Subgroups — C₂₉×#21467 #20316367

Order 7424.

1342 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3002	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₉×#444	C₂	1	2	yes	maximal, complemented
4	C₂₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1876	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1871	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1866	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1789	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1765	C₂	1	2	yes	maximal, complemented
11	C₂₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₂₉×#135	C₂²	1	2	yes	—
14	C₂×C₂₉×#131	—	2	8	no	—
15	C₂×C₂₉×#131	—	2	1	no	—
16	C₂×C₂₉×#131	—	2	1	no	—
17	C₂×C₂₉×#131	C₂²	1	2	yes	—
18	C₂×C₂₉×#131	C₂²	1	2	yes	—
19	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic, complemented
20	C₂²×M₁₆×C₂₉	—	2	1	no	—
21	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₂₉	—	2	1	no	—
23	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₂₉×#525	C₂²	1	1	yes	characteristic
25	C₂₉×#452	C₄	1	2	yes	complemented
26	C₂₉×#451	C₄	1	1	yes	characteristic, complemented
27	C₂₉×#450	C₄	1	1	yes	characteristic, complemented
28	C₂₉×#449	C₄	1	2	yes	complemented
29	C₂₉×#448	C₄	1	1	yes	characteristic, complemented
30	C₂₉×#447	C₄	1	1	yes	characteristic, complemented
31	C₂₉×#444	—	2	8	no	—
32	C₂₉×#435	—	2	1	no	—
33	C₂₉×#435	—	2	1	no	—
34	C₈×D₄×C₂₉	—	2	1	no	—
35	C₈×D₄×C₂₉	—	2	1	no	—
36	C₂×C₂₉×#108	C₂²	1	2	yes	complemented
37	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₉×#104	C₂²	1	2	yes	—
39	C₂×C₂₉×#104	C₂²	1	2	yes	—
40	C₂×C₂₉×#104	C₂²	1	2	yes	complemented
41	C₂₉×#416	C₂²	1	2	yes	—
42	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#407	C₂²	1	1	yes	characteristic
44	C₂×C₂₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₉×#97	C₂²	1	2	yes	complemented
47	C₄×C₂²⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
48	C₂₉×#341	C₂²	1	2	yes	complemented
49	C₂₉×#339	C₂²	1	2	yes	complemented
50	C₂₉×#336	C₂²	1	2	yes	complemented
51	C₂×#41×C₂₉	—	2	4	no	—
52	C₂×#41×C₂₉	—	2	4	no	—
53	C₂×#41×C₂₉	—	2	1	no	—
54	C₂×#41×C₂₉	—	2	1	no	—
55	C₂×#41×C₂₉	C₂×C₄	1	2	yes	—
56	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
57	C₂×#41×C₂₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
59	C₂²×D₄×C₂₉	—	2	1	no	—
60	C₂²×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₂₉	—	2	1	no	—
62	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
63	C₂₉×#135	—	2	4	no	—
64	C₂₉×#135	—	2	4	no	—
65	C₂×Q₁₆×C₂₉	C₂×C₄	1	2	yes	—
66	C₂×SD₁₆×C₂₉	C₂×C₄	1	2	yes	—
67	C₂×SD₁₆×C₂₉	C₂×C₄	1	2	yes	—
68	C₂×D₈×C₂₉	C₂×C₄	1	2	yes	—
69	C₂₉×#131	—	2	8	no	—
70	C₂₉×#131	—	2	8	no	—
71	C₂₉×#131	—	2	4	no	—
72	C₂₉×#131	—	2	4	no	—
73	C₂₉×#131	—	2	4	no	—
74	C₂₉×#131	—	2	4	no	—
