Subgroups — C₂₉×#18025 #20312925

Order 7424.

630 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1594	C₂	1	2	yes	maximal, complemented
5	C₂₉×#1583	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1581	C₂	1	2	yes	maximal, complemented
7	C₂₉×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#532	C₂²	1	1	yes	characteristic
13	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×#482	C₄	1	2	yes	—
15	C₂₉×#477	C₄	1	1	yes	characteristic
16	C₂₉×#476	C₄	1	1	yes	characteristic
17	C₂₉×#460	C₄	1	1	yes	characteristic
18	C₂₉×#459	C₄	1	1	yes	characteristic
19	C₂₉×#449	C₄	1	2	yes	—
20	C₈×Q₈×C₂₉	C₂²	1	2	yes	—
21	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
22	C₄×D₈×C₂₉	C₂²	1	2	yes	—
23	C₂₉×#436	—	2	1	no	—
24	C₂₉×#436	—	2	2	no	—
25	C₂₉×#436	C₂²	1	2	yes	—
26	C₂₉×#436	C₂²	1	2	yes	—
27	C₈×D₄×C₂₉	—	2	1	no	—
28	C₈×D₄×C₂₉	C₂²	1	2	yes	—
29	C₂₉×#431	—	2	1	no	—
30	C₂₉×#431	C₂²	1	1	yes	characteristic
31	C₂₉×#431	C₂²	1	1	yes	characteristic
32	C₂₉×#431	C₂²	1	1	yes	characteristic
33	C₂₉×#423	—	2	1	no	—
34	C₂₉×#423	C₂²	1	1	yes	characteristic
35	C₂₉×#408	—	2	2	no	—
36	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#335	C₂²	1	2	yes	—
38	C₂₉×#334	C₂²	1	2	yes	—
39	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₂₉×D₄⋊C₈	C₂²	1	2	yes	—
44	C₂₉×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂₉×#322	C₂²	1	2	yes	—
46	C₂₉×#322	C₂²	1	2	yes	—
47	C₂×#41×C₂₉	—	2	1	no	—
48	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₂₉	C₂×C₄	1	2	yes	—
50	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₂₉	—	2	1	no	—
52	C₂×M₁₆×C₂₉	—	2	2	no	—
53	C₂×M₁₆×C₂₉	—	2	2	no	—
54	C₂²×C₈×C₂₉	—	2	1	no	—
55	C₂²×C₈×C₂₉	—	2	2	no	—
56	C₂₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
57	C₂₉×#127	C₂×C₄	1	1	yes	characteristic
58	C₂₉×#124	—	2	1	no	—
59	C₂₉×#121	—	2	1	no	—
60	C₂₉×#121	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₂₉	—	2	1	no	—
64	C₄×D₄×C₂₉	—	2	1	no	—
65	C₄×D₄×C₂₉	—	2	1	no	—
66	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₂₉	C₂³	1	2	yes	—
68	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
69	C₂₉×#117	—	2	1	no	—
70	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₂₉	—	2	1	no	—
72	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
73	C₂₉×#107	C₂×C₄	1	2	yes	—
74	C₂₉×#106	C₂×C₄	1	2	yes	—
75	C₂₉×C₄⋊C₈	—	2	2	no	—
76	C₂₉×C₄⋊C₈	—	2	1	no	—
77	C₂₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂₉×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
80	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
81	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₂₉×#103	C₂×C₄	1	2	yes	—
85	C₂₉×#102	C₂×C₄	1	2	yes	—
86	C₂₉×#102	C₂×C₄	1	2	yes	—
87	C₂₉×#102	C₂×C₄	1	2	yes	—
88	C₂₉×C₂²⋊C₈	—	2	1	no	—
89	C₂₉×C₂²⋊C₈	—	2	2	no	—
90	C₂₉×C₂²⋊C₈	—	2	2	no	—
91	C₂₉×C₂²⋊C₈	—	2	2	no	—
92	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
94	C₄×C₈×C₂₉	—	2	2	no	—
95	C₄×C₈×C₂₉	—	2	1	no	—
