Subgroups — C₂₉×#19875 #20314775

Order 7424.

682 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3391	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3354	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1715	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1624	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#135	—	2	1	no	—
17	C₂₉×#555	C₂²	1	1	yes	characteristic
18	C₂₉×#550	C₂²	1	1	yes	characteristic
19	C₂₉×#550	C₂²	1	1	yes	characteristic
20	C₂₉×#547	C₂²	1	1	yes	characteristic
21	C₂₉×#498	C₂²	1	1	yes	characteristic
22	C₂₉×#493	—	2	1	no	—
23	C₂₉×#493	C₂²	1	1	yes	characteristic
24	C₂₉×#492	C₂²	1	1	yes	characteristic
25	C₂₉×#492	C₂²	1	1	yes	characteristic
26	C₂₉×#486	C₂²	1	1	yes	characteristic
27	C₂₉×#486	C₂²	1	1	yes	characteristic
28	C₂₉×#482	—	2	1	no	—
29	C₂₉×#482	—	2	1	no	—
30	C₂₉×#481	—	2	1	no	—
31	C₂₉×#477	C₂²	1	1	yes	characteristic
32	C₂₉×#476	C₂²	1	1	yes	characteristic
33	C₂₉×#474	C₂²	1	1	yes	characteristic
34	C₂₉×#469	—	2	1	no	—
35	C₂₉×#466	—	2	1	no	—
36	C₂₉×#465	—	2	1	no	—
37	C₂₉×#462	C₂²	1	1	yes	characteristic
38	C₂₉×#459	—	2	1	no	—
39	C₂₉×#459	—	2	1	no	—
40	C₂₉×#459	C₂²	1	1	yes	characteristic
41	C₂₉×#459	C₂²	1	1	yes	characteristic
42	C₂₉×#459	C₂²	1	1	yes	characteristic
43	C₂₉×#459	C₂²	1	1	yes	characteristic
44	C₂₉×#452	—	2	1	no	—
45	C₂₉×#449	—	2	1	no	—
46	C₂₉×#449	—	2	1	no	—
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×D₈×C₂₉	—	2	1	no	—
50	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
51	C₂₉×#436	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₂₉×#428	—	2	1	no	—
55	C₂₉×#416	—	2	1	no	—
56	C₂₉×#334	C₂²	1	1	yes	characteristic
57	C₂₉×#334	C₂²	1	1	yes	characteristic
58	C₂₉×#333	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#331	C₂²	1	1	yes	characteristic
61	C₂₉×#331	C₂²	1	1	yes	characteristic
62	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂×#41×C₂₉	—	2	1	no	—
69	C₂×#41×C₂₉	—	2	1	no	—
70	C₂₉×#135	—	4	4	no	—
71	C₂×Q₁₆×C₂₉	—	2	1	no	—
72	C₂×SD₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	2	1	no	—
74	C₂×SD₁₆×C₂₉	—	4	1	no	—
75	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
76	C₂×D₈×C₂₉	—	2	1	no	—
77	C₂×D₈×C₂₉	—	2	1	no	—
78	C₂×D₈×C₂₉	—	2	1	no	—
79	C₂×D₈×C₂₉	—	2	1	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×D₈×C₂₉	—	2	1	no	—
82	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
83	C₂×M₁₆×C₂₉	—	2	1	no	—
84	C₂²×C₈×C₂₉	—	2	1	no	—
85	C₂²×C₈×C₂₉	—	2	1	no	—
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₂₉×#127	—	2	1	no	—
89	C₂₉×#127	—	2	1	no	—
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#124	—	4	1	no	—
93	C₂₉×#123	—	4	1	no	—
94	C₂₉×C₂²⋊Q₈	—	2	1	no	—
95	C₂₉×#121	—	2	1	no	—
96	C₂₉×#121	—	2	1	no	—
97	C₂₉×#121	—	2	1	no	—
98	C₂₉×#121	—	2	1	no	—
99	C₂₉×#121	—	2	1	no	—
100	C₂₉×#121	—	4	1	no	—
101	C₂₉×#121	—	4	1	no	—
102	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₂₉	—	2	1	no	—
104	C₄×D₄×C₂₉	—	2	1	no	—
