Subgroups — C₂₉×#23809 #20318709

Order 7424.

974 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2326	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#2097	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2096	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2092	C₂	1	1	yes	maximal, characteristic
11	C₂₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2015	C₂	1	1	yes	maximal, characteristic
13	C₂₉×#2015	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#2013	C₂	1	1	yes	maximal, characteristic
15	C₂₉×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×C₄⋊Q₈	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×Q₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#441	—	2	4	no	—
27	C₂₉×#440	—	2	4	no	—
28	C₄×Q₁₆×C₂₉	—	2	4	no	—
29	C₄×SD₁₆×C₂₉	—	2	4	no	—
30	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#106	C₂²	1	1	yes	characteristic
33	C₂×C₂₉×#106	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×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
41	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₉×#97	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
44	C₂₉×#391	C₂²	1	1	yes	characteristic
45	C₂₉×#391	C₂²	1	1	yes	characteristic
46	C₂₉×#391	C₂²	1	1	yes	characteristic
47	C₂₉×#390	C₂²	1	1	yes	characteristic
48	C₂₉×#388	—	2	2	no	—
49	C₂₉×#387	—	2	2	no	—
50	C₂₉×#387	—	2	2	no	—
51	C₂₉×#385	—	2	2	no	—
52	C₂₉×#384	C₂²	1	1	yes	characteristic
53	C₂₉×#382	C₂²	1	1	yes	characteristic
54	C₂₉×#376	C₂²	1	1	yes	characteristic
55	C₂₉×#336	C₂²	1	1	yes	characteristic
56	C₂₉×#336	C₂²	1	1	yes	characteristic
57	C₂₉×#336	C₂²	1	1	yes	characteristic
58	C₂₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
61	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₂₉	—	2	1	no	—
64	C₂×Q₁₆×C₂₉	—	2	2	no	—
65	C₂×Q₁₆×C₂₉	—	2	2	no	—
66	C₂×Q₁₆×C₂₉	—	2	2	no	—
67	C₂×Q₁₆×C₂₉	—	2	2	no	—
68	C₂×Q₁₆×C₂₉	—	2	2	no	—
69	C₂×Q₁₆×C₂₉	—	2	2	no	—
70	C₂×SD₁₆×C₂₉	—	2	2	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	—	2	2	no	—
76	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
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	C₂₉×C₄⋊Q₈	—	2	2	no	—
81	C₂₉×C₄⋊Q₈	—	2	2	no	—
82	C₂₉×#124	—	2	2	no	—
83	C₂₉×#124	—	2	2	no	—
84	C₄×Q₈×C₂₉	—	2	2	no	—
85	C₄×Q₈×C₂₉	—	2	2	no	—
86	C₄×Q₈×C₂₉	—	2	2	no	—
87	C₄×Q₈×C₂₉	—	2	2	no	—
88	C₄×Q₈×C₂₉	—	2	2	no	—
89	C₄×Q₈×C₂₉	—	2	2	no	—
90	C₄×D₄×C₂₉	—	2	2	no	—
91	C₄×D₄×C₂₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
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×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
104	C₂×C₄²×C₂₉	—	2	1	no	—
105	C₂×C₄²×C₂₉	—	2	1	no	—
106	C₂×C₄²×C₂₉	—	2	1	no	—
107	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
110	C₂₉×#107	—	2	2	no	—
111	C₂₉×#107	—	2	2	no	—
112	C₂₉×#106	—	2	2	no	—
113	C₂₉×#106	—	2	2	no	—
