Subgroups — C₂₉×#18822 #20313722

Order 7424.

966 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3228	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1650	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1647	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1561	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1486	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂₉×#556	C₂²	1	1	yes	characteristic
18	C₂₉×#554	—	2	1	no	—
19	C₂₉×#552	—	2	1	no	—
20	C₂₉×#551	—	2	2	no	—
21	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂₉×#548	—	2	1	no	—
23	C₂₉×#547	C₂²	1	1	yes	characteristic
24	C₂₉×#547	C₂²	1	1	yes	characteristic
25	C₂₉×#546	—	2	1	no	—
26	C₂₉×#542	—	2	1	no	—
27	C₂₉×#539	—	2	2	no	—
28	C₂₉×#533	C₂²	1	1	yes	characteristic
29	C₂₉×#532	C₂²	1	1	yes	characteristic
30	C₂₉×#529	C₂²	1	1	yes	characteristic
31	C₂₉×#525	—	2	1	no	—
32	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
33	C₂₉×#520	—	2	1	no	—
34	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#500	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#498	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
38	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#482	—	2	2	no	—
40	C₂₉×#478	—	2	2	no	—
41	C₂₉×#478	—	2	1	no	—
42	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#469	—	2	1	no	—
45	C₂₉×#468	—	2	1	no	—
46	C₂₉×#463	—	2	1	no	—
47	C₂₉×#463	—	2	1	no	—
48	C₂₉×#463	—	2	1	no	—
49	C₂₉×#461	C₂²	1	1	yes	characteristic
50	C₂₉×#461	C₂²	1	1	yes	characteristic
51	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×#459	C₂²	1	1	yes	characteristic
53	C₂₉×#459	C₂²	1	1	yes	characteristic
54	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
55	C₂₉×#431	C₂²	1	1	yes	characteristic
56	C₂₉×#423	C₂²	1	1	yes	characteristic
57	C₂₉×#423	C₂²	1	1	yes	characteristic
58	C₂₉×#417	—	2	1	no	—
59	C₂₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#332	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#332	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#332	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂²×Q₈×C₂₉	—	2	1	no	—
75	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₂₉	—	2	1	no	—
77	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
78	C₂×SD₁₆×C₂₉	—	2	1	no	—
79	C₂×SD₁₆×C₂₉	—	2	1	no	—
80	C₂×SD₁₆×C₂₉	—	2	1	no	—
81	C₂×D₈×C₂₉	—	2	1	no	—
82	C₂×D₈×C₂₉	—	2	1	no	—
83	C₂×D₈×C₂₉	—	2	1	no	—
84	C₂×M₁₆×C₂₉	—	2	1	no	—
85	C₂×M₁₆×C₂₉	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	—	2	1	no	—
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#126	—	2	2	no	—
92	C₂₉×#126	—	2	2	no	—
93	C₂₉×#126	—	2	1	no	—
94	C₂₉×#125	—	2	2	no	—
95	C₂₉×#125	D₄	1	1	yes	characteristic
96	C₂₉×#125	D₄	1	2	yes	—
97	C₂₉×#124	—	2	2	no	—
98	C₂₉×#124	—	2	1	no	—
99	C₂₉×#124	—	2	1	no	—
100	C₂₉×#124	D₄	1	1	yes	characteristic
101	C₂₉×#123	—	2	2	no	—
102	C₂₉×#123	—	2	2	no	—
103	C₂₉×#123	—	2	1	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×#123	—	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	1	no	—