75	C₂₉×#131	D₄	1	8	yes	complemented
76	C₂×M₁₆×C₂₉	—	2	8	no	—
77	C₂×M₁₆×C₂₉	—	2	1	no	—
78	C₂×M₁₆×C₂₉	—	2	4	no	—
79	C₂×M₁₆×C₂₉	—	2	2	no	—
80	C₂×M₁₆×C₂₉	—	2	2	no	—
81	C₂×M₁₆×C₂₉	—	2	1	no	—
82	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
83	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
85	C₂²×C₈×C₂₉	—	2	8	no	—
86	C₂²×C₈×C₂₉	—	2	1	no	—
87	C₂²×C₈×C₂₉	—	2	2	no	—
88	C₂²×C₈×C₂₉	—	2	2	no	—
89	C₂²×C₈×C₂₉	—	2	4	no	—
90	C₂²×C₈×C₂₉	—	2	1	no	—
91	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
92	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
95	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
96	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
98	C₂₉×#123	—	2	1	no	—
99	C₂₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
100	C₂₉×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
101	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
102	C₂₉×#121	C₂×C₄	1	1	yes	characteristic
103	C₂₉×#120	—	2	1	no	—
104	C₄×D₄×C₂₉	—	2	1	no	—
105	C₄×D₄×C₂₉	—	2	1	no	—
106	C₂₉×#117	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
108	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
109	C₂₉×#108	—	2	4	no	—
110	C₂₉×C₄⋊C₈	—	2	1	no	—
111	C₂₉×C₄⋊C₈	—	2	1	no	—
112	C₂₉×#104	—	2	4	no	—
113	C₂₉×#104	—	2	4	no	—
114	C₂₉×#104	—	2	4	no	—
115	C₂₉×#103	C₂×C₄	1	2	yes	—
116	C₂₉×#103	C₂×C₄	1	2	yes	—
117	C₂₉×#102	C₂×C₄	1	2	yes	—
118	C₂₉×#102	C₂×C₄	1	2	yes	—
119	C₂₉×C₂²⋊C₈	—	2	1	no	—
120	C₂₉×C₂²⋊C₈	—	2	1	no	—
121	C₂₉×C₂²⋊C₈	—	2	1	no	—
122	C₂₉×C₂²⋊C₈	—	2	1	no	—
123	C₂₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₂₉×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₂₉×C₂²⋊C₈	C₂×C₄	1	2	yes	—
126	C₂₉×#97	—	2	1	no	—
127	C₂₉×#97	—	2	4	no	—
128	C₄×C₈×C₂₉	—	2	1	no	—
129	C₂₉×#95	—	2	1	no	—
130	C₂⁴×C₂₉	—	2	1	no	—
131	C₂⁴×C₂₉	#41	1	1	yes	characteristic
132	#41×C₂₉	—	2	4	no	—
133	#41×C₂₉	—	2	8	no	—
134	#41×C₂₉	—	2	4	no	—
135	#41×C₂₉	—	2	4	no	—
136	#41×C₂₉	—	2	4	no	—
137	#41×C₂₉	—	2	2	no	—
138	#41×C₂₉	—	2	2	no	—
139	#41×C₂₉	—	2	2	no	—
140	#41×C₂₉	—	2	2	no	—
141	#41×C₂₉	C₂×D₄	1	4	yes	—
142	#41×C₂₉	#41	1	4	yes	—
143	C₂×Q₈×C₂₉	—	2	4	no	—
144	C₂×Q₈×C₂₉	—	2	1	no	—
145	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₂₉	C₂²×C₄	1	2	yes	—
147	C₂×D₄×C₂₉	—	2	8	no	—
148	C₂×D₄×C₂₉	—	2	2	no	—
149	C₂×D₄×C₂₉	—	2	2	no	—
150	C₂×D₄×C₂₉	—	2	4	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	—	2	1	no	—
155	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×D₄×C₂₉	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₂₉	—	2	4	no	—
158	C₂²×C₄×C₂₉	—	2	4	no	—
159	C₂²×C₄×C₂₉	—	2	1	no	—
160	C₂²×C₄×C₂₉	—	2	2	no	—
161	C₂²×C₄×C₂₉	—	2	2	no	—
162	C₂²×C₄×C₂₉	—	2	2	no	—
163	C₂²×C₄×C₂₉	—	2	2	no	—
164	C₂²×C₄×C₂₉	—	2	1	no	—
165	C₂²×C₄×C₂₉	—	2	2	no	—
