Subgroups — C₂₉×#18053 #20312953

Order 7424.

624 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2991	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₉×#137	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1587	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1583	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1579	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1488	C₂	1	1	yes	maximal, characteristic
14	C₂₉×#1487	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×#137	C₄	1	1	yes	characteristic
17	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#446	—	2	1	no	—
20	C₂₉×#446	—	2	1	no	—
21	C₂₉×#446	C₂²	1	1	yes	characteristic
22	C₂₉×#446	C₂²	1	1	yes	characteristic
23	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
24	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
26	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
27	C₂₉×#441	C₄	1	1	yes	characteristic
28	C₂₉×#441	C₄	1	1	yes	characteristic
29	C₂₉×#440	C₄	1	1	yes	characteristic
30	C₂₉×#440	C₄	1	1	yes	characteristic
31	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
33	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
35	C₂₉×#436	—	2	1	no	—
36	C₂₉×#436	—	2	1	no	—
37	C₂₉×#436	C₂²	1	1	yes	characteristic
38	C₂₉×#436	C₂²	1	1	yes	characteristic
39	C₂₉×#432	—	2	1	no	—
40	C₂₉×#432	C₂²	1	1	yes	characteristic
41	C₂₉×#431	—	2	1	no	—
42	C₂₉×#431	—	2	1	no	—
43	C₂₉×#431	C₂²	1	1	yes	characteristic
44	C₂₉×#431	C₂²	1	1	yes	characteristic
45	C₂₉×#428	C₄	1	1	yes	characteristic
46	C₂₉×#423	—	2	1	no	—
47	C₂₉×#423	C₂²	1	1	yes	characteristic
48	C₂₉×#419	C₄	1	1	yes	characteristic
49	C₂₉×#417	C₄	1	1	yes	characteristic
50	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
51	C₂₉×#335	C₂²	1	1	yes	characteristic
52	C₂₉×#335	C₂²	1	1	yes	characteristic
53	C₂₉×#334	C₂²	1	1	yes	characteristic
54	C₂₉×#334	C₂²	1	1	yes	characteristic
55	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×#322	C₂²	1	1	yes	characteristic
64	C₂₉×#322	C₂²	1	1	yes	characteristic
65	C₂₉×#322	C₂²	1	1	yes	characteristic
66	C₈²×C₂₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
69	C₂₉×#137	—	2	4	no	—
70	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
71	C₂×Q₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
73	C₂×SD₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
74	C₂×M₁₆×C₂₉	—	2	1	no	—
75	C₂×M₁₆×C₂₉	—	2	1	no	—
76	C₂×M₁₆×C₂₉	—	2	1	no	—
77	C₂×M₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
78	C₂×M₁₆×C₂₉	C₂×C₄	1	1	yes	characteristic
79	C₄×Q₈×C₂₉	—	2	1	no	—
80	C₄×Q₈×C₂₉	—	2	1	no	—
81	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₂₉	C₂×C₄	1	1	yes	characteristic
84	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
86	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₂₉	—	2	1	no	—
88	C₄×D₄×C₂₉	—	2	1	no	—
89	C₄×D₄×C₂₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
91	C₂₉×#117	—	2	1	no	—
92	C₂₉×#117	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₂₉	—	2	1	no	—
96	C₂×C₄²×C₂₉	—	2	1	no	—
97	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
98	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
99	C₂₉×#107	C₂×C₄	1	1	yes	characteristic
100	C₂₉×#106	C₂×C₄	1	1	yes	characteristic
101	C₂₉×#106	C₂×C₄	1	1	yes	characteristic
102	C₂₉×C₄⋊C₈	—	2	1	no	—
103	C₂₉×C₄⋊C₈	—	2	1	no	—
104	C₂₉×C₄⋊C₈	—	2	1	no	—
105	C₂₉×C₄⋊C₈	—	2	1	no	—
106	C₂₉×C₄⋊C₈	—	2	1	no	—
107	C₂₉×C₄⋊C₈	—	2	1	no	—
108	C₂₉×C₄⋊C₈	—	2	1	no	—
109	C₂₉×C₄⋊C₈	—	2	1	no	—
110	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
111	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
112	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
114	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
117	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
118	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
119	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
120	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
121	C₂₉×#103	C₂×C₄	1	1	yes	characteristic
