Subgroups — C₂₉×#18494 #20313394

Order 7424.

944 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1638	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1635	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×#1626	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1544	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#557	C₂²	1	1	yes	characteristic
17	C₂₉×#556	—	2	1	no	—
18	C₂₉×#556	C₂²	1	1	yes	characteristic
19	C₂₉×#552	—	2	2	no	—
20	C₂₉×#552	—	2	1	no	—
21	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂₉×#548	—	2	1	no	—
23	C₂₉×#547	—	2	1	no	—
24	C₂₉×#547	C₂²	1	1	yes	characteristic
25	C₂₉×#533	—	2	1	no	—
26	C₂₉×#533	C₂²	1	1	yes	characteristic
27	C₂₉×#532	C₂²	1	1	yes	characteristic
28	C₂₉×#529	—	2	1	no	—
29	C₂₉×#529	—	2	2	no	—
30	C₄×#41×C₂₉	—	2	1	no	—
31	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
32	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₂₉	—	2	1	no	—
34	C₂₉×#488	—	2	2	no	—
35	C₂₉×#487	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#486	C₂²	1	1	yes	characteristic
38	C₂₉×#486	C₂²	1	1	yes	characteristic
39	C₂₉×#482	—	2	1	no	—
40	C₂₉×#482	—	2	1	no	—
41	C₂₉×#477	C₂²	1	1	yes	characteristic
42	C₂₉×#477	C₂²	1	1	yes	characteristic
43	C₂₉×#476	C₂²	1	1	yes	characteristic
44	C₂₉×#476	C₂²	1	1	yes	characteristic
45	C₂₉×#460	C₂²	1	1	yes	characteristic
46	C₂₉×#460	C₂²	1	1	yes	characteristic
47	C₂₉×#459	C₂²	1	1	yes	characteristic
48	C₂₉×#459	C₂²	1	1	yes	characteristic
49	C₂₉×#449	—	2	1	no	—
50	C₂₉×#449	—	2	1	no	—
51	C₄×SD₁₆×C₂₉	—	2	1	no	—
52	C₄×SD₁₆×C₂₉	—	2	1	no	—
53	C₄×D₈×C₂₉	—	2	1	no	—
54	C₄×D₈×C₂₉	—	2	1	no	—
55	C₂₉×#431	C₂²	1	1	yes	characteristic
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#416	—	2	2	no	—
58	C₂×C₄×C₈×C₂₉	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×#332	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×Q₈⋊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
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
74	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
75	C₂²×Q₈×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	C₂×D₈×C₂₉	—	2	1	no	—
80	C₂²×C₈×C₂₉	—	2	1	no	—
81	C₂₉×C₄⋊Q₈	—	2	1	no	—
82	C₂₉×C₄⋊Q₈	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₉×#127	C₂³	1	1	yes	characteristic
87	C₂₉×#126	—	2	2	no	—
88	C₂₉×#126	—	2	2	no	—
89	C₂₉×#126	—	2	2	no	—
90	C₂₉×#125	—	2	2	no	—
91	C₂₉×#125	—	2	2	no	—
92	C₂₉×#125	—	2	1	no	—
93	C₂₉×#125	D₄	1	2	yes	—
94	C₂₉×#124	—	2	2	no	—
95	C₂₉×#124	—	2	1	no	—
96	C₂₉×#124	—	2	1	no	—
97	C₂₉×#123	—	2	2	no	—
98	C₂₉×#123	—	2	2	no	—
99	C₂₉×#123	—	2	2	no	—
100	C₂₉×C₂²⋊Q₈	—	2	2	no	—
101	C₂₉×C₂²⋊Q₈	—	2	1	no	—
102	C₂₉×C₂²⋊Q₈	—	2	1	no	—
103	C₂₉×C₂²⋊Q₈	—	2	1	no	—
104	C₂₉×C₂²⋊Q₈	—	2	1	no	—
105	C₂₉×C₂²⋊Q₈	—	2	2	no	—
106	C₂₉×C₂²⋊Q₈	—	2	1	no	—
107	C₂₉×#121	—	2	2	no	—
108	C₂₉×#121	—	2	1	no	—
