Subgroups — C₂₉×#19720 #20314620

Order 7424.

656 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3231	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3231	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3229	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#3209	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#3185	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#3165	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1718	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1718	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1716	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1716	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1707	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1707	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1453	C₂	1	1	yes	maximal, characteristic
16	C₂₉×#533	C₂²	1	1	yes	characteristic
17	C₂₉×#533	C₂²	1	1	yes	characteristic
18	C₂₉×#533	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂₉×#501	—	2	2	no	—
21	C₂₉×#500	C₂²	1	1	yes	characteristic
22	C₂₉×#500	C₂²	1	1	yes	characteristic
23	C₂₉×#500	C₂²	1	1	yes	characteristic
24	C₂₉×#500	C₂²	1	1	yes	characteristic
25	C₂₉×#498	C₂²	1	1	yes	characteristic
26	C₂₉×#498	C₂²	1	1	yes	characteristic
27	C₂₉×#498	C₂²	1	1	yes	characteristic
28	C₂₉×#498	C₂²	1	1	yes	characteristic
29	C₂₉×#498	C₂²	1	1	yes	characteristic
30	C₂₉×#498	C₂²	1	1	yes	characteristic
31	C₂₉×#498	C₂²	1	1	yes	characteristic
32	C₂₉×#494	C₂²	1	1	yes	characteristic
33	C₂₉×#494	C₂²	1	1	yes	characteristic
34	C₂₉×#494	C₂²	1	1	yes	characteristic
35	C₂₉×#487	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#487	C₂²	1	1	yes	characteristic
38	C₂₉×#487	C₂²	1	1	yes	characteristic
39	C₂₉×#487	C₂²	1	1	yes	characteristic
40	C₂₉×#487	C₂²	1	1	yes	characteristic
41	C₂₉×#487	C₂²	1	1	yes	characteristic
42	C₂₉×#487	C₂²	1	1	yes	characteristic
43	C₂₉×#487	C₂²	1	1	yes	characteristic
44	C₂₉×#487	C₂²	1	1	yes	characteristic
45	C₂₉×#485	—	2	2	no	—
46	C₂₉×#485	—	2	2	no	—
47	C₂₉×#483	—	2	2	no	—
48	C₂₉×#479	—	2	2	no	—
49	C₂₉×#479	—	2	2	no	—
50	C₂₉×#475	—	2	2	no	—
51	C₂₉×#470	—	2	2	no	—
52	C₂₉×#462	—	2	2	no	—
53	C₂₉×#451	—	2	2	no	—
54	C₂₉×#441	—	2	2	no	—
55	C₂₉×#431	C₂²	1	1	yes	characteristic
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#428	—	2	2	no	—
58	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#322	C₂²	1	1	yes	characteristic
60	C₂₉×#322	C₂²	1	1	yes	characteristic
61	C₂₉×#322	C₂²	1	1	yes	characteristic
62	C₈²×C₂₉	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₉	—	2	1	no	—
64	C₂×Q₁₆×C₂₉	—	2	2	no	—
65	C₂×Q₁₆×C₂₉	—	2	2	no	—
66	C₂×Q₁₆×C₂₉	—	2	2	no	—
67	C₂×M₁₆×C₂₉	D₄	1	2	yes	—
68	C₂₉×C₄⋊Q₈	—	2	1	no	—
69	C₂₉×C₄⋊Q₈	—	2	1	no	—
70	C₂₉×C₄⋊Q₈	—	2	1	no	—
71	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
74	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
75	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₂₉×#125	—	2	1	no	—
80	C₂₉×#125	—	2	1	no	—
81	C₂₉×#125	—	2	1	no	—
82	C₂₉×C₂²⋊Q₈	—	2	1	no	—
83	C₂₉×C₂²⋊Q₈	—	2	1	no	—
84	C₂₉×C₂²⋊Q₈	—	2	1	no	—
85	C₂₉×C₂²⋊Q₈	—	2	1	no	—
86	C₂₉×C₂²⋊Q₈	—	2	1	no	—
87	C₂₉×C₂²⋊Q₈	—	2	1	no	—
88	C₄×Q₈×C₂₉	—	2	1	no	—
89	C₄×Q₈×C₂₉	—	2	1	no	—
90	C₄×Q₈×C₂₉	—	2	1	no	—
91	C₄×Q₈×C₂₉	—	2	1	no	—
92	C₄×Q₈×C₂₉	—	2	1	no	—
