Subgroups — D₂₉×#465 #16829048

Order 3712.

564 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#121×D₂₉	C₂	1	1	yes	maximal, characteristic
5	#14271395	C₂	1	1	yes	maximal, characteristic, complemented
6	#14271394	C₂	1	1	yes	maximal, characteristic, complemented
7	#14271393	C₂	1	1	yes	maximal, characteristic, complemented
8	#14271392	C₂	1	1	yes	maximal, characteristic, complemented
9	#14271391	C₂	1	1	yes	maximal, characteristic, complemented
10	#14271390	C₂	1	1	yes	maximal, characteristic, complemented
11	#14271389	C₂	1	1	yes	maximal, characteristic, complemented
12	#106×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#103×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₂₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₂₉	—	2	1	no	—
18	C₂×D₄×D₂₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
22	C₂₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂₉×#121	C₂²	1	1	yes	characteristic
24	#11745308	C₂²	1	1	yes	characteristic, complemented
25	C₂×#90784	C₂²	1	1	yes	characteristic, complemented
26	#11745301	—	2	1	no	—
27	#11745300	C₂²	1	1	yes	characteristic
28	C₂×#90783	C₂²	1	1	yes	characteristic, complemented
29	#11745292	C₂²	1	1	yes	characteristic
30	#11745286	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#6597	C₂²	1	1	yes	characteristic, complemented
32	SD₁₆×D₂₉	—	2	4	no	—
33	C₂×#90773	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₈×D₂₉	—	2	4	no	—
35	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₈×D₂₉	C₂²	1	1	yes	characteristic, complemented
39	#11745259	C₂²	1	1	yes	characteristic, complemented
40	#11745258	—	2	1	no	—
41	#11745257	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₂₉	—	2	1	no	—
43	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
44	C₄⋊C₄×D₂₉	C₂²	1	1	yes	characteristic
45	#11745246	—	2	1	no	—
46	C₂²⋊C₄×D₂₉	—	2	1	no	—
47	C₂²⋊C₄×D₂₉	—	2	1	no	—
48	#11745240	—	2	1	no	—
49	C₂₉×#106	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#103	C₂²	1	1	yes	characteristic, complemented
51	C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
52	#11745183	C₂²	1	1	yes	characteristic, complemented
53	#11745180	C₂²	1	1	yes	characteristic, complemented
54	#11745169	C₂²	1	1	yes	characteristic, complemented
55	#11745165	C₂²	1	1	yes	characteristic, complemented
56	#11745164	C₂²	1	1	yes	characteristic, complemented
57	#11745158	C₂²	1	1	yes	characteristic, complemented
58	#11745157	C₂²	1	1	yes	characteristic, complemented
59	#11745156	C₂²	1	1	yes	characteristic, complemented
60	#11745156	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₂₉	—	2	1	no	—
62	C₂³×D₂₉	D₄	1	1	yes	characteristic
63	C₂×Q₈×C₂₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₂₉	—	2	1	no	—
65	C₂×D₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₂₉	—	2	1	no	—
68	C₂×C₂²⋊D₂₉	—	2	1	no	—
