Subgroups — C₂₉×#22677 #20317577

Order 7424.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2351	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₄⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1864	C₂	1	1	yes	maximal, characteristic
10	C₂₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1862	C₂	1	1	yes	maximal, characteristic
12	C₂₉×#1847	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1804	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₂₉	—	2	1	no	—
24	C₂₉×#440	—	2	4	no	—
25	C₂₉×#440	C₄	1	8	yes	complemented
26	C₄×SD₁₆×C₂₉	—	2	4	no	—
27	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
30	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₉×#103	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×#97	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#389	—	2	1	no	—
43	C₂₉×#389	—	2	1	no	—
44	C₂₉×#389	C₂²	1	1	yes	characteristic
45	C₂₉×#389	C₂²	1	1	yes	characteristic
46	C₂₉×#389	C₂²	1	1	yes	characteristic
47	C₂₉×#389	C₂²	1	1	yes	characteristic
48	C₂₉×#385	—	2	1	no	—
49	C₂₉×#385	—	2	1	no	—
50	C₂₉×#384	C₂²	1	1	yes	characteristic
51	C₂₉×#382	—	2	1	no	—
52	C₂₉×#382	C₂²	1	1	yes	characteristic
53	C₂₉×#380	—	2	1	no	—
54	C₄×C₄⋊C₄×C₂₉	—	2	1	no	—
55	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
56	C₂₉×#340	C₂²	1	1	yes	characteristic
57	C₂₉×#340	C₂²	1	1	yes	characteristic
58	C₂₉×#340	C₂²	1	1	yes	characteristic
59	C₂₉×#340	C₂²	1	1	yes	characteristic
60	C₂₉×#336	C₂²	1	1	yes	characteristic
61	C₂₉×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₉	—	2	1	no	—
65	C₂³×C₄×C₂₉	—	2	1	no	—
66	C₂³×C₄×C₂₉	—	2	1	no	—
67	C₂×SD₁₆×C₂₉	C₂×C₄	1	4	yes	—
68	C₂×SD₁₆×C₂₉	D₄	1	4	yes	—
69	C₂×SD₁₆×C₂₉	Q₈	1	4	yes	—
70	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
74	C₄×Q₈×C₂₉	—	2	2	no	—
75	C₄×Q₈×C₂₉	—	2	2	no	—
76	C₄×Q₈×C₂₉	—	2	2	no	—
77	C₄×Q₈×C₂₉	—	4	1	no	—
78	C₄×Q₈×C₂₉	—	4	1	no	—
79	C₄×Q₈×C₂₉	C₂×C₄	1	4	yes	complemented
80	C₄×D₄×C₂₉	—	2	2	no	—
81	C₄×D₄×C₂₉	—	2	2	no	—
82	C₄×D₄×C₂₉	—	2	2	no	—
83	C₄×D₄×C₂₉	—	4	1	no	—
84	C₄×D₄×C₂₉	—	4	1	no	—
85	C₄×D₄×C₂₉	C₂×C₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₂₉	—	2	1	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	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₉	—	4	4	no	—
96	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₂₉	D₄	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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
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×#107	—	4	1	no	—
115	C₂₉×#107	C₂×C₄	1	4	yes	complemented
116	C₂₉×#106	—	2	2	no	—
117	C₂₉×#106	—	4	1	no	—
118	C₂₉×C₄⋊C₈	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#103	—	2	2	no	—
121	C₂₉×#103	C₂×C₄	1	4	yes	complemented
122	C₂₉×#102	—	2	2	no	—
123	C₂₉×#102	—	2	2	no	—
124	C₂₉×#102	C₂×C₄	1	4	yes	—
125	C₂₉×#97	—	2	2	no	—
126	C₂₉×#97	C₂×C₄	1	4	yes	complemented
127	C₄×C₈×C₂₉	—	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	D₄	1	1	yes	characteristic
135	C₂₉×#95	D₄	1	1	yes	characteristic
136	C₂⁴×C₂₉	—	2	1	no	—
137	C₂×Q₈×C₂₉	—	2	1	no	—
138	C₂×Q₈×C₂₉	—	2	1	no	—
139	C₂×Q₈×C₂₉	—	2	1	no	—
140	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
141	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₂₉	C₂×Q₈	1	2	yes	—
143	C₂×D₄×C₂₉	—	2	1	no	—
