Subgroups — C₂₉×#19814 #20314714

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3384	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3380	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1723	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1696	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1644	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1632	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1580	C₂	1	1	yes	maximal, characteristic
16	C₂₉×#554	C₂²	1	1	yes	characteristic
17	C₂₉×#554	C₂²	1	1	yes	characteristic
18	C₂₉×#554	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#501	—	2	1	no	—
21	C₂₉×#500	C₂²	1	1	yes	characteristic
22	C₂₉×#500	C₂²	1	1	yes	characteristic
23	C₂₉×#499	—	2	1	no	—
24	C₂₉×#498	C₂²	1	1	yes	characteristic
25	C₂₉×#494	C₂²	1	1	yes	characteristic
26	C₂₉×#487	C₂²	1	1	yes	characteristic
27	C₂₉×#487	C₂²	1	1	yes	characteristic
28	C₂₉×#484	—	2	1	no	—
29	C₂₉×#484	—	2	1	no	—
30	C₂₉×#484	—	2	1	no	—
31	C₂₉×#478	—	2	1	no	—
32	C₂₉×#478	—	2	1	no	—
33	C₂₉×#478	—	2	1	no	—
34	C₂₉×#477	C₂²	1	1	yes	characteristic
35	C₂₉×#477	C₂²	1	1	yes	characteristic
36	C₂₉×#477	C₂²	1	1	yes	characteristic
37	C₂₉×#476	—	2	1	no	—
38	C₂₉×#476	C₂²	1	1	yes	characteristic
39	C₂₉×#476	C₂²	1	1	yes	characteristic
40	C₂₉×#476	C₂²	1	1	yes	characteristic
41	C₂₉×#474	C₂²	1	1	yes	characteristic
42	C₂₉×#467	—	2	1	no	—
43	C₂₉×#467	—	2	1	no	—
44	C₂₉×#462	C₂²	1	1	yes	characteristic
45	C₂₉×#451	—	2	1	no	—
46	C₂₉×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₂₉×#442	—	2	1	no	—
49	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
50	C₄×D₈×C₂₉	—	2	1	no	—
51	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#107	—	2	1	no	—
55	C₂×C₂₉×#103	—	2	1	no	—
56	C₂₉×#335	C₂²	1	1	yes	characteristic
57	C₂₉×#334	C₂²	1	1	yes	characteristic
58	C₂₉×#333	C₂²	1	1	yes	characteristic
59	C₂₉×#333	C₂²	1	1	yes	characteristic
60	C₂₉×#333	C₂²	1	1	yes	characteristic
61	C₂₉×#332	C₂²	1	1	yes	characteristic
62	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×#322	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₂₉	—	2	1	no	—
68	C₂×Q₁₆×C₂₉	—	2	1	no	—
69	C₂×Q₁₆×C₂₉	—	4	1	no	—
70	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
71	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₂₉	—	2	1	no	—
73	C₂²×C₈×C₂₉	—	2	1	no	—
74	C₂₉×C₄⋊Q₈	—	2	1	no	—
75	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₂₉×#125	—	2	1	no	—
80	C₂₉×#125	—	2	1	no	—
81	C₂₉×#125	—	2	1	no	—
82	C₂₉×C₂²⋊Q₈	—	2	1	no	—
83	C₂₉×C₂²⋊Q₈	—	2	1	no	—
84	C₂₉×C₂²⋊Q₈	—	2	1	no	—
85	C₂₉×C₂²⋊Q₈	—	2	1	no	—
86	C₂₉×C₂²⋊Q₈	—	4	1	no	—
87	C₂₉×C₂²⋊Q₈	—	4	1	no	—
88	C₂₉×C₂²⋊Q₈	—	4	1	no	—
89	C₂₉×C₂²⋊Q₈	—	4	1	no	—
90	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₂₉	—	2	1	no	—
93	C₄×D₄×C₂₉	—	2	1	no	—
94	C₄×D₄×C₂₉	—	2	1	no	—
95	C₄×D₄×C₂₉	—	2	1	no	—
96	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
