Subgroups — C₂₉×#25830 #20320730

Order 7424.

1054 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3503	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3079	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2868	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#2060	C₂	1	4	yes	maximal, complemented
6	C₂₉×#1997	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1859	C₂	1	4	yes	maximal
9	C₄×C₂₉×#104	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₂₉	—	2	1	no	—
11	C₂₉×#557	—	2	1	no	—
12	C₂₉×#554	—	2	1	no	—
13	C₂₉×#554	—	2	2	no	—
14	D₄×Q₈×C₂₉	—	2	2	no	—
15	D₄×Q₈×C₂₉	—	2	1	no	—
16	C₂₉×#544	—	2	2	no	—
17	C₂₉×#544	C₂²	1	2	yes	—
18	C₂₉×#533	—	2	1	no	—
19	C₂₉×#533	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×C₄⋊Q₈	—	2	1	no	—
21	C₂×C₂₉×C₄⋊Q₈	—	2	2	no	—
22	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂₉×#520	C₂²	1	2	yes	—
25	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#501	—	2	2	no	—
27	C₂₉×#500	—	2	1	no	—
28	C₂₉×#498	—	2	1	no	—
29	C₂₉×#477	—	2	1	no	—
30	C₂₉×#476	—	2	1	no	—
31	C₂₉×#475	—	2	1	no	—
32	C₂₉×#474	—	2	1	no	—
33	C₂₉×#428	C₂²	1	2	yes	—
34	C₂₉×#428	C₂²	1	4	yes	—
35	C₂₉×#423	C₂²	1	1	yes	characteristic
36	C₂×C₂₉×#104	C₂²	1	2	yes	—
37	C₂₉×#417	C₂²	1	2	yes	—
38	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
39	C₂₉×#384	—	2	2	no	—
40	C₂₉×#384	C₂²	1	4	yes	—
41	C₄³×C₂₉	C₂²	1	1	yes	characteristic
42	C₂₉×#343	C₂²	1	4	yes	—
43	C₂₉×#339	C₂²	1	4	yes	—
44	C₂₉×#339	C₂²	1	2	yes	—
45	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₂₉	—	2	2	no	—
47	C₂²×Q₈×C₂₉	—	2	1	no	—
48	C₂²×Q₈×C₂₉	D₄	1	2	yes	—
49	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
50	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
51	C₂₉×C₄⋊Q₈	—	2	2	no	—
52	C₂₉×C₄⋊Q₈	—	2	2	no	—
53	C₂₉×C₄⋊Q₈	—	2	4	no	—
54	C₂₉×C₄⋊Q₈	—	2	2	no	—
55	C₂₉×C₄⋊Q₈	—	2	2	no	—
56	C₂₉×C₄⋊Q₈	—	2	1	no	—
57	C₂₉×C₄⋊Q₈	—	2	1	no	—
58	C₂₉×C₄⋊Q₈	—	2	1	no	—
59	C₂₉×C₄⋊Q₈	—	2	1	no	—
60	C₂₉×C₄⋊Q₈	—	2	1	no	—
61	C₂₉×C₄⋊Q₈	—	2	1	no	—
62	C₂₉×C₄⋊Q₈	—	2	1	no	—
63	C₂₉×C₄⋊Q₈	—	2	1	no	—
64	C₂₉×C₄⋊Q₈	—	4	8	no	—
65	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
67	C₂₉×#125	—	2	4	no	—
68	C₂₉×#125	—	2	2	no	—
69	C₂₉×#125	—	2	2	no	—
70	C₂₉×#125	D₄	1	2	yes	—
71	C₂₉×C₂²⋊Q₈	—	2	2	no	—
72	C₂₉×C₂²⋊Q₈	—	2	2	no	—
73	C₂₉×C₂²⋊Q₈	—	2	4	no	—
74	C₂₉×C₂²⋊Q₈	—	2	4	no	—
75	C₂₉×C₂²⋊Q₈	—	2	1	no	—
76	C₂₉×C₂²⋊Q₈	—	2	1	no	—
77	C₂₉×C₂²⋊Q₈	—	2	4	no	—
78	C₄×Q₈×C₂₉	—	2	2	no	—
79	C₄×Q₈×C₂₉	—	2	2	no	—
80	C₄×Q₈×C₂₉	—	2	2	no	—
81	C₄×Q₈×C₂₉	—	2	1	no	—
82	C₄×Q₈×C₂₉	—	2	1	no	—
83	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
84	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
85	C₄×D₄×C₂₉	—	2	2	no	—
