Subgroups — C₂₉×#19916 #20314816

Order 7424.

610 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3373	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3331	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1711	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1701	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1680	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1677	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1643	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1640	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#559	C₂²	1	1	yes	characteristic
17	C₂₉×#554	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#547	C₂²	1	1	yes	characteristic
20	C₂₉×#489	—	2	1	no	—
21	C₂₉×#488	—	2	1	no	—
22	C₂₉×#487	C₂²	1	1	yes	characteristic
23	C₂₉×#487	C₂²	1	1	yes	characteristic
24	C₂₉×#487	C₂²	1	1	yes	characteristic
25	C₂₉×#486	C₂²	1	1	yes	characteristic
26	C₂₉×#486	C₂²	1	1	yes	characteristic
27	C₂₉×#486	C₂²	1	1	yes	characteristic
28	C₂₉×#483	—	2	1	no	—
29	C₂₉×#483	—	2	1	no	—
30	C₂₉×#478	—	2	1	no	—
31	C₂₉×#477	C₂²	1	1	yes	characteristic
32	C₂₉×#476	—	2	1	no	—
33	C₂₉×#476	C₂²	1	1	yes	characteristic
34	C₂₉×#475	C₂²	1	1	yes	characteristic
35	C₂₉×#475	C₂²	1	1	yes	characteristic
36	C₂₉×#470	—	2	1	no	—
37	C₂₉×#465	—	2	1	no	—
38	C₂₉×#463	—	2	1	no	—
39	C₂₉×#463	—	2	1	no	—
40	C₂₉×#462	C₂²	1	1	yes	characteristic
41	C₂₉×#461	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×#448	—	2	1	no	—
46	C₂₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂₉×#442	—	2	1	no	—
49	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
50	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
51	C₄×D₈×C₂₉	—	2	1	no	—
52	C₂₉×#436	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₂₉×#417	—	2	1	no	—
55	C₂×C₂₉×#103	—	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×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#331	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	C₈²×C₂₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂²×Q₈×C₂₉	—	2	1	no	—
69	C₂×Q₁₆×C₂₉	—	2	1	no	—
70	C₂×SD₁₆×C₂₉	—	2	1	no	—
71	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
73	C₂×D₈×C₂₉	—	2	1	no	—
74	C₂×D₈×C₂₉	—	2	1	no	—
75	C₂×M₁₆×C₂₉	—	2	1	no	—
76	C₂²×C₈×C₂₉	—	2	1	no	—
77	C₂₉×C₄⋊Q₈	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₉×#127	C₂³	1	1	yes	characteristic
82	C₂₉×#125	—	2	1	no	—
83	C₂₉×#124	—	2	1	no	—
84	C₂₉×#124	—	2	1	no	—
85	C₂₉×#123	—	4	1	no	—
86	C₂₉×#123	—	4	1	no	—
87	C₂₉×C₂²⋊Q₈	—	2	1	no	—
88	C₂₉×C₂²⋊Q₈	—	2	1	no	—
89	C₂₉×C₂²⋊Q₈	—	2	1	no	—
90	C₂₉×C₂²⋊Q₈	—	4	1	no	—
91	C₂₉×C₂²⋊Q₈	—	4	1	no	—
92	C₂₉×#121	—	2	1	no	—
93	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
94	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₂₉	—	2	1	no	—
96	C₄×D₄×C₂₉	—	2	1	no	—
97	C₄×D₄×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	—	2	1	no	—
99	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
103	C₂₉×#107	—	2	1	no	—
104	C₂₉×#106	—	2	1	no	—
105	C₂₉×#106	—	2	1	no	—
106	C₂₉×#106	—	2	1	no	—
107	C₂₉×#106	D₄	1	1	yes	characteristic
108	C₂₉×#106	D₄	1	1	yes	characteristic
109	C₂₉×C₄⋊C₈	—	2	1	no	—
110	C₂₉×C₄⋊C₈	—	2	1	no	—
111	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₂₉×#103	—	2	1	no	—
116	C₂₉×#103	—	2	1	no	—
117	C₂₉×#103	—	2	1	no	—
118	C₂₉×#103	—	2	1	no	—
119	C₂₉×#103	—	2	1	no	—
120	C₂₉×#103	—	2	1	no	—
121	C₂₉×#103	—	2	1	no	—
122	C₂₉×#103	—	2	1	no	—