109	C₂₉×#121	—	2	1	no	—
110	C₂₉×#121	—	2	1	no	—
111	C₄×Q₈×C₂₉	—	2	2	no	—
112	C₄×Q₈×C₂₉	—	2	2	no	—
113	C₄×Q₈×C₂₉	—	2	1	no	—
114	C₄×Q₈×C₂₉	—	2	1	no	—
115	C₄×Q₈×C₂₉	—	2	1	no	—
116	C₄×Q₈×C₂₉	—	2	1	no	—
117	C₄×Q₈×C₂₉	—	2	1	no	—
118	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
119	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
120	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
122	C₄×D₄×C₂₉	—	2	2	no	—
123	C₄×D₄×C₂₉	—	2	2	no	—
124	C₄×D₄×C₂₉	—	2	1	no	—
125	C₄×D₄×C₂₉	—	2	1	no	—
126	C₄×D₄×C₂₉	—	2	1	no	—
127	C₄×D₄×C₂₉	—	2	1	no	—
128	C₄×D₄×C₂₉	—	2	1	no	—
129	C₄×D₄×C₂₉	—	2	1	no	—
130	C₄×D₄×C₂₉	—	2	1	no	—
131	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
132	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
133	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
135	C₂₉×#117	—	2	2	no	—
136	C₂₉×#117	—	2	2	no	—
137	C₂₉×#117	—	2	1	no	—
138	C₂₉×#117	—	2	1	no	—
139	C₂₉×#117	—	2	1	no	—
140	C₂₉×#117	D₄	1	1	yes	characteristic
141	C₂₉×#117	D₄	1	1	yes	characteristic
142	C₂₉×#117	D₄	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
144	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₂×C₄²×C₂₉	—	2	2	no	—
146	C₂×C₄²×C₂₉	—	2	1	no	—
147	C₂×C₄²×C₂₉	—	2	1	no	—
148	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
149	C₂₉×#107	—	2	1	no	—
150	C₂₉×#107	—	2	1	no	—
151	C₂₉×#106	—	2	1	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
154	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
155	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
156	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₂₉×#103	—	2	1	no	—
158	C₂₉×#103	—	2	1	no	—
159	C₂₉×#103	—	2	2	no	—
160	C₂₉×#103	—	2	2	no	—
161	C₂₉×#102	—	2	1	no	—
162	C₂₉×#102	—	2	1	no	—
163	C₂₉×#102	—	2	1	no	—
164	C₂₉×#102	—	2	1	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	2	no	—
168	C₂₉×#102	—	2	2	no	—
169	C₂₉×C₂²⋊C₈	—	2	1	no	—
170	C₂₉×C₂²⋊C₈	—	2	1	no	—
171	C₄×C₈×C₂₉	—	2	1	no	—
172	C₄×C₈×C₂₉	—	2	1	no	—
173	C₄×C₈×C₂₉	—	2	1	no	—
174	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	#41×C₂₉	—	2	2	no	—
177	#41×C₂₉	—	2	2	no	—
178	#41×C₂₉	—	4	1	no	—
179	#41×C₂₉	—	4	1	no	—
180	#41×C₂₉	—	4	4	no	—
181	#41×C₂₉	—	4	2	no	—
182	#41×C₂₉	—	4	2	no	—
183	C₂×Q₈×C₂₉	—	2	2	no	—
184	C₂×Q₈×C₂₉	—	2	1	no	—
185	C₂×Q₈×C₂₉	—	2	1	no	—
186	C₂×Q₈×C₂₉	—	2	1	no	—
187	C₂×Q₈×C₂₉	—	4	2	no	—
188	C₂×Q₈×C₂₉	—	4	2	no	—
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₂₉	—	2	2	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	2	1	no	—
194	C₂×D₄×C₂₉	—	2	1	no	—
195	C₂×D₄×C₂₉	—	2	1	no	—
196	C₂×D₄×C₂₉	—	2	1	no	—
197	C₂×D₄×C₂₉	—	4	1	no	—
198	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₉	—	2	2	no	—
201	C₂²×C₄×C₂₉	—	2	2	no	—
202	C₂²×C₄×C₂₉	—	2	1	no	—
203	C₂²×C₄×C₂₉	—	2	1	no	—
204	C₂²×C₄×C₂₉	—	2	1	no	—
205	C₂²×C₄×C₂₉	—	2	1	no	—
