Subgroups — C₂₉×#19992 #20314892

Order 7424.

622 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3358	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3304	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3299	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1708	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1684	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1652	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1651	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1622	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#556	C₂²	1	1	yes	characteristic
17	C₂₉×#554	C₂²	1	1	yes	characteristic
18	C₂₉×#550	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
20	C₂₉×#498	C₂²	1	1	yes	characteristic
21	C₂₉×#492	C₂²	1	1	yes	characteristic
22	C₂₉×#488	—	2	1	no	—
23	C₂₉×#487	C₂²	1	1	yes	characteristic
24	C₂₉×#487	C₂²	1	1	yes	characteristic
25	C₂₉×#486	—	2	1	no	—
26	C₂₉×#486	C₂²	1	1	yes	characteristic
27	C₂₉×#486	C₂²	1	1	yes	characteristic
28	C₂₉×#484	—	2	1	no	—
29	C₂₉×#482	—	2	1	no	—
30	C₂₉×#479	—	2	1	no	—
31	C₂₉×#477	C₂²	1	1	yes	characteristic
32	C₂₉×#476	C₂²	1	1	yes	characteristic
33	C₂₉×#475	C₂²	1	1	yes	characteristic
34	C₂₉×#474	—	2	1	no	—
35	C₂₉×#474	C₂²	1	1	yes	characteristic
36	C₂₉×#467	—	2	1	no	—
37	C₂₉×#465	—	2	1	no	—
38	C₂₉×#463	—	2	1	no	—
39	C₂₉×#462	C₂²	1	1	yes	characteristic
40	C₂₉×#461	C₂²	1	1	yes	characteristic
41	C₂₉×#460	C₂²	1	1	yes	characteristic
42	C₂₉×#459	—	2	1	no	—
43	C₂₉×#459	C₂²	1	1	yes	characteristic
44	C₂₉×#452	—	2	1	no	—
45	C₂₉×#451	—	2	1	no	—
46	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
48	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
49	C₄×SD₁₆×C₂₉	—	2	1	no	—
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	C₂₉×#416	—	2	1	no	—
55	C₂×C₂₉×#103	—	2	1	no	—
56	C₂₉×#335	C₂²	1	1	yes	characteristic
57	C₂₉×#335	C₂²	1	1	yes	characteristic
58	C₂₉×#333	C₂²	1	1	yes	characteristic
59	C₂₉×#332	C₂²	1	1	yes	characteristic
60	C₂₉×#332	C₂²	1	1	yes	characteristic
61	C₂₉×#331	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	C₈²×C₂₉	C₂²	1	1	yes	characteristic
67	C₂×#41×C₂₉	—	2	1	no	—
68	C₂²×Q₈×C₂₉	—	2	1	no	—
69	C₂×Q₁₆×C₂₉	—	2	1	no	—
70	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
71	C₂×SD₁₆×C₂₉	—	2	1	no	—
72	C₂×SD₁₆×C₂₉	—	2	1	no	—
73	C₂×SD₁₆×C₂₉	—	4	1	no	—
74	C₂×D₈×C₂₉	—	2	1	no	—
75	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₂₉	—	2	1	no	—
77	C₂²×C₈×C₂₉	—	2	1	no	—
78	C₂₉×C₄⋊Q₈	—	2	1	no	—
79	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₂₉×#127	—	2	1	no	—
83	C₂₉×#127	C₂³	1	1	yes	characteristic
84	C₂₉×#126	—	4	1	no	—
85	C₂₉×#125	—	2	1	no	—
86	C₂₉×#124	—	2	1	no	—
87	C₂₉×C₂²⋊Q₈	—	2	1	no	—
88	C₂₉×C₂²⋊Q₈	—	2	1	no	—
89	C₂₉×C₂²⋊Q₈	—	2	1	no	—
90	C₂₉×C₂²⋊Q₈	—	4	1	no	—
91	C₂₉×C₂²⋊Q₈	—	4	1	no	—
92	C₂₉×#121	—	2	1	no	—
93	C₂₉×#121	—	4	1	no	—
94	C₄×Q₈×C₂₉	—	2	1	no	—
95	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₂₉	—	2	1	no	—
98	C₄×D₄×C₂₉	—	2	1	no	—
99	C₄×D₄×C₂₉	—	2	1	no	—
100	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
