Subgroups — C₂₉×#26848 #20321748

Order 7424.

718 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3136	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3096	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2063	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2061	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2004	C₂	1	1	yes	maximal, characteristic
9	C₂₉×#1958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1937	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1888	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1860	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
17	C₂₉×#544	C₂²	1	1	yes	characteristic
18	C₂₉×#535	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×#124	C₂²	1	1	yes	characteristic
20	C₂₉×#520	C₂²	1	1	yes	characteristic
21	C₂₉×#519	C₂²	1	1	yes	characteristic
22	C₂₉×#490	—	2	1	no	—
23	C₂₉×#489	—	2	1	no	—
24	C₂₉×#488	—	2	1	no	—
25	C₂₉×#486	—	2	1	no	—
26	C₂₉×#482	—	2	1	no	—
27	C₂₉×#482	—	2	1	no	—
28	C₂₉×#481	—	2	1	no	—
29	C₂₉×#480	—	2	1	no	—
30	C₂₉×#479	—	2	1	no	—
31	C₂₉×#479	—	2	1	no	—
32	C₂₉×#477	—	2	1	no	—
33	C₂₉×#475	—	2	1	no	—
34	C₂₉×#441	—	2	1	no	—
35	C₂₉×#440	—	2	1	no	—
36	C₄×Q₁₆×C₂₉	—	2	1	no	—
37	C₄×SD₁₆×C₂₉	—	2	1	no	—
38	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
39	C₂₉×#428	C₂²	1	1	yes	characteristic
40	C₂₉×#428	C₂²	1	1	yes	characteristic
41	C₂₉×#428	C₂²	1	1	yes	characteristic
42	C₂₉×#427	C₂²	1	1	yes	characteristic
43	C₂₉×#424	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
45	C₂₉×#419	C₂²	1	1	yes	characteristic
46	C₂₉×#418	C₂²	1	1	yes	characteristic
47	C₂₉×#418	C₂²	1	1	yes	characteristic
48	C₂₉×#417	C₂²	1	1	yes	characteristic
49	C₂₉×#416	C₂²	1	1	yes	characteristic
50	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
51	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
52	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
53	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
56	C₂₉×#408	C₂²	1	1	yes	characteristic
57	C₂₉×#405	C₂²	1	1	yes	characteristic
58	C₂₉×#405	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
60	C₂₉×#382	C₂²	1	1	yes	characteristic
61	C₂₉×#343	C₂²	1	1	yes	characteristic
62	C₂₉×#343	C₂²	1	1	yes	characteristic
63	C₂₉×#341	C₂²	1	1	yes	characteristic
64	C₂₉×#339	C₂²	1	1	yes	characteristic
65	C₂₉×#339	C₂²	1	1	yes	characteristic
66	C₂₉×#339	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
70	C₂₉×#137	—	2	2	no	—
71	C₂₉×#137	—	2	2	no	—
72	C₂×Q₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	2	1	no	—
74	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
77	C₂×M₁₆×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	C₂₉×C₄⋊Q₈	—	2	1	no	—
81	C₂₉×C₄⋊Q₈	—	2	1	no	—
82	C₂₉×#127	—	2	1	no	—
83	C₂₉×#125	—	2	1	no	—
84	C₂₉×#125	—	2	1	no	—
85	C₂₉×#124	—	2	1	no	—
86	C₂₉×#124	—	2	2	no	—
87	C₂₉×#124	—	2	2	no	—
88	C₂₉×C₂²⋊Q₈	—	4	1	no	—
89	C₂₉×#121	—	2	1	no	—
90	C₂₉×#121	—	2	1	no	—
91	C₂₉×#120	—	4	1	no	—
92	C₄×Q₈×C₂₉	—	2	1	no	—
93	C₄×Q₈×C₂₉	—	2	1	no	—
