Subgroups — C₂₉×#24639 #20319539

Order 7424.

906 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2544	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2014	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1982	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#1959	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1928	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1925	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1802	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
21	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
24	C₂₉×#464	—	2	4	no	—
25	C₂₉×#440	—	2	4	no	—
26	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
41	C₂₉×#394	—	2	1	no	—
42	C₂₉×#394	—	2	1	no	—
43	C₂₉×#391	C₂²	1	1	yes	characteristic
44	C₂₉×#391	C₂²	1	1	yes	characteristic
45	C₂₉×#391	C₂²	1	1	yes	characteristic
46	C₂₉×#390	C₂²	1	1	yes	characteristic
47	C₂₉×#387	—	2	1	no	—
48	C₂₉×#387	—	2	1	no	—
49	C₂₉×#386	—	2	1	no	—
50	C₂₉×#386	—	2	1	no	—
51	C₂₉×#384	C₂²	1	1	yes	characteristic
52	C₂₉×#382	—	2	1	no	—
53	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
54	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#336	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	—	2	1	no	—
64	C₂²×D₄×C₂₉	—	2	1	no	—
65	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₂₉	—	2	1	no	—
68	C₂×Q₁₆×C₂₉	—	2	2	no	—
69	C₂×Q₁₆×C₂₉	—	4	1	no	—
70	C₂×Q₁₆×C₂₉	—	4	1	no	—
71	C₂×SD₁₆×C₂₉	—	2	2	no	—
72	C₂×SD₁₆×C₂₉	—	2	2	no	—
73	C₂×SD₁₆×C₂₉	—	2	2	no	—
74	C₂×SD₁₆×C₂₉	—	2	2	no	—
75	C₂×SD₁₆×C₂₉	—	4	1	no	—
76	C₂×SD₁₆×C₂₉	—	4	1	no	—
77	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
81	C₂₉×#127	—	2	2	no	—
82	C₂₉×#127	—	4	1	no	—
83	C₂₉×#124	—	2	2	no	—
84	C₂₉×#124	—	2	2	no	—
85	C₂₉×#124	—	2	2	no	—
86	C₂₉×#124	—	4	1	no	—
87	C₄×Q₈×C₂₉	—	2	2	no	—
88	C₄×Q₈×C₂₉	D₄	1	4	yes	complemented
89	C₄×D₄×C₂₉	—	2	2	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
107	C₂×C₄²×C₂₉	—	2	1	no	—
108	C₂×C₄²×C₂₉	—	2	1	no	—
109	C₂×C₄²×C₂₉	—	2	1	no	—
110	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
113	C₂₉×#107	—	2	2	no	—
114	C₂₉×C₄⋊C₈	—	2	2	no	—
115	C₂₉×C₄⋊C₈	—	4	1	no	—
116	C₂₉×C₄⋊C₈	—	4	1	no	—
117	C₂₉×#103	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	4	1	no	—
121	C₂₉×#102	—	2	2	no	—
122	C₂₉×#102	—	2	2	no	—
123	C₂₉×#102	—	2	2	no	—
124	C₂₉×#102	—	4	1	no	—
125	C₂₉×#102	—	4	1	no	—
126	C₂₉×#102	—	4	1	no	—
127	C₂₉×#97	—	2	2	no	—
128	C₂₉×#95	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂₉×#95	—	2	1	no	—
131	C₂₉×#95	—	2	1	no	—
132	C₂₉×#95	—	2	1	no	—
133	C₂₉×#95	—	2	1	no	—
134	C₂₉×#95	—	2	1	no	—
135	C₂₉×#95	—	2	1	no	—
136	C₂₉×#95	D₄	1	1	yes	characteristic
137	C₂₉×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₉	—	2	1	no	—
139	C₂⁴×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	—	2	1	no	—