102	C₂₉×#117	—	2	1	no	—
103	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
104	C₂₉×#107	—	2	1	no	—
105	C₂₉×#107	—	2	1	no	—
106	C₂₉×#107	D₄	1	1	yes	characteristic
107	C₂₉×#107	D₄	1	1	yes	characteristic
108	C₂₉×#106	—	2	1	no	—
109	C₂₉×#106	—	2	1	no	—
110	C₂₉×#106	—	4	1	no	—
111	C₂₉×C₄⋊C₈	—	2	1	no	—
112	C₂₉×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₂₉×#103	—	2	1	no	—
118	C₂₉×#103	—	2	1	no	—
119	C₂₉×#103	—	2	1	no	—
120	C₂₉×#103	—	2	1	no	—
121	C₂₉×#103	—	2	1	no	—
122	C₂₉×#103	—	2	1	no	—
123	C₂₉×#103	—	2	1	no	—
124	C₂₉×#103	—	2	1	no	—
125	C₂₉×#103	D₄	1	1	yes	characteristic
126	C₂₉×#103	D₄	1	1	yes	characteristic
127	C₂₉×#102	—	2	1	no	—
128	C₂₉×#102	—	2	1	no	—
129	C₂₉×#102	—	2	1	no	—
130	C₂₉×#102	—	2	1	no	—
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	C₄×C₈×C₂₉	—	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	#41×C₂₉	—	4	2	no	—
145	#41×C₂₉	—	8	1	no	—
146	C₂×Q₈×C₂₉	—	2	1	no	—
147	C₂×Q₈×C₂₉	—	2	1	no	—
148	C₂×Q₈×C₂₉	—	2	1	no	—
149	C₂×Q₈×C₂₉	—	4	1	no	—
150	C₂×Q₈×C₂₉	—	4	2	no	—
151	C₂×Q₈×C₂₉	—	8	1	no	—
152	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₂₉	—	2	1	no	—
155	C₂×D₄×C₂₉	—	2	1	no	—
156	C₂×D₄×C₂₉	—	2	1	no	—
157	C₂×D₄×C₂₉	—	4	1	no	—
158	C₂×D₄×C₂₉	—	4	1	no	—
159	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₂₉	—	2	1	no	—
162	C₂²×C₄×C₂₉	—	2	1	no	—
163	C₂²×C₄×C₂₉	—	4	1	no	—
164	C₂²×C₄×C₂₉	—	4	1	no	—
165	C₂²×C₄×C₂₉	—	4	1	no	—
166	Q₁₆×C₂₉	—	2	2	no	—
167	Q₁₆×C₂₉	—	8	1	no	—
168	SD₁₆×C₂₉	—	4	2	no	—
169	SD₁₆×C₂₉	—	8	2	no	—
170	SD₁₆×C₂₉	—	8	1	no	—
171	D₈×C₂₉	—	2	2	no	—
172	D₈×C₂₉	—	4	2	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	—	8	1	no	—
179	C₂×C₈×C₂₉	—	8	1	no	—
180	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₂₉	C₂×D₄	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	C₄⋊C₄×C₂₉	—	2	1	no	—
185	C₄⋊C₄×C₂₉	—	2	1	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	—	4	1	no	—
193	C₄⋊C₄×C₂₉	—	4	1	no	—
194	C₄⋊C₄×C₂₉	—	4	1	no	—
195	C₄⋊C₄×C₂₉	—	4	1	no	—
196	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
200	C₂²⋊C₄×C₂₉	—	2	1	no	—
201	C₂²⋊C₄×C₂₉	—	2	1	no	—
202	C₂²⋊C₄×C₂₉	—	4	1	no	—
203	C₂²⋊C₄×C₂₉	—	4	1	no	—
204	C₂²⋊C₄×C₂₉	—	4	1	no	—
205	C₂²⋊C₄×C₂₉	—	4	1	no	—
206	C₂²⋊C₄×C₂₉	—	4	1	no	—
207	C₄²×C₂₉	—	2	1	no	—
208	C₄²×C₂₉	—	2	1	no	—
209	C₄²×C₂₉	—	4	1	no	—
210	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
211	#19992	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₂₉	—	2	1	no	—
213	C₂³×C₂₉	—	2	1	no	—
214	C₂³×C₂₉	—	4	1	no	—
215	Q₈×C₂₉	—	2	1	no	—
216	Q₈×C₂₉	—	2	1	no	—
217	Q₈×C₂₉	—	2	1	no	—
218	Q₈×C₂₉	—	4	1	no	—
219	Q₈×C₂₉	—	4	1	no	—
220	Q₈×C₂₉	—	4	1	no	—
221	Q₈×C₂₉	—	4	1	no	—
222	Q₈×C₂₉	—	8	2	no	—
223	Q₈×C₂₉	—	8	1	no	—
224	Q₈×C₂₉	#135	1	2	yes	—
225	D₄×C₂₉	—	2	1	no	—
226	D₄×C₂₉	—	2	1	no	—
227	D₄×C₂₉	—	2	1	no	—
228	D₄×C₂₉	—	4	1	no	—
229	D₄×C₂₉	—	4	1	no	—
230	D₄×C₂₉	—	4	1	no	—
231	D₄×C₂₉	—	4	1	no	—
232	D₄×C₂₉	—	8	2	no	—
233	D₄×C₂₉	—	8	1	no	—
234	D₄×C₂₉	—	16	1	no	—
235	D₄×C₂₉	#135	1	2	yes	—
236	C₂×C₄×C₂₉	—	2	1	no	—
237	C₂×C₄×C₂₉	—	2	1	no	—
238	C₂×C₄×C₂₉	—	2	1	no	—