94	C₄×Q₈×C₂₉	—	2	1	no	—
95	C₄×Q₈×C₂₉	—	2	1	no	—
96	C₄×Q₈×C₂₉	—	2	1	no	—
97	C₄×D₄×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	—	4	1	no	—
99	C₂₉×#117	—	2	1	no	—
100	C₂₉×#117	—	4	1	no	—
101	C₂₉×#117	C₂³	1	1	yes	characteristic
102	C₂₉×#117	C₂³	1	1	yes	characteristic
103	C₂₉×#117	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₂₉	—	4	1	no	—
108	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
109	C₂₉×#108	—	2	2	no	—
110	C₂₉×#107	—	2	1	no	—
111	C₂₉×#107	—	2	1	no	—
112	C₂₉×#107	—	2	1	no	—
113	C₂₉×#107	D₄	1	1	yes	characteristic
114	C₂₉×#107	D₄	1	1	yes	characteristic
115	C₂₉×#106	—	2	1	no	—
116	C₂₉×#106	—	2	1	no	—
117	C₂₉×#106	—	2	1	no	—
118	C₂₉×#106	D₄	1	1	yes	characteristic
119	C₂₉×#106	D₄	1	1	yes	characteristic
120	C₂₉×C₄⋊C₈	—	2	1	no	—
121	C₂₉×C₄⋊C₈	—	2	1	no	—
122	C₂₉×#104	—	2	2	no	—
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	2	1	no	—
125	C₂₉×#103	—	2	1	no	—
126	C₂₉×#103	—	2	1	no	—
127	C₂₉×#103	—	2	1	no	—
128	C₂₉×#103	—	2	1	no	—
129	C₂₉×#103	—	2	1	no	—
130	C₂₉×#103	D₄	1	1	yes	characteristic
131	C₂₉×#103	D₄	1	1	yes	characteristic
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	2	1	no	—
134	C₂₉×#102	—	2	1	no	—
135	C₂₉×#102	—	2	1	no	—
136	C₂₉×#102	—	2	1	no	—
137	C₂₉×#102	—	2	1	no	—
138	C₂₉×#102	—	2	1	no	—
139	C₂₉×#102	—	2	1	no	—
140	C₂₉×#102	—	2	1	no	—
141	C₂₉×#102	D₄	1	1	yes	characteristic
142	C₂₉×#102	D₄	1	1	yes	characteristic
143	C₂₉×#101	—	2	2	no	—
144	C₂₉×#100	—	2	2	no	—
145	C₂₉×C₂²⋊C₈	—	2	1	no	—
146	C₂₉×C₂²⋊C₈	—	2	1	no	—
147	C₂₉×#97	—	2	1	no	—
148	C₂₉×#97	—	2	1	no	—
149	C₄×C₈×C₂₉	—	2	1	no	—
150	C₄×C₈×C₂₉	—	2	1	no	—
151	C₄×C₈×C₂₉	—	2	2	no	—
152	C₂₉×#95	—	4	1	no	—
153	C₂⁴×C₂₉	—	2	1	no	—
154	#41×C₂₉	—	2	1	no	—
155	#41×C₂₉	—	2	1	no	—
156	#41×C₂₉	—	2	1	no	—
157	#41×C₂₉	—	2	1	no	—
158	C₂×Q₈×C₂₉	—	2	1	no	—
159	C₂×Q₈×C₂₉	—	2	1	no	—
160	C₂×Q₈×C₂₉	—	2	1	no	—
161	C₂×Q₈×C₂₉	—	2	1	no	—
162	C₂×Q₈×C₂₉	—	2	1	no	—
163	C₂×Q₈×C₂₉	—	4	1	no	—
164	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
165	C₂×Q₈×C₂₉	#41	1	2	yes	—
166	C₂×D₄×C₂₉	—	2	1	no	—
167	C₂×D₄×C₂₉	—	2	1	no	—
168	C₂×D₄×C₂₉	—	2	1	no	—
169	C₂×D₄×C₂₉	—	2	1	no	—
170	C₂×D₄×C₂₉	—	2	1	no	—
171	C₂×D₄×C₂₉	—	2	1	no	—
172	C₂×D₄×C₂₉	—	2	1	no	—
173	C₂×D₄×C₂₉	—	4	1	no	—
174	C₂×D₄×C₂₉	—	4	1	no	—
175	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₉	—	2	1	no	—
177	C₂²×C₄×C₂₉	—	2	1	no	—
178	C₂²×C₄×C₂₉	—	2	1	no	—
179	C₂²×C₄×C₂₉	—	2	1	no	—
180	C₂²×C₄×C₂₉	—	2	1	no	—
181	C₂²×C₄×C₂₉	—	4	1	no	—
182	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
183	Q₁₆×C₂₉	—	2	4	no	—
184	SD₁₆×C₂₉	—	2	4	no	—
185	M₁₆×C₂₉	—	2	1	no	—
186	M₁₆×C₂₉	—	2	1	no	—
187	M₁₆×C₂₉	—	2	1	no	—
188	M₁₆×C₂₉	—	2	1	no	—
189	M₁₆×C₂₉	—	2	1	no	—
190	M₁₆×C₂₉	—	2	1	no	—
191	M₁₆×C₂₉	—	2	1	no	—
192	M₁₆×C₂₉	#41	1	2	yes	—
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	—	2	1	no	—
201	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
210	C₄⋊C₄×C₂₉	—	4	1	no	—
211	C₄⋊C₄×C₂₉	—	4	1	no	—
212	C₄⋊C₄×C₂₉	—	4	1	no	—