105	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
108	C₂₉×#117	—	2	1	no	—
109	C₂₉×#117	—	2	1	no	—
110	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
111	C₂₉×#107	—	2	1	no	—
112	C₂₉×#107	—	2	1	no	—
113	C₂₉×#107	D₄	1	1	yes	characteristic
114	C₂₉×#106	—	2	1	no	—
115	C₂₉×#106	—	2	1	no	—
116	C₂₉×#106	—	2	1	no	—
117	C₂₉×#106	D₄	1	1	yes	characteristic
118	C₂₉×C₄⋊C₈	—	2	1	no	—
119	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	2	1	no	—
125	C₂₉×#103	D₄	1	1	yes	characteristic
126	C₂₉×#102	—	2	1	no	—
127	C₂₉×#102	—	2	1	no	—
128	C₂₉×#102	—	2	1	no	—
129	C₂₉×#102	—	2	1	no	—
130	C₂₉×#102	—	2	1	no	—
131	C₂₉×#102	—	2	1	no	—
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	2	1	no	—
134	C₂₉×#102	—	4	1	no	—
135	C₂₉×#102	D₄	1	1	yes	characteristic
136	C₂₉×#102	D₄	1	1	yes	characteristic
137	C₂₉×#102	D₄	1	1	yes	characteristic
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×C₂²⋊C₈	—	2	1	no	—
140	C₂₉×C₂²⋊C₈	—	2	1	no	—
141	C₄×C₈×C₂₉	—	2	1	no	—
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
145	#41×C₂₉	—	4	2	no	—
146	#41×C₂₉	—	4	2	no	—
147	#41×C₂₉	—	4	2	no	—
148	#41×C₂₉	—	8	1	no	—
149	#41×C₂₉	—	8	1	no	—
150	#41×C₂₉	—	8	1	no	—
151	C₂×Q₈×C₂₉	—	2	1	no	—
152	C₂×Q₈×C₂₉	—	2	1	no	—
153	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₂₉	—	2	1	no	—
155	C₂×D₄×C₂₉	—	2	1	no	—
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	2	1	no	—
158	C₂×D₄×C₂₉	—	2	1	no	—
159	C₂×D₄×C₂₉	—	2	1	no	—
160	C₂×D₄×C₂₉	—	4	1	no	—
161	C₂×D₄×C₂₉	—	4	1	no	—
162	C₂×D₄×C₂₉	—	4	1	no	—
163	C₂×D₄×C₂₉	—	4	1	no	—
164	C₂×D₄×C₂₉	—	4	1	no	—
165	C₂×D₄×C₂₉	—	4	1	no	—
166	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	—	2	1	no	—
170	C₂²×C₄×C₂₉	—	2	1	no	—
171	C₂²×C₄×C₂₉	—	2	1	no	—
172	C₂²×C₄×C₂₉	—	4	1	no	—
173	C₂²×C₄×C₂₉	—	4	1	no	—
174	C₂²×C₄×C₂₉	—	4	1	no	—
175	Q₁₆×C₂₉	—	4	2	no	—
176	SD₁₆×C₂₉	—	2	2	no	—
177	SD₁₆×C₂₉	—	4	2	no	—
178	SD₁₆×C₂₉	—	8	1	no	—
179	SD₁₆×C₂₉	—	8	2	no	—
180	D₈×C₂₉	—	2	2	no	—
181	D₈×C₂₉	—	4	2	no	—
182	D₈×C₂₉	—	4	2	no	—
183	D₈×C₂₉	—	8	1	no	—
184	D₈×C₂₉	—	8	1	no	—
185	D₈×C₂₉	—	8	1	no	—
186	D₈×C₂₉	—	8	1	no	—
187	M₁₆×C₂₉	—	4	2	no	—
188	C₂×C₈×C₂₉	—	2	1	no	—
189	C₂×C₈×C₂₉	—	2	1	no	—
190	C₂×C₈×C₂₉	—	2	1	no	—
191	C₂×C₈×C₂₉	—	2	1	no	—
192	C₂×C₈×C₂₉	—	2	1	no	—
193	C₂×C₈×C₂₉	—	4	2	no	—
194	C₂×C₈×C₂₉	—	8	1	no	—
195	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₂₉	—	2	1	no	—
200	C₄⋊C₄×C₂₉	—	2	1	no	—
201	C₄⋊C₄×C₂₉	—	2	1	no	—
202	C₄⋊C₄×C₂₉	—	2	1	no	—
203	C₄⋊C₄×C₂₉	—	2	1	no	—
204	C₄⋊C₄×C₂₉	—	4	1	no	—
205	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₂₉	—	2	1	no	—
210	C₂²⋊C₄×C₂₉	—	2	1	no	—
211	C₂²⋊C₄×C₂₉	—	2	1	no	—
212	C₂²⋊C₄×C₂₉	—	4	1	no	—
213	C₂²⋊C₄×C₂₉	—	4	1	no	—
214	C₂²⋊C₄×C₂₉	—	4	1	no	—
215	C₂²⋊C₄×C₂₉	—	4	1	no	—
216	C₂²⋊C₄×C₂₉	—	4	1	no	—
217	C₄²×C₂₉	—	2	1	no	—
218	C₄²×C₂₉	—	4	1	no	—
219	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
220	#19875	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₂₉	—	2	1	no	—
222	C₂³×C₂₉	—	2	1	no	—
223	C₂³×C₂₉	—	2	1	no	—
