Subgroups — C₂₉×#19805 #20314705

Order 7424.

640 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#3276	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1716	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1691	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1645	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#137	—	2	1	no	—
17	Q₈²×C₂₉	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#547	C₂²	1	1	yes	characteristic
21	C₂₉×#498	—	2	1	no	—
22	C₂₉×#498	—	2	1	no	—
23	C₂₉×#498	C₂²	1	1	yes	characteristic
24	C₂₉×#498	C₂²	1	1	yes	characteristic
25	C₂₉×#498	C₂²	1	1	yes	characteristic
26	C₂₉×#494	C₂²	1	1	yes	characteristic
27	C₂₉×#487	C₂²	1	1	yes	characteristic
28	C₂₉×#487	C₂²	1	1	yes	characteristic
29	C₂₉×#483	—	2	1	no	—
30	C₂₉×#476	—	2	1	no	—
31	C₂₉×#476	—	2	1	no	—
32	C₂₉×#476	C₂²	1	1	yes	characteristic
33	C₂₉×#476	C₂²	1	1	yes	characteristic
34	C₂₉×#475	—	2	1	no	—
35	C₂₉×#475	—	2	1	no	—
36	C₂₉×#475	C₂²	1	1	yes	characteristic
37	C₂₉×#475	C₂²	1	1	yes	characteristic
38	C₂₉×#475	C₂²	1	1	yes	characteristic
39	C₂₉×#470	—	2	1	no	—
40	C₂₉×#465	—	2	1	no	—
41	C₂₉×#462	C₂²	1	1	yes	characteristic
42	C₂₉×#461	C₂²	1	1	yes	characteristic
43	C₂₉×#461	C₂²	1	1	yes	characteristic
44	C₂₉×#452	—	2	1	no	—
45	C₂₉×#451	—	2	1	no	—
46	C₂₉×#448	—	2	1	no	—
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₂₉	—	2	1	no	—
50	C₄×SD₁₆×C₂₉	—	2	1	no	—
51	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
52	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
53	C₂₉×#436	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#103	—	2	1	no	—
56	C₂₉×#335	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×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#332	C₂²	1	1	yes	characteristic
62	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊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	C₂²×Q₈×C₂₉	—	2	1	no	—
69	C₂²×Q₈×C₂₉	—	2	1	no	—
70	C₂₉×#137	—	4	4	no	—
71	C₂×Q₁₆×C₂₉	—	2	1	no	—
72	C₂×Q₁₆×C₂₉	—	2	1	no	—
73	C₂×Q₁₆×C₂₉	—	2	1	no	—
74	C₂×SD₁₆×C₂₉	—	2	1	no	—
75	C₂×SD₁₆×C₂₉	—	2	1	no	—
76	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
78	C₂×M₁₆×C₂₉	—	2	1	no	—
79	C₂²×C₈×C₂₉	—	2	1	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	—	4	1	no	—
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×#123	—	4	1	no	—
90	C₂₉×C₂²⋊Q₈	—	2	1	no	—
91	C₂₉×C₂²⋊Q₈	—	2	1	no	—
92	C₂₉×C₂²⋊Q₈	—	2	1	no	—
93	C₂₉×C₂²⋊Q₈	—	4	1	no	—
94	C₂₉×C₂²⋊Q₈	—	4	1	no	—
95	C₂₉×#121	—	2	1	no	—
96	C₄×Q₈×C₂₉	—	2	1	no	—
97	C₄×Q₈×C₂₉	—	2	1	no	—
98	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₂₉	—	2	1	no	—
101	C₄×D₄×C₂₉	—	2	1	no	—
102	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₂₉×#106	—	2	1	no	—
106	C₂₉×#106	—	2	1	no	—
107	C₂₉×#106	—	2	1	no	—
108	C₂₉×#106	—	2	1	no	—
109	C₂₉×#106	—	2	1	no	—
110	C₂₉×#106	—	2	1	no	—
111	C₂₉×#106	—	2	1	no	—
112	C₂₉×#106	—	2	1	no	—
113	C₂₉×#106	—	2	1	no	—
114	C₂₉×#106	—	4	1	no	—
115	C₂₉×#106	D₄	1	1	yes	characteristic
116	C₂₉×#106	D₄	1	1	yes	characteristic
117	C₂₉×C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
126	C₂₉×#103	—	2	1	no	—
127	C₂₉×#103	—	2	1	no	—
128	C₂₉×#103	—	2	1	no	—
129	C₂₉×#103	—	2	1	no	—
130	C₂₉×#103	—	2	1	no	—
131	C₂₉×#103	—	4	1	no	—
132	C₂₉×#103	D₄	1	1	yes	characteristic
133	C₂₉×#103	D₄	1	1	yes	characteristic
134	C₂₉×#102	—	2	1	no	—
135	C₂₉×#102	—	2	1	no	—
