Subgroups — C₂₉×#18910 #20313810

Order 7424.

954 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1636	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1626	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#557	C₂²	1	1	yes	characteristic
17	C₂₉×#553	—	2	2	no	—
18	C₂₉×#553	—	2	1	no	—
19	C₂₉×#550	—	2	1	no	—
20	C₂₉×#550	—	2	1	no	—
21	C₂₉×#550	C₂²	1	1	yes	characteristic
22	C₂₉×#550	C₂²	1	1	yes	characteristic
23	C₂₉×#547	—	2	1	no	—
24	C₂₉×#547	C₂²	1	1	yes	characteristic
25	C₂₉×#540	—	2	2	no	—
26	C₂₉×#540	—	2	1	no	—
27	C₂₉×#532	—	2	1	no	—
28	C₂₉×#532	C₂²	1	1	yes	characteristic
29	C₂₉×#532	C₂²	1	1	yes	characteristic
30	C₂₉×#529	—	2	1	no	—
31	C₂₉×#529	C₂²	1	1	yes	characteristic
32	C₂₉×#520	—	2	1	no	—
33	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#493	C₂²	1	1	yes	characteristic
35	C₂₉×#492	C₂²	1	1	yes	characteristic
36	C₂₉×#487	C₂²	1	1	yes	characteristic
37	C₂₉×#486	C₂²	1	1	yes	characteristic
38	C₂₉×#482	—	2	1	no	—
39	C₂₉×#478	—	2	1	no	—
40	C₂₉×#477	C₂²	1	1	yes	characteristic
41	C₂₉×#477	C₂²	1	1	yes	characteristic
42	C₂₉×#476	C₂²	1	1	yes	characteristic
43	C₂₉×#476	C₂²	1	1	yes	characteristic
44	C₂₉×#466	—	2	1	no	—
45	C₂₉×#465	—	2	1	no	—
46	C₂₉×#463	—	2	1	no	—
47	C₂₉×#463	—	2	2	no	—
48	C₂₉×#460	C₂²	1	1	yes	characteristic
49	C₂₉×#460	C₂²	1	1	yes	characteristic
50	C₂₉×#459	C₂²	1	1	yes	characteristic
51	C₂₉×#459	C₂²	1	1	yes	characteristic
52	C₂₉×#449	—	2	1	no	—
53	C₂₉×#449	—	2	2	no	—
54	C₄×SD₁₆×C₂₉	—	2	1	no	—
55	C₄×D₈×C₂₉	—	2	1	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic
57	C₂₉×#431	C₂²	1	1	yes	characteristic
58	C₂×C₂₉×C₄⋊C₈	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×#331	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂×#41×C₂₉	—	2	1	no	—
75	C₂×#41×C₂₉	—	2	1	no	—
76	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₂₉	—	2	1	no	—
78	C₂×SD₁₆×C₂₉	—	2	1	no	—
79	C₂×SD₁₆×C₂₉	—	2	2	no	—
80	C₂×D₈×C₂₉	—	2	1	no	—
81	C₂×D₈×C₂₉	—	2	2	no	—
82	C₂×D₈×C₂₉	—	2	1	no	—
83	C₂²×C₈×C₂₉	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	—	2	1	no	—
85	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₂₉×#127	—	2	2	no	—
88	C₂₉×#127	—	2	1	no	—
89	C₂₉×#127	—	2	1	no	—
90	C₂₉×#127	C₂³	1	1	yes	characteristic
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#126	—	2	2	no	—
93	C₂₉×#126	—	2	1	no	—
94	C₂₉×#125	—	2	2	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	D₄	1	1	yes	characteristic
97	C₂₉×#124	—	2	1	no	—
98	C₂₉×#124	—	2	1	no	—
99	C₂₉×#124	D₄	1	1	yes	characteristic
100	C₂₉×#123	—	2	2	no	—
101	C₂₉×#123	—	2	2	no	—
102	C₂₉×#123	—	2	2	no	—
103	C₂₉×#123	—	2	1	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×C₂²⋊Q₈	—	2	1	no	—
106	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
107	C₂₉×#121	—	2	2	no	—
108	C₂₉×#121	—	2	2	no	—
109	C₂₉×#121	—	2	2	no	—