144	C₂×D₄×C₂₉	—	2	1	no	—
145	C₂×D₄×C₂₉	—	2	1	no	—
146	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
147	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₂₉	C₂×Q₈	1	2	yes	—
149	C₂²×C₄×C₂₉	—	2	1	no	—
150	C₂²×C₄×C₂₉	—	2	1	no	—
151	C₂²×C₄×C₂₉	—	2	1	no	—
152	C₂²×C₄×C₂₉	—	2	4	no	—
153	C₂²×C₄×C₂₉	—	2	1	no	—
154	C₂²×C₄×C₂₉	—	2	1	no	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	4	2	no	—
158	C₂²×C₄×C₂₉	—	4	2	no	—
159	C₂²×C₄×C₂₉	—	4	2	no	—
160	C₂²×C₄×C₂₉	—	4	2	no	—
161	C₂²×C₄×C₂₉	—	4	2	no	—
162	C₂²×C₄×C₂₉	—	4	2	no	—
163	C₂²×C₄×C₂₉	—	8	1	no	—
164	C₂²×C₄×C₂₉	—	8	1	no	—
165	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
172	SD₁₆×C₂₉	C₄⋊C₄	1	16	yes	complemented
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	—	2	1	no	—
179	C₂×C₈×C₂₉	—	2	1	no	—
180	C₂×C₈×C₂₉	—	2	1	no	—
181	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
182	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
184	C₂×C₈×C₂₉	C₂×Q₈	1	2	yes	—
185	C₄⋊C₄×C₂₉	—	2	4	no	—
186	C₄⋊C₄×C₂₉	—	2	2	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	—	2	1	no	—
197	C₄⋊C₄×C₂₉	—	4	1	no	—
198	C₄⋊C₄×C₂₉	—	4	2	no	—
199	C₄⋊C₄×C₂₉	—	4	2	no	—
200	C₄⋊C₄×C₂₉	—	4	2	no	—
201	C₄⋊C₄×C₂₉	—	4	2	no	—
202	C₄⋊C₄×C₂₉	—	4	2	no	—
203	C₄⋊C₄×C₂₉	—	4	2	no	—
204	C₄⋊C₄×C₂₉	—	4	2	no	—
205	C₄⋊C₄×C₂₉	—	8	1	no	—
206	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
207	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
208	C₂²⋊C₄×C₂₉	—	2	4	no	—
209	C₂²⋊C₄×C₂₉	—	4	2	no	—
210	C₂²⋊C₄×C₂₉	—	4	2	no	—
211	C₄²×C₂₉	—	2	4	no	—
212	C₄²×C₂₉	—	2	1	no	—
213	C₄²×C₂₉	—	2	1	no	—
214	C₄²×C₂₉	—	2	1	no	—
215	C₄²×C₂₉	—	2	1	no	—
216	C₄²×C₂₉	—	4	2	no	—
217	C₄²×C₂₉	—	4	2	no	—
218	C₄²×C₂₉	C₂²×C₄	1	2	yes	—
219	C₄²×C₂₉	#41	1	2	yes	—
220	#22677	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂³×C₂₉	—	2	2	no	—
222	C₂³×C₂₉	—	2	2	no	—
223	C₂³×C₂₉	—	2	2	no	—
224	C₂³×C₂₉	—	4	1	no	—
225	C₂³×C₂₉	—	4	1	no	—
226	C₂³×C₂₉	—	4	1	no	—
227	C₂³×C₂₉	—	4	1	no	—
228	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₂₉	—	2	2	no	—
230	Q₈×C₂₉	—	2	2	no	—
231	Q₈×C₂₉	—	2	2	no	—
232	Q₈×C₂₉	C₂×C₄⋊C₄	1	4	yes	complemented
233	D₄×C₂₉	—	2	2	no	—
234	D₄×C₂₉	—	2	2	no	—
235	D₄×C₂₉	—	2	2	no	—
236	D₄×C₂₉	C₂×C₄⋊C₄	1	4	yes	—
237	C₂×C₄×C₂₉	—	2	2	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	2	2	no	—
240	C₂×C₄×C₂₉	—	2	2	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	2	1	no	—
243	C₂×C₄×C₂₉	—	2	1	no	—
244	C₂×C₄×C₂₉	—	2	1	no	—
245	C₂×C₄×C₂₉	—	2	1	no	—
246	C₂×C₄×C₂₉	—	2	2	no	—
247	C₂×C₄×C₂₉	—	2	2	no	—
248	C₂×C₄×C₂₉	—	2	1	no	—
249	C₂×C₄×C₂₉	—	2	1	no	—
250	C₂×C₄×C₂₉	—	2	1	no	—
251	C₂×C₄×C₂₉	—	2	1	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	1	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	4	8	no	—
258	C₂×C₄×C₂₉	—	4	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	1	no	—
262	C₂×C₄×C₂₉	—	4	1	no	—
263	C₂×C₄×C₂₉	—	4	1	no	—
264	C₂×C₄×C₂₉	—	4	1	no	—
265	C₂×C₄×C₂₉	—	4	1	no	—
266	C₂×C₄×C₂₉	—	4	1	no	—
267	C₂×C₄×C₂₉	—	4	1	no	—
268	C₂×C₄×C₂₉	—	4	1	no	—
269	C₂×C₄×C₂₉	—	4	1	no	—
270	C₂×C₄×C₂₉	—	4	1	no	—
271	C₂×C₄×C₂₉	—	4	1	no	—
272	C₂×C₄×C₂₉	—	4	1	no	—
273	C₂×C₄×C₂₉	—	4	1	no	—
274	C₂×C₄×C₂₉	—	8	4	no	—
275	C₂×C₄×C₂₉	—	8	4	no	—
276	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
277	C₂×C₄×C₂₉	C₄×D₄	1	2	yes	—