213	C₄⋊C₄×C₂₉	—	4	1	no	—
214	C₄⋊C₄×C₂₉	—	4	1	no	—
215	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
218	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
219	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
220	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
221	C₂²⋊C₄×C₂₉	—	2	1	no	—
222	C₂²⋊C₄×C₂₉	—	2	1	no	—
223	C₂²⋊C₄×C₂₉	—	2	1	no	—
224	C₂²⋊C₄×C₂₉	—	4	4	no	—
225	C₂²⋊C₄×C₂₉	—	4	1	no	—
226	C₂²⋊C₄×C₂₉	—	4	1	no	—
227	C₂²⋊C₄×C₂₉	—	4	1	no	—
228	C₄²×C₂₉	—	2	1	no	—
229	C₄²×C₂₉	—	2	1	no	—
230	C₄²×C₂₉	—	2	1	no	—
231	C₄²×C₂₉	—	2	1	no	—
232	C₄²×C₂₉	—	4	1	no	—
233	C₄²×C₂₉	—	4	1	no	—
234	C₄²×C₂₉	—	4	1	no	—
235	C₄²×C₂₉	#41	1	2	yes	—
236	#26848	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₂₉	—	2	1	no	—
238	C₂³×C₂₉	—	4	1	no	—
239	C₂³×C₂₉	—	4	1	no	—
240	C₂³×C₂₉	—	4	1	no	—
241	C₂³×C₂₉	—	8	1	no	—
242	C₂³×C₂₉	—	8	1	no	—
243	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
244	Q₈×C₂₉	—	2	2	no	—
245	Q₈×C₂₉	—	2	1	no	—
246	Q₈×C₂₉	—	2	1	no	—
247	Q₈×C₂₉	—	2	2	no	—
248	Q₈×C₂₉	—	4	1	no	—
249	Q₈×C₂₉	—	4	1	no	—
250	Q₈×C₂₉	—	16	1	no	—
251	D₄×C₂₉	—	2	1	no	—
252	D₄×C₂₉	—	2	1	no	—
253	D₄×C₂₉	—	4	1	no	—
254	D₄×C₂₉	—	4	1	no	—
255	D₄×C₂₉	—	4	1	no	—
256	D₄×C₂₉	—	4	1	no	—
257	D₄×C₂₉	—	4	1	no	—
258	D₄×C₂₉	—	4	1	no	—
259	D₄×C₂₉	—	16	1	no	—
260	D₄×C₂₉	—	16	1	no	—
261	C₂×C₄×C₂₉	—	2	1	no	—
262	C₂×C₄×C₂₉	—	2	1	no	—
263	C₂×C₄×C₂₉	—	2	1	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	2	no	—
269	C₂×C₄×C₂₉	—	2	2	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	—	4	1	no	—
275	C₂×C₄×C₂₉	—	4	1	no	—
276	C₂×C₄×C₂₉	—	4	1	no	—
277	C₂×C₄×C₂₉	—	4	1	no	—
278	C₂×C₄×C₂₉	—	8	1	no	—
279	C₂×C₄×C₂₉	—	8	1	no	—
280	C₂×C₄×C₂₉	—	16	1	no	—
281	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
287	C₈×C₂₉	—	2	2	no	—
288	C₈×C₂₉	—	2	1	no	—
289	C₈×C₂₉	—	2	1	no	—
290	C₈×C₂₉	—	2	1	no	—
291	C₈×C₂₉	—	2	1	no	—
292	C₈×C₂₉	—	4	1	no	—
293	C₈×C₂₉	—	4	1	no	—
294	C₈×C₂₉	—	4	1	no	—
295	#3136	C₂×C₂₉	1	1	yes	characteristic
296	#3096	C₂×C₂₉	1	1	yes	characteristic
297	#3082	C₂×C₂₉	1	1	yes	characteristic, complemented
298	#2947	C₂×C₂₉	1	1	yes	characteristic, complemented
299	#2063	C₂×C₂₉	1	1	yes	characteristic, complemented
300	#2061	C₂×C₂₉	1	1	yes	characteristic, complemented
301	#2052	C₂×C₂₉	1	1	yes	characteristic, complemented
302	#2004	C₂×C₂₉	1	1	yes	characteristic
303	#1958	C₂×C₂₉	1	1	yes	characteristic, complemented
304	#1937	C₂×C₂₉	1	1	yes	characteristic, complemented
305	#1931	C₂×C₂₉	1	1	yes	characteristic, complemented
306	#1930	C₂×C₂₉	1	1	yes	characteristic, complemented
307	#1888	C₂×C₂₉	1	1	yes	characteristic, complemented
308	#1860	C₂×C₂₉	1	1	yes	characteristic, complemented
309	#1772	C₂×C₂₉	1	1	yes	characteristic, complemented
310	C₂²×C₂₉	—	2	1	no	—
311	C₂²×C₂₉	—	2	1	no	—
312	C₂²×C₂₉	—	4	1	no	—
313	C₂²×C₂₉	—	4	1	no	—
314	C₂²×C₂₉	—	4	1	no	—
315	C₂²×C₂₉	—	8	2	no	—
316	C₂²×C₂₉	—	8	1	no	—
317	C₂²×C₂₉	—	8	1	no	—
318	C₂²×C₂₉	—	8	1	no	—
319	C₂²×C₂₉	—	16	1	no	—
320	C₂²×C₂₉	#542	1	1	yes	characteristic