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	C₄×C₈×C₂₉	—	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	—	8	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	—	4	1	no	—
152	C₂×Q₈×C₂₉	—	4	1	no	—
153	C₂×Q₈×C₂₉	—	4	1	no	—
154	C₂×Q₈×C₂₉	—	4	2	no	—
155	C₂×Q₈×C₂₉	—	4	2	no	—
156	C₂×Q₈×C₂₉	—	8	1	no	—
157	C₂×Q₈×C₂₉	—	8	1	no	—
158	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₂₉	—	4	1	no	—
161	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₂₉	—	4	1	no	—
168	Q₁₆×C₂₉	—	4	2	no	—
169	Q₁₆×C₂₉	—	4	2	no	—
170	Q₁₆×C₂₉	—	8	1	no	—
171	SD₁₆×C₂₉	—	2	2	no	—
172	SD₁₆×C₂₉	—	4	2	no	—
173	SD₁₆×C₂₉	—	8	1	no	—
174	SD₁₆×C₂₉	SD₁₆	1	4	yes	complemented
175	M₁₆×C₂₉	—	4	2	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	2	1	no	—
179	C₂×C₈×C₂₉	—	2	1	no	—
180	C₂×C₈×C₂₉	—	2	1	no	—
181	C₂×C₈×C₂₉	—	8	1	no	—
182	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₄⋊C₄×C₂₉	—	2	1	no	—
187	C₄⋊C₄×C₂₉	—	2	1	no	—
188	C₄⋊C₄×C₂₉	—	2	1	no	—
189	C₄⋊C₄×C₂₉	—	2	1	no	—
190	C₄⋊C₄×C₂₉	—	2	1	no	—
191	C₄⋊C₄×C₂₉	—	2	1	no	—
192	C₄⋊C₄×C₂₉	—	2	1	no	—
193	C₄⋊C₄×C₂₉	—	2	1	no	—
194	C₄⋊C₄×C₂₉	—	2	1	no	—
195	C₄⋊C₄×C₂₉	—	2	1	no	—
196	C₄⋊C₄×C₂₉	—	4	1	no	—
197	C₄⋊C₄×C₂₉	—	4	1	no	—
198	C₄⋊C₄×C₂₉	—	4	1	no	—
199	C₄⋊C₄×C₂₉	—	4	1	no	—
200	C₄⋊C₄×C₂₉	—	4	1	no	—
201	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₂₉	—	2	1	no	—
206	C₂²⋊C₄×C₂₉	—	2	1	no	—
207	C₂²⋊C₄×C₂₉	—	4	1	no	—
208	C₂²⋊C₄×C₂₉	—	4	1	no	—
209	C₂²⋊C₄×C₂₉	—	4	1	no	—
210	C₄²×C₂₉	—	2	1	no	—
211	C₄²×C₂₉	—	2	1	no	—
212	C₄²×C₂₉	—	4	1	no	—
213	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
214	#19805	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂³×C₂₉	—	2	1	no	—
216	C₂³×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	2	1	no	—
218	Q₈×C₂₉	—	2	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	4	1	no	—
223	Q₈×C₂₉	—	4	1	no	—
224	Q₈×C₂₉	—	4	1	no	—
225	Q₈×C₂₉	—	8	2	no	—
226	Q₈×C₂₉	—	8	2	no	—
227	Q₈×C₂₉	—	8	1	no	—
228	Q₈×C₂₉	—	16	1	no	—
229	Q₈×C₂₉	C₂×SD₁₆	1	2	yes	—
230	Q₈×C₂₉	#137	1	2	yes	complemented
231	D₄×C₂₉	—	2	1	no	—
232	D₄×C₂₉	—	2	1	no	—
233	D₄×C₂₉	—	2	1	no	—
234	D₄×C₂₉	—	8	2	no	—
235	D₄×C₂₉	C₂×SD₁₆	1	2	yes	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	2	1	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	8	2	no	—
251	C₂×C₄×C₂₉	—	8	2	no	—
252	C₂×C₄×C₂₉	—	8	2	no	—
253	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₂₉	—	2	1	no	—
257	C₈×C₂₉	—	2	1	no	—
258	C₈×C₂₉	—	2	1	no	—
259	C₈×C₂₉	—	4	1	no	—
260	C₈×C₂₉	—	4	1	no	—
261	C₈×C₂₉	—	4	1	no	—
262	C₈×C₂₉	—	4	1	no	—
263	C₈×C₂₉	—	4	1	no	—
264	C₈×C₂₉	C₂×SD₁₆	1	2	yes	—
265	Q₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
266	Q₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#3298	C₂×C₂₉	1	1	yes	characteristic
268	#3276	C₂×C₂₉	1	1	yes	characteristic
269	#1716	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1691	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1680	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1671	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1670	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1645	C₂×C₂₉	1	1	yes	characteristic, complemented
277	#1635	C₂×C₂₉	1	1	yes	characteristic
278	#1583	C₂×C₂₉	1	1	yes	characteristic, complemented
279	SD₁₆⋊C₈	C₂×C₂₉	1	1	yes	characteristic, complemented
280	C₂²×C₂₉	—	2	2	no	—
281	C₂²×C₂₉	—	4	1	no	—
282	C₂²×C₂₉	—	4	1	no	—
283	C₂²×C₂₉	—	4	1	no	—
284	C₂²×C₂₉	—	4	1	no	—
285	C₂²×C₂₉	—	4	1	no	—
286	C₂²×C₂₉	D₄²	1	1	yes	characteristic
287	C₄×C₂₉	—	2	2	no	—
288	C₄×C₂₉	—	2	2	no	—
289	C₄×C₂₉	—	2	1	no	—
