Subgroups — C₂₉×#9235 #20304135

Order 7424.

550 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3101	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2293	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1486	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1276	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#533	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₂₉×#117	—	2	1	no	—
11	C₂₉×#483	—	2	1	no	—
12	C₂₉×#476	C₄	1	2	yes	complemented
13	C₂₉×#461	C₄	1	2	yes	complemented
14	C₂₉×#450	—	2	1	no	—
15	C₄×SD₁₆×C₂₉	—	2	2	no	—
16	C₂₉×#431	C₂²	1	1	yes	characteristic
17	C₂₉×#431	C₂²	1	1	yes	characteristic
18	C₂₉×#423	C₂²	1	1	yes	characteristic
19	C₂₉×#390	—	2	1	no	—
20	C₂₉×#389	—	2	1	no	—
21	C₂₉×#388	—	2	2	no	—
22	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊C₄×C₂₉	—	2	1	no	—
24	C₄³×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#339	—	2	1	no	—
26	C₂₉×#339	—	2	1	no	—
27	C₂₉×#328	—	2	2	no	—
28	C₂₉×D₄⋊C₈	—	2	2	no	—
29	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₂₉	—	2	1	no	—
31	C₂×SD₁₆×C₂₉	—	2	2	no	—
32	C₂×M₁₆×C₂₉	—	2	1	no	—
33	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
34	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
35	C₂₉×#125	—	2	1	no	—
36	C₂₉×C₂²⋊Q₈	—	2	1	no	—
37	C₂₉×C₂²⋊Q₈	—	2	1	no	—
38	C₄×Q₈×C₂₉	—	2	1	no	—
39	C₄×Q₈×C₂₉	—	2	1	no	—
40	C₄×D₄×C₂₉	—	2	1	no	—
41	C₄×D₄×C₂₉	—	2	1	no	—
42	C₄×D₄×C₂₉	C₂×C₄	1	2	yes	—
43	C₄×D₄×C₂₉	D₄	1	2	yes	—
44	C₂₉×#117	—	2	1	no	—
45	C₂₉×#117	—	4	2	no	—
46	C₂₉×#117	—	4	2	no	—
47	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
53	C₂×C₄²×C₂₉	—	2	1	no	—
54	C₂×C₄²×C₂₉	—	2	1	no	—
55	C₂×C₄²×C₂₉	—	2	1	no	—
56	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₂₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
59	C₂₉×#106	—	2	2	no	—
60	C₂₉×C₄⋊C₈	—	2	1	no	—
61	C₂₉×C₄⋊C₈	—	2	1	no	—
62	C₂₉×C₄⋊C₈	—	2	1	no	—
63	C₂₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	C₂₉×#103	—	2	2	no	—
65	C₂₉×#102	—	2	2	no	—
66	C₂₉×C₂²⋊C₈	—	2	1	no	—
67	C₂₉×C₂²⋊C₈	—	2	1	no	—
68	C₄×C₈×C₂₉	—	2	1	no	—
69	C₄×C₈×C₂₉	—	2	1	no	—
70	C₂₉×#95	—	2	2	no	—
71	C₂₉×#95	D₄	1	2	yes	—
72	C₂⁴×C₂₉	—	2	1	no	—
73	C₂×Q₈×C₂₉	—	2	1	no	—
74	C₂×Q₈×C₂₉	—	2	1	no	—
75	C₂×D₄×C₂₉	—	2	1	no	—
76	C₂×D₄×C₂₉	—	4	2	no	—
77	C₂×D₄×C₂₉	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₂₉	—	2	1	no	—
79	C₂²×C₄×C₂₉	—	2	1	no	—
80	C₂²×C₄×C₂₉	—	2	1	no	—
81	C₂²×C₄×C₂₉	—	2	2	no	—
82	C₂²×C₄×C₂₉	—	2	2	no	—
83	C₂²×C₄×C₂₉	—	2	2	no	—
84	C₂²×C₄×C₂₉	—	4	1	no	—
85	C₂²×C₄×C₂₉	—	4	1	no	—
86	C₂²×C₄×C₂₉	—	4	1	no	—
87	C₂²×C₄×C₂₉	—	4	1	no	—
88	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
91	SD₁₆×C₂₉	—	4	4	no	—
92	M₁₆×C₂₉	—	4	1	no	—
93	M₁₆×C₂₉	—	4	1	no	—
94	C₂×C₈×C₂₉	—	2	2	no	—
95	C₂×C₈×C₂₉	—	4	1	no	—
96	C₂×C₈×C₂₉	—	4	1	no	—
97	C₄⋊C₄×C₂₉	—	2	1	no	—
98	C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₄⋊C₄×C₂₉	—	2	1	no	—
101	C₄⋊C₄×C₂₉	—	2	1	no	—
102	C₄⋊C₄×C₂₉	—	4	2	no	—
103	C₄⋊C₄×C₂₉	—	4	4	no	—
104	C₄⋊C₄×C₂₉	—	4	1	no	—
105	C₄⋊C₄×C₂₉	—	4	1	no	—
106	C₄⋊C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
107	C₂²⋊C₄×C₂₉	—	2	2	no	—
108	C₂²⋊C₄×C₂₉	—	2	2	no	—
109	C₂²⋊C₄×C₂₉	—	4	4	no	—
110	C₂²⋊C₄×C₂₉	—	4	4	no	—
111	C₂²⋊C₄×C₂₉	—	4	1	no	—
112	C₄²×C₂₉	—	2	1	no	—
113	C₄²×C₂₉	—	2	1	no	—
114	C₄²×C₂₉	—	2	1	no	—
115	C₄²×C₂₉	—	4	2	no	—
116	C₄²×C₂₉	—	4	2	no	—
117	C₄²×C₂₉	—	4	1	no	—
118	C₄²×C₂₉	—	4	1	no	—
