Subgroups — C₂₉×#28937 #20323837

Order 7424.

770 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3136	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3063	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3062	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2061	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2040	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2004	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2003	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
20	C₂₉×#544	C₂²	1	1	yes	characteristic
21	C₂₉×#537	C₂²	1	1	yes	characteristic
22	C₂₉×#536	C₂²	1	1	yes	characteristic
23	C₂₉×#535	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
25	C₂₉×#491	—	2	1	no	—
26	C₂₉×#490	—	2	1	no	—
27	C₂₉×#489	—	2	1	no	—
28	C₂₉×#489	—	2	1	no	—
29	C₂₉×#488	—	2	1	no	—
30	C₂₉×#488	—	2	1	no	—
31	C₂₉×#487	—	2	1	no	—
32	C₂₉×#486	—	2	1	no	—
33	C₂₉×#470	—	2	1	no	—
34	C₂₉×#469	—	2	1	no	—
35	C₂₉×#468	—	2	1	no	—
36	C₂₉×#468	—	2	1	no	—
37	C₂₉×#467	—	2	1	no	—
38	C₂₉×#466	—	2	1	no	—
39	C₂₉×#465	—	2	1	no	—
40	C₂₉×#465	—	2	1	no	—
41	C₂₉×#428	C₂²	1	1	yes	characteristic
42	C₂₉×#428	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
45	C₂₉×#419	C₂²	1	1	yes	characteristic
46	C₂₉×#418	C₂²	1	1	yes	characteristic
47	C₂₉×#417	C₂²	1	1	yes	characteristic
48	C₂₉×#417	C₂²	1	1	yes	characteristic
49	C₂₉×#416	C₂²	1	1	yes	characteristic
50	C₂₉×#416	C₂²	1	1	yes	characteristic
51	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
53	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
56	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
57	C₂₉×#405	C₂²	1	1	yes	characteristic
58	C₂₉×#405	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
60	C₂₉×#382	C₂²	1	1	yes	characteristic
61	C₂₉×#343	C₂²	1	1	yes	characteristic
62	C₂₉×#343	C₂²	1	1	yes	characteristic
63	C₂₉×#341	C₂²	1	1	yes	characteristic
64	C₂₉×#341	C₂²	1	1	yes	characteristic
65	C₂₉×#339	C₂²	1	1	yes	characteristic
66	C₂₉×#339	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
68	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂₉×#137	—	2	2	no	—
72	C₂₉×#137	—	4	1	no	—
73	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
74	C₂₉×AGL(1,ℤ/8)	—	4	1	no	—
75	C₂×Q₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×D₈×C₂₉	—	2	1	no	—
79	C₂₉×#131	—	2	2	no	—
80	C₂₉×#131	—	2	2	no	—
81	C₂₉×#131	—	4	1	no	—
82	C₂₉×#131	—	4	1	no	—
83	C₂×M₁₆×C₂₉	—	2	1	no	—
84	C₂×M₁₆×C₂₉	—	2	1	no	—
85	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₂₉	—	2	1	no	—
90	C₂²×C₈×C₂₉	—	2	1	no	—
91	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
93	C₂₉×C₄⋊Q₈	—	2	1	no	—
94	C₂₉×C₄⋊Q₈	—	2	1	no	—
95	C₂₉×C₄⋊Q₈	—	2	1	no	—
96	C₂₉×#127	—	2	1	no	—
97	C₂₉×#125	—	2	1	no	—
98	C₂₉×#125	—	2	1	no	—
99	C₂₉×#124	—	2	1	no	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	—	2	2	no	—
