Subgroups — C₂₉×#19808 #20314708

Order 7424.

624 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3381	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3359	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3335	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#3276	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1716	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1679	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1654	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1653	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#137	—	2	1	no	—
17	C₂₉×#557	C₂²	1	1	yes	characteristic
18	C₂₉×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#547	C₂²	1	1	yes	characteristic
21	C₂₉×#499	—	2	1	no	—
22	C₂₉×#498	C₂²	1	1	yes	characteristic
23	C₂₉×#498	C₂²	1	1	yes	characteristic
24	C₂₉×#498	C₂²	1	1	yes	characteristic
25	C₂₉×#494	C₂²	1	1	yes	characteristic
26	C₂₉×#487	—	2	1	no	—
27	C₂₉×#487	C₂²	1	1	yes	characteristic
28	C₂₉×#487	C₂²	1	1	yes	characteristic
29	C₂₉×#483	—	2	1	no	—
30	C₂₉×#481	—	2	1	no	—
31	C₂₉×#479	—	2	1	no	—
32	C₂₉×#478	—	2	1	no	—
33	C₂₉×#477	C₂²	1	1	yes	characteristic
34	C₂₉×#476	C₂²	1	1	yes	characteristic
35	C₂₉×#475	—	2	1	no	—
36	C₂₉×#475	C₂²	1	1	yes	characteristic
37	C₂₉×#475	C₂²	1	1	yes	characteristic
38	C₂₉×#474	C₂²	1	1	yes	characteristic
39	C₂₉×#470	—	2	1	no	—
40	C₂₉×#465	—	2	1	no	—
41	C₂₉×#462	C₂²	1	1	yes	characteristic
42	C₂₉×#461	—	2	1	no	—
43	C₂₉×#461	C₂²	1	1	yes	characteristic
44	C₂₉×#461	C₂²	1	1	yes	characteristic
45	C₂₉×#452	—	2	1	no	—
46	C₂₉×#451	—	2	1	no	—
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₂₉	—	2	1	no	—
50	C₄×SD₁₆×C₂₉	—	2	1	no	—
51	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#436	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#106	—	2	1	no	—
56	C₂₉×#335	C₂²	1	1	yes	characteristic
57	C₂₉×#334	C₂²	1	1	yes	characteristic
58	C₂₉×#333	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#332	C₂²	1	1	yes	characteristic
62	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂²×Q₈×C₂₉	—	2	1	no	—
69	C₂₉×#137	—	4	4	no	—
70	C₂×Q₁₆×C₂₉	—	2	1	no	—
71	C₂×Q₁₆×C₂₉	—	2	1	no	—
72	C₂×Q₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	2	1	no	—
74	C₂×SD₁₆×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
76	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
77	C₂×M₁₆×C₂₉	—	2	1	no	—
78	C₂²×C₈×C₂₉	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	—	2	1	no	—
80	C₂₉×C₄⋊Q₈	—	2	1	no	—
81	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₉×#125	—	2	1	no	—
86	C₂₉×#125	—	2	1	no	—
87	C₂₉×#125	—	4	1	no	—
88	C₂₉×#123	—	4	1	no	—
89	C₂₉×C₂²⋊Q₈	—	2	1	no	—
90	C₂₉×C₂²⋊Q₈	—	2	1	no	—
91	C₂₉×C₂²⋊Q₈	—	2	1	no	—
92	C₂₉×C₂²⋊Q₈	—	4	1	no	—
93	C₂₉×C₂²⋊Q₈	—	4	1	no	—
94	C₂₉×#121	—	2	1	no	—
95	C₄×Q₈×C₂₉	—	2	1	no	—
96	C₄×Q₈×C₂₉	—	2	1	no	—
97	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₂₉	—	2	1	no	—
100	C₄×D₄×C₂₉	—	2	1	no	—
101	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
102	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₂₉×#107	—	2	1	no	—
106	C₂₉×#107	—	2	1	no	—
107	C₂₉×#106	—	2	1	no	—
108	C₂₉×#106	—	2	1	no	—
109	C₂₉×#106	—	2	1	no	—
110	C₂₉×#106	—	2	1	no	—
111	C₂₉×#106	—	2	1	no	—
112	C₂₉×#106	—	2	1	no	—
113	C₂₉×#106	—	2	1	no	—
114	C₂₉×#106	—	4	1	no	—
115	C₂₉×#106	D₄	1	1	yes	characteristic
116	C₂₉×#106	D₄	1	1	yes	characteristic
117	C₂₉×C₄⋊C₈	—	2	1	no	—
118	C₂₉×C₄⋊C₈	—	2	1	no	—
119	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	2	1	no	—
125	C₂₉×#103	—	2	1	no	—
126	C₂₉×#103	—	2	1	no	—
127	C₂₉×#103	—	2	1	no	—