119	C₄²×C₂₉	—	4	1	no	—
120	C₄²×C₂₉	SD₁₆	1	2	yes	complemented
121	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₂₉	#41	1	1	yes	characteristic
124	C₄²×C₂₉	#41	1	1	yes	characteristic
125	#9235	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂³×C₂₉	—	2	2	no	—
127	C₂³×C₂₉	—	4	2	no	—
128	C₂³×C₂₉	—	4	2	no	—
129	C₂³×C₂₉	—	4	1	no	—
130	C₂³×C₂₉	—	4	1	no	—
131	C₂³×C₂₉	#120	1	1	yes	characteristic
132	Q₈×C₂₉	—	4	2	no	—
133	Q₈×C₂₉	—	8	1	no	—
134	D₄×C₂₉	—	2	2	no	—
135	D₄×C₂₉	—	2	2	no	—
136	D₄×C₂₉	—	4	2	no	—
137	C₂×C₄×C₂₉	—	2	2	no	—
138	C₂×C₄×C₂₉	—	2	2	no	—
139	C₂×C₄×C₂₉	—	2	2	no	—
140	C₂×C₄×C₂₉	—	2	2	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	—	4	1	no	—
148	C₂×C₄×C₂₉	—	4	2	no	—
149	C₂×C₄×C₂₉	—	4	2	no	—
150	C₂×C₄×C₂₉	—	4	2	no	—
151	C₂×C₄×C₂₉	—	4	2	no	—
152	C₂×C₄×C₂₉	—	4	2	no	—
153	C₂×C₄×C₂₉	—	4	2	no	—
154	C₂×C₄×C₂₉	—	4	1	no	—
155	C₂×C₄×C₂₉	—	4	1	no	—
156	C₂×C₄×C₂₉	—	4	2	no	—
157	C₂×C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₂₉	#123	1	1	yes	characteristic
163	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₂₉	#135	1	1	yes	characteristic
165	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₂₉	#137	1	1	yes	characteristic
167	C₈×C₂₉	—	4	2	no	—
168	C₈×C₂₉	—	8	1	no	—
169	C₈×C₂₉	—	8	1	no	—
170	#3101	C₂×C₂₉	1	1	yes	characteristic
171	#2293	C₂×C₂₉	1	1	yes	characteristic
172	#1994	C₂×C₂₉	1	1	yes	characteristic, complemented
173	#1503	C₂×C₂₉	1	1	yes	characteristic, complemented
174	#1486	C₂×C₂₉	1	1	yes	characteristic
175	#1303	C₂×C₂₉	1	1	yes	characteristic, complemented
176	#1276	C₂×C₂₉	1	1	yes	characteristic, complemented
177	C₂²×C₂₉	—	2	1	no	—
178	C₂²×C₂₉	—	2	1	no	—
179	C₂²×C₂₉	—	4	2	no	—
180	C₂²×C₂₉	—	4	2	no	—
181	C₂²×C₂₉	—	4	2	no	—
182	C₂²×C₂₉	—	8	2	no	—
183	C₂²×C₂₉	—	8	2	no	—
184	C₂²×C₂₉	#386	1	1	yes	characteristic
185	C₂²×C₂₉	#450	1	1	yes	characteristic
186	C₂²×C₂₉	#452	1	1	yes	characteristic
187	C₄×C₂₉	—	2	1	no	—
188	C₄×C₂₉	—	2	1	no	—
189	C₄×C₂₉	—	2	1	no	—
190	C₄×C₂₉	—	4	2	no	—
191	C₄×C₂₉	—	4	2	no	—
192	C₄×C₂₉	—	4	2	no	—
193	C₄×C₂₉	—	8	2	no	—
194	C₄×C₂₉	—	8	1	no	—
195	C₄×C₂₉	—	8	1	no	—
196	C₄×C₂₉	#421	1	2	yes	—
197	C₄×C₂₉	C₄×SD₁₆	1	1	yes	characteristic
198	C₄×C₂₉	#440	1	1	yes	characteristic
199	C₄×C₂₉	#461	1	1	yes	characteristic
200	C₄×C₂₉	#463	1	1	yes	characteristic
201	#533	C₂²×C₂₉	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
203	C₂×#117	—	2	1	no	—
204	#483	—	2	1	no	—
205	#476	C₄×C₂₉	1	2	yes	complemented
206	#461	C₄×C₂₉	1	2	yes	complemented
207	#450	—	2	1	no	—
208	C₄×SD₁₆	—	2	2	no	—
209	#431	C₂²×C₂₉	1	1	yes	characteristic
210	#431	C₂²×C₂₉	1	1	yes	characteristic
211	#423	C₂²×C₂₉	1	1	yes	characteristic
212	#390	—	2	1	no	—
213	#389	—	2	1	no	—
214	#388	—	2	2	no	—
215	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
216	C₄×C₂²⋊C₄	—	2	1	no	—
217	C₄³	C₂²×C₂₉	1	1	yes	characteristic
218	#339	—	2	1	no	—
219	#339	—	2	1	no	—
220	#328	—	2	2	no	—
221	D₄⋊C₈	—	2	2	no	—
222	C₂×C₂₉	—	2	1	no	—
223	C₂×C₂₉	—	2	1	no	—
224	C₂×C₂₉	—	8	2	no	—
225	C₂×C₂₉	#1877	1	1	yes	characteristic
226	C₂×C₂₉	#1897	1	1	yes	characteristic
227	C₂×C₂₉	#1906	1	1	yes	characteristic
228	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
229	C₂³×C₄	—	2	1	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
233	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
234	#125	—	2	1	no	—
235	C₂²⋊Q₈	—	2	1	no	—
