Subgroups — C₂₉×#19168 #20314068

Order 7424.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3100	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×M₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1703	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1697	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1683	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1677	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×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×#489	—	2	2	no	—
17	C₂₉×#487	C₂²	1	2	yes	complemented
18	C₂₉×#486	C₂²	1	2	yes	complemented
19	C₂₉×#480	—	2	1	no	—
20	C₂₉×#476	—	2	1	no	—
21	C₂₉×#476	—	2	1	no	—
22	C₂₉×#476	C₂²	1	2	yes	—
23	C₂₉×#476	C₂²	1	2	yes	—
24	C₂₉×#474	C₂²	1	1	yes	characteristic
25	C₂₉×#474	C₂²	1	1	yes	characteristic
26	C₂₉×#459	C₂²	1	1	yes	characteristic
27	C₂₉×#459	C₂²	1	1	yes	characteristic
28	C₂₉×#447	—	2	1	no	—
29	C₄×D₈×C₂₉	—	2	1	no	—
30	C₄×D₈×C₂₉	—	2	1	no	—
31	C₂₉×#436	C₂²	1	2	yes	—
32	C₂₉×#435	—	2	2	no	—
33	C₈×D₄×C₂₉	C₂²	1	2	yes	—
34	C₂₉×#431	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#106	—	2	1	no	—
36	C₂₉×#423	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂₉×#417	—	2	1	no	—
39	C₂₉×#417	—	2	1	no	—
40	C₂×C₂₉×#102	—	2	1	no	—
41	C₂₉×#407	—	2	1	no	—
42	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
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×#333	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×D₈×C₂₉	—	2	1	no	—
54	C₂×D₈×C₂₉	—	2	1	no	—
55	C₂×M₁₆×C₂₉	—	2	1	no	—
56	C₂×M₁₆×C₂₉	—	2	2	no	—
57	C₂×M₁₆×C₂₉	—	4	4	no	—
58	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
59	C₂×M₁₆×C₂₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₂₉	—	2	1	no	—
61	C₂²×C₈×C₂₉	—	2	2	no	—
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×C₄⋊Q₈	—	2	1	no	—
64	C₂₉×C₄⋊Q₈	—	2	1	no	—
65	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
67	C₂₉×#127	C₂³	1	1	yes	characteristic
68	C₂₉×#124	—	2	1	no	—
69	C₂₉×#121	—	2	1	no	—
70	C₂₉×#121	—	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	—	2	1	no	—
75	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
76	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
77	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
78	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
83	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
84	C₂₉×#107	—	2	1	no	—
85	C₂₉×#107	—	2	1	no	—
86	C₂₉×#106	—	2	2	no	—
87	C₂₉×#106	—	2	2	no	—
88	C₂₉×C₄⋊C₈	—	2	1	no	—
89	C₂₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	2	yes	—
94	C₂₉×#103	—	2	2	no	—
95	C₂₉×#103	—	2	2	no	—
96	C₂₉×#102	—	2	1	no	—
97	C₂₉×#102	—	2	1	no	—
98	C₂₉×#102	—	2	2	no	—
99	C₂₉×#102	—	2	2	no	—
100	C₂₉×#102	—	2	2	no	—
101	C₂₉×#102	—	2	2	no	—
102	C₂₉×#102	—	2	1	no	—
103	C₂₉×#102	—	2	1	no	—
104	C₂₉×C₂²⋊C₈	—	2	1	no	—
105	C₂₉×C₂²⋊C₈	—	2	2	no	—
106	C₂₉×C₂²⋊C₈	—	2	2	no	—
107	C₂₉×#97	D₄	1	2	yes	—
108	C₄×C₈×C₂₉	—	2	1	no	—
109	C₄×C₈×C₂₉	C₂³	1	2	yes	—
110	C₂⁴×C₂₉	—	2	1	no	—
111	#41×C₂₉	—	4	2	no	—
112	#41×C₂₉	—	4	2	no	—
113	C₂×Q₈×C₂₉	—	2	1	no	—
114	C₂×Q₈×C₂₉	—	2	2	no	—
115	C₂×Q₈×C₂₉	—	4	1	no	—
116	C₂×Q₈×C₂₉	—	8	2	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	2	no	—
132	C₂²×C₄×C₂₉	—	4	2	no	—
133	C₂²×C₄×C₂₉	—	4	1	no	—
134	C₂²×C₄×C₂₉	—	4	1	no	—
135	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
138	D₈×C₂₉	—	4	2	no	—
139	D₈×C₂₉	—	4	2	no	—