128	C₂₉×#103	—	2	1	no	—
129	C₂₉×#103	—	2	1	no	—
130	C₂₉×#103	—	2	1	no	—
131	C₂₉×#103	—	4	1	no	—
132	C₂₉×#103	D₄	1	1	yes	characteristic
133	C₂₉×#103	D₄	1	1	yes	characteristic
134	C₂₉×#102	—	2	1	no	—
135	C₂₉×#102	—	2	1	no	—
136	C₂₉×#102	D₄	1	1	yes	characteristic
137	C₂₉×#102	D₄	1	1	yes	characteristic
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×C₂²⋊C₈	—	2	1	no	—
140	C₄×C₈×C₂₉	—	2	1	no	—
141	C₄×C₈×C₂₉	—	2	1	no	—
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
145	#41×C₂₉	—	4	2	no	—
146	#41×C₂₉	—	8	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	—	4	1	no	—
152	C₂×Q₈×C₂₉	—	4	2	no	—
153	C₂×Q₈×C₂₉	—	8	1	no	—
154	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₂₉	—	4	1	no	—
157	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	4	1	no	—
162	C₂²×C₄×C₂₉	—	4	1	no	—
163	C₂²×C₄×C₂₉	—	4	1	no	—
164	Q₁₆×C₂₉	—	4	2	no	—
165	Q₁₆×C₂₉	—	4	2	no	—
166	Q₁₆×C₂₉	—	8	1	no	—
167	SD₁₆×C₂₉	—	4	1	no	—
168	SD₁₆×C₂₉	—	4	2	no	—
169	SD₁₆×C₂₉	—	4	2	no	—
170	SD₁₆×C₂₉	SD₁₆	1	4	yes	complemented
171	M₁₆×C₂₉	—	4	2	no	—
172	C₂×C₈×C₂₉	—	2	1	no	—
173	C₂×C₈×C₂₉	—	2	1	no	—
174	C₂×C₈×C₂₉	—	2	1	no	—
175	C₂×C₈×C₂₉	—	2	1	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	—	4	2	no	—
178	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	1	no	—
189	C₄⋊C₄×C₂₉	—	2	1	no	—
190	C₄⋊C₄×C₂₉	—	2	1	no	—
191	C₄⋊C₄×C₂₉	—	2	1	no	—
192	C₄⋊C₄×C₂₉	—	4	1	no	—
193	C₄⋊C₄×C₂₉	—	4	1	no	—
194	C₄⋊C₄×C₂₉	—	4	1	no	—
195	C₄⋊C₄×C₂₉	—	4	1	no	—
196	C₄⋊C₄×C₂₉	—	4	1	no	—
197	C₄⋊C₄×C₂₉	—	4	1	no	—
198	C₄⋊C₄×C₂₉	—	4	1	no	—
199	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂²⋊C₄×C₂₉	—	2	1	no	—
204	C₂²⋊C₄×C₂₉	—	2	1	no	—
205	C₂²⋊C₄×C₂₉	—	4	1	no	—
206	C₂²⋊C₄×C₂₉	—	4	1	no	—
207	C₂²⋊C₄×C₂₉	—	4	1	no	—
208	C₄²×C₂₉	—	2	1	no	—
209	C₄²×C₂₉	—	2	1	no	—
210	C₄²×C₂₉	—	4	1	no	—
211	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
212	#19808	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₂₉	—	2	1	no	—
214	C₂³×C₂₉	—	2	1	no	—
215	Q₈×C₂₉	—	2	1	no	—
216	Q₈×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	2	1	no	—
218	Q₈×C₂₉	—	4	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	4	1	no	—
223	Q₈×C₂₉	—	4	1	no	—
224	Q₈×C₂₉	—	8	2	no	—
225	Q₈×C₂₉	—	8	1	no	—
226	Q₈×C₂₉	C₂×SD₁₆	1	2	yes	—
227	D₄×C₂₉	—	2	1	no	—
228	D₄×C₂₉	—	2	1	no	—
229	D₄×C₂₉	—	2	1	no	—
230	D₄×C₂₉	—	8	2	no	—
231	D₄×C₂₉	C₂×SD₁₆	1	2	yes	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	1	no	—
234	C₂×C₄×C₂₉	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	4	1	no	—
239	C₂×C₄×C₂₉	—	4	1	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	8	2	no	—
247	C₂×C₄×C₂₉	—	8	2	no	—
248	C₂×C₄×C₂₉	—	16	1	no	—
249	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
252	C₈×C₂₉	—	2	1	no	—
253	C₈×C₂₉	—	2	1	no	—
254	C₈×C₂₉	—	2	1	no	—
255	C₈×C₂₉	—	4	1	no	—
256	C₈×C₂₉	—	4	1	no	—
257	C₈×C₂₉	—	4	1	no	—
258	C₈×C₂₉	—	4	1	no	—
259	C₈×C₂₉	—	4	1	no	—
260	C₈×C₂₉	C₂×SD₁₆	1	2	yes	—
261	#3381	C₂×C₂₉	1	1	yes	characteristic, complemented
262	#3359	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#3335	C₂×C₂₉	1	1	yes	characteristic
264	#3276	C₂×C₂₉	1	1	yes	characteristic
265	#1716	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1691	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1679	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1672	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1670	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1654	C₂×C₂₉	1	1	yes	characteristic
271	#1653	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1643	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1583	C₂×C₂₉	1	1	yes	characteristic, complemented
