Subgroups — C₂₉×#25055 #20319955

Order 7424.

724 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3099	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3098	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3060	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2078	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2039	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1859	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
18	C₂₉×#537	C₂²	1	1	yes	characteristic
19	C₂₉×#537	C₂²	1	1	yes	characteristic
20	C₂₉×#520	C₂²	1	1	yes	characteristic
21	C₂₉×#520	C₂²	1	1	yes	characteristic
22	C₂₉×#485	—	2	1	no	—
23	C₂₉×#485	—	2	1	no	—
24	C₂₉×#484	—	2	1	no	—
25	C₂₉×#483	—	2	1	no	—
26	C₂₉×#482	—	2	1	no	—
27	C₂₉×#482	—	2	1	no	—
28	C₂₉×#481	—	2	1	no	—
29	C₂₉×#480	—	2	1	no	—
30	C₂₉×#470	—	2	1	no	—
31	C₂₉×#469	—	2	1	no	—
32	C₂₉×#465	—	2	1	no	—
33	C₂₉×#465	—	2	1	no	—
34	C₂₉×#440	—	2	1	no	—
35	C₂₉×#440	—	2	1	no	—
36	C₄×Q₁₆×C₂₉	—	2	1	no	—
37	C₄×D₈×C₂₉	—	2	1	no	—
38	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
39	C₂₉×#428	C₂²	1	1	yes	characteristic
40	C₂₉×#428	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
45	C₂×C₂₉×#104	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×#417	C₂²	1	1	yes	characteristic
49	C₂₉×#417	C₂²	1	1	yes	characteristic
50	C₂₉×#417	C₂²	1	1	yes	characteristic
51	C₂₉×#417	C₂²	1	1	yes	characteristic
52	C₂₉×#417	C₂²	1	1	yes	characteristic
53	C₂₉×#417	C₂²	1	1	yes	characteristic
54	C₂₉×#416	C₂²	1	1	yes	characteristic
55	C₂₉×#408	C₂²	1	1	yes	characteristic
56	C₂₉×#408	C₂²	1	1	yes	characteristic
57	C₂₉×#405	C₂²	1	1	yes	characteristic
58	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
59	C₂₉×#384	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×#343	C₂²	1	1	yes	characteristic
64	C₂₉×#343	C₂²	1	1	yes	characteristic
65	C₂₉×#341	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	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
70	C₂₉×#135	—	2	2	no	—
71	C₂₉×#135	—	2	2	no	—
72	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
75	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
76	C₂₉×#131	—	2	2	no	—
77	C₂₉×#131	—	2	2	no	—
78	C₂×M₁₆×C₂₉	—	2	1	no	—
79	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
82	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₉	—	2	1	no	—
84	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₂₉×C₂²⋊Q₈	—	2	1	no	—
87	C₂₉×C₂²⋊Q₈	—	2	1	no	—
88	C₂₉×C₂²⋊Q₈	—	2	1	no	—
89	C₂₉×C₂²⋊Q₈	—	2	1	no	—
90	C₂₉×#121	—	2	1	no	—
91	C₂₉×#121	—	2	1	no	—
92	C₂₉×#121	—	2	1	no	—
93	C₂₉×#121	—	2	1	no	—
94	C₂₉×#121	—	4	1	no	—
95	C₂₉×#121	—	4	1	no	—
96	C₄×Q₈×C₂₉	—	2	1	no	—
97	C₄×Q₈×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	—	2	1	no	—
99	C₄×D₄×C₂₉	—	2	1	no	—
100	C₄×D₄×C₂₉	—	4	1	no	—
101	C₄×D₄×C₂₉	—	4	1	no	—
102	C₂₉×#117	—	2	1	no	—
103	C₂₉×#117	—	2	1	no	—
104	C₂₉×#117	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