102	C₂₉×#124	—	4	1	no	—
103	C₂₉×#123	—	4	1	no	—
104	C₂₉×C₂²⋊Q₈	—	2	1	no	—
105	C₂₉×C₂²⋊Q₈	—	2	1	no	—
106	C₂₉×C₂²⋊Q₈	—	2	1	no	—
107	C₂₉×C₂²⋊Q₈	—	2	1	no	—
108	C₂₉×C₂²⋊Q₈	—	4	1	no	—
109	C₂₉×#121	—	2	1	no	—
110	C₂₉×#121	—	2	1	no	—
111	C₂₉×#121	—	2	1	no	—
112	C₂₉×#121	—	2	1	no	—
113	C₂₉×#121	—	4	1	no	—
114	C₂₉×#120	—	4	1	no	—
115	C₂₉×#117	C₂³	1	1	yes	characteristic
116	C₂₉×#117	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
120	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
121	C₂₉×#107	—	2	1	no	—
122	C₂₉×#107	—	2	1	no	—
123	C₂₉×#106	—	2	1	no	—
124	C₂₉×#106	—	2	1	no	—
125	C₂₉×#104	—	2	2	no	—
126	C₂₉×#104	—	2	2	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	—	2	1	no	—
132	C₂₉×#103	—	2	1	no	—
133	C₂₉×#103	—	2	1	no	—
134	C₂₉×#103	—	2	1	no	—
135	C₂₉×#103	D₄	1	1	yes	characteristic
136	C₂₉×#103	D₄	1	1	yes	characteristic
137	C₂₉×#103	D₄	1	1	yes	characteristic
138	C₂₉×#103	D₄	1	1	yes	characteristic
139	C₂₉×#102	—	2	1	no	—
140	C₂₉×#102	—	2	1	no	—
141	C₂₉×#102	—	2	1	no	—
142	C₂₉×#102	—	2	1	no	—
143	C₂₉×#102	—	2	1	no	—
144	C₂₉×#102	—	2	1	no	—
145	C₂₉×#102	—	2	1	no	—
146	C₂₉×#102	—	2	1	no	—
147	C₂₉×#102	D₄	1	1	yes	characteristic
148	C₂₉×#102	D₄	1	1	yes	characteristic
149	C₂₉×#102	D₄	1	1	yes	characteristic
150	C₂₉×#102	D₄	1	1	yes	characteristic
151	C₂₉×#101	—	2	2	no	—
152	C₂₉×#100	—	2	2	no	—
153	C₂₉×#97	—	2	1	no	—
154	C₂₉×#97	—	2	1	no	—
155	C₄×C₈×C₂₉	—	2	1	no	—
156	C₄×C₈×C₂₉	—	2	1	no	—
157	C₄×C₈×C₂₉	—	4	1	no	—
158	C₂₉×#95	—	4	1	no	—
159	C₂⁴×C₂₉	—	2	1	no	—
160	#41×C₂₉	—	2	1	no	—
161	#41×C₂₉	—	2	1	no	—
162	#41×C₂₉	—	2	1	no	—
163	#41×C₂₉	—	2	1	no	—
164	#41×C₂₉	—	2	1	no	—
165	#41×C₂₉	—	2	1	no	—
166	#41×C₂₉	—	2	1	no	—
167	#41×C₂₉	—	2	1	no	—
168	C₂×Q₈×C₂₉	—	2	1	no	—
169	C₂×Q₈×C₂₉	—	2	1	no	—
170	C₂×Q₈×C₂₉	—	2	1	no	—
171	C₂×Q₈×C₂₉	—	2	1	no	—
172	C₂×Q₈×C₂₉	—	2	1	no	—
173	C₂×Q₈×C₂₉	—	2	1	no	—
174	C₂×Q₈×C₂₉	—	4	1	no	—
175	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₂₉	—	2	1	no	—
178	C₂×D₄×C₂₉	—	2	1	no	—
179	C₂×D₄×C₂₉	—	2	1	no	—
180	C₂×D₄×C₂₉	—	2	1	no	—
181	C₂×D₄×C₂₉	—	2	1	no	—
182	C₂×D₄×C₂₉	—	2	1	no	—
183	C₂×D₄×C₂₉	—	2	1	no	—
184	C₂×D₄×C₂₉	—	2	1	no	—
185	C₂×D₄×C₂₉	—	4	1	no	—
186	C₂×D₄×C₂₉	—	4	1	no	—
187	C₂×D₄×C₂₉	—	4	1	no	—
188	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₂₉	—	2	1	no	—
191	C₂²×C₄×C₂₉	—	2	1	no	—
192	C₂²×C₄×C₂₉	—	2	1	no	—
193	C₂²×C₄×C₂₉	—	2	1	no	—
194	C₂²×C₄×C₂₉	—	2	1	no	—
195	C₂²×C₄×C₂₉	—	2	1	no	—
196	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
197	Q₁₆×C₂₉	—	4	2	no	—
198	SD₁₆×C₂₉	—	4	2	no	—
199	SD₁₆×C₂₉	—	4	2	no	—
200	D₈×C₂₉	—	4	2	no	—
201	M₁₆×C₂₉	—	2	1	no	—
202	M₁₆×C₂₉	—	2	1	no	—
203	M₁₆×C₂₉	—	2	1	no	—
204	M₁₆×C₂₉	—	2	1	no	—
205	M₁₆×C₂₉	—	2	1	no	—
206	M₁₆×C₂₉	—	2	1	no	—
207	M₁₆×C₂₉	—	4	2	no	—
208	M₁₆×C₂₉	—	4	2	no	—
209	M₁₆×C₂₉	#41	1	2	yes	—
210	M₁₆×C₂₉	#41	1	2	yes	—