141	C₂×Q₈×C₂₉	—	2	1	no	—
142	C₂×Q₈×C₂₉	—	2	1	no	—
143	C₂×Q₈×C₂₉	—	2	1	no	—
144	C₂×Q₈×C₂₉	—	2	1	no	—
145	C₂×Q₈×C₂₉	—	2	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	—	2	1	no	—
150	C₂×Q₈×C₂₉	—	2	1	no	—
151	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₂₉	—	2	1	no	—
153	C₂×D₄×C₂₉	—	2	1	no	—
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	—	2	1	no	—
161	C₂×D₄×C₂₉	—	2	1	no	—
162	C₂×D₄×C₂₉	—	2	1	no	—
163	C₂×D₄×C₂₉	—	4	2	no	—
164	C₂×D₄×C₂₉	—	4	2	no	—
165	C₂×D₄×C₂₉	—	4	2	no	—
166	C₂×D₄×C₂₉	—	4	2	no	—
167	C₂×D₄×C₂₉	—	8	1	no	—
168	C₂×D₄×C₂₉	—	8	1	no	—
169	C₂×D₄×C₂₉	#41	1	2	yes	—
170	C₂²×C₄×C₂₉	—	2	1	no	—
171	C₂²×C₄×C₂₉	—	2	1	no	—
172	C₂²×C₄×C₂₉	—	2	1	no	—
173	C₂²×C₄×C₂₉	—	2	1	no	—
174	C₂²×C₄×C₂₉	—	2	1	no	—
175	C₂²×C₄×C₂₉	—	2	1	no	—
176	C₂²×C₄×C₂₉	—	4	2	no	—
177	C₂²×C₄×C₂₉	—	8	1	no	—
178	C₂²×C₄×C₂₉	—	8	1	no	—
179	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
186	Q₁₆×C₂₉	—	4	4	no	—
187	SD₁₆×C₂₉	—	2	8	no	—
188	SD₁₆×C₂₉	—	4	4	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	—	2	1	no	—
194	C₂×C₈×C₂₉	—	2	1	no	—
195	C₂×C₈×C₂₉	—	2	1	no	—
196	C₂×C₈×C₂₉	—	2	1	no	—
197	C₂×C₈×C₂₉	—	2	1	no	—
198	C₂×C₈×C₂₉	—	2	1	no	—
199	C₂×C₈×C₂₉	—	2	1	no	—
200	C₂×C₈×C₂₉	#41	1	2	yes	—
201	C₄⋊C₄×C₂₉	—	2	4	no	—
202	C₄⋊C₄×C₂₉	—	2	2	no	—
203	C₄⋊C₄×C₂₉	—	2	1	no	—
204	C₄⋊C₄×C₂₉	—	2	1	no	—
205	C₄⋊C₄×C₂₉	—	2	1	no	—
206	C₄⋊C₄×C₂₉	—	2	1	no	—
207	C₄⋊C₄×C₂₉	—	2	1	no	—
208	C₄⋊C₄×C₂₉	—	2	1	no	—
209	C₄⋊C₄×C₂₉	—	2	1	no	—
210	C₄⋊C₄×C₂₉	—	4	1	no	—
211	C₄⋊C₄×C₂₉	—	4	2	no	—
212	C₄⋊C₄×C₂₉	—	8	1	no	—
213	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
214	C₂²⋊C₄×C₂₉	—	4	2	no	—
215	C₂²⋊C₄×C₂₉	—	4	2	no	—
216	C₂²⋊C₄×C₂₉	—	4	2	no	—
217	C₂²⋊C₄×C₂₉	—	4	2	no	—
218	C₂²⋊C₄×C₂₉	—	4	2	no	—
219	C₂²⋊C₄×C₂₉	—	8	1	no	—
220	C₂²⋊C₄×C₂₉	—	8	1	no	—
221	C₄²×C₂₉	—	2	4	no	—
222	C₄²×C₂₉	—	2	1	no	—
223	C₄²×C₂₉	—	2	1	no	—
224	C₄²×C₂₉	—	2	1	no	—
225	C₄²×C₂₉	—	2	1	no	—
226	C₄²×C₂₉	—	8	1	no	—
227	C₄²×C₂₉	—	8	1	no	—
228	C₄²×C₂₉	C₂×D₄	1	2	yes	—
229	C₄²×C₂₉	#41	1	2	yes	—
230	#24639	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂³×C₂₉	—	2	2	no	—
232	C₂³×C₂₉	—	4	1	no	—
233	C₂³×C₂₉	—	4	1	no	—
234	C₂³×C₂₉	—	4	1	no	—
235	C₂³×C₂₉	—	4	1	no	—
236	C₂³×C₂₉	—	4	1	no	—
237	C₂³×C₂₉	—	4	1	no	—
238	C₂³×C₂₉	—	4	1	no	—
239	C₂³×C₂₉	—	4	1	no	—
240	C₂³×C₂₉	—	4	1	no	—
241	C₂³×C₂₉	—	4	1	no	—
242	C₂³×C₂₉	—	4	1	no	—
243	C₂³×C₂₉	—	4	1	no	—
244	C₂³×C₂₉	—	4	1	no	—
245	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
246	Q₈×C₂₉	—	2	2	no	—
247	Q₈×C₂₉	—	2	2	no	—
248	Q₈×C₂₉	—	4	1	no	—
249	Q₈×C₂₉	—	4	1	no	—
250	Q₈×C₂₉	—	4	1	no	—
251	Q₈×C₂₉	—	4	1	no	—
252	Q₈×C₂₉	—	4	1	no	—
253	Q₈×C₂₉	—	4	1	no	—
254	D₄×C₂₉	—	2	2	no	—
255	D₄×C₂₉	—	2	2	no	—
256	D₄×C₂₉	—	4	1	no	—
257	D₄×C₂₉	—	4	1	no	—