278	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
279	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₂₉	C₂²×Q₈	1	1	yes	characteristic
282	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
284	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
285	C₈×C₂₉	—	2	2	no	—
286	C₈×C₂₉	—	4	1	no	—
287	C₈×C₂₉	—	4	1	no	—
288	C₈×C₂₉	C₂×C₄⋊C₄	1	4	yes	complemented
289	C₂×#440	C₂×C₂₉	1	1	yes	characteristic
290	C₂×#440	C₂×C₂₉	1	1	yes	characteristic
291	C₂×C₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic
292	#2351	C₂×C₂₉	1	1	yes	characteristic, complemented
293	D₄×C₄⋊C₄	C₂×C₂₉	1	1	yes	characteristic
294	#1943	C₂×C₂₉	1	1	yes	characteristic, complemented
295	#1942	C₂×C₂₉	1	1	yes	characteristic, complemented
296	#1865	C₂×C₂₉	1	1	yes	characteristic, complemented
297	#1864	C₂×C₂₉	1	1	yes	characteristic
298	#1863	C₂×C₂₉	1	1	yes	characteristic, complemented
299	#1862	C₂×C₂₉	1	1	yes	characteristic
300	#1847	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#1804	C₂×C₂₉	1	1	yes	characteristic
302	#1803	C₂×C₂₉	1	1	yes	characteristic, complemented
303	#1771	C₂×C₂₉	1	1	yes	characteristic, complemented
304	C₂²×C₂₉	—	2	4	no	—
305	C₂²×C₂₉	—	4	2	no	—
306	C₂²×C₂₉	—	4	2	no	—
307	C₂²×C₂₉	—	4	2	no	—
308	C₂²×C₂₉	—	4	2	no	—
309	C₂²×C₂₉	—	4	2	no	—
310	C₂²×C₂₉	—	4	2	no	—
311	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₂₉	D₄²	1	1	yes	characteristic
313	C₂²×C₂₉	D₄×Q₈	1	1	yes	characteristic
314	C₂²×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₂²×C₂₉	#575	1	1	yes	characteristic
316	C₂²×C₂₉	#577	1	1	yes	characteristic
317	C₂²×C₂₉	#578	1	1	yes	characteristic
318	C₄×C₂₉	—	2	4	no	—
319	C₄×C₂₉	—	2	2	no	—
320	C₄×C₂₉	—	2	2	no	—
321	C₄×C₂₉	—	2	2	no	—
322	C₄×C₂₉	—	4	2	no	—
323	C₄×C₂₉	—	4	2	no	—
324	C₄×C₂₉	—	4	1	no	—
325	C₄×C₂₉	—	4	1	no	—
326	C₄×C₂₉	—	4	1	no	—
327	C₄×C₂₉	—	8	1	no	—
328	C₄×C₂₉	—	8	1	no	—
329	C₄×C₂₉	—	8	1	no	—
330	C₄×C₂₉	—	8	1	no	—
331	C₄×C₂₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
332	C₄×C₂₉	#520	1	1	yes	characteristic
333	C₄×C₂₉	#547	1	1	yes	characteristic
334	C₄×C₂₉	#554	1	1	yes	characteristic
335	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
336	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
339	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
340	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	—	2	1	no	—
343	#440	—	2	4	no	—
344	#440	C₄×C₂₉	1	8	yes	complemented
345	C₄×SD₁₆	—	2	4	no	—
346	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
347	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
348	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
349	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
351	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
352	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
353	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
355	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
356	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
357	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
358	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
359	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
360	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
361	#389	—	2	1	no	—
362	#389	—	2	1	no	—
