Subgroups — C₂₉×#26990 #20321890

Order 7424.

766 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3098	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3063	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3044	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2089	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2038	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2007	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1937	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×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1857	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×#137	C₂²	1	1	yes	characteristic
18	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
21	C₂₉×#537	C₂²	1	1	yes	characteristic
22	C₂₉×#536	C₂²	1	1	yes	characteristic
23	C₂₉×#520	C₂²	1	1	yes	characteristic
24	C₂₉×#519	C₂²	1	1	yes	characteristic
25	C₂₉×#485	—	2	1	no	—
26	C₂₉×#484	—	2	1	no	—
27	C₂₉×#482	—	2	1	no	—
28	C₂₉×#480	—	2	1	no	—
29	C₂₉×#470	—	2	1	no	—
30	C₂₉×#468	—	2	1	no	—
31	C₂₉×#467	—	2	1	no	—
32	C₂₉×#465	—	2	1	no	—
33	C₂₉×#464	—	2	1	no	—
34	C₂₉×#464	—	2	1	no	—
35	C₂₉×#462	—	2	1	no	—
36	C₂₉×#462	—	2	1	no	—
37	C₂₉×#441	—	2	1	no	—
38	C₂₉×#440	—	2	1	no	—
39	C₄×Q₁₆×C₂₉	—	2	1	no	—
40	C₄×SD₁₆×C₂₉	—	2	1	no	—
41	C₂₉×#428	C₂²	1	1	yes	characteristic
42	C₂₉×#428	C₂²	1	1	yes	characteristic
43	C₂₉×#428	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
45	C₂₉×#424	C₂²	1	1	yes	characteristic
46	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
47	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
48	C₂₉×#419	C₂²	1	1	yes	characteristic
49	C₂₉×#417	C₂²	1	1	yes	characteristic
50	C₂₉×#416	C₂²	1	1	yes	characteristic
51	C₂₉×#416	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
53	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
56	C₂₉×#408	C₂²	1	1	yes	characteristic
57	C₂₉×#405	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#391	C₂²	1	1	yes	characteristic
60	C₂₉×#391	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×Q₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂₉×#137	—	2	2	no	—
72	C₂₉×#137	—	2	2	no	—
73	C₂₉×#137	—	2	2	no	—
74	C₂₉×#137	—	2	2	no	—
75	C₂₉×#137	—	4	1	no	—
76	C₂₉×#137	—	4	1	no	—
77	C₂×Q₁₆×C₂₉	—	2	1	no	—
78	C₂×Q₁₆×C₂₉	—	2	1	no	—
79	C₂×Q₁₆×C₂₉	—	2	1	no	—
80	C₂×Q₁₆×C₂₉	—	2	2	no	—
81	C₂×Q₁₆×C₂₉	—	2	1	no	—
82	C₂×Q₁₆×C₂₉	—	2	1	no	—
83	C₂×Q₁₆×C₂₉	—	4	1	no	—
84	C₂×SD₁₆×C₂₉	—	2	1	no	—
85	C₂×SD₁₆×C₂₉	—	2	1	no	—
86	C₂×SD₁₆×C₂₉	—	2	1	no	—
87	C₂₉×#131	—	2	2	no	—
88	C₂₉×#131	—	4	1	no	—
89	C₂×M₁₆×C₂₉	—	2	1	no	—
90	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₉	—	2	1	no	—
95	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
97	C₂₉×C₄⋊Q₈	—	2	1	no	—
98	C₂₉×#124	—	2	1	no	—
99	C₂₉×#123	—	4	1	no	—
100	C₂₉×C₂²⋊Q₈	—	2	1	no	—
101	C₂₉×C₂²⋊Q₈	—	2	1	no	—
102	C₂₉×C₂²⋊Q₈	—	2	1	no	—
103	C₂₉×C₂²⋊Q₈	—	2	1	no	—
104	C₂₉×#121	—	2	1	no	—
105	C₂₉×#121	—	2	1	no	—
106	C₂₉×#121	—	4	1	no	—