224	C₂³×C₂₉	—	4	1	no	—
225	C₂³×C₂₉	—	4	1	no	—
226	Q₈×C₂₉	—	2	1	no	—
227	Q₈×C₂₉	—	4	1	no	—
228	Q₈×C₂₉	—	4	1	no	—
229	Q₈×C₂₉	—	8	1	no	—
230	Q₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
231	D₄×C₂₉	—	2	1	no	—
232	D₄×C₂₉	—	2	1	no	—
233	D₄×C₂₉	—	2	1	no	—
234	D₄×C₂₉	—	2	1	no	—
235	D₄×C₂₉	—	2	1	no	—
236	D₄×C₂₉	—	2	1	no	—
237	D₄×C₂₉	—	4	1	no	—
238	D₄×C₂₉	—	4	1	no	—
239	D₄×C₂₉	—	4	1	no	—
240	D₄×C₂₉	—	4	1	no	—
241	D₄×C₂₉	—	4	1	no	—
242	D₄×C₂₉	—	4	1	no	—
243	D₄×C₂₉	—	4	1	no	—
244	D₄×C₂₉	—	4	1	no	—
245	D₄×C₂₉	—	8	2	no	—
246	D₄×C₂₉	—	8	2	no	—
247	D₄×C₂₉	—	8	1	no	—
248	D₄×C₂₉	—	8	1	no	—
249	D₄×C₂₉	—	8	2	no	—
250	D₄×C₂₉	—	16	1	no	—
251	D₄×C₂₉	—	16	1	no	—
252	D₄×C₂₉	—	16	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	2	1	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	no	—
263	C₂×C₄×C₂₉	—	4	1	no	—
264	C₂×C₄×C₂₉	—	4	1	no	—
265	C₂×C₄×C₂₉	—	4	1	no	—
266	C₂×C₄×C₂₉	—	8	2	no	—
267	C₂×C₄×C₂₉	—	8	2	no	—
268	C₂×C₄×C₂₉	—	8	2	no	—
269	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
272	C₈×C₂₉	—	2	1	no	—
273	C₈×C₂₉	—	2	1	no	—
274	C₈×C₂₉	—	2	1	no	—
275	C₈×C₂₉	—	4	1	no	—
276	C₈×C₂₉	—	4	1	no	—
277	C₈×C₂₉	—	4	1	no	—
278	C₈×C₂₉	—	4	1	no	—
279	C₈×C₂₉	—	4	1	no	—
280	C₈×C₂₉	#135	1	2	yes	complemented
281	#3391	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#3354	C₂×C₂₉	1	1	yes	characteristic, complemented
283	#3305	C₂×C₂₉	1	1	yes	characteristic, complemented
284	#3284	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#1715	C₂×C₂₉	1	1	yes	characteristic, complemented
286	#1687	C₂×C₂₉	1	1	yes	characteristic, complemented
287	#1677	C₂×C₂₉	1	1	yes	characteristic, complemented
288	#1672	C₂×C₂₉	1	1	yes	characteristic, complemented
289	#1665	C₂×C₂₉	1	1	yes	characteristic, complemented
290	#1641	C₂×C₂₉	1	1	yes	characteristic, complemented
291	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
292	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
293	#1624	C₂×C₂₉	1	1	yes	characteristic, complemented
294	#1583	C₂×C₂₉	1	1	yes	characteristic, complemented
295	#1580	C₂×C₂₉	1	1	yes	characteristic, complemented
296	C₂²×C₂₉	—	4	1	no	—
297	C₂²×C₂₉	—	4	1	no	—
298	C₂²×C₂₉	—	4	1	no	—
299	C₂²×C₂₉	—	4	1	no	—
300	C₂²×C₂₉	—	4	1	no	—
301	C₂²×C₂₉	—	4	1	no	—
302	C₂²×C₂₉	—	4	1	no	—
303	C₂²×C₂₉	—	4	1	no	—
304	C₂²×C₂₉	—	4	1	no	—
305	C₂²×C₂₉	—	8	1	no	—
306	C₂²×C₂₉	—	8	1	no	—
307	C₂²×C₂₉	—	8	1	no	—
308	C₂²×C₂₉	—	8	1	no	—
309	C₂²×C₂₉	—	8	1	no	—
310	C₂²×C₂₉	—	8	1	no	—
311	C₂²×C₂₉	D₄²	1	1	yes	characteristic
312	C₄×C₂₉	—	2	2	no	—
313	C₄×C₂₉	—	2	1	no	—
314	C₄×C₂₉	—	4	1	no	—
315	C₄×C₂₉	—	4	1	no	—
316	C₄×C₂₉	—	4	1	no	—
317	C₄×C₂₉	—	4	1	no	—
318	C₄×C₂₉	—	8	1	no	—
319	C₄×C₂₉	—	8	1	no	—
320	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
321	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
322	C₄×C₂₉	#576	1	1	yes	characteristic
323	C₄×C₂₉	#577	1	1	yes	characteristic
324	C₂×#135	—	2	1	no	—
325	#555	C₂²×C₂₉	1	1	yes	characteristic