112	C₂₉×C₂²⋊Q₈	—	2	1	no	—
113	C₂₉×C₂²⋊Q₈	—	2	1	no	—
114	C₂₉×C₂²⋊Q₈	—	2	2	no	—
115	C₂₉×C₂²⋊Q₈	—	2	1	no	—
116	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
117	C₂₉×#121	—	2	2	no	—
118	C₂₉×#121	—	2	1	no	—
119	C₂₉×#121	—	2	1	no	—
120	C₂₉×#121	—	2	1	no	—
121	C₂₉×#121	—	2	1	no	—
122	C₂₉×#121	D₄	1	1	yes	characteristic
123	C₂₉×#120	—	2	2	no	—
124	C₄×Q₈×C₂₉	—	2	1	no	—
125	C₄×Q₈×C₂₉	—	2	1	no	—
126	C₄×Q₈×C₂₉	—	2	1	no	—
127	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₂₉	—	2	2	no	—
129	C₄×D₄×C₂₉	—	2	2	no	—
130	C₄×D₄×C₂₉	—	2	2	no	—
131	C₄×D₄×C₂₉	—	2	1	no	—
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	—	2	1	no	—
134	C₄×D₄×C₂₉	—	2	1	no	—
135	C₄×D₄×C₂₉	—	2	1	no	—
136	C₄×D₄×C₂₉	—	2	1	no	—
137	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
138	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
139	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
140	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
141	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
142	C₂₉×#117	—	2	2	no	—
143	C₂₉×#117	—	2	1	no	—
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	D₄	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
147	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
151	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
152	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
153	C₂₉×#107	—	2	1	no	—
154	C₂₉×#107	—	2	2	no	—
155	C₂₉×#106	—	2	1	no	—
156	C₂₉×#106	—	2	2	no	—
157	C₂₉×C₄⋊C₈	—	2	1	no	—
158	C₂₉×C₄⋊C₈	—	2	1	no	—
159	C₂₉×C₄⋊C₈	—	2	1	no	—
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
164	C₂₉×#103	—	2	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#103	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×#102	—	2	1	no	—
172	C₂₉×#102	—	2	2	no	—
173	C₂₉×#102	—	2	2	no	—
174	C₂₉×C₂²⋊C₈	—	2	1	no	—
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
177	C₂⁴×C₂₉	—	2	1	no	—
178	#41×C₂₉	—	4	2	no	—
179	#41×C₂₉	—	4	2	no	—
180	#41×C₂₉	—	4	2	no	—
181	#41×C₂₉	—	4	2	no	—
182	#41×C₂₉	—	8	1	no	—
183	#41×C₂₉	—	8	1	no	—
184	C₂×Q₈×C₂₉	—	2	2	no	—
185	C₂×Q₈×C₂₉	—	2	1	no	—
186	C₂×Q₈×C₂₉	—	2	1	no	—
187	C₂×Q₈×C₂₉	—	2	1	no	—
188	C₂×Q₈×C₂₉	—	8	1	no	—
189	C₂×Q₈×C₂₉	—	8	1	no	—
190	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₂₉	—	2	2	no	—
192	C₂×D₄×C₂₉	—	2	2	no	—
193	C₂×D₄×C₂₉	—	2	1	no	—
194	C₂×D₄×C₂₉	—	2	2	no	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	—	2	1	no	—
197	C₂×D₄×C₂₉	—	2	1	no	—
198	C₂×D₄×C₂₉	—	2	1	no	—
199	C₂×D₄×C₂₉	—	4	1	no	—
200	C₂×D₄×C₂₉	—	4	1	no	—
201	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₉	—	2	2	no	—
205	C₂²×C₄×C₂₉	—	2	2	no	—
206	C₂²×C₄×C₂₉	—	2	2	no	—
207	C₂²×C₄×C₂₉	—	2	1	no	—
208	C₂²×C₄×C₂₉	—	2	1	no	—
209	C₂²×C₄×C₂₉	—	2	1	no	—
210	C₂²×C₄×C₂₉	—	2	1	no	—
211	C₂²×C₄×C₂₉	—	2	1	no	—
212	C₂²×C₄×C₂₉	—	2	1	no	—
213	C₂²×C₄×C₂₉	—	4	1	no	—
214	C₂²×C₄×C₂₉	—	8	1	no	—
215	C₂²×C₄×C₂₉	—	8	1	no	—
