Subgroups — C₂₉×#19986 #20314886

Order 7424.

656 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3362	C₂	1	2	yes	maximal, complemented
3	C₂₉×#3287	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1678	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1631	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1623	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#135	—	2	1	no	—
13	Q₈²×C₂₉	C₂²	1	2	yes	—
14	C₂₉×#550	C₂²	1	2	yes	—
15	C₂₉×#500	—	2	1	no	—
16	C₂₉×#500	C₂²	1	1	yes	characteristic
17	C₂₉×#493	C₂²	1	1	yes	characteristic
18	C₂₉×#492	C₂²	1	2	yes	—
19	C₂₉×#486	—	2	2	no	—
20	C₂₉×#486	C₂²	1	2	yes	—
21	C₂₉×#477	—	2	2	no	—
22	C₂₉×#477	C₂²	1	2	yes	—
23	C₂₉×#476	—	2	2	no	—
24	C₂₉×#476	C₂²	1	2	yes	—
25	C₂₉×#466	—	2	1	no	—
26	C₂₉×#460	—	2	2	no	—
27	C₂₉×#460	C₂²	1	2	yes	—
28	C₂₉×#460	C₂²	1	2	yes	—
29	C₂₉×#449	—	2	2	no	—
30	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₂₉	C₂²	1	2	yes	—
32	C₄×Q₁₆×C₂₉	—	2	1	no	—
33	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₂₉	—	2	2	no	—
35	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
36	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#335	C₂²	1	1	yes	characteristic
38	C₂₉×#334	C₂²	1	1	yes	characteristic
39	C₂₉×#333	C₂²	1	2	yes	—
40	C₂₉×#331	C₂²	1	2	yes	—
41	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₂₉×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₂₉	C₂²	1	1	yes	characteristic
45	C₂×#41×C₂₉	—	2	2	no	—
46	C₂₉×#135	—	4	4	no	—
47	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₂₉	—	2	2	no	—
49	C₂×SD₁₆×C₂₉	—	2	2	no	—
50	C₂×SD₁₆×C₂₉	—	4	2	no	—
51	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
52	C₂×D₈×C₂₉	—	2	1	no	—
53	C₂×D₈×C₂₉	—	2	1	no	—
54	C₂²×C₈×C₂₉	—	2	1	no	—
55	C₂₉×C₄⋊Q₈	—	2	2	no	—
56	C₂₉×C₄⋊Q₈	—	2	2	no	—
57	C₂₉×C₄⋊Q₈	—	4	2	no	—
58	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₂₉×#127	—	2	2	no	—
60	C₂₉×#127	C₂³	1	2	yes	—
61	C₂₉×#121	—	2	2	no	—
62	C₂₉×#121	—	4	2	no	—
63	C₄×Q₈×C₂₉	—	2	2	no	—
64	C₄×Q₈×C₂₉	—	2	2	no	—
65	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
67	C₄×D₄×C₂₉	—	2	2	no	—
68	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂₉×#107	—	2	1	no	—
70	C₂₉×#107	—	2	1	no	—
71	C₂₉×#107	—	2	2	no	—
72	C₂₉×#107	D₄	1	1	yes	characteristic
73	C₂₉×#106	—	2	2	no	—
74	C₂₉×#106	D₄	1	1	yes	characteristic
75	C₂₉×C₄⋊C₈	—	2	2	no	—
76	C₂₉×C₄⋊C₈	—	2	1	no	—
77	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
79	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₂₉×#103	—	2	2	no	—
81	C₂₉×#103	D₄	1	1	yes	characteristic
82	C₂₉×#103	D₄	1	2	yes	—
83	C₂₉×#102	—	2	2	no	—
84	C₂₉×#102	—	2	2	no	—
85	C₂₉×#102	—	2	2	no	—
86	C₂₉×#102	—	2	2	no	—
87	C₂₉×#102	—	2	2	no	—
88	C₂₉×#102	D₄	1	1	yes	characteristic
89	C₂₉×C₂²⋊C₈	—	2	1	no	—
90	C₄×C₈×C₂₉	—	2	2	no	—