122	C₂₉×#102	C₂×C₄	1	1	yes	characteristic
123	C₂₉×#102	C₂×C₄	1	1	yes	characteristic
124	C₂₉×C₂²⋊C₈	—	2	1	no	—
125	C₂₉×C₂²⋊C₈	—	2	1	no	—
126	C₂₉×C₂²⋊C₈	—	2	1	no	—
127	C₂₉×C₂²⋊C₈	—	2	1	no	—
128	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
129	C₂₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₂₉×#97	—	2	1	no	—
131	C₂₉×#97	—	2	1	no	—
132	C₂₉×#97	—	2	1	no	—
133	C₂₉×#97	C₂×C₄	1	1	yes	characteristic
134	C₂₉×#97	C₂×C₄	1	1	yes	characteristic
135	C₄×C₈×C₂₉	—	2	1	no	—
136	C₄×C₈×C₂₉	—	2	1	no	—
137	C₄×C₈×C₂₉	—	2	1	no	—
138	C₄×C₈×C₂₉	—	2	1	no	—
139	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
145	#41×C₂₉	—	2	2	no	—
146	#41×C₂₉	—	4	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	2	no	—
149	C₂×Q₈×C₂₉	—	4	1	no	—
150	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×Q₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₂₉	—	2	1	no	—
154	C₂×D₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
163	Q₁₆×C₂₉	—	2	2	no	—
164	Q₁₆×C₂₉	M₁₆	1	4	yes	complemented
165	SD₁₆×C₂₉	—	2	2	no	—
166	SD₁₆×C₂₉	—	2	2	no	—
167	M₁₆×C₂₉	—	2	2	no	—
168	M₁₆×C₂₉	—	4	1	no	—
169	M₁₆×C₂₉	—	8	1	no	—
170	M₁₆×C₂₉	—	8	1	no	—
171	M₁₆×C₂₉	—	8	1	no	—
172	C₂×C₈×C₂₉	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₂₉	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₂₉	—	2	1	no	—
198	C₂²⋊C₄×C₂₉	—	2	1	no	—
199	C₂²⋊C₄×C₂₉	—	2	1	no	—
200	C₄²×C₂₉	—	2	1	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	—	2	1	no	—
206	C₄²×C₂₉	—	2	1	no	—
207	C₄²×C₂₉	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₂₉	#41	1	1	yes	characteristic
210	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
211	#18053	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₂₉	—	2	1	no	—
213	C₂³×C₂₉	C₄×D₄	1	1	yes	characteristic
214	Q₈×C₂₉	—	2	1	no	—
215	Q₈×C₂₉	—	2	1	no	—
216	Q₈×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	2	1	no	—
218	Q₈×C₂₉	—	4	2	no	—
219	Q₈×C₂₉	C₂×M₁₆	1	2	yes	—
220	Q₈×C₂₉	C₂×M₁₆	1	2	yes	—
221	D₄×C₂₉	—	2	1	no	—
222	D₄×C₂₉	—	2	1	no	—
223	D₄×C₂₉	—	4	2	no	—
224	C₂×C₄×C₂₉	—	2	1	no	—
225	C₂×C₄×C₂₉	—	2	1	no	—
226	C₂×C₄×C₂₉	—	2	1	no	—
227	C₂×C₄×C₂₉	—	2	1	no	—
228	C₂×C₄×C₂₉	—	2	1	no	—
229	C₂×C₄×C₂₉	—	2	1	no	—
230	C₂×C₄×C₂₉	—	2	1	no	—
231	C₂×C₄×C₂₉	—	2	1	no	—
232	C₂×C₄×C₂₉	—	2	1	no	—
233	C₂×C₄×C₂₉	—	2	1	no	—
234	C₂×C₄×C₂₉	—	2	1	no	—
235	C₂×C₄×C₂₉	—	4	1	no	—
236	C₂×C₄×C₂₉	—	4	2	no	—
237	C₂×C₄×C₂₉	—	4	2	no	—
238	C₂×C₄×C₂₉	—	4	2	no	—
239	C₂×C₄×C₂₉	—	4	2	no	—
240	C₂×C₄×C₂₉	—	4	1	no	—
241	C₂×C₄×C₂₉	—	4	1	no	—
242	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₂₉	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₂₉	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
248	C₈×C₂₉	—	2	1	no	—
249	C₈×C₂₉	—	2	1	no	—
250	C₈×C₂₉	—	2	1	no	—
251	C₈×C₂₉	—	2	1	no	—
252	C₈×C₂₉	—	2	1	no	—
253	C₈×C₂₉	—	2	1	no	—
254	C₈×C₂₉	—	2	1	no	—
255	C₈×C₂₉	—	4	1	no	—
256	C₈×C₂₉	—	4	1	no	—
257	C₈×C₂₉	—	4	1	no	—
258	C₈×C₂₉	—	4	1	no	—
259	C₈×C₂₉	—	4	1	no	—
260	C₈×C₂₉	—	4	1	no	—
261	C₈×C₂₉	C₂×M₁₆	1	2	yes	—
262	#2991	C₂×C₂₉	1	1	yes	characteristic
263	#2984	C₂×C₂₉	1	1	yes	characteristic, complemented
264	C₄×#137	C₂×C₂₉	1	1	yes	characteristic
265	#1592	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1590	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1588	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1587	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1584	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1583	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1579	C₂×C₂₉	1	1	yes	characteristic, complemented
272	C₈×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1569	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1488	C₂×C₂₉	1	1	yes	characteristic
275	#1487	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1453	C₂×C₂₉	1	1	yes	characteristic, complemented
277	C₂²×C₂₉	—	2	1	no	—
278	C₂²×C₂₉	—	2	1	no	—
279	C₂²×C₂₉	—	2	1	no	—
280	C₂²×C₂₉	—	4	1	no	—
281	C₂²×C₂₉	—	4	1	no	—
282	C₂²×C₂₉	—	4	1	no	—