114	C₂₉×#103	—	2	2	no	—
115	C₂₉×#103	—	2	2	no	—
116	C₂₉×#103	—	2	2	no	—
117	C₂₉×#103	—	2	2	no	—
118	C₂₉×#103	—	2	2	no	—
119	C₂₉×#103	—	2	2	no	—
120	C₂₉×#102	—	2	2	no	—
121	C₂₉×#102	—	2	2	no	—
122	C₂₉×#97	D₄	1	4	yes	—
123	C₄×C₈×C₂₉	D₄	1	4	yes	—
124	C₂₉×#95	—	2	2	no	—
125	C₂₉×#95	—	2	2	no	—
126	C₂₉×#95	—	2	2	no	—
127	C₂₉×#95	—	2	2	no	—
128	C₂₉×#95	D₄	1	2	yes	—
129	C₂₉×#95	D₄	1	2	yes	—
130	C₂⁴×C₂₉	—	2	1	no	—
131	C₂×Q₈×C₂₉	—	2	1	no	—
132	C₂×Q₈×C₂₉	—	2	1	no	—
133	C₂×Q₈×C₂₉	—	2	1	no	—
134	C₂×Q₈×C₂₉	—	2	1	no	—
135	C₂×Q₈×C₂₉	—	2	1	no	—
136	C₂×Q₈×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	—	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	#41	1	2	yes	—
147	C₂×Q₈×C₂₉	#41	1	2	yes	—
148	C₂×Q₈×C₂₉	#41	1	2	yes	—
149	C₂×D₄×C₂₉	—	2	1	no	—
150	C₂×D₄×C₂₉	—	2	1	no	—
151	C₂×D₄×C₂₉	—	2	1	no	—
152	C₂×D₄×C₂₉	—	2	1	no	—
153	C₂×D₄×C₂₉	—	2	1	no	—
154	C₂×D₄×C₂₉	#41	1	2	yes	—
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	2	1	no	—
158	C₂²×C₄×C₂₉	—	2	1	no	—
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	1	no	—
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	4	2	no	—
163	C₂²×C₄×C₂₉	—	8	2	no	—
164	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
169	Q₁₆×C₂₉	—	2	8	no	—
170	Q₁₆×C₂₉	—	2	8	no	—
171	SD₁₆×C₂₉	—	2	8	no	—
172	SD₁₆×C₂₉	—	2	8	no	—
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	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
184	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
185	C₄⋊C₄×C₂₉	—	2	8	no	—
186	C₄⋊C₄×C₂₉	—	2	1	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	—	4	2	no	—
195	C₄⋊C₄×C₂₉	—	4	2	no	—
196	C₄⋊C₄×C₂₉	—	4	2	no	—
197	C₄⋊C₄×C₂₉	—	8	2	no	—
198	C₂²⋊C₄×C₂₉	—	2	8	no	—
199	C₂²⋊C₄×C₂₉	—	4	2	no	—
200	C₂²⋊C₄×C₂₉	—	8	2	no	—
201	C₄²×C₂₉	—	2	1	no	—
202	C₄²×C₂₉	—	2	1	no	—
203	C₄²×C₂₉	—	2	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	—	4	2	no	—
206	C₄²×C₂₉	—	4	2	no	—
207	C₄²×C₂₉	—	4	2	no	—
208	C₄²×C₂₉	C₂×D₄	1	2	yes	—
209	C₄²×C₂₉	C₂×D₄	1	2	yes	—
210	#23809	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₂₉	—	2	2	no	—
212	C₂³×C₂₉	—	4	1	no	—
213	C₂³×C₂₉	—	4	1	no	—
214	C₂³×C₂₉	—	4	2	no	—
215	C₂³×C₂₉	—	4	2	no	—
216	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₂₉	—	2	2	no	—
218	Q₈×C₂₉	—	2	2	no	—
219	Q₈×C₂₉	—	2	2	no	—
220	Q₈×C₂₉	—	2	2	no	—
221	Q₈×C₂₉	—	2	2	no	—
222	Q₈×C₂₉	—	2	2	no	—
223	Q₈×C₂₉	—	4	1	no	—
224	Q₈×C₂₉	—	4	1	no	—
225	Q₈×C₂₉	—	4	1	no	—
226	Q₈×C₂₉	—	4	1	no	—
227	Q₈×C₂₉	—	4	1	no	—
228	Q₈×C₂₉	—	4	1	no	—
229	D₄×C₂₉	—	2	2	no	—
230	D₄×C₂₉	—	2	2	no	—
231	D₄×C₂₉	—	4	1	no	—
232	D₄×C₂₉	—	4	1	no	—
233	C₂×C₄×C₂₉	—	2	2	no	—
234	C₂×C₄×C₂₉	—	2	2	no	—
235	C₂×C₄×C₂₉	—	2	2	no	—
236	C₂×C₄×C₂₉	—	2	2	no	—
237	C₂×C₄×C₂₉	—	2	2	no	—
238	C₂×C₄×C₂₉	—	2	2	no	—
239	C₂×C₄×C₂₉	—	2	2	no	—
240	C₂×C₄×C₂₉	—	2	2	no	—
241	C₂×C₄×C₂₉	—	2	2	no	—
242	C₂×C₄×C₂₉	—	2	2	no	—
