Subgroups — C₂₉×#19462 #20314362

Order 7424.

680 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3227	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3109	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2974	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1701	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1691	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1681	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₂₉	—	2	1	no	—
13	C₂₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#498	C₂²	1	2	yes	complemented
17	C₂₉×#486	C₂²	1	2	yes	complemented
18	C₂₉×#481	—	2	1	no	—
19	C₂₉×#481	—	2	1	no	—
20	C₂₉×#481	—	2	1	no	—
21	C₂₉×#476	—	2	2	no	—
22	C₂₉×#476	C₂²	1	1	yes	characteristic
23	C₂₉×#476	C₂²	1	1	yes	characteristic
24	C₂₉×#461	—	2	1	no	—
25	C₂₉×#461	—	2	1	no	—
26	C₂₉×#461	C₂²	1	2	yes	—
27	C₂₉×#461	C₂²	1	2	yes	—
28	C₂₉×#459	C₂²	1	1	yes	characteristic
29	C₂₉×#459	C₂²	1	1	yes	characteristic
30	C₂₉×#447	—	2	1	no	—
31	C₂₉×#442	—	2	1	no	—
32	C₂₉×#442	—	2	1	no	—
33	C₂₉×#436	C₂²	1	2	yes	—
34	C₂₉×#435	—	2	2	no	—
35	C₈×D₄×C₂₉	C₂²	1	2	yes	—
36	C₂₉×#432	C₂²	1	1	yes	characteristic
37	C₂₉×#432	C₂²	1	1	yes	characteristic
38	C₂₉×#431	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#103	—	2	1	no	—
41	C₂₉×#407	—	2	1	no	—
42	C₂×C₂₉×C₂²⋊C₈	—	2	1	no	—
43	C₂₉×#335	C₂²	1	2	yes	complemented
44	C₂₉×#334	C₂²	1	2	yes	complemented
45	C₂₉×#333	C₂²	1	2	yes	complemented
46	C₂₉×#332	C₂²	1	2	yes	complemented
47	C₂₉×#332	C₂²	1	2	yes	complemented
48	C₂₉×#331	C₂²	1	2	yes	complemented
49	C₂×#41×C₂₉	—	2	1	no	—
50	C₂²×Q₈×C₂₉	—	2	1	no	—
51	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₂₉	—	2	1	no	—
53	C₂×SD₁₆×C₂₉	—	2	2	no	—
54	C₂×SD₁₆×C₂₉	—	2	2	no	—
55	C₂×SD₁₆×C₂₉	—	4	4	no	—
56	C₂×D₈×C₂₉	—	2	1	no	—
57	C₂×D₈×C₂₉	—	2	1	no	—
58	C₂×M₁₆×C₂₉	—	2	2	no	—
59	C₂²×C₈×C₂₉	—	2	1	no	—
60	C₂²×C₈×C₂₉	—	2	2	no	—
61	C₂₉×C₄⋊Q₈	—	2	1	no	—
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×C₄⋊Q₈	—	2	1	no	—
64	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₂₉×#127	C₂³	1	1	yes	characteristic
67	C₂₉×#124	—	2	1	no	—
68	C₂₉×#121	—	2	1	no	—
69	C₂₉×#121	—	2	1	no	—
70	C₄×D₄×C₂₉	—	2	1	no	—
71	C₄×D₄×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	—	2	1	no	—
73	C₄×D₄×C₂₉	—	2	1	no	—
74	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
75	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
76	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
77	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
82	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
83	C₂₉×#106	—	2	2	no	—
84	C₂₉×#106	—	2	2	no	—
85	C₂₉×#106	—	2	1	no	—
86	C₂₉×#106	—	2	1	no	—
87	C₂₉×C₄⋊C₈	—	2	1	no	—
88	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
89	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
90	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
92	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
93	C₂₉×#103	—	2	2	no	—
94	C₂₉×#103	—	2	2	no	—
95	C₂₉×#102	—	2	1	no	—
96	C₂₉×#102	—	2	1	no	—
97	C₂₉×#102	—	2	2	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#102	—	2	1	no	—
100	C₂₉×#102	—	2	1	no	—
101	C₂₉×C₂²⋊C₈	—	2	1	no	—
102	C₂₉×C₂²⋊C₈	—	2	1	no	—
103	C₂₉×C₂²⋊C₈	—	2	2	no	—
104	C₂₉×C₂²⋊C₈	—	2	2	no	—
105	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
106	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