206	C₂²×C₄×C₂₉	—	2	1	no	—
207	C₂²×C₄×C₂₉	—	2	1	no	—
208	C₂²×C₄×C₂₉	—	4	1	no	—
209	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
212	SD₁₆×C₂₉	—	4	2	no	—
213	SD₁₆×C₂₉	—	4	2	no	—
214	D₈×C₂₉	—	4	2	no	—
215	D₈×C₂₉	—	4	2	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	—	2	1	no	—
221	C₂×C₈×C₂₉	—	2	1	no	—
222	C₂×C₈×C₂₉	—	4	2	no	—
223	C₄⋊C₄×C₂₉	—	2	2	no	—
224	C₄⋊C₄×C₂₉	—	2	2	no	—
225	C₄⋊C₄×C₂₉	—	2	2	no	—
226	C₄⋊C₄×C₂₉	—	2	2	no	—
227	C₄⋊C₄×C₂₉	—	2	2	no	—
228	C₄⋊C₄×C₂₉	—	2	2	no	—
229	C₄⋊C₄×C₂₉	—	2	1	no	—
230	C₄⋊C₄×C₂₉	—	2	2	no	—
231	C₄⋊C₄×C₂₉	—	2	2	no	—
232	C₄⋊C₄×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	2	1	no	—
235	C₄⋊C₄×C₂₉	—	2	1	no	—
236	C₄⋊C₄×C₂₉	—	2	1	no	—
237	C₄⋊C₄×C₂₉	—	2	1	no	—
238	C₄⋊C₄×C₂₉	—	2	1	no	—
239	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
241	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
244	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
245	C₂²⋊C₄×C₂₉	—	2	2	no	—
246	C₂²⋊C₄×C₂₉	—	2	2	no	—
247	C₂²⋊C₄×C₂₉	—	2	2	no	—
248	C₂²⋊C₄×C₂₉	—	2	2	no	—
249	C₂²⋊C₄×C₂₉	—	2	1	no	—
250	C₂²⋊C₄×C₂₉	—	2	1	no	—
251	C₂²⋊C₄×C₂₉	—	2	2	no	—
252	C₂²⋊C₄×C₂₉	—	2	1	no	—
253	C₂²⋊C₄×C₂₉	—	2	1	no	—
254	C₂²⋊C₄×C₂₉	—	2	1	no	—
255	C₂²⋊C₄×C₂₉	—	2	1	no	—
256	C₂²⋊C₄×C₂₉	—	4	1	no	—
257	C₂²⋊C₄×C₂₉	—	4	1	no	—
258	C₄²×C₂₉	—	2	2	no	—
259	C₄²×C₂₉	—	2	2	no	—
260	C₄²×C₂₉	—	2	1	no	—
261	C₄²×C₂₉	—	2	1	no	—
262	C₄²×C₂₉	—	2	1	no	—
263	C₄²×C₂₉	—	2	1	no	—
264	C₄²×C₂₉	—	2	2	no	—
265	C₄²×C₂₉	—	2	1	no	—
266	C₄²×C₂₉	—	2	1	no	—
267	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
271	#18494	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂³×C₂₉	—	2	1	no	—
273	C₂³×C₂₉	—	2	1	no	—
274	C₂³×C₂₉	—	4	1	no	—
275	C₂³×C₂₉	#120	1	1	yes	characteristic
276	Q₈×C₂₉	—	2	1	no	—
277	Q₈×C₂₉	—	2	1	no	—
278	Q₈×C₂₉	—	2	1	no	—
279	Q₈×C₂₉	—	4	4	no	—
280	Q₈×C₂₉	—	4	2	no	—
281	Q₈×C₂₉	—	4	1	no	—
282	Q₈×C₂₉	—	4	1	no	—
283	Q₈×C₂₉	—	4	1	no	—
284	Q₈×C₂₉	—	4	1	no	—
285	Q₈×C₂₉	#135	1	2	yes	—
286	D₄×C₂₉	—	2	1	no	—
287	D₄×C₂₉	—	2	1	no	—
288	D₄×C₂₉	—	2	1	no	—
289	D₄×C₂₉	—	4	2	no	—
290	D₄×C₂₉	—	4	2	no	—
291	D₄×C₂₉	—	4	2	no	—
292	D₄×C₂₉	—	4	4	no	—
293	D₄×C₂₉	—	4	1	no	—
294	D₄×C₂₉	—	4	1	no	—
295	D₄×C₂₉	—	4	1	no	—
296	D₄×C₂₉	—	4	1	no	—
297	D₄×C₂₉	—	8	2	no	—
298	D₄×C₂₉	#135	1	2	yes	—
299	C₂×C₄×C₂₉	—	2	1	no	—
300	C₂×C₄×C₂₉	—	2	1	no	—
301	C₂×C₄×C₂₉	—	2	1	no	—
302	C₂×C₄×C₂₉	—	2	1	no	—
303	C₂×C₄×C₂₉	—	2	1	no	—
304	C₂×C₄×C₂₉	—	2	2	no	—
305	C₂×C₄×C₂₉	—	2	1	no	—
306	C₂×C₄×C₂₉	—	2	1	no	—
307	C₂×C₄×C₂₉	—	2	1	no	—
308	C₂×C₄×C₂₉	—	2	2	no	—
309	C₂×C₄×C₂₉	—	2	1	no	—
310	C₂×C₄×C₂₉	—	2	1	no	—
311	C₂×C₄×C₂₉	—	2	2	no	—
312	C₂×C₄×C₂₉	—	4	2	no	—
313	C₂×C₄×C₂₉	—	4	2	no	—
314	C₂×C₄×C₂₉	—	4	4	no	—
315	C₂×C₄×C₂₉	—	4	4	no	—
316	C₂×C₄×C₂₉	—	4	1	no	—
317	C₂×C₄×C₂₉	—	4	1	no	—
318	C₂×C₄×C₂₉	—	4	1	no	—
319	C₂×C₄×C₂₉	—	4	1	no	—
320	C₂×C₄×C₂₉	—	4	2	no	—