86	C₄×D₄×C₂₉	—	2	1	no	—
87	C₄×D₄×C₂₉	—	2	1	no	—
88	C₄×D₄×C₂₉	—	2	4	no	—
89	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
90	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
91	C₂₉×#117	—	2	2	no	—
92	C₂₉×#117	—	2	1	no	—
93	C₂₉×#117	C₂³	1	1	yes	characteristic
94	C₂₉×#117	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₂₉	—	2	8	no	—
98	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
100	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
102	C₂×C₄²×C₂₉	—	2	1	no	—
103	C₂×C₄²×C₂₉	—	2	1	no	—
104	C₂×C₄²×C₂₉	—	2	1	no	—
105	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
106	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
107	C₂₉×#107	—	2	2	no	—
108	C₂₉×#107	—	2	4	no	—
109	C₂₉×#106	—	2	2	no	—
110	C₂₉×#106	—	2	4	no	—
111	C₂₉×C₄⋊C₈	—	2	1	no	—
112	C₂₉×C₄⋊C₈	—	2	1	no	—
113	C₂₉×#104	Q₈	1	8	yes	complemented
114	C₂₉×#103	—	2	2	no	—
115	C₂₉×#102	—	2	2	no	—
116	C₂₉×#97	—	2	1	no	—
117	C₄×C₈×C₂₉	—	2	1	no	—
118	#41×C₂₉	—	2	2	no	—
119	#41×C₂₉	C₂×Q₈	1	4	yes	—
120	C₂×Q₈×C₂₉	—	2	4	no	—
121	C₂×Q₈×C₂₉	—	2	1	no	—
122	C₂×Q₈×C₂₉	—	2	2	no	—
123	C₂×Q₈×C₂₉	—	2	1	no	—
124	C₂×Q₈×C₂₉	—	2	2	no	—
125	C₂×Q₈×C₂₉	—	4	4	no	—
126	C₂×Q₈×C₂₉	—	4	4	no	—
127	C₂×Q₈×C₂₉	—	4	1	no	—
128	C₂×Q₈×C₂₉	—	4	1	no	—
129	C₂×Q₈×C₂₉	—	8	4	no	—
130	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₂₉	—	2	1	no	—
132	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₂₉	—	2	2	no	—
134	C₂²×C₄×C₂₉	—	2	1	no	—
135	C₂²×C₄×C₂₉	—	2	4	no	—
136	C₂²×C₄×C₂₉	—	2	1	no	—
137	C₂²×C₄×C₂₉	—	2	1	no	—
138	C₂²×C₄×C₂₉	—	2	2	no	—
139	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₂₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
143	M₁₆×C₂₉	—	2	2	no	—
144	M₁₆×C₂₉	—	2	4	no	—
145	M₁₆×C₂₉	C₂×Q₈	1	4	yes	complemented
146	C₂×C₈×C₂₉	—	2	2	no	—
147	C₂×C₈×C₂₉	—	2	2	no	—
148	C₄⋊C₄×C₂₉	—	2	4	no	—
149	C₄⋊C₄×C₂₉	—	2	4	no	—
150	C₄⋊C₄×C₂₉	—	2	4	no	—
151	C₄⋊C₄×C₂₉	—	2	4	no	—
152	C₄⋊C₄×C₂₉	—	2	1	no	—
153	C₄⋊C₄×C₂₉	—	2	2	no	—
154	C₄⋊C₄×C₂₉	—	2	2	no	—
155	C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₄⋊C₄×C₂₉	—	2	1	no	—
157	C₄⋊C₄×C₂₉	—	2	1	no	—
158	C₄⋊C₄×C₂₉	—	2	2	no	—
159	C₄⋊C₄×C₂₉	—	2	2	no	—
160	C₄⋊C₄×C₂₉	—	2	2	no	—
161	C₄⋊C₄×C₂₉	—	2	2	no	—
162	C₄⋊C₄×C₂₉	—	2	2	no	—
163	C₄⋊C₄×C₂₉	—	2	2	no	—
164	C₄⋊C₄×C₂₉	—	4	16	no	—
165	C₄⋊C₄×C₂₉	—	4	1	no	—
166	C₄⋊C₄×C₂₉	—	4	1	no	—
167	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
171	C₂²⋊C₄×C₂₉	—	2	4	no	—
172	C₂²⋊C₄×C₂₉	—	2	2	no	—
173	C₂²⋊C₄×C₂₉	—	2	1	no	—
174	C₂²⋊C₄×C₂₉	—	2	1	no	—
175	C₂²⋊C₄×C₂₉	—	2	1	no	—
176	C₄²×C₂₉	—	2	4	no	—
177	C₄²×C₂₉	—	2	4	no	—
178	C₄²×C₂₉	—	2	4	no	—
179	C₄²×C₂₉	—	2	1	no	—
180	C₄²×C₂₉	—	2	1	no	—
181	C₄²×C₂₉	—	2	1	no	—
182	C₄²×C₂₉	—	2	2	no	—