211	C₂×C₈×C₂₉	—	2	1	no	—
212	C₂×C₈×C₂₉	—	2	1	no	—
213	C₂×C₈×C₂₉	—	2	1	no	—
214	C₂×C₈×C₂₉	—	2	1	no	—
215	C₂×C₈×C₂₉	—	2	1	no	—
216	C₂×C₈×C₂₉	—	2	1	no	—
217	C₂×C₈×C₂₉	—	2	1	no	—
218	C₂×C₈×C₂₉	—	2	1	no	—
219	C₂×C₈×C₂₉	—	4	2	no	—
220	C₂×C₈×C₂₉	—	4	2	no	—
221	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
222	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
223	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
224	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
225	C₄⋊C₄×C₂₉	—	2	1	no	—
226	C₄⋊C₄×C₂₉	—	2	1	no	—
227	C₄⋊C₄×C₂₉	—	2	1	no	—
228	C₄⋊C₄×C₂₉	—	2	1	no	—
229	C₄⋊C₄×C₂₉	—	4	1	no	—
230	C₄⋊C₄×C₂₉	—	4	1	no	—
231	C₄⋊C₄×C₂₉	—	4	1	no	—
232	C₄⋊C₄×C₂₉	—	4	1	no	—
233	C₄⋊C₄×C₂₉	—	4	1	no	—
234	C₄⋊C₄×C₂₉	—	4	1	no	—
235	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
236	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
237	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
238	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
239	C₂²⋊C₄×C₂₉	—	2	1	no	—
240	C₂²⋊C₄×C₂₉	—	2	1	no	—
241	C₂²⋊C₄×C₂₉	—	4	1	no	—
242	C₂²⋊C₄×C₂₉	—	4	1	no	—
243	C₂²⋊C₄×C₂₉	—	4	1	no	—
244	C₂²⋊C₄×C₂₉	—	4	1	no	—
245	C₂²⋊C₄×C₂₉	—	4	1	no	—
246	C₂²⋊C₄×C₂₉	—	4	1	no	—
247	C₂²⋊C₄×C₂₉	—	4	4	no	—
248	C₄²×C₂₉	—	2	1	no	—
249	C₄²×C₂₉	—	2	1	no	—
250	C₄²×C₂₉	—	2	1	no	—
251	C₄²×C₂₉	#41	1	2	yes	—
252	#28937	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂³×C₂₉	—	2	1	no	—
254	C₂³×C₂₉	—	2	1	no	—
255	C₂³×C₂₉	—	4	1	no	—
256	C₂³×C₂₉	—	4	1	no	—
257	C₂³×C₂₉	—	4	1	no	—
258	C₂³×C₂₉	—	8	1	no	—
259	C₂³×C₂₉	—	8	1	no	—
260	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
261	Q₈×C₂₉	—	2	1	no	—
262	Q₈×C₂₉	—	2	1	no	—
263	Q₈×C₂₉	—	2	1	no	—
264	Q₈×C₂₉	—	2	1	no	—
265	Q₈×C₂₉	—	4	1	no	—
266	Q₈×C₂₉	—	4	1	no	—
267	Q₈×C₂₉	—	4	1	no	—
268	Q₈×C₂₉	—	4	1	no	—
269	Q₈×C₂₉	—	16	1	no	—
270	D₄×C₂₉	—	2	1	no	—
271	D₄×C₂₉	—	2	1	no	—
272	D₄×C₂₉	—	2	1	no	—
273	D₄×C₂₉	—	2	1	no	—
274	D₄×C₂₉	—	4	1	no	—
275	D₄×C₂₉	—	4	1	no	—
276	D₄×C₂₉	—	4	1	no	—
277	D₄×C₂₉	—	4	1	no	—
278	D₄×C₂₉	—	4	1	no	—
279	D₄×C₂₉	—	4	1	no	—
280	D₄×C₂₉	—	4	1	no	—
281	D₄×C₂₉	—	4	1	no	—
282	D₄×C₂₉	—	16	1	no	—
283	D₄×C₂₉	—	16	1	no	—
284	D₄×C₂₉	—	16	1	no	—
285	C₂×C₄×C₂₉	—	2	2	no	—
286	C₂×C₄×C₂₉	—	2	1	no	—
287	C₂×C₄×C₂₉	—	2	1	no	—
288	C₂×C₄×C₂₉	—	2	1	no	—
289	C₂×C₄×C₂₉	—	2	1	no	—
290	C₂×C₄×C₂₉	—	2	1	no	—
291	C₂×C₄×C₂₉	—	2	1	no	—
292	C₂×C₄×C₂₉	—	4	1	no	—
293	C₂×C₄×C₂₉	—	4	1	no	—
294	C₂×C₄×C₂₉	—	4	1	no	—
295	C₂×C₄×C₂₉	—	4	1	no	—
296	C₂×C₄×C₂₉	—	4	1	no	—
297	C₂×C₄×C₂₉	—	4	1	no	—
298	C₂×C₄×C₂₉	—	4	1	no	—
299	C₂×C₄×C₂₉	—	4	1	no	—
300	C₂×C₄×C₂₉	—	4	1	no	—
301	C₂×C₄×C₂₉	—	4	1	no	—
302	C₂×C₄×C₂₉	—	4	1	no	—
303	C₂×C₄×C₂₉	—	8	1	no	—
304	C₂×C₄×C₂₉	—	8	1	no	—
305	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
311	C₈×C₂₉	—	2	1	no	—
312	C₈×C₂₉	—	2	1	no	—
313	C₈×C₂₉	—	2	1	no	—
314	C₈×C₂₉	—	2	1	no	—