239	C₂×C₄×C₂₉	—	2	1	no	—
240	C₂×C₄×C₂₉	—	2	1	no	—
241	C₂×C₄×C₂₉	—	2	1	no	—
242	C₂×C₄×C₂₉	—	4	1	no	—
243	C₂×C₄×C₂₉	—	4	1	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	—	8	2	no	—
250	C₂×C₄×C₂₉	—	8	2	no	—
251	C₂×C₄×C₂₉	—	16	1	no	—
252	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₈×C₂₉	—	2	2	no	—
256	C₈×C₂₉	—	2	1	no	—
257	C₈×C₂₉	—	2	1	no	—
258	C₈×C₂₉	—	2	1	no	—
259	C₈×C₂₉	—	2	1	no	—
260	C₈×C₂₉	—	4	1	no	—
261	C₈×C₂₉	—	4	1	no	—
262	C₈×C₂₉	—	4	1	no	—
263	C₈×C₂₉	—	4	1	no	—
264	#3360	C₂×C₂₉	1	1	yes	characteristic, complemented
265	#3358	C₂×C₂₉	1	1	yes	characteristic
266	#3304	C₂×C₂₉	1	1	yes	characteristic, complemented
267	#3299	C₂×C₂₉	1	1	yes	characteristic, complemented
268	#1708	C₂×C₂₉	1	1	yes	characteristic, complemented
269	#1684	C₂×C₂₉	1	1	yes	characteristic, complemented
270	#1683	C₂×C₂₉	1	1	yes	characteristic, complemented
271	#1682	C₂×C₂₉	1	1	yes	characteristic, complemented
272	#1681	C₂×C₂₉	1	1	yes	characteristic, complemented
273	#1652	C₂×C₂₉	1	1	yes	characteristic, complemented
274	#1651	C₂×C₂₉	1	1	yes	characteristic, complemented
275	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
276	#1622	C₂×C₂₉	1	1	yes	characteristic, complemented
277	C₈×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
278	C₈×D₈	C₂×C₂₉	1	1	yes	characteristic, complemented
279	C₂²×C₂₉	—	2	2	no	—
280	C₂²×C₂₉	—	4	1	no	—
281	C₂²×C₂₉	—	4	1	no	—
282	C₂²×C₂₉	—	4	1	no	—
283	C₂²×C₂₉	—	4	1	no	—
284	C₂²×C₂₉	—	4	1	no	—
285	C₂²×C₂₉	—	8	1	no	—
286	C₂²×C₂₉	—	8	1	no	—
287	C₂²×C₂₉	—	8	1	no	—
288	C₂²×C₂₉	D₄²	1	1	yes	characteristic
289	C₄×C₂₉	—	2	2	no	—
290	C₄×C₂₉	—	2	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	—	4	1	no	—
296	C₄×C₂₉	—	8	1	no	—
297	C₄×C₂₉	—	8	1	no	—
298	C₄×C₂₉	—	8	1	no	—
299	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
300	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
301	C₄×C₂₉	#576	1	1	yes	characteristic
302	C₄×C₂₉	#578	1	1	yes	characteristic
303	#556	C₂²×C₂₉	1	1	yes	characteristic
304	#554	C₂²×C₂₉	1	1	yes	characteristic
305	#550	C₂²×C₂₉	1	1	yes	characteristic
306	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
307	#498	C₂²×C₂₉	1	1	yes	characteristic
308	#492	C₂²×C₂₉	1	1	yes	characteristic
309	#488	—	2	1	no	—
310	#487	C₂²×C₂₉	1	1	yes	characteristic
311	#487	C₂²×C₂₉	1	1	yes	characteristic
312	#486	—	2	1	no	—
313	#486	C₂²×C₂₉	1	1	yes	characteristic
314	#486	C₂²×C₂₉	1	1	yes	characteristic
315	#484	—	2	1	no	—
316	#482	—	2	1	no	—
317	#479	—	2	1	no	—
318	#477	C₂²×C₂₉	1	1	yes	characteristic
319	#476	C₂²×C₂₉	1	1	yes	characteristic
320	#475	C₂²×C₂₉	1	1	yes	characteristic
321	#474	—	2	1	no	—
322	#474	C₂²×C₂₉	1	1	yes	characteristic
323	#467	—	2	1	no	—
324	#465	—	2	1	no	—
325	#463	—	2	1	no	—
326	#462	C₂²×C₂₉	1	1	yes	characteristic
327	#461	C₂²×C₂₉	1	1	yes	characteristic
328	#460	C₂²×C₂₉	1	1	yes	characteristic
329	#459	—	2	1	no	—
330	#459	C₂²×C₂₉	1	1	yes	characteristic
331	#452	—	2	1	no	—
332	#451	—	2	1	no	—
333	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
334	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