93	C₄×Q₈×C₂₉	—	2	1	no	—
94	C₂₉×#117	—	2	1	no	—
95	C₂₉×#117	—	2	1	no	—
96	C₂₉×#117	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
100	C₂₉×#107	—	2	2	no	—
101	C₂₉×#107	—	2	2	no	—
102	C₂₉×#107	—	2	2	no	—
103	C₂₉×#107	—	2	2	no	—
104	C₂₉×#106	—	2	2	no	—
105	C₂₉×#106	—	2	2	no	—
106	C₂₉×#106	—	2	2	no	—
107	C₂₉×#106	—	2	2	no	—
108	C₂₉×#106	—	2	2	no	—
109	C₂₉×#106	—	2	2	no	—
110	C₂₉×#106	—	2	2	no	—
111	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
112	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
113	C₂₉×#103	—	2	2	no	—
114	C₂₉×#103	—	2	2	no	—
115	C₂₉×#103	—	2	2	no	—
116	C₂₉×#103	—	2	2	no	—
117	C₂₉×#103	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#103	—	2	2	no	—
122	C₂₉×#103	—	2	2	no	—
123	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
124	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
125	C₂₉×#97	D₄	1	2	yes	—
126	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
130	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₂₉	—	2	1	no	—
133	C₂×Q₈×C₂₉	—	2	1	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	4	1	no	—
141	C₂×Q₈×C₂₉	—	8	2	no	—
142	C₂²×C₄×C₂₉	—	4	1	no	—
143	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₂₉	—	4	4	no	—
147	Q₁₆×C₂₉	—	8	2	no	—
148	Q₁₆×C₂₉	—	8	2	no	—
149	M₁₆×C₂₉	—	2	4	no	—
150	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₂₉	—	2	1	no	—
157	C₄⋊C₄×C₂₉	—	2	1	no	—
158	C₄⋊C₄×C₂₉	—	2	1	no	—
159	C₄⋊C₄×C₂₉	—	2	1	no	—
160	C₄⋊C₄×C₂₉	—	2	1	no	—
161	C₄⋊C₄×C₂₉	—	2	1	no	—
162	C₄⋊C₄×C₂₉	—	2	1	no	—
163	C₄⋊C₄×C₂₉	—	2	1	no	—
164	C₄⋊C₄×C₂₉	—	2	1	no	—
165	C₄⋊C₄×C₂₉	—	2	1	no	—
166	C₄⋊C₄×C₂₉	—	2	1	no	—
167	C₄⋊C₄×C₂₉	—	2	1	no	—
168	C₄⋊C₄×C₂₉	—	2	1	no	—
169	C₄⋊C₄×C₂₉	—	2	1	no	—
170	C₄⋊C₄×C₂₉	—	2	1	no	—
171	C₄⋊C₄×C₂₉	—	2	1	no	—
172	C₄⋊C₄×C₂₉	—	4	1	no	—
173	C₄⋊C₄×C₂₉	—	4	1	no	—
174	C₄⋊C₄×C₂₉	—	4	1	no	—
175	C₄⋊C₄×C₂₉	—	4	1	no	—
176	C₄⋊C₄×C₂₉	—	4	1	no	—
177	C₄⋊C₄×C₂₉	—	4	1	no	—
178	C₄⋊C₄×C₂₉	—	4	1	no	—
179	C₄⋊C₄×C₂₉	—	4	1	no	—
180	C₂²⋊C₄×C₂₉	—	4	1	no	—
181	C₂²⋊C₄×C₂₉	—	4	1	no	—
182	C₂²⋊C₄×C₂₉	—	4	1	no	—
183	C₄²×C₂₉	—	4	1	no	—
184	C₄²×C₂₉	—	4	1	no	—
185	C₄²×C₂₉	—	4	1	no	—
186	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
190	#19720	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂³×C₂₉	#127	1	1	yes	characteristic
192	Q₈×C₂₉	—	4	2	no	—
193	Q₈×C₂₉	—	4	2	no	—
194	Q₈×C₂₉	—	4	2	no	—
195	Q₈×C₂₉	—	4	2	no	—
196	Q₈×C₂₉	—	4	2	no	—
197	Q₈×C₂₉	—	4	2	no	—
198	Q₈×C₂₉	—	4	2	no	—
199	Q₈×C₂₉	—	4	2	no	—
200	Q₈×C₂₉	—	8	2	no	—
201	C₂×C₄×C₂₉	—	2	2	no	—
202	C₂×C₄×C₂₉	—	2	2	no	—
203	C₂×C₄×C₂₉	—	2	2	no	—
204	C₂×C₄×C₂₉	—	4	1	no	—
205	C₂×C₄×C₂₉	—	4	1	no	—
206	C₂×C₄×C₂₉	—	4	1	no	—
207	C₂×C₄×C₂₉	—	4	1	no	—
208	C₂×C₄×C₂₉	—	4	1	no	—
209	C₂×C₄×C₂₉	—	4	1	no	—
210	C₂×C₄×C₂₉	—	4	1	no	—
211	C₂×C₄×C₂₉	—	4	1	no	—
212	C₂×C₄×C₂₉	—	8	2	no	—
213	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
214	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
215	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₂₉	—	2	2	no	—
220	C₈×C₂₉	—	2	2	no	—
221	C₈×C₂₉	—	2	2	no	—
222	C₈×C₂₉	—	2	2	no	—
223	C₈×C₂₉	—	2	2	no	—
224	C₈×C₂₉	#137	1	4	yes	—
225	#3231	C₂×C₂₉	1	1	yes	characteristic
226	#3231	C₂×C₂₉	1	1	yes	characteristic
227	#3229	C₂×C₂₉	1	1	yes	characteristic
228	#3209	C₂×C₂₉	1	1	yes	characteristic