96	C₄×C₈×C₂₉	—	2	1	no	—
97	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₂₉	C₂³	1	2	yes	—
100	C₄×C₈×C₂₉	C₂³	1	2	yes	—
101	#41×C₂₉	—	2	2	no	—
102	#41×C₂₉	—	4	1	no	—
103	#41×C₂₉	—	8	1	no	—
104	#41×C₂₉	—	8	1	no	—
105	C₂×Q₈×C₂₉	—	2	1	no	—
106	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₂₉	—	2	1	no	—
108	C₂×D₄×C₂₉	—	2	2	no	—
109	C₂×D₄×C₂₉	—	2	1	no	—
110	C₂×D₄×C₂₉	—	2	1	no	—
111	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₂₉	—	2	1	no	—
114	C₂²×C₄×C₂₉	—	2	1	no	—
115	C₂²×C₄×C₂₉	—	2	1	no	—
116	C₂²×C₄×C₂₉	—	2	2	no	—
117	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
120	SD₁₆×C₂₉	—	2	4	no	—
121	D₈×C₂₉	—	4	2	no	—
122	M₁₆×C₂₉	—	8	2	no	—
123	M₁₆×C₂₉	—	8	2	no	—
124	M₁₆×C₂₉	—	8	1	no	—
125	C₂×C₈×C₂₉	—	2	1	no	—
126	C₂×C₈×C₂₉	—	2	1	no	—
127	C₂×C₈×C₂₉	—	2	2	no	—
128	C₂×C₈×C₂₉	—	2	1	no	—
129	C₂×C₈×C₂₉	—	2	1	no	—
130	C₂×C₈×C₂₉	—	4	2	no	—
131	C₂×C₈×C₂₉	—	8	2	no	—
132	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₂₉	—	2	1	no	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	2	1	no	—
139	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₂₉	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₂₉	—	2	1	no	—
143	C₂²⋊C₄×C₂₉	—	2	1	no	—
144	C₂²⋊C₄×C₂₉	—	2	2	no	—
145	C₂²⋊C₄×C₂₉	—	2	1	no	—
146	C₂²⋊C₄×C₂₉	—	2	2	no	—
147	C₄²×C₂₉	—	2	1	no	—
148	C₄²×C₂₉	—	2	1	no	—
149	C₄²×C₂₉	—	2	1	no	—
150	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₂₉	#41	1	1	yes	characteristic
153	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
154	#18025	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂³×C₂₉	—	2	1	no	—
156	C₂³×C₂₉	—	2	2	no	—
157	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
158	Q₈×C₂₉	—	2	1	no	—
159	Q₈×C₂₉	—	8	1	no	—
160	Q₈×C₂₉	#131	1	2	yes	—
161	D₄×C₂₉	—	2	2	no	—
162	D₄×C₂₉	—	2	1	no	—
163	D₄×C₂₉	—	2	1	no	—
164	D₄×C₂₉	—	2	2	no	—
165	D₄×C₂₉	—	4	2	no	—
166	D₄×C₂₉	—	4	2	no	—
167	D₄×C₂₉	—	8	1	no	—
168	D₄×C₂₉	—	8	2	no	—
169	C₂×C₄×C₂₉	—	2	1	no	—
170	C₂×C₄×C₂₉	—	2	1	no	—
171	C₂×C₄×C₂₉	—	2	1	no	—
172	C₂×C₄×C₂₉	—	2	1	no	—
173	C₂×C₄×C₂₉	—	2	1	no	—
174	C₂×C₄×C₂₉	—	2	2	no	—
175	C₂×C₄×C₂₉	—	2	1	no	—
176	C₂×C₄×C₂₉	—	2	1	no	—
177	C₂×C₄×C₂₉	—	2	2	no	—
178	C₂×C₄×C₂₉	—	4	2	no	—
179	C₂×C₄×C₂₉	—	4	2	no	—
180	C₂×C₄×C₂₉	—	4	1	no	—
181	C₂×C₄×C₂₉	—	4	2	no	—
182	C₂×C₄×C₂₉	—	4	1	no	—
183	C₂×C₄×C₂₉	—	4	2	no	—
184	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₂₉	—	2	2	no	—
191	C₈×C₂₉	—	2	2	no	—
192	C₈×C₂₉	—	2	2	no	—
193	C₈×C₂₉	—	2	2	no	—
194	C₈×C₂₉	—	4	1	no	—
195	C₈×C₂₉	—	4	1	no	—
196	C₈×C₂₉	—	4	1	no	—
197	C₈×C₂₉	—	4	2	no	—
198	C₈×C₂₉	—	4	1	no	—
199	#3106	C₂×C₂₉	1	1	yes	characteristic
200	#2991	C₂×C₂₉	1	1	yes	characteristic, complemented
201	#2979	C₂×C₂₉	1	1	yes	characteristic, complemented
202	#1594	C₂×C₂₉	1	2	yes	complemented
203	#1583	C₂×C₂₉	1	2	yes	complemented
204	#1581	C₂×C₂₉	1	2	yes	complemented
205	SD₁₆⋊C₈	C₂×C₂₉	1	2	yes	complemented
206	#1574	C₂×C₂₉	1	1	yes	characteristic, complemented