321	C₂²×C₂₉	D₄²	1	1	yes	characteristic
322	C₂²×C₂₉	#551	1	1	yes	characteristic
323	C₄×C₂₉	—	4	2	no	—
324	C₄×C₂₉	—	4	1	no	—
325	C₄×C₂₉	—	4	2	no	—
326	C₄×C₂₉	—	4	1	no	—
327	C₄×C₂₉	—	4	1	no	—
328	C₄×C₂₉	—	4	1	no	—
329	C₄×C₂₉	—	4	1	no	—
330	C₄×C₂₉	—	4	1	no	—
331	C₄×C₂₉	—	4	1	no	—
332	C₄×C₂₉	—	8	1	no	—
333	C₄×C₂₉	—	8	1	no	—
334	C₄×C₂₉	#525	1	1	yes	characteristic
335	C₄×C₂₉	#532	1	1	yes	characteristic
336	C₄×C₂₉	#547	1	1	yes	characteristic
337	C₄×C₂₉	#548	1	1	yes	characteristic
338	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
339	#544	C₂²×C₂₉	1	1	yes	characteristic
340	#535	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
342	#520	C₂²×C₂₉	1	1	yes	characteristic
343	#519	C₂²×C₂₉	1	1	yes	characteristic
344	#490	—	2	1	no	—
345	#489	—	2	1	no	—
346	#488	—	2	1	no	—
347	#486	—	2	1	no	—
348	#482	—	2	1	no	—
349	#482	—	2	1	no	—
350	#481	—	2	1	no	—
351	#480	—	2	1	no	—
352	#479	—	2	1	no	—
353	#479	—	2	1	no	—
354	#477	—	2	1	no	—
355	#475	—	2	1	no	—
356	#441	—	2	1	no	—
357	#440	—	2	1	no	—
358	C₄×Q₁₆	—	2	1	no	—
359	C₄×SD₁₆	—	2	1	no	—
360	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
361	#428	C₂²×C₂₉	1	1	yes	characteristic
362	#428	C₂²×C₂₉	1	1	yes	characteristic
363	#428	C₂²×C₂₉	1	1	yes	characteristic
364	#427	C₂²×C₂₉	1	1	yes	characteristic
365	#424	C₂²×C₂₉	1	1	yes	characteristic
366	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
367	#419	C₂²×C₂₉	1	1	yes	characteristic
368	#418	C₂²×C₂₉	1	1	yes	characteristic
369	#418	C₂²×C₂₉	1	1	yes	characteristic
370	#417	C₂²×C₂₉	1	1	yes	characteristic
371	#416	C₂²×C₂₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
374	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
375	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
376	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
377	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
378	#408	C₂²×C₂₉	1	1	yes	characteristic
379	#405	C₂²×C₂₉	1	1	yes	characteristic
380	#405	C₂²×C₂₉	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
382	#382	C₂²×C₂₉	1	1	yes	characteristic
383	#343	C₂²×C₂₉	1	1	yes	characteristic
384	#343	C₂²×C₂₉	1	1	yes	characteristic
385	#341	C₂²×C₂₉	1	1	yes	characteristic
386	#339	C₂²×C₂₉	1	1	yes	characteristic
387	#339	C₂²×C₂₉	1	1	yes	characteristic
388	#339	C₂²×C₂₉	1	1	yes	characteristic
389	C₂×C₂₉	—	2	1	no	—
390	C₂×C₂₉	—	2	1	no	—
391	C₂×C₂₉	—	8	1	no	—
392	C₂×C₂₉	—	16	1	no	—
393	C₂×C₂₉	#2461	1	1	yes	characteristic
394	C₂×C₂₉	#3290	1	1	yes	characteristic
395	C₂×C₂₉	#3290	1	1	yes	characteristic
396	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
397	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
398	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
399	#137	—	2	2	no	—
400	#137	—	2	2	no	—
401	C₂×Q₁₆	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
404	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
405	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
406	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
