Subgroups — C₂₉×#10068 #20304968

Order 7424.

670 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#461	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#2542	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₂₉	—	2	1	no	—
9	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
10	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₂₉×C₂²⋊Q₈	—	2	2	no	—
12	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₂₉×#498	—	2	2	no	—
14	C₂₉×#498	—	2	2	no	—
15	C₂₉×#461	—	2	2	no	—
16	C₂₉×#461	—	2	2	no	—
17	C₂×C₂₉×#106	—	2	2	no	—
18	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₉×#103	—	2	1	no	—
21	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
22	C₂₉×#399	—	2	2	no	—
23	C₂₉×#390	—	2	1	no	—
24	C₂₉×#384	—	2	1	no	—
25	C₄×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#340	—	2	2	no	—
27	C₂₉×#332	—	2	2	no	—
28	C₂₉×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₂₉	—	2	1	no	—
30	C₂²×Q₈×C₂₉	—	2	1	no	—
31	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₂₉	—	2	1	no	—
33	C₂×SD₁₆×C₂₉	—	2	4	no	—
34	C₂×SD₁₆×C₂₉	—	4	2	no	—
35	C₂×SD₁₆×C₂₉	—	4	2	no	—
36	C₂²×C₈×C₂₉	—	2	1	no	—
37	C₂²×C₈×C₂₉	—	2	1	no	—
38	C₂²×C₈×C₂₉	—	2	1	no	—
39	C₂₉×C₄⋊Q₈	—	2	1	no	—
40	C₂₉×C₄⋊Q₈	—	2	1	no	—
41	C₂₉×C₄⋊Q₈	—	2	1	no	—
42	C₂₉×C₄⋊Q₈	—	2	1	no	—
43	C₂₉×C₄⋊Q₈	—	2	1	no	—
44	C₂₉×C₄⋊Q₈	—	2	1	no	—
45	C₂₉×C₄⋊Q₈	—	2	1	no	—
46	C₂₉×C₄⋊Q₈	D₄	1	2	yes	—
47	C₂₉×C₂²⋊Q₈	—	4	4	no	—
48	C₂₉×C₂²⋊Q₈	—	4	4	no	—
49	C₄×D₄×C₂₉	—	2	1	no	—
50	C₄×D₄×C₂₉	—	2	1	no	—
51	C₄×D₄×C₂₉	—	2	1	no	—
52	C₄×D₄×C₂₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₂₉	D₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
62	C₂×C₄²×C₂₉	—	2	1	no	—
63	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
64	C₂₉×#106	—	2	8	no	—
65	C₂₉×C₄⋊C₈	—	2	1	no	—
66	C₂₉×C₄⋊C₈	—	2	1	no	—
67	C₂₉×C₄⋊C₈	—	2	1	no	—
68	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
69	C₂₉×#103	—	2	4	no	—
70	C₄×C₈×C₂₉	—	2	1	no	—
71	C₄×C₈×C₂₉	D₄	1	2	yes	—
72	C₂₉×#95	—	2	1	no	—
73	C₂⁴×C₂₉	—	2	1	no	—
74	C₂×Q₈×C₂₉	—	2	2	no	—
75	C₂×Q₈×C₂₉	—	4	1	no	—
76	C₂×Q₈×C₂₉	—	4	1	no	—
77	C₂×Q₈×C₂₉	—	4	1	no	—
78	C₂×Q₈×C₂₉	—	4	2	no	—
79	C₂×Q₈×C₂₉	—	4	2	no	—
80	C₂×Q₈×C₂₉	—	4	1	no	—
81	C₂×Q₈×C₂₉	—	4	1	no	—
82	C₂×Q₈×C₂₉	—	4	1	no	—
83	C₂×Q₈×C₂₉	—	4	1	no	—
84	C₂×D₄×C₂₉	—	2	1	no	—
85	C₂×D₄×C₂₉	—	2	1	no	—
86	C₂×D₄×C₂₉	—	2	1	no	—
87	C₂×D₄×C₂₉	—	2	1	no	—
88	C₂×D₄×C₂₉	—	2	1	no	—
89	C₂×D₄×C₂₉	SD₁₆	1	2	yes	—
90	C₂²×C₄×C₂₉	—	2	2	no	—
91	C₂²×C₄×C₂₉	—	2	2	no	—
92	C₂²×C₄×C₂₉	—	2	1	no	—
93	C₂²×C₄×C₂₉	—	4	1	no	—
94	C₂²×C₄×C₂₉	—	4	1	no	—
95	C₂²×C₄×C₂₉	—	4	1	no	—
96	C₂²×C₄×C₂₉	—	4	2	no	—
97	C₂²×C₄×C₂₉	—	4	2	no	—