108	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
113	C₂₉×#108	—	2	2	no	—
114	C₂₉×#107	—	2	1	no	—
115	C₂₉×#107	—	2	1	no	—
116	C₂₉×#107	—	2	1	no	—
117	C₂₉×#107	—	2	1	no	—
118	C₂₉×#107	—	2	1	no	—
119	C₂₉×#107	—	2	1	no	—
120	C₂₉×#106	—	2	1	no	—
121	C₂₉×#106	—	2	1	no	—
122	C₂₉×#106	—	2	1	no	—
123	C₂₉×#106	—	2	1	no	—
124	C₂₉×#106	—	2	1	no	—
125	C₂₉×#106	—	2	1	no	—
126	C₂₉×#104	—	2	2	no	—
127	C₂₉×#104	—	2	2	no	—
128	C₂₉×#104	—	2	2	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×#102	—	2	1	no	—
138	C₂₉×#102	—	2	1	no	—
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	D₄	1	1	yes	characteristic
144	C₂₉×#102	D₄	1	1	yes	characteristic
145	C₂₉×C₂²⋊C₈	—	2	1	no	—
146	C₂₉×C₂²⋊C₈	—	2	1	no	—
147	C₂₉×C₂²⋊C₈	—	2	1	no	—
148	C₂₉×C₂²⋊C₈	—	2	1	no	—
149	C₂₉×#97	—	2	1	no	—
150	C₂₉×#97	—	2	2	no	—
151	C₄×C₈×C₂₉	—	2	1	no	—
152	C₂₉×#95	—	4	1	no	—
153	#41×C₂₉	—	2	1	no	—
154	#41×C₂₉	—	2	1	no	—
155	#41×C₂₉	—	2	1	no	—
156	#41×C₂₉	—	2	1	no	—
157	#41×C₂₉	—	2	1	no	—
158	#41×C₂₉	—	2	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	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₂₉	—	2	1	no	—
169	C₂×D₄×C₂₉	—	2	1	no	—
170	C₂×D₄×C₂₉	—	2	1	no	—
171	C₂×D₄×C₂₉	—	4	1	no	—
172	C₂×D₄×C₂₉	—	4	1	no	—
173	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
175	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₉	—	2	1	no	—
177	C₂²×C₄×C₂₉	—	2	1	no	—
178	C₂²×C₄×C₂₉	—	2	1	no	—
179	C₂²×C₄×C₂₉	—	2	1	no	—
180	C₂²×C₄×C₂₉	—	2	1	no	—
181	C₂²×C₄×C₂₉	—	2	1	no	—
182	C₂²×C₄×C₂₉	—	2	1	no	—
183	C₂²×C₄×C₂₉	—	2	1	no	—
184	C₂²×C₄×C₂₉	—	4	1	no	—
185	C₂²×C₄×C₂₉	—	4	1	no	—
186	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₂₉	—	2	2	no	—
188	SD₁₆×C₂₉	—	2	2	no	—
189	SD₁₆×C₂₉	—	2	2	no	—
190	D₈×C₂₉	—	2	2	no	—
191	M₁₆×C₂₉	—	2	1	no	—
192	M₁₆×C₂₉	—	2	1	no	—
193	M₁₆×C₂₉	—	2	1	no	—
194	M₁₆×C₂₉	—	2	1	no	—
195	M₁₆×C₂₉	—	2	1	no	—
196	M₁₆×C₂₉	—	2	1	no	—
197	M₁₆×C₂₉	—	2	1	no	—
198	M₁₆×C₂₉	—	2	1	no	—
199	M₁₆×C₂₉	—	4	2	no	—
200	C₂×C₈×C₂₉	—	2	1	no	—
201	C₂×C₈×C₂₉	—	2	1	no	—
202	C₂×C₈×C₂₉	—	2	1	no	—
203	C₂×C₈×C₂₉	—	2	1	no	—
204	C₂×C₈×C₂₉	—	2	1	no	—
205	C₂×C₈×C₂₉	—	2	1	no	—
206	C₂×C₈×C₂₉	—	4	2	no	—
207	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₈×C₂₉	#41	1	2	yes	—
212	C₂×C₈×C₂₉	#41	1	2	yes	—
213	C₄⋊C₄×C₂₉	—	2	1	no	—
214	C₄⋊C₄×C₂₉	—	2	1	no	—
215	C₄⋊C₄×C₂₉	—	2	1	no	—
216	C₄⋊C₄×C₂₉	—	2	1	no	—
217	C₄⋊C₄×C₂₉	—	2	1	no	—
218	C₄⋊C₄×C₂₉	—	2	1	no	—
219	C₄⋊C₄×C₂₉	—	2	1	no	—
220	C₄⋊C₄×C₂₉	—	2	1	no	—
221	C₄⋊C₄×C₂₉	—	4	1	no	—
222	C₄⋊C₄×C₂₉	—	4	1	no	—
223	C₄⋊C₄×C₂₉	—	4	1	no	—
224	C₄⋊C₄×C₂₉	—	4	1	no	—
225	C₄⋊C₄×C₂₉	—	8	2	no	—
226	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
227	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
228	C₂²⋊C₄×C₂₉	—	2	1	no	—
229	C₂²⋊C₄×C₂₉	—	4	1	no	—
230	C₂²⋊C₄×C₂₉	—	4	1	no	—
231	C₂²⋊C₄×C₂₉	—	4	1	no	—
232	C₂²⋊C₄×C₂₉	—	4	1	no	—
233	C₂²⋊C₄×C₂₉	—	4	1	no	—
234	C₂²⋊C₄×C₂₉	—	4	1	no	—