275	SD₁₆⋊C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
276	C₂²×C₂₉	—	2	2	no	—
277	C₂²×C₂₉	—	4	1	no	—
278	C₂²×C₂₉	—	4	1	no	—
279	C₂²×C₂₉	—	4	1	no	—
280	C₂²×C₂₉	—	4	1	no	—
281	C₂²×C₂₉	—	4	1	no	—
282	C₂²×C₂₉	D₄²	1	1	yes	characteristic
283	C₄×C₂₉	—	2	2	no	—
284	C₄×C₂₉	—	2	1	no	—
285	C₄×C₂₉	—	4	1	no	—
286	C₄×C₂₉	—	4	1	no	—
287	C₄×C₂₉	—	4	1	no	—
288	C₄×C₂₉	—	4	1	no	—
289	C₄×C₂₉	—	4	1	no	—
290	C₄×C₂₉	—	8	1	no	—
291	C₄×C₂₉	—	8	1	no	—
292	C₄×C₂₉	—	8	1	no	—
293	C₄×C₂₉	—	8	1	no	—
294	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
295	C₄×C₂₉	#575	1	1	yes	characteristic
296	C₄×C₂₉	#577	1	1	yes	characteristic
297	C₄×C₂₉	#578	1	1	yes	characteristic
298	C₂×#137	—	2	1	no	—
299	#557	C₂²×C₂₉	1	1	yes	characteristic
300	#554	C₂²×C₂₉	1	1	yes	characteristic
301	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
302	#547	C₂²×C₂₉	1	1	yes	characteristic
303	#499	—	2	1	no	—
304	#498	C₂²×C₂₉	1	1	yes	characteristic
305	#498	C₂²×C₂₉	1	1	yes	characteristic
306	#498	C₂²×C₂₉	1	1	yes	characteristic
307	#494	C₂²×C₂₉	1	1	yes	characteristic
308	#487	—	2	1	no	—
309	#487	C₂²×C₂₉	1	1	yes	characteristic
310	#487	C₂²×C₂₉	1	1	yes	characteristic
311	#483	—	2	1	no	—
312	#481	—	2	1	no	—
313	#479	—	2	1	no	—
314	#478	—	2	1	no	—
315	#477	C₂²×C₂₉	1	1	yes	characteristic
316	#476	C₂²×C₂₉	1	1	yes	characteristic
317	#475	—	2	1	no	—
318	#475	C₂²×C₂₉	1	1	yes	characteristic
319	#475	C₂²×C₂₉	1	1	yes	characteristic
320	#474	C₂²×C₂₉	1	1	yes	characteristic
321	#470	—	2	1	no	—
322	#465	—	2	1	no	—
323	#462	C₂²×C₂₉	1	1	yes	characteristic
324	#461	—	2	1	no	—
325	#461	C₂²×C₂₉	1	1	yes	characteristic
326	#461	C₂²×C₂₉	1	1	yes	characteristic
327	#452	—	2	1	no	—
328	#451	—	2	1	no	—
329	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
330	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
331	C₄×SD₁₆	—	2	1	no	—
332	C₄×SD₁₆	—	2	1	no	—
333	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
334	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
335	#436	C₂²×C₂₉	1	1	yes	characteristic
336	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×#106	—	2	1	no	—
338	#335	C₂²×C₂₉	1	1	yes	characteristic
339	#334	C₂²×C₂₉	1	1	yes	characteristic
340	#333	C₂²×C₂₉	1	1	yes	characteristic
341	#332	C₂²×C₂₉	1	1	yes	characteristic
342	#332	C₂²×C₂₉	1	1	yes	characteristic
343	#332	C₂²×C₂₉	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
345	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
346	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
347	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
348	#322	C₂²×C₂₉	1	1	yes	characteristic
349	C₂×C₂₉	—	4	2	no	—
350	C₂×C₂₉	—	8	1	no	—
351	C₂×C₂₉	#3269	1	1	yes	characteristic
352	C₂×C₂₉	D₄×SD₁₆	1	1	yes	characteristic
353	C₂×C₂₉	#3289	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂²×Q₈	—	2	1	no	—
356	#137	—	4	4	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×Q₁₆	—	2	1	no	—
359	C₂×Q₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
363	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
364	C₂×M₁₆	—	2	1	no	—
365	C₂²×C₈	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#125	—	4	1	no	—
375	#123	—	4	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	4	1	no	—
380	C₂²⋊Q₈	—	4	1	no	—
381	#121	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
385	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
389	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	#107	—	2	1	no	—
393	#107	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	4	1	no	—