110	C₂₉×#121	—	2	2	no	—
111	C₂₉×#121	—	2	2	no	—
112	C₂₉×#121	—	2	1	no	—
113	C₂₉×#121	—	2	2	no	—
114	C₂₉×#121	—	2	2	no	—
115	C₂₉×#121	—	2	1	no	—
116	C₂₉×#121	—	2	1	no	—
117	C₂₉×#121	—	2	1	no	—
118	C₂₉×#121	—	2	1	no	—
119	C₂₉×#121	—	2	1	no	—
120	C₂₉×#121	D₄	1	2	yes	—
121	C₂₉×#121	D₄	1	1	yes	characteristic
122	C₄×Q₈×C₂₉	—	2	1	no	—
123	C₄×Q₈×C₂₉	—	2	1	no	—
124	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
126	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
127	C₄×D₄×C₂₉	—	2	2	no	—
128	C₄×D₄×C₂₉	—	2	2	no	—
129	C₄×D₄×C₂₉	—	2	2	no	—
130	C₄×D₄×C₂₉	—	2	2	no	—
131	C₄×D₄×C₂₉	—	2	1	no	—
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	—	2	1	no	—
134	C₄×D₄×C₂₉	—	2	1	no	—
135	C₄×D₄×C₂₉	—	2	1	no	—
136	C₄×D₄×C₂₉	—	2	1	no	—
137	C₄×D₄×C₂₉	—	2	1	no	—
138	C₄×D₄×C₂₉	—	2	1	no	—
139	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
140	C₄×D₄×C₂₉	D₄	1	2	yes	—
141	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₂₉×#117	—	2	2	no	—
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
148	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
149	C₂×C₄²×C₂₉	—	2	1	no	—
150	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
151	C₂₉×#107	—	2	1	no	—
152	C₂₉×#107	—	2	1	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×C₄⋊C₈	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×#103	—	2	1	no	—
162	C₂₉×#103	—	2	1	no	—
163	C₂₉×#103	—	2	2	no	—
164	C₂₉×#102	—	2	1	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	2	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×C₂²⋊C₈	—	2	1	no	—
172	C₂₉×C₂²⋊C₈	—	2	1	no	—
173	C₄×C₈×C₂₉	—	2	1	no	—
174	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	#41×C₂₉	—	2	2	no	—
177	#41×C₂₉	—	4	1	no	—
178	#41×C₂₉	—	4	2	no	—
179	#41×C₂₉	—	4	2	no	—
180	#41×C₂₉	—	8	1	no	—
181	#41×C₂₉	—	8	1	no	—
182	#41×C₂₉	—	8	1	no	—
183	#41×C₂₉	—	8	1	no	—
184	#41×C₂₉	—	8	1	no	—
185	#41×C₂₉	—	8	1	no	—
186	#41×C₂₉	—	8	2	no	—
187	C₂×Q₈×C₂₉	—	2	1	no	—
188	C₂×Q₈×C₂₉	—	2	1	no	—
189	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
191	C₂×D₄×C₂₉	—	2	2	no	—
192	C₂×D₄×C₂₉	—	2	1	no	—
193	C₂×D₄×C₂₉	—	2	2	no	—
194	C₂×D₄×C₂₉	—	2	2	no	—
195	C₂×D₄×C₂₉	—	2	2	no	—
196	C₂×D₄×C₂₉	—	2	2	no	—
197	C₂×D₄×C₂₉	—	2	1	no	—
198	C₂×D₄×C₂₉	—	2	2	no	—
199	C₂×D₄×C₂₉	—	2	1	no	—
200	C₂×D₄×C₂₉	—	2	1	no	—
201	C₂×D₄×C₂₉	—	2	1	no	—
202	C₂×D₄×C₂₉	—	2	1	no	—
203	C₂×D₄×C₂₉	—	2	1	no	—
204	C₂×D₄×C₂₉	—	4	1	no	—
205	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
206	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
207	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₂₉	—	2	2	no	—
209	C₂²×C₄×C₂₉	—	2	2	no	—
210	C₂²×C₄×C₂₉	—	2	2	no	—
211	C₂²×C₄×C₂₉	—	2	1	no	—
212	C₂²×C₄×C₂₉	—	2	1	no	—
213	C₂²×C₄×C₂₉	—	2	1	no	—
214	C₂²×C₄×C₂₉	—	2	1	no	—
215	C₂²×C₄×C₂₉	—	2	2	no	—
216	C₂²×C₄×C₂₉	—	4	1	no	—