216	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
219	SD₁₆×C₂₉	—	4	2	no	—
220	SD₁₆×C₂₉	—	4	2	no	—
221	SD₁₆×C₂₉	—	8	1	no	—
222	D₈×C₂₉	—	4	2	no	—
223	D₈×C₂₉	—	4	2	no	—
224	D₈×C₂₉	—	8	1	no	—
225	M₁₆×C₂₉	—	4	2	no	—
226	M₁₆×C₂₉	—	8	1	no	—
227	C₂×C₈×C₂₉	—	2	1	no	—
228	C₂×C₈×C₂₉	—	2	1	no	—
229	C₂×C₈×C₂₉	—	2	1	no	—
230	C₂×C₈×C₂₉	—	2	1	no	—
231	C₂×C₈×C₂₉	—	2	1	no	—
232	C₂×C₈×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	2	2	no	—
234	C₄⋊C₄×C₂₉	—	2	2	no	—
235	C₄⋊C₄×C₂₉	—	2	2	no	—
236	C₄⋊C₄×C₂₉	—	2	2	no	—
237	C₄⋊C₄×C₂₉	—	2	1	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	2	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	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
252	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
254	C₂²⋊C₄×C₂₉	—	2	2	no	—
255	C₂²⋊C₄×C₂₉	—	2	2	no	—
256	C₂²⋊C₄×C₂₉	—	2	2	no	—
257	C₂²⋊C₄×C₂₉	—	2	2	no	—
258	C₂²⋊C₄×C₂₉	—	2	2	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	2	2	no	—
261	C₂²⋊C₄×C₂₉	—	2	1	no	—
262	C₂²⋊C₄×C₂₉	—	2	1	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	C₂²⋊C₄×C₂₉	—	2	1	no	—
269	C₂²⋊C₄×C₂₉	—	4	1	no	—
270	C₂²⋊C₄×C₂₉	—	4	1	no	—
271	C₄²×C₂₉	—	2	2	no	—
272	C₄²×C₂₉	—	2	2	no	—
273	C₄²×C₂₉	—	2	1	no	—
274	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
278	#18822	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂³×C₂₉	—	2	1	no	—
280	C₂³×C₂₉	—	2	1	no	—
281	C₂³×C₂₉	—	2	1	no	—
282	C₂³×C₂₉	—	4	2	no	—
283	C₂³×C₂₉	—	4	2	no	—
284	C₂³×C₂₉	—	4	1	no	—
285	C₂³×C₂₉	—	8	1	no	—
286	C₂³×C₂₉	#120	1	1	yes	characteristic
287	Q₈×C₂₉	—	2	1	no	—
288	Q₈×C₂₉	—	2	1	no	—
289	Q₈×C₂₉	—	4	1	no	—
290	Q₈×C₂₉	—	4	1	no	—
291	Q₈×C₂₉	—	4	1	no	—
292	Q₈×C₂₉	—	4	1	no	—
293	Q₈×C₂₉	—	4	1	no	—
294	Q₈×C₂₉	—	4	1	no	—
295	Q₈×C₂₉	—	8	2	no	—
296	D₄×C₂₉	—	2	1	no	—
297	D₄×C₂₉	—	2	1	no	—
298	D₄×C₂₉	—	2	1	no	—
299	D₄×C₂₉	—	2	1	no	—
300	D₄×C₂₉	—	2	1	no	—
301	D₄×C₂₉	—	4	2	no	—
302	D₄×C₂₉	—	4	2	no	—
303	D₄×C₂₉	—	4	2	no	—
304	D₄×C₂₉	—	4	4	no	—
305	D₄×C₂₉	—	4	1	no	—
306	D₄×C₂₉	—	4	1	no	—
307	D₄×C₂₉	—	4	1	no	—
308	D₄×C₂₉	—	4	1	no	—
309	D₄×C₂₉	—	8	2	no	—
310	D₄×C₂₉	—	8	2	no	—
311	D₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
312	C₂×C₄×C₂₉	—	2	1	no	—
313	C₂×C₄×C₂₉	—	2	1	no	—
314	C₂×C₄×C₂₉	—	2	1	no	—
315	C₂×C₄×C₂₉	—	2	1	no	—
316	C₂×C₄×C₂₉	—	2	1	no	—
317	C₂×C₄×C₂₉	—	2	2	no	—
318	C₂×C₄×C₂₉	—	2	1	no	—
319	C₂×C₄×C₂₉	—	2	1	no	—
320	C₂×C₄×C₂₉	—	2	2	no	—
321	C₂×C₄×C₂₉	—	2	1	no	—
322	C₂×C₄×C₂₉	—	2	1	no	—
323	C₂×C₄×C₂₉	—	4	1	no	—
324	C₂×C₄×C₂₉	—	4	4	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	—	4	1	no	—
329	C₂×C₄×C₂₉	—	4	1	no	—
330	C₂×C₄×C₂₉	—	4	1	no	—
331	C₂×C₄×C₂₉	—	4	1	no	—
332	C₂×C₄×C₂₉	—	8	1	no	—
333	C₂×C₄×C₂₉	—	8	1	no	—
334	C₂×C₄×C₂₉	—	8	2	no	—
335	C₂×C₄×C₂₉	—	8	1	no	—
336	C₂×C₄×C₂₉	—	8	2	no	—
337	C₂×C₄×C₂₉	—	8	2	no	—
338	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
339	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
340	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