183	C₄²×C₂₉	—	2	2	no	—
184	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₂₉	C₂×Q₈	1	4	yes	complemented
189	#25830	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂³×C₂₉	—	2	1	no	—
191	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
192	Q₈×C₂₉	—	2	1	no	—
193	Q₈×C₂₉	—	4	4	no	—
194	Q₈×C₂₉	—	4	2	no	—
195	Q₈×C₂₉	—	4	2	no	—
196	Q₈×C₂₉	—	8	2	no	—
197	Q₈×C₂₉	—	8	2	no	—
198	Q₈×C₂₉	—	8	4	no	—
199	Q₈×C₂₉	—	8	2	no	—
200	Q₈×C₂₉	C₄⋊Q₈	1	2	yes	complemented
201	D₄×C₂₉	—	2	4	no	—
202	D₄×C₂₉	—	2	1	no	—
203	D₄×C₂₉	C₄⋊Q₈	1	2	yes	complemented
204	C₂×C₄×C₂₉	—	2	4	no	—
205	C₂×C₄×C₂₉	—	2	4	no	—
206	C₂×C₄×C₂₉	—	2	1	no	—
207	C₂×C₄×C₂₉	—	2	4	no	—
208	C₂×C₄×C₂₉	—	2	4	no	—
209	C₂×C₄×C₂₉	—	2	2	no	—
210	C₂×C₄×C₂₉	—	2	2	no	—
211	C₂×C₄×C₂₉	—	2	2	no	—
212	C₂×C₄×C₂₉	—	2	1	no	—
213	C₂×C₄×C₂₉	—	2	1	no	—
214	C₂×C₄×C₂₉	—	2	4	no	—
215	C₂×C₄×C₂₉	—	2	2	no	—
216	C₂×C₄×C₂₉	—	4	2	no	—
217	C₂×C₄×C₂₉	—	4	2	no	—
218	C₂×C₄×C₂₉	—	4	4	no	—
219	C₂×C₄×C₂₉	—	4	4	no	—
220	C₂×C₄×C₂₉	—	4	2	no	—
221	C₂×C₄×C₂₉	—	8	4	no	—
222	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
223	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
224	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
225	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
226	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₂₉	C₂²×Q₈	1	2	yes	—
229	C₂×C₄×C₂₉	2₋¹⁺⁴	1	2	yes	—
230	C₈×C₂₉	—	2	4	no	—
231	C₈×C₂₉	—	4	2	no	—
232	#3503	C₂×C₂₉	1	1	yes	characteristic
233	#3165	C₂×C₂₉	1	1	yes	characteristic, complemented
234	#3079	C₂×C₂₉	1	1	yes	characteristic
235	#2868	C₂×C₂₉	1	1	yes	characteristic, complemented
236	#2060	C₂×C₂₉	1	4	yes	complemented
237	#1997	C₂×C₂₉	1	1	yes	characteristic, complemented
238	#1994	C₂×C₂₉	1	1	yes	characteristic, complemented
239	#1859	C₂×C₂₉	1	4	yes	—
240	C₄×#104	C₂×C₂₉	1	1	yes	characteristic
241	C₂²×C₂₉	—	2	1	no	—
242	C₂²×C₂₉	—	2	1	no	—
243	C₂²×C₂₉	—	2	2	no	—
244	C₂²×C₂₉	—	4	1	no	—
245	C₂²×C₂₉	—	4	1	no	—
246	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
247	C₂²×C₂₉	D₄×Q₈	1	2	yes	—
248	C₄×C₂₉	—	2	8	no	—
249	C₄×C₂₉	—	2	2	no	—
250	C₄×C₂₉	—	2	1	no	—
251	C₄×C₂₉	—	2	1	no	—
252	C₄×C₂₉	—	4	1	no	—
253	C₄×C₂₉	—	4	4	no	—
254	C₄×C₂₉	—	4	2	no	—
255	C₄×C₂₉	—	4	1	no	—
256	C₄×C₂₉	—	4	2	no	—
257	C₄×C₂₉	—	8	2	no	—
258	C₄×C₂₉	#453	1	2	yes	—
259	C₄×C₂₉	#456	1	2	yes	—
260	C₄×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
261	C₄×C₂₉	#536	1	1	yes	characteristic
262	C₄×C₂₉	D₄×Q₈	1	2	yes	—
263	Q₈²	—	2	1	no	—
264	#557	—	2	1	no	—
265	#554	—	2	1	no	—
266	#554	—	2	2	no	—
267	D₄×Q₈	—	2	2	no	—
268	D₄×Q₈	—	2	1	no	—
269	#544	—	2	2	no	—
270	#544	C₂²×C₂₉	1	2	yes	—
271	#533	—	2	1	no	—