140	M₁₆×C₂₉	—	2	2	no	—
141	M₁₆×C₂₉	—	2	2	no	—
142	M₁₆×C₂₉	—	4	4	no	—
143	M₁₆×C₂₉	—	4	2	no	—
144	C₂×C₈×C₂₉	—	2	2	no	—
145	C₂×C₈×C₂₉	—	2	2	no	—
146	C₂×C₈×C₂₉	—	2	1	no	—
147	C₂×C₈×C₂₉	—	2	1	no	—
148	C₂×C₈×C₂₉	—	4	4	no	—
149	C₂×C₈×C₂₉	—	4	2	no	—
150	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	2	2	no	—
154	C₄⋊C₄×C₂₉	—	2	2	no	—
155	C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₄⋊C₄×C₂₉	—	2	1	no	—
157	C₄⋊C₄×C₂₉	—	4	1	no	—
158	C₄⋊C₄×C₂₉	—	4	1	no	—
159	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²⋊C₄×C₂₉	—	2	1	no	—
162	C₂²⋊C₄×C₂₉	—	2	1	no	—
163	C₂²⋊C₄×C₂₉	—	2	1	no	—
164	C₂²⋊C₄×C₂₉	—	2	1	no	—
165	C₂²⋊C₄×C₂₉	—	4	1	no	—
166	C₂²⋊C₄×C₂₉	—	4	1	no	—
167	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₂₉	#41	1	1	yes	characteristic
170	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
171	#19168	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₂₉	—	2	1	no	—
173	C₂³×C₂₉	—	2	1	no	—
174	C₂³×C₂₉	—	4	2	no	—
175	C₂³×C₂₉	—	4	2	no	—
176	C₂³×C₂₉	—	4	1	no	—
177	C₂³×C₂₉	—	8	1	no	—
178	C₂³×C₂₉	#121	1	1	yes	characteristic
179	Q₈×C₂₉	—	4	1	no	—
180	Q₈×C₂₉	—	4	1	no	—
181	Q₈×C₂₉	—	8	2	no	—
182	Q₈×C₂₉	—	8	2	no	—
183	D₄×C₂₉	—	2	1	no	—
184	D₄×C₂₉	—	2	1	no	—
185	D₄×C₂₉	—	2	1	no	—
186	D₄×C₂₉	—	4	2	no	—
187	D₄×C₂₉	—	4	1	no	—
188	D₄×C₂₉	—	4	1	no	—
189	D₄×C₂₉	—	4	1	no	—
190	D₄×C₂₉	—	4	1	no	—
191	D₄×C₂₉	—	8	1	no	—
192	D₄×C₂₉	—	8	2	no	—
193	D₄×C₂₉	#137	1	2	yes	—
194	C₂×C₄×C₂₉	—	2	1	no	—
195	C₂×C₄×C₂₉	—	2	1	no	—
196	C₂×C₄×C₂₉	—	2	1	no	—
197	C₂×C₄×C₂₉	—	2	1	no	—
198	C₂×C₄×C₂₉	—	4	1	no	—
199	C₂×C₄×C₂₉	—	4	2	no	—
200	C₂×C₄×C₂₉	—	4	1	no	—
201	C₂×C₄×C₂₉	—	4	1	no	—
202	C₂×C₄×C₂₉	—	4	1	no	—
203	C₂×C₄×C₂₉	—	4	1	no	—
204	C₂×C₄×C₂₉	—	4	2	no	—
205	C₂×C₄×C₂₉	—	4	2	no	—
206	C₂×C₄×C₂₉	—	4	1	no	—
207	C₂×C₄×C₂₉	—	4	2	no	—
208	C₂×C₄×C₂₉	—	8	2	no	—
209	C₂×C₄×C₂₉	—	8	2	no	—
210	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
211	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
212	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
213	C₂×C₄×C₂₉	#135	1	2	yes	—
214	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
215	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
218	C₈×C₂₉	—	2	2	no	—
219	C₈×C₂₉	—	2	2	no	—
220	C₈×C₂₉	—	4	2	no	—
221	C₈×C₂₉	—	4	1	no	—
222	C₈×C₂₉	—	4	2	no	—
223	C₈×C₂₉	—	4	1	no	—
224	#3141	C₂×C₂₉	1	1	yes	characteristic, complemented
225	#3100	C₂×C₂₉	1	1	yes	characteristic
226	C₂×#476	C₂×C₂₉	1	1	yes	characteristic, complemented
227	D₄×M₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
228	#1703	C₂×C₂₉	1	2	yes	complemented
229	#1697	C₂×C₂₉	1	2	yes	complemented
230	#1683	C₂×C₂₉	1	2	yes	complemented
231	#1677	C₂×C₂₉	1	2	yes	complemented
232	#1565	C₂×C₂₉	1	1	yes	characteristic, complemented
233	#1548	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#1547	C₂×C₂₉	1	1	yes	characteristic, complemented
235	C₂²×C₂₉	—	2	1	no	—
236	C₂²×C₂₉	—	2	1	no	—
237	C₂²×C₂₉	—	2	2	no	—
238	C₂²×C₂₉	—	4	1	no	—
239	C₂²×C₂₉	—	4	1	no	—
240	C₂²×C₂₉	—	4	1	no	—
241	C₂²×C₂₉	—	4	1	no	—
242	C₂²×C₂₉	—	4	1	no	—
243	C₂²×C₂₉	—	8	4	no	—
244	C₂²×C₂₉	—	8	1	no	—
245	C₂²×C₂₉	—	8	1	no	—
246	C₂²×C₂₉	—	8	1	no	—
247	C₂²×C₂₉	#463	1	2	yes	—
248	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
249	C₄×C₂₉	—	2	1	no	—
250	C₄×C₂₉	—	2	1	no	—
251	C₄×C₂₉	—	2	1	no	—
252	C₄×C₂₉	—	4	1	no	—
253	C₄×C₂₉	—	4	1	no	—
254	C₄×C₂₉	—	8	1	no	—
255	C₄×C₂₉	—	8	2	no	—