341	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
344	C₈×C₂₉	—	4	1	no	—
345	C₈×C₂₉	—	4	1	no	—
346	C₈×C₂₉	—	4	1	no	—
347	C₈×C₂₉	—	4	1	no	—
348	C₈×C₂₉	—	4	1	no	—
349	C₈×C₂₉	—	4	1	no	—
350	#3520	C₂×C₂₉	1	1	yes	characteristic, complemented
351	#3251	C₂×C₂₉	1	1	yes	characteristic, complemented
352	#3228	C₂×C₂₉	1	1	yes	characteristic, complemented
353	#3036	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#1654	C₂×C₂₉	1	1	yes	characteristic, complemented
355	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
356	#1650	C₂×C₂₉	1	1	yes	characteristic, complemented
357	#1647	C₂×C₂₉	1	1	yes	characteristic, complemented
358	#1628	C₂×C₂₉	1	1	yes	characteristic, complemented
359	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
360	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
361	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
362	#1561	C₂×C₂₉	1	1	yes	characteristic, complemented
363	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
364	#1486	C₂×C₂₉	1	1	yes	characteristic, complemented
365	C₂²×C₂₉	—	2	1	no	—
366	C₂²×C₂₉	—	2	2	no	—
367	C₂²×C₂₉	—	2	1	no	—
368	C₂²×C₂₉	—	2	1	no	—
369	C₂²×C₂₉	—	4	1	no	—
370	C₂²×C₂₉	—	4	1	no	—
371	C₂²×C₂₉	—	4	1	no	—
372	C₂²×C₂₉	—	4	1	no	—
373	C₂²×C₂₉	—	4	1	no	—
374	C₂²×C₂₉	—	4	1	no	—
375	C₂²×C₂₉	—	4	1	no	—
376	C₂²×C₂₉	—	4	1	no	—
377	C₂²×C₂₉	—	8	4	no	—
378	C₂²×C₂₉	—	8	1	no	—
379	C₂²×C₂₉	—	8	1	no	—
380	C₂²×C₂₉	—	8	1	no	—
381	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
382	C₄×C₂₉	—	2	1	no	—
383	C₄×C₂₉	—	2	1	no	—
384	C₄×C₂₉	—	2	1	no	—
385	C₄×C₂₉	—	2	1	no	—
386	C₄×C₂₉	—	4	1	no	—
387	C₄×C₂₉	—	4	2	no	—
388	C₄×C₂₉	—	4	1	no	—
389	C₄×C₂₉	—	4	1	no	—
390	C₄×C₂₉	—	4	2	no	—
391	C₄×C₂₉	—	4	1	no	—
392	C₄×C₂₉	—	4	1	no	—
393	C₄×C₂₉	—	8	1	no	—
394	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
395	C₄×C₂₉	#575	1	1	yes	characteristic
396	C₄×C₂₉	#576	1	1	yes	characteristic
397	C₄×C₂₉	#577	1	1	yes	characteristic
398	C₂×AGL(1,ℤ/8)	—	2	1	no	—
399	#556	C₂²×C₂₉	1	1	yes	characteristic
400	#554	—	2	1	no	—
401	#552	—	2	1	no	—
402	#551	—	2	2	no	—
403	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
404	#548	—	2	1	no	—
405	#547	C₂²×C₂₉	1	1	yes	characteristic
406	#547	C₂²×C₂₉	1	1	yes	characteristic
407	#546	—	2	1	no	—
408	#542	—	2	1	no	—
409	#539	—	2	2	no	—
410	#533	C₂²×C₂₉	1	1	yes	characteristic
411	#532	C₂²×C₂₉	1	1	yes	characteristic
412	#529	C₂²×C₂₉	1	1	yes	characteristic
413	#525	—	2	1	no	—
414	C₂×C₂²⋊Q₈	—	2	1	no	—
415	#520	—	2	1	no	—
416	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
417	#500	C₂²×C₂₉	1	1	yes	characteristic, complemented
418	#498	C₂²×C₂₉	1	1	yes	characteristic, complemented
419	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
420	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
421	#482	—	2	2	no	—
422	#478	—	2	2	no	—
423	#478	—	2	1	no	—
424	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