101	C₂₉×#107	—	2	1	no	—
102	C₂₉×#107	—	2	1	no	—
103	C₂₉×#107	—	2	1	no	—
104	C₂₉×#107	—	2	1	no	—
105	C₂₉×#107	—	2	1	no	—
106	C₂₉×#107	—	2	1	no	—
107	C₂₉×#107	—	2	1	no	—
108	C₂₉×#107	—	2	1	no	—
109	C₂₉×#107	D₄	1	1	yes	characteristic
110	C₂₉×#107	D₄	1	1	yes	characteristic
111	C₂₉×#106	—	2	1	no	—
112	C₂₉×#106	—	2	1	no	—
113	C₂₉×#106	—	2	1	no	—
114	C₂₉×#106	—	2	1	no	—
115	C₂₉×#106	—	2	1	no	—
116	C₂₉×C₄⋊C₈	—	2	1	no	—
117	C₂₉×C₄⋊C₈	—	2	1	no	—
118	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₂₉×#103	—	2	1	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	—	4	1	no	—
129	C₂₉×#103	D₄	1	1	yes	characteristic
130	C₂₉×#103	D₄	1	1	yes	characteristic
131	C₂₉×#102	—	2	1	no	—
132	C₂₉×#102	—	2	1	no	—
133	C₂₉×#102	—	2	1	no	—
134	C₂₉×#102	—	2	1	no	—
135	C₂₉×#102	D₄	1	1	yes	characteristic
136	C₂₉×#102	D₄	1	1	yes	characteristic
137	C₂₉×C₂²⋊C₈	—	2	1	no	—
138	C₂₉×C₂²⋊C₈	—	2	1	no	—
139	C₂₉×#97	—	2	1	no	—
140	C₄×C₈×C₂₉	—	2	1	no	—
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	C₂×Q₈×C₂₉	—	2	1	no	—
145	C₂×Q₈×C₂₉	—	2	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	4	1	no	—
149	C₂×Q₈×C₂₉	—	4	2	no	—
150	C₂×Q₈×C₂₉	—	8	1	no	—
151	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₉	—	2	1	no	—
156	C₂²×C₄×C₂₉	—	2	1	no	—
157	C₂²×C₄×C₂₉	—	4	1	no	—
158	C₂²×C₄×C₂₉	—	4	1	no	—
159	C₂²×C₄×C₂₉	—	4	1	no	—
160	C₂²×C₄×C₂₉	—	4	1	no	—
161	Q₁₆×C₂₉	—	4	1	no	—
162	Q₁₆×C₂₉	—	8	1	no	—
163	Q₁₆×C₂₉	—	8	2	no	—
164	D₈×C₂₉	Q₁₆	1	4	yes	complemented
165	C₂×C₈×C₂₉	—	2	1	no	—
166	C₂×C₈×C₂₉	—	2	1	no	—
167	C₂×C₈×C₂₉	—	2	1	no	—
168	C₂×C₈×C₂₉	—	2	1	no	—
169	C₂×C₈×C₂₉	—	2	1	no	—
170	C₂×C₈×C₂₉	—	4	2	no	—
171	C₂×C₈×C₂₉	—	8	1	no	—
172	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
173	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
176	C₄⋊C₄×C₂₉	—	2	1	no	—
177	C₄⋊C₄×C₂₉	—	2	1	no	—
178	C₄⋊C₄×C₂₉	—	2	1	no	—
179	C₄⋊C₄×C₂₉	—	2	1	no	—
180	C₄⋊C₄×C₂₉	—	2	1	no	—
181	C₄⋊C₄×C₂₉	—	2	1	no	—
182	C₄⋊C₄×C₂₉	—	2	1	no	—
183	C₄⋊C₄×C₂₉	—	2	1	no	—
184	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	no	—
186	C₄⋊C₄×C₂₉	—	4	1	no	—
187	C₄⋊C₄×C₂₉	—	4	1	no	—
188	C₄⋊C₄×C₂₉	—	4	1	no	—
189	C₄⋊C₄×C₂₉	—	4	1	no	—
190	C₄⋊C₄×C₂₉	—	4	1	no	—
191	C₄⋊C₄×C₂₉	—	4	1	no	—
192	C₄⋊C₄×C₂₉	—	4	1	no	—
193	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
196	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₂₉	—	2	1	no	—
198	C₂²⋊C₄×C₂₉	—	2	1	no	—
199	C₂²⋊C₄×C₂₉	—	4	1	no	—
200	C₂²⋊C₄×C₂₉	—	4	1	no	—
201	C₂²⋊C₄×C₂₉	—	4	1	no	—
202	C₂²⋊C₄×C₂₉	—	4	1	no	—
203	C₄²×C₂₉	—	2	1	no	—
204	C₄²×C₂₉	—	2	1	no	—
205	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
206	#19814	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₂₉	—	2	1	no	—
208	C₂³×C₂₉	—	2	1	no	—
209	Q₈×C₂₉	—	2	1	no	—
210	Q₈×C₂₉	—	2	1	no	—
211	Q₈×C₂₉	—	2	1	no	—
212	Q₈×C₂₉	—	2	1	no	—
213	Q₈×C₂₉	—	4	1	no	—
214	Q₈×C₂₉	—	4	1	no	—
215	Q₈×C₂₉	—	8	1	no	—
216	Q₈×C₂₉	—	8	1	no	—