229	#3185	C₂×C₂₉	1	1	yes	characteristic
230	#3165	C₂×C₂₉	1	1	yes	characteristic
231	#1723	C₂×C₂₉	1	1	yes	characteristic, complemented
232	#1723	C₂×C₂₉	1	1	yes	characteristic, complemented
233	#1718	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#1718	C₂×C₂₉	1	1	yes	characteristic, complemented
235	#1716	C₂×C₂₉	1	1	yes	characteristic, complemented
236	#1716	C₂×C₂₉	1	1	yes	characteristic, complemented
237	#1707	C₂×C₂₉	1	1	yes	characteristic, complemented
238	#1707	C₂×C₂₉	1	1	yes	characteristic, complemented
239	#1453	C₂×C₂₉	1	1	yes	characteristic
240	C₂²×C₂₉	—	2	1	no	—
241	C₂²×C₂₉	—	2	1	no	—
242	C₂²×C₂₉	—	2	1	no	—
243	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
244	C₄×C₂₉	—	2	1	no	—
245	C₄×C₂₉	—	2	1	no	—
246	C₄×C₂₉	—	2	1	no	—
247	C₄×C₂₉	—	8	1	no	—
248	C₄×C₂₉	—	8	1	no	—
249	C₄×C₂₉	—	8	1	no	—
250	C₄×C₂₉	—	8	1	no	—
251	C₄×C₂₉	—	8	1	no	—
252	C₄×C₂₉	—	8	1	no	—
253	C₄×C₂₉	—	8	1	no	—
254	C₄×C₂₉	—	8	1	no	—
255	C₄×C₂₉	C₂×#137	1	2	yes	—
256	C₄×C₂₉	#577	1	2	yes	—
257	C₄×C₂₉	#578	1	2	yes	—
258	#533	C₂²×C₂₉	1	1	yes	characteristic
259	#533	C₂²×C₂₉	1	1	yes	characteristic
260	#533	C₂²×C₂₉	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
262	#501	—	2	2	no	—
263	#500	C₂²×C₂₉	1	1	yes	characteristic
264	#500	C₂²×C₂₉	1	1	yes	characteristic
265	#500	C₂²×C₂₉	1	1	yes	characteristic
266	#500	C₂²×C₂₉	1	1	yes	characteristic
267	#498	C₂²×C₂₉	1	1	yes	characteristic
268	#498	C₂²×C₂₉	1	1	yes	characteristic
269	#498	C₂²×C₂₉	1	1	yes	characteristic
270	#498	C₂²×C₂₉	1	1	yes	characteristic
271	#498	C₂²×C₂₉	1	1	yes	characteristic
272	#498	C₂²×C₂₉	1	1	yes	characteristic
273	#498	C₂²×C₂₉	1	1	yes	characteristic
274	#494	C₂²×C₂₉	1	1	yes	characteristic
275	#494	C₂²×C₂₉	1	1	yes	characteristic
276	#494	C₂²×C₂₉	1	1	yes	characteristic
277	#487	C₂²×C₂₉	1	1	yes	characteristic
278	#487	C₂²×C₂₉	1	1	yes	characteristic
279	#487	C₂²×C₂₉	1	1	yes	characteristic
280	#487	C₂²×C₂₉	1	1	yes	characteristic
281	#487	C₂²×C₂₉	1	1	yes	characteristic
282	#487	C₂²×C₂₉	1	1	yes	characteristic
283	#487	C₂²×C₂₉	1	1	yes	characteristic
284	#487	C₂²×C₂₉	1	1	yes	characteristic
285	#487	C₂²×C₂₉	1	1	yes	characteristic
286	#487	C₂²×C₂₉	1	1	yes	characteristic
287	#485	—	2	2	no	—
288	#485	—	2	2	no	—
289	#483	—	2	2	no	—
290	#479	—	2	2	no	—
291	#479	—	2	2	no	—
292	#475	—	2	2	no	—
293	#470	—	2	2	no	—
294	#462	—	2	2	no	—
295	#451	—	2	2	no	—
296	#441	—	2	2	no	—
297	#431	C₂²×C₂₉	1	1	yes	characteristic
298	#431	C₂²×C₂₉	1	1	yes	characteristic
299	#428	—	2	2	no	—
300	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
301	#322	C₂²×C₂₉	1	1	yes	characteristic
302	#322	C₂²×C₂₉	1	1	yes	characteristic
303	#322	C₂²×C₂₉	1	1	yes	characteristic
304	C₈²	C₂²×C₂₉	1	1	yes	characteristic
305	C₂×C₂₉	—	4	1	no	—
306	C₂×C₂₉	#3152	1	1	yes	characteristic
307	C₂×C₂₉	#3154	1	1	yes	characteristic
308	C₂×C₂₉	#3156	1	1	yes	characteristic
309	C₂²×Q₈	—	2	1	no	—
310	C₂×Q₁₆	—	2	2	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×M₁₆	D₄×C₂₉	1	2	yes	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
318	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
319	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
324	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
325	#125	—	2	1	no	—