272	#533	C₂²×C₂₉	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	—	2	1	no	—
274	C₂×C₄⋊Q₈	—	2	2	no	—
275	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
277	#520	C₂²×C₂₉	1	2	yes	—
278	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
279	#501	—	2	2	no	—
280	#500	—	2	1	no	—
281	#498	—	2	1	no	—
282	#477	—	2	1	no	—
283	#476	—	2	1	no	—
284	#475	—	2	1	no	—
285	#474	—	2	1	no	—
286	#428	C₂²×C₂₉	1	2	yes	—
287	#428	C₂²×C₂₉	1	4	yes	—
288	#423	C₂²×C₂₉	1	1	yes	characteristic
289	C₂×#104	C₂²×C₂₉	1	2	yes	—
290	#417	C₂²×C₂₉	1	2	yes	—
291	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
292	#384	—	2	2	no	—
293	#384	C₂²×C₂₉	1	4	yes	—
294	C₄³	C₂²×C₂₉	1	1	yes	characteristic
295	#343	C₂²×C₂₉	1	4	yes	—
296	#339	C₂²×C₂₉	1	2	yes	—
297	#339	C₂²×C₂₉	1	4	yes	—
298	C₂×C₂₉	—	2	2	no	—
299	C₂×C₂₉	—	4	2	no	—
300	C₂×C₂₉	#2434	1	1	yes	characteristic
301	C₂×C₂₉	C₂×#453	1	1	yes	characteristic
302	C₂×C₂₉	C₂×#456	1	1	yes	characteristic
303	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
304	C₂²×Q₈	—	2	2	no	—
305	C₂²×Q₈	—	2	1	no	—
306	C₂²×Q₈	D₄×C₂₉	1	2	yes	—
307	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
308	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
309	C₄⋊Q₈	—	2	2	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	4	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	4	8	no	—
323	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
324	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
325	#125	—	2	4	no	—
326	#125	—	2	2	no	—
327	#125	—	2	2	no	—
328	#125	D₄×C₂₉	1	2	yes	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
342	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
348	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
349	#117	—	2	2	no	—
350	#117	—	2	1	no	—
351	#117	C₂³×C₂₉	1	1	yes	characteristic
352	#117	C₂³×C₂₉	1	2	yes	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	8	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
364	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
365	#107	—	2	2	no	—
366	#107	—	2	4	no	—
367	#106	—	2	2	no	—
368	#106	—	2	4	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	2	1	no	—
371	#104	Q₈×C₂₉	1	8	yes	complemented
372	#103	—	2	2	no	—
373	#102	—	2	2	no	—
374	#97	—	2	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₂₉	#25830	1	1	yes	characteristic, direct product factor, Sylow
377	#41	—	2	2	no	—
378	#41	C₂×Q₈×C₂₉	1	4	yes	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	4	4	no	—
385	C₂×Q₈	—	4	4	no	—
386	C₂×Q₈	—	4	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	8	4	no	—
389	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₂₉	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	4	no	—