235	C₄²×C₂₉	—	2	1	no	—
236	C₄²×C₂₉	—	2	1	no	—
237	C₄²×C₂₉	—	4	1	no	—
238	C₄²×C₂₉	—	4	1	no	—
239	C₄²×C₂₉	#41	1	2	yes	—
240	#25055	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂³×C₂₉	—	2	1	no	—
242	C₂³×C₂₉	—	2	1	no	—
243	C₂³×C₂₉	—	2	1	no	—
244	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
245	Q₈×C₂₉	—	2	1	no	—
246	Q₈×C₂₉	—	2	1	no	—
247	Q₈×C₂₉	—	2	1	no	—
248	Q₈×C₂₉	—	2	1	no	—
249	Q₈×C₂₉	—	2	1	no	—
250	Q₈×C₂₉	—	2	1	no	—
251	D₄×C₂₉	—	2	1	no	—
252	D₄×C₂₉	—	2	1	no	—
253	D₄×C₂₉	—	2	1	no	—
254	D₄×C₂₉	—	2	1	no	—
255	D₄×C₂₉	—	2	1	no	—
256	D₄×C₂₉	—	2	1	no	—
257	D₄×C₂₉	—	4	1	no	—
258	D₄×C₂₉	—	4	1	no	—
259	D₄×C₂₉	—	4	1	no	—
260	D₄×C₂₉	—	4	1	no	—
261	D₄×C₂₉	—	4	1	no	—
262	D₄×C₂₉	—	4	1	no	—
263	D₄×C₂₉	—	16	1	no	—
264	D₄×C₂₉	—	16	1	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	1	no	—
267	C₂×C₄×C₂₉	—	2	1	no	—
268	C₂×C₄×C₂₉	—	2	1	no	—
269	C₂×C₄×C₂₉	—	2	1	no	—
270	C₂×C₄×C₂₉	—	2	2	no	—
271	C₂×C₄×C₂₉	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	4	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	4	1	no	—
279	C₂×C₄×C₂₉	—	4	1	no	—
280	C₂×C₄×C₂₉	—	4	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	8	1	no	—
284	C₂×C₄×C₂₉	—	8	1	no	—
285	C₂×C₄×C₂₉	—	8	1	no	—
286	C₂×C₄×C₂₉	—	8	1	no	—
287	C₂×C₄×C₂₉	—	16	1	no	—
288	C₂×C₄×C₂₉	—	16	1	no	—
289	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
295	C₈×C₂₉	—	2	1	no	—
296	C₈×C₂₉	—	2	1	no	—
297	C₈×C₂₉	—	4	1	no	—
298	C₈×C₂₉	—	4	1	no	—
299	C₈×C₂₉	—	4	1	no	—
300	C₈×C₂₉	—	4	1	no	—
301	C₈×C₂₉	#123	1	2	yes	—
302	C₈×C₂₉	#123	1	2	yes	—
303	#3099	C₂×C₂₉	1	1	yes	characteristic, complemented
304	#3098	C₂×C₂₉	1	1	yes	characteristic, complemented
305	#3060	C₂×C₂₉	1	1	yes	characteristic
306	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
307	#2079	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#2078	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#2040	C₂×C₂₉	1	1	yes	characteristic, complemented
310	#2039	C₂×C₂₉	1	1	yes	characteristic, complemented
311	#1975	C₂×C₂₉	1	1	yes	characteristic, complemented
312	#1951	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#1860	C₂×C₂₉	1	1	yes	characteristic, complemented
314	#1859	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#1847	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#1816	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#1765	C₂×C₂₉	1	1	yes	characteristic, complemented
318	C₂²×C₂₉	—	2	1	no	—
319	C₂²×C₂₉	—	2	1	no	—
320	C₂²×C₂₉	—	4	1	no	—
321	C₂²×C₂₉	—	4	1	no	—
322	C₂²×C₂₉	—	4	1	no	—
323	C₂²×C₂₉	—	4	1	no	—
324	C₂²×C₂₉	—	4	1	no	—
325	C₂²×C₂₉	—	4	1	no	—
326	C₂²×C₂₉	—	4	1	no	—
327	C₂²×C₂₉	—	4	1	no	—
328	C₂²×C₂₉	—	4	1	no	—
329	C₂²×C₂₉	#542	1	1	yes	characteristic
330	C₂²×C₂₉	D₄²	1	1	yes	characteristic
331	C₂²×C₂₉	#553	1	1	yes	characteristic
332	C₄×C₂₉	—	4	2	no	—
333	C₄×C₂₉	—	4	1	no	—
334	C₄×C₂₉	—	4	1	no	—
335	C₄×C₂₉	—	4	1	no	—
336	C₄×C₂₉	—	4	1	no	—