258	D₄×C₂₉	—	4	1	no	—
259	D₄×C₂₉	—	4	1	no	—
260	D₄×C₂₉	—	4	1	no	—
261	D₄×C₂₉	—	4	1	no	—
262	D₄×C₂₉	—	8	4	no	—
263	D₄×C₂₉	—	8	4	no	—
264	C₂×C₄×C₂₉	—	2	1	no	—
265	C₂×C₄×C₂₉	—	2	1	no	—
266	C₂×C₄×C₂₉	—	2	1	no	—
267	C₂×C₄×C₂₉	—	2	1	no	—
268	C₂×C₄×C₂₉	—	2	1	no	—
269	C₂×C₄×C₂₉	—	2	1	no	—
270	C₂×C₄×C₂₉	—	2	2	no	—
271	C₂×C₄×C₂₉	—	2	2	no	—
272	C₂×C₄×C₂₉	—	2	1	no	—
273	C₂×C₄×C₂₉	—	2	1	no	—
274	C₂×C₄×C₂₉	—	2	1	no	—
275	C₂×C₄×C₂₉	—	2	1	no	—
276	C₂×C₄×C₂₉	—	2	1	no	—
277	C₂×C₄×C₂₉	—	2	1	no	—
278	C₂×C₄×C₂₉	—	2	1	no	—
279	C₂×C₄×C₂₉	—	2	1	no	—
280	C₂×C₄×C₂₉	—	2	1	no	—
281	C₂×C₄×C₂₉	—	4	1	no	—
282	C₂×C₄×C₂₉	—	4	1	no	—
283	C₂×C₄×C₂₉	—	4	1	no	—
284	C₂×C₄×C₂₉	—	4	1	no	—
285	C₂×C₄×C₂₉	—	4	1	no	—
286	C₂×C₄×C₂₉	—	4	1	no	—
287	C₂×C₄×C₂₉	—	4	1	no	—
288	C₂×C₄×C₂₉	—	4	1	no	—
289	C₂×C₄×C₂₉	—	4	1	no	—
290	C₂×C₄×C₂₉	—	4	1	no	—
291	C₂×C₄×C₂₉	—	4	1	no	—
292	C₂×C₄×C₂₉	—	4	1	no	—
293	C₂×C₄×C₂₉	—	4	1	no	—
294	C₂×C₄×C₂₉	—	4	1	no	—
295	C₂×C₄×C₂₉	—	4	1	no	—
296	C₂×C₄×C₂₉	—	4	1	no	—
297	C₂×C₄×C₂₉	—	8	4	no	—
298	C₂×C₄×C₂₉	#121	1	2	yes	—
299	C₂×C₄×C₂₉	#121	1	2	yes	—
300	C₂×C₄×C₂₉	#137	1	2	yes	—
301	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
307	C₈×C₂₉	—	2	2	no	—
308	C₈×C₂₉	—	4	1	no	—
309	C₈×C₂₉	—	4	1	no	—
310	C₈×C₂₉	—	4	1	no	—
311	C₂×#464	C₂×C₂₉	1	1	yes	characteristic, complemented
312	C₂×#440	C₂×C₂₉	1	1	yes	characteristic, complemented
313	#2544	C₂×C₂₉	1	1	yes	characteristic
314	#2355	C₂×C₂₉	1	1	yes	characteristic, complemented
315	#2056	C₂×C₂₉	1	1	yes	characteristic, complemented
316	#2055	C₂×C₂₉	1	1	yes	characteristic, complemented
317	#2015	C₂×C₂₉	1	1	yes	characteristic, complemented
318	#2014	C₂×C₂₉	1	1	yes	characteristic
319	#1983	C₂×C₂₉	1	1	yes	characteristic, complemented
320	#1982	C₂×C₂₉	1	1	yes	characteristic
321	#1959	C₂×C₂₉	1	1	yes	characteristic, complemented
322	#1940	C₂×C₂₉	1	1	yes	characteristic, complemented
323	#1928	C₂×C₂₉	1	1	yes	characteristic, complemented
324	#1925	C₂×C₂₉	1	1	yes	characteristic, complemented
325	#1802	C₂×C₂₉	1	1	yes	characteristic, complemented
326	C₂²×C₂₉	—	4	2	no	—
327	C₂²×C₂₉	—	4	2	no	—
328	C₂²×C₂₉	—	4	2	no	—
329	C₂²×C₂₉	—	8	1	no	—
330	C₂²×C₂₉	—	8	1	no	—
331	C₂²×C₂₉	—	8	1	no	—
332	C₂²×C₂₉	—	8	1	no	—
333	C₂²×C₂₉	—	8	1	no	—
334	C₂²×C₂₉	—	8	1	no	—
335	C₂²×C₂₉	—	8	1	no	—
336	C₂²×C₂₉	—	8	1	no	—
337	C₂²×C₂₉	—	8	1	no	—
338	C₂²×C₂₉	—	8	1	no	—
339	C₂²×C₂₉	—	8	1	no	—
340	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
341	C₂²×C₂₉	#546	1	1	yes	characteristic
342	C₂²×C₂₉	#550	1	1	yes	characteristic
343	C₂²×C₂₉	C₂×#137	1	1	yes	characteristic
344	C₂²×C₂₉	#575	1	1	yes	characteristic
345	C₂²×C₂₉	#576	1	1	yes	characteristic
346	C₂²×C₂₉	#577	1	1	yes	characteristic
347	C₄×C₂₉	—	2	2	no	—
348	C₄×C₂₉	—	2	2	no	—
349	C₄×C₂₉	—	2	2	no	—
350	C₄×C₂₉	—	4	2	no	—