98	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
101	SD₁₆×C₂₉	—	4	8	no	—
102	C₂×C₈×C₂₉	—	2	4	no	—
103	C₂×C₈×C₂₉	—	2	2	no	—
104	C₂×C₈×C₂₉	—	2	2	no	—
105	C₂×C₈×C₂₉	—	4	1	no	—
106	C₂×C₈×C₂₉	—	4	1	no	—
107	C₂×C₈×C₂₉	—	4	1	no	—
108	C₂×C₈×C₂₉	—	4	2	no	—
109	C₄⋊C₄×C₂₉	—	2	2	no	—
110	C₄⋊C₄×C₂₉	—	2	2	no	—
111	C₄⋊C₄×C₂₉	—	2	1	no	—
112	C₄⋊C₄×C₂₉	—	2	2	no	—
113	C₄⋊C₄×C₂₉	—	2	2	no	—
114	C₄⋊C₄×C₂₉	—	2	1	no	—
115	C₄⋊C₄×C₂₉	—	2	2	no	—
116	C₄⋊C₄×C₂₉	—	4	8	no	—
117	C₄⋊C₄×C₂₉	—	4	1	no	—
118	C₄⋊C₄×C₂₉	—	4	1	no	—
119	C₄⋊C₄×C₂₉	—	4	1	no	—
120	C₄⋊C₄×C₂₉	—	4	1	no	—
121	C₄⋊C₄×C₂₉	SD₁₆	1	4	yes	complemented
122	C₂²⋊C₄×C₂₉	—	4	8	no	—
123	C₂²⋊C₄×C₂₉	—	4	1	no	—
124	C₂²⋊C₄×C₂₉	—	4	1	no	—
125	C₄²×C₂₉	—	4	1	no	—
126	C₄²×C₂₉	—	4	1	no	—
127	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₂₉	#41	1	1	yes	characteristic
131	#10068	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₂₉	—	2	2	no	—
133	C₂³×C₂₉	—	4	1	no	—
134	C₂³×C₂₉	—	4	1	no	—
135	C₂³×C₂₉	—	4	2	no	—
136	C₂³×C₂₉	—	4	2	no	—
137	C₂³×C₂₉	#120	1	1	yes	characteristic
138	Q₈×C₂₉	—	4	2	no	—
139	Q₈×C₂₉	—	4	2	no	—
140	Q₈×C₂₉	—	8	2	no	—
141	Q₈×C₂₉	—	8	1	no	—
142	Q₈×C₂₉	—	8	1	no	—
143	Q₈×C₂₉	—	8	1	no	—
144	Q₈×C₂₉	—	8	1	no	—
145	D₄×C₂₉	—	2	2	no	—
146	D₄×C₂₉	—	2	2	no	—
147	D₄×C₂₉	—	4	1	no	—
148	D₄×C₂₉	—	4	1	no	—
149	C₂×C₄×C₂₉	—	2	2	no	—
150	C₂×C₄×C₂₉	—	2	4	no	—
151	C₂×C₄×C₂₉	—	4	2	no	—
152	C₂×C₄×C₂₉	—	4	2	no	—
153	C₂×C₄×C₂₉	—	4	1	no	—
154	C₂×C₄×C₂₉	—	4	2	no	—
155	C₂×C₄×C₂₉	—	4	2	no	—
156	C₂×C₄×C₂₉	—	4	4	no	—
157	C₂×C₄×C₂₉	—	4	2	no	—
158	C₂×C₄×C₂₉	—	8	1	no	—
159	C₂×C₄×C₂₉	—	8	1	no	—
160	C₂×C₄×C₂₉	—	8	2	no	—
161	C₂×C₄×C₂₉	—	8	1	no	—
162	C₂×C₄×C₂₉	—	8	1	no	—
163	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
165	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₂₉	#127	1	1	yes	characteristic
169	C₂×C₄×C₂₉	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
171	C₂×C₄×C₂₉	#135	1	1	yes	characteristic
172	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₂₉	#137	1	1	yes	characteristic
175	C₈×C₂₉	—	2	4	no	—
176	C₈×C₂₉	—	4	2	no	—
177	C₈×C₂₉	—	8	1	no	—
178	C₂×#498	C₂×C₂₉	1	1	yes	characteristic, complemented
179	C₂×#461	C₂×C₂₉	1	1	yes	characteristic
180	#2542	C₂×C₂₉	1	1	yes	characteristic
181	#1988	C₂×C₂₉	1	1	yes	characteristic, complemented
182	C₂×#332	C₂×C₂₉	1	1	yes	characteristic, complemented
183	C₂×D₄⋊C₈	C₂×C₂₉	1	1	yes	characteristic
184	#1279	C₂×C₂₉	1	1	yes	characteristic, complemented
185	C₂²×C₂₉	—	4	4	no	—
186	C₂²×C₂₉	—	4	2	no	—
187	C₂²×C₂₉	—	8	2	no	—
188	C₂²×C₂₉	—	8	1	no	—
189	C₂²×C₂₉	—	8	1	no	—
190	C₂²×C₂₉	#392	1	1	yes	characteristic
