Subgroups — C₂₉×#18933 #20313833

Order 7424.

858 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3544	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1646	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1634	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1633	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#563	—	2	2	no	—
17	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
18	C₂₉×#555	C₂²	1	1	yes	characteristic
19	C₂₉×#554	C₂²	1	1	yes	characteristic
20	C₂₉×#554	C₂²	1	1	yes	characteristic
21	C₂₉×#552	—	2	1	no	—
22	C₂₉×#552	—	2	1	no	—
23	C₂₉×#547	—	2	1	no	—
24	C₂₉×#547	—	2	1	no	—
25	C₂₉×#544	—	2	1	no	—
26	C₂₉×#544	—	2	1	no	—
27	C₂₉×#542	—	2	1	no	—
28	C₂₉×#542	—	2	1	no	—
29	C₂₉×#536	—	2	2	no	—
30	C₂₉×#533	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂₉×#529	C₂²	1	1	yes	characteristic
33	C₂₉×#529	C₂²	1	1	yes	characteristic
34	C₂₉×#499	—	2	1	no	—
35	C₂₉×#494	C₂²	1	1	yes	characteristic
36	C₂₉×#494	C₂²	1	1	yes	characteristic
37	C₂₉×#488	—	2	1	no	—
38	C₂₉×#487	C₂²	1	1	yes	characteristic
39	C₂₉×#487	C₂²	1	1	yes	characteristic
40	C₂₉×#485	—	2	1	no	—
41	C₂₉×#482	—	2	1	no	—
42	C₂₉×#479	—	2	1	no	—
43	C₂₉×#477	C₂²	1	1	yes	characteristic
44	C₂₉×#477	C₂²	1	1	yes	characteristic
45	C₂₉×#476	C₂²	1	1	yes	characteristic
46	C₂₉×#476	C₂²	1	1	yes	characteristic
47	C₂₉×#475	C₂²	1	1	yes	characteristic
48	C₂₉×#474	C₂²	1	1	yes	characteristic
49	C₂₉×#470	—	2	1	no	—
50	C₂₉×#468	—	2	1	no	—
51	C₂₉×#464	—	2	1	no	—
52	C₂₉×#462	—	2	2	no	—
53	C₂₉×#462	C₂²	1	1	yes	characteristic
54	C₂₉×#461	C₂²	1	1	yes	characteristic
55	C₂₉×#451	—	2	2	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#431	C₂²	1	1	yes	characteristic
58	C₂₉×#423	C₂²	1	1	yes	characteristic
59	C₂₉×#333	C₂²	1	1	yes	characteristic
60	C₂₉×#333	C₂²	1	1	yes	characteristic
61	C₂₉×#333	C₂²	1	1	yes	characteristic
62	C₂₉×#333	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	2	no	—
72	C₂²×Q₈×C₂₉	D₄	1	2	yes	—
73	C₂×Q₁₆×C₂₉	—	2	2	no	—
74	C₂×Q₁₆×C₂₉	—	2	2	no	—
75	C₂×Q₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	—	2	1	no	—
77	C₂×M₁₆×C₂₉	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	—	2	2	no	—
79	C₂₉×C₄⋊Q₈	—	2	2	no	—
80	C₂₉×C₄⋊Q₈	—	2	1	no	—
81	C₂₉×C₄⋊Q₈	—	2	1	no	—
82	C₂₉×C₄⋊Q₈	—	2	1	no	—
83	C₂₉×C₄⋊Q₈	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	D₄	1	2	yes	—
85	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₂₉×#126	—	2	2	no	—
90	C₂₉×#126	—	2	2	no	—
91	C₂₉×#126	—	2	1	no	—
92	C₂₉×#126	—	2	1	no	—
93	C₂₉×#125	—	2	2	no	—
94	C₂₉×#125	—	2	2	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	—	2	1	no	—
97	C₂₉×#125	—	2	1	no	—
98	C₂₉×#125	D₄	1	1	yes	characteristic
99	C₂₉×#125	D₄	1	1	yes	characteristic
100	C₂₉×#124	—	2	2	no	—
101	C₂₉×#124	—	2	2	no	—
102	C₂₉×#124	D₄	1	1	yes	characteristic
103	C₂₉×#124	D₄	1	1	yes	characteristic
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×#123	—	2	2	no	—
106	C₂₉×#123	—	2	2	no	—
107	C₂₉×#123	—	2	2	no	—
