Subgroups — C₂₉×#19504 #20314404

Order 7424.

652 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3205	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1697	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1685	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1677	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1554	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#533	C₂²	1	1	yes	characteristic
13	C₂₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
15	C₂₉×#501	—	2	1	no	—
16	C₂₉×#493	—	2	1	no	—
17	C₂₉×#492	C₂²	1	1	yes	characteristic
18	C₂₉×#492	C₂²	1	1	yes	characteristic
19	C₂₉×#490	—	2	1	no	—
20	C₂₉×#486	—	2	1	no	—
21	C₂₉×#486	C₂²	1	1	yes	characteristic
22	C₂₉×#486	C₂²	1	1	yes	characteristic
23	C₂₉×#482	—	2	2	no	—
24	C₂₉×#476	C₂²	1	2	yes	complemented
25	C₂₉×#474	C₂²	1	2	yes	complemented
26	C₂₉×#460	—	2	2	no	—
27	C₂₉×#459	C₂²	1	2	yes	—
28	C₂₉×#459	C₂²	1	2	yes	—
29	C₂₉×#450	—	2	2	no	—
30	C₂₉×#447	—	2	2	no	—
31	C₂₉×#436	C₂²	1	2	yes	complemented
32	C₂₉×#435	—	2	2	no	—
33	C₈×D₄×C₂₉	C₂²	1	2	yes	complemented
34	C₂₉×#432	C₂²	1	1	yes	characteristic
35	C₂₉×#432	C₂²	1	1	yes	characteristic
36	C₂₉×#431	C₂²	1	1	yes	characteristic
37	C₂₉×#431	C₂²	1	1	yes	characteristic
38	C₂₉×#408	—	2	2	no	—
39	C₂₉×#335	C₂²	1	2	yes	complemented
40	C₂₉×#334	C₂²	1	2	yes	complemented
41	C₂₉×#333	C₂²	1	2	yes	complemented
42	C₂₉×#332	C₂²	1	2	yes	complemented
43	C₂₉×#331	C₂²	1	2	yes	—
44	C₂₉×#331	C₂²	1	2	yes	—
45	C₂×#41×C₂₉	—	2	1	no	—
46	C₂²×D₄×C₂₉	—	2	1	no	—
47	C₂²×D₄×C₂₉	—	2	1	no	—
48	C₂²×D₄×C₂₉	—	2	1	no	—
49	C₂×SD₁₆×C₂₉	—	2	2	no	—
50	C₂×SD₁₆×C₂₉	—	2	2	no	—
51	C₂×D₈×C₂₉	—	2	2	no	—
52	C₂×D₈×C₂₉	—	2	2	no	—
53	C₂×M₁₆×C₂₉	—	2	2	no	—
54	C₂²×C₈×C₂₉	—	2	2	no	—
55	C₂₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₂₉×#127	—	2	1	no	—
59	C₂₉×#127	—	2	1	no	—
60	C₂₉×#127	—	2	1	no	—
61	C₂₉×#127	D₄	1	1	yes	characteristic
62	C₂₉×#127	C₂³	1	1	yes	characteristic
63	C₂₉×#127	C₂³	1	1	yes	characteristic
64	C₂₉×#125	—	2	1	no	—
65	C₂₉×#124	—	2	1	no	—
66	C₂₉×C₂²⋊Q₈	—	2	1	no	—
67	C₂₉×C₂²⋊Q₈	—	2	1	no	—
68	C₂₉×#121	—	2	1	no	—
69	C₂₉×#121	D₄	1	2	yes	—
70	C₄×Q₈×C₂₉	—	2	1	no	—
71	C₄×Q₈×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	—	2	1	no	—
73	C₄×D₄×C₂₉	C₂³	1	2	yes	—
74	C₂₉×#117	—	2	1	no	—
75	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
76	C₂₉×#107	—	2	2	no	—
77	C₂₉×#106	—	2	2	no	—
78	C₂₉×C₄⋊C₈	D₄	1	2	yes	—
79	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
80	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
81	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
82	C₂₉×#102	—	2	2	no	—
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	—	2	2	no	—
88	C₂₉×C₂²⋊C₈	—	2	1	no	—
89	C₂₉×C₂²⋊C₈	—	2	1	no	—