243	C₂×C₄×C₂₉	—	2	2	no	—
244	C₂×C₄×C₂₉	—	4	1	no	—
245	C₂×C₄×C₂₉	—	4	1	no	—
246	C₂×C₄×C₂₉	—	4	1	no	—
247	C₂×C₄×C₂₉	—	4	1	no	—
248	C₂×C₄×C₂₉	—	4	1	no	—
249	C₂×C₄×C₂₉	—	4	1	no	—
250	C₂×C₄×C₂₉	—	4	1	no	—
251	C₂×C₄×C₂₉	—	4	1	no	—
252	C₂×C₄×C₂₉	—	4	1	no	—
253	C₂×C₄×C₂₉	—	4	1	no	—
254	C₂×C₄×C₂₉	—	4	2	no	—
255	C₂×C₄×C₂₉	—	4	2	no	—
256	C₂×C₄×C₂₉	—	4	2	no	—
257	C₂×C₄×C₂₉	—	4	2	no	—
258	C₂×C₄×C₂₉	—	8	4	no	—
259	C₂×C₄×C₂₉	#127	1	2	yes	—
260	C₂×C₄×C₂₉	#127	1	2	yes	—
261	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
267	C₈×C₂₉	—	2	2	no	—
268	C₈×C₂₉	—	2	2	no	—
269	C₈×C₂₉	—	2	2	no	—
270	C₈×C₂₉	—	2	2	no	—
271	C₂×#441	C₂×C₂₉	1	1	yes	characteristic, complemented
272	C₂×#440	C₂×C₂₉	1	1	yes	characteristic
273	C₂×C₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
274	C₂×C₄×SD₁₆	C₂×C₂₉	1	1	yes	characteristic
275	#2327	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#2326	C₂×C₂₉	1	1	yes	characteristic
277	#2097	C₂×C₂₉	1	1	yes	characteristic, complemented
278	#2096	C₂×C₂₉	1	1	yes	characteristic, complemented
279	#2095	C₂×C₂₉	1	1	yes	characteristic, complemented
280	#2092	C₂×C₂₉	1	1	yes	characteristic
281	#2016	C₂×C₂₉	1	1	yes	characteristic, complemented
282	#2015	C₂×C₂₉	1	1	yes	characteristic
283	#2015	C₂×C₂₉	1	1	yes	characteristic
284	#2013	C₂×C₂₉	1	1	yes	characteristic
285	#1746	C₂×C₂₉	1	1	yes	characteristic, complemented
286	C₂²×C₂₉	—	4	4	no	—
287	C₂²×C₂₉	—	4	2	no	—
288	C₂²×C₂₉	—	8	2	no	—
289	C₂²×C₂₉	—	8	1	no	—
290	C₂²×C₂₉	—	8	1	no	—
291	C₂²×C₂₉	#525	1	1	yes	characteristic
292	C₂²×C₂₉	#525	1	1	yes	characteristic
293	C₂²×C₂₉	C₂×#127	1	1	yes	characteristic
294	C₂²×C₂₉	#577	1	2	yes	—
295	C₂²×C₂₉	#578	1	2	yes	—
296	C₄×C₂₉	—	2	2	no	—
297	C₄×C₂₉	—	2	2	no	—
298	C₄×C₂₉	—	4	2	no	—
299	C₄×C₂₉	—	4	2	no	—
300	C₄×C₂₉	—	4	2	no	—
301	C₄×C₂₉	—	4	2	no	—
302	C₄×C₂₉	—	4	2	no	—
303	C₄×C₂₉	—	8	1	no	—
304	C₄×C₂₉	—	8	1	no	—
305	C₄×C₂₉	—	8	1	no	—
306	C₄×C₂₉	—	8	1	no	—
307	C₄×C₂₉	#525	1	1	yes	characteristic
308	C₄×C₂₉	#525	1	1	yes	characteristic
309	C₄×C₂₉	#525	1	1	yes	characteristic
310	C₄×C₂₉	#525	1	1	yes	characteristic
311	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
312	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
313	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
314	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
316	C₂×#124	C₂²×C₂₉	1	1	yes	characteristic
317	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
318	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
319	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
321	#441	—	2	4	no	—
322	#440	—	2	4	no	—
323	C₄×Q₁₆	—	2	4	no	—
324	C₄×SD₁₆	—	2	4	no	—
325	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
326	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
327	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×#106	C₂²×C₂₉	1	1	yes	characteristic