337	C₄×C₂₉	—	4	1	no	—
338	C₄×C₂₉	—	8	1	no	—
339	C₄×C₂₉	—	8	1	no	—
340	C₄×C₂₉	—	8	1	no	—
341	C₄×C₂₉	—	8	1	no	—
342	C₄×C₂₉	C₂×#123	1	1	yes	characteristic
343	C₄×C₂₉	#532	1	1	yes	characteristic
344	C₄×C₂₉	#547	1	1	yes	characteristic
345	C₄×C₂₉	#547	1	1	yes	characteristic
346	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
347	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
348	#537	C₂²×C₂₉	1	1	yes	characteristic
349	#537	C₂²×C₂₉	1	1	yes	characteristic
350	#520	C₂²×C₂₉	1	1	yes	characteristic
351	#520	C₂²×C₂₉	1	1	yes	characteristic
352	#485	—	2	1	no	—
353	#485	—	2	1	no	—
354	#484	—	2	1	no	—
355	#483	—	2	1	no	—
356	#482	—	2	1	no	—
357	#482	—	2	1	no	—
358	#481	—	2	1	no	—
359	#480	—	2	1	no	—
360	#470	—	2	1	no	—
361	#469	—	2	1	no	—
362	#465	—	2	1	no	—
363	#465	—	2	1	no	—
364	#440	—	2	1	no	—
365	#440	—	2	1	no	—
366	C₄×Q₁₆	—	2	1	no	—
367	C₄×D₈	—	2	1	no	—
368	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
369	#428	C₂²×C₂₉	1	1	yes	characteristic
370	#428	C₂²×C₂₉	1	1	yes	characteristic
371	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
378	#417	C₂²×C₂₉	1	1	yes	characteristic
379	#417	C₂²×C₂₉	1	1	yes	characteristic
380	#417	C₂²×C₂₉	1	1	yes	characteristic
381	#417	C₂²×C₂₉	1	1	yes	characteristic
382	#417	C₂²×C₂₉	1	1	yes	characteristic
383	#417	C₂²×C₂₉	1	1	yes	characteristic
384	#416	C₂²×C₂₉	1	1	yes	characteristic
385	#408	C₂²×C₂₉	1	1	yes	characteristic
386	#408	C₂²×C₂₉	1	1	yes	characteristic
387	#405	C₂²×C₂₉	1	1	yes	characteristic
388	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
389	#384	C₂²×C₂₉	1	1	yes	characteristic
390	#382	C₂²×C₂₉	1	1	yes	characteristic
391	#343	C₂²×C₂₉	1	1	yes	characteristic
392	#343	C₂²×C₂₉	1	1	yes	characteristic
393	#343	C₂²×C₂₉	1	1	yes	characteristic
394	#343	C₂²×C₂₉	1	1	yes	characteristic
395	#341	C₂²×C₂₉	1	1	yes	characteristic
396	#339	C₂²×C₂₉	1	1	yes	characteristic
397	C₂×C₂₉	—	2	1	no	—
398	C₂×C₂₉	—	2	1	no	—
399	C₂×C₂₉	—	8	1	no	—
400	C₂×C₂₉	—	8	1	no	—
401	C₂×C₂₉	—	8	1	no	—
402	C₂×C₂₉	#2422	1	1	yes	characteristic
403	C₂×C₂₉	#3288	1	1	yes	characteristic
404	C₂×C₂₉	#3289	1	1	yes	characteristic
405	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
406	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
407	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
408	#135	—	2	2	no	—
409	#135	—	2	2	no	—
410	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
411	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
412	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
413	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
414	#131	—	2	2	no	—
415	#131	—	2	2	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
418	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
419	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
420	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
421	C₂²×C₈	—	2	1	no	—