290	C₄×C₂₉	—	4	1	no	—
291	C₄×C₂₉	—	4	1	no	—
292	C₄×C₂₉	—	4	1	no	—
293	C₄×C₂₉	—	4	1	no	—
294	C₄×C₂₉	—	8	1	no	—
295	C₄×C₂₉	—	8	1	no	—
296	C₄×C₂₉	—	8	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
299	C₄×C₂₉	C₂×#137	1	1	yes	characteristic
300	C₄×C₂₉	#577	1	1	yes	characteristic
301	C₄×C₂₉	#577	1	1	yes	characteristic
302	C₂×#137	—	2	1	no	—
303	Q₈²	C₂²×C₂₉	1	1	yes	characteristic
304	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
305	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
306	#547	C₂²×C₂₉	1	1	yes	characteristic
307	#498	—	2	1	no	—
308	#498	—	2	1	no	—
309	#498	C₂²×C₂₉	1	1	yes	characteristic
310	#498	C₂²×C₂₉	1	1	yes	characteristic
311	#498	C₂²×C₂₉	1	1	yes	characteristic
312	#494	C₂²×C₂₉	1	1	yes	characteristic
313	#487	C₂²×C₂₉	1	1	yes	characteristic
314	#487	C₂²×C₂₉	1	1	yes	characteristic
315	#483	—	2	1	no	—
316	#476	—	2	1	no	—
317	#476	—	2	1	no	—
318	#476	C₂²×C₂₉	1	1	yes	characteristic
319	#476	C₂²×C₂₉	1	1	yes	characteristic
320	#475	—	2	1	no	—
321	#475	—	2	1	no	—
322	#475	C₂²×C₂₉	1	1	yes	characteristic
323	#475	C₂²×C₂₉	1	1	yes	characteristic
324	#475	C₂²×C₂₉	1	1	yes	characteristic
325	#470	—	2	1	no	—
326	#465	—	2	1	no	—
327	#462	C₂²×C₂₉	1	1	yes	characteristic
328	#461	C₂²×C₂₉	1	1	yes	characteristic
329	#461	C₂²×C₂₉	1	1	yes	characteristic
330	#452	—	2	1	no	—
331	#451	—	2	1	no	—
332	#448	—	2	1	no	—
333	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
334	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
335	C₄×SD₁₆	—	2	1	no	—
336	C₄×SD₁₆	—	2	1	no	—
337	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
338	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
339	#436	C₂²×C₂₉	1	1	yes	characteristic
340	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#103	—	2	1	no	—
342	#335	C₂²×C₂₉	1	1	yes	characteristic
343	#334	C₂²×C₂₉	1	1	yes	characteristic
344	#333	C₂²×C₂₉	1	1	yes	characteristic
345	#332	C₂²×C₂₉	1	1	yes	characteristic
346	#332	C₂²×C₂₉	1	1	yes	characteristic
347	#332	C₂²×C₂₉	1	1	yes	characteristic
348	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
349	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
350	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
351	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
352	#322	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×C₂₉	—	4	2	no	—
354	C₂×C₂₉	—	8	1	no	—
355	C₂×C₂₉	#3266	1	1	yes	characteristic
356	C₂×C₂₉	D₄×SD₁₆	1	1	yes	characteristic
357	C₂×C₂₉	#3289	1	1	yes	characteristic
358	C₂×#41	—	2	1	no	—
359	C₂²×Q₈	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	#137	—	4	4	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	—	2	1	no	—
364	C₂×Q₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	2	1	no	—
367	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
368	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
369	C₂×M₁₆	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	—	4	1	no	—
376	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
380	#123	—	4	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	4	1	no	—
385	C₂²⋊Q₈	—	4	1	no	—
386	#121	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
390	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	—	2	1	no	—
399	#106	—	2	1	no	—
400	#106	—	2	1	no	—
401	#106	—	2	1	no	—
402	#106	—	2	1	no	—
403	#106	—	2	1	no	—
404	#106	—	2	1	no	—
405	#106	—	4	1	no	—
406	#106	D₄×C₂₉	1	1	yes	characteristic