217	Q₈×C₂₉	—	8	1	no	—
218	Q₈×C₂₉	—	8	2	no	—
219	D₄×C₂₉	—	2	1	no	—
220	D₄×C₂₉	—	2	1	no	—
221	D₄×C₂₉	C₂×Q₁₆	1	2	yes	—
222	D₄×C₂₉	C₂×Q₁₆	1	2	yes	—
223	C₂×C₄×C₂₉	—	2	1	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	—	4	1	no	—
230	C₂×C₄×C₂₉	—	4	1	no	—
231	C₂×C₄×C₂₉	—	4	1	no	—
232	C₂×C₄×C₂₉	—	4	1	no	—
233	C₂×C₄×C₂₉	—	4	1	no	—
234	C₂×C₄×C₂₉	—	4	1	no	—
235	C₂×C₄×C₂₉	—	4	1	no	—
236	C₂×C₄×C₂₉	—	4	1	no	—
237	C₂×C₄×C₂₉	—	8	2	no	—
238	C₂×C₄×C₂₉	—	16	1	no	—
239	C₂×C₄×C₂₉	—	16	1	no	—
240	C₂×C₄×C₂₉	—	16	1	no	—
241	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
244	C₈×C₂₉	—	2	1	no	—
245	C₈×C₂₉	—	2	1	no	—
246	C₈×C₂₉	—	2	1	no	—
247	C₈×C₂₉	—	4	1	no	—
248	C₈×C₂₉	—	4	1	no	—
249	C₈×C₂₉	—	4	1	no	—
250	C₈×C₂₉	—	4	1	no	—
251	C₈×C₂₉	—	4	1	no	—
252	C₈×C₂₉	C₂×Q₁₆	1	2	yes	—
253	#3384	C₂×C₂₉	1	1	yes	characteristic
254	#3380	C₂×C₂₉	1	1	yes	characteristic
255	#3338	C₂×C₂₉	1	1	yes	characteristic, complemented
256	#3299	C₂×C₂₉	1	1	yes	characteristic, complemented
257	#1723	C₂×C₂₉	1	1	yes	characteristic, complemented
258	#1696	C₂×C₂₉	1	1	yes	characteristic, complemented
259	#1683	C₂×C₂₉	1	1	yes	characteristic, complemented
260	#1675	C₂×C₂₉	1	1	yes	characteristic, complemented
261	#1672	C₂×C₂₉	1	1	yes	characteristic, complemented
262	#1644	C₂×C₂₉	1	1	yes	characteristic, complemented
263	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
264	#1632	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#1632	C₂×C₂₉	1	1	yes	characteristic, complemented
266	#1584	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#1580	C₂×C₂₉	1	1	yes	characteristic
268	C₂²×C₂₉	—	2	2	no	—
269	C₂²×C₂₉	—	2	2	no	—
270	C₂²×C₂₉	—	4	1	no	—
271	C₂²×C₂₉	—	4	1	no	—
272	C₂²×C₂₉	—	4	1	no	—
273	C₂²×C₂₉	—	4	1	no	—
274	C₂²×C₂₉	D₄²	1	1	yes	characteristic
275	C₄×C₂₉	—	2	1	no	—
276	C₄×C₂₉	—	4	1	no	—
277	C₄×C₂₉	—	4	1	no	—
278	C₄×C₂₉	—	4	1	no	—
279	C₄×C₂₉	—	4	1	no	—
280	C₄×C₂₉	—	4	1	no	—
281	C₄×C₂₉	—	4	1	no	—
282	C₄×C₂₉	—	8	1	no	—
283	C₄×C₂₉	—	8	1	no	—
284	C₄×C₂₉	—	8	1	no	—
285	C₄×C₂₉	—	8	1	no	—
286	C₄×C₂₉	C₂²×Q₁₆	1	1	yes	characteristic
287	C₄×C₂₉	#575	1	1	yes	characteristic
288	C₄×C₂₉	#577	1	1	yes	characteristic
289	C₄×C₂₉	#578	1	1	yes	characteristic
290	#554	C₂²×C₂₉	1	1	yes	characteristic
291	#554	C₂²×C₂₉	1	1	yes	characteristic
292	#554	C₂²×C₂₉	1	1	yes	characteristic
293	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
294	#501	—	2	1	no	—
295	#500	C₂²×C₂₉	1	1	yes	characteristic
296	#500	C₂²×C₂₉	1	1	yes	characteristic
297	#499	—	2	1	no	—
298	#498	C₂²×C₂₉	1	1	yes	characteristic
299	#494	C₂²×C₂₉	1	1	yes	characteristic
300	#487	C₂²×C₂₉	1	1	yes	characteristic
301	#487	C₂²×C₂₉	1	1	yes	characteristic
302	#484	—	2	1	no	—
303	#484	—	2	1	no	—
304	#484	—	2	1	no	—
305	#478	—	2	1	no	—
306	#478	—	2	1	no	—
307	#478	—	2	1	no	—
308	#477	C₂²×C₂₉	1	1	yes	characteristic
309	#477	C₂²×C₂₉	1	1	yes	characteristic
310	#477	C₂²×C₂₉	1	1	yes	characteristic