107	C₂₉×#97	—	2	1	no	—
108	C₂₉×#97	—	2	1	no	—
109	C₄×C₈×C₂₉	C₂³	1	2	yes	—
110	C₂⁴×C₂₉	—	2	1	no	—
111	#41×C₂₉	—	8	2	no	—
112	C₂×Q₈×C₂₉	—	2	2	no	—
113	C₂×Q₈×C₂₉	—	2	1	no	—
114	C₂×Q₈×C₂₉	—	4	2	no	—
115	C₂×Q₈×C₂₉	—	4	2	no	—
116	C₂×Q₈×C₂₉	—	4	1	no	—
117	C₂×D₄×C₂₉	—	2	2	no	—
118	C₂×D₄×C₂₉	—	2	1	no	—
119	C₂×D₄×C₂₉	—	2	1	no	—
120	C₂×D₄×C₂₉	—	2	1	no	—
121	C₂×D₄×C₂₉	—	2	1	no	—
122	C₂×D₄×C₂₉	—	4	1	no	—
123	C₂×D₄×C₂₉	—	4	1	no	—
124	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	—	2	1	no	—
127	C₂²×C₄×C₂₉	—	2	1	no	—
128	C₂²×C₄×C₂₉	—	2	1	no	—
129	C₂²×C₄×C₂₉	—	2	1	no	—
130	C₂²×C₄×C₂₉	—	2	1	no	—
131	C₂²×C₄×C₂₉	—	4	1	no	—
132	C₂²×C₄×C₂₉	—	4	1	no	—
133	C₂²×C₄×C₂₉	—	8	2	no	—
134	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
137	SD₁₆×C₂₉	—	4	4	no	—
138	SD₁₆×C₂₉	—	4	4	no	—
139	D₈×C₂₉	—	4	2	no	—
140	D₈×C₂₉	—	4	2	no	—
141	M₁₆×C₂₉	—	8	2	no	—
142	C₂×C₈×C₂₉	—	2	2	no	—
143	C₂×C₈×C₂₉	—	2	2	no	—
144	C₂×C₈×C₂₉	—	2	1	no	—
145	C₂×C₈×C₂₉	—	2	1	no	—
146	C₂×C₈×C₂₉	—	4	2	no	—
147	C₂×C₈×C₂₉	—	8	2	no	—
148	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₂₉	—	2	1	no	—
151	C₄⋊C₄×C₂₉	—	2	2	no	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	2	1	no	—
154	C₄⋊C₄×C₂₉	—	2	2	no	—
155	C₄⋊C₄×C₂₉	—	4	1	no	—
156	C₄⋊C₄×C₂₉	—	4	1	no	—
157	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₂₉	—	2	1	no	—
160	C₂²⋊C₄×C₂₉	—	2	1	no	—
161	C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂²⋊C₄×C₂₉	—	4	1	no	—
164	C₂²⋊C₄×C₂₉	—	4	1	no	—
165	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₂₉	#41	1	1	yes	characteristic
168	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
169	#19462	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₂₉	—	2	1	no	—
171	C₂³×C₂₉	—	2	1	no	—
172	C₂³×C₂₉	—	4	2	no	—
173	C₂³×C₂₉	—	4	2	no	—
174	C₂³×C₂₉	—	4	1	no	—
175	C₂³×C₂₉	—	8	1	no	—
176	C₂³×C₂₉	#121	1	1	yes	characteristic
177	Q₈×C₂₉	—	4	2	no	—
178	Q₈×C₂₉	—	4	2	no	—
179	Q₈×C₂₉	—	8	1	no	—
180	Q₈×C₂₉	—	8	2	no	—
181	D₄×C₂₉	—	2	1	no	—
182	D₄×C₂₉	—	2	1	no	—
183	D₄×C₂₉	—	2	1	no	—
184	D₄×C₂₉	—	4	2	no	—
185	D₄×C₂₉	—	4	1	no	—
186	D₄×C₂₉	—	4	1	no	—
187	D₄×C₂₉	—	4	2	no	—
188	D₄×C₂₉	—	8	1	no	—
189	D₄×C₂₉	—	8	2	no	—
190	D₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₂₉	—	2	2	no	—
192	C₂×C₄×C₂₉	—	2	1	no	—
193	C₂×C₄×C₂₉	—	2	1	no	—
194	C₂×C₄×C₂₉	—	2	2	no	—
195	C₂×C₄×C₂₉	—	2	1	no	—
196	C₂×C₄×C₂₉	—	2	1	no	—
197	C₂×C₄×C₂₉	—	4	2	no	—
198	C₂×C₄×C₂₉	—	4	2	no	—
199	C₂×C₄×C₂₉	—	4	1	no	—
200	C₂×C₄×C₂₉	—	4	2	no	—
201	C₂×C₄×C₂₉	—	8	1	no	—
202	C₂×C₄×C₂₉	—	8	1	no	—
203	C₂×C₄×C₂₉	—	8	2	no	—
204	C₂×C₄×C₂₉	—	8	1	no	—
205	C₂×C₄×C₂₉	—	8	2	no	—
206	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
208	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
212	C₈×C₂₉	—	2	2	no	—
213	C₈×C₂₉	—	2	2	no	—
214	C₈×C₂₉	—	4	2	no	—
215	C₈×C₂₉	—	4	1	no	—
216	C₈×C₂₉	—	4	1	no	—
217	C₈×C₂₉	—	4	2	no	—
218	#3227	C₂×C₂₉	1	1	yes	characteristic, complemented
219	#3109	C₂×C₂₉	1	1	yes	characteristic
220	C₂×#461	C₂×C₂₉	1	1	yes	characteristic, complemented
221	#2974	C₂×C₂₉	1	1	yes	characteristic, complemented
222	#1701	C₂×C₂₉	1	2	yes	complemented
223	#1691	C₂×C₂₉	1	2	yes	complemented
224	#1681	C₂×C₂₉	1	2	yes	complemented
225	#1671	C₂×C₂₉	1	2	yes	complemented
226	#1573	C₂×C₂₉	1	1	yes	characteristic, complemented
227	#1556	C₂×C₂₉	1	1	yes	characteristic, complemented