315	C₈×C₂₉	—	2	2	no	—
316	C₈×C₂₉	—	2	2	no	—
317	C₈×C₂₉	—	4	1	no	—
318	C₈×C₂₉	—	4	1	no	—
319	#3137	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#3136	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#3063	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#3062	C₂×C₂₉	1	1	yes	characteristic
323	#2061	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#2040	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#2004	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#2003	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1958	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1931	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1930	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1908	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#1907	C₂×C₂₉	1	1	yes	characteristic, complemented
332	#1764	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1764	C₂×C₂₉	1	1	yes	characteristic, complemented
334	C₂²×C₂₉	—	2	1	no	—
335	C₂²×C₂₉	—	2	1	no	—
336	C₂²×C₂₉	—	4	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	—	4	1	no	—
339	C₂²×C₂₉	—	4	1	no	—
340	C₂²×C₂₉	—	4	1	no	—
341	C₂²×C₂₉	—	4	1	no	—
342	C₂²×C₂₉	—	8	2	no	—
343	C₂²×C₂₉	—	8	1	no	—
344	C₂²×C₂₉	—	8	1	no	—
345	C₂²×C₂₉	—	8	1	no	—
346	C₂²×C₂₉	—	16	1	no	—
347	C₂²×C₂₉	#538	1	1	yes	characteristic
348	C₂²×C₂₉	D₄²	1	1	yes	characteristic
349	C₂²×C₂₉	#555	1	1	yes	characteristic
350	C₄×C₂₉	—	4	2	no	—
351	C₄×C₂₉	—	4	1	no	—
352	C₄×C₂₉	—	4	1	no	—
353	C₄×C₂₉	—	4	1	no	—
354	C₄×C₂₉	—	4	1	no	—
355	C₄×C₂₉	—	4	1	no	—
356	C₄×C₂₉	—	4	1	no	—
357	C₄×C₂₉	—	8	1	no	—
358	C₄×C₂₉	—	8	1	no	—
359	C₄×C₂₉	—	8	1	no	—
360	C₄×C₂₉	#532	1	1	yes	characteristic
361	C₄×C₂₉	#532	1	1	yes	characteristic
362	C₄×C₂₉	#546	1	1	yes	characteristic
363	C₄×C₂₉	#546	1	1	yes	characteristic
364	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
365	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
368	#544	C₂²×C₂₉	1	1	yes	characteristic
369	#537	C₂²×C₂₉	1	1	yes	characteristic
370	#536	C₂²×C₂₉	1	1	yes	characteristic
371	#535	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
373	#491	—	2	1	no	—
374	#490	—	2	1	no	—
375	#489	—	2	1	no	—
376	#489	—	2	1	no	—
377	#488	—	2	1	no	—
378	#488	—	2	1	no	—
379	#487	—	2	1	no	—
380	#486	—	2	1	no	—
381	#470	—	2	1	no	—
382	#469	—	2	1	no	—
383	#468	—	2	1	no	—
384	#468	—	2	1	no	—
385	#467	—	2	1	no	—
386	#466	—	2	1	no	—
387	#465	—	2	1	no	—
388	#465	—	2	1	no	—
389	#428	C₂²×C₂₉	1	1	yes	characteristic
390	#428	C₂²×C₂₉	1	1	yes	characteristic
391	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
392	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
393	#419	C₂²×C₂₉	1	1	yes	characteristic
394	#418	C₂²×C₂₉	1	1	yes	characteristic
395	#417	C₂²×C₂₉	1	1	yes	characteristic
396	#417	C₂²×C₂₉	1	1	yes	characteristic
397	#416	C₂²×C₂₉	1	1	yes	characteristic