236	C₂²⋊Q₈	—	2	1	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂×C₄×C₂₉	1	2	yes	—
242	C₄×D₄	D₄×C₂₉	1	2	yes	—
243	#117	—	2	1	no	—
244	#117	—	4	2	no	—
245	#117	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
256	C₂×C₄²	D₄×C₂₉	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
258	#106	—	2	2	no	—
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
263	#103	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂²⋊C₈	—	2	1	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	—	2	1	no	—
269	#95	—	2	2	no	—
270	#95	D₄×C₂₉	1	2	yes	—
271	C₂₉	#9235	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁴	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	C₂²⋊C₄×C₂₉	1	2	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
291	SD₁₆	—	4	4	no	—
292	M₁₆	—	4	1	no	—
293	M₁₆	—	4	1	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	2	no	—
309	C₂²⋊C₄	—	4	4	no	—
310	C₂²⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	4	2	no	—
316	C₄²	—	4	2	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	SD₁₆×C₂₉	1	2	yes	complemented
321	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
322	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
323	C₄²	#41×C₂₉	1	1	yes	characteristic
324	C₄²	#41×C₂₉	1	1	yes	characteristic
325	C₂³	—	2	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₂₉×#120	1	1	yes	characteristic
331	Q₈	—	4	2	no	—
332	Q₈	—	8	1	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
358	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
359	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
360	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
361	C₂×C₄	C₂₉×#123	1	1	yes	characteristic
362	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
363	C₂×C₄	C₂₉×#135	1	1	yes	characteristic
364	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
365	C₂×C₄	C₂₉×#137	1	1	yes	characteristic
366	C₈	—	4	2	no	—
367	C₈	—	8	1	no	—
368	C₈	—	8	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	C₂₉×#386	1	1	yes	characteristic
377	C₂²	C₂₉×#450	1	1	yes	characteristic
378	C₂²	C₂₉×#452	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₂₉×#421	1	2	yes	—
389	C₄	C₄×SD₁₆×C₂₉	1	1	yes	characteristic
390	C₄	C₂₉×#440	1	1	yes	characteristic
391	C₄	C₂₉×#461	1	1	yes	characteristic
392	C₄	C₂₉×#463	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	8	2	no	—
396	C₂	C₂₉×#1877	1	1	yes	characteristic
397	C₂	C₂₉×#1897	1	1	yes	characteristic
398	C₂	C₂₉×#1906	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#121
commutator	C₄²	C₂²×C₄×C₂₉
Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
socle	C₂²×C₂₉	#386
prime radical	C₂²×D₄×C₂₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#1994	C₂	semidirect
4. C₂₉×#1503	C₂	semidirect
6. C₂₉×#1303	C₂	semidirect
7. C₂₉×#1276	C₂	semidirect
12. C₂₉×#476	C₄	semidirect
13. C₂₉×#461	C₄	semidirect
120. C₄²×C₂₉	SD₁₆	semidirect
125. #9235	C₂₉	direct (N × H)
172. #1994	C₂×C₂₉	semidirect
173. #1503	C₂×C₂₉	semidirect
175. #1303	C₂×C₂₉	semidirect
176. #1276	C₂×C₂₉	semidirect
205. #476	C₄×C₂₉	semidirect
206. #461	C₄×C₂₉	semidirect
271. C₂₉	#9235	direct (N × H)
320. C₄²	SD₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3101	2
C₂₉×#2293	2
C₂₉×#1994	2
C₂₉×#1503	2
C₂₉×#1486	2
C₂₉×#1303	2
C₂₉×#1276	2
#9235	29

Subgroups — C29×#9235 #20304135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#9235 #20304135