69	C₂×C₂²⋊D₂₉	—	2	1	no	—
70	C₂²×Dic₂₉	D₄	1	1	yes	characteristic
71	Q₈×D₂₉	—	2	2	no	—
72	Q₈×D₂₉	—	2	2	no	—
73	D₄×D₂₉	—	2	2	no	—
74	D₄×D₂₉	—	2	2	no	—
75	D₄×D₂₉	—	4	4	no	—
76	C₂×D₁₁₆	—	2	1	no	—
77	C₂×D₁₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₄×D₂₉	—	2	2	no	—
79	C₂×C₄×D₂₉	—	2	2	no	—
80	C₂×C₄×D₂₉	—	2	1	no	—
81	C₂×C₄×D₂₉	—	2	1	no	—
82	C₂×C₄×D₂₉	—	2	1	no	—
83	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
84	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
85	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
86	C₂×C₄×D₂₉	C₂³	1	1	yes	characteristic
87	C₂×Dic₅₈	—	2	1	no	—
88	C₂×Dic₅₈	C₂³	1	1	yes	characteristic
89	SD₁₆×C₂₉	—	2	2	no	—
90	C₂×C₈×C₂₉	—	2	2	no	—
91	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₂₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂²⋊C₄×C₂₉	—	2	1	no	—
97	C₂²⋊C₄×C₂₉	—	2	1	no	—
98	C₂²⋊Dic₂₉	—	2	1	no	—
99	C₂²⋊Dic₂₉	—	2	1	no	—
100	#90784	—	2	2	no	—
101	#90783	—	2	2	no	—
102	#90781	—	2	1	no	—
103	#90781	—	2	1	no	—
104	#90781	—	2	1	no	—
105	#90781	—	2	1	no	—
106	C₄⋊Dic₂₉	—	2	1	no	—
107	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
108	C₄⋊Dic₂₉	C₂³	1	1	yes	characteristic
109	#90779	—	2	1	no	—
110	#90779	—	2	1	no	—
111	#90779	—	2	1	no	—
112	#90779	—	2	1	no	—
113	C₂×#6597	—	2	2	no	—
114	C₂×#6597	C₂³	1	1	yes	characteristic
115	C₂×#6597	C₂³	1	1	yes	characteristic
116	#90773	—	2	2	no	—
117	C₈×D₂₉	—	2	2	no	—
118	C₈×D₂₉	—	2	2	no	—
119	C₈×D₂₉	—	2	2	no	—
120	C₈×D₂₉	D₄	1	4	yes	complemented
121	C₂³×C₂₉	—	2	1	no	—
122	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×D₂₉	—	2	2	no	—
124	C₂²×D₂₉	—	2	2	no	—
125	C₂²×D₂₉	—	2	1	no	—
126	C₂²×D₂₉	—	4	2	no	—
127	C₂²×D₂₉	—	4	2	no	—
128	C₂²×D₂₉	—	4	2	no	—
129	C₂²×D₂₉	SD₁₆	1	4	yes	complemented
130	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₂₉	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₂₉	—	2	1	no	—
133	Q₈×C₂₉	—	2	1	no	—
134	D₄×C₂₉	—	2	1	no	—
135	D₄×C₂₉	—	2	1	no	—
136	D₄×C₂₉	—	4	2	no	—
137	C₂×C₄×C₂₉	—	2	1	no	—
138	C₂×C₄×C₂₉	—	2	1	no	—
139	C₂×C₄×C₂₉	—	2	1	no	—
140	C₂×C₄×C₂₉	—	2	1	no	—
141	C₂×C₄×C₂₉	—	2	1	no	—
142	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
144	C₂²⋊D₂₉	—	4	2	no	—
145	C₂²⋊D₂₉	—	4	2	no	—
146	C₂²⋊D₂₉	—	4	2	no	—
147	C₂×Dic₂₉	—	2	2	no	—
148	C₂×Dic₂₉	—	2	1	no	—
149	C₂×Dic₂₉	—	2	1	no	—
150	C₂×Dic₂₉	—	2	1	no	—
151	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
153	D₁₁₆	—	2	1	no	—
154	D₁₁₆	—	2	1	no	—
155	D₁₁₆	—	4	2	no	—
156	C₄×D₂₉	—	2	2	no	—
157	C₄×D₂₉	—	2	1	no	—
158	C₄×D₂₉	—	2	1	no	—
159	C₄×D₂₉	—	2	2	no	—
160	C₄×D₂₉	—	4	2	no	—
161	C₄×D₂₉	—	4	2	no	—
162	C₄×D₂₉	—	4	2	no	—
163	C₄×D₂₉	C₂×D₄	1	2	yes	—
164	C₄×D₂₉	#41	1	2	yes	—
165	Dic₅₈	—	2	1	no	—
166	Dic₅₈	—	2	1	no	—
167	Dic₅₈	—	4	2	no	—
168	C₈×C₂₉	—	2	1	no	—
169	C₈×C₂₉	C₂×D₄	1	2	yes	complemented
170	#6597	—	2	1	no	—