326	#550	C₂²×C₂₉	1	1	yes	characteristic
327	#550	C₂²×C₂₉	1	1	yes	characteristic
328	#547	C₂²×C₂₉	1	1	yes	characteristic
329	#498	C₂²×C₂₉	1	1	yes	characteristic
330	#493	—	2	1	no	—
331	#493	C₂²×C₂₉	1	1	yes	characteristic
332	#492	C₂²×C₂₉	1	1	yes	characteristic
333	#492	C₂²×C₂₉	1	1	yes	characteristic
334	#486	C₂²×C₂₉	1	1	yes	characteristic
335	#486	C₂²×C₂₉	1	1	yes	characteristic
336	#482	—	2	1	no	—
337	#482	—	2	1	no	—
338	#481	—	2	1	no	—
339	#477	C₂²×C₂₉	1	1	yes	characteristic
340	#476	C₂²×C₂₉	1	1	yes	characteristic
341	#474	C₂²×C₂₉	1	1	yes	characteristic
342	#469	—	2	1	no	—
343	#466	—	2	1	no	—
344	#465	—	2	1	no	—
345	#462	C₂²×C₂₉	1	1	yes	characteristic
346	#459	—	2	1	no	—
347	#459	—	2	1	no	—
348	#459	C₂²×C₂₉	1	1	yes	characteristic
349	#459	C₂²×C₂₉	1	1	yes	characteristic
350	#459	C₂²×C₂₉	1	1	yes	characteristic
351	#459	C₂²×C₂₉	1	1	yes	characteristic
352	#452	—	2	1	no	—
353	#449	—	2	1	no	—
354	#449	—	2	1	no	—
355	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
356	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
357	C₄×D₈	—	2	1	no	—
358	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
359	#436	C₂²×C₂₉	1	1	yes	characteristic
360	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
361	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
362	#428	—	2	1	no	—
363	#416	—	2	1	no	—
364	#334	C₂²×C₂₉	1	1	yes	characteristic
365	#334	C₂²×C₂₉	1	1	yes	characteristic
366	#333	C₂²×C₂₉	1	1	yes	characteristic
367	#332	C₂²×C₂₉	1	1	yes	characteristic
368	#331	C₂²×C₂₉	1	1	yes	characteristic
369	#331	C₂²×C₂₉	1	1	yes	characteristic
370	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
371	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
372	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
373	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
374	#322	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×C₂₉	—	8	1	no	—
376	C₂×C₂₉	—	8	1	no	—
377	C₂×C₂₉	—	8	1	no	—
378	C₂×C₂₉	—	16	1	no	—
379	C₂×C₂₉	—	16	1	no	—
380	C₂×C₂₉	#3264	1	1	yes	characteristic
381	C₂×C₂₉	#3284	1	1	yes	characteristic
382	C₂×C₂₉	#3288	1	1	yes	characteristic
383	C₂×#41	—	2	1	no	—
384	C₂×#41	—	2	1	no	—
385	C₂×#41	—	2	1	no	—
386	#135	—	4	4	no	—
387	C₂×Q₁₆	—	2	1	no	—
388	C₂×SD₁₆	—	2	1	no	—
389	C₂×SD₁₆	—	2	1	no	—
390	C₂×SD₁₆	—	4	1	no	—
391	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
392	C₂×D₈	—	2	1	no	—
393	C₂×D₈	—	2	1	no	—
394	C₂×D₈	—	2	1	no	—
395	C₂×D₈	—	2	1	no	—
396	C₂×D₈	—	2	1	no	—
397	C₂×D₈	—	2	1	no	—
398	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
399	C₂×M₁₆	—	2	1	no	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
403	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
404	#127	—	2	1	no	—
405	#127	—	2	1	no	—
406	#127	C₂³×C₂₉	1	1	yes	characteristic
407	#127	C₂³×C₂₉	1	1	yes	characteristic
408	#124	—	4	1	no	—
409	#123	—	4	1	no	—
410	C₂²⋊Q₈	—	2	1	no	—
411	#121	—	2	1	no	—
412	#121	—	2	1	no	—
413	#121	—	2	1	no	—
414	#121	—	2	1	no	—
415	#121	—	2	1	no	—