409	C₄⋊Q₈	—	2	1	no	—
410	C₄⋊Q₈	—	2	1	no	—
411	#127	—	2	1	no	—
412	#125	—	2	1	no	—
413	#125	—	2	1	no	—
414	#124	—	2	1	no	—
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	C₂²⋊Q₈	—	4	1	no	—
418	#121	—	2	1	no	—
419	#121	—	2	1	no	—
420	#120	—	4	1	no	—
421	C₄×Q₈	—	2	1	no	—
422	C₄×Q₈	—	2	1	no	—
423	C₄×Q₈	—	2	1	no	—
424	C₄×Q₈	—	2	1	no	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×D₄	—	2	1	no	—
427	C₄×D₄	—	4	1	no	—
428	#117	—	2	1	no	—
429	#117	—	4	1	no	—
430	#117	C₂³×C₂₉	1	1	yes	characteristic
431	#117	C₂³×C₂₉	1	1	yes	characteristic
432	#117	C₂³×C₂₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	—	4	1	no	—
437	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
438	#108	—	2	2	no	—
439	#107	—	2	1	no	—
440	#107	—	2	1	no	—
441	#107	—	2	1	no	—
442	#107	D₄×C₂₉	1	1	yes	characteristic
443	#107	D₄×C₂₉	1	1	yes	characteristic
444	#106	—	2	1	no	—
445	#106	—	2	1	no	—
446	#106	—	2	1	no	—
447	#106	D₄×C₂₉	1	1	yes	characteristic
448	#106	D₄×C₂₉	1	1	yes	characteristic
449	C₄⋊C₈	—	2	1	no	—
450	C₄⋊C₈	—	2	1	no	—
451	#104	—	2	2	no	—
452	#103	—	2	1	no	—
453	#103	—	2	1	no	—
454	#103	—	2	1	no	—
455	#103	—	2	1	no	—
456	#103	—	2	1	no	—
457	#103	—	2	1	no	—
458	#103	—	2	1	no	—
459	#103	D₄×C₂₉	1	1	yes	characteristic
460	#103	D₄×C₂₉	1	1	yes	characteristic
461	#102	—	2	1	no	—
462	#102	—	2	1	no	—
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	1	no	—
466	#102	—	2	1	no	—
467	#102	—	2	1	no	—
468	#102	—	2	1	no	—
469	#102	—	2	1	no	—
470	#102	D₄×C₂₉	1	1	yes	characteristic
471	#102	D₄×C₂₉	1	1	yes	characteristic
472	#101	—	2	2	no	—
473	#100	—	2	2	no	—
474	C₂²⋊C₈	—	2	1	no	—
475	C₂²⋊C₈	—	2	1	no	—
476	#97	—	2	1	no	—
477	#97	—	2	1	no	—
478	C₄×C₈	—	2	1	no	—
479	C₄×C₈	—	2	1	no	—
480	C₄×C₈	—	2	2	no	—
481	#95	—	4	1	no	—
482	C₂₉	#26848	1	1	yes	characteristic, direct product factor, Sylow
483	C₂⁴	—	2	1	no	—
484	#41	—	2	1	no	—
485	#41	—	2	1	no	—
486	#41	—	2	1	no	—
487	#41	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	4	1	no	—
494	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
495	C₂×Q₈	#41×C₂₉	1	2	yes	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	4	1	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	4	1	no	—
512	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
513	Q₁₆	—	2	4	no	—
514	SD₁₆	—	2	4	no	—
515	M₁₆	—	2	1	no	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	#41×C₂₉	1	2	yes	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
532	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
533	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
534	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	1	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	4	1	no	—
543	C₄⋊C₄	—	4	1	no	—
544	C₄⋊C₄	—	4	1	no	—
545	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
546	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
547	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
548	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