321	C₂×C₄×C₂₉	—	4	2	no	—
322	C₂×C₄×C₂₉	—	4	1	no	—
323	C₂×C₄×C₂₉	—	8	2	no	—
324	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
325	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
326	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
327	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
330	C₈×C₂₉	—	4	1	no	—
331	C₈×C₂₉	—	4	1	no	—
332	C₈×C₂₉	—	4	1	no	—
333	C₈×C₂₉	—	4	1	no	—
334	C₈×C₂₉	—	4	1	no	—
335	C₈×C₂₉	—	4	1	no	—
336	#3482	C₂×C₂₉	1	1	yes	characteristic, complemented
337	#3131	C₂×C₂₉	1	1	yes	characteristic, complemented
338	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
339	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
340	#1638	C₂×C₂₉	1	1	yes	characteristic, complemented
341	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
342	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
343	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
344	#1628	C₂×C₂₉	1	1	yes	characteristic, complemented
345	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
346	#1626	C₂×C₂₉	1	1	yes	characteristic, complemented
347	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#1544	C₂×C₂₉	1	1	yes	characteristic, complemented
349	#1476	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#1476	C₂×C₂₉	1	1	yes	characteristic, complemented
351	C₂²×C₂₉	—	2	1	no	—
352	C₂²×C₂₉	—	2	1	no	—
353	C₂²×C₂₉	—	2	2	no	—
354	C₂²×C₂₉	—	2	1	no	—
355	C₂²×C₂₉	—	4	1	no	—
356	C₂²×C₂₉	—	4	1	no	—
357	C₂²×C₂₉	—	4	1	no	—
358	C₂²×C₂₉	—	4	1	no	—
359	C₂²×C₂₉	—	4	1	no	—
360	C₂²×C₂₉	—	8	1	no	—
361	C₂²×C₂₉	—	8	1	no	—
362	C₂²×C₂₉	—	8	1	no	—
363	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
364	C₄×C₂₉	—	2	1	no	—
365	C₄×C₂₉	—	2	1	no	—
366	C₄×C₂₉	—	2	2	no	—
367	C₄×C₂₉	—	2	1	no	—
368	C₄×C₂₉	—	4	1	no	—
369	C₄×C₂₉	—	4	1	no	—
370	C₄×C₂₉	—	4	2	no	—
371	C₄×C₂₉	—	4	2	no	—
372	C₄×C₂₉	—	4	1	no	—
373	C₄×C₂₉	—	4	1	no	—
374	C₄×C₂₉	—	4	1	no	—
375	C₄×C₂₉	—	8	1	no	—
376	C₄×C₂₉	#454	1	2	yes	—
377	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
378	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
379	C₄×C₂₉	#575	1	1	yes	characteristic
380	C₄×C₂₉	#575	1	1	yes	characteristic
381	#557	C₂²×C₂₉	1	1	yes	characteristic
382	#556	—	2	1	no	—
383	#556	C₂²×C₂₉	1	1	yes	characteristic
384	#552	—	2	2	no	—
385	#552	—	2	1	no	—
386	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
387	#548	—	2	1	no	—
388	#547	—	2	1	no	—
389	#547	C₂²×C₂₉	1	1	yes	characteristic
390	#533	—	2	1	no	—
391	#533	C₂²×C₂₉	1	1	yes	characteristic
392	#532	C₂²×C₂₉	1	1	yes	characteristic
393	#529	—	2	1	no	—
394	#529	—	2	2	no	—
395	C₄×#41	—	2	1	no	—
396	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
397	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
398	C₂×C₄×Q₈	—	2	1	no	—
399	#488	—	2	2	no	—
400	#487	C₂²×C₂₉	1	1	yes	characteristic