351	C₄×C₂₉	—	4	2	no	—
352	C₄×C₂₉	—	4	1	no	—
353	C₄×C₂₉	—	4	1	no	—
354	C₄×C₂₉	—	4	1	no	—
355	C₄×C₂₉	—	8	1	no	—
356	C₄×C₂₉	—	8	1	no	—
357	C₄×C₂₉	—	8	1	no	—
358	C₄×C₂₉	—	8	1	no	—
359	C₄×C₂₉	#525	1	1	yes	characteristic
360	C₄×C₂₉	#535	1	1	yes	characteristic
361	C₄×C₂₉	#553	1	1	yes	characteristic
362	C₄×C₂₉	#555	1	1	yes	characteristic
363	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
364	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
365	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
367	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
368	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
369	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
370	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
371	#464	—	2	4	no	—
372	#440	—	2	4	no	—
373	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
378	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
379	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
380	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
382	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
383	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
384	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
385	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
386	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
387	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
388	#394	—	2	1	no	—
389	#394	—	2	1	no	—
390	#391	C₂²×C₂₉	1	1	yes	characteristic
391	#391	C₂²×C₂₉	1	1	yes	characteristic
392	#391	C₂²×C₂₉	1	1	yes	characteristic
393	#390	C₂²×C₂₉	1	1	yes	characteristic
394	#387	—	2	1	no	—
395	#387	—	2	1	no	—
396	#386	—	2	1	no	—
397	#386	—	2	1	no	—
398	#384	C₂²×C₂₉	1	1	yes	characteristic
399	#382	—	2	1	no	—
400	C₄×C₄⋊C₄	—	2	1	no	—
401	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
402	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
403	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
404	#340	C₂²×C₂₉	1	1	yes	characteristic
405	#340	C₂²×C₂₉	1	1	yes	characteristic
406	#336	C₂²×C₂₉	1	1	yes	characteristic
407	#336	C₂²×C₂₉	1	1	yes	characteristic
408	C₂×C₂₉	—	8	2	no	—
409	C₂×C₂₉	—	16	1	no	—
410	C₂×C₂₉	#2414	1	1	yes	characteristic
411	C₂×C₂₉	#3037	1	1	yes	characteristic
412	C₂×C₂₉	#3045	1	1	yes	characteristic
413	C₂×C₂₉	#3311	1	1	yes	characteristic
414	C₂×C₂₉	#3314	1	1	yes	characteristic
415	C₂×C₂₉	#3400	1	1	yes	characteristic
416	C₂×C₂₉	#3403	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
418	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
419	C₂²×D₄	—	2	1	no	—
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
422	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
423	C₂³×C₄	—	2	1	no	—
424	C₂×Q₁₆	—	2	2	no	—
425	C₂×Q₁₆	—	4	1	no	—
426	C₂×Q₁₆	—	4	1	no	—