171	#6597	C₂×D₄	1	2	yes	complemented
172	C₂×#465	—	29	1	no	maximal, Sylow
173	C₂²×C₂₉	—	2	1	no	—
174	C₂²×C₂₉	—	2	1	no	—
175	C₂²×C₂₉	—	4	1	no	—
176	C₂²×C₂₉	—	4	1	no	—
177	C₂²×C₂₉	—	4	1	no	—
178	C₂²×C₂₉	C₂×SD₁₆	1	2	yes	complemented
179	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×D₂₉	—	2	1	no	—
181	C₂×D₂₉	—	2	1	no	—
182	C₂×D₂₉	—	2	8	no	—
183	C₂×D₂₉	—	4	1	no	—
184	C₂×D₂₉	—	4	1	no	—
185	C₂×D₂₉	—	4	1	no	—
186	C₂×D₂₉	—	8	4	no	—
187	C₂×D₂₉	#121	1	2	yes	—
188	C₂×D₂₉	C₂×SD₁₆	1	2	yes	—
189	C₂×D₂₉	C₂×SD₁₆	1	2	yes	complemented
190	C₂×D₂₉	#135	1	2	yes	—
191	C₄×C₂₉	—	2	1	no	—
192	C₄×C₂₉	—	4	1	no	—
193	C₄×C₂₉	—	4	1	no	—
194	C₄×C₂₉	—	4	1	no	—
195	C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
196	C₄×C₂₉	C₂×#41	1	1	yes	characteristic
197	Dic₂₉	—	2	1	no	—
198	Dic₂₉	—	4	1	no	—
199	Dic₂₉	—	4	1	no	—
200	Dic₂₉	—	4	1	no	—
201	Dic₂₉	#121	1	2	yes	—
202	C₂²×SD₁₆	—	29	1	no	—
203	C₂³×C₈	—	29	1	no	—
204	C₂×C₂²⋊Q₈	—	29	1	no	—
205	C₂×#121	—	29	1	no	—
206	#465	—	29	1	no	—
207	#465	—	29	1	no	—
208	#465	—	29	1	no	—
209	#465	—	29	1	no	—
210	#465	—	29	1	no	—
211	#465	—	29	1	no	—
212	#465	—	29	1	no	—
213	#465	D₂₉	1	1	yes	characteristic, direct product factor
214	C₂×#106	—	29	1	no	—
215	C₂×#103	—	29	1	no	—
216	C₂×#102	—	29	1	no	—
217	C₂×C₂₉	—	2	2	no	—
218	C₂×C₂₉	—	8	1	no	—
219	C₂×C₂₉	C₂×#121	1	1	yes	characteristic
220	C₂×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
221	C₂×C₂₉	C₂×#135	1	1	yes	characteristic
222	D₂₉	—	2	2	no	—
223	D₂₉	—	8	1	no	—
224	D₂₉	#465	1	4	yes	direct product factor
225	C₂²×Q₈	—	29	1	no	—
226	C₂²×D₄	—	29	1	no	—
227	C₂²×D₄	—	58	1	no	—
228	C₂³×C₄	—	29	1	no	—
229	C₂×SD₁₆	—	29	1	no	—
230	C₂×SD₁₆	—	29	1	no	—
231	C₂×SD₁₆	—	29	1	no	—
232	C₂×SD₁₆	—	58	4	no	—
233	C₂×SD₁₆	C₂×D₂₉	1	1	yes	characteristic, complemented
234	C₂²×C₈	—	29	1	no	—
235	C₂²×C₈	—	29	1	no	—
236	C₂²×C₈	—	29	1	no	—
237	C₂²×C₈	—	29	1	no	—
238	C₂²×C₈	—	29	1	no	—
239	C₂²×C₈	—	58	4	no	—
240	C₂²×C₈	C₂×D₂₉	1	1	yes	characteristic, complemented
241	C₂²⋊Q₈	—	29	1	no	—
242	C₂²⋊Q₈	—	29	1	no	—
243	C₂²⋊Q₈	—	29	1	no	—
244	C₂²⋊Q₈	—	58	1	no	—
245	C₂²⋊Q₈	—	58	1	no	—
246	C₂²⋊Q₈	C₂×D₂₉	1	1	yes	characteristic, complemented
247	#121	—	29	1	no	—
248	#121	—	29	1	no	—
249	#121	—	29	1	no	—
250	#121	—	58	1	no	—
251	#121	—	58	1	no	—
252	#121	C₂×D₂₉	1	1	yes	characteristic
253	C₂×C₄⋊C₄	—	29	1	no	—
254	C₂×C₄⋊C₄	—	29	1	no	—
255	C₂×C₄⋊C₄	—	58	1	no	—
256	C₂×C₂²⋊C₄	—	58	1	no	—
257	C₂×C₂²⋊C₄	—	58	1	no	—
258	#106	—	29	1	no	—
259	#106	—	29	1	no	—
260	#106	—	29	1	no	—
261	#106	C₂×D₂₉	1	1	yes	characteristic, complemented
262	#103	—	29	1	no	—
263	#103	—	29	1	no	—
264	#103	—	29	1	no	—
265	#103	C₂×D₂₉	1	1	yes	characteristic, complemented
266	#102	—	29	1	no	—
267	#102	—	29	1	no	—
268	#102	—	29	1	no	—
269	#102	C₂×D₂₉	1	1	yes	characteristic, complemented
270	C₂₉	C₂×#465	1	1	yes	characteristic, complemented, Sylow