401	#487	C₂²×C₂₉	1	1	yes	characteristic
402	#486	C₂²×C₂₉	1	1	yes	characteristic
403	#486	C₂²×C₂₉	1	1	yes	characteristic
404	#482	—	2	1	no	—
405	#482	—	2	1	no	—
406	#477	C₂²×C₂₉	1	1	yes	characteristic
407	#477	C₂²×C₂₉	1	1	yes	characteristic
408	#476	C₂²×C₂₉	1	1	yes	characteristic
409	#476	C₂²×C₂₉	1	1	yes	characteristic
410	#460	C₂²×C₂₉	1	1	yes	characteristic
411	#460	C₂²×C₂₉	1	1	yes	characteristic
412	#459	C₂²×C₂₉	1	1	yes	characteristic
413	#459	C₂²×C₂₉	1	1	yes	characteristic
414	#449	—	2	1	no	—
415	#449	—	2	1	no	—
416	C₄×SD₁₆	—	2	1	no	—
417	C₄×SD₁₆	—	2	1	no	—
418	C₄×D₈	—	2	1	no	—
419	C₄×D₈	—	2	1	no	—
420	#431	C₂²×C₂₉	1	1	yes	characteristic
421	#431	C₂²×C₂₉	1	1	yes	characteristic
422	#416	—	2	2	no	—
423	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
424	#332	C₂²×C₂₉	1	1	yes	characteristic
425	#332	C₂²×C₂₉	1	1	yes	characteristic
426	#332	C₂²×C₂₉	1	1	yes	characteristic
427	#332	C₂²×C₂₉	1	1	yes	characteristic
428	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
429	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
430	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
431	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
432	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
433	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
434	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
435	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
436	C₂×C₂₉	—	4	1	no	—
437	C₂×C₂₉	—	4	2	no	—
438	C₂×C₂₉	—	8	1	no	—
439	C₂×C₂₉	—	16	1	no	—
440	C₂×C₂₉	#3002	1	1	yes	characteristic
441	C₂×C₂₉	#3002	1	1	yes	characteristic
442	C₂×C₂₉	C₂×#454	1	1	yes	characteristic
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
446	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
447	C₂²×Q₈	—	2	1	no	—
448	C₂×SD₁₆	—	2	1	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×D₈	—	2	1	no	—
451	C₂×D₈	—	2	1	no	—
452	C₂²×C₈	—	2	1	no	—
453	C₄⋊Q₈	—	2	1	no	—
454	C₄⋊Q₈	—	2	1	no	—
455	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
456	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
457	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
458	#127	C₂³×C₂₉	1	1	yes	characteristic
459	#126	—	2	2	no	—
460	#126	—	2	2	no	—
461	#126	—	2	2	no	—
462	#125	—	2	2	no	—
463	#125	—	2	2	no	—
464	#125	—	2	1	no	—
465	#125	D₄×C₂₉	1	2	yes	—
466	#124	—	2	2	no	—
467	#124	—	2	1	no	—
468	#124	—	2	1	no	—
469	#123	—	2	2	no	—
470	#123	—	2	2	no	—
471	#123	—	2	2	no	—
472	C₂²⋊Q₈	—	2	2	no	—
473	C₂²⋊Q₈	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	#121	—	2	2	no	—
480	#121	—	2	1	no	—
481	#121	—	2	1	no	—
482	#121	—	2	1	no	—
483	C₄×Q₈	—	2	2	no	—
484	C₄×Q₈	—	2	2	no	—
485	C₄×Q₈	—	2	1	no	—
486	C₄×Q₈	—	2	1	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	—	2	1	no	—
489	C₄×Q₈	—	2	1	no	—