335	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
336	C₄×SD₁₆	—	2	1	no	—
337	C₄×D₈	—	2	1	no	—
338	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
339	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
340	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
341	#416	—	2	1	no	—
342	C₂×#103	—	2	1	no	—
343	#335	C₂²×C₂₉	1	1	yes	characteristic
344	#335	C₂²×C₂₉	1	1	yes	characteristic
345	#333	C₂²×C₂₉	1	1	yes	characteristic
346	#332	C₂²×C₂₉	1	1	yes	characteristic
347	#332	C₂²×C₂₉	1	1	yes	characteristic
348	#331	C₂²×C₂₉	1	1	yes	characteristic
349	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
350	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
351	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
352	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
353	C₈²	C₂²×C₂₉	1	1	yes	characteristic
354	C₂×C₂₉	—	4	2	no	—
355	C₂×C₂₉	—	8	1	no	—
356	C₂×C₂₉	—	16	1	no	—
357	C₂×C₂₉	#3280	1	1	yes	characteristic
358	C₂×C₂₉	#3285	1	1	yes	characteristic
359	C₂×C₂₉	#3291	1	1	yes	characteristic
360	C₂×#41	—	2	1	no	—
361	C₂²×Q₈	—	2	1	no	—
362	C₂×Q₁₆	—	2	1	no	—
363	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
364	C₂×SD₁₆	—	2	1	no	—
365	C₂×SD₁₆	—	2	1	no	—
366	C₂×SD₁₆	—	4	1	no	—
367	C₂×D₈	—	2	1	no	—
368	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₄⋊Q₈	—	2	1	no	—
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	#127	—	2	1	no	—
376	#127	C₂³×C₂₉	1	1	yes	characteristic
377	#126	—	4	1	no	—
378	#125	—	2	1	no	—
379	#124	—	2	1	no	—
380	C₂²⋊Q₈	—	2	1	no	—
381	C₂²⋊Q₈	—	2	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	4	1	no	—
384	C₂²⋊Q₈	—	4	1	no	—
385	#121	—	2	1	no	—
386	#121	—	4	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
389	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
395	#117	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	#107	—	2	1	no	—
398	#107	—	2	1	no	—
399	#107	D₄×C₂₉	1	1	yes	characteristic
400	#107	D₄×C₂₉	1	1	yes	characteristic
401	#106	—	2	1	no	—
402	#106	—	2	1	no	—
403	#106	—	4	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	—	2	1	no	—
406	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
408	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
409	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
410	#103	—	2	1	no	—
411	#103	—	2	1	no	—
412	#103	—	2	1	no	—
413	#103	—	2	1	no	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	1	no	—
418	#103	D₄×C₂₉	1	1	yes	characteristic
419	#103	D₄×C₂₉	1	1	yes	characteristic
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	2	1	no	—
423	#102	—	2	1	no	—
424	#102	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	D₄×C₂₉	1	1	yes	characteristic
429	#102	D₄×C₂₉	1	1	yes	characteristic
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	—	2	1	no	—
434	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
437	C₂₉	#19992	1	1	yes	characteristic, direct product factor, Sylow
438	#41	—	4	2	no	—
439	#41	—	8	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	2	no	—
445	C₂×Q₈	—	8	1	no	—