425	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
426	#469	—	2	1	no	—
427	#468	—	2	1	no	—
428	#463	—	2	1	no	—
429	#463	—	2	1	no	—
430	#463	—	2	1	no	—
431	#461	C₂²×C₂₉	1	1	yes	characteristic
432	#461	C₂²×C₂₉	1	1	yes	characteristic
433	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
434	#459	C₂²×C₂₉	1	1	yes	characteristic
435	#459	C₂²×C₂₉	1	1	yes	characteristic
436	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
437	#431	C₂²×C₂₉	1	1	yes	characteristic
438	#423	C₂²×C₂₉	1	1	yes	characteristic
439	#423	C₂²×C₂₉	1	1	yes	characteristic
440	#417	—	2	1	no	—
441	#332	C₂²×C₂₉	1	1	yes	characteristic, complemented
442	#332	C₂²×C₂₉	1	1	yes	characteristic, complemented
443	#332	C₂²×C₂₉	1	1	yes	characteristic, complemented
444	#332	C₂²×C₂₉	1	1	yes	characteristic, complemented
445	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
446	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
447	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
448	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
449	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
450	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
451	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
452	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
453	C₂×C₂₉	—	4	1	no	—
454	C₂×C₂₉	—	4	2	no	—
455	C₂×C₂₉	—	8	1	no	—
456	C₂×C₂₉	—	8	1	no	—
457	C₂×C₂₉	—	16	1	no	—
458	C₂×C₂₉	#3006	1	1	yes	characteristic
459	C₂×C₂₉	#3012	1	1	yes	characteristic
460	C₂×C₂₉	#3020	1	1	yes	characteristic
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂×#41	—	2	1	no	—
464	C₂²×Q₈	—	2	1	no	—
465	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
466	C₂³×C₄	—	2	1	no	—
467	AGL(1,ℤ/8)	—	4	4	no	—
468	C₂×SD₁₆	—	2	1	no	—
469	C₂×SD₁₆	—	2	1	no	—
470	C₂×SD₁₆	—	2	1	no	—
471	C₂×D₈	—	2	1	no	—
472	C₂×D₈	—	2	1	no	—
473	C₂×D₈	—	2	1	no	—
474	C₂×M₁₆	—	2	1	no	—
475	C₂×M₁₆	—	2	1	no	—
476	C₄⋊Q₈	—	2	1	no	—
477	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
480	#127	C₂³×C₂₉	1	1	yes	characteristic
481	#126	—	2	2	no	—
482	#126	—	2	2	no	—
483	#126	—	2	1	no	—
484	#125	—	2	2	no	—
485	#125	D₄×C₂₉	1	1	yes	characteristic
486	#125	D₄×C₂₉	1	2	yes	—
487	#124	—	2	2	no	—
488	#124	—	2	1	no	—
489	#124	—	2	1	no	—
490	#124	D₄×C₂₉	1	1	yes	characteristic
491	#123	—	2	2	no	—
492	#123	—	2	2	no	—
493	#123	—	2	1	no	—
494	#123	—	2	2	no	—
495	#123	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	—	2	1	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	1	no	—
506	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
507	#121	—	2	2	no	—
508	#121	—	2	1	no	—
509	#121	—	2	1	no	—
510	#121	—	2	1	no	—
511	#121	—	2	1	no	—
512	#121	D₄×C₂₉	1	1	yes	characteristic
513	#120	—	2	2	no	—
514	C₄×Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	—	2	1	no	—
526	C₄×D₄	—	2	1	no	—
527	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
528	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
529	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