217	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
220	SD₁₆×C₂₉	—	4	2	no	—
221	SD₁₆×C₂₉	—	8	1	no	—
222	SD₁₆×C₂₉	—	8	2	no	—
223	D₈×C₂₉	—	4	2	no	—
224	D₈×C₂₉	—	8	1	no	—
225	D₈×C₂₉	—	8	2	no	—
226	C₂×C₈×C₂₉	—	2	1	no	—
227	C₂×C₈×C₂₉	—	2	1	no	—
228	C₂×C₈×C₂₉	—	2	1	no	—
229	C₂×C₈×C₂₉	—	2	1	no	—
230	C₂×C₈×C₂₉	—	2	1	no	—
231	C₂×C₈×C₂₉	—	2	1	no	—
232	C₂×C₈×C₂₉	—	8	1	no	—
233	C₄⋊C₄×C₂₉	—	2	2	no	—
234	C₄⋊C₄×C₂₉	—	2	2	no	—
235	C₄⋊C₄×C₂₉	—	2	2	no	—
236	C₄⋊C₄×C₂₉	—	2	2	no	—
237	C₄⋊C₄×C₂₉	—	2	1	no	—
238	C₄⋊C₄×C₂₉	—	2	1	no	—
239	C₄⋊C₄×C₂₉	—	2	1	no	—
240	C₄⋊C₄×C₂₉	—	2	1	no	—
241	C₄⋊C₄×C₂₉	—	2	1	no	—
242	C₄⋊C₄×C₂₉	—	2	1	no	—
243	C₄⋊C₄×C₂₉	—	2	1	no	—
244	C₄⋊C₄×C₂₉	—	2	1	no	—
245	C₄⋊C₄×C₂₉	—	2	1	no	—
246	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
247	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
248	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
251	C₂²⋊C₄×C₂₉	—	2	2	no	—
252	C₂²⋊C₄×C₂₉	—	2	2	no	—
253	C₂²⋊C₄×C₂₉	—	2	2	no	—
254	C₂²⋊C₄×C₂₉	—	2	1	no	—
255	C₂²⋊C₄×C₂₉	—	2	1	no	—
256	C₂²⋊C₄×C₂₉	—	2	1	no	—
257	C₂²⋊C₄×C₂₉	—	2	1	no	—
258	C₂²⋊C₄×C₂₉	—	2	2	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	2	1	no	—
261	C₂²⋊C₄×C₂₉	—	2	2	no	—
262	C₂²⋊C₄×C₂₉	—	2	1	no	—
263	C₂²⋊C₄×C₂₉	—	2	1	no	—
264	C₂²⋊C₄×C₂₉	—	4	1	no	—
265	C₂²⋊C₄×C₂₉	—	4	1	no	—
266	C₄²×C₂₉	—	2	2	no	—
267	C₄²×C₂₉	—	2	1	no	—
268	C₄²×C₂₉	—	2	1	no	—
269	C₄²×C₂₉	—	2	1	no	—
270	C₄²×C₂₉	—	2	1	no	—
271	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
275	#18910	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₂₉	—	2	1	no	—
277	C₂³×C₂₉	—	2	1	no	—
278	C₂³×C₂₉	—	2	2	no	—
279	C₂³×C₂₉	—	4	1	no	—
280	C₂³×C₂₉	#120	1	1	yes	characteristic
281	Q₈×C₂₉	—	2	1	no	—
282	Q₈×C₂₉	—	2	1	no	—
283	Q₈×C₂₉	—	2	1	no	—
284	Q₈×C₂₉	—	4	2	no	—
285	Q₈×C₂₉	—	4	1	no	—
286	Q₈×C₂₉	—	4	1	no	—
287	Q₈×C₂₉	#135	1	2	yes	—
288	D₄×C₂₉	—	2	1	no	—
289	D₄×C₂₉	—	2	1	no	—
290	D₄×C₂₉	—	2	1	no	—
291	D₄×C₂₉	—	2	1	no	—
292	D₄×C₂₉	—	4	2	no	—
293	D₄×C₂₉	—	4	2	no	—
294	D₄×C₂₉	—	4	4	no	—
295	D₄×C₂₉	—	4	2	no	—
296	D₄×C₂₉	—	4	1	no	—
297	D₄×C₂₉	—	4	1	no	—
298	D₄×C₂₉	—	4	1	no	—
299	D₄×C₂₉	—	4	1	no	—
300	D₄×C₂₉	—	4	1	no	—
301	D₄×C₂₉	—	4	1	no	—
302	D₄×C₂₉	—	4	1	no	—
303	D₄×C₂₉	—	4	1	no	—
304	D₄×C₂₉	—	8	1	no	—
305	D₄×C₂₉	—	8	2	no	—
306	D₄×C₂₉	—	8	2	no	—
307	D₄×C₂₉	—	8	2	no	—
308	D₄×C₂₉	—	8	2	no	—
309	D₄×C₂₉	—	8	2	no	—
310	D₄×C₂₉	—	8	2	no	—
311	C₂×C₄×C₂₉	—	2	1	no	—
312	C₂×C₄×C₂₉	—	2	1	no	—
313	C₂×C₄×C₂₉	—	2	1	no	—
314	C₂×C₄×C₂₉	—	2	1	no	—
315	C₂×C₄×C₂₉	—	2	1	no	—
316	C₂×C₄×C₂₉	—	2	1	no	—
317	C₂×C₄×C₂₉	—	2	1	no	—
318	C₂×C₄×C₂₉	—	2	1	no	—
319	C₂×C₄×C₂₉	—	2	1	no	—
320	C₂×C₄×C₂₉	—	2	2	no	—
321	C₂×C₄×C₂₉	—	2	1	no	—
322	C₂×C₄×C₂₉	—	4	1	no	—
323	C₂×C₄×C₂₉	—	4	2	no	—
324	C₂×C₄×C₂₉	—	4	4	no	—
325	C₂×C₄×C₂₉	—	4	1	no	—
326	C₂×C₄×C₂₉	—	4	1	no	—
327	C₂×C₄×C₂₉	—	4	1	no	—
328	C₂×C₄×C₂₉	—	4	1	no	—