166	C₂²×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₂₉	C₂²×C₄	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	#41	1	1	yes	characteristic
171	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
172	Q₁₆×C₂₉	—	2	4	no	—
173	SD₁₆×C₂₉	—	2	4	no	—
174	SD₁₆×C₂₉	—	2	4	no	—
175	D₈×C₂₉	—	2	4	no	—
176	M₁₆×C₂₉	—	2	4	no	—
177	M₁₆×C₂₉	—	2	8	no	—
178	M₁₆×C₂₉	—	2	2	no	—
179	M₁₆×C₂₉	—	2	8	no	—
180	M₁₆×C₂₉	—	2	2	no	—
181	M₁₆×C₂₉	—	2	2	no	—
182	M₁₆×C₂₉	—	4	2	no	—
183	M₁₆×C₂₉	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₂₉	—	2	4	no	—
185	C₂×C₈×C₂₉	—	2	8	no	—
186	C₂×C₈×C₂₉	—	2	2	no	—
187	C₂×C₈×C₂₉	—	2	2	no	—
188	C₂×C₈×C₂₉	—	2	2	no	—
189	C₂×C₈×C₂₉	—	2	2	no	—
190	C₂×C₈×C₂₉	—	2	2	no	—
191	C₂×C₈×C₂₉	—	2	8	no	—
192	C₂×C₈×C₂₉	—	2	2	no	—
193	C₂×C₈×C₂₉	—	2	2	no	—
194	C₂×C₈×C₂₉	—	2	2	no	—
195	C₂×C₈×C₂₉	—	2	1	no	—
196	C₂×C₈×C₂₉	—	2	1	no	—
197	C₂×C₈×C₂₉	—	4	2	no	—
198	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
199	C₂×C₈×C₂₉	C₂²×C₄	1	2	yes	—
200	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₂₉	C₂×D₄	1	4	yes	—
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	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
209	C₂²⋊C₄×C₂₉	—	2	1	no	—
210	C₂²⋊C₄×C₂₉	—	2	1	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	—	4	2	no	—
215	C₄²×C₂₉	—	2	1	no	—
216	C₄²×C₂₉	—	2	2	no	—
217	C₄²×C₂₉	—	2	2	no	—
218	#21467	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂³×C₂₉	—	2	4	no	—
220	C₂³×C₂₉	—	2	2	no	—
221	C₂³×C₂₉	—	2	2	no	—
222	C₂³×C₂₉	—	2	2	no	—
223	C₂³×C₂₉	—	2	1	no	—
224	C₂³×C₂₉	—	4	1	no	—
225	C₂³×C₂₉	—	4	2	no	—
226	C₂³×C₂₉	—	4	2	no	—
227	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
228	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
229	C₂³×C₂₉	C₂×#41	1	1	yes	characteristic
230	Q₈×C₂₉	—	2	4	no	—
231	Q₈×C₂₉	—	2	2	no	—
232	Q₈×C₂₉	—	2	2	no	—
233	Q₈×C₂₉	C₄×D₄	1	4	yes	—
234	D₄×C₂₉	—	2	8	no	—
235	D₄×C₂₉	—	2	4	no	—
236	D₄×C₂₉	—	2	4	no	—
237	D₄×C₂₉	—	2	4	no	—
238	D₄×C₂₉	—	2	2	no	—
239	D₄×C₂₉	—	2	2	no	—
240	D₄×C₂₉	—	4	2	no	—
241	D₄×C₂₉	—	4	2	no	—
242	D₄×C₂₉	—	4	2	no	—
243	D₄×C₂₉	C₄×D₄	1	4	yes	—
244	C₂×C₄×C₂₉	—	2	4	no	—
245	C₂×C₄×C₂₉	—	2	8	no	—
246	C₂×C₄×C₂₉	—	2	2	no	—
247	C₂×C₄×C₂₉	—	2	2	no	—
248	C₂×C₄×C₂₉	—	2	2	no	—
249	C₂×C₄×C₂₉	—	2	2	no	—
250	C₂×C₄×C₂₉	—	2	1	no	—
251	C₂×C₄×C₂₉	—	2	4	no	—
252	C₂×C₄×C₂₉	—	2	1	no	—
253	C₂×C₄×C₂₉	—	2	1	no	—
254	C₂×C₄×C₂₉	—	2	4	no	—
255	C₂×C₄×C₂₉	—	2	1	no	—
256	C₂×C₄×C₂₉	—	2	1	no	—
257	C₂×C₄×C₂₉	—	2	1	no	—
258	C₂×C₄×C₂₉	—	2	1	no	—
259	C₂×C₄×C₂₉	—	4	1	no	—
260	C₂×C₄×C₂₉	—	4	1	no	—
261	C₂×C₄×C₂₉	—	4	2	no	—
262	C₂×C₄×C₂₉	—	4	2	no	—
263	C₂×C₄×C₂₉	—	4	2	no	—
264	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
267	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
270	C₈×C₂₉	—	2	2	no	—
271	C₈×C₂₉	—	2	2	no	—