108	C₂₉×#123	—	2	1	no	—
109	C₂₉×#123	—	2	1	no	—
110	C₂₉×C₂²⋊Q₈	—	2	2	no	—
111	C₂₉×C₂²⋊Q₈	—	2	2	no	—
112	C₂₉×C₂²⋊Q₈	—	2	2	no	—
113	C₂₉×C₂²⋊Q₈	—	2	2	no	—
114	C₂₉×C₂²⋊Q₈	—	2	2	no	—
115	C₂₉×C₂²⋊Q₈	—	2	2	no	—
116	C₂₉×C₂²⋊Q₈	—	2	1	no	—
117	C₂₉×C₂²⋊Q₈	—	2	1	no	—
118	C₂₉×C₂²⋊Q₈	—	2	1	no	—
119	C₂₉×C₂²⋊Q₈	—	2	1	no	—
120	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
121	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
122	C₂₉×#121	—	2	1	no	—
123	C₂₉×#121	—	2	1	no	—
124	C₂₉×#121	D₄	1	1	yes	characteristic
125	C₂₉×#121	D₄	1	1	yes	characteristic
126	C₄×Q₈×C₂₉	—	2	1	no	—
127	C₄×Q₈×C₂₉	—	2	1	no	—
128	C₄×Q₈×C₂₉	—	2	1	no	—
129	C₄×Q₈×C₂₉	—	2	1	no	—
130	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	—	2	1	no	—
134	C₄×D₄×C₂₉	—	2	1	no	—
135	C₄×D₄×C₂₉	—	2	1	no	—
136	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
138	C₂₉×#117	—	2	2	no	—
139	C₂₉×#117	—	2	1	no	—
140	C₂₉×#117	—	2	1	no	—
141	C₂₉×#117	—	2	1	no	—
142	C₂₉×#117	—	2	1	no	—
143	C₂₉×#117	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
147	C₂×C₄⋊C₄×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×#107	—	2	1	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×C₄⋊C₈	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×#103	—	2	2	no	—
162	C₂₉×#103	—	2	2	no	—
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#103	—	2	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#103	—	2	1	no	—
167	C₂₉×#103	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×C₂²⋊C₈	—	2	1	no	—
172	C₂₉×C₂²⋊C₈	—	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	—	8	4	no	—
177	C₂×Q₈×C₂₉	—	2	2	no	—
178	C₂×Q₈×C₂₉	—	2	2	no	—
179	C₂×Q₈×C₂₉	—	2	1	no	—
180	C₂×Q₈×C₂₉	—	2	1	no	—
181	C₂×Q₈×C₂₉	—	8	2	no	—
182	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₂₉	—	2	1	no	—
187	C₂×D₄×C₂₉	—	2	1	no	—
188	C₂×D₄×C₂₉	—	2	2	no	—
189	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₉	—	2	2	no	—
192	C₂²×C₄×C₂₉	—	2	2	no	—
193	C₂²×C₄×C₂₉	—	2	2	no	—
194	C₂²×C₄×C₂₉	—	2	1	no	—
195	C₂²×C₄×C₂₉	—	2	1	no	—
196	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	Q₁₆×C₂₉	—	8	1	no	—
200	Q₁₆×C₂₉	—	8	2	no	—
201	Q₁₆×C₂₉	—	8	2	no	—
202	SD₁₆×C₂₉	—	8	1	no	—
203	M₁₆×C₂₉	—	8	1	no	—
204	C₂×C₈×C₂₉	—	2	1	no	—
205	C₂×C₈×C₂₉	—	2	1	no	—
206	C₂×C₈×C₂₉	—	2	1	no	—
207	C₂×C₈×C₂₉	—	2	1	no	—
208	C₂×C₈×C₂₉	—	2	1	no	—
209	C₂×C₈×C₂₉	—	2	1	no	—
210	C₄⋊C₄×C₂₉	—	2	2	no	—
211	C₄⋊C₄×C₂₉	—	2	2	no	—
212	C₄⋊C₄×C₂₉	—	2	2	no	—
213	C₄⋊C₄×C₂₉	—	2	2	no	—
214	C₄⋊C₄×C₂₉	—	2	2	no	—
215	C₄⋊C₄×C₂₉	—	2	2	no	—
216	C₄⋊C₄×C₂₉	—	2	2	no	—
217	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
222	C₄⋊C₄×C₂₉	—	2	1	no	—
223	C₄⋊C₄×C₂₉	—	2	1	no	—
224	C₄⋊C₄×C₂₉	—	2	1	no	—
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	—	2	1	no	—
230	C₄⋊C₄×C₂₉	—	2	1	no	—
231	C₄⋊C₄×C₂₉	—	2	1	no	—
232	C₄⋊C₄×C₂₉	—	2	1	no	—
233	C₄⋊C₄×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	4	1	no	—
235	C₄⋊C₄×C₂₉	—	4	1	no	—
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	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
