Subgroups — C₂₉×#19935 #20314835

Order 7424.

646 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3396	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3373	C₂	1	2	yes	maximal, complemented
3	D₄×Q₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1709	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1702	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1667	C₂	1	1	yes	maximal, characteristic
8	C₂₉×#1640	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1627	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₂₉	—	2	1	no	—
13	C₂₉×#559	C₂²	1	2	yes	—
14	D₄×Q₈×C₂₉	C₂²	1	2	yes	—
15	C₂₉×#495	—	2	1	no	—
16	C₂₉×#494	C₂²	1	1	yes	characteristic
17	C₂₉×#493	C₂²	1	1	yes	characteristic
18	C₂₉×#489	—	2	2	no	—
19	C₂₉×#486	C₂²	1	2	yes	—
20	C₂₉×#486	C₂²	1	2	yes	—
21	C₂₉×#476	—	2	2	no	—
22	C₂₉×#475	C₂²	1	2	yes	—
23	C₂₉×#467	—	2	1	no	—
24	C₂₉×#463	—	2	2	no	—
25	C₂₉×#463	—	2	2	no	—
26	C₂₉×#462	C₂²	1	2	yes	—
27	C₂₉×#460	C₂²	1	2	yes	—
28	C₂₉×#459	C₂²	1	2	yes	—
29	C₂₉×#451	—	2	2	no	—
30	C₂₉×#446	C₂²	1	2	yes	—
31	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic
32	C₂₉×#442	—	2	2	no	—
33	C₄×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
35	C₄×D₈×C₂₉	—	2	1	no	—
36	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic
37	C₂₉×#335	C₂²	1	1	yes	characteristic
38	C₂₉×#334	C₂²	1	1	yes	characteristic
39	C₂₉×#332	C₂²	1	2	yes	—
40	C₂₉×#331	C₂²	1	2	yes	—
41	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₂₉×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₂₉	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₂₉	—	2	2	no	—
46	C₂×Q₁₆×C₂₉	—	2	2	no	—
47	C₂×Q₁₆×C₂₉	—	2	1	no	—
48	C₂×Q₁₆×C₂₉	—	2	1	no	—
49	C₂×Q₁₆×C₂₉	—	4	4	no	—
50	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
51	C₂×SD₁₆×C₂₉	—	2	2	no	—
52	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
53	C₂×D₈×C₂₉	—	2	2	no	—
54	C₂×D₈×C₂₉	—	2	1	no	—
55	C₂×D₈×C₂₉	—	2	1	no	—
56	C₂²×C₈×C₂₉	—	2	1	no	—
57	C₂₉×C₄⋊Q₈	—	2	2	no	—
58	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₂₉×#127	C₂³	1	2	yes	—
60	C₂₉×#124	—	2	2	no	—
61	C₂₉×#124	—	2	2	no	—
62	C₂₉×#123	—	4	2	no	—
63	C₂₉×C₂²⋊Q₈	—	2	2	no	—
64	C₂₉×C₂²⋊Q₈	—	4	2	no	—
65	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
67	C₄×D₄×C₂₉	—	2	2	no	—
68	C₄×D₄×C₂₉	—	2	2	no	—
69	C₄×D₄×C₂₉	—	2	2	no	—
70	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
71	C₂₉×#107	D₄	1	1	yes	characteristic
72	C₂₉×#106	—	2	2	no	—
73	C₂₉×#106	D₄	1	1	yes	characteristic
74	C₂₉×C₄⋊C₈	—	2	1	no	—
75	C₂₉×C₄⋊C₈	—	2	2	no	—
76	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
79	C₂₉×#103	—	2	2	no	—
80	C₂₉×#103	—	2	2	no	—
81	C₂₉×#103	D₄	1	1	yes	characteristic
82	C₂₉×#103	D₄	1	2	yes	—