446	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
454	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	—	4	1	no	—
459	C₂²×C₄	—	4	1	no	—
460	Q₁₆	—	2	2	no	—
461	Q₁₆	—	8	1	no	—
462	SD₁₆	—	4	2	no	—
463	SD₁₆	—	8	2	no	—
464	SD₁₆	—	8	1	no	—
465	D₈	—	2	2	no	—
466	D₈	—	4	2	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	8	1	no	—
473	C₂×C₈	—	8	1	no	—
474	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
475	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
476	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
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	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
492	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₂²⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	4	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	2	1	no	—
510	Q₈	—	2	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	no	—
515	Q₈	—	8	2	no	—
516	Q₈	—	8	1	no	—
517	Q₈	C₂₉×#135	1	2	yes	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	8	2	no	—
526	D₄	—	8	1	no	—
527	D₄	—	16	1	no	—
528	D₄	C₂₉×#135	1	2	yes	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	16	1	no	—
545	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
547	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
548	C₈	—	2	2	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	D₄²×C₂₉	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
578	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
579	C₄	C₂₉×#576	1	1	yes	characteristic
580	C₄	C₂₉×#578	1	1	yes	characteristic
581	C₂	—	4	2	no	—
582	C₂	—	8	1	no	—
583	C₂	—	16	1	no	—
584	C₂	C₂₉×#3280	1	1	yes	characteristic
585	C₂	C₂₉×#3285	1	1	yes	characteristic
586	C₂	C₂₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3358	C₂
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
1. C₂₉×#3360	C₂	semidirect
3. C₂₉×#3304	C₂	semidirect
4. C₂₉×#3299	C₂	semidirect
5. C₂₉×#1708	C₂	semidirect
6. C₂₉×#1684	C₂	semidirect
7. C₂₉×#1683	C₂	semidirect
8. C₂₉×#1682	C₂	semidirect
9. C₂₉×#1681	C₂	semidirect
10. C₂₉×#1652	C₂	semidirect
11. C₂₉×#1651	C₂	semidirect
12. C₂₉×#1631	C₂	semidirect
13. C₂₉×#1622	C₂	semidirect
14. C₈×Q₁₆×C₂₉	C₂	semidirect
15. C₈×D₈×C₂₉	C₂	semidirect
211. #19992	C₂₉	direct (N × H)
264. #3360	C₂×C₂₉	semidirect
266. #3304	C₂×C₂₉	semidirect
267. #3299	C₂×C₂₉	semidirect
268. #1708	C₂×C₂₉	semidirect
269. #1684	C₂×C₂₉	semidirect
270. #1683	C₂×C₂₉	semidirect
271. #1682	C₂×C₂₉	semidirect
272. #1681	C₂×C₂₉	semidirect
273. #1652	C₂×C₂₉	semidirect
274. #1651	C₂×C₂₉	semidirect
275. #1631	C₂×C₂₉	semidirect
276. #1622	C₂×C₂₉	semidirect
277. C₈×Q₁₆	C₂×C₂₉	semidirect
278. C₈×D₈	C₂×C₂₉	semidirect
437. C₂₉	#19992	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×#3360	2
C₂₉×#3358	2
C₂₉×#3304	2
C₂₉×#3299	2
C₂₉×#1708	2
C₂₉×#1684	2
C₂₉×#1683	2
C₂₉×#1682	2
C₂₉×#1681	2
C₂₉×#1652	2
C₂₉×#1651	2
C₂₉×#1631	2
C₂₉×#1622	2
C₈×Q₁₆×C₂₉	2
C₈×D₈×C₂₉	2
#19992	29

Subgroups — C29×#19992 #20314892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19992 #20314892