422	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
424	C₂²⋊Q₈	—	2	1	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	1	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	#121	—	2	1	no	—
429	#121	—	2	1	no	—
430	#121	—	2	1	no	—
431	#121	—	2	1	no	—
432	#121	—	4	1	no	—
433	#121	—	4	1	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×D₄	—	2	1	no	—
437	C₄×D₄	—	2	1	no	—
438	C₄×D₄	—	4	1	no	—
439	C₄×D₄	—	4	1	no	—
440	#117	—	2	1	no	—
441	#117	—	2	1	no	—
442	#117	C₂³×C₂₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	4	1	no	—
446	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
451	#108	—	2	2	no	—
452	#107	—	2	1	no	—
453	#107	—	2	1	no	—
454	#107	—	2	1	no	—
455	#107	—	2	1	no	—
456	#107	—	2	1	no	—
457	#107	—	2	1	no	—
458	#106	—	2	1	no	—
459	#106	—	2	1	no	—
460	#106	—	2	1	no	—
461	#106	—	2	1	no	—
462	#106	—	2	1	no	—
463	#106	—	2	1	no	—
464	#104	—	2	2	no	—
465	#104	—	2	2	no	—
466	#104	—	2	2	no	—
467	#103	—	2	1	no	—
468	#103	—	2	1	no	—
469	#103	—	2	1	no	—
470	#103	—	2	1	no	—
471	#103	—	2	1	no	—
472	#103	—	2	1	no	—
473	#103	D₄×C₂₉	1	1	yes	characteristic
474	#103	D₄×C₂₉	1	1	yes	characteristic
475	#102	—	2	1	no	—
476	#102	—	2	1	no	—
477	#102	—	2	1	no	—
478	#102	—	2	1	no	—
479	#102	—	2	1	no	—
480	#102	—	2	1	no	—
481	#102	D₄×C₂₉	1	1	yes	characteristic
482	#102	D₄×C₂₉	1	1	yes	characteristic
483	C₂²⋊C₈	—	2	1	no	—
484	C₂²⋊C₈	—	2	1	no	—
485	C₂²⋊C₈	—	2	1	no	—
486	C₂²⋊C₈	—	2	1	no	—
487	#97	—	2	1	no	—
488	#97	—	2	2	no	—
489	C₄×C₈	—	2	1	no	—
490	#95	—	4	1	no	—
491	C₂₉	#25055	1	1	yes	characteristic, direct product factor, Sylow
492	#41	—	2	1	no	—
493	#41	—	2	1	no	—
494	#41	—	2	1	no	—
495	#41	—	2	1	no	—
496	#41	—	2	1	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	2	1	no	—
502	#41	—	2	1	no	—
503	#41	—	2	1	no	—
504	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
505	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
506	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	—	4	1	no	—
512	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
513	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
514	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	4	1	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
526	Q₁₆	—	2	2	no	—
527	SD₁₆	—	2	2	no	—
528	SD₁₆	—	2	2	no	—
529	D₈	—	2	2	no	—
530	M₁₆	—	2	1	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	4	2	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	4	2	no	—
546	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
548	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
549	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
550	C₂×C₈	#41×C₂₉	1	2	yes	—
551	C₂×C₈	#41×C₂₉	1	2	yes	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	4	1	no	—
561	C₄⋊C₄	—	4	1	no	—
562	C₄⋊C₄	—	4	1	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	—	8	2	no	—
565	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