83	C₂₉×#102	—	2	2	no	—
84	C₂₉×#102	—	2	2	no	—
85	C₂₉×#102	—	2	2	no	—
86	C₂₉×#102	—	2	2	no	—
87	C₂₉×#102	—	4	2	no	—
88	C₂₉×#102	D₄	1	1	yes	characteristic
89	C₂₉×C₂²⋊C₈	—	2	1	no	—
90	C₂₉×#97	—	2	2	no	—
91	C₄×C₈×C₂₉	—	2	1	no	—
92	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₂₉	—	2	2	no	—
96	C₂×Q₈×C₂₉	—	4	2	no	—
97	C₂×Q₈×C₂₉	—	4	4	no	—
98	C₂×Q₈×C₂₉	—	8	2	no	—
99	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₂₉	—	2	2	no	—
102	C₂×D₄×C₂₉	—	2	2	no	—
103	C₂×D₄×C₂₉	—	2	2	no	—
104	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₂₉	—	2	1	no	—
106	C₂²×C₄×C₂₉	—	4	2	no	—
107	C₂²×C₄×C₂₉	—	4	2	no	—
108	Q₁₆×C₂₉	—	2	2	no	—
109	Q₁₆×C₂₉	—	4	4	no	—
110	Q₁₆×C₂₉	—	4	2	no	—
111	Q₁₆×C₂₉	—	8	1	no	—
112	SD₁₆×C₂₉	—	2	2	no	—
113	SD₁₆×C₂₉	—	8	2	no	—
114	D₈×C₂₉	—	4	4	no	—
115	D₈×C₂₉	—	4	2	no	—
116	D₈×C₂₉	—	8	1	no	—
117	C₂×C₈×C₂₉	—	2	1	no	—
118	C₂×C₈×C₂₉	—	2	2	no	—
119	C₂×C₈×C₂₉	—	2	1	no	—
120	C₂×C₈×C₂₉	—	2	1	no	—
121	C₂×C₈×C₂₉	—	4	2	no	—
122	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₂₉	—	2	2	no	—
127	C₄⋊C₄×C₂₉	—	2	1	no	—
128	C₄⋊C₄×C₂₉	—	2	2	no	—
129	C₄⋊C₄×C₂₉	—	2	2	no	—
130	C₄⋊C₄×C₂₉	—	4	2	no	—
131	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₂₉	—	2	1	no	—
135	C₂²⋊C₄×C₂₉	—	4	2	no	—
136	C₂²⋊C₄×C₂₉	—	4	2	no	—
137	C₂²⋊C₄×C₂₉	—	4	2	no	—
138	C₂²⋊C₄×C₂₉	—	4	2	no	—
139	C₄²×C₂₉	—	2	1	no	—
140	C₄²×C₂₉	—	2	2	no	—
141	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
142	#19935	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₂₉	—	2	1	no	—
144	C₂³×C₂₉	—	4	2	no	—
145	Q₈×C₂₉	—	2	1	no	—
146	Q₈×C₂₉	—	2	2	no	—
147	Q₈×C₂₉	—	2	2	no	—
148	Q₈×C₂₉	—	2	1	no	—
149	Q₈×C₂₉	—	4	2	no	—
150	Q₈×C₂₉	—	4	2	no	—
151	Q₈×C₂₉	—	8	4	no	—
152	D₄×C₂₉	—	2	1	no	—
153	D₄×C₂₉	—	4	2	no	—
154	D₄×C₂₉	—	4	2	no	—
155	D₄×C₂₉	—	4	2	no	—
156	D₄×C₂₉	—	4	2	no	—
157	D₄×C₂₉	—	8	2	no	—
158	D₄×C₂₉	#135	1	2	yes	—
159	C₂×C₄×C₂₉	—	2	1	no	—
160	C₂×C₄×C₂₉	—	2	2	no	—
161	C₂×C₄×C₂₉	—	2	1	no	—
162	C₂×C₄×C₂₉	—	2	2	no	—
163	C₂×C₄×C₂₉	—	2	1	no	—
164	C₂×C₄×C₂₉	—	4	1	no	—
165	C₂×C₄×C₂₉	—	4	1	no	—
166	C₂×C₄×C₂₉	—	4	2	no	—
167	C₂×C₄×C₂₉	—	8	4	no	—
168	C₂×C₄×C₂₉	—	16	2	no	—
169	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₈×C₂₉	—	2	1	no	—
173	C₈×C₂₉	—	2	1	no	—
174	C₈×C₂₉	—	2	1	no	—
175	C₈×C₂₉	—	4	1	no	—
176	C₈×C₂₉	—	4	2	no	—
177	C₈×C₂₉	—	4	1	no	—
178	C₈×C₂₉	—	4	1	no	—
179	C₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
180	#3396	C₂×C₂₉	1	1	yes	characteristic, complemented
181	#3373	C₂×C₂₉	1	2	yes	complemented
182	D₄×Q₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
183	#1709	C₂×C₂₉	1	1	yes	characteristic, complemented
184	#1702	C₂×C₂₉	1	2	yes	complemented
185	#1670	C₂×C₂₉	1	1	yes	characteristic, complemented