283	C₂²×C₂₉	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₂₉	—	2	1	no	—
285	C₄×C₂₉	—	2	2	no	—
286	C₄×C₂₉	—	2	2	no	—
287	C₄×C₂₉	—	2	1	no	—
288	C₄×C₂₉	—	2	1	no	—
289	C₄×C₂₉	—	2	1	no	—
290	C₄×C₂₉	—	4	1	no	—
291	C₄×C₂₉	—	4	1	no	—
292	C₄×C₂₉	—	4	1	no	—
293	C₄×C₂₉	—	4	1	no	—
294	C₄×C₂₉	—	4	1	no	—
295	C₄×C₂₉	C₂²×M₁₆	1	1	yes	characteristic
296	C₄×C₂₉	#568	1	1	yes	characteristic
297	C₄×C₂₉	#577	1	1	yes	characteristic
298	C₄×C₂₉	#578	1	1	yes	characteristic
299	C₂×#137	C₄×C₂₉	1	1	yes	characteristic
300	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
302	#446	—	2	1	no	—
303	#446	—	2	1	no	—
304	#446	C₂²×C₂₉	1	1	yes	characteristic
305	#446	C₂²×C₂₉	1	1	yes	characteristic
306	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
307	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
308	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
309	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
310	#441	C₄×C₂₉	1	1	yes	characteristic
311	#441	C₄×C₂₉	1	1	yes	characteristic
312	#440	C₄×C₂₉	1	1	yes	characteristic
313	#440	C₄×C₂₉	1	1	yes	characteristic
314	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
315	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
316	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
317	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
318	#436	—	2	1	no	—
319	#436	—	2	1	no	—
320	#436	C₂²×C₂₉	1	1	yes	characteristic
321	#436	C₂²×C₂₉	1	1	yes	characteristic
322	#432	—	2	1	no	—
323	#432	C₂²×C₂₉	1	1	yes	characteristic
324	#431	—	2	1	no	—
325	#431	—	2	1	no	—
326	#431	C₂²×C₂₉	1	1	yes	characteristic
327	#431	C₂²×C₂₉	1	1	yes	characteristic
328	#428	C₄×C₂₉	1	1	yes	characteristic
329	#423	—	2	1	no	—
330	#423	C₂²×C₂₉	1	1	yes	characteristic
331	#419	C₄×C₂₉	1	1	yes	characteristic
332	#417	C₄×C₂₉	1	1	yes	characteristic
333	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
334	#335	C₂²×C₂₉	1	1	yes	characteristic
335	#335	C₂²×C₂₉	1	1	yes	characteristic
336	#334	C₂²×C₂₉	1	1	yes	characteristic
337	#334	C₂²×C₂₉	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
339	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
341	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
343	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
344	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
345	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
346	#322	C₂²×C₂₉	1	1	yes	characteristic
347	#322	C₂²×C₂₉	1	1	yes	characteristic
348	#322	C₂²×C₂₉	1	1	yes	characteristic
349	C₈²	C₂²×C₂₉	1	1	yes	characteristic
350	C₂×C₂₉	—	4	1	no	—
351	C₂×C₂₉	—	8	1	no	—
352	C₂×C₂₉	D₄×M₁₆	1	1	yes	characteristic
353	C₂×C₂₉	#2947	1	1	yes	characteristic
354	C₂×C₂₉	#2955	1	1	yes	characteristic
355	C₂×#41	C₂×C₄×C₂₉	1	1	yes	characteristic
356	C₂²×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
357	#137	—	2	4	no	—
358	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
359	C₂×Q₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
361	C₂×SD₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
366	C₂×M₁₆	C₂×C₄×C₂₉	1	1	yes	characteristic
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
370	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
371	C₄×Q₈	C₂×C₄×C₂₉	1	1	yes	characteristic
372	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
373	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
374	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
375	C₄×D₄	—	2	1	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	C₂×C₄×C₂₉	1	1	yes	characteristic
378	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
379	#117	—	2	1	no	—
380	#117	C₂×C₄×C₂₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
386	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
387	#107	C₂×C₄×C₂₉	1	1	yes	characteristic
388	#106	C₂×C₄×C₂₉	1	1	yes	characteristic
389	#106	C₂×C₄×C₂₉	1	1	yes	characteristic
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
399	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