272	C₈×C₂₉	—	2	1	no	—
273	C₈×C₂₉	—	2	4	no	—
274	C₈×C₂₉	—	2	1	no	—
275	C₈×C₂₉	—	4	1	no	—
276	C₈×C₂₉	—	4	1	no	—
277	C₈×C₂₉	#120	1	2	yes	—
278	C₈×C₂₉	#120	1	2	yes	—
279	C₂²×#131	C₂×C₂₉	1	1	yes	characteristic, complemented
280	#3002	C₂×C₂₉	1	1	yes	characteristic
281	C₂×#444	C₂×C₂₉	1	2	yes	complemented
282	#2929	C₂×C₂₉	1	1	yes	characteristic, complemented
283	#1876	C₂×C₂₉	1	2	yes	complemented
284	#1871	C₂×C₂₉	1	1	yes	characteristic, complemented
285	#1866	C₂×C₂₉	1	2	yes	complemented
286	#1855	C₂×C₂₉	1	1	yes	characteristic, complemented
287	#1789	C₂×C₂₉	1	1	yes	characteristic, complemented
288	#1765	C₂×C₂₉	1	2	yes	complemented
289	#1752	C₂×C₂₉	1	1	yes	characteristic, complemented
290	C₂²×C₂₉	—	2	1	no	—
291	C₂²×C₂₉	—	2	1	no	—
292	C₂²×C₂₉	—	2	1	no	—
293	C₂²×C₂₉	—	2	1	no	—
294	C₂²×C₂₉	—	2	1	no	—
295	C₂²×C₂₉	—	2	1	no	—
296	C₂²×C₂₉	—	2	1	no	—
297	C₂²×C₂₉	—	2	4	no	—
298	C₂²×C₂₉	—	4	4	no	—
299	C₂²×C₂₉	—	4	8	no	—
300	C₂²×C₂₉	—	4	2	no	—
301	C₂²×C₂₉	—	4	2	no	—
302	C₂²×C₂₉	—	4	1	no	—
303	C₂²×C₂₉	—	4	1	no	—
304	C₂²×C₂₉	—	4	1	no	—
305	C₂²×C₂₉	#444	1	2	yes	complemented
306	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
307	C₂²×C₂₉	#525	1	2	yes	—
308	C₄×C₂₉	—	2	1	no	—
309	C₄×C₂₉	—	2	4	no	—
310	C₄×C₂₉	—	2	1	no	—
311	C₄×C₂₉	—	4	1	no	—
312	C₄×C₂₉	—	4	1	no	—
313	C₄×C₂₉	—	4	1	no	—
314	C₄×C₂₉	—	8	2	no	—
315	C₄×C₂₉	C₂×C₄×D₄	1	2	yes	—
316	C₄×C₂₉	C₂×#120	1	1	yes	characteristic
317	C₄×C₂₉	#525	1	1	yes	characteristic
318	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
319	C₂×#135	C₂²×C₂₉	1	2	yes	—
320	C₂×#131	—	2	8	no	—
321	C₂×#131	—	2	1	no	—
322	C₂×#131	—	2	1	no	—
323	C₂×#131	C₂²×C₂₉	1	2	yes	—
324	C₂×#131	C₂²×C₂₉	1	2	yes	—
325	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic, complemented
326	C₂²×M₁₆	—	2	1	no	—
327	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
328	C₂³×C₈	—	2	1	no	—
329	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
330	#525	C₂²×C₂₉	1	1	yes	characteristic
331	#452	C₄×C₂₉	1	2	yes	complemented
332	#451	C₄×C₂₉	1	1	yes	characteristic, complemented
333	#450	C₄×C₂₉	1	1	yes	characteristic, complemented
334	#449	C₄×C₂₉	1	2	yes	complemented
335	#448	C₄×C₂₉	1	1	yes	characteristic, complemented
336	#447	C₄×C₂₉	1	1	yes	characteristic, complemented
337	#444	—	2	8	no	—
338	#435	—	2	1	no	—
339	#435	—	2	1	no	—
340	C₈×D₄	—	2	1	no	—
341	C₈×D₄	—	2	1	no	—
342	C₂×#108	C₂²×C₂₉	1	2	yes	complemented
343	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
344	C₂×#104	C₂²×C₂₉	1	2	yes	—
345	C₂×#104	C₂²×C₂₉	1	2	yes	—
346	C₂×#104	C₂²×C₂₉	1	2	yes	complemented
347	#416	C₂²×C₂₉	1	2	yes	—
348	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
349	#407	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
351	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