107	C₄×Q₈×C₂₉	—	2	1	no	—
108	C₄×Q₈×C₂₉	—	2	1	no	—
109	C₄×Q₈×C₂₉	—	2	1	no	—
110	C₄×Q₈×C₂₉	—	2	1	no	—
111	C₄×Q₈×C₂₉	—	2	1	no	—
112	C₄×D₄×C₂₉	—	2	1	no	—
113	C₄×D₄×C₂₉	—	4	1	no	—
114	C₂₉×#117	—	2	1	no	—
115	C₂₉×#117	—	4	1	no	—
116	C₂₉×#117	C₂³	1	1	yes	characteristic
117	C₂₉×#117	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
119	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
122	C₂₉×#107	—	2	1	no	—
123	C₂₉×#107	—	2	1	no	—
124	C₂₉×#107	—	2	1	no	—
125	C₂₉×#107	—	2	1	no	—
126	C₂₉×#107	—	2	1	no	—
127	C₂₉×#106	—	2	1	no	—
128	C₂₉×#106	—	2	1	no	—
129	C₂₉×#106	—	2	1	no	—
130	C₂₉×C₄⋊C₈	—	2	1	no	—
131	C₂₉×C₄⋊C₈	—	2	1	no	—
132	C₂₉×#104	—	2	2	no	—
133	C₂₉×#104	—	4	1	no	—
134	C₂₉×#103	—	2	1	no	—
135	C₂₉×#103	—	2	1	no	—
136	C₂₉×#103	—	2	1	no	—
137	C₂₉×#103	—	2	1	no	—
138	C₂₉×#103	—	2	1	no	—
139	C₂₉×#103	—	2	1	no	—
140	C₂₉×#103	—	2	1	no	—
141	C₂₉×#103	D₄	1	1	yes	characteristic
142	C₂₉×#103	D₄	1	1	yes	characteristic
143	C₂₉×#103	D₄	1	1	yes	characteristic
144	C₂₉×#103	D₄	1	1	yes	characteristic
145	C₂₉×#102	—	2	1	no	—
146	C₂₉×#102	D₄	1	1	yes	characteristic
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×#101	—	2	2	no	—
151	C₂₉×#101	—	2	2	no	—
152	C₂₉×C₂²⋊C₈	—	2	1	no	—
153	C₂₉×C₂²⋊C₈	—	2	1	no	—
154	C₂₉×#97	—	2	1	no	—
155	C₄×C₈×C₂₉	—	2	1	no	—
156	C₄×C₈×C₂₉	—	4	1	no	—
157	C₂₉×#95	—	4	1	no	—
158	C₂₉×#95	—	4	1	no	—
159	#41×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	C₂×Q₈×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	—	2	1	no	—
175	C₂×Q₈×C₂₉	—	2	1	no	—
176	C₂×Q₈×C₂₉	—	2	1	no	—
177	C₂×Q₈×C₂₉	—	2	1	no	—
178	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂×Q₈×C₂₉	#41	1	2	yes	—
181	C₂×D₄×C₂₉	—	2	1	no	—
182	C₂×D₄×C₂₉	—	2	1	no	—
183	C₂×D₄×C₂₉	—	4	1	no	—
184	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₂₉	—	2	1	no	—
187	C₂²×C₄×C₂₉	—	2	1	no	—
188	C₂²×C₄×C₂₉	—	2	1	no	—
189	C₂²×C₄×C₂₉	—	2	1	no	—
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	—	4	1	no	—
194	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
195	Q₁₆×C₂₉	—	2	4	no	—
196	Q₁₆×C₂₉	—	4	2	no	—
197	Q₁₆×C₂₉	—	4	2	no	—
198	Q₁₆×C₂₉	—	4	2	no	—
199	Q₁₆×C₂₉	—	4	2	no	—
200	SD₁₆×C₂₉	—	2	4	no	—
201	SD₁₆×C₂₉	—	4	2	no	—
202	SD₁₆×C₂₉	—	4	2	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	—	2	1	no	—
208	M₁₆×C₂₉	—	2	1	no	—
209	M₁₆×C₂₉	—	4	2	no	—
210	M₁₆×C₂₉	#41	1	2	yes	—
211	M₁₆×C₂₉	#41	1	2	yes	—
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	—	2	1	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	C₄²×C₂₉	—	2	1	no	—
247	C₄²×C₂₉	—	2	1	no	—
248	C₄²×C₂₉	—	2	1	no	—
249	C₄²×C₂₉	—	2	1	no	—
250	C₄²×C₂₉	—	4	1	no	—
251	C₄²×C₂₉	—	4	1	no	—
252	C₄²×C₂₉	—	4	1	no	—
253	#26990	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂³×C₂₉	—	2	1	no	—
255	C₂³×C₂₉	—	2	1	no	—
256	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
257	Q₈×C₂₉	—	2	2	no	—
258	Q₈×C₂₉	—	2	1	no	—
259	Q₈×C₂₉	—	2	1	no	—
260	Q₈×C₂₉	—	2	2	no	—
261	Q₈×C₂₉	—	2	1	no	—
262	Q₈×C₂₉	—	2	1	no	—