329	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
330	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
331	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
332	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
333	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
334	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
335	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
336	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
337	C₂×#97	C₂²×C₂₉	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
339	#391	C₂²×C₂₉	1	1	yes	characteristic
340	#391	C₂²×C₂₉	1	1	yes	characteristic
341	#391	C₂²×C₂₉	1	1	yes	characteristic
342	#390	C₂²×C₂₉	1	1	yes	characteristic
343	#388	—	2	2	no	—
344	#387	—	2	2	no	—
345	#387	—	2	2	no	—
346	#385	—	2	2	no	—
347	#384	C₂²×C₂₉	1	1	yes	characteristic
348	#382	C₂²×C₂₉	1	1	yes	characteristic
349	#376	C₂²×C₂₉	1	1	yes	characteristic
350	#336	C₂²×C₂₉	1	1	yes	characteristic
351	#336	C₂²×C₂₉	1	1	yes	characteristic
352	#336	C₂²×C₂₉	1	1	yes	characteristic
353	#336	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×C₂₉	—	8	2	no	—
355	C₂×C₂₉	#2397	1	1	yes	characteristic
356	C₂×C₂₉	#3120	1	2	yes	—
357	C₂×C₂₉	#3121	1	2	yes	—
358	C₂×C₂₉	#3154	1	1	yes	characteristic
359	C₂×C₂₉	#3156	1	1	yes	characteristic
360	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
361	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
362	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂×Q₁₆	—	2	2	no	—
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×Q₁₆	—	2	2	no	—
369	C₂×Q₁₆	—	2	2	no	—
370	C₂×Q₁₆	—	2	2	no	—
371	C₂×SD₁₆	—	2	2	no	—
372	C₂×SD₁₆	—	2	2	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	2	no	—
377	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
381	C₄⋊Q₈	—	2	2	no	—
382	C₄⋊Q₈	—	2	2	no	—
383	#124	—	2	2	no	—
384	#124	—	2	2	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	—	2	2	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	2	no	—
398	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
411	#107	—	2	2	no	—
412	#107	—	2	2	no	—
413	#106	—	2	2	no	—
414	#106	—	2	2	no	—
415	#103	—	2	2	no	—
416	#103	—	2	2	no	—
417	#103	—	2	2	no	—
418	#103	—	2	2	no	—
419	#103	—	2	2	no	—
420	#103	—	2	2	no	—
421	#102	—	2	2	no	—
422	#102	—	2	2	no	—
423	#97	D₄×C₂₉	1	4	yes	—
424	C₄×C₈	D₄×C₂₉	1	4	yes	—
425	#95	—	2	2	no	—
426	#95	—	2	2	no	—
427	#95	—	2	2	no	—
428	#95	—	2	2	no	—
429	#95	D₄×C₂₉	1	2	yes	—
430	#95	D₄×C₂₉	1	2	yes	—
431	C₂₉	#23809	1	1	yes	characteristic, direct product factor, Sylow
432	C₂⁴	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	#41×C₂₉	1	2	yes	—
449	C₂×Q₈	#41×C₂₉	1	2	yes	—
450	C₂×Q₈	#41×C₂₉	1	2	yes	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	#41×C₂₉	1	2	yes	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	8	2	no	—