416	#121	—	4	1	no	—
417	#121	—	4	1	no	—
418	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
419	C₄×D₄	—	2	1	no	—
420	C₄×D₄	—	2	1	no	—
421	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
422	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
423	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
424	#117	—	2	1	no	—
425	#117	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	#107	—	2	1	no	—
428	#107	—	2	1	no	—
429	#107	D₄×C₂₉	1	1	yes	characteristic
430	#106	—	2	1	no	—
431	#106	—	2	1	no	—
432	#106	—	2	1	no	—
433	#106	D₄×C₂₉	1	1	yes	characteristic
434	C₄⋊C₈	—	2	1	no	—
435	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
436	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
438	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
439	#103	—	2	1	no	—
440	#103	—	2	1	no	—
441	#103	D₄×C₂₉	1	1	yes	characteristic
442	#102	—	2	1	no	—
443	#102	—	2	1	no	—
444	#102	—	2	1	no	—
445	#102	—	2	1	no	—
446	#102	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	4	1	no	—
451	#102	D₄×C₂₉	1	1	yes	characteristic
452	#102	D₄×C₂₉	1	1	yes	characteristic
453	#102	D₄×C₂₉	1	1	yes	characteristic
454	C₂²⋊C₈	—	2	1	no	—
455	C₂²⋊C₈	—	2	1	no	—
456	C₂²⋊C₈	—	2	1	no	—
457	C₄×C₈	—	2	1	no	—
458	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
459	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
460	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
461	C₂₉	#19875	1	1	yes	characteristic, direct product factor, Sylow
462	#41	—	4	2	no	—
463	#41	—	4	2	no	—
464	#41	—	4	2	no	—
465	#41	—	8	1	no	—
466	#41	—	8	1	no	—
467	#41	—	8	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	4	1	no	—
478	C₂×D₄	—	4	1	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	—	4	1	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂×D₄	—	4	1	no	—
483	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
484	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
485	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	4	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	1	no	—
492	Q₁₆	—	4	2	no	—
493	SD₁₆	—	2	2	no	—
494	SD₁₆	—	4	2	no	—
495	SD₁₆	—	8	1	no	—
496	SD₁₆	—	8	2	no	—
497	D₈	—	2	2	no	—
498	D₈	—	4	2	no	—
499	D₈	—	4	2	no	—
500	D₈	—	8	1	no	—
501	D₈	—	8	1	no	—
502	D₈	—	8	1	no	—
503	D₈	—	8	1	no	—
504	M₁₆	—	4	2	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	4	2	no	—
511	C₂×C₈	—	8	1	no	—
512	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
513	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
514	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
515	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	4	1	no	—
522	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	4	1	no	—
530	C₂²⋊C₄	—	4	1	no	—
531	C₂²⋊C₄	—	4	1	no	—
532	C₂²⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	4	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	4	1	no	—
536	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	4	1	no	—
544	Q₈	—	4	1	no	—