91	C₄×C₈×C₂₉	—	2	1	no	—
92	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
95	#41×C₂₉	—	4	4	no	—
96	#41×C₂₉	—	8	2	no	—
97	C₂×Q₈×C₂₉	—	2	2	no	—
98	C₂×Q₈×C₂₉	—	4	2	no	—
99	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₂₉	—	2	2	no	—
102	C₂×D₄×C₂₉	—	2	2	no	—
103	C₂×D₄×C₂₉	—	2	2	no	—
104	C₂×D₄×C₂₉	—	4	2	no	—
105	C₂×D₄×C₂₉	—	4	2	no	—
106	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₂₉	—	2	1	no	—
108	C₂²×C₄×C₂₉	—	4	2	no	—
109	Q₁₆×C₂₉	SD₁₆	1	4	yes	complemented
110	SD₁₆×C₂₉	—	2	2	no	—
111	SD₁₆×C₂₉	—	4	4	no	—
112	SD₁₆×C₂₉	—	4	4	no	—
113	SD₁₆×C₂₉	—	8	4	no	—
114	D₈×C₂₉	—	4	2	no	—
115	D₈×C₂₉	—	8	1	no	—
116	C₂×C₈×C₂₉	—	2	1	no	—
117	C₂×C₈×C₂₉	—	2	1	no	—
118	C₂×C₈×C₂₉	—	2	2	no	—
119	C₂×C₈×C₂₉	—	2	1	no	—
120	C₂×C₈×C₂₉	—	4	2	no	—
121	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₂₉	—	2	2	no	—
126	C₄⋊C₄×C₂₉	—	2	1	no	—
127	C₄⋊C₄×C₂₉	—	2	2	no	—
128	C₄⋊C₄×C₂₉	—	2	2	no	—
129	C₄⋊C₄×C₂₉	—	4	2	no	—
130	C₄⋊C₄×C₂₉	—	4	2	no	—
131	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₂₉	—	2	1	no	—
135	C₂²⋊C₄×C₂₉	—	4	2	no	—
136	C₄²×C₂₉	—	2	2	no	—
137	C₄²×C₂₉	—	2	1	no	—
138	C₄²×C₂₉	—	4	2	no	—
139	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
140	#19986	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₂₉	—	2	1	no	—
142	C₂³×C₂₉	—	4	2	no	—
143	Q₈×C₂₉	—	2	2	no	—
144	Q₈×C₂₉	—	2	1	no	—
145	Q₈×C₂₉	—	8	2	no	—
146	Q₈×C₂₉	—	16	2	no	—
147	Q₈×C₂₉	C₂×SD₁₆	1	4	yes	—
148	Q₈×C₂₉	#135	1	2	yes	complemented
149	D₄×C₂₉	—	2	1	no	—
150	D₄×C₂₉	—	2	1	no	—
151	D₄×C₂₉	—	4	2	no	—
152	D₄×C₂₉	—	4	2	no	—
153	D₄×C₂₉	—	4	2	no	—
154	D₄×C₂₉	—	4	2	no	—
155	D₄×C₂₉	—	8	4	no	—
156	D₄×C₂₉	—	8	2	no	—
157	D₄×C₂₉	—	16	2	no	—
158	C₂×C₄×C₂₉	—	2	1	no	—
159	C₂×C₄×C₂₉	—	2	2	no	—
160	C₂×C₄×C₂₉	—	2	2	no	—
161	C₂×C₄×C₂₉	—	2	1	no	—
162	C₂×C₄×C₂₉	—	2	1	no	—
163	C₂×C₄×C₂₉	—	4	1	no	—
164	C₂×C₄×C₂₉	—	4	1	no	—
165	C₂×C₄×C₂₉	—	4	2	no	—
166	C₂×C₄×C₂₉	—	8	4	no	—
167	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
170	C₈×C₂₉	—	2	2	no	—
171	C₈×C₂₉	—	2	1	no	—
172	C₈×C₂₉	—	2	1	no	—
173	C₈×C₂₉	—	2	1	no	—
174	C₈×C₂₉	—	4	1	no	—
175	C₈×C₂₉	—	4	2	no	—
176	C₈×C₂₉	—	4	1	no	—
177	C₈×C₂₉	C₂×SD₁₆	1	2	yes	—
178	Q₈×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
179	#3362	C₂×C₂₉	1	2	yes	complemented
180	#3287	C₂×C₂₉	1	1	yes	characteristic
181	#1706	C₂×C₂₉	1	1	yes	characteristic, complemented
182	#1678	C₂×C₂₉	1	2	yes	complemented
183	#1675	C₂×C₂₉	1	1	yes	characteristic, complemented
184	#1668	C₂×C₂₉	1	1	yes	characteristic, complemented
185	#1631	C₂×C₂₉	1	2	yes	complemented
186	#1623	C₂×C₂₉	1	2	yes	complemented
187	C₈×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
188	C₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
189	C₂²×C₂₉	—	4	1	no	—
190	C₂²×C₂₉	—	4	1	no	—
191	C₂²×C₂₉	—	4	1	no	—
