂₉	—	2	2	no	—
28	C₂²×C₈×C₂₉	—	2	2	no	—
29	C₂₉×#124	—	2	1	no	—
30	C₂₉×#124	—	2	1	no	—
31	C₂₉×#124	D₄	1	2	yes	—
32	C₂₉×#124	Q₈	1	2	yes	—
33	C₄×Q₈×C₂₉	—	4	2	no	—
34	C₄×D₄×C₂₉	—	4	2	no	—
35	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
39	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
40	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
41	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
42	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
43	C₂×C₄²×C₂₉	—	2	1	no	—
44	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
51	C₂₉×C₄⋊C₈	—	2	4	no	—
52	C₂₉×C₄⋊C₈	—	2	4	no	—
53	C₂₉×#97	—	2	2	no	—
54	C₂₉×#97	—	2	2	no	—
55	C₂₉×#97	—	2	2	no	—
56	C₂₉×#97	—	2	2	no	—
57	C₂₉×#95	—	2	1	no	—
58	C₂₉×#95	—	2	1	no	—
59	C₂₉×#95	—	2	1	no	—
60	C₂₉×#95	—	2	1	no	—
61	C₂⁴×C₂₉	—	2	1	no	—
62	C₂×Q₈×C₂₉	—	2	1	no	—
63	C₂×Q₈×C₂₉	—	4	1	no	—
64	C₂×Q₈×C₂₉	—	4	1	no	—
65	C₂×Q₈×C₂₉	C₄⋊C₄	1	2	yes	—
66	C₂×D₄×C₂₉	—	2	1	no	—
67	C₂×D₄×C₂₉	—	4	1	no	—
68	C₂×D₄×C₂₉	—	4	1	no	—
69	C₂×D₄×C₂₉	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₂₉	—	2	1	no	—
71	C₂²×C₄×C₂₉	—	2	1	no	—
72	C₂²×C₄×C₂₉	—	2	1	no	—
73	C₂²×C₄×C₂₉	—	4	2	no	—
74	C₂²×C₄×C₂₉	—	4	2	no	—
75	C₂²×C₄×C₂₉	—	4	2	no	—
76	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
83	C₂×C₈×C₂₉	—	2	4	no	—
84	C₂×C₈×C₂₉	—	2	4	no	—
85	C₂×C₈×C₂₉	—	4	2	no	—
86	C₂×C₈×C₂₉	—	4	2	no	—
87	C₂×C₈×C₂₉	—	4	2	no	—
88	C₂×C₈×C₂₉	—	4	2	no	—
89	C₄⋊C₄×C₂₉	—	4	1	no	—
90	C₄⋊C₄×C₂₉	—	4	1	no	—
91	C₄⋊C₄×C₂₉	—	4	2	no	—
92	C₂²⋊C₄×C₂₉	—	2	2	no	—
93	C₂²⋊C₄×C₂₉	—	2	2	no	—
94	C₂²⋊C₄×C₂₉	—	2	2	no	—
95	C₂²⋊C₄×C₂₉	—	2	2	no	—
96	C₂²⋊C₄×C₂₉	—	4	2	no	—
97	C₂²⋊C₄×C₂₉	—	4	2	no	—
98	C₂²⋊C₄×C₂₉	—	4	2	no	—
99	C₄²×C₂₉	—	2	2	no	—
100	C₄²×C₂₉	—	2	2	no	—
101	C₄²×C₂₉	—	2	2	no	—
102	C₄²×C₂₉	—	4	1	no	—
103	C₄²×C₂₉	—	4	1	no	—
104	C₄²×C₂₉	—	4	1	no	—
105	C₄²×C₂₉	—	4	2	no	—
106	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₂₉	C₂×Q₈	1	1	yes	characteristic
108	C₄²×C₂₉	#41	1	1	yes	characteristic
109	C₄²×C₂₉	#41	1	1	yes	characteristic
110	#8581	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₂₉	—	2	2	no	—
112	C₂³×C₂₉	—	4	1	no	—
113	C₂³×C₂₉	—	4	1	no	—
114	C₂³×C₂₉	—	4	1	no	—
115	C₂³×C₂₉	—	4	1	no	—
116	C₂³×C₂₉	—	4	1	no	—
117	C₂³×C₂₉	—	4	1	no	—
118	C₂³×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	Q₈×C₂₉	—	4	2	no	—
120	Q₈×C₂₉	—	4	2	no	—
121	D₄×C₂₉	—	4	2	no	—
122	D₄×C₂₉	—	4	2	no	—
123	C₂×C₄×C₂₉	—	2	1	no	—
124	C₂×C₄×C₂₉	—	2	1	no	—
125	C₂×C₄×C₂₉	—	2	1	no	—
126	C₂×C₄×C₂₉	—	2	1	no	—
127	C₂×C₄×C₂₉	—	2	1	no	—
128	C₂×C₄×C₂₉	—	2	1	no	—
129	C₂×C₄×C₂₉	—	2	1	no	—
130	C₂×C₄×C₂₉	—	2	1	no	—
131	C₂×C₄×C₂₉	—	2	1	no	—
132	C₂×C₄×C₂₉	—	2	1	no	—
133	C₂×C₄×C₂₉	—	2	1	no	—
134	C₂×C₄×C₂₉	—	2	1	no	—
135	C₂×C₄×C₂₉	—	2	2	no	—
136	C₂×C₄×C₂₉	—	2	1	no	—
137	C₂×C₄×C₂₉	—	2	1	no	—
138	C₂×C₄×C₂₉	—	2	1	no	—