191	C₂²×C₂₉	#448	1	1	yes	characteristic
192	C₂²×C₂₉	#449	1	1	yes	characteristic
193	C₂²×C₂₉	#450	1	2	yes	—
194	C₂²×C₂₉	#456	1	2	yes	—
195	C₄×C₂₉	—	2	1	no	—
196	C₄×C₂₉	—	2	1	no	—
197	C₄×C₂₉	—	4	4	no	—
198	C₄×C₂₉	—	8	2	no	—
199	C₄×C₂₉	—	8	1	no	—
200	C₄×C₂₉	—	8	2	no	—
201	C₄×C₂₉	#450	1	1	yes	characteristic
202	C₄×C₂₉	#452	1	1	yes	characteristic
203	C₄×C₂₉	#460	1	2	yes	—
204	C₄×C₂₉	#465	1	1	yes	characteristic
205	C₄×C₂₉	#468	1	1	yes	characteristic
206	C₄×C₂₉	#492	1	1	yes	characteristic
207	C₄×C₂₉	#496	1	1	yes	characteristic
208	C₂²×SD₁₆	—	2	1	no	—
209	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
210	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
211	C₂×C₂²⋊Q₈	—	2	2	no	—
212	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
213	#498	—	2	2	no	—
214	#498	—	2	2	no	—
215	#461	—	2	2	no	—
216	#461	—	2	2	no	—
217	C₂×#106	—	2	2	no	—
218	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
220	C₂×#103	—	2	1	no	—
221	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
222	#399	—	2	2	no	—
223	#390	—	2	1	no	—
224	#384	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
226	#340	—	2	2	no	—
227	#332	—	2	2	no	—
228	D₄⋊C₈	—	2	2	no	—
229	C₂×C₂₉	—	8	2	no	—
230	C₂×C₂₉	#1651	1	2	yes	—
231	C₂×C₂₉	#1654	1	2	yes	—
232	C₂×C₂₉	#2000	1	1	yes	characteristic
233	C₂×C₂₉	#2005	1	1	yes	characteristic
234	C₂×C₂₉	#2014	1	1	yes	characteristic
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×SD₁₆	—	4	2	no	—
241	C₂×SD₁₆	—	4	2	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	D₄×C₂₉	1	2	yes	—
253	C₂²⋊Q₈	—	4	4	no	—
254	C₂²⋊Q₈	—	4	4	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	4	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
265	C₂×C₄⋊C₄	D₄×C₂₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	4	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
270	#106	—	2	8	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
275	#103	—	2	4	no	—
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	D₄×C₂₉	1	2	yes	—
278	#95	—	2	1	no	—
279	C₂₉	#10068	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	—	2	1	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	1	no	—
284	C₂×Q₈	—	4	1	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×Q₈	—	4	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	SD₁₆×C₂₉	1	2	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
308	SD₁₆	—	4	8	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	8	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	SD₁₆×C₂₉	1	4	yes	complemented
329	C₂²⋊C₄	—	4	8	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