545	Q₈	—	8	1	no	—
546	Q₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
547	D₄	—	2	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	2	1	no	—
551	D₄	—	2	1	no	—
552	D₄	—	2	1	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	D₄	—	4	1	no	—
557	D₄	—	4	1	no	—
558	D₄	—	4	1	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	8	2	no	—
562	D₄	—	8	2	no	—
563	D₄	—	8	1	no	—
564	D₄	—	8	1	no	—
565	D₄	—	8	2	no	—
566	D₄	—	16	1	no	—
567	D₄	—	16	1	no	—
568	D₄	—	16	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	—	8	2	no	—
584	C₂×C₄	—	8	2	no	—
585	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
586	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
587	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
588	C₈	—	2	1	no	—
589	C₈	—	2	1	no	—
590	C₈	—	2	1	no	—
591	C₈	—	4	1	no	—
592	C₈	—	4	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₈	C₂₉×#135	1	2	yes	complemented
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	8	1	no	—
607	C₂²	—	8	1	no	—
608	C₂²	—	8	1	no	—
609	C₂²	—	8	1	no	—
610	C₂²	—	8	1	no	—
611	C₂²	—	8	1	no	—
612	C₂²	D₄²×C₂₉	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	1	no	—
619	C₄	—	8	1	no	—
620	C₄	—	8	1	no	—
621	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
622	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
623	C₄	C₂₉×#576	1	1	yes	characteristic
624	C₄	C₂₉×#577	1	1	yes	characteristic
625	C₂	—	8	1	no	—
626	C₂	—	8	1	no	—
627	C₂	—	8	1	no	—
628	C₂	—	16	1	no	—
629	C₂	—	16	1	no	—
630	C₂	C₂₉×#3264	1	1	yes	characteristic
631	C₂	C₂₉×#3284	1	1	yes	characteristic
632	C₂	C₂₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3391	C₂	semidirect
2. C₂₉×#3354	C₂	semidirect
3. C₂₉×#3305	C₂	semidirect
4. C₂₉×#3284	C₂	semidirect
5. C₂₉×#1715	C₂	semidirect
6. C₂₉×#1687	C₂	semidirect
7. C₂₉×#1677	C₂	semidirect
8. C₂₉×#1672	C₂	semidirect
9. C₂₉×#1665	C₂	semidirect
10. C₂₉×#1641	C₂	semidirect
11. C₂₉×#1631	C₂	semidirect
12. C₂₉×#1625	C₂	semidirect
13. C₂₉×#1624	C₂	semidirect
14. C₂₉×#1583	C₂	semidirect
15. C₂₉×#1580	C₂	semidirect
220. #19875	C₂₉	direct (N × H)
280. C₈×C₂₉	#135	semidirect
281. #3391	C₂×C₂₉	semidirect
282. #3354	C₂×C₂₉	semidirect
283. #3305	C₂×C₂₉	semidirect
284. #3284	C₂×C₂₉	semidirect
285. #1715	C₂×C₂₉	semidirect
286. #1687	C₂×C₂₉	semidirect
287. #1677	C₂×C₂₉	semidirect
288. #1672	C₂×C₂₉	semidirect
289. #1665	C₂×C₂₉	semidirect
290. #1641	C₂×C₂₉	semidirect
291. #1631	C₂×C₂₉	semidirect
292. #1625	C₂×C₂₉	semidirect
293. #1624	C₂×C₂₉	semidirect
294. #1583	C₂×C₂₉	semidirect
295. #1580	C₂×C₂₉	semidirect
461. C₂₉	#19875	direct (N × H)
596. C₈	C₂₉×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3391	2
C₂₉×#3354	2
C₂₉×#3305	2
C₂₉×#3284	2
C₂₉×#1715	2
C₂₉×#1687	2
C₂₉×#1677	2
C₂₉×#1672	2
C₂₉×#1665	2
C₂₉×#1641	2
C₂₉×#1631	2
C₂₉×#1625	2
C₂₉×#1624	2
C₂₉×#1583	2
C₂₉×#1580	2
#19875	29

Subgroups — C29×#19875 #20314775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19875 #20314775