311	#476	—	2	1	no	—
312	#476	C₂²×C₂₉	1	1	yes	characteristic
313	#476	C₂²×C₂₉	1	1	yes	characteristic
314	#476	C₂²×C₂₉	1	1	yes	characteristic
315	#474	C₂²×C₂₉	1	1	yes	characteristic
316	#467	—	2	1	no	—
317	#467	—	2	1	no	—
318	#462	C₂²×C₂₉	1	1	yes	characteristic
319	#451	—	2	1	no	—
320	#446	C₂²×C₂₉	1	1	yes	characteristic
321	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
322	#442	—	2	1	no	—
323	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
324	C₄×D₈	—	2	1	no	—
325	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
326	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
327	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
328	C₂×#107	—	2	1	no	—
329	C₂×#103	—	2	1	no	—
330	#335	C₂²×C₂₉	1	1	yes	characteristic
331	#334	C₂²×C₂₉	1	1	yes	characteristic
332	#333	C₂²×C₂₉	1	1	yes	characteristic
333	#333	C₂²×C₂₉	1	1	yes	characteristic
334	#333	C₂²×C₂₉	1	1	yes	characteristic
335	#332	C₂²×C₂₉	1	1	yes	characteristic
336	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
338	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
339	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
340	#322	C₂²×C₂₉	1	1	yes	characteristic
341	C₂×C₂₉	—	4	2	no	—
342	C₂×C₂₉	—	4	2	no	—
343	C₂×C₂₉	#3267	1	1	yes	characteristic
344	C₂×C₂₉	D₄×Q₁₆	1	1	yes	characteristic
345	C₂×C₂₉	#3288	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂×Q₁₆	—	2	1	no	—
348	C₂×Q₁₆	—	4	1	no	—
349	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
350	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
358	#125	—	2	1	no	—
359	#125	—	2	1	no	—
360	#125	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	4	1	no	—
366	C₂²⋊Q₈	—	4	1	no	—
367	C₂²⋊Q₈	—	4	1	no	—
368	C₂²⋊Q₈	—	4	1	no	—
369	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
370	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
376	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	#107	—	2	1	no	—
381	#107	—	2	1	no	—
382	#107	—	2	1	no	—
383	#107	—	2	1	no	—
384	#107	—	2	1	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#107	—	2	1	no	—
388	#107	D₄×C₂₉	1	1	yes	characteristic
389	#107	D₄×C₂₉	1	1	yes	characteristic
390	#106	—	2	1	no	—
391	#106	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
401	#103	—	2	1	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#103	—	2	1	no	—
407	#103	—	4	1	no	—
408	#103	D₄×C₂₉	1	1	yes	characteristic
409	#103	D₄×C₂₉	1	1	yes	characteristic
410	#102	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	D₄×C₂₉	1	1	yes	characteristic
415	#102	D₄×C₂₉	1	1	yes	characteristic
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	#97	—	2	1	no	—
419	C₄×C₈	—	2	1	no	—
420	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
422	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
423	C₂₉	#19814	1	1	yes	characteristic, direct product factor, Sylow