263	Q₈×C₂₉	—	4	1	no	—
264	Q₈×C₂₉	—	4	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	D₄×C₂₉	—	2	1	no	—
270	D₄×C₂₉	—	2	1	no	—
271	D₄×C₂₉	—	2	1	no	—
272	D₄×C₂₉	—	2	1	no	—
273	D₄×C₂₉	—	4	1	no	—
274	D₄×C₂₉	—	4	1	no	—
275	D₄×C₂₉	—	4	1	no	—
276	D₄×C₂₉	—	4	1	no	—
277	D₄×C₂₉	—	16	1	no	—
278	C₂×C₄×C₂₉	—	2	2	no	—
279	C₂×C₄×C₂₉	—	2	1	no	—
280	C₂×C₄×C₂₉	—	2	1	no	—
281	C₂×C₄×C₂₉	—	2	1	no	—
282	C₂×C₄×C₂₉	—	2	1	no	—
283	C₂×C₄×C₂₉	—	2	1	no	—
284	C₂×C₄×C₂₉	—	2	1	no	—
285	C₂×C₄×C₂₉	—	2	2	no	—
286	C₂×C₄×C₂₉	—	4	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	4	1	no	—
289	C₂×C₄×C₂₉	—	4	1	no	—
290	C₂×C₄×C₂₉	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	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	—	8	1	no	—
300	C₂×C₄×C₂₉	—	8	1	no	—
301	C₂×C₄×C₂₉	—	16	1	no	—
302	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
308	C₈×C₂₉	—	2	2	no	—
309	C₈×C₂₉	—	2	1	no	—
310	C₈×C₂₉	—	2	1	no	—
311	C₈×C₂₉	—	2	1	no	—
312	C₈×C₂₉	—	2	1	no	—
313	C₈×C₂₉	—	2	2	no	—
314	C₈×C₂₉	—	4	1	no	—
315	C₈×C₂₉	—	4	1	no	—
316	#3098	C₂×C₂₉	1	1	yes	characteristic
317	#3063	C₂×C₂₉	1	1	yes	characteristic
318	#3044	C₂×C₂₉	1	1	yes	characteristic, complemented
319	#2947	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#2089	C₂×C₂₉	1	1	yes	characteristic, complemented
321	#2038	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#2020	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#2007	C₂×C₂₉	1	1	yes	characteristic
324	#1969	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1937	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1930	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1908	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1882	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1857	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1764	C₂×C₂₉	1	1	yes	characteristic, complemented
331	C₂²×C₂₉	—	2	1	no	—
332	C₂²×C₂₉	—	2	1	no	—
333	C₂²×C₂₉	—	4	1	no	—
334	C₂²×C₂₉	—	4	1	no	—
335	C₂²×C₂₉	—	4	1	no	—
336	C₂²×C₂₉	—	4	1	no	—
337	C₂²×C₂₉	—	4	1	no	—
338	C₂²×C₂₉	—	4	1	no	—
339	C₂²×C₂₉	#540	1	1	yes	characteristic
340	C₂²×C₂₉	D₄²	1	1	yes	characteristic
341	C₂²×C₂₉	#553	1	1	yes	characteristic
342	C₄×C₂₉	—	4	2	no	—
343	C₄×C₂₉	—	4	1	no	—
344	C₄×C₂₉	—	4	1	no	—
345	C₄×C₂₉	—	4	2	no	—
346	C₄×C₂₉	—	4	1	no	—
347	C₄×C₂₉	—	4	1	no	—
348	C₄×C₂₉	—	4	1	no	—
349	C₄×C₂₉	—	4	1	no	—
350	C₄×C₂₉	—	8	1	no	—
351	C₄×C₂₉	—	8	1	no	—
352	C₄×C₂₉	—	8	1	no	—
353	C₄×C₂₉	#525	1	1	yes	characteristic
354	C₄×C₂₉	#532	1	1	yes	characteristic
355	C₄×C₂₉	#546	1	1	yes	characteristic
356	C₄×C₂₉	#546	1	1	yes	characteristic
357	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
360	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
361	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
362	#537	C₂²×C₂₉	1	1	yes	characteristic
363	#536	C₂²×C₂₉	1	1	yes	characteristic
364	#520	C₂²×C₂₉	1	1	yes	characteristic
365	#519	C₂²×C₂₉	1	1	yes	characteristic