240	C₂²⋊C₄×C₂₉	—	2	2	no	—
241	C₂²⋊C₄×C₂₉	—	2	2	no	—
242	C₂²⋊C₄×C₂₉	—	2	2	no	—
243	C₂²⋊C₄×C₂₉	—	2	2	no	—
244	C₂²⋊C₄×C₂₉	—	2	1	no	—
245	C₂²⋊C₄×C₂₉	—	2	1	no	—
246	C₂²⋊C₄×C₂₉	—	2	1	no	—
247	C₂²⋊C₄×C₂₉	—	2	1	no	—
248	C₂²⋊C₄×C₂₉	—	2	1	no	—
249	C₂²⋊C₄×C₂₉	—	2	1	no	—
250	C₂²⋊C₄×C₂₉	—	2	1	no	—
251	C₂²⋊C₄×C₂₉	—	2	1	no	—
252	C₂²⋊C₄×C₂₉	—	2	1	no	—
253	C₂²⋊C₄×C₂₉	—	2	1	no	—
254	C₂²⋊C₄×C₂₉	—	4	1	no	—
255	C₄²×C₂₉	—	2	2	no	—
256	C₄²×C₂₉	—	2	2	no	—
257	C₄²×C₂₉	—	2	1	no	—
258	C₄²×C₂₉	—	2	1	no	—
259	C₄²×C₂₉	—	4	1	no	—
260	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
264	#18933	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₂₉	—	2	1	no	—
266	C₂³×C₂₉	—	2	1	no	—
267	C₂³×C₂₉	#120	1	1	yes	characteristic
268	Q₈×C₂₉	—	2	1	no	—
269	Q₈×C₂₉	—	2	1	no	—
270	Q₈×C₂₉	—	2	1	no	—
271	Q₈×C₂₉	—	2	1	no	—
272	Q₈×C₂₉	—	4	2	no	—
273	Q₈×C₂₉	—	4	2	no	—
274	Q₈×C₂₉	—	4	2	no	—
275	Q₈×C₂₉	—	4	1	no	—
276	Q₈×C₂₉	—	4	1	no	—
277	Q₈×C₂₉	—	8	2	no	—
278	Q₈×C₂₉	—	8	2	no	—
279	D₄×C₂₉	—	2	1	no	—
280	D₄×C₂₉	—	2	1	no	—
281	D₄×C₂₉	—	2	1	no	—
282	D₄×C₂₉	—	2	1	no	—
283	D₄×C₂₉	—	4	2	no	—
284	D₄×C₂₉	—	4	2	no	—
285	D₄×C₂₉	—	8	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	—	2	1	no	—
293	C₂×C₄×C₂₉	—	2	1	no	—
294	C₂×C₄×C₂₉	—	2	2	no	—
295	C₂×C₄×C₂₉	—	2	1	no	—
296	C₂×C₄×C₂₉	—	2	1	no	—
297	C₂×C₄×C₂₉	—	2	2	no	—
298	C₂×C₄×C₂₉	—	4	1	no	—
299	C₂×C₄×C₂₉	—	4	4	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	—	4	1	no	—
304	C₂×C₄×C₂₉	—	4	1	no	—
305	C₂×C₄×C₂₉	—	4	1	no	—
306	C₂×C₄×C₂₉	—	8	2	no	—
307	C₂×C₄×C₂₉	—	8	2	no	—
308	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
310	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
311	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
314	C₈×C₂₉	—	4	1	no	—
315	C₈×C₂₉	—	4	1	no	—
316	C₈×C₂₉	—	4	1	no	—
317	C₈×C₂₉	—	4	1	no	—
318	C₈×C₂₉	—	4	1	no	—
319	C₈×C₂₉	—	4	1	no	—
320	#3544	C₂×C₂₉	1	1	yes	characteristic
321	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#3233	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#3209	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1646	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
326	#1644	C₂×C₂₉	1	1	yes	characteristic, complemented
327	#1643	C₂×C₂₉	1	1	yes	characteristic, complemented
328	#1634	C₂×C₂₉	1	1	yes	characteristic, complemented
329	#1633	C₂×C₂₉	1	1	yes	characteristic, complemented
330	#1632	C₂×C₂₉	1	1	yes	characteristic, complemented
331	#1632	C₂×C₂₉	1	1	yes	characteristic, complemented
332	#1548	C₂×C₂₉	1	1	yes	characteristic, complemented
333	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
334	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
335	C₂²×C₂₉	—	2	1	no	—
336	C₂²×C₂₉	—	2	1	no	—
337	C₂²×C₂₉	—	2	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	—	4	1	no	—
343	C₂²×C₂₉	—	4	1	no	—
344	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
345	C₄×C₂₉	—	2	1	no	—
346	C₄×C₂₉	—	2	1	no	—
347	C₄×C₂₉	—	2	1	no	—