256	C₄×C₂₉	#463	1	2	yes	—
257	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
258	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
260	C₄×C₂₉	#575	1	1	yes	characteristic
261	C₂²×M₁₆	—	2	1	no	—
262	#532	C₂²×C₂₉	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
264	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
265	#489	—	2	2	no	—
266	#487	C₂²×C₂₉	1	2	yes	complemented
267	#486	C₂²×C₂₉	1	2	yes	complemented
268	#480	—	2	1	no	—
269	#476	—	2	1	no	—
270	#476	—	2	1	no	—
271	#476	C₂²×C₂₉	1	2	yes	—
272	#476	C₂²×C₂₉	1	2	yes	—
273	#474	C₂²×C₂₉	1	1	yes	characteristic
274	#474	C₂²×C₂₉	1	1	yes	characteristic
275	#459	C₂²×C₂₉	1	1	yes	characteristic
276	#459	C₂²×C₂₉	1	1	yes	characteristic
277	#447	—	2	1	no	—
278	C₄×D₈	—	2	1	no	—
279	C₄×D₈	—	2	1	no	—
280	#436	C₂²×C₂₉	1	2	yes	—
281	#435	—	2	2	no	—
282	C₈×D₄	C₂²×C₂₉	1	2	yes	—
283	#431	C₂²×C₂₉	1	1	yes	characteristic
284	C₂×#106	—	2	1	no	—
285	#423	C₂²×C₂₉	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
287	#417	—	2	1	no	—
288	#417	—	2	1	no	—
289	C₂×#102	—	2	1	no	—
290	#407	—	2	1	no	—
291	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
292	#335	C₂²×C₂₉	1	2	yes	complemented
293	#334	C₂²×C₂₉	1	2	yes	complemented
294	#333	C₂²×C₂₉	1	2	yes	complemented
295	#333	C₂²×C₂₉	1	2	yes	complemented
296	#332	C₂²×C₂₉	1	2	yes	complemented
297	#331	C₂²×C₂₉	1	2	yes	complemented
298	C₂×C₂₉	—	2	2	no	—
299	C₂×C₂₉	—	4	2	no	—
300	C₂×C₂₉	—	8	1	no	—
301	C₂×C₂₉	—	16	1	no	—
302	C₂×C₂₉	C₂×#463	1	1	yes	characteristic
303	C₂×C₂₉	#3056	1	1	yes	characteristic
304	C₂×C₂₉	#3068	1	1	yes	characteristic
305	C₂×#41	—	2	1	no	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
308	C₂³×C₄	—	2	1	no	—
309	C₂×D₈	—	2	1	no	—
310	C₂×D₈	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	4	4	no	—
314	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
315	C₂×M₁₆	D₄×C₂₉	1	1	yes	characteristic
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	—	2	2	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
322	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
323	#127	C₂³×C₂₉	1	1	yes	characteristic
324	#124	—	2	1	no	—
325	#121	—	2	1	no	—
326	#121	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
332	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
333	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
334	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
340	#107	—	2	1	no	—
341	#107	—	2	1	no	—
342	#106	—	2	2	no	—
343	#106	—	2	2	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
347	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
348	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
349	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
350	#103	—	2	2	no	—
351	#103	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	1	no	—
355	#102	—	2	1	no	—
356	#102	—	2	2	no	—
357	#102	—	2	2	no	—
358	#102	—	2	1	no	—
359	#102	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	#97	D₄×C₂₉	1	2	yes	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	C₂³×C₂₉	1	2	yes	—
366	C₂₉	#19168	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	—	2	1	no	—
368	#41	—	4	2	no	—
369	#41	—	4	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	—	8	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	—	4	1	no	—
381	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
382	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