352	C₂×#97	C₂²×C₂₉	1	2	yes	complemented
353	C₄×C₂²⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
354	#341	C₂²×C₂₉	1	2	yes	complemented
355	#339	C₂²×C₂₉	1	2	yes	complemented
356	#336	C₂²×C₂₉	1	2	yes	complemented
357	C₂×C₂₉	—	2	2	no	—
358	C₂×C₂₉	—	2	2	no	—
359	C₂×C₂₉	—	4	1	no	—
360	C₂×C₂₉	—	4	4	no	—
361	C₂×C₂₉	—	8	1	no	—
362	C₂×C₂₉	C₄×#120	1	1	yes	characteristic
363	C₂×C₂₉	C₂×#444	1	1	yes	characteristic
364	C₂×C₂₉	#2955	1	1	yes	characteristic
365	C₂×#41	—	2	4	no	—
366	C₂×#41	—	2	4	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	C₂×C₄×C₂₉	1	2	yes	—
370	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
371	C₂×#41	C₂³×C₂₉	1	2	yes	—
372	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
375	C₂³×C₄	—	2	1	no	—
376	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
377	#135	—	2	4	no	—
378	#135	—	2	4	no	—
379	C₂×Q₁₆	C₂×C₄×C₂₉	1	2	yes	—
380	C₂×SD₁₆	C₂×C₄×C₂₉	1	2	yes	—
381	C₂×SD₁₆	C₂×C₄×C₂₉	1	2	yes	—
382	C₂×D₈	C₂×C₄×C₂₉	1	2	yes	—
383	#131	—	2	8	no	—
384	#131	—	2	8	no	—
385	#131	—	2	4	no	—
386	#131	—	2	4	no	—
387	#131	—	2	4	no	—
388	#131	—	2	4	no	—
389	#131	D₄×C₂₉	1	8	yes	complemented
390	C₂×M₁₆	—	2	8	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	4	no	—
393	C₂×M₁₆	—	2	2	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
398	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
399	C₂²×C₈	—	2	8	no	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	2	2	no	—
402	C₂²×C₈	—	2	2	no	—
403	C₂²×C₈	—	2	4	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
406	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
407	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
408	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
410	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
412	#123	—	2	1	no	—
413	C₂²⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
414	C₂²⋊Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
415	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
416	#121	C₂×C₄×C₂₉	1	1	yes	characteristic
417	#120	—	2	1	no	—
418	C₄×D₄	—	2	1	no	—
419	C₄×D₄	—	2	1	no	—
420	#117	C₂³×C₂₉	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
423	#108	—	2	4	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	—	2	1	no	—
426	#104	—	2	4	no	—
427	#104	—	2	4	no	—
428	#104	—	2	4	no	—
429	#103	C₂×C₄×C₂₉	1	2	yes	—
430	#103	C₂×C₄×C₂₉	1	2	yes	—
431	#102	C₂×C₄×C₂₉	1	2	yes	—
432	#102	C₂×C₄×C₂₉	1	2	yes	—
433	C₂²⋊C₈	—	2	1	no	—
434	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
438	C₂²⋊C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
439	C₂²⋊C₈	C₂×C₄×C₂₉	1	2	yes	—
440	#97	—	2	4	no	—
441	#97	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	#95	—	2	1	no	—
444	C₂₉	#21467	1	1	yes	characteristic, direct product factor, Sylow