348	C₄×C₂₉	—	2	1	no	—
349	C₄×C₂₉	—	4	1	no	—
350	C₄×C₂₉	—	4	1	no	—
351	C₄×C₂₉	—	4	1	no	—
352	C₄×C₂₉	—	4	1	no	—
353	C₄×C₂₉	—	4	2	no	—
354	C₄×C₂₉	—	4	2	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	#577	1	1	yes	characteristic
360	C₄×C₂₉	#578	1	1	yes	characteristic
361	C₄×C₂₉	#578	1	1	yes	characteristic
362	C₄×C₂₉	#578	1	1	yes	characteristic
363	#563	—	2	2	no	—
364	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
365	#555	C₂²×C₂₉	1	1	yes	characteristic
366	#554	C₂²×C₂₉	1	1	yes	characteristic
367	#554	C₂²×C₂₉	1	1	yes	characteristic
368	#552	—	2	1	no	—
369	#552	—	2	1	no	—
370	#547	—	2	1	no	—
371	#547	—	2	1	no	—
372	#544	—	2	1	no	—
373	#544	—	2	1	no	—
374	#542	—	2	1	no	—
375	#542	—	2	1	no	—
376	#536	—	2	2	no	—
377	#533	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
379	#529	C₂²×C₂₉	1	1	yes	characteristic
380	#529	C₂²×C₂₉	1	1	yes	characteristic
381	#499	—	2	1	no	—
382	#494	C₂²×C₂₉	1	1	yes	characteristic
383	#494	C₂²×C₂₉	1	1	yes	characteristic
384	#488	—	2	1	no	—
385	#487	C₂²×C₂₉	1	1	yes	characteristic
386	#487	C₂²×C₂₉	1	1	yes	characteristic
387	#485	—	2	1	no	—
388	#482	—	2	1	no	—
389	#479	—	2	1	no	—
390	#477	C₂²×C₂₉	1	1	yes	characteristic
391	#477	C₂²×C₂₉	1	1	yes	characteristic
392	#476	C₂²×C₂₉	1	1	yes	characteristic
393	#476	C₂²×C₂₉	1	1	yes	characteristic
394	#475	C₂²×C₂₉	1	1	yes	characteristic
395	#474	C₂²×C₂₉	1	1	yes	characteristic
396	#470	—	2	1	no	—
397	#468	—	2	1	no	—
398	#464	—	2	1	no	—
399	#462	—	2	2	no	—
400	#462	C₂²×C₂₉	1	1	yes	characteristic
401	#461	C₂²×C₂₉	1	1	yes	characteristic
402	#451	—	2	2	no	—
403	#431	C₂²×C₂₉	1	1	yes	characteristic
404	#431	C₂²×C₂₉	1	1	yes	characteristic
405	#423	C₂²×C₂₉	1	1	yes	characteristic
406	#333	C₂²×C₂₉	1	1	yes	characteristic
407	#333	C₂²×C₂₉	1	1	yes	characteristic
408	#333	C₂²×C₂₉	1	1	yes	characteristic
409	#333	C₂²×C₂₉	1	1	yes	characteristic
410	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
411	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
412	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
413	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
414	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
415	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
416	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
417	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
418	C₂×C₂₉	—	4	1	no	—
419	C₂×C₂₉	—	8	1	no	—
420	C₂×C₂₉	—	8	1	no	—
421	C₂×C₂₉	#3011	1	1	yes	characteristic
422	C₂×C₂₉	#3013	1	1	yes	characteristic
423	C₂×C₂₉	#3019	1	1	yes	characteristic
424	C₂×#41	—	2	2	no	—
425	C₂²×Q₈	D₄×C₂₉	1	2	yes	—
426	C₂×Q₁₆	—	2	2	no	—
427	C₂×Q₁₆	—	2	2	no	—
428	C₂×Q₁₆	—	2	1	no	—
429	C₂×SD₁₆	—	2	1	no	—
430	C₂×M₁₆	—	2	1	no	—
431	C₄⋊Q₈	—	2	2	no	—
432	C₄⋊Q₈	—	2	2	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	D₄×C₂₉	1	2	yes	—
438	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
439	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