271	C₂⁴	—	29	1	no	—
272	C₂⁴	—	58	1	no	—
273	C₂×Q₈	—	29	1	no	—
274	C₂×Q₈	—	58	1	no	—
275	C₂×Q₈	—	58	2	no	—
276	C₂×Q₈	—	58	2	no	—
277	C₂×Q₈	C₂²×D₂₉	1	1	yes	characteristic
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	29	1	no	—
280	C₂×D₄	—	58	1	no	—
281	C₂×D₄	—	58	2	no	—
282	C₂×D₄	—	58	2	no	—
283	C₂×D₄	—	58	1	no	—
284	C₂×D₄	—	58	1	no	—
285	C₂×D₄	—	58	1	no	—
286	C₂×D₄	—	116	4	no	—
287	C₂×D₄	C₂²×D₂₉	1	1	yes	characteristic
288	C₂²×C₄	—	29	1	no	—
289	C₂²×C₄	—	29	1	no	—
290	C₂²×C₄	—	29	1	no	—
291	C₂²×C₄	—	29	1	no	—
292	C₂²×C₄	—	29	1	no	—
293	C₂²×C₄	—	58	2	no	—
294	C₂²×C₄	—	58	2	no	—
295	C₂²×C₄	—	58	1	no	—
296	C₂²×C₄	—	58	1	no	—
297	C₂²×C₄	—	58	1	no	—
298	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
299	SD₁₆	—	2	2	no	—
300	SD₁₆	—	58	2	no	—
301	SD₁₆	—	58	2	no	—
302	SD₁₆	—	58	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	29	1	no	—
305	C₂×C₈	—	29	4	no	—
306	C₂×C₈	—	29	1	no	—
307	C₂×C₈	—	58	2	no	—
308	C₂×C₈	—	58	2	no	—
309	C₂×C₈	—	58	2	no	—
310	C₂×C₈	—	58	2	no	—
311	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₂₉	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	29	1	no	—
315	C₄⋊C₄	—	29	1	no	—
316	C₄⋊C₄	—	58	1	no	—
317	C₄⋊C₄	—	58	1	no	—
318	C₄⋊C₄	—	58	1	no	—
319	C₄⋊C₄	—	58	1	no	—
320	C₄⋊C₄	—	58	1	no	—
321	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
322	C₄⋊C₄	C₂²×D₂₉	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	1	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	58	1	no	—
326	C₂²⋊C₄	—	58	1	no	—
327	C₂²⋊C₄	—	58	1	no	—
328	C₂²⋊C₄	—	58	1	no	—
329	C₂²⋊C₄	—	58	1	no	—
330	C₂²⋊C₄	—	58	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	29	1	no	—
333	C₂³	—	29	1	no	—
334	C₂³	—	29	4	no	—
335	C₂³	—	58	2	no	—
336	C₂³	—	58	2	no	—
337	C₂³	—	58	1	no	—
338	C₂³	—	116	2	no	—
339	C₂³	—	116	2	no	—
340	C₂³	—	116	2	no	—
341	C₂³	D₄×D₂₉	1	1	yes	characteristic
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	58	1	no	—
345	Q₈	—	58	1	no	—
346	Q₈	—	116	2	no	—
347	D₄	—	2	1	no	—
348	D₄	—	2	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	58	1	no	—
351	D₄	—	58	1	no	—
352	D₄	—	116	2	no	—
353	D₄	—	116	2	no	—
354	D₄	—	116	2	no	—
355	D₄	—	116	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	29	1	no	—
362	C₂×C₄	—	29	2	no	—
363	C₂×C₄	—	29	2	no	—
364	C₂×C₄	—	29	1	no	—
365	C₂×C₄	—	58	2	no	—
366	C₂×C₄	—	58	2	no	—
367	C₂×C₄	—	58	2	no	—
368	C₂×C₄	—	58	1	no	—
369	C₂×C₄	—	58	1	no	—
370	C₂×C₄	—	58	1	no	—
371	C₂×C₄	—	58	1	no	—
372	C₂×C₄	—	58	1	no	—
373	C₂×C₄	—	116	2	no	—
374	C₂×C₄	—	116	2	no	—
375	C₂×C₄	—	116	2	no	—
376	C₂×C₄	D₄×D₂₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	29	2	no	—
380	C₈	—	58	1	no	—
381	C₈	D₄×D₂₉	1	2	yes	complemented
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	29	2	no	—
388	C₂²	—	29	2	no	—
389	C₂²	—	29	2	no	—
390	C₂²	—	29	2	no	—
391	C₂²	—	58	8	no	—