530	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
531	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
532	#117	—	2	2	no	—
533	#117	—	2	1	no	—
534	#117	—	2	1	no	—
535	#117	D₄×C₂₉	1	2	yes	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
543	#107	—	2	1	no	—
544	#107	—	2	2	no	—
545	#106	—	2	1	no	—
546	#106	—	2	2	no	—
547	C₄⋊C₈	—	2	1	no	—
548	C₄⋊C₈	—	2	1	no	—
549	C₄⋊C₈	—	2	1	no	—
550	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#103	—	2	1	no	—
557	#102	—	2	1	no	—
558	#102	—	2	1	no	—
559	#102	—	2	1	no	—
560	#102	—	2	1	no	—
561	#102	—	2	1	no	—
562	#102	—	2	2	no	—
563	#102	—	2	2	no	—
564	C₂²⋊C₈	—	2	1	no	—
565	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
566	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
567	C₂₉	#18822	1	1	yes	characteristic, direct product factor, Sylow
568	C₂⁴	—	2	1	no	—
569	#41	—	4	2	no	—
570	#41	—	4	2	no	—
571	#41	—	4	2	no	—
572	#41	—	4	2	no	—
573	#41	—	8	1	no	—
574	#41	—	8	1	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	8	1	no	—
580	C₂×Q₈	—	8	1	no	—
581	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	4	1	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
593	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
594	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	8	1	no	—
606	C₂²×C₄	—	8	1	no	—
607	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
610	SD₁₆	—	4	2	no	—
611	SD₁₆	—	4	2	no	—
612	SD₁₆	—	8	1	no	—
613	D₈	—	4	2	no	—
614	D₈	—	4	2	no	—
615	D₈	—	8	1	no	—
616	M₁₆	—	4	2	no	—
617	M₁₆	—	8	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
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	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
643	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₄²	—	2	2	no	—
663	C₄²	—	2	2	no	—
664	C₄²	—	2	1	no	—
665	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
666	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
667	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
668	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	8	1	no	—
676	C₂³	C₂₉×#120	1	1	yes	characteristic
677	Q₈	—	2	1	no	—
678	Q₈	—	2	1	no	—
679	Q₈	—	4	1	no	—
680	Q₈	—	4	1	no	—
681	Q₈	—	4	1	no	—
682	Q₈	—	4	1	no	—
683	Q₈	—	4	1	no	—
684	Q₈	—	4	1	no	—
685	Q₈	—	8	2	no	—
686	D₄	—	2	1	no	—
687	D₄	—	2	1	no	—
688	D₄	—	2	1	no	—
689	D₄	—	2	1	no	—
690	D₄	—	2	1	no	—
691	D₄	—	4	2	no	—
692	D₄	—	4	2	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	8	2	no	—
700	D₄	—	8	2	no	—
701	D₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	8	1	no	—
723	C₂×C₄	—	8	1	no	—
724	C₂×C₄	—	8	2	no	—
725	C₂×C₄	—	8	1	no	—
726	C₂×C₄	—	8	2	no	—
727	C₂×C₄	—	8	2	no	—
728	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
729	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
730	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
734	C₈	—	4	1	no	—
735	C₈	—	4	1	no	—
736	C₈	—	4	1	no	—
737	C₈	—	4	1	no	—
738	C₈	—	4	1	no	—