440	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
441	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
442	#126	—	2	2	no	—
443	#126	—	2	2	no	—
444	#126	—	2	1	no	—
445	#126	—	2	1	no	—
446	#125	—	2	2	no	—
447	#125	—	2	2	no	—
448	#125	—	2	1	no	—
449	#125	—	2	1	no	—
450	#125	—	2	1	no	—
451	#125	D₄×C₂₉	1	1	yes	characteristic
452	#125	D₄×C₂₉	1	1	yes	characteristic
453	#124	—	2	2	no	—
454	#124	—	2	2	no	—
455	#124	D₄×C₂₉	1	1	yes	characteristic
456	#124	D₄×C₂₉	1	1	yes	characteristic
457	#123	—	2	2	no	—
458	#123	—	2	2	no	—
459	#123	—	2	2	no	—
460	#123	—	2	2	no	—
461	#123	—	2	1	no	—
462	#123	—	2	1	no	—
463	C₂²⋊Q₈	—	2	2	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	1	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	—	2	1	no	—
472	C₂²⋊Q₈	—	2	1	no	—
473	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
474	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	D₄×C₂₉	1	1	yes	characteristic
478	#121	D₄×C₂₉	1	1	yes	characteristic
479	C₄×Q₈	—	2	1	no	—
480	C₄×Q₈	—	2	1	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
484	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	1	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
490	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
491	#117	—	2	2	no	—
492	#117	—	2	1	no	—
493	#117	—	2	1	no	—
494	#117	—	2	1	no	—
495	#117	—	2	1	no	—
496	#117	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
502	#107	—	2	1	no	—
503	#107	—	2	1	no	—
504	#107	—	2	1	no	—
505	#106	—	2	1	no	—
506	#106	—	2	1	no	—
507	#106	—	2	1	no	—
508	C₄⋊C₈	—	2	1	no	—
509	C₄⋊C₈	—	2	1	no	—
510	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
511	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
512	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
513	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
514	#103	—	2	2	no	—
515	#103	—	2	2	no	—
516	#103	—	2	1	no	—
517	#103	—	2	1	no	—
518	#103	—	2	1	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#102	—	2	1	no	—
522	#102	—	2	1	no	—
523	#102	—	2	1	no	—
524	C₂²⋊C₈	—	2	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	C₄×C₈	—	2	1	no	—
527	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
528	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
529	C₂₉	#18933	1	1	yes	characteristic, direct product factor, Sylow
530	#41	—	8	4	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	8	2	no	—
536	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
537	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
538	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
539	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
544	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
552	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
553	Q₁₆	—	8	1	no	—
554	Q₁₆	—	8	2	no	—
555	Q₁₆	—	8	2	no	—
556	SD₁₆	—	8	1	no	—
557	M₁₆	—	8	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
591	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