139	C₂×C₄×C₂₉	—	4	1	no	—
140	C₂×C₄×C₂₉	—	4	1	no	—
141	C₂×C₄×C₂₉	—	4	1	no	—
142	C₂×C₄×C₂₉	—	4	1	no	—
143	C₂×C₄×C₂₉	—	4	1	no	—
144	C₂×C₄×C₂₉	—	4	1	no	—
145	C₂×C₄×C₂₉	—	4	1	no	—
146	C₂×C₄×C₂₉	—	4	1	no	—
147	C₂×C₄×C₂₉	—	8	4	no	—
148	C₂×C₄×C₂₉	#100	1	2	yes	—
149	C₂×C₄×C₂₉	#104	1	2	yes	—
150	C₂×C₄×C₂₉	#104	1	2	yes	—
151	C₂×C₄×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₂₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₂₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₈×C₂₉	—	4	4	no	—
158	C₈×C₂₉	—	4	4	no	—
159	C₄×#124	C₂×C₂₉	1	1	yes	characteristic
160	#1767	C₂×C₂₉	1	1	yes	characteristic, complemented
161	#1767	C₂×C₂₉	1	1	yes	characteristic, complemented
162	C₂×#329	C₂×C₂₉	1	2	yes	—
163	#1295	C₂×C₂₉	1	2	yes	complemented
164	C₂²×C₂₉	—	4	2	no	—
165	C₂²×C₂₉	—	4	2	no	—
166	C₂²×C₂₉	—	4	2	no	—
167	C₂²×C₂₉	—	8	1	no	—
168	C₂²×C₂₉	—	8	1	no	—
169	C₂²×C₂₉	—	8	1	no	—
170	C₂²×C₂₉	—	8	1	no	—
171	C₂²×C₂₉	#380	1	1	yes	characteristic
172	C₂²×C₂₉	C₂×#100	1	1	yes	characteristic
173	C₂²×C₂₉	#413	1	1	yes	characteristic
174	C₂²×C₂₉	C₂×#104	1	1	yes	characteristic
175	C₂²×C₂₉	C₂×#104	1	1	yes	characteristic
176	C₂²×C₂₉	#421	1	1	yes	characteristic
177	C₂²×C₂₉	#421	1	1	yes	characteristic
178	C₄×C₂₉	—	2	1	no	—
179	C₄×C₂₉	—	2	1	no	—
180	C₄×C₂₉	—	2	1	no	—
181	C₄×C₂₉	—	2	1	no	—
182	C₄×C₂₉	—	2	1	no	—
183	C₄×C₂₉	—	2	1	no	—
184	C₄×C₂₉	—	2	2	no	—
185	C₄×C₂₉	—	2	2	no	—
186	C₄×C₂₉	—	2	2	no	—
187	C₄×C₂₉	—	4	2	no	—
188	C₄×C₂₉	—	4	1	no	—
189	C₄×C₂₉	—	8	1	no	—
190	C₄×C₂₉	—	8	1	no	—
191	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
192	C₂×C₄×Q₈	C₄×C₂₉	1	1	yes	characteristic
193	C₂×C₄×D₄	C₄×C₂₉	1	1	yes	characteristic
194	C₂×C₄⋊C₈	—	2	1	no	—
195	C₂×C₄⋊C₈	—	2	1	no	—
196	C₂×#97	C₂²×C₂₉	1	2	yes	—
197	C₂×#97	C₂²×C₂₉	1	2	yes	—
198	#391	C₄×C₂₉	1	1	yes	characteristic
199	#390	C₄×C₂₉	1	1	yes	characteristic
200	#388	—	2	1	no	—
201	#388	—	2	1	no	—
202	#382	C₂²×C₂₉	1	1	yes	characteristic
203	C₄×C₂²⋊C₄	—	2	1	no	—
204	C₄×C₂²⋊C₄	—	2	1	no	—
205	C₄³	C₂²×C₂₉	1	1	yes	characteristic
206	#336	—	2	1	no	—
207	#336	—	2	1	no	—
208	#329	—	2	4	no	—
209	C₂×C₂₉	—	8	2	no	—
210	C₂×C₂₉	#1524	1	1	yes	characteristic
211	C₂×C₂₉	#1527	1	1	yes	characteristic
212	C₂×C₂₉	#1530	1	1	yes	characteristic
213	C₂×C₂₉	#1535	1	1	yes	characteristic
214	C₂×C₂₉	#1800	1	1	yes	characteristic
215	C₂×C₂₉	#1806	1	1	yes	characteristic
216	C₂×C₂₉	#1806	1	1	yes	characteristic
217	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
218	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
219	C₂³×C₄	—	2	1	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	#124	—	2	1	no	—
223	#124	—	2	1	no	—
224	#124	D₄×C₂₉	1	2	yes	—
225	#124	Q₈×C₂₉	1	2	yes	—
226	C₄×Q₈	—	4	2	no	—
227	C₄×D₄	—	4	2	no	—
228	C₂×C₄⋊C₄	—	2	1	no	—