427	C₂×SD₁₆	—	2	2	no	—
428	C₂×SD₁₆	—	2	2	no	—
429	C₂×SD₁₆	—	2	2	no	—
430	C₂×SD₁₆	—	2	2	no	—
431	C₂×SD₁₆	—	4	1	no	—
432	C₂×SD₁₆	—	4	1	no	—
433	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
434	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
437	#127	—	2	2	no	—
438	#127	—	4	1	no	—
439	#124	—	2	2	no	—
440	#124	—	2	2	no	—
441	#124	—	2	2	no	—
442	#124	—	4	1	no	—
443	C₄×Q₈	—	2	2	no	—
444	C₄×Q₈	D₄×C₂₉	1	4	yes	complemented
445	C₄×D₄	—	2	2	no	—
446	C₄×D₄	—	2	2	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
469	#107	—	2	2	no	—
470	C₄⋊C₈	—	2	2	no	—
471	C₄⋊C₈	—	4	1	no	—
472	C₄⋊C₈	—	4	1	no	—
473	#103	—	2	2	no	—
474	#103	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	—	4	1	no	—
477	#102	—	2	2	no	—
478	#102	—	2	2	no	—
479	#102	—	2	2	no	—
480	#102	—	4	1	no	—
481	#102	—	4	1	no	—
482	#102	—	4	1	no	—
483	#97	—	2	2	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	D₄×C₂₉	1	1	yes	characteristic
493	#95	D₄×C₂₉	1	1	yes	characteristic
494	C₂₉	#24639	1	1	yes	characteristic, direct product factor, Sylow
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	4	2	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	8	1	no	—
525	C₂×D₄	—	8	1	no	—
526	C₂×D₄	#41×C₂₉	1	2	yes	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	8	1	no	—
535	C₂²×C₄	—	8	1	no	—
536	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
541	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
542	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
543	Q₁₆	—	4	4	no	—
544	SD₁₆	—	2	8	no	—
545	SD₁₆	—	4	4	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	#41×C₂₉	1	2	yes	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	4	1	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	8	1	no	—
570	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
571	C₂²⋊C₄	—	4	2	no	—
572	C₂²⋊C₄	—	4	2	no	—
573	C₂²⋊C₄	—	4	2	no	—
574	C₂²⋊C₄	—	4	2	no	—
575	C₂²⋊C₄	—	4	2	no	—
576	C₂²⋊C₄	—	8	1	no	—
577	C₂²⋊C₄	—	8	1	no	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	8	1	no	—
584	C₄²	—	8	1	no	—
585	C₄²	C₂×D₄×C₂₉	1	2	yes	—
586	C₄²	#41×C₂₉	1	2	yes	—
587	C₂³	—	2	2	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	—	4	1	no	—
592	C₂³	—	4	1	no	—
593	C₂³	—	4	1	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
602	Q₈	—	2	2	no	—
603	Q₈	—	2	2	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	4	1	no	—
608	Q₈	—	4	1	no	—
609	Q₈	—	4	1	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	1	no	—
615	D₄	—	4	1	no	—
616	D₄	—	4	1	no	—
617	D₄	—	4	1	no	—
618	D₄	—	8	4	no	—
619	D₄	—	8	4	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	8	4	no	—
654	C₂×C₄	C₂₉×#121	1	2	yes	—
655	C₂×C₄	C₂₉×#121	1	2	yes	—
656	C₂×C₄	C₂₉×#137	1	2	yes	—
657	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