407	#106	D₄×C₂₉	1	1	yes	characteristic
408	C₄⋊C₈	—	2	1	no	—
409	C₄⋊C₈	—	2	1	no	—
410	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	—	2	1	no	—
419	#103	—	2	1	no	—
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	4	1	no	—
423	#103	D₄×C₂₉	1	1	yes	characteristic
424	#103	D₄×C₂₉	1	1	yes	characteristic
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	D₄×C₂₉	1	1	yes	characteristic
428	#102	D₄×C₂₉	1	1	yes	characteristic
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
436	C₂₉	#19805	1	1	yes	characteristic, direct product factor, Sylow
437	#41	—	4	2	no	—
438	#41	—	8	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	—	4	1	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	—	4	2	no	—
448	C₂×Q₈	—	8	1	no	—
449	C₂×Q₈	—	8	1	no	—
450	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
451	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
454	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	Q₁₆	—	4	2	no	—
461	Q₁₆	—	4	2	no	—
462	Q₁₆	—	8	1	no	—
463	SD₁₆	—	2	2	no	—
464	SD₁₆	—	4	2	no	—
465	SD₁₆	—	8	1	no	—
466	SD₁₆	SD₁₆×C₂₉	1	4	yes	complemented
467	M₁₆	—	4	2	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	8	1	no	—
474	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
496	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	8	2	no	—
517	Q₈	—	8	2	no	—
518	Q₈	—	8	1	no	—
519	Q₈	—	16	1	no	—
520	Q₈	C₂×SD₁₆×C₂₉	1	2	yes	—
521	Q₈	C₂₉×#137	1	2	yes	complemented
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	2	1	no	—
525	D₄	—	8	2	no	—
526	D₄	C₂×SD₁₆×C₂₉	1	2	yes	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
546	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	C₂×SD₁₆×C₂₉	1	2	yes	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	D₄²×C₂₉	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
575	C₄	C₂×C₂₉×#137	1	1	yes	characteristic
576	C₄	C₂₉×#577	1	1	yes	characteristic
577	C₄	C₂₉×#577	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	8	1	no	—
580	C₂	C₂₉×#3266	1	1	yes	characteristic
581	C₂	D₄×SD₁₆×C₂₉	1	1	yes	characteristic
582	C₂	C₂₉×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#547	C₂²
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. Q₈×SD₁₆×C₂₉	C₂	semidirect
2. Q₈×SD₁₆×C₂₉	C₂	semidirect
5. C₂₉×#1716	C₂	semidirect
6. C₂₉×#1691	C₂	semidirect
7. C₂₉×#1680	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1670	C₂	semidirect
10. C₂₉×#1651	C₂	semidirect
11. C₂₉×#1651	C₂	semidirect
12. C₂₉×#1645	C₂	semidirect
14. C₂₉×#1583	C₂	semidirect
15. C₂₉×SD₁₆⋊C₈	C₂	semidirect
174. SD₁₆×C₂₉	SD₁₆	semidirect
214. #19805	C₂₉	direct (N × H)
230. Q₈×C₂₉	#137	semidirect
265. Q₈×SD₁₆	C₂×C₂₉	semidirect
266. Q₈×SD₁₆	C₂×C₂₉	semidirect
269. #1716	C₂×C₂₉	semidirect
270. #1691	C₂×C₂₉	semidirect
271. #1680	C₂×C₂₉	semidirect
272. #1671	C₂×C₂₉	semidirect
273. #1670	C₂×C₂₉	semidirect
274. #1651	C₂×C₂₉	semidirect
275. #1651	C₂×C₂₉	semidirect
276. #1645	C₂×C₂₉	semidirect
278. #1583	C₂×C₂₉	semidirect
279. SD₁₆⋊C₈	C₂×C₂₉	semidirect
436. C₂₉	#19805	direct (N × H)
466. SD₁₆	SD₁₆×C₂₉	semidirect
521. Q₈	C₂₉×#137	semidirect

Maximal subgroups

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

subgroup	index
Q₈×SD₁₆×C₂₉	2
C₂₉×#3298	2
C₂₉×#3276	2
C₂₉×#1716	2
C₂₉×#1691	2
C₂₉×#1680	2
C₂₉×#1671	2
C₂₉×#1670	2
C₂₉×#1651	2
C₂₉×#1645	2
C₂₉×#1635	2
C₂₉×#1583	2
C₂₉×SD₁₆⋊C₈	2
#19805	29

Subgroups — C29×#19805 #20314705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19805 #20314705