207	#1492	C₂×C₂₉	1	1	yes	characteristic, complemented
208	#1476	C₂×C₂₉	1	1	yes	characteristic, complemented
209	#1452	C₂×C₂₉	1	1	yes	characteristic, complemented
210	C₂²×C₂₉	—	2	1	no	—
211	C₂²×C₂₉	—	2	1	no	—
212	C₂²×C₂₉	—	2	1	no	—
213	C₂²×C₂₉	—	4	1	no	—
214	C₂²×C₂₉	—	4	2	no	—
215	C₂²×C₂₉	—	4	2	no	—
216	C₂²×C₂₉	—	4	1	no	—
217	C₂²×C₂₉	—	4	1	no	—
218	C₂²×C₂₉	—	4	2	no	—
219	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₂₉	—	2	1	no	—
221	C₄×C₂₉	—	2	2	no	—
222	C₄×C₂₉	—	2	1	no	—
223	C₄×C₂₉	—	2	1	no	—
224	C₄×C₂₉	—	4	1	no	—
225	C₄×C₂₉	—	4	2	no	—
226	C₄×C₂₉	—	4	1	no	—
227	C₄×C₂₉	#444	1	2	yes	—
228	C₄×C₂₉	C₂×#131	1	1	yes	characteristic
229	C₄×C₂₉	#568	1	1	yes	characteristic
230	C₄×C₂₉	#576	1	1	yes	characteristic
231	C₄×C₂₉	#577	1	1	yes	characteristic
232	#532	C₂²×C₂₉	1	1	yes	characteristic
233	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
234	#482	C₄×C₂₉	1	2	yes	—
235	#477	C₄×C₂₉	1	1	yes	characteristic
236	#476	C₄×C₂₉	1	1	yes	characteristic
237	#460	C₄×C₂₉	1	1	yes	characteristic
238	#459	C₄×C₂₉	1	1	yes	characteristic
239	#449	C₄×C₂₉	1	2	yes	—
240	C₈×Q₈	C₂²×C₂₉	1	2	yes	—
241	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
242	C₄×D₈	C₂²×C₂₉	1	2	yes	—
243	#436	—	2	1	no	—
244	#436	—	2	2	no	—
245	#436	C₂²×C₂₉	1	2	yes	—
246	#436	C₂²×C₂₉	1	2	yes	—
247	C₈×D₄	—	2	1	no	—
248	C₈×D₄	C₂²×C₂₉	1	2	yes	—
249	#431	—	2	1	no	—
250	#431	C₂²×C₂₉	1	1	yes	characteristic
251	#431	C₂²×C₂₉	1	1	yes	characteristic
252	#431	C₂²×C₂₉	1	1	yes	characteristic
253	#423	—	2	1	no	—
254	#423	C₂²×C₂₉	1	1	yes	characteristic
255	#408	—	2	2	no	—
256	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
257	#335	C₂²×C₂₉	1	2	yes	—
258	#334	C₂²×C₂₉	1	2	yes	—
259	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
260	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
261	D₄⋊C₈	C₂²×C₂₉	1	2	yes	—
262	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
263	D₄⋊C₈	C₂²×C₂₉	1	2	yes	—
264	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
265	#322	C₂²×C₂₉	1	2	yes	—
266	#322	C₂²×C₂₉	1	2	yes	—
267	C₂×C₂₉	—	4	1	no	—
268	C₂×C₂₉	—	8	1	no	—
269	C₂×C₂₉	—	8	2	no	—
270	C₂×C₂₉	#2933	1	1	yes	characteristic
271	C₂×C₂₉	#2946	1	1	yes	characteristic
272	C₂×C₂₉	C₂×#444	1	1	yes	characteristic
273	C₂×#41	—	2	1	no	—
274	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
275	C₂×SD₁₆	C₂×C₄×C₂₉	1	2	yes	—
276	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
283	#127	C₂×C₄×C₂₉	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#121	—	2	1	no	—
286	#121	C₂×C₄×C₂₉	1	2	yes	—
287	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
288	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
293	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
294	C₄×D₄	C₂³×C₂₉	1	2	yes	—
295	#117	—	2	1	no	—
296	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
299	#107	C₂×C₄×C₂₉	1	2	yes	—