445	C₂⁴	—	2	1	no	—
446	C₂⁴	#41×C₂₉	1	1	yes	characteristic
447	#41	—	2	4	no	—
448	#41	—	2	8	no	—
449	#41	—	2	4	no	—
450	#41	—	2	4	no	—
451	#41	—	2	4	no	—
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	C₂×D₄×C₂₉	1	4	yes	—
457	#41	#41×C₂₉	1	4	yes	—
458	C₂×Q₈	—	2	4	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
461	C₂×Q₈	C₂²×C₄×C₂₉	1	2	yes	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
471	C₂×D₄	C₂²×C₄×C₂₉	1	2	yes	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
485	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
487	Q₁₆	—	2	4	no	—
488	SD₁₆	—	2	4	no	—
489	SD₁₆	—	2	4	no	—
490	D₈	—	2	4	no	—
491	M₁₆	—	2	4	no	—
492	M₁₆	—	2	8	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	8	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	—	4	2	no	—
498	M₁₆	C₂×D₄×C₂₉	1	4	yes	—
499	C₂×C₈	—	2	4	no	—
500	C₂×C₈	—	2	8	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	8	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	4	2	no	—
513	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
514	C₂×C₈	C₂²×C₄×C₂₉	1	2	yes	—
515	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
516	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
517	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
518	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
519	C₂×C₈	C₂×D₄×C₂₉	1	4	yes	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	—	2	1	no	—
528	C₂²⋊C₄	—	2	1	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	2	no	—
541	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
542	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
543	C₂³	C₂×#41×C₂₉	1	1	yes	characteristic
544	Q₈	—	2	4	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	2	2	no	—
547	Q₈	C₄×D₄×C₂₉	1	4	yes	—
548	D₄	—	2	8	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	4	no	—
551	D₄	—	2	4	no	—
552	D₄	—	2	2	no	—
553	D₄	—	2	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	D₄	C₄×D₄×C₂₉	1	4	yes	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	4	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	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
579	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
580	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
582	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
583	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
584	C₈	—	2	2	no	—
585	C₈	—	2	2	no	—
586	C₈	—	2	1	no	—
587	C₈	—	2	4	no	—
588	C₈	—	2	1	no	—
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	C₂₉×#120	1	2	yes	—
592	C₈	C₂₉×#120	1	2	yes	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	1	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	4	8	no	—
603	C₂²	—	4	2	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	C₂₉×#444	1	2	yes	complemented