228	#1551	C₂×C₂₉	1	1	yes	characteristic, complemented
229	C₂²×C₂₉	—	2	1	no	—
230	C₂²×C₂₉	—	2	1	no	—
231	C₂²×C₂₉	—	2	2	no	—
232	C₂²×C₂₉	—	4	1	no	—
233	C₂²×C₂₉	—	4	1	no	—
234	C₂²×C₂₉	—	4	1	no	—
235	C₂²×C₂₉	—	4	1	no	—
236	C₂²×C₂₉	—	4	1	no	—
237	C₂²×C₂₉	—	8	4	no	—
238	C₂²×C₂₉	—	8	1	no	—
239	C₂²×C₂₉	—	8	1	no	—
240	C₂²×C₂₉	—	8	1	no	—
241	C₂²×C₂₉	#471	1	2	yes	—
242	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
243	C₄×C₂₉	—	2	1	no	—
244	C₄×C₂₉	—	2	1	no	—
245	C₄×C₂₉	—	2	1	no	—
246	C₄×C₂₉	—	2	1	no	—
247	C₄×C₂₉	—	4	1	no	—
248	C₄×C₂₉	—	4	1	no	—
249	C₄×C₂₉	—	8	2	no	—
250	C₄×C₂₉	—	8	1	no	—
251	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₄×C₂₉	#575	1	1	yes	characteristic
253	C₄×C₂₉	#577	1	2	yes	—
254	C₂²×SD₁₆	—	2	1	no	—
255	#532	C₂²×C₂₉	1	1	yes	characteristic
256	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
258	#498	C₂²×C₂₉	1	2	yes	complemented
259	#486	C₂²×C₂₉	1	2	yes	complemented
260	#481	—	2	1	no	—
261	#481	—	2	1	no	—
262	#481	—	2	1	no	—
263	#476	—	2	2	no	—
264	#476	C₂²×C₂₉	1	1	yes	characteristic
265	#476	C₂²×C₂₉	1	1	yes	characteristic
266	#461	—	2	1	no	—
267	#461	—	2	1	no	—
268	#461	C₂²×C₂₉	1	2	yes	—
269	#461	C₂²×C₂₉	1	2	yes	—
270	#459	C₂²×C₂₉	1	1	yes	characteristic
271	#459	C₂²×C₂₉	1	1	yes	characteristic
272	#447	—	2	1	no	—
273	#442	—	2	1	no	—
274	#442	—	2	1	no	—
275	#436	C₂²×C₂₉	1	2	yes	—
276	#435	—	2	2	no	—
277	C₈×D₄	C₂²×C₂₉	1	2	yes	—
278	#432	C₂²×C₂₉	1	1	yes	characteristic
279	#432	C₂²×C₂₉	1	1	yes	characteristic
280	#431	C₂²×C₂₉	1	1	yes	characteristic
281	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
282	C₂×#103	—	2	1	no	—
283	#407	—	2	1	no	—
284	C₂×C₂²⋊C₈	—	2	1	no	—
285	#335	C₂²×C₂₉	1	2	yes	complemented
286	#334	C₂²×C₂₉	1	2	yes	complemented
287	#333	C₂²×C₂₉	1	2	yes	complemented
288	#332	C₂²×C₂₉	1	2	yes	complemented
289	#332	C₂²×C₂₉	1	2	yes	complemented
290	#331	C₂²×C₂₉	1	2	yes	complemented
291	C₂×C₂₉	—	2	2	no	—
292	C₂×C₂₉	—	4	2	no	—
293	C₂×C₂₉	—	8	1	no	—
294	C₂×C₂₉	—	16	1	no	—
295	C₂×C₂₉	#3042	1	1	yes	characteristic
296	C₂×C₂₉	#3055	1	1	yes	characteristic
297	C₂×C₂₉	C₂×#471	1	1	yes	characteristic
298	C₂×#41	—	2	1	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂×SD₁₆	—	2	2	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	4	4	no	—
305	C₂×D₈	—	2	1	no	—
306	C₂×D₈	—	2	1	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
315	#127	C₂³×C₂₉	1	1	yes	characteristic
316	#124	—	2	1	no	—
317	#121	—	2	1	no	—
318	#121	—	2	1	no	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
324	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
325	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
326	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
332	#106	—	2	2	no	—
333	#106	—	2	2	no	—
334	#106	—	2	1	no	—
335	#106	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
338	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
339	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
340	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
341	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
342	#103	—	2	2	no	—
343	#103	—	2	2	no	—
344	#102	—	2	1	no	—
345	#102	—	2	1	no	—
346	#102	—	2	2	no	—
347	#102	—	2	2	no	—
348	#102	—	2	1	no	—
349	#102	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	—	2	1	no	—
352	C₂²⋊C₈	—	2	2	no	—
353	C₂²⋊C₈	—	2	2	no	—