366	#485	—	2	1	no	—
367	#484	—	2	1	no	—
368	#482	—	2	1	no	—
369	#480	—	2	1	no	—
370	#470	—	2	1	no	—
371	#468	—	2	1	no	—
372	#467	—	2	1	no	—
373	#465	—	2	1	no	—
374	#464	—	2	1	no	—
375	#464	—	2	1	no	—
376	#462	—	2	1	no	—
377	#462	—	2	1	no	—
378	#441	—	2	1	no	—
379	#440	—	2	1	no	—
380	C₄×Q₁₆	—	2	1	no	—
381	C₄×SD₁₆	—	2	1	no	—
382	#428	C₂²×C₂₉	1	1	yes	characteristic
383	#428	C₂²×C₂₉	1	1	yes	characteristic
384	#428	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
386	#424	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
389	#419	C₂²×C₂₉	1	1	yes	characteristic
390	#417	C₂²×C₂₉	1	1	yes	characteristic
391	#416	C₂²×C₂₉	1	1	yes	characteristic
392	#416	C₂²×C₂₉	1	1	yes	characteristic
393	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
394	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
395	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
396	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
397	#408	C₂²×C₂₉	1	1	yes	characteristic
398	#405	C₂²×C₂₉	1	1	yes	characteristic
399	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
400	#391	C₂²×C₂₉	1	1	yes	characteristic
401	#391	C₂²×C₂₉	1	1	yes	characteristic
402	#343	C₂²×C₂₉	1	1	yes	characteristic
403	#343	C₂²×C₂₉	1	1	yes	characteristic
404	#341	C₂²×C₂₉	1	1	yes	characteristic
405	#341	C₂²×C₂₉	1	1	yes	characteristic
406	#339	C₂²×C₂₉	1	1	yes	characteristic
407	#339	C₂²×C₂₉	1	1	yes	characteristic
408	C₂×C₂₉	—	2	1	no	—
409	C₂×C₂₉	—	2	1	no	—
410	C₂×C₂₉	—	8	1	no	—
411	C₂×C₂₉	—	8	1	no	—
412	C₂×C₂₉	#2464	1	1	yes	characteristic
413	C₂×C₂₉	#3290	1	1	yes	characteristic
414	C₂×C₂₉	#3293	1	1	yes	characteristic
415	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
416	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
418	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
419	#137	—	2	2	no	—
420	#137	—	2	2	no	—
421	#137	—	2	2	no	—
422	#137	—	2	2	no	—
423	#137	—	4	1	no	—
424	#137	—	4	1	no	—
425	C₂×Q₁₆	—	2	1	no	—
426	C₂×Q₁₆	—	2	1	no	—
427	C₂×Q₁₆	—	2	1	no	—
428	C₂×Q₁₆	—	2	2	no	—
429	C₂×Q₁₆	—	2	1	no	—
430	C₂×Q₁₆	—	2	1	no	—
431	C₂×Q₁₆	—	4	1	no	—
432	C₂×SD₁₆	—	2	1	no	—
433	C₂×SD₁₆	—	2	1	no	—
434	C₂×SD₁₆	—	2	1	no	—
435	#131	—	2	2	no	—
436	#131	—	4	1	no	—
437	C₂×M₁₆	—	2	1	no	—
438	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
439	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
440	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
441	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
442	C₂²×C₈	—	2	1	no	—
443	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
445	C₄⋊Q₈	—	2	1	no	—
446	#124	—	2	1	no	—
447	#123	—	4	1	no	—
448	C₂²⋊Q₈	—	2	1	no	—
449	C₂²⋊Q₈	—	2	1	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	#121	—	2	1	no	—
453	#121	—	2	1	no	—
454	#121	—	4	1	no	—
455	C₄×Q₈	—	2	1	no	—
456	C₄×Q₈	—	2	1	no	—
457	C₄×Q₈	—	2	1	no	—
458	C₄×Q₈	—	2	1	no	—
459	C₄×Q₈	—	2	1	no	—
460	C₄×D₄	—	2	1	no	—
461	C₄×D₄	—	4	1	no	—
462	#117	—	2	1	no	—
463	#117	—	4	1	no	—