329	C₂×C₄×C₂₉	—	4	1	no	—
330	C₂×C₄×C₂₉	—	8	1	no	—
331	C₂×C₄×C₂₉	—	8	2	no	—
332	C₂×C₄×C₂₉	—	8	2	no	—
333	C₂×C₄×C₂₉	—	8	2	no	—
334	C₂×C₄×C₂₉	—	8	2	no	—
335	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
336	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
337	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
338	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
341	C₈×C₂₉	—	4	1	no	—
342	C₈×C₂₉	—	4	1	no	—
343	C₈×C₂₉	—	4	1	no	—
344	C₈×C₂₉	—	4	1	no	—
345	C₈×C₂₉	—	4	1	no	—
346	C₈×C₂₉	—	4	1	no	—
347	#3517	C₂×C₂₉	1	1	yes	characteristic, complemented
348	#3247	C₂×C₂₉	1	1	yes	characteristic, complemented
349	#3207	C₂×C₂₉	1	1	yes	characteristic, complemented
350	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
351	#1636	C₂×C₂₉	1	1	yes	characteristic, complemented
352	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
353	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
355	#1626	C₂×C₂₉	1	1	yes	characteristic, complemented
356	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
357	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
358	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
359	#1540	C₂×C₂₉	1	1	yes	characteristic, complemented
360	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
361	#1477	C₂×C₂₉	1	1	yes	characteristic, complemented
362	C₂²×C₂₉	—	2	1	no	—
363	C₂²×C₂₉	—	2	1	no	—
364	C₂²×C₂₉	—	2	1	no	—
365	C₂²×C₂₉	—	4	1	no	—
366	C₂²×C₂₉	—	4	2	no	—
367	C₂²×C₂₉	—	4	1	no	—
368	C₂²×C₂₉	—	4	1	no	—
369	C₂²×C₂₉	—	4	1	no	—
370	C₂²×C₂₉	—	4	2	no	—
371	C₂²×C₂₉	—	4	1	no	—
372	C₂²×C₂₉	—	4	2	no	—
373	C₂²×C₂₉	—	4	1	no	—
374	C₂²×C₂₉	—	8	1	no	—
375	C₂²×C₂₉	—	8	1	no	—
376	C₂²×C₂₉	—	8	1	no	—
377	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
378	C₄×C₂₉	—	2	1	no	—
379	C₄×C₂₉	—	2	2	no	—
380	C₄×C₂₉	—	2	1	no	—
381	C₄×C₂₉	—	2	1	no	—
382	C₄×C₂₉	—	2	1	no	—
383	C₄×C₂₉	—	4	1	no	—
384	C₄×C₂₉	—	4	1	no	—
385	C₄×C₂₉	—	4	1	no	—
386	C₄×C₂₉	—	4	2	no	—
387	C₄×C₂₉	—	4	1	no	—
388	C₄×C₂₉	—	4	1	no	—
389	C₄×C₂₉	—	8	1	no	—
390	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
391	C₄×C₂₉	#575	1	1	yes	characteristic
392	C₄×C₂₉	#576	1	1	yes	characteristic
393	C₄×C₂₉	#577	1	1	yes	characteristic
394	#557	C₂²×C₂₉	1	1	yes	characteristic
395	#553	—	2	2	no	—
396	#553	—	2	1	no	—
397	#550	—	2	1	no	—
398	#550	—	2	1	no	—
399	#550	C₂²×C₂₉	1	1	yes	characteristic
400	#550	C₂²×C₂₉	1	1	yes	characteristic
401	#547	—	2	1	no	—
402	#547	C₂²×C₂₉	1	1	yes	characteristic
403	#540	—	2	2	no	—
404	#540	—	2	1	no	—
405	#532	—	2	1	no	—
406	#532	C₂²×C₂₉	1	1	yes	characteristic
407	#532	C₂²×C₂₉	1	1	yes	characteristic
408	#529	—	2	1	no	—
409	#529	C₂²×C₂₉	1	1	yes	characteristic
410	#520	—	2	1	no	—
411	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
412	#493	C₂²×C₂₉	1	1	yes	characteristic
413	#492	C₂²×C₂₉	1	1	yes	characteristic