566	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	4	1	no	—
577	C₄²	—	4	1	no	—
578	C₄²	#41×C₂₉	1	2	yes	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
583	Q₈	—	2	1	no	—
584	Q₈	—	2	1	no	—
585	Q₈	—	2	1	no	—
586	Q₈	—	2	1	no	—
587	Q₈	—	2	1	no	—
588	Q₈	—	2	1	no	—
589	D₄	—	2	1	no	—
590	D₄	—	2	1	no	—
591	D₄	—	2	1	no	—
592	D₄	—	2	1	no	—
593	D₄	—	2	1	no	—
594	D₄	—	2	1	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	D₄	—	16	1	no	—
602	D₄	—	16	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	1	no	—
622	C₂×C₄	—	8	1	no	—
623	C₂×C₄	—	8	1	no	—
624	C₂×C₄	—	8	1	no	—
625	C₂×C₄	—	16	1	no	—
626	C₂×C₄	—	16	1	no	—
627	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
629	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
631	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
632	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
633	C₈	—	2	1	no	—
634	C₈	—	2	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₈	C₂₉×#123	1	2	yes	—
640	C₈	C₂₉×#123	1	2	yes	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	C₂₉×#542	1	1	yes	characteristic
653	C₂²	D₄²×C₂₉	1	1	yes	characteristic
654	C₂²	C₂₉×#553	1	1	yes	characteristic
655	C₄	—	4	2	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	C₂×C₂₉×#123	1	1	yes	characteristic
666	C₄	C₂₉×#532	1	1	yes	characteristic
667	C₄	C₂₉×#547	1	1	yes	characteristic
668	C₄	C₂₉×#547	1	1	yes	characteristic
669	C₂	—	2	1	no	—
670	C₂	—	2	1	no	—
671	C₂	—	8	1	no	—
672	C₂	—	8	1	no	—
673	C₂	—	8	1	no	—
674	C₂	C₂₉×#2422	1	1	yes	characteristic
675	C₂	C₂₉×#3288	1	1	yes	characteristic
676	C₂	C₂₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#3060	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×#3099	C₂	semidirect
2. C₂₉×#3098	C₂	semidirect
4. C₂₉×#2951	C₂	semidirect
5. C₂₉×#2079	C₂	semidirect
6. C₂₉×#2078	C₂	semidirect
7. C₂₉×#2040	C₂	semidirect
8. C₂₉×#2039	C₂	semidirect
9. C₂₉×#1975	C₂	semidirect
10. C₂₉×#1951	C₂	semidirect
11. C₂₉×#1860	C₂	semidirect
12. C₂₉×#1859	C₂	semidirect
13. C₂₉×#1847	C₂	semidirect
14. C₂₉×#1816	C₂	semidirect
15. C₂₉×#1765	C₂	semidirect
240. #25055	C₂₉	direct (N × H)
303. #3099	C₂×C₂₉	semidirect
304. #3098	C₂×C₂₉	semidirect
306. #2951	C₂×C₂₉	semidirect
307. #2079	C₂×C₂₉	semidirect
308. #2078	C₂×C₂₉	semidirect
309. #2040	C₂×C₂₉	semidirect
310. #2039	C₂×C₂₉	semidirect
311. #1975	C₂×C₂₉	semidirect
312. #1951	C₂×C₂₉	semidirect
313. #1860	C₂×C₂₉	semidirect
314. #1859	C₂×C₂₉	semidirect
315. #1847	C₂×C₂₉	semidirect
316. #1816	C₂×C₂₉	semidirect
317. #1765	C₂×C₂₉	semidirect
491. C₂₉	#25055	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×#3099	2
C₂₉×#3098	2
C₂₉×#3060	2
C₂₉×#2951	2
C₂₉×#2079	2
C₂₉×#2078	2
C₂₉×#2040	2
C₂₉×#2039	2
C₂₉×#1975	2
C₂₉×#1951	2
C₂₉×#1860	2
C₂₉×#1859	2
C₂₉×#1847	2
C₂₉×#1816	2
C₂₉×#1765	2
#25055	29

Subgroups — C29×#25055 #20319955

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25055 #20319955