550	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	1	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	4	1	no	—
563	C₄²	—	4	1	no	—
564	C₄²	—	4	1	no	—
565	C₄²	#41×C₂₉	1	2	yes	—
566	C₂³	—	2	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	8	1	no	—
571	C₂³	—	8	1	no	—
572	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	1	no	—
575	Q₈	—	2	1	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	—	16	1	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	16	1	no	—
589	D₄	—	16	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	8	1	no	—
608	C₂×C₄	—	8	1	no	—
609	C₂×C₄	—	16	1	no	—
610	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
612	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
613	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
615	C₂×C₄	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	2	1	no	—
618	C₈	—	2	1	no	—
619	C₈	—	2	1	no	—
620	C₈	—	2	1	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	4	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	4	1	no	—
628	C₂²	—	4	1	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	8	1	no	—
631	C₂²	—	8	1	no	—
632	C₂²	—	8	1	no	—
633	C₂²	—	16	1	no	—
634	C₂²	C₂₉×#542	1	1	yes	characteristic
635	C₂²	D₄²×C₂₉	1	1	yes	characteristic
636	C₂²	C₂₉×#551	1	1	yes	characteristic
637	C₄	—	4	2	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	1	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	C₂₉×#525	1	1	yes	characteristic
649	C₄	C₂₉×#532	1	1	yes	characteristic
650	C₄	C₂₉×#547	1	1	yes	characteristic
651	C₄	C₂₉×#548	1	1	yes	characteristic
652	C₂	—	2	1	no	—
653	C₂	—	2	1	no	—
654	C₂	—	8	1	no	—
655	C₂	—	16	1	no	—
656	C₂	C₂₉×#2461	1	1	yes	characteristic
657	C₂	C₂₉×#3290	1	1	yes	characteristic
658	C₂	C₂₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂₉×#535	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#3082	C₂	semidirect
4. C₂₉×#2947	C₂	semidirect
5. C₂₉×#2063	C₂	semidirect
6. C₂₉×#2061	C₂	semidirect
7. C₂₉×#2052	C₂	semidirect
9. C₂₉×#1958	C₂	semidirect
10. C₂₉×#1937	C₂	semidirect
11. C₂₉×#1931	C₂	semidirect
12. C₂₉×#1930	C₂	semidirect
13. C₂₉×#1888	C₂	semidirect
14. C₂₉×#1860	C₂	semidirect
15. C₂₉×#1772	C₂	semidirect
236. #26848	C₂₉	direct (N × H)
297. #3082	C₂×C₂₉	semidirect
298. #2947	C₂×C₂₉	semidirect
299. #2063	C₂×C₂₉	semidirect
300. #2061	C₂×C₂₉	semidirect
301. #2052	C₂×C₂₉	semidirect
303. #1958	C₂×C₂₉	semidirect
304. #1937	C₂×C₂₉	semidirect
305. #1931	C₂×C₂₉	semidirect
306. #1930	C₂×C₂₉	semidirect
307. #1888	C₂×C₂₉	semidirect
308. #1860	C₂×C₂₉	semidirect
309. #1772	C₂×C₂₉	semidirect
482. C₂₉	#26848	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×#3136	2
C₂₉×#3096	2
C₂₉×#3082	2
C₂₉×#2947	2
C₂₉×#2063	2
C₂₉×#2061	2
C₂₉×#2052	2
C₂₉×#2004	2
C₂₉×#1958	2
C₂₉×#1937	2
C₂₉×#1931	2
C₂₉×#1930	2
C₂₉×#1888	2
C₂₉×#1860	2
C₂₉×#1772	2
#26848	29

Subgroups — C29×#26848 #20321748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#26848 #20321748