490	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
491	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
492	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
493	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	1	no	—
497	C₄×D₄	—	2	1	no	—
498	C₄×D₄	—	2	1	no	—
499	C₄×D₄	—	2	1	no	—
500	C₄×D₄	—	2	1	no	—
501	C₄×D₄	—	2	1	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
504	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
505	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
506	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
507	#117	—	2	2	no	—
508	#117	—	2	2	no	—
509	#117	—	2	1	no	—
510	#117	—	2	1	no	—
511	#117	—	2	1	no	—
512	#117	D₄×C₂₉	1	1	yes	characteristic
513	#117	D₄×C₂₉	1	1	yes	characteristic
514	#117	D₄×C₂₉	1	2	yes	—
515	C₂×C₄⋊C₄	—	2	2	no	—
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₄²	—	2	2	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
521	#107	—	2	1	no	—
522	#107	—	2	1	no	—
523	#106	—	2	1	no	—
524	#106	—	2	1	no	—
525	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
526	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
527	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
528	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
529	#103	—	2	1	no	—
530	#103	—	2	1	no	—
531	#103	—	2	2	no	—
532	#103	—	2	2	no	—
533	#102	—	2	1	no	—
534	#102	—	2	1	no	—
535	#102	—	2	2	no	—
536	#102	—	2	2	no	—
537	#102	—	2	1	no	—
538	#102	—	2	1	no	—
539	#102	—	2	1	no	—
540	#102	—	2	1	no	—
541	C₂²⋊C₈	—	2	1	no	—
542	C₂²⋊C₈	—	2	1	no	—
543	C₄×C₈	—	2	1	no	—
544	C₄×C₈	—	2	1	no	—
545	C₄×C₈	—	2	1	no	—
546	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
547	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
548	C₂₉	#18494	1	1	yes	characteristic, direct product factor, Sylow
549	#41	—	2	2	no	—
550	#41	—	2	2	no	—
551	#41	—	4	1	no	—
552	#41	—	4	1	no	—
553	#41	—	4	4	no	—
554	#41	—	4	2	no	—
555	#41	—	4	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	4	2	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
563	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	4	1	no	—
571	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
572	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	4	1	no	—
582	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
585	SD₁₆	—	4	2	no	—
586	SD₁₆	—	4	2	no	—
587	D₈	—	4	2	no	—
588	D₈	—	4	2	no	—
589	C₂×C₈	—	2	1	no	—
590	C₂×C₈	—	2	1	no	—
591	C₂×C₈	—	2	1	no	—
592	C₂×C₈	—	2	1	no	—
593	C₂×C₈	—	2	1	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	4	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
613	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
614	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
615	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
616	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