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	4	1	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	8	1	no	—
431	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
432	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
433	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
434	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	Q₁₆	—	4	1	no	—
442	Q₁₆	—	8	1	no	—
443	Q₁₆	—	8	2	no	—
444	D₈	Q₁₆×C₂₉	1	4	yes	complemented
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	4	2	no	—
451	C₂×C₈	—	8	1	no	—
452	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
453	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
454	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	—	4	1	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
474	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	8	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	—	8	1	no	—
497	Q₈	—	8	2	no	—
498	D₄	—	2	1	no	—
499	D₄	—	2	1	no	—
500	D₄	C₂×Q₁₆×C₂₉	1	2	yes	—
501	D₄	C₂×Q₁₆×C₂₉	1	2	yes	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	—	16	1	no	—
518	C₂×C₄	—	16	1	no	—
519	C₂×C₄	—	16	1	no	—
520	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
522	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	C₂×Q₁₆×C₂₉	1	2	yes	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	D₄²×C₂₉	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₂²×Q₁₆×C₂₉	1	1	yes	characteristic
551	C₄	C₂₉×#575	1	1	yes	characteristic
552	C₄	C₂₉×#577	1	1	yes	characteristic
553	C₄	C₂₉×#578	1	1	yes	characteristic
554	C₂	—	4	2	no	—
555	C₂	—	4	2	no	—
556	C₂	C₂₉×#3267	1	1	yes	characteristic
557	C₂	D₄×Q₁₆×C₂₉	1	1	yes	characteristic
558	C₂	C₂₉×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂×D₈×C₂₉	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#3338	C₂	semidirect
4. C₂₉×#3299	C₂	semidirect
5. C₂₉×#1723	C₂	semidirect
6. C₂₉×#1696	C₂	semidirect
7. C₂₉×#1683	C₂	semidirect
8. C₂₉×#1675	C₂	semidirect
9. C₂₉×#1672	C₂	semidirect
10. C₂₉×#1644	C₂	semidirect
11. C₂₉×#1637	C₂	semidirect
12. C₂₉×#1632	C₂	semidirect
13. C₂₉×#1632	C₂	semidirect
14. C₂₉×#1584	C₂	semidirect
164. D₈×C₂₉	Q₁₆	semidirect
206. #19814	C₂₉	direct (N × H)
255. #3338	C₂×C₂₉	semidirect
256. #3299	C₂×C₂₉	semidirect
257. #1723	C₂×C₂₉	semidirect
258. #1696	C₂×C₂₉	semidirect
259. #1683	C₂×C₂₉	semidirect
260. #1675	C₂×C₂₉	semidirect
261. #1672	C₂×C₂₉	semidirect
262. #1644	C₂×C₂₉	semidirect
263. #1637	C₂×C₂₉	semidirect
264. #1632	C₂×C₂₉	semidirect
265. #1632	C₂×C₂₉	semidirect
266. #1584	C₂×C₂₉	semidirect
423. C₂₉	#19814	direct (N × H)
444. D₈	Q₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3384	2
C₂₉×#3380	2
C₂₉×#3338	2
C₂₉×#3299	2
C₂₉×#1723	2
C₂₉×#1696	2
C₂₉×#1683	2
C₂₉×#1675	2
C₂₉×#1672	2
C₂₉×#1644	2
C₂₉×#1637	2
C₂₉×#1632	2
C₂₉×#1584	2
C₂₉×#1580	2
#19814	29

Subgroups — C29×#19814 #20314714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19814 #20314714