392	C₂²	—	58	1	no	—
393	C₂²	—	58	1	no	—
394	C₂²	—	116	1	no	—
395	C₂²	—	116	1	no	—
396	C₂²	—	116	1	no	—
397	C₂²	—	232	4	no	—
398	C₂²	SD₁₆×D₂₉	1	2	yes	complemented
399	C₂²	C₂×D₄×D₂₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	29	2	no	—
405	C₄	—	58	1	no	—
406	C₄	—	116	1	no	—
407	C₄	—	116	1	no	—
408	C₄	—	116	1	no	—
409	C₄	C₂×D₄×D₂₉	1	1	yes	characteristic
410	C₄	#41×D₂₉	1	1	yes	characteristic
411	C₂	—	2	2	no	—
412	C₂	—	8	1	no	—
413	C₂	—	29	4	no	—
414	C₂	—	58	2	no	—
415	C₂	—	232	1	no	—
416	C₂	#121×D₂₉	1	1	yes	characteristic
417	C₂	C₂×SD₁₆×D₂₉	1	1	yes	characteristic
418	C₂	#135×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂₉×#465	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	#121×D₂₉	C₂
hypercenter	#465	D₂₉
hypocenter	C₂₉	C₂×#465
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #465

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₂₉	C₂	semidirect
2. C₂²×C₈×D₂₉	C₂	semidirect
3. C₂²⋊Q₈×D₂₉	C₂	semidirect
5. #14271395	C₂	semidirect
6. #14271394	C₂	semidirect
7. #14271393	C₂	semidirect
8. #14271392	C₂	semidirect
9. #14271391	C₂	semidirect
10. #14271390	C₂	semidirect
11. #14271389	C₂	semidirect
12. #106×D₂₉	C₂	semidirect
13. #103×D₂₉	C₂	semidirect
14. #102×D₂₉	C₂	semidirect
15. C₂₉×#465	C₂	semidirect
20. C₂×SD₁₆×C₂₉	C₂²	semidirect
21. C₂²×C₈×C₂₉	C₂²	semidirect
22. C₂₉×C₂²⋊Q₈	C₂²	semidirect
24. #11745308	C₂²	semidirect
25. C₂×#90784	C₂²	semidirect
28. C₂×#90783	C₂²	semidirect
30. #11745286	C₂²	semidirect
31. C₂²×#6597	C₂²	semidirect
33. C₂×#90773	C₂²	semidirect
37. C₂×C₈×D₂₉	C₂²	semidirect
38. C₂×C₈×D₂₉	C₂²	semidirect
39. #11745259	C₂²	semidirect
49. C₂₉×#106	C₂²	semidirect
50. C₂₉×#103	C₂²	semidirect
51. C₂₉×#102	C₂²	semidirect
52. #11745183	C₂²	semidirect
53. #11745180	C₂²	semidirect
54. #11745169	C₂²	semidirect
55. #11745165	C₂²	semidirect
56. #11745164	C₂²	semidirect
57. #11745158	C₂²	semidirect
58. #11745157	C₂²	semidirect
59. #11745156	C₂²	semidirect
60. #11745156	C₂²	semidirect
120. C₈×D₂₉	D₄	semidirect
129. C₂²×D₂₉	SD₁₆	semidirect
169. C₈×C₂₉	C₂×D₄	semidirect
171. #6597	C₂×D₄	semidirect
178. C₂²×C₂₉	C₂×SD₁₆	semidirect
189. C₂×D₂₉	C₂×SD₁₆	semidirect
213. #465	D₂₉	direct (N × H)
224. D₂₉	#465	direct (N × H)
233. C₂×SD₁₆	C₂×D₂₉	semidirect
240. C₂²×C₈	C₂×D₂₉	semidirect
246. C₂²⋊Q₈	C₂×D₂₉	semidirect
261. #106	C₂×D₂₉	semidirect
265. #103	C₂×D₂₉	semidirect
269. #102	C₂×D₂₉	semidirect
270. C₂₉	C₂×#465	semidirect
381. C₈	D₄×D₂₉	semidirect
398. C₂²	SD₁₆×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₂₉	2
C₂²×C₈×D₂₉	2
C₂²⋊Q₈×D₂₉	2
#121×D₂₉	2
#14271395	2
#14271394	2
#14271393	2
#14271392	2
#14271391	2
#14271390	2
#14271389	2
#106×D₂₉	2
#103×D₂₉	2
#102×D₂₉	2
C₂₉×#465	2
C₂×#465	29

Subgroups — D29×#465 #16829048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×#465 #16829048