592	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	4	1	no	—
614	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
615	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
616	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
617	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	C₂₉×#120	1	1	yes	characteristic
621	Q₈	—	2	1	no	—
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	2	1	no	—
625	Q₈	—	4	2	no	—
626	Q₈	—	4	2	no	—
627	Q₈	—	4	2	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	8	2	no	—
631	Q₈	—	8	2	no	—
632	D₄	—	2	1	no	—
633	D₄	—	2	1	no	—
634	D₄	—	2	1	no	—
635	D₄	—	2	1	no	—
636	D₄	—	4	2	no	—
637	D₄	—	4	2	no	—
638	D₄	—	8	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	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	2	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	4	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	2	no	—
660	C₂×C₄	—	8	2	no	—
661	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
662	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
663	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
664	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
667	C₈	—	4	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	4	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	C₂×C₂₉×#120	1	1	yes	characteristic
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	C₂₉×#577	1	1	yes	characteristic
698	C₄	C₂₉×#578	1	1	yes	characteristic
699	C₄	C₂₉×#578	1	1	yes	characteristic
700	C₄	C₂₉×#578	1	1	yes	characteristic
701	C₂	—	4	1	no	—
702	C₂	—	8	1	no	—
703	C₂	—	8	1	no	—
704	C₂	C₂₉×#3011	1	1	yes	characteristic
705	C₂	C₂₉×#3013	1	1	yes	characteristic
706	C₂	C₂₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3544	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#3252	C₂	semidirect
3. C₂₉×#3233	C₂	semidirect
4. C₂₉×#3209	C₂	semidirect
5. C₂₉×#1646	C₂	semidirect
6. C₂₉×#1645	C₂	semidirect
7. C₂₉×#1644	C₂	semidirect
8. C₂₉×#1643	C₂	semidirect
9. C₂₉×#1634	C₂	semidirect
10. C₂₉×#1633	C₂	semidirect
11. C₂₉×#1632	C₂	semidirect
12. C₂₉×#1632	C₂	semidirect
13. C₂₉×#1548	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1482	C₂	semidirect
264. #18933	C₂₉	direct (N × H)
321. #3252	C₂×C₂₉	semidirect
322. #3233	C₂×C₂₉	semidirect
323. #3209	C₂×C₂₉	semidirect
324. #1646	C₂×C₂₉	semidirect
325. #1645	C₂×C₂₉	semidirect
326. #1644	C₂×C₂₉	semidirect
327. #1643	C₂×C₂₉	semidirect
328. #1634	C₂×C₂₉	semidirect
329. #1633	C₂×C₂₉	semidirect
330. #1632	C₂×C₂₉	semidirect
331. #1632	C₂×C₂₉	semidirect
332. #1548	C₂×C₂₉	semidirect
333. #1495	C₂×C₂₉	semidirect
334. #1482	C₂×C₂₉	semidirect
529. C₂₉	#18933	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×#3544	2
C₂₉×#3252	2
C₂₉×#3233	2
C₂₉×#3209	2
C₂₉×#1646	2
C₂₉×#1645	2
C₂₉×#1644	2
C₂₉×#1643	2
C₂₉×#1634	2
C₂₉×#1633	2
C₂₉×#1632	2
C₂₉×#1548	2
C₂₉×#1495	2
C₂₉×#1482	2
#18933	29

Subgroups — C29×#18933 #20313833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18933 #20313833