398	#416	C₂²×C₂₉	1	1	yes	characteristic
399	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
400	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
401	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
402	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
403	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
404	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
405	#405	C₂²×C₂₉	1	1	yes	characteristic
406	#405	C₂²×C₂₉	1	1	yes	characteristic
407	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
408	#382	C₂²×C₂₉	1	1	yes	characteristic
409	#343	C₂²×C₂₉	1	1	yes	characteristic
410	#343	C₂²×C₂₉	1	1	yes	characteristic
411	#341	C₂²×C₂₉	1	1	yes	characteristic
412	#341	C₂²×C₂₉	1	1	yes	characteristic
413	#339	C₂²×C₂₉	1	1	yes	characteristic
414	#339	C₂²×C₂₉	1	1	yes	characteristic
415	C₂×C₂₉	—	2	1	no	—
416	C₂×C₂₉	—	2	1	no	—
417	C₂×C₂₉	—	8	1	no	—
418	C₂×C₂₉	—	8	1	no	—
419	C₂×C₂₉	—	16	1	no	—
420	C₂×C₂₉	#2555	1	1	yes	characteristic
421	C₂×C₂₉	#3290	1	1	yes	characteristic
422	C₂×C₂₉	#3290	1	1	yes	characteristic
423	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
424	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
425	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
426	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
427	#137	—	2	2	no	—
428	#137	—	4	1	no	—
429	AGL(1,ℤ/8)	—	2	2	no	—
430	AGL(1,ℤ/8)	—	4	1	no	—
431	C₂×Q₁₆	—	2	1	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×SD₁₆	—	2	1	no	—
434	C₂×D₈	—	2	1	no	—
435	#131	—	2	2	no	—
436	#131	—	2	2	no	—
437	#131	—	4	1	no	—
438	#131	—	4	1	no	—
439	C₂×M₁₆	—	2	1	no	—
440	C₂×M₁₆	—	2	1	no	—
441	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
442	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
444	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
445	C₂²×C₈	—	2	1	no	—
446	C₂²×C₈	—	2	1	no	—
447	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
449	C₄⋊Q₈	—	2	1	no	—
450	C₄⋊Q₈	—	2	1	no	—
451	C₄⋊Q₈	—	2	1	no	—
452	#127	—	2	1	no	—
453	#125	—	2	1	no	—
454	#125	—	2	1	no	—
455	#124	—	2	1	no	—
456	#124	—	2	1	no	—
457	#124	—	2	2	no	—
458	#124	—	4	1	no	—
459	#123	—	4	1	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	—	2	1	no	—
463	C₂²⋊Q₈	—	2	1	no	—
464	C₂²⋊Q₈	—	4	1	no	—
465	#121	—	2	1	no	—
466	#121	—	2	1	no	—
467	#121	—	2	1	no	—
468	#121	—	2	1	no	—
469	#121	—	4	1	no	—
470	#120	—	4	1	no	—
471	#117	C₂³×C₂₉	1	1	yes	characteristic
472	#117	C₂³×C₂₉	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
475	C₂×C₂²⋊C₄	—	4	1	no	—
476	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
477	#107	—	2	1	no	—
478	#107	—	2	1	no	—
479	#106	—	2	1	no	—
480	#106	—	2	1	no	—
481	#104	—	2	2	no	—
482	#104	—	2	2	no	—
483	#103	—	2	1	no	—
484	#103	—	2	1	no	—
485	#103	—	2	1	no	—
486	#103	—	2	1	no	—
487	#103	—	2	1	no	—
488	#103	—	2	1	no	—