186	#1667	C₂×C₂₉	1	1	yes	characteristic
187	#1640	C₂×C₂₉	1	2	yes	complemented
188	#1627	C₂×C₂₉	1	2	yes	complemented
189	#1591	C₂×C₂₉	1	1	yes	characteristic, complemented
190	C₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
191	C₂²×C₂₉	—	2	2	no	—
192	C₂²×C₂₉	—	4	1	no	—
193	C₂²×C₂₉	—	4	1	no	—
194	C₂²×C₂₉	—	8	2	no	—
195	C₂²×C₂₉	—	8	2	no	—
196	C₂²×C₂₉	—	8	2	no	—
197	C₂²×C₂₉	D₄²	1	1	yes	characteristic
198	C₄×C₂₉	—	2	1	no	—
199	C₄×C₂₉	—	4	1	no	—
200	C₄×C₂₉	—	4	2	no	—
201	C₄×C₂₉	—	4	1	no	—
202	C₄×C₂₉	—	4	2	no	—
203	C₄×C₂₉	—	4	1	no	—
204	C₄×C₂₉	—	8	2	no	—
205	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
206	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
207	C₄×C₂₉	#576	1	1	yes	characteristic
208	C₄×C₂₉	#578	1	1	yes	characteristic
209	C₂²×Q₁₆	—	2	1	no	—
210	#559	C₂²×C₂₉	1	2	yes	—
211	D₄×Q₈	C₂²×C₂₉	1	2	yes	—
212	#495	—	2	1	no	—
213	#494	C₂²×C₂₉	1	1	yes	characteristic
214	#493	C₂²×C₂₉	1	1	yes	characteristic
215	#489	—	2	2	no	—
216	#486	C₂²×C₂₉	1	2	yes	—
217	#486	C₂²×C₂₉	1	2	yes	—
218	#476	—	2	2	no	—
219	#475	C₂²×C₂₉	1	2	yes	—
220	#467	—	2	1	no	—
221	#463	—	2	2	no	—
222	#463	—	2	2	no	—
223	#462	C₂²×C₂₉	1	2	yes	—
224	#460	C₂²×C₂₉	1	2	yes	—
225	#459	C₂²×C₂₉	1	2	yes	—
226	#451	—	2	2	no	—
227	#446	C₂²×C₂₉	1	2	yes	—
228	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic
229	#442	—	2	2	no	—
230	C₄×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
231	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
232	C₄×D₈	—	2	1	no	—
233	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic
234	#335	C₂²×C₂₉	1	1	yes	characteristic
235	#334	C₂²×C₂₉	1	1	yes	characteristic
236	#332	C₂²×C₂₉	1	2	yes	—
237	#331	C₂²×C₂₉	1	2	yes	—
238	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
239	Q₈⋊C₈	C₂²×C₂₉	1	2	yes	—
240	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
241	C₈²	C₂²×C₂₉	1	1	yes	characteristic
242	C₂×C₂₉	—	4	2	no	—
243	C₂×C₂₉	—	16	2	no	—
244	C₂×C₂₉	#3274	1	1	yes	characteristic
245	C₂×C₂₉	#3285	1	1	yes	characteristic
246	C₂×C₂₉	#3290	1	1	yes	characteristic
247	C₂²×Q₈	—	2	2	no	—
248	C₂×Q₁₆	—	2	2	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	4	4	no	—
252	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
261	#127	C₂³×C₂₉	1	2	yes	—
262	#124	—	2	2	no	—
263	#124	—	2	2	no	—
264	#123	—	4	2	no	—
265	C₂²⋊Q₈	—	2	2	no	—
266	C₂²⋊Q₈	—	4	2	no	—
267	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
268	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
273	#107	D₄×C₂₉	1	1	yes	characteristic
274	#106	—	2	2	no	—
275	#106	D₄×C₂₉	1	1	yes	characteristic
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
279	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