229	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₂₉	1	1	yes	characteristic
239	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
244	C₄⋊C₈	—	2	4	no	—
245	C₄⋊C₈	—	2	4	no	—
246	#97	—	2	2	no	—
247	#97	—	2	2	no	—
248	#97	—	2	2	no	—
249	#97	—	2	2	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	C₂₉	#8581	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁴	—	2	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	4	1	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	C₄⋊C₄×C₂₉	1	2	yes	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	4	1	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	C₄⋊C₄×C₂₉	1	2	yes	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	4	2	no	—
280	C₂×C₈	—	4	2	no	—
281	C₂×C₈	—	4	2	no	—
282	C₂×C₈	—	4	2	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	4	2	no	—
291	C₂²⋊C₄	—	4	2	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	4	1	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	2	no	—
300	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
301	C₄²	C₂×Q₈×C₂₉	1	1	yes	characteristic
302	C₄²	#41×C₂₉	1	1	yes	characteristic
303	C₄²	#41×C₂₉	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	C₂₉×#100	1	2	yes	—
342	C₂×C₄	C₂₉×#104	1	2	yes	—
343	C₂×C₄	C₂₉×#104	1	2	yes	—
344	C₂×C₄	C₂×C₄⋊C₄×C₂₉	1	1	yes	characteristic
345	C₂×C₄	C₂₉×#117	1	1	yes	characteristic
346	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
347	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
348	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
349	C₂×C₄	C₂₉×C₂²⋊Q₈	1	1	yes	characteristic
350	C₈	—	4	4	no	—
351	C₈	—	4	4	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	C₂₉×#380	1	1	yes	characteristic
360	C₂²	C₂×C₂₉×#100	1	1	yes	characteristic
361	C₂²	C₂₉×#413	1	1	yes	characteristic
362	C₂²	C₂×C₂₉×#104	1	1	yes	characteristic
363	C₂²	C₂×C₂₉×#104	1	1	yes	characteristic
364	C₂²	C₂₉×#421	1	1	yes	characteristic
365	C₂²	C₂₉×#421	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₂	—	8	2	no	—
380	C₂	C₂₉×#1524	1	1	yes	characteristic
381	C₂	C₂₉×#1527	1	1	yes	characteristic
382	C₂	C₂₉×#1530	1	1	yes	characteristic
383	C₂	C₂₉×#1535	1	1	yes	characteristic
384	C₂	C₂₉×#1800	1	1	yes	characteristic
385	C₂	C₂₉×#1806	1	1	yes	characteristic
386	C₂	C₂₉×#1806	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄³×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#1767	C₂	semidirect
3. C₂₉×#1767	C₂	semidirect
5. C₂₉×#1295	C₂	semidirect
110. #8581	C₂₉	direct (N × H)
160. #1767	C₂×C₂₉	semidirect
161. #1767	C₂×C₂₉	semidirect
163. #1295	C₂×C₂₉	semidirect
254. C₂₉	#8581	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₂₉×#124	2
C₂₉×#1767	2
C₂×C₂₉×#329	2
C₂₉×#1295	2
#8581	29

Subgroups — C29×#8581 #20303481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#8581 #20303481