658	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
659	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
660	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
661	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
662	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
663	C₈	—	2	2	no	—
664	C₈	—	4	1	no	—
665	C₈	—	4	1	no	—
666	C₈	—	4	1	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	8	1	no	—
671	C₂²	—	8	1	no	—
672	C₂²	—	8	1	no	—
673	C₂²	—	8	1	no	—
674	C₂²	—	8	1	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	—	8	1	no	—
680	C₂²	—	8	1	no	—
681	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
682	C₂²	C₂₉×#546	1	1	yes	characteristic
683	C₂²	C₂₉×#550	1	1	yes	characteristic
684	C₂²	C₂×C₂₉×#137	1	1	yes	characteristic
685	C₂²	C₂₉×#575	1	1	yes	characteristic
686	C₂²	C₂₉×#576	1	1	yes	characteristic
687	C₂²	C₂₉×#577	1	1	yes	characteristic
688	C₄	—	2	2	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	8	1	no	—
697	C₄	—	8	1	no	—
698	C₄	—	8	1	no	—
699	C₄	—	8	1	no	—
700	C₄	C₂₉×#525	1	1	yes	characteristic
701	C₄	C₂₉×#535	1	1	yes	characteristic
702	C₄	C₂₉×#553	1	1	yes	characteristic
703	C₄	C₂₉×#555	1	1	yes	characteristic
704	C₂	—	8	2	no	—
705	C₂	—	16	1	no	—
706	C₂	C₂₉×#2414	1	1	yes	characteristic
707	C₂	C₂₉×#3037	1	1	yes	characteristic
708	C₂	C₂₉×#3045	1	1	yes	characteristic
709	C₂	C₂₉×#3311	1	1	yes	characteristic
710	C₂	C₂₉×#3314	1	1	yes	characteristic
711	C₂	C₂₉×#3400	1	1	yes	characteristic
712	C₂	C₂₉×#3403	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₄×C₄⋊C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#464	C₂	semidirect
2. C₂×C₂₉×#440	C₂	semidirect
4. C₂₉×#2355	C₂	semidirect
5. C₂₉×#2056	C₂	semidirect
6. C₂₉×#2055	C₂	semidirect
7. C₂₉×#2015	C₂	semidirect
9. C₂₉×#1983	C₂	semidirect
11. C₂₉×#1959	C₂	semidirect
12. C₂₉×#1940	C₂	semidirect
13. C₂₉×#1928	C₂	semidirect
14. C₂₉×#1925	C₂	semidirect
15. C₂₉×#1802	C₂	semidirect
88. C₄×Q₈×C₂₉	D₄	semidirect
230. #24639	C₂₉	direct (N × H)
311. C₂×#464	C₂×C₂₉	semidirect
312. C₂×#440	C₂×C₂₉	semidirect
314. #2355	C₂×C₂₉	semidirect
315. #2056	C₂×C₂₉	semidirect
316. #2055	C₂×C₂₉	semidirect
317. #2015	C₂×C₂₉	semidirect
319. #1983	C₂×C₂₉	semidirect
321. #1959	C₂×C₂₉	semidirect
322. #1940	C₂×C₂₉	semidirect
323. #1928	C₂×C₂₉	semidirect
324. #1925	C₂×C₂₉	semidirect
325. #1802	C₂×C₂₉	semidirect
444. C₄×Q₈	D₄×C₂₉	semidirect
494. C₂₉	#24639	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#464	2
C₂×C₂₉×#440	2
C₂₉×#2544	2
C₂₉×#2355	2
C₂₉×#2056	2
C₂₉×#2055	2
C₂₉×#2015	2
C₂₉×#2014	2
C₂₉×#1983	2
C₂₉×#1982	2
C₂₉×#1959	2
C₂₉×#1940	2
C₂₉×#1928	2
C₂₉×#1925	2
C₂₉×#1802	2
#24639	29

Subgroups — C29×#24639 #20319539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24639 #20319539