464	#117	C₂³×C₂₉	1	1	yes	characteristic
465	#117	C₂³×C₂₉	1	1	yes	characteristic
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
468	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
470	#107	—	2	1	no	—
471	#107	—	2	1	no	—
472	#107	—	2	1	no	—
473	#107	—	2	1	no	—
474	#107	—	2	1	no	—
475	#106	—	2	1	no	—
476	#106	—	2	1	no	—
477	#106	—	2	1	no	—
478	C₄⋊C₈	—	2	1	no	—
479	C₄⋊C₈	—	2	1	no	—
480	#104	—	2	2	no	—
481	#104	—	4	1	no	—
482	#103	—	2	1	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	D₄×C₂₉	1	1	yes	characteristic
490	#103	D₄×C₂₉	1	1	yes	characteristic
491	#103	D₄×C₂₉	1	1	yes	characteristic
492	#103	D₄×C₂₉	1	1	yes	characteristic
493	#102	—	2	1	no	—
494	#102	D₄×C₂₉	1	1	yes	characteristic
495	#102	D₄×C₂₉	1	1	yes	characteristic
496	#102	D₄×C₂₉	1	1	yes	characteristic
497	#102	D₄×C₂₉	1	1	yes	characteristic
498	#101	—	2	2	no	—
499	#101	—	2	2	no	—
500	C₂²⋊C₈	—	2	1	no	—
501	C₂²⋊C₈	—	2	1	no	—
502	#97	—	2	1	no	—
503	C₄×C₈	—	2	1	no	—
504	C₄×C₈	—	4	1	no	—
505	#95	—	4	1	no	—
506	#95	—	4	1	no	—
507	C₂₉	#26990	1	1	yes	characteristic, direct product factor, Sylow
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	#41	—	2	1	no	—
511	#41	—	2	1	no	—
512	#41	—	2	1	no	—
513	#41	—	2	1	no	—
514	#41	—	2	1	no	—
515	#41	—	2	1	no	—
516	C₂×Q₈	—	2	1	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	1	no	—
521	C₂×Q₈	—	2	1	no	—
522	C₂×Q₈	—	2	1	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
528	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
529	C₂×Q₈	#41×C₂₉	1	2	yes	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	1	no	—
532	C₂×D₄	—	4	1	no	—
533	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
534	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	4	1	no	—
543	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
544	Q₁₆	—	2	4	no	—
545	Q₁₆	—	4	2	no	—
546	Q₁₆	—	4	2	no	—
547	Q₁₆	—	4	2	no	—
548	Q₁₆	—	4	2	no	—
549	SD₁₆	—	2	4	no	—
550	SD₁₆	—	4	2	no	—
551	SD₁₆	—	4	2	no	—
552	M₁₆	—	2	1	no	—
553	M₁₆	—	2	1	no	—
554	M₁₆	—	2	1	no	—
555	M₁₆	—	2	1	no	—
556	M₁₆	—	2	1	no	—
557	M₁₆	—	2	1	no	—
558	M₁₆	—	4	2	no	—
559	M₁₆	#41×C₂₉	1	2	yes	—
560	M₁₆	#41×C₂₉	1	2	yes	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	4	2	no	—
570	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
571	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
572	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
573	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	4	1	no	—
579	C₄⋊C₄	—	4	1	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	—	4	1	no	—
582	C₄⋊C₄	—	4	1	no	—
583	C₄⋊C₄	—	4	1	no	—
584	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
585	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
586	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
587	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
588	C₂²⋊C₄	—	2	1	no	—
589	C₂²⋊C₄	—	2	1	no	—
590	C₂²⋊C₄	—	4	1	no	—
591	C₂²⋊C₄	—	4	1	no	—
592	C₂²⋊C₄	—	4	1	no	—