394	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
395	D₈	—	4	2	no	—
396	D₈	—	4	2	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	4	4	no	—
400	M₁₆	—	4	2	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	4	4	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
408	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
417	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	4	1	no	—
423	C₂²⋊C₄	—	4	1	no	—
424	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
426	C₄²	#41×C₂₉	1	1	yes	characteristic
427	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	8	1	no	—
434	C₂³	C₂₉×#121	1	1	yes	characteristic
435	Q₈	—	4	1	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	8	2	no	—
438	Q₈	—	8	2	no	—
439	D₄	—	2	1	no	—
440	D₄	—	2	1	no	—
441	D₄	—	2	1	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	1	no	—
447	D₄	—	8	1	no	—
448	D₄	—	8	2	no	—
449	D₄	C₂₉×#137	1	2	yes	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
467	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
468	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
469	C₂×C₄	C₂₉×#135	1	2	yes	—
470	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	1	no	—
478	C₈	—	4	2	no	—
479	C₈	—	4	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	8	4	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	C₂₉×#463	1	2	yes	—
493	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	2	no	—
501	C₄	C₂₉×#463	1	2	yes	—
502	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
503	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
504	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
505	C₄	C₂₉×#575	1	1	yes	characteristic
506	C₂	—	2	2	no	—
507	C₂	—	4	2	no	—
508	C₂	—	8	1	no	—
509	C₂	—	16	1	no	—
510	C₂	C₂×C₂₉×#463	1	1	yes	characteristic
511	C₂	C₂₉×#3056	1	1	yes	characteristic
512	C₂	C₂₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3100	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×#3141	C₂	semidirect
3. C₂×C₂₉×#476	C₂	semidirect
4. D₄×M₁₆×C₂₉	C₂	semidirect
5. C₂₉×#1703	C₂	semidirect
6. C₂₉×#1697	C₂	semidirect
7. C₂₉×#1683	C₂	semidirect
8. C₂₉×#1677	C₂	semidirect
9. C₂₉×#1565	C₂	semidirect
10. C₂₉×#1548	C₂	semidirect
11. C₂₉×#1547	C₂	semidirect
17. C₂₉×#487	C₂²	semidirect
18. C₂₉×#486	C₂²	semidirect
43. C₂₉×#335	C₂²	semidirect
44. C₂₉×#334	C₂²	semidirect
45. C₂₉×#333	C₂²	semidirect
46. C₂₉×#333	C₂²	semidirect
47. C₂₉×#332	C₂²	semidirect
48. C₂₉×#331	C₂²	semidirect
171. #19168	C₂₉	direct (N × H)
224. #3141	C₂×C₂₉	semidirect
226. C₂×#476	C₂×C₂₉	semidirect
227. D₄×M₁₆	C₂×C₂₉	semidirect
228. #1703	C₂×C₂₉	semidirect
229. #1697	C₂×C₂₉	semidirect
230. #1683	C₂×C₂₉	semidirect
231. #1677	C₂×C₂₉	semidirect
232. #1565	C₂×C₂₉	semidirect
233. #1548	C₂×C₂₉	semidirect
234. #1547	C₂×C₂₉	semidirect
266. #487	C₂²×C₂₉	semidirect
267. #486	C₂²×C₂₉	semidirect
292. #335	C₂²×C₂₉	semidirect
293. #334	C₂²×C₂₉	semidirect
294. #333	C₂²×C₂₉	semidirect
295. #333	C₂²×C₂₉	semidirect
296. #332	C₂²×C₂₉	semidirect
297. #331	C₂²×C₂₉	semidirect
366. C₂₉	#19168	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×#3141	2
C₂₉×#3100	2
C₂×C₂₉×#476	2
D₄×M₁₆×C₂₉	2
C₂₉×#1703	2
C₂₉×#1697	2
C₂₉×#1683	2
C₂₉×#1677	2
C₂₉×#1565	2
C₂₉×#1548	2
C₂₉×#1547	2
#19168	29

Subgroups — C29×#19168 #20314068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19168 #20314068