363	#389	C₂²×C₂₉	1	1	yes	characteristic
364	#389	C₂²×C₂₉	1	1	yes	characteristic
365	#389	C₂²×C₂₉	1	1	yes	characteristic
366	#389	C₂²×C₂₉	1	1	yes	characteristic
367	#385	—	2	1	no	—
368	#385	—	2	1	no	—
369	#384	C₂²×C₂₉	1	1	yes	characteristic
370	#382	—	2	1	no	—
371	#382	C₂²×C₂₉	1	1	yes	characteristic
372	#380	—	2	1	no	—
373	C₄×C₄⋊C₄	—	2	1	no	—
374	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
375	#340	C₂²×C₂₉	1	1	yes	characteristic
376	#340	C₂²×C₂₉	1	1	yes	characteristic
377	#340	C₂²×C₂₉	1	1	yes	characteristic
378	#340	C₂²×C₂₉	1	1	yes	characteristic
379	#336	C₂²×C₂₉	1	1	yes	characteristic
380	#336	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×C₂₉	—	4	4	no	—
382	C₂×C₂₉	D₄×C₄⋊C₄	1	1	yes	characteristic
383	C₂×C₂₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
384	C₂×C₂₉	#2947	1	1	yes	characteristic
385	C₂×C₂₉	#3265	1	1	yes	characteristic
386	C₂×C₂₉	#3269	1	1	yes	characteristic
387	C₂×C₂₉	#3386	1	1	yes	characteristic
388	C₂×C₂₉	#3388	1	1	yes	characteristic
389	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
390	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	2	1	no	—
394	C₂×SD₁₆	C₂×C₄×C₂₉	1	4	yes	—
395	C₂×SD₁₆	D₄×C₂₉	1	4	yes	—
396	C₂×SD₁₆	Q₈×C₂₉	1	4	yes	—
397	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
401	C₄×Q₈	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₄×Q₈	—	4	1	no	—
405	C₄×Q₈	—	4	1	no	—
406	C₄×Q₈	C₂×C₄×C₂₉	1	4	yes	complemented
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	4	1	no	—
411	C₄×D₄	—	4	1	no	—
412	C₄×D₄	C₂×C₄×C₂₉	1	4	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	4	4	no	—
423	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
440	#107	—	2	2	no	—
441	#107	—	4	1	no	—
442	#107	C₂×C₄×C₂₉	1	4	yes	complemented
443	#106	—	2	2	no	—
444	#106	—	4	1	no	—
445	C₄⋊C₈	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#103	C₂×C₄×C₂₉	1	4	yes	complemented
449	#102	—	2	2	no	—
450	#102	—	2	2	no	—
451	#102	C₂×C₄×C₂₉	1	4	yes	—
452	#97	—	2	2	no	—
453	#97	C₂×C₄×C₂₉	1	4	yes	complemented
454	C₄×C₈	—	2	2	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	D₄×C₂₉	1	1	yes	characteristic
462	#95	D₄×C₂₉	1	1	yes	characteristic
463	C₂₉	#22677	1	1	yes	characteristic, direct product factor, Sylow
464	C₂⁴	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
469	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
470	C₂×Q₈	C₂×Q₈×C₂₉	1	2	yes	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
475	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
476	C₂×D₄	C₂×Q₈×C₂₉	1	2	yes	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	4	2	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	8	1	no	—
492	C₂²×C₄	—	8	1	no	—
493	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
500	SD₁₆	C₄⋊C₄×C₂₉	1	16	yes	complemented
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
510	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
511	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
512	C₂×C₈	C₂×Q₈×C₂₉	1	2	yes	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	4	1	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	—	4	2	no	—
530	C₄⋊C₄	—	4	2	no	—
531	C₄⋊C₄	—	4	2	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	8	1	no	—
534	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