300	#106	C₂×C₄×C₂₉	1	2	yes	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
304	C₄⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
305	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
306	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
308	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
310	#103	C₂×C₄×C₂₉	1	2	yes	—
311	#102	C₂×C₄×C₂₉	1	2	yes	—
312	#102	C₂×C₄×C₂₉	1	2	yes	—
313	#102	C₂×C₄×C₂₉	1	2	yes	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
319	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
324	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₂₉	1	2	yes	—
326	C₄×C₈	C₂³×C₂₉	1	2	yes	—
327	C₂₉	#18025	1	1	yes	characteristic, direct product factor, Sylow
328	#41	—	2	2	no	—
329	#41	—	4	1	no	—
330	#41	—	8	1	no	—
331	#41	—	8	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
339	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
346	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
347	SD₁₆	—	2	4	no	—
348	D₈	—	4	2	no	—
349	M₁₆	—	8	2	no	—
350	M₁₆	—	8	2	no	—
351	M₁₆	—	8	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	8	2	no	—
359	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×C₄×C₂₉	1	2	yes	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
379	C₄²	#41×C₂₉	1	1	yes	characteristic
380	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	8	1	no	—
386	Q₈	C₂₉×#131	1	2	yes	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	C₂₉×#444	1	2	yes	—
443	C₄	C₂×C₂₉×#131	1	1	yes	characteristic
444	C₄	C₂₉×#568	1	1	yes	characteristic
445	C₄	C₂₉×#576	1	1	yes	characteristic
446	C₄	C₂₉×#577	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	8	2	no	—
450	C₂	C₂₉×#2933	1	1	yes	characteristic
451	C₂	C₂₉×#2946	1	1	yes	characteristic
452	C₂	C₂×C₂₉×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₄²	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂₉×#3106	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂₉×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#2991	C₂	semidirect
3. C₂₉×#2979	C₂	semidirect
4. C₂₉×#1594	C₂	semidirect
5. C₂₉×#1583	C₂	semidirect
6. C₂₉×#1581	C₂	semidirect
7. C₂₉×SD₁₆⋊C₈	C₂	semidirect
8. C₂₉×#1574	C₂	semidirect
9. C₂₉×#1492	C₂	semidirect
10. C₂₉×#1476	C₂	semidirect
11. C₂₉×#1452	C₂	semidirect
154. #18025	C₂₉	direct (N × H)
200. #2991	C₂×C₂₉	semidirect
201. #2979	C₂×C₂₉	semidirect
202. #1594	C₂×C₂₉	semidirect
203. #1583	C₂×C₂₉	semidirect
204. #1581	C₂×C₂₉	semidirect
205. SD₁₆⋊C₈	C₂×C₂₉	semidirect
206. #1574	C₂×C₂₉	semidirect
207. #1492	C₂×C₂₉	semidirect
208. #1476	C₂×C₂₉	semidirect
209. #1452	C₂×C₂₉	semidirect
327. C₂₉	#18025	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×#3106	2
C₂₉×#2991	2
C₂₉×#2979	2
C₂₉×#1594	2
C₂₉×#1583	2
C₂₉×#1581	2
C₂₉×SD₁₆⋊C₈	2
C₂₉×#1574	2
C₂₉×#1492	2
C₂₉×#1476	2
C₂₉×#1452	2
#18025	29

Subgroups — C29×#18025 #20312925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18025 #20312925