404	M₁₆	C₂×Q₈×C₂₉	1	4	yes	complemented
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	4	16	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
427	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
428	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
429	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	4	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
445	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
446	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
447	C₄²	C₂×Q₈×C₂₉	1	4	yes	complemented
448	C₂³	—	2	1	no	—
449	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
450	Q₈	—	2	1	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	8	2	no	—
455	Q₈	—	8	2	no	—
456	Q₈	—	8	4	no	—
457	Q₈	—	8	2	no	—
458	Q₈	C₂₉×C₄⋊Q₈	1	2	yes	complemented
459	D₄	—	2	4	no	—
460	D₄	—	2	1	no	—
461	D₄	C₂₉×C₄⋊Q₈	1	2	yes	complemented
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
481	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
482	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
483	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
486	C₂×C₄	C₂²×Q₈×C₂₉	1	2	yes	—
487	C₂×C₄	C₂₉×2₋¹⁺⁴	1	2	yes	—
488	C₈	—	2	4	no	—
489	C₈	—	4	2	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
496	C₂²	D₄×Q₈×C₂₉	1	2	yes	—
497	C₄	—	2	8	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	1	no	—
505	C₄	—	4	2	no	—
506	C₄	—	8	2	no	—
507	C₄	C₂₉×#453	1	2	yes	—
508	C₄	C₂₉×#456	1	2	yes	—
509	C₄	C₂×C₂₉×C₄⋊Q₈	1	1	yes	characteristic
510	C₄	C₂₉×#536	1	1	yes	characteristic
511	C₄	D₄×Q₈×C₂₉	1	2	yes	—
512	C₂	—	2	2	no	—
513	C₂	—	4	2	no	—
514	C₂	C₂₉×#2434	1	1	yes	characteristic
515	C₂	C₂×C₂₉×#453	1	1	yes	characteristic
516	C₂	C₂×C₂₉×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#3165	C₂	semidirect
4. C₂₉×#2868	C₂	semidirect
5. C₂₉×#2060	C₂	semidirect
6. C₂₉×#1997	C₂	semidirect
7. C₂₉×#1994	C₂	semidirect
113. C₂₉×#104	Q₈	semidirect
145. M₁₆×C₂₉	C₂×Q₈	semidirect
188. C₄²×C₂₉	C₂×Q₈	semidirect
189. #25830	C₂₉	direct (N × H)
200. Q₈×C₂₉	C₄⋊Q₈	semidirect
203. D₄×C₂₉	C₄⋊Q₈	semidirect
233. #3165	C₂×C₂₉	semidirect
235. #2868	C₂×C₂₉	semidirect
236. #2060	C₂×C₂₉	semidirect
237. #1997	C₂×C₂₉	semidirect
238. #1994	C₂×C₂₉	semidirect
371. #104	Q₈×C₂₉	semidirect
376. C₂₉	#25830	direct (N × H)
404. M₁₆	C₂×Q₈×C₂₉	semidirect
447. C₄²	C₂×Q₈×C₂₉	semidirect
458. Q₈	C₂₉×C₄⋊Q₈	semidirect
461. D₄	C₂₉×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#3503	2
C₂₉×#3165	2
C₂₉×#3079	2
C₂₉×#2868	2
C₂₉×#2060	2
C₂₉×#1997	2
C₂₉×#1994	2
C₂₉×#1859	2
C₄×C₂₉×#104	2
#25830	29

Subgroups — C29×#25830 #20320730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25830 #20320730