414	#487	C₂²×C₂₉	1	1	yes	characteristic
415	#486	C₂²×C₂₉	1	1	yes	characteristic
416	#482	—	2	1	no	—
417	#478	—	2	1	no	—
418	#477	C₂²×C₂₉	1	1	yes	characteristic
419	#477	C₂²×C₂₉	1	1	yes	characteristic
420	#476	C₂²×C₂₉	1	1	yes	characteristic
421	#476	C₂²×C₂₉	1	1	yes	characteristic
422	#466	—	2	1	no	—
423	#465	—	2	1	no	—
424	#463	—	2	1	no	—
425	#463	—	2	2	no	—
426	#460	C₂²×C₂₉	1	1	yes	characteristic
427	#460	C₂²×C₂₉	1	1	yes	characteristic
428	#459	C₂²×C₂₉	1	1	yes	characteristic
429	#459	C₂²×C₂₉	1	1	yes	characteristic
430	#449	—	2	1	no	—
431	#449	—	2	2	no	—
432	C₄×SD₁₆	—	2	1	no	—
433	C₄×D₈	—	2	1	no	—
434	#431	C₂²×C₂₉	1	1	yes	characteristic
435	#431	C₂²×C₂₉	1	1	yes	characteristic
436	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
437	#332	C₂²×C₂₉	1	1	yes	characteristic
438	#332	C₂²×C₂₉	1	1	yes	characteristic
439	#331	C₂²×C₂₉	1	1	yes	characteristic
440	#331	C₂²×C₂₉	1	1	yes	characteristic
441	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
442	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
443	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
444	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
445	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
446	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
447	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
448	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
449	C₂×C₂₉	—	4	1	no	—
450	C₂×C₂₉	—	8	1	no	—
451	C₂×C₂₉	—	8	1	no	—
452	C₂×C₂₉	—	8	2	no	—
453	C₂×C₂₉	—	16	1	no	—
454	C₂×C₂₉	#3002	1	1	yes	characteristic
455	C₂×C₂₉	#3012	1	1	yes	characteristic
456	C₂×C₂₉	#3021	1	1	yes	characteristic
457	C₂×#41	—	2	1	no	—
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
463	C₂×SD₁₆	—	2	1	no	—
464	C₂×SD₁₆	—	2	1	no	—
465	C₂×SD₁₆	—	2	2	no	—
466	C₂×D₈	—	2	1	no	—
467	C₂×D₈	—	2	2	no	—
468	C₂×D₈	—	2	1	no	—
469	C₂²×C₈	—	2	1	no	—
470	C₄⋊Q₈	—	2	1	no	—
471	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
472	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
473	#127	—	2	2	no	—
474	#127	—	2	1	no	—
475	#127	—	2	1	no	—
476	#127	C₂³×C₂₉	1	1	yes	characteristic
477	#127	C₂³×C₂₉	1	1	yes	characteristic
478	#126	—	2	2	no	—
479	#126	—	2	1	no	—
480	#125	—	2	2	no	—
481	#125	—	2	1	no	—
482	#125	D₄×C₂₉	1	1	yes	characteristic
483	#124	—	2	1	no	—
484	#124	—	2	1	no	—
485	#124	D₄×C₂₉	1	1	yes	characteristic
486	#123	—	2	2	no	—
487	#123	—	2	2	no	—
488	#123	—	2	2	no	—
489	#123	—	2	1	no	—
490	#123	—	2	2	no	—
491	C₂²⋊Q₈	—	2	1	no	—
492	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
493	#121	—	2	2	no	—
494	#121	—	2	2	no	—
495	#121	—	2	2	no	—
496	#121	—	2	2	no	—
497	#121	—	2	2	no	—
498	#121	—	2	1	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	—	2	1	no	—
505	#121	—	2	1	no	—
506	#121	D₄×C₂₉	1	1	yes	characteristic