489	#103	—	2	1	no	—
490	#103	—	2	1	no	—
491	#103	D₄×C₂₉	1	1	yes	characteristic
492	#103	D₄×C₂₉	1	1	yes	characteristic
493	#103	D₄×C₂₉	1	1	yes	characteristic
494	#103	D₄×C₂₉	1	1	yes	characteristic
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	#102	—	2	1	no	—
498	#102	—	2	1	no	—
499	#102	—	2	1	no	—
500	#102	—	2	1	no	—
501	#102	—	2	1	no	—
502	#102	—	2	1	no	—
503	#102	D₄×C₂₉	1	1	yes	characteristic
504	#102	D₄×C₂₉	1	1	yes	characteristic
505	#102	D₄×C₂₉	1	1	yes	characteristic
506	#102	D₄×C₂₉	1	1	yes	characteristic
507	#101	—	2	2	no	—
508	#100	—	2	2	no	—
509	#97	—	2	1	no	—
510	#97	—	2	1	no	—
511	C₄×C₈	—	2	1	no	—
512	C₄×C₈	—	2	1	no	—
513	C₄×C₈	—	4	1	no	—
514	#95	—	4	1	no	—
515	C₂₉	#28937	1	1	yes	characteristic, direct product factor, Sylow
516	C₂⁴	—	2	1	no	—
517	#41	—	2	1	no	—
518	#41	—	2	1	no	—
519	#41	—	2	1	no	—
520	#41	—	2	1	no	—
521	#41	—	2	1	no	—
522	#41	—	2	1	no	—
523	#41	—	2	1	no	—
524	#41	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	4	1	no	—
532	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
533	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	—	2	1	no	—
536	C₂×D₄	—	2	1	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
546	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
554	Q₁₆	—	4	2	no	—
555	SD₁₆	—	4	2	no	—
556	SD₁₆	—	4	2	no	—
557	D₈	—	4	2	no	—
558	M₁₆	—	2	1	no	—
559	M₁₆	—	2	1	no	—
560	M₁₆	—	2	1	no	—
561	M₁₆	—	2	1	no	—
562	M₁₆	—	2	1	no	—
563	M₁₆	—	2	1	no	—
564	M₁₆	—	4	2	no	—
565	M₁₆	—	4	2	no	—
566	M₁₆	#41×C₂₉	1	2	yes	—
567	M₁₆	#41×C₂₉	1	2	yes	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	—	2	1	no	—
571	C₂×C₈	—	2	1	no	—
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	4	2	no	—
577	C₂×C₈	—	4	2	no	—
578	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
579	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
580	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
581	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	4	1	no	—
587	C₄⋊C₄	—	4	1	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	—	4	1	no	—
592	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
594	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
595	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	4	1	no	—
599	C₂²⋊C₄	—	4	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₂²⋊C₄	—	4	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	4	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	#41×C₂₉	1	2	yes	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	8	1	no	—
615	C₂³	—	8	1	no	—
616	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
617	Q₈	—	2	1	no	—
618	Q₈	—	2	1	no	—
619	Q₈	—	2	1	no	—
620	Q₈	—	2	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	16	1	no	—
626	D₄	—	2	1	no	—
627	D₄	—	2	1	no	—
628	D₄	—	2	1	no	—
629	D₄	—	2	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	4	1	no	—