354	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
355	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
356	#97	—	2	1	no	—
357	#97	—	2	1	no	—
358	C₄×C₈	C₂³×C₂₉	1	2	yes	—
359	C₂₉	#19462	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	—	2	1	no	—
361	#41	—	8	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
375	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	8	2	no	—
384	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
386	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
387	SD₁₆	—	4	4	no	—
388	SD₁₆	—	4	4	no	—
389	D₈	—	4	2	no	—
390	D₈	—	4	2	no	—
391	M₁₆	—	8	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	—	8	2	no	—
398	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
417	C₄²	#41×C₂₉	1	1	yes	characteristic
418	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	8	1	no	—
425	C₂³	C₂₉×#121	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	8	1	no	—
429	Q₈	—	8	2	no	—
430	D₄	—	2	1	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	2	no	—
437	D₄	—	8	1	no	—
438	D₄	—	8	2	no	—
439	D₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	8	1	no	—
451	C₂×C₄	—	8	1	no	—
452	C₂×C₄	—	8	2	no	—
453	C₂×C₄	—	8	1	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
456	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
457	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	8	4	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	—	8	1	no	—
479	C₂²	C₂₉×#471	1	2	yes	—
480	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	1	no	—
489	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
490	C₄	C₂₉×#575	1	1	yes	characteristic
491	C₄	C₂₉×#577	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	16	1	no	—
496	C₂	C₂₉×#3042	1	1	yes	characteristic
497	C₂	C₂₉×#3055	1	1	yes	characteristic
498	C₂	C₂×C₂₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3109	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
1. C₂₉×#3227	C₂	semidirect
3. C₂×C₂₉×#461	C₂	semidirect
4. C₂₉×#2974	C₂	semidirect
5. C₂₉×#1701	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1681	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1573	C₂	semidirect
10. C₂₉×#1556	C₂	semidirect
11. C₂₉×#1551	C₂	semidirect
16. C₂₉×#498	C₂²	semidirect
17. C₂₉×#486	C₂²	semidirect
43. C₂₉×#335	C₂²	semidirect
44. C₂₉×#334	C₂²	semidirect
45. C₂₉×#333	C₂²	semidirect
46. C₂₉×#332	C₂²	semidirect
47. C₂₉×#332	C₂²	semidirect
48. C₂₉×#331	C₂²	semidirect
169. #19462	C₂₉	direct (N × H)
218. #3227	C₂×C₂₉	semidirect
220. C₂×#461	C₂×C₂₉	semidirect
221. #2974	C₂×C₂₉	semidirect
222. #1701	C₂×C₂₉	semidirect
223. #1691	C₂×C₂₉	semidirect
224. #1681	C₂×C₂₉	semidirect
225. #1671	C₂×C₂₉	semidirect
226. #1573	C₂×C₂₉	semidirect
227. #1556	C₂×C₂₉	semidirect
228. #1551	C₂×C₂₉	semidirect
258. #498	C₂²×C₂₉	semidirect
259. #486	C₂²×C₂₉	semidirect
285. #335	C₂²×C₂₉	semidirect
286. #334	C₂²×C₂₉	semidirect
287. #333	C₂²×C₂₉	semidirect
288. #332	C₂²×C₂₉	semidirect
289. #332	C₂²×C₂₉	semidirect
290. #331	C₂²×C₂₉	semidirect
359. C₂₉	#19462	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×#3227	2
C₂₉×#3109	2
C₂×C₂₉×#461	2
C₂₉×#2974	2
C₂₉×#1701	2
C₂₉×#1691	2
C₂₉×#1681	2
C₂₉×#1671	2
C₂₉×#1573	2
C₂₉×#1556	2
C₂₉×#1551	2
#19462	29

Subgroups — C29×#19462 #20314362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19462 #20314362