739	C₈	—	4	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	1	no	—
752	C₂²	—	8	4	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
757	C₄	—	2	1	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	1	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	1	no	—
767	C₄	—	4	1	no	—
768	C₄	—	8	1	no	—
769	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
770	C₄	C₂₉×#575	1	1	yes	characteristic
771	C₄	C₂₉×#576	1	1	yes	characteristic
772	C₄	C₂₉×#577	1	1	yes	characteristic
773	C₂	—	4	1	no	—
774	C₂	—	4	2	no	—
775	C₂	—	8	1	no	—
776	C₂	—	8	1	no	—
777	C₂	—	16	1	no	—
778	C₂	C₂₉×#3006	1	1	yes	characteristic
779	C₂	C₂₉×#3012	1	1	yes	characteristic
780	C₂	C₂₉×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. C₂₉×#3520	C₂	semidirect
2. C₂₉×#3251	C₂	semidirect
3. C₂₉×#3228	C₂	semidirect
4. C₂₉×#3036	C₂	semidirect
5. C₂₉×#1654	C₂	semidirect
6. C₂₉×#1651	C₂	semidirect
7. C₂₉×#1650	C₂	semidirect
8. C₂₉×#1647	C₂	semidirect
9. C₂₉×#1628	C₂	semidirect
10. C₂₉×#1627	C₂	semidirect
11. C₂₉×#1625	C₂	semidirect
12. C₂₉×#1625	C₂	semidirect
13. C₂₉×#1561	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1486	C₂	semidirect
35. C₂₉×#500	C₂²	semidirect
36. C₂₉×#498	C₂²	semidirect
37. C₂₉×#486	C₂²	semidirect
38. C₂₉×#486	C₂²	semidirect
42. C₂₉×#475	C₂²	semidirect
43. C₂₉×#474	C₂²	semidirect
51. C₂₉×#460	C₂²	semidirect
54. C₂₉×#459	C₂²	semidirect
59. C₂₉×#332	C₂²	semidirect
60. C₂₉×#332	C₂²	semidirect
61. C₂₉×#332	C₂²	semidirect
62. C₂₉×#332	C₂²	semidirect
63. C₂₉×Q₈⋊C₈	C₂²	semidirect
64. C₂₉×Q₈⋊C₈	C₂²	semidirect
69. C₂₉×D₄⋊C₈	C₂²	semidirect
70. C₂₉×D₄⋊C₈	C₂²	semidirect
278. #18822	C₂₉	direct (N × H)
350. #3520	C₂×C₂₉	semidirect
351. #3251	C₂×C₂₉	semidirect
352. #3228	C₂×C₂₉	semidirect
353. #3036	C₂×C₂₉	semidirect
354. #1654	C₂×C₂₉	semidirect
355. #1651	C₂×C₂₉	semidirect
356. #1650	C₂×C₂₉	semidirect
357. #1647	C₂×C₂₉	semidirect
358. #1628	C₂×C₂₉	semidirect
359. #1627	C₂×C₂₉	semidirect
360. #1625	C₂×C₂₉	semidirect
361. #1625	C₂×C₂₉	semidirect
362. #1561	C₂×C₂₉	semidirect
363. #1495	C₂×C₂₉	semidirect
364. #1486	C₂×C₂₉	semidirect
417. #500	C₂²×C₂₉	semidirect
418. #498	C₂²×C₂₉	semidirect
419. #486	C₂²×C₂₉	semidirect
420. #486	C₂²×C₂₉	semidirect
424. #475	C₂²×C₂₉	semidirect
425. #474	C₂²×C₂₉	semidirect
433. #460	C₂²×C₂₉	semidirect
436. #459	C₂²×C₂₉	semidirect
441. #332	C₂²×C₂₉	semidirect
442. #332	C₂²×C₂₉	semidirect
443. #332	C₂²×C₂₉	semidirect
444. #332	C₂²×C₂₉	semidirect
445. Q₈⋊C₈	C₂²×C₂₉	semidirect
446. Q₈⋊C₈	C₂²×C₂₉	semidirect
451. D₄⋊C₈	C₂²×C₂₉	semidirect
452. D₄⋊C₈	C₂²×C₂₉	semidirect
567. C₂₉	#18822	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×#3520	2
C₂₉×#3251	2
C₂₉×#3228	2
C₂₉×#3036	2
C₂₉×#1654	2
C₂₉×#1651	2
C₂₉×#1650	2
C₂₉×#1647	2
C₂₉×#1628	2
C₂₉×#1627	2
C₂₉×#1625	2
C₂₉×#1561	2
C₂₉×#1495	2
C₂₉×#1486	2
#18822	29

Subgroups — C29×#18822 #20313722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18822 #20313722