402	#106	D₄×C₂₉	1	1	yes	characteristic
403	#106	D₄×C₂₉	1	1	yes	characteristic
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	4	1	no	—
419	#103	D₄×C₂₉	1	1	yes	characteristic
420	#103	D₄×C₂₉	1	1	yes	characteristic
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	D₄×C₂₉	1	1	yes	characteristic
424	#102	D₄×C₂₉	1	1	yes	characteristic
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
432	C₂₉	#19808	1	1	yes	characteristic, direct product factor, Sylow
433	#41	—	4	2	no	—
434	#41	—	8	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	4	1	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	8	1	no	—
442	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
443	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
446	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	Q₁₆	—	4	2	no	—
453	Q₁₆	—	4	2	no	—
454	Q₁₆	—	8	1	no	—
455	SD₁₆	—	4	1	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	4	2	no	—
458	SD₁₆	SD₁₆×C₂₉	1	4	yes	complemented
459	M₁₆	—	4	2	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	4	2	no	—
466	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
469	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₄⋊C₄	—	4	1	no	—
483	C₄⋊C₄	—	4	1	no	—
484	C₄⋊C₄	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
488	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	4	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	4	1	no	—
499	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	8	2	no	—
512	Q₈	—	8	1	no	—
513	Q₈	C₂×SD₁₆×C₂₉	1	2	yes	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	2	1	no	—
517	D₄	—	8	2	no	—
518	D₄	C₂×SD₁₆×C₂₉	1	2	yes	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	16	1	no	—
536	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
538	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	C₂×SD₁₆×C₂₉	1	2	yes	—
548	C₂²	—	2	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	D₄²×C₂₉	1	1	yes	characteristic
555	C₄	—	2	2	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
567	C₄	C₂₉×#575	1	1	yes	characteristic
568	C₄	C₂₉×#577	1	1	yes	characteristic
569	C₄	C₂₉×#578	1	1	yes	characteristic
570	C₂	—	4	2	no	—
571	C₂	—	8	1	no	—
572	C₂	C₂₉×#3269	1	1	yes	characteristic
573	C₂	D₄×SD₁₆×C₂₉	1	1	yes	characteristic
574	C₂	C₂₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#547	C₂²
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. C₂₉×#3381	C₂	semidirect
2. C₂₉×#3359	C₂	semidirect
5. C₂₉×#1716	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1679	C₂	semidirect
8. C₂₉×#1672	C₂	semidirect
9. C₂₉×#1670	C₂	semidirect
11. C₂₉×#1653	C₂	semidirect
12. C₂₉×#1643	C₂	semidirect
13. C₂₉×#1637	C₂	semidirect
14. C₂₉×#1583	C₂	semidirect
15. C₂₉×SD₁₆⋊C₈	C₂	semidirect
170. SD₁₆×C₂₉	SD₁₆	semidirect
212. #19808	C₂₉	direct (N × H)
261. #3381	C₂×C₂₉	semidirect
262. #3359	C₂×C₂₉	semidirect
265. #1716	C₂×C₂₉	semidirect
266. #1691	C₂×C₂₉	semidirect
267. #1679	C₂×C₂₉	semidirect
268. #1672	C₂×C₂₉	semidirect
269. #1670	C₂×C₂₉	semidirect
271. #1653	C₂×C₂₉	semidirect
272. #1643	C₂×C₂₉	semidirect
273. #1637	C₂×C₂₉	semidirect
274. #1583	C₂×C₂₉	semidirect
275. SD₁₆⋊C₈	C₂×C₂₉	semidirect
432. C₂₉	#19808	direct (N × H)
458. SD₁₆	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×#3381	2
C₂₉×#3359	2
C₂₉×#3335	2
C₂₉×#3276	2
C₂₉×#1716	2
C₂₉×#1691	2
C₂₉×#1679	2
C₂₉×#1672	2
C₂₉×#1670	2
C₂₉×#1654	2
C₂₉×#1653	2
C₂₉×#1643	2
C₂₉×#1637	2
C₂₉×#1583	2
C₂₉×SD₁₆⋊C₈	2
#19808	29

Subgroups — C29×#19808 #20314708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19808 #20314708