280	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#103	D₄×C₂₉	1	1	yes	characteristic
284	#103	D₄×C₂₉	1	2	yes	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	4	2	no	—
290	#102	D₄×C₂₉	1	1	yes	characteristic
291	C₂²⋊C₈	—	2	1	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
297	C₂₉	#19935	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	4	4	no	—
301	C₂×Q₈	—	8	2	no	—
302	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
303	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	Q₁₆	—	2	2	no	—
312	Q₁₆	—	4	4	no	—
313	Q₁₆	—	4	2	no	—
314	Q₁₆	—	8	1	no	—
315	SD₁₆	—	2	2	no	—
316	SD₁₆	—	8	2	no	—
317	D₈	—	4	4	no	—
318	D₈	—	4	2	no	—
319	D₈	—	8	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
335	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
336	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	2	no	—
344	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	2	1	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	8	4	no	—
354	D₄	—	2	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	2	no	—
360	D₄	C₂₉×#135	1	2	yes	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	—	16	2	no	—
371	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
373	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	D₄²×C₂₉	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
397	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
398	C₄	C₂₉×#576	1	1	yes	characteristic
399	C₄	C₂₉×#578	1	1	yes	characteristic
400	C₂	—	4	2	no	—
401	C₂	—	16	2	no	—
402	C₂	C₂₉×#3274	1	1	yes	characteristic
403	C₂	C₂₉×#3285	1	1	yes	characteristic
404	C₂	C₂₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#1667	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×#3396	C₂	semidirect
2. C₂₉×#3373	C₂	semidirect
3. D₄×Q₁₆×C₂₉	C₂	semidirect
4. C₂₉×#1709	C₂	semidirect
5. C₂₉×#1702	C₂	semidirect
6. C₂₉×#1670	C₂	semidirect
8. C₂₉×#1640	C₂	semidirect
9. C₂₉×#1627	C₂	semidirect
10. C₂₉×#1591	C₂	semidirect
11. C₈×SD₁₆×C₂₉	C₂	semidirect
142. #19935	C₂₉	direct (N × H)
180. #3396	C₂×C₂₉	semidirect
181. #3373	C₂×C₂₉	semidirect
182. D₄×Q₁₆	C₂×C₂₉	semidirect
183. #1709	C₂×C₂₉	semidirect
184. #1702	C₂×C₂₉	semidirect
185. #1670	C₂×C₂₉	semidirect
187. #1640	C₂×C₂₉	semidirect
188. #1627	C₂×C₂₉	semidirect
189. #1591	C₂×C₂₉	semidirect
190. C₈×SD₁₆	C₂×C₂₉	semidirect
297. C₂₉	#19935	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×#3396	2
C₂₉×#3373	2
D₄×Q₁₆×C₂₉	2
C₂₉×#1709	2
C₂₉×#1702	2
C₂₉×#1670	2
C₂₉×#1667	2
C₂₉×#1640	2
C₂₉×#1627	2
C₂₉×#1591	2
C₈×SD₁₆×C₂₉	2
#19935	29

Subgroups — C29×#19935 #20314835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19935 #20314835