507	#121	D₄×C₂₉	1	2	yes	—
508	C₄×Q₈	—	2	1	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
511	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
512	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	1	no	—
518	C₄×D₄	—	2	1	no	—
519	C₄×D₄	—	2	1	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
526	C₄×D₄	D₄×C₂₉	1	2	yes	—
527	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
528	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
529	#117	—	2	2	no	—
530	#117	—	2	1	no	—
531	#117	—	2	1	no	—
532	#117	D₄×C₂₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
537	#107	—	2	1	no	—
538	#107	—	2	1	no	—
539	#106	—	2	1	no	—
540	#106	—	2	1	no	—
541	C₄⋊C₈	—	2	1	no	—
542	C₄⋊C₈	—	2	1	no	—
543	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
544	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
545	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
546	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
547	#103	—	2	1	no	—
548	#103	—	2	1	no	—
549	#103	—	2	2	no	—
550	#102	—	2	1	no	—
551	#102	—	2	1	no	—
552	#102	—	2	1	no	—
553	#102	—	2	1	no	—
554	#102	—	2	2	no	—
555	#102	—	2	1	no	—
556	#102	—	2	1	no	—
557	C₂²⋊C₈	—	2	1	no	—
558	C₂²⋊C₈	—	2	1	no	—
559	C₄×C₈	—	2	1	no	—
560	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
562	C₂₉	#18910	1	1	yes	characteristic, direct product factor, Sylow
563	#41	—	2	2	no	—
564	#41	—	4	1	no	—
565	#41	—	4	2	no	—
566	#41	—	4	2	no	—
567	#41	—	8	1	no	—
568	#41	—	8	1	no	—
569	#41	—	8	1	no	—
570	#41	—	8	1	no	—
571	#41	—	8	1	no	—
572	#41	—	8	1	no	—
573	#41	—	8	2	no	—
574	C₂×Q₈	—	2	1	no	—
575	C₂×Q₈	—	2	1	no	—
576	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
577	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	1	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	2	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	1	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
593	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
594	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
607	SD₁₆	—	4	2	no	—
608	SD₁₆	—	8	1	no	—
609	SD₁₆	—	8	2	no	—
610	D₈	—	4	2	no	—
611	D₈	—	8	1	no	—
612	D₈	—	8	2	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	8	1	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
636	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	4	1	no	—
652	C₂²⋊C₄	—	4	1	no	—
653	C₄²	—	2	2	no	—
654	C₄²	—	2	1	no	—
655	C₄²	—	2	1	no	—
656	C₄²	—	2	1	no	—
657	C₄²	—	2	1	no	—
658	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
659	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
660	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
661	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	4	1	no	—
666	C₂³	C₂₉×#120	1	1	yes	characteristic
667	Q₈	—	2	1	no	—
668	Q₈	—	2	1	no	—
669	Q₈	—	2	1	no	—
670	Q₈	—	4	2	no	—