192	C₂²×C₂₉	—	8	2	no	—
193	C₂²×C₂₉	—	8	2	no	—
194	C₂²×C₂₉	—	8	2	no	—
195	C₂²×C₂₉	D₄²	1	1	yes	characteristic
196	C₄×C₂₉	—	2	4	no	—
197	C₄×C₂₉	—	2	2	no	—
198	C₄×C₂₉	—	2	1	no	—
199	C₄×C₂₉	—	4	1	no	—
200	C₄×C₂₉	—	4	2	no	—
201	C₄×C₂₉	—	4	1	no	—
202	C₄×C₂₉	—	8	2	no	—
203	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
204	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
205	C₄×C₂₉	#577	1	1	yes	characteristic
206	C₄×C₂₉	#578	1	1	yes	characteristic
207	C₂×#135	—	2	1	no	—
208	Q₈²	C₂²×C₂₉	1	2	yes	—
209	#550	C₂²×C₂₉	1	2	yes	—
210	#500	—	2	1	no	—
211	#500	C₂²×C₂₉	1	1	yes	characteristic
212	#493	C₂²×C₂₉	1	1	yes	characteristic
213	#492	C₂²×C₂₉	1	2	yes	—
214	#486	—	2	2	no	—
215	#486	C₂²×C₂₉	1	2	yes	—
216	#477	—	2	2	no	—
217	#477	C₂²×C₂₉	1	2	yes	—
218	#476	—	2	2	no	—
219	#476	C₂²×C₂₉	1	2	yes	—
220	#466	—	2	1	no	—
221	#460	—	2	2	no	—
222	#460	C₂²×C₂₉	1	2	yes	—
223	#460	C₂²×C₂₉	1	2	yes	—
224	#449	—	2	2	no	—
225	C₈×Q₈	C₂²×C₂₉	1	2	yes	—
226	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
227	C₄×Q₁₆	—	2	1	no	—
228	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
229	C₄×SD₁₆	—	2	2	no	—
230	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
231	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
232	#335	C₂²×C₂₉	1	1	yes	characteristic
233	#334	C₂²×C₂₉	1	1	yes	characteristic
234	#333	C₂²×C₂₉	1	2	yes	—
235	#331	C₂²×C₂₉	1	2	yes	—
236	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
237	Q₈⋊C₈	C₂²×C₂₉	1	2	yes	—
238	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
239	C₈²	C₂²×C₂₉	1	1	yes	characteristic
240	C₂×C₂₉	—	8	1	no	—
241	C₂×C₂₉	—	16	2	no	—
242	C₂×C₂₉	D₄×SD₁₆	1	1	yes	characteristic
243	C₂×C₂₉	#3285	1	1	yes	characteristic
244	C₂×C₂₉	#3292	1	1	yes	characteristic
245	C₂×#41	—	2	2	no	—
246	#135	—	4	4	no	—
247	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	4	2	no	—
251	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	4	2	no	—
258	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
259	#127	—	2	2	no	—
260	#127	C₂³×C₂₉	1	2	yes	—
261	#121	—	2	2	no	—
262	#121	—	4	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	—	2	2	no	—
265	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
266	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
269	#107	—	2	1	no	—
270	#107	—	2	1	no	—
271	#107	—	2	2	no	—
272	#107	D₄×C₂₉	1	1	yes	characteristic
273	#106	—	2	2	no	—
274	#106	D₄×C₂₉	1	1	yes	characteristic
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
279	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
280	#103	—	2	2	no	—
281	#103	D₄×C₂₉	1	1	yes	characteristic
282	#103	D₄×C₂₉	1	2	yes	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	D₄×C₂₉	1	1	yes	characteristic
289	C₂²⋊C₈	—	2	1	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