404	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
405	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
406	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
407	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
408	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
409	#103	C₂×C₄×C₂₉	1	1	yes	characteristic
410	#102	C₂×C₄×C₂₉	1	1	yes	characteristic
411	#102	C₂×C₄×C₂₉	1	1	yes	characteristic
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
417	C₂²⋊C₈	D₄×C₂₉	1	1	yes	characteristic
418	#97	—	2	1	no	—
419	#97	—	2	1	no	—
420	#97	—	2	1	no	—
421	#97	C₂×C₄×C₂₉	1	1	yes	characteristic
422	#97	C₂×C₄×C₂₉	1	1	yes	characteristic
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
428	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
429	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
433	C₂₉	#18053	1	1	yes	characteristic, direct product factor, Sylow
434	#41	—	2	2	no	—
435	#41	—	4	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
440	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
441	C₂×Q₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
451	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
452	Q₁₆	—	2	2	no	—
453	Q₁₆	M₁₆×C₂₉	1	4	yes	complemented
454	SD₁₆	—	2	2	no	—
455	SD₁₆	—	2	2	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	4	1	no	—
458	M₁₆	—	8	1	no	—
459	M₁₆	—	8	1	no	—
460	M₁₆	—	8	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
468	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
469	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
470	C₂×C₈	C₂²×C₄×C₂₉	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×C₄×C₂₉	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	C₂²×C₄×C₂₉	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
498	C₄²	#41×C₂₉	1	1	yes	characteristic
499	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	C₄×D₄×C₂₉	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	4	2	no	—
507	Q₈	C₂×M₁₆×C₂₉	1	2	yes	—
508	Q₈	C₂×M₁₆×C₂₉	1	2	yes	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	4	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
531	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
532	C₂×C₄	C₄×D₄×C₂₉	1	1	yes	characteristic
533	C₂×C₄	C₂³×C₄×C₂₉	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	C₂×M₁₆×C₂₉	1	2	yes	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	C₂×C₄×D₄×C₂₉	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	C₂²×M₁₆×C₂₉	1	1	yes	characteristic
569	C₄	C₂₉×#568	1	1	yes	characteristic
570	C₄	C₂₉×#577	1	1	yes	characteristic
571	C₄	C₂₉×#578	1	1	yes	characteristic
572	C₂	—	4	1	no	—
573	C₂	—	8	1	no	—
574	C₂	D₄×M₁₆×C₂₉	1	1	yes	characteristic
575	C₂	C₂₉×#2947	1	1	yes	characteristic
576	C₂	C₂₉×#2955	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	C₂×#41×C₂₉	C₂×C₄
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×#2984	C₂	semidirect
4. C₂₉×#1592	C₂	semidirect
5. C₂₉×#1590	C₂	semidirect
6. C₂₉×#1588	C₂	semidirect
7. C₂₉×#1587	C₂	semidirect
8. C₂₉×#1584	C₂	semidirect
9. C₂₉×#1583	C₂	semidirect
10. C₂₉×#1579	C₂	semidirect
11. C₈×Q₁₆×C₂₉	C₂	semidirect
12. C₂₉×#1569	C₂	semidirect
14. C₂₉×#1487	C₂	semidirect
15. C₂₉×#1453	C₂	semidirect
164. Q₁₆×C₂₉	M₁₆	semidirect
211. #18053	C₂₉	direct (N × H)
263. #2984	C₂×C₂₉	semidirect
265. #1592	C₂×C₂₉	semidirect
266. #1590	C₂×C₂₉	semidirect
267. #1588	C₂×C₂₉	semidirect
268. #1587	C₂×C₂₉	semidirect
269. #1584	C₂×C₂₉	semidirect
270. #1583	C₂×C₂₉	semidirect
271. #1579	C₂×C₂₉	semidirect
272. C₈×Q₁₆	C₂×C₂₉	semidirect
273. #1569	C₂×C₂₉	semidirect
275. #1487	C₂×C₂₉	semidirect
276. #1453	C₂×C₂₉	semidirect
433. C₂₉	#18053	direct (N × H)
453. Q₁₆	M₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#2991	2
C₂₉×#2984	2
C₄×C₂₉×#137	2
C₂₉×#1592	2
C₂₉×#1590	2
C₂₉×#1588	2
C₂₉×#1587	2
C₂₉×#1584	2
C₂₉×#1583	2
C₂₉×#1579	2
C₈×Q₁₆×C₂₉	2
C₂₉×#1569	2
C₂₉×#1488	2
C₂₉×#1487	2
C₂₉×#1453	2
#18053	29

Subgroups — C29×#18053 #20312953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18053 #20312953