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	4	1	no	—
125	C₂₉×#103	D₄	1	1	yes	characteristic
126	C₂₉×#103	D₄	1	1	yes	characteristic
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×C₂²⋊C₈	—	2	1	no	—
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×#97	—	2	1	no	—
140	C₄×C₈×C₂₉	—	2	1	no	—
141	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	#41×C₂₉	—	4	2	no	—
145	#41×C₂₉	—	8	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	4	1	no	—
150	C₂×Q₈×C₂₉	—	4	2	no	—
151	C₂×Q₈×C₂₉	—	8	1	no	—
152	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
158	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	4	1	no	—
163	C₂²×C₄×C₂₉	—	4	1	no	—
164	C₂²×C₄×C₂₉	—	4	1	no	—
165	C₂²×C₄×C₂₉	—	4	1	no	—
166	Q₁₆×C₂₉	—	8	1	no	—
167	SD₁₆×C₂₉	—	2	2	no	—
168	SD₁₆×C₂₉	—	4	1	no	—
169	SD₁₆×C₂₉	—	8	1	no	—
170	D₈×C₂₉	—	4	2	no	—
171	D₈×C₂₉	—	4	2	no	—
172	M₁₆×C₂₉	—	8	1	no	—
173	C₂×C₈×C₂₉	—	2	1	no	—
174	C₂×C₈×C₂₉	—	2	1	no	—
175	C₂×C₈×C₂₉	—	2	1	no	—
176	C₂×C₈×C₂₉	—	2	1	no	—
177	C₂×C₈×C₂₉	—	2	1	no	—
178	C₂×C₈×C₂₉	—	8	1	no	—
179	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
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	—	4	1	no	—
192	C₄⋊C₄×C₂₉	—	4	1	no	—
193	C₄⋊C₄×C₂₉	—	4	1	no	—
194	C₄⋊C₄×C₂₉	—	4	1	no	—
195	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₂₉	—	2	1	no	—
200	C₂²⋊C₄×C₂₉	—	2	1	no	—
201	C₂²⋊C₄×C₂₉	—	4	1	no	—
202	C₂²⋊C₄×C₂₉	—	4	1	no	—
203	C₂²⋊C₄×C₂₉	—	4	1	no	—
204	C₂²⋊C₄×C₂₉	—	4	1	no	—
205	C₂²⋊C₄×C₂₉	—	4	1	no	—
206	C₂²⋊C₄×C₂₉	—	4	1	no	—
207	C₄²×C₂₉	—	2	1	no	—
208	C₄²×C₂₉	—	2	1	no	—
209	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
210	#19916	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₂₉	—	2	1	no	—
212	C₂³×C₂₉	—	2	1	no	—
213	C₂³×C₂₉	—	4	1	no	—
214	Q₈×C₂₉	—	2	1	no	—
215	Q₈×C₂₉	—	2	1	no	—
216	Q₈×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	2	1	no	—
218	Q₈×C₂₉	—	4	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	8	1	no	—
223	Q₈×C₂₉	—	8	2	no	—
224	D₄×C₂₉	—	2	1	no	—
225	D₄×C₂₉	—	2	1	no	—
226	D₄×C₂₉	—	2	1	no	—
227	D₄×C₂₉	—	4	1	no	—
228	D₄×C₂₉	—	4	1	no	—
229	D₄×C₂₉	—	4	1	no	—
230	D₄×C₂₉	—	4	1	no	—
231	D₄×C₂₉	—	8	1	no	—
232	D₄×C₂₉	—	8	2	no	—
233	D₄×C₂₉	#135	1	2	yes	—
234	C₂×C₄×C₂₉	—	2	1	no	—
235	C₂×C₄×C₂₉	—	2	1	no	—
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	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	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	—	8	2	no	—
248	C₂×C₄×C₂₉	—	8	2	no	—
249	C₂×C₄×C₂₉	—	16	1	no	—
250	C₂×C₄×C₂₉	—	16	1	no	—
251	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
254	C₈×C₂₉	—	2	1	no	—
255	C₈×C₂₉	—	2	1	no	—
256	C₈×C₂₉	—	2	1	no	—
257	C₈×C₂₉	—	2	1	no	—
258	C₈×C₂₉	—	4	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	#3373	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#3361	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#3331	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#3298	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1711	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1704	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1701	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1680	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1677	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1643	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1640	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1625	C₂×C₂₉	1	1	yes	characteristic