335	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
337	C₄²	#41×C₂₉	1	1	yes	characteristic
338	C₂³	—	2	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂₉×#120	1	1	yes	characteristic
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	8	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	Q₈	—	8	1	no	—
350	Q₈	—	8	1	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	—	8	1	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	—	8	1	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
370	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
371	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
372	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
373	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
374	C₂×C₄	C₂₉×#127	1	1	yes	characteristic
375	C₂×C₄	C₂×SD₁₆×C₂₉	1	1	yes	characteristic
376	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
377	C₂×C₄	C₂₉×#135	1	1	yes	characteristic
378	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂×C₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
380	C₂×C₄	C₂₉×#137	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	4	2	no	—
383	C₈	—	8	1	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	C₂₉×#392	1	1	yes	characteristic
390	C₂²	C₂₉×#448	1	1	yes	characteristic
391	C₂²	C₂₉×#449	1	1	yes	characteristic
392	C₂²	C₂₉×#450	1	2	yes	—
393	C₂²	C₂₉×#456	1	2	yes	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	4	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂₉×#450	1	1	yes	characteristic
401	C₄	C₂₉×#452	1	1	yes	characteristic
402	C₄	C₂₉×#460	1	2	yes	—
403	C₄	C₂₉×#465	1	1	yes	characteristic
404	C₄	C₂₉×#468	1	1	yes	characteristic
405	C₄	C₂₉×#492	1	1	yes	characteristic
406	C₄	C₂₉×#496	1	1	yes	characteristic
407	C₂	—	8	2	no	—
408	C₂	C₂₉×#1651	1	2	yes	—
409	C₂	C₂₉×#1654	1	2	yes	—
410	C₂	C₂₉×#2000	1	1	yes	characteristic
411	C₂	C₂₉×#2005	1	1	yes	characteristic
412	C₂	C₂₉×#2014	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₉×#498	C₂	semidirect
4. C₂₉×#1988	C₂	semidirect
5. C₂×C₂₉×#332	C₂	semidirect
7. C₂₉×#1279	C₂	semidirect
121. C₄⋊C₄×C₂₉	SD₁₆	semidirect
131. #10068	C₂₉	direct (N × H)
178. C₂×#498	C₂×C₂₉	semidirect
181. #1988	C₂×C₂₉	semidirect
182. C₂×#332	C₂×C₂₉	semidirect
184. #1279	C₂×C₂₉	semidirect
279. C₂₉	#10068	direct (N × H)
328. C₄⋊C₄	SD₁₆×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#498	2
C₂×C₂₉×#461	2
C₂₉×#2542	2
C₂₉×#1988	2
C₂×C₂₉×#332	2
C₂×C₂₉×D₄⋊C₈	2
C₂₉×#1279	2
#10068	29

Subgroups — C29×#10068 #20304968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#10068 #20304968