326	#125	—	2	1	no	—
327	#125	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×Q₈	—	2	1	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	#117	—	2	1	no	—
341	#117	—	2	1	no	—
342	#117	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
346	#107	—	2	2	no	—
347	#107	—	2	2	no	—
348	#107	—	2	2	no	—
349	#107	—	2	2	no	—
350	#106	—	2	2	no	—
351	#106	—	2	2	no	—
352	#106	—	2	2	no	—
353	#106	—	2	2	no	—
354	#106	—	2	2	no	—
355	#106	—	2	2	no	—
356	#106	—	2	2	no	—
357	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
358	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
359	#103	—	2	2	no	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	#103	—	2	2	no	—
363	#103	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	2	no	—
367	#103	—	2	2	no	—
368	#103	—	2	2	no	—
369	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
370	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
371	#97	D₄×C₂₉	1	2	yes	—
372	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
373	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
374	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
375	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
376	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂₉	#19720	1	1	yes	characteristic, direct product factor, Sylow
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	8	2	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
393	Q₁₆	—	4	4	no	—
394	Q₁₆	—	8	2	no	—
395	Q₁₆	—	8	2	no	—
396	M₁₆	—	2	4	no	—
397	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
400	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
401	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₄²	—	4	1	no	—
433	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
436	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
437	C₂³	C₂₉×#127	1	1	yes	characteristic
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	8	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
460	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
461	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	C₂₉×#137	1	4	yes	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	C₂×C₂₉×#137	1	2	yes	—
487	C₄	C₂₉×#577	1	2	yes	—
488	C₄	C₂₉×#578	1	2	yes	—
489	C₂	—	4	1	no	—
490	C₂	C₂₉×#3152	1	1	yes	characteristic
491	C₂	C₂₉×#3154	1	1	yes	characteristic
492	C₂	C₂₉×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂³×C₂₉	#127
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
7. C₂₉×#1723	C₂	semidirect
8. C₂₉×#1723	C₂	semidirect
9. C₂₉×#1718	C₂	semidirect
10. C₂₉×#1718	C₂	semidirect
11. C₂₉×#1716	C₂	semidirect
12. C₂₉×#1716	C₂	semidirect
13. C₂₉×#1707	C₂	semidirect
14. C₂₉×#1707	C₂	semidirect
190. #19720	C₂₉	direct (N × H)
231. #1723	C₂×C₂₉	semidirect
232. #1723	C₂×C₂₉	semidirect
233. #1718	C₂×C₂₉	semidirect
234. #1718	C₂×C₂₉	semidirect
235. #1716	C₂×C₂₉	semidirect
236. #1716	C₂×C₂₉	semidirect
237. #1707	C₂×C₂₉	semidirect
238. #1707	C₂×C₂₉	semidirect
378. C₂₉	#19720	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×#3231	2
C₂₉×#3229	2
C₂₉×#3209	2
C₂₉×#3185	2
C₂₉×#3165	2
C₂₉×#1723	2
C₂₉×#1718	2
C₂₉×#1716	2
C₂₉×#1707	2
C₂₉×#1453	2
#19720	29

Subgroups — C29×#19720 #20314620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19720 #20314620