593	C₂²⋊C₄	—	4	1	no	—
594	C₂²⋊C₄	—	4	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	4	1	no	—
600	C₄²	—	4	1	no	—
601	C₄²	—	4	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	2	1	no	—
604	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	2	1	no	—
607	Q₈	—	2	1	no	—
608	Q₈	—	2	2	no	—
609	Q₈	—	2	1	no	—
610	Q₈	—	2	1	no	—
611	Q₈	—	4	1	no	—
612	Q₈	—	4	1	no	—
613	Q₈	—	4	1	no	—
614	Q₈	—	4	1	no	—
615	Q₈	—	4	1	no	—
616	Q₈	—	4	1	no	—
617	D₄	—	2	1	no	—
618	D₄	—	2	1	no	—
619	D₄	—	2	1	no	—
620	D₄	—	2	1	no	—
621	D₄	—	4	1	no	—
622	D₄	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	16	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	8	1	no	—
648	C₂×C₄	—	8	1	no	—
649	C₂×C₄	—	16	1	no	—
650	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
651	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
652	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
653	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
654	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
655	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	2	1	no	—
658	C₈	—	2	1	no	—
659	C₈	—	2	1	no	—
660	C₈	—	2	1	no	—
661	C₈	—	2	2	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	C₂₉×#540	1	1	yes	characteristic
673	C₂²	D₄²×C₂₉	1	1	yes	characteristic
674	C₂²	C₂₉×#553	1	1	yes	characteristic
675	C₄	—	4	2	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₂₉×#525	1	1	yes	characteristic
687	C₄	C₂₉×#532	1	1	yes	characteristic
688	C₄	C₂₉×#546	1	1	yes	characteristic
689	C₄	C₂₉×#546	1	1	yes	characteristic
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	8	1	no	—
693	C₂	—	8	1	no	—
694	C₂	C₂₉×#2464	1	1	yes	characteristic
695	C₂	C₂₉×#3290	1	1	yes	characteristic
696	C₂	C₂₉×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#537	C₂²
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
3. C₂₉×#3044	C₂	semidirect
4. C₂₉×#2947	C₂	semidirect
5. C₂₉×#2089	C₂	semidirect
6. C₂₉×#2038	C₂	semidirect
7. C₂₉×#2020	C₂	semidirect
9. C₂₉×#1969	C₂	semidirect
10. C₂₉×#1937	C₂	semidirect
11. C₂₉×#1930	C₂	semidirect
12. C₂₉×#1908	C₂	semidirect
13. C₂₉×#1882	C₂	semidirect
14. C₂₉×#1857	C₂	semidirect
15. C₂₉×#1764	C₂	semidirect
253. #26990	C₂₉	direct (N × H)
318. #3044	C₂×C₂₉	semidirect
319. #2947	C₂×C₂₉	semidirect
320. #2089	C₂×C₂₉	semidirect
321. #2038	C₂×C₂₉	semidirect
322. #2020	C₂×C₂₉	semidirect
324. #1969	C₂×C₂₉	semidirect
325. #1937	C₂×C₂₉	semidirect
326. #1930	C₂×C₂₉	semidirect
327. #1908	C₂×C₂₉	semidirect
328. #1882	C₂×C₂₉	semidirect
329. #1857	C₂×C₂₉	semidirect
330. #1764	C₂×C₂₉	semidirect
507. C₂₉	#26990	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×#3098	2
C₂₉×#3063	2
C₂₉×#3044	2
C₂₉×#2947	2
C₂₉×#2089	2
C₂₉×#2038	2
C₂₉×#2020	2
C₂₉×#2007	2
C₂₉×#1969	2
C₂₉×#1937	2
C₂₉×#1930	2
C₂₉×#1908	2
C₂₉×#1882	2
C₂₉×#1857	2
C₂₉×#1764	2
#26990	29

Subgroups — C29×#26990 #20321890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26990 #20321890