295	C₂₉	#19986	1	1	yes	characteristic, direct product factor, Sylow
296	#41	—	4	4	no	—
297	#41	—	8	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
301	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	Q₁₆	SD₁₆×C₂₉	1	4	yes	complemented
311	SD₁₆	—	2	2	no	—
312	SD₁₆	—	4	4	no	—
313	SD₁₆	—	4	4	no	—
314	SD₁₆	—	8	4	no	—
315	D₈	—	4	2	no	—
316	D₈	—	8	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
333	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
334	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	4	2	no	—
340	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
341	C₂³	—	2	1	no	—
342	C₂³	—	4	2	no	—
343	Q₈	—	2	2	no	—
344	Q₈	—	2	1	no	—
345	Q₈	—	8	2	no	—
346	Q₈	—	16	2	no	—
347	Q₈	C₂×SD₁₆×C₂₉	1	4	yes	—
348	Q₈	C₂₉×#135	1	2	yes	complemented
349	D₄	—	2	1	no	—
350	D₄	—	2	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	8	4	no	—
356	D₄	—	8	2	no	—
357	D₄	—	16	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
369	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	1	no	—
377	C₈	C₂×SD₁₆×C₂₉	1	2	yes	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	D₄²×C₂₉	1	1	yes	characteristic
385	C₄	—	2	4	no	—
386	C₄	—	2	2	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	8	2	no	—
392	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
393	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
394	C₄	C₂₉×#577	1	1	yes	characteristic
395	C₄	C₂₉×#578	1	1	yes	characteristic
396	C₂	—	8	1	no	—
397	C₂	—	16	2	no	—
398	C₂	D₄×SD₁₆×C₂₉	1	1	yes	characteristic
399	C₂	C₂₉×#3285	1	1	yes	characteristic
400	C₂	C₂₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3287	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×Q₁₆×C₂₉	C₂	semidirect
2. C₂₉×#3362	C₂	semidirect
4. C₂₉×#1706	C₂	semidirect
5. C₂₉×#1678	C₂	semidirect
6. C₂₉×#1675	C₂	semidirect
7. C₂₉×#1668	C₂	semidirect
8. C₂₉×#1631	C₂	semidirect
9. C₂₉×#1623	C₂	semidirect
10. C₈×Q₁₆×C₂₉	C₂	semidirect
11. C₈×SD₁₆×C₂₉	C₂	semidirect
109. Q₁₆×C₂₉	SD₁₆	semidirect
140. #19986	C₂₉	direct (N × H)
148. Q₈×C₂₉	#135	semidirect
178. Q₈×Q₁₆	C₂×C₂₉	semidirect
179. #3362	C₂×C₂₉	semidirect
181. #1706	C₂×C₂₉	semidirect
182. #1678	C₂×C₂₉	semidirect
183. #1675	C₂×C₂₉	semidirect
184. #1668	C₂×C₂₉	semidirect
185. #1631	C₂×C₂₉	semidirect
186. #1623	C₂×C₂₉	semidirect
187. C₈×Q₁₆	C₂×C₂₉	semidirect
188. C₈×SD₁₆	C₂×C₂₉	semidirect
295. C₂₉	#19986	direct (N × H)
310. Q₁₆	SD₁₆×C₂₉	semidirect
348. Q₈	C₂₉×#135	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Q₁₆×C₂₉	2
C₂₉×#3362	2
C₂₉×#3287	2
C₂₉×#1706	2
C₂₉×#1678	2
C₂₉×#1675	2
C₂₉×#1668	2
C₂₉×#1631	2
C₂₉×#1623	2
C₈×Q₁₆×C₂₉	2
C₈×SD₁₆×C₂₉	2
#19986	29

Subgroups — C29×#19986 #20314886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19986 #20314886