276	#1590	C₂×C₂₉	1	1	yes	characteristic, complemented
277	C₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
278	C₂²×C₂₉	—	2	2	no	—
279	C₂²×C₂₉	—	4	1	no	—
280	C₂²×C₂₉	—	4	1	no	—
281	C₂²×C₂₉	—	4	1	no	—
282	C₂²×C₂₉	—	4	1	no	—
283	C₂²×C₂₉	—	4	1	no	—
284	C₂²×C₂₉	—	8	1	no	—
285	C₂²×C₂₉	—	8	1	no	—
286	C₂²×C₂₉	—	8	1	no	—
287	C₂²×C₂₉	D₄²	1	1	yes	characteristic
288	C₄×C₂₉	—	2	1	no	—
289	C₄×C₂₉	—	4	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	—	4	1	no	—
295	C₄×C₂₉	—	8	1	no	—
296	C₄×C₂₉	—	8	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
299	C₄×C₂₉	#575	1	1	yes	characteristic
300	C₄×C₂₉	#577	1	1	yes	characteristic
301	C₄×C₂₉	#577	1	1	yes	characteristic
302	#559	C₂²×C₂₉	1	1	yes	characteristic
303	#554	C₂²×C₂₉	1	1	yes	characteristic
304	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
305	#547	C₂²×C₂₉	1	1	yes	characteristic
306	#489	—	2	1	no	—
307	#488	—	2	1	no	—
308	#487	C₂²×C₂₉	1	1	yes	characteristic
309	#487	C₂²×C₂₉	1	1	yes	characteristic
310	#487	C₂²×C₂₉	1	1	yes	characteristic
311	#486	C₂²×C₂₉	1	1	yes	characteristic
312	#486	C₂²×C₂₉	1	1	yes	characteristic
313	#486	C₂²×C₂₉	1	1	yes	characteristic
314	#483	—	2	1	no	—
315	#483	—	2	1	no	—
316	#478	—	2	1	no	—
317	#477	C₂²×C₂₉	1	1	yes	characteristic
318	#476	—	2	1	no	—
319	#476	C₂²×C₂₉	1	1	yes	characteristic
320	#475	C₂²×C₂₉	1	1	yes	characteristic
321	#475	C₂²×C₂₉	1	1	yes	characteristic
322	#470	—	2	1	no	—
323	#465	—	2	1	no	—
324	#463	—	2	1	no	—
325	#463	—	2	1	no	—
326	#462	C₂²×C₂₉	1	1	yes	characteristic
327	#461	C₂²×C₂₉	1	1	yes	characteristic
328	#459	C₂²×C₂₉	1	1	yes	characteristic
329	#459	C₂²×C₂₉	1	1	yes	characteristic
330	#452	—	2	1	no	—
331	#448	—	2	1	no	—
332	#446	C₂²×C₂₉	1	1	yes	characteristic
333	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
334	#442	—	2	1	no	—
335	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
336	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
337	C₄×D₈	—	2	1	no	—
338	#436	C₂²×C₂₉	1	1	yes	characteristic
339	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
340	#417	—	2	1	no	—
341	C₂×#103	—	2	1	no	—
342	#334	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	#331	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	C₈²	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×C₂₉	—	4	2	no	—
354	C₂×C₂₉	—	8	1	no	—
355	C₂×C₂₉	—	16	1	no	—
356	C₂×C₂₉	#3275	1	1	yes	characteristic
357	C₂×C₂₉	#3282	1	1	yes	characteristic
358	C₂×C₂₉	#3290	1	1	yes	characteristic
359	C₂×#41	—	2	1	no	—
360	C₂²×Q₈	—	2	1	no	—
361	C₂×Q₁₆	—	2	1	no	—
362	C₂×SD₁₆	—	2	1	no	—
363	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
364	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
365	C₂×D₈	—	2	1	no	—
366	C₂×D₈	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₄⋊Q₈	—	2	1	no	—
370	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
373	#127	C₂³×C₂₉	1	1	yes	characteristic
374	#125	—	2	1	no	—
375	#124	—	2	1	no	—
376	#124	—	2	1	no	—
377	#123	—	4	1	no	—
378	#123	—	4	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	4	1	no	—
383	C₂²⋊Q₈	—	4	1	no	—
384	#121	—	2	1	no	—
385	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
392	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	#107	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	—	2	1	no	—
399	#106	D₄×C₂₉	1	1	yes	characteristic
400	#106	D₄×C₂₉	1	1	yes	characteristic