671	Q₈	—	4	1	no	—
672	Q₈	—	4	1	no	—
673	Q₈	C₂₉×#135	1	2	yes	—
674	D₄	—	2	1	no	—
675	D₄	—	2	1	no	—
676	D₄	—	2	1	no	—
677	D₄	—	2	1	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	2	no	—
680	D₄	—	4	4	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	1	no	—
683	D₄	—	4	1	no	—
684	D₄	—	4	1	no	—
685	D₄	—	4	1	no	—
686	D₄	—	4	1	no	—
687	D₄	—	4	1	no	—
688	D₄	—	4	1	no	—
689	D₄	—	4	1	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	1	no	—
692	D₄	—	8	2	no	—
693	D₄	—	8	2	no	—
694	D₄	—	8	2	no	—
695	D₄	—	8	2	no	—
696	D₄	—	8	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	8	2	no	—
717	C₂×C₄	—	8	1	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
722	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
723	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
727	C₈	—	4	1	no	—
728	C₈	—	4	1	no	—
729	C₈	—	4	1	no	—
730	C₈	—	4	1	no	—
731	C₈	—	4	1	no	—
732	C₈	—	4	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	1	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	1	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
749	C₄	—	2	1	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	8	1	no	—
761	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
762	C₄	C₂₉×#575	1	1	yes	characteristic
763	C₄	C₂₉×#576	1	1	yes	characteristic
764	C₄	C₂₉×#577	1	1	yes	characteristic
765	C₂	—	4	1	no	—
766	C₂	—	8	1	no	—
767	C₂	—	8	1	no	—
768	C₂	—	8	2	no	—
769	C₂	—	16	1	no	—
770	C₂	C₂₉×#3002	1	1	yes	characteristic
771	C₂	C₂₉×#3012	1	1	yes	characteristic
772	C₂	C₂₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3517	C₂	semidirect
2. C₂₉×#3247	C₂	semidirect
3. C₂₉×#3207	C₂	semidirect
4. C₂₉×#3106	C₂	semidirect
5. C₂₉×#1636	C₂	semidirect
6. C₂₉×#1635	C₂	semidirect
7. C₂₉×#1631	C₂	semidirect
8. C₂₉×#1631	C₂	semidirect
9. C₂₉×#1626	C₂	semidirect
10. C₂₉×#1625	C₂	semidirect
11. C₂₉×#1621	C₂	semidirect
12. C₂₉×#1621	C₂	semidirect
13. C₂₉×#1540	C₂	semidirect
14. C₂₉×#1482	C₂	semidirect
15. C₂₉×#1477	C₂	semidirect
275. #18910	C₂₉	direct (N × H)
347. #3517	C₂×C₂₉	semidirect
348. #3247	C₂×C₂₉	semidirect
349. #3207	C₂×C₂₉	semidirect
350. #3106	C₂×C₂₉	semidirect
351. #1636	C₂×C₂₉	semidirect
352. #1635	C₂×C₂₉	semidirect
353. #1631	C₂×C₂₉	semidirect
354. #1631	C₂×C₂₉	semidirect
355. #1626	C₂×C₂₉	semidirect
356. #1625	C₂×C₂₉	semidirect
357. #1621	C₂×C₂₉	semidirect
358. #1621	C₂×C₂₉	semidirect
359. #1540	C₂×C₂₉	semidirect
360. #1482	C₂×C₂₉	semidirect
361. #1477	C₂×C₂₉	semidirect
562. C₂₉	#18910	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×#3517	2
C₂₉×#3247	2
C₂₉×#3207	2
C₂₉×#3106	2
C₂₉×#1636	2
C₂₉×#1635	2
C₂₉×#1631	2
C₂₉×#1626	2
C₂₉×#1625	2
C₂₉×#1621	2
C₂₉×#1540	2
C₂₉×#1482	2
C₂₉×#1477	2
#18910	29

Subgroups — C29×#18910 #20313810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18910 #20313810