632	D₄	—	4	1	no	—
633	D₄	—	4	1	no	—
634	D₄	—	4	1	no	—
635	D₄	—	4	1	no	—
636	D₄	—	4	1	no	—
637	D₄	—	4	1	no	—
638	D₄	—	16	1	no	—
639	D₄	—	16	1	no	—
640	D₄	—	16	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	8	1	no	—
660	C₂×C₄	—	8	1	no	—
661	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
662	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
663	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
664	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
665	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
666	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
667	C₈	—	2	1	no	—
668	C₈	—	2	1	no	—
669	C₈	—	2	1	no	—
670	C₈	—	2	1	no	—
671	C₈	—	2	2	no	—
672	C₈	—	2	2	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	—	4	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	8	2	no	—
684	C₂²	—	8	1	no	—
685	C₂²	—	8	1	no	—
686	C₂²	—	8	1	no	—
687	C₂²	—	16	1	no	—
688	C₂²	C₂₉×#538	1	1	yes	characteristic
689	C₂²	D₄²×C₂₉	1	1	yes	characteristic
690	C₂²	C₂₉×#555	1	1	yes	characteristic
691	C₄	—	4	2	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	1	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	C₂₉×#532	1	1	yes	characteristic
702	C₄	C₂₉×#532	1	1	yes	characteristic
703	C₄	C₂₉×#546	1	1	yes	characteristic
704	C₄	C₂₉×#546	1	1	yes	characteristic
705	C₂	—	2	1	no	—
706	C₂	—	2	1	no	—
707	C₂	—	8	1	no	—
708	C₂	—	8	1	no	—
709	C₂	—	16	1	no	—
710	C₂	C₂₉×#2555	1	1	yes	characteristic
711	C₂	C₂₉×#3290	1	1	yes	characteristic
712	C₂	C₂₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#3062	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3137	C₂	semidirect
2. C₂₉×#3136	C₂	semidirect
3. C₂₉×#3063	C₂	semidirect
5. C₂₉×#2061	C₂	semidirect
6. C₂₉×#2040	C₂	semidirect
7. C₂₉×#2004	C₂	semidirect
8. C₂₉×#2003	C₂	semidirect
9. C₂₉×#1958	C₂	semidirect
10. C₂₉×#1931	C₂	semidirect
11. C₂₉×#1930	C₂	semidirect
12. C₂₉×#1908	C₂	semidirect
13. C₂₉×#1907	C₂	semidirect
14. C₂₉×#1764	C₂	semidirect
15. C₂₉×#1764	C₂	semidirect
252. #28937	C₂₉	direct (N × H)
319. #3137	C₂×C₂₉	semidirect
320. #3136	C₂×C₂₉	semidirect
321. #3063	C₂×C₂₉	semidirect
323. #2061	C₂×C₂₉	semidirect
324. #2040	C₂×C₂₉	semidirect
325. #2004	C₂×C₂₉	semidirect
326. #2003	C₂×C₂₉	semidirect
327. #1958	C₂×C₂₉	semidirect
328. #1931	C₂×C₂₉	semidirect
329. #1930	C₂×C₂₉	semidirect
330. #1908	C₂×C₂₉	semidirect
331. #1907	C₂×C₂₉	semidirect
332. #1764	C₂×C₂₉	semidirect
333. #1764	C₂×C₂₉	semidirect
515. C₂₉	#28937	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×#3137	2
C₂₉×#3136	2
C₂₉×#3063	2
C₂₉×#3062	2
C₂₉×#2061	2
C₂₉×#2040	2
C₂₉×#2004	2
C₂₉×#2003	2
C₂₉×#1958	2
C₂₉×#1931	2
C₂₉×#1930	2
C₂₉×#1908	2
C₂₉×#1907	2
C₂₉×#1764	2
#28937	29

Subgroups — C29×#28937 #20323837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#28937 #20323837