466	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
471	Q₁₆	—	2	8	no	—
472	Q₁₆	—	2	8	no	—
473	SD₁₆	—	2	8	no	—
474	SD₁₆	—	2	8	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
484	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
485	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
486	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
487	C₄⋊C₄	—	2	8	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	8	2	no	—
500	C₂²⋊C₄	—	2	8	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₂²⋊C₄	—	8	2	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₄²	C₂×D₄×C₂₉	1	2	yes	—
511	C₄²	C₂×D₄×C₂₉	1	2	yes	—
512	C₂³	—	2	2	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	2	no	—
516	C₂³	—	4	2	no	—
517	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	—	4	1	no	—
527	Q₈	—	4	1	no	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	1	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	8	4	no	—
560	C₂×C₄	C₂₉×#127	1	2	yes	—
561	C₂×C₄	C₂₉×#127	1	2	yes	—
562	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
564	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
565	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
566	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
568	C₈	—	2	2	no	—
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₂₉×#525	1	1	yes	characteristic
578	C₂²	C₂₉×#525	1	1	yes	characteristic
579	C₂²	C₂×C₂₉×#127	1	1	yes	characteristic
580	C₂²	C₂₉×#577	1	2	yes	—
581	C₂²	C₂₉×#578	1	2	yes	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	—	8	1	no	—
592	C₄	—	8	1	no	—
593	C₄	C₂₉×#525	1	1	yes	characteristic
594	C₄	C₂₉×#525	1	1	yes	characteristic
595	C₄	C₂₉×#525	1	1	yes	characteristic
596	C₄	C₂₉×#525	1	1	yes	characteristic
597	C₂	—	8	2	no	—
598	C₂	C₂₉×#2397	1	1	yes	characteristic
599	C₂	C₂₉×#3120	1	2	yes	—
600	C₂	C₂₉×#3121	1	2	yes	—
601	C₂	C₂₉×#3154	1	1	yes	characteristic
602	C₂	C₂₉×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#441	C₂	semidirect
3. C₂×C₄×Q₁₆×C₂₉	C₂	semidirect
5. C₂₉×#2327	C₂	semidirect
7. C₂₉×#2097	C₂	semidirect
8. C₂₉×#2096	C₂	semidirect
9. C₂₉×#2095	C₂	semidirect
11. C₂₉×#2016	C₂	semidirect
15. C₂₉×#1746	C₂	semidirect
210. #23809	C₂₉	direct (N × H)
271. C₂×#441	C₂×C₂₉	semidirect
273. C₂×C₄×Q₁₆	C₂×C₂₉	semidirect
275. #2327	C₂×C₂₉	semidirect
277. #2097	C₂×C₂₉	semidirect
278. #2096	C₂×C₂₉	semidirect
279. #2095	C₂×C₂₉	semidirect
281. #2016	C₂×C₂₉	semidirect
285. #1746	C₂×C₂₉	semidirect
431. C₂₉	#23809	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×#441	2
C₂×C₂₉×#440	2
C₂×C₄×Q₁₆×C₂₉	2
C₂×C₄×SD₁₆×C₂₉	2
C₂₉×#2327	2
C₂₉×#2326	2
C₂₉×#2097	2
C₂₉×#2096	2
C₂₉×#2095	2
C₂₉×#2092	2
C₂₉×#2016	2
C₂₉×#2015	2
C₂₉×#2013	2
C₂₉×#1746	2
#23809	29

Subgroups — C29×#23809 #20318709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#23809 #20318709