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	4	1	no	—
417	#103	D₄×C₂₉	1	1	yes	characteristic
418	#103	D₄×C₂₉	1	1	yes	characteristic
419	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	4	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	#97	—	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	#19916	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	—	4	1	no	—
443	C₂×Q₈	—	4	2	no	—
444	C₂×Q₈	—	8	1	no	—
445	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
446	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
452	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	Q₁₆	—	8	1	no	—
460	SD₁₆	—	2	2	no	—
461	SD₁₆	—	4	1	no	—
462	SD₁₆	—	8	1	no	—
463	D₈	—	4	2	no	—
464	D₈	—	4	2	no	—
465	M₁₆	—	8	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	8	1	no	—
472	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
485	C₄⋊C₄	—	4	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	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	—	8	1	no	—
515	Q₈	—	8	2	no	—
516	D₄	—	2	1	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	8	1	no	—
524	D₄	—	8	2	no	—
525	D₄	C₂₉×#135	1	2	yes	—
526	C₂×C₄	—	2	1	no	—
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	—	4	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	—	8	2	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	16	1	no	—
542	C₂×C₄	—	16	1	no	—
543	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
545	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
546	C₈	—	2	1	no	—
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	C₂²	—	2	2	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	8	1	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	D₄²×C₂₉	1	1	yes	characteristic
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	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
576	C₄	C₂₉×#575	1	1	yes	characteristic
577	C₄	C₂₉×#577	1	1	yes	characteristic
578	C₄	C₂₉×#577	1	1	yes	characteristic
579	C₂	—	4	2	no	—
580	C₂	—	8	1	no	—
581	C₂	—	16	1	no	—
582	C₂	C₂₉×#3275	1	1	yes	characteristic
583	C₂	C₂₉×#3282	1	1	yes	characteristic
584	C₂	C₂₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#1625	C₂
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×#3373	C₂	semidirect
2. C₂₉×#3361	C₂	semidirect
3. C₂₉×#3331	C₂	semidirect
4. C₂₉×#3298	C₂	semidirect
5. C₂₉×#1711	C₂	semidirect
6. C₂₉×#1704	C₂	semidirect
7. C₂₉×#1701	C₂	semidirect
8. C₂₉×#1680	C₂	semidirect
9. C₂₉×#1677	C₂	semidirect
10. C₂₉×#1643	C₂	semidirect
11. C₂₉×#1640	C₂	semidirect
12. C₂₉×#1637	C₂	semidirect
14. C₂₉×#1590	C₂	semidirect
15. C₈×SD₁₆×C₂₉	C₂	semidirect
210. #19916	C₂₉	direct (N × H)
263. #3373	C₂×C₂₉	semidirect
264. #3361	C₂×C₂₉	semidirect
265. #3331	C₂×C₂₉	semidirect
266. #3298	C₂×C₂₉	semidirect
267. #1711	C₂×C₂₉	semidirect
268. #1704	C₂×C₂₉	semidirect
269. #1701	C₂×C₂₉	semidirect
270. #1680	C₂×C₂₉	semidirect
271. #1677	C₂×C₂₉	semidirect
272. #1643	C₂×C₂₉	semidirect
273. #1640	C₂×C₂₉	semidirect
274. #1637	C₂×C₂₉	semidirect
276. #1590	C₂×C₂₉	semidirect
277. C₈×SD₁₆	C₂×C₂₉	semidirect
436. C₂₉	#19916	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×#3373	2
C₂₉×#3361	2
C₂₉×#3331	2
C₂₉×#3298	2
C₂₉×#1711	2
C₂₉×#1704	2
C₂₉×#1701	2
C₂₉×#1680	2
C₂₉×#1677	2
C₂₉×#1643	2
C₂₉×#1640	2
C₂₉×#1637	2
C₂₉×#1625	2
C₂₉×#1590	2
C₈×SD₁₆×C₂₉	2
#19916	29

Subgroups — C29×#19916 #20314816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19916 #20314816