535	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	—	4	2	no	—
538	C₂²⋊C₄	—	4	2	no	—
539	C₄²	—	2	4	no	—
540	C₄²	—	2	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	4	2	no	—
545	C₄²	—	4	2	no	—
546	C₄²	C₂²×C₄×C₂₉	1	2	yes	—
547	C₄²	#41×C₂₉	1	2	yes	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	C₂×C₄⋊C₄×C₂₉	1	4	yes	complemented
560	D₄	—	2	2	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	C₂×C₄⋊C₄×C₂₉	1	4	yes	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	8	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	8	4	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
604	C₂×C₄	C₄×D₄×C₂₉	1	2	yes	—
605	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
606	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
608	C₂×C₄	C₂²×Q₈×C₂₉	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
610	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	C₂×C₄⋊C₄×C₂₉	1	4	yes	complemented
616	C₂²	—	2	4	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
624	C₂²	D₄²×C₂₉	1	1	yes	characteristic
625	C₂²	D₄×Q₈×C₂₉	1	1	yes	characteristic
626	C₂²	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
627	C₂²	C₂₉×#575	1	1	yes	characteristic
628	C₂²	C₂₉×#577	1	1	yes	characteristic
629	C₂²	C₂₉×#578	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₂²×C₄⋊C₄×C₂₉	1	1	yes	characteristic
644	C₄	C₂₉×#520	1	1	yes	characteristic
645	C₄	C₂₉×#547	1	1	yes	characteristic
646	C₄	C₂₉×#554	1	1	yes	characteristic
647	C₂	—	4	4	no	—
648	C₂	D₄×C₄⋊C₄×C₂₉	1	1	yes	characteristic
649	C₂	C₄×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
650	C₂	C₂₉×#2947	1	1	yes	characteristic
651	C₂	C₂₉×#3265	1	1	yes	characteristic
652	C₂	C₂₉×#3269	1	1	yes	characteristic
653	C₂	C₂₉×#3386	1	1	yes	characteristic
654	C₂	C₂₉×#3388	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂×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
4. C₂₉×#2351	C₂	semidirect
6. C₂₉×#1943	C₂	semidirect
7. C₂₉×#1942	C₂	semidirect
8. C₂₉×#1865	C₂	semidirect
10. C₂₉×#1863	C₂	semidirect
12. C₂₉×#1847	C₂	semidirect
14. C₂₉×#1803	C₂	semidirect
15. C₂₉×#1771	C₂	semidirect
25. C₂₉×#440	C₄	semidirect
79. C₄×Q₈×C₂₉	C₂×C₄	semidirect
115. C₂₉×#107	C₂×C₄	semidirect
121. C₂₉×#103	C₂×C₄	semidirect
126. C₂₉×#97	C₂×C₄	semidirect
172. SD₁₆×C₂₉	C₄⋊C₄	semidirect
220. #22677	C₂₉	direct (N × H)
232. Q₈×C₂₉	C₂×C₄⋊C₄	semidirect
288. C₈×C₂₉	C₂×C₄⋊C₄	semidirect
292. #2351	C₂×C₂₉	semidirect
294. #1943	C₂×C₂₉	semidirect
295. #1942	C₂×C₂₉	semidirect
296. #1865	C₂×C₂₉	semidirect
298. #1863	C₂×C₂₉	semidirect
300. #1847	C₂×C₂₉	semidirect
302. #1803	C₂×C₂₉	semidirect
303. #1771	C₂×C₂₉	semidirect
344. #440	C₄×C₂₉	semidirect
406. C₄×Q₈	C₂×C₄×C₂₉	semidirect
442. #107	C₂×C₄×C₂₉	semidirect
448. #103	C₂×C₄×C₂₉	semidirect
453. #97	C₂×C₄×C₂₉	semidirect
463. C₂₉	#22677	direct (N × H)
500. SD₁₆	C₄⋊C₄×C₂₉	semidirect
559. Q₈	C₂×C₄⋊C₄×C₂₉	semidirect
615. C₈	C₂×C₄⋊C₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#440	2
C₂×C₄×SD₁₆×C₂₉	2
C₂₉×#2351	2
D₄×C₄⋊C₄×C₂₉	2
C₂₉×#1943	2
C₂₉×#1942	2
C₂₉×#1865	2
C₂₉×#1864	2
C₂₉×#1863	2
C₂₉×#1862	2
C₂₉×#1847	2
C₂₉×#1804	2
C₂₉×#1803	2
C₂₉×#1771	2
#22677	29

Subgroups — C29×#22677 #20317577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#22677 #20317577