617	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	2	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	1	no	—
629	C₂²⋊C₄	—	4	1	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
643	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	C₂₉×#120	1	1	yes	characteristic
648	Q₈	—	2	1	no	—
649	Q₈	—	2	1	no	—
650	Q₈	—	2	1	no	—
651	Q₈	—	4	4	no	—
652	Q₈	—	4	2	no	—
653	Q₈	—	4	1	no	—
654	Q₈	—	4	1	no	—
655	Q₈	—	4	1	no	—
656	Q₈	—	4	1	no	—
657	Q₈	C₂₉×#135	1	2	yes	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	2	1	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	1	no	—
666	D₄	—	4	1	no	—
667	D₄	—	4	1	no	—
668	D₄	—	4	1	no	—
669	D₄	—	8	2	no	—
670	D₄	C₂₉×#135	1	2	yes	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
697	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
698	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
699	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
702	C₈	—	4	1	no	—
703	C₈	—	4	1	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	8	1	no	—
718	C₂²	—	8	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	8	1	no	—
733	C₄	C₂₉×#454	1	2	yes	—
734	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
735	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
736	C₄	C₂₉×#575	1	1	yes	characteristic
737	C₄	C₂₉×#575	1	1	yes	characteristic
738	C₂	—	4	1	no	—
739	C₂	—	4	2	no	—
740	C₂	—	8	1	no	—
741	C₂	—	16	1	no	—
742	C₂	C₂₉×#3002	1	1	yes	characteristic
743	C₂	C₂₉×#3002	1	1	yes	characteristic
744	C₂	C₂×C₂₉×#454	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3482	C₂	semidirect
2. C₂₉×#3131	C₂	semidirect
3. C₂₉×#3106	C₂	semidirect
4. C₂₉×#3106	C₂	semidirect
5. C₂₉×#1638	C₂	semidirect
6. C₂₉×#1637	C₂	semidirect
7. C₂₉×#1636	C₂	semidirect
8. C₂₉×#1635	C₂	semidirect
9. C₂₉×#1628	C₂	semidirect
10. C₂₉×#1627	C₂	semidirect
11. C₂₉×#1626	C₂	semidirect
12. C₂₉×#1625	C₂	semidirect
13. C₂₉×#1544	C₂	semidirect
14. C₂₉×#1476	C₂	semidirect
15. C₂₉×#1476	C₂	semidirect
271. #18494	C₂₉	direct (N × H)
336. #3482	C₂×C₂₉	semidirect
337. #3131	C₂×C₂₉	semidirect
338. #3106	C₂×C₂₉	semidirect
339. #3106	C₂×C₂₉	semidirect
340. #1638	C₂×C₂₉	semidirect
341. #1637	C₂×C₂₉	semidirect
342. #1636	C₂×C₂₉	semidirect
343. #1635	C₂×C₂₉	semidirect
344. #1628	C₂×C₂₉	semidirect
345. #1627	C₂×C₂₉	semidirect
346. #1626	C₂×C₂₉	semidirect
347. #1625	C₂×C₂₉	semidirect
348. #1544	C₂×C₂₉	semidirect
349. #1476	C₂×C₂₉	semidirect
350. #1476	C₂×C₂₉	semidirect
548. C₂₉	#18494	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×#3482	2
C₂₉×#3131	2
C₂₉×#3106	2
C₂₉×#1638	2
C₂₉×#1637	2
C₂₉×#1636	2
C₂₉×#1635	2
C₂₉×#1628	2
C₂₉×#1627	2
C₂₉×#1626	2
C₂₉×#1625	2
C₂₉×#1544	2
C₂₉×#1476	2
#18494	29

Subgroups — C29×#18494 #20313394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18494 #20313394