609	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
610	C₂²	C₂₉×#525	1	2	yes	—
611	C₄	—	2	1	no	—
612	C₄	—	2	4	no	—
613	C₄	—	2	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	1	no	—
617	C₄	—	8	2	no	—
618	C₄	C₂×C₄×D₄×C₂₉	1	2	yes	—
619	C₄	C₂×C₂₉×#120	1	1	yes	characteristic
620	C₄	C₂₉×#525	1	1	yes	characteristic
621	C₂	—	2	2	no	—
622	C₂	—	2	2	no	—
623	C₂	—	4	1	no	—
624	C₂	—	4	4	no	—
625	C₂	—	8	1	no	—
626	C₂	C₄×C₂₉×#120	1	1	yes	characteristic
627	C₂	C₂×C₂₉×#444	1	1	yes	characteristic
628	C₂	C₂₉×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂×C₄×D₄
prime radical	C₂₉×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂³×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₉×#131	C₂	semidirect
3. C₂×C₂₉×#444	C₂	semidirect
4. C₂₉×#2929	C₂	semidirect
5. C₂₉×#1876	C₂	semidirect
6. C₂₉×#1871	C₂	semidirect
7. C₂₉×#1866	C₂	semidirect
8. C₂₉×#1855	C₂	semidirect
9. C₂₉×#1789	C₂	semidirect
10. C₂₉×#1765	C₂	semidirect
11. C₂₉×#1752	C₂	semidirect
19. C₂×C₂₉×#131	C₂²	semidirect
25. C₂₉×#452	C₄	semidirect
26. C₂₉×#451	C₄	semidirect
27. C₂₉×#450	C₄	semidirect
28. C₂₉×#449	C₄	semidirect
29. C₂₉×#448	C₄	semidirect
30. C₂₉×#447	C₄	semidirect
36. C₂×C₂₉×#108	C₂²	semidirect
37. C₂₉×#424	C₂²	semidirect
40. C₂×C₂₉×#104	C₂²	semidirect
42. C₂₉×#408	C₂²	semidirect
45. C₂₉×#405	C₂²	semidirect
46. C₂×C₂₉×#97	C₂²	semidirect
48. C₂₉×#341	C₂²	semidirect
49. C₂₉×#339	C₂²	semidirect
50. C₂₉×#336	C₂²	semidirect
75. C₂₉×#131	D₄	semidirect
218. #21467	C₂₉	direct (N × H)
279. C₂²×#131	C₂×C₂₉	semidirect
281. C₂×#444	C₂×C₂₉	semidirect
282. #2929	C₂×C₂₉	semidirect
283. #1876	C₂×C₂₉	semidirect
284. #1871	C₂×C₂₉	semidirect
285. #1866	C₂×C₂₉	semidirect
286. #1855	C₂×C₂₉	semidirect
287. #1789	C₂×C₂₉	semidirect
288. #1765	C₂×C₂₉	semidirect
289. #1752	C₂×C₂₉	semidirect
305. C₂²×C₂₉	#444	semidirect
325. C₂×#131	C₂²×C₂₉	semidirect
331. #452	C₄×C₂₉	semidirect
332. #451	C₄×C₂₉	semidirect
333. #450	C₄×C₂₉	semidirect
334. #449	C₄×C₂₉	semidirect
335. #448	C₄×C₂₉	semidirect
336. #447	C₄×C₂₉	semidirect
342. C₂×#108	C₂²×C₂₉	semidirect
343. #424	C₂²×C₂₉	semidirect
346. C₂×#104	C₂²×C₂₉	semidirect
348. #408	C₂²×C₂₉	semidirect
351. #405	C₂²×C₂₉	semidirect
352. C₂×#97	C₂²×C₂₉	semidirect
354. #341	C₂²×C₂₉	semidirect
355. #339	C₂²×C₂₉	semidirect
356. #336	C₂²×C₂₉	semidirect
389. #131	D₄×C₂₉	semidirect
444. C₂₉	#21467	direct (N × H)
608. C₂²	C₂₉×#444	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂₉×#131	2
C₂₉×#3002	2
C₂×C₂₉×#444	2
C₂₉×#2929	2
C₂₉×#1876	2
C₂₉×#1871	2
C₂₉×#1866	2
C₂₉×#1855	2
C₂₉×#1789	2
C₂₉×#1765	2
C₂₉×#1752	2
#21467	29

Subgroups — C29×#21467 #20316367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#21467 #20316367