90	C₂₉×C₂²⋊C₈	—	2	1	no	—
91	C₂₉×C₂²⋊C₈	—	2	2	no	—
92	C₂₉×C₂²⋊C₈	—	2	2	no	—
93	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
94	C₂₉×#97	—	2	1	no	—
95	C₂₉×#97	—	2	1	no	—
96	C₄×C₈×C₂₉	—	2	1	no	—
97	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
99	C₂⁴×C₂₉	—	4	1	no	—
100	#41×C₂₉	—	8	2	no	—
101	C₂×Q₈×C₂₉	—	2	1	no	—
102	C₂×Q₈×C₂₉	—	2	1	no	—
103	C₂×Q₈×C₂₉	—	2	1	no	—
104	C₂×D₄×C₂₉	—	2	2	no	—
105	C₂×D₄×C₂₉	—	2	1	no	—
106	C₂×D₄×C₂₉	—	2	1	no	—
107	C₂×D₄×C₂₉	—	2	1	no	—
108	C₂×D₄×C₂₉	—	2	1	no	—
109	C₂×D₄×C₂₉	—	2	1	no	—
110	C₂×D₄×C₂₉	—	2	1	no	—
111	C₂×D₄×C₂₉	—	2	1	no	—
112	C₂×D₄×C₂₉	—	2	1	no	—
113	C₂×D₄×C₂₉	—	4	1	no	—
114	C₂×D₄×C₂₉	—	4	1	no	—
115	C₂×D₄×C₂₉	—	4	1	no	—
116	C₂×D₄×C₂₉	—	8	2	no	—
117	C₂×D₄×C₂₉	—	8	2	no	—
118	C₂×D₄×C₂₉	—	8	2	no	—
119	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₂₉	—	2	2	no	—
121	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
124	SD₁₆×C₂₉	—	8	2	no	—
125	SD₁₆×C₂₉	—	8	2	no	—
126	D₈×C₂₉	—	8	2	no	—
127	D₈×C₂₉	—	8	2	no	—
128	M₁₆×C₂₉	—	8	2	no	—
129	C₂×C₈×C₂₉	—	2	2	no	—
130	C₂×C₈×C₂₉	—	2	2	no	—
131	C₂×C₈×C₂₉	—	2	2	no	—
132	C₂×C₈×C₂₉	—	8	2	no	—
133	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₂₉	—	2	1	no	—
136	C₄⋊C₄×C₂₉	—	2	1	no	—
137	C₄⋊C₄×C₂₉	—	2	1	no	—
138	C₄⋊C₄×C₂₉	—	2	1	no	—
139	C₄⋊C₄×C₂₉	—	2	1	no	—
140	C₄⋊C₄×C₂₉	—	4	1	no	—
141	C₄⋊C₄×C₂₉	—	4	1	no	—
142	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₂₉	—	2	2	no	—
144	C₂²⋊C₄×C₂₉	—	2	2	no	—
145	C₂²⋊C₄×C₂₉	—	4	1	no	—
146	C₄²×C₂₉	—	4	1	no	—
147	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₂₉	#41	1	1	yes	characteristic
150	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
151	#19504	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₂₉	—	2	2	no	—
153	C₂³×C₂₉	—	4	1	no	—
154	C₂³×C₂₉	—	4	1	no	—
155	C₂³×C₂₉	—	8	2	no	—
156	C₂³×C₂₉	—	8	2	no	—
157	C₂³×C₂₉	—	8	2	no	—
158	C₂³×C₂₉	#121	1	1	yes	characteristic
159	Q₈×C₂₉	—	4	2	no	—
160	Q₈×C₂₉	—	8	1	no	—
161	Q₈×C₂₉	—	8	1	no	—
162	D₄×C₂₉	—	2	2	no	—
163	D₄×C₂₉	—	2	2	no	—
164	D₄×C₂₉	—	4	2	no	—
165	D₄×C₂₉	—	4	2	no	—
166	D₄×C₂₉	—	4	2	no	—
167	D₄×C₂₉	—	4	2	no	—
168	D₄×C₂₉	—	8	1	no	—
169	D₄×C₂₉	—	8	1	no	—
170	D₄×C₂₉	—	8	1	no	—
171	D₄×C₂₉	—	8	1	no	—
172	D₄×C₂₉	—	8	2	no	—
173	D₄×C₂₉	—	8	2	no	—
174	D₄×C₂₉	—	8	2	no	—
175	D₄×C₂₉	—	8	2	no	—
176	C₂×C₄×C₂₉	—	2	2	no	—
177	C₂×C₄×C₂₉	—	2	2	no	—
178	C₂×C₄×C₂₉	—	2	2	no	—
179	C₂×C₄×C₂₉	—	4	1	no	—
180	C₂×C₄×C₂₉	—	4	2	no	—
181	C₂×C₄×C₂₉	—	4	2	no	—
182	C₂×C₄×C₂₉	—	4	1	no	—
183	C₂×C₄×C₂₉	—	4	1	no	—
184	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₂₉	—	2	2	no	—
191	C₈×C₂₉	—	2	2	no	—
192	C₈×C₂₉	—	4	2	no	—
193	C₈×C₂₉	—	4	2	no	—
194	C₈×C₂₉	—	4	2	no	—
195	#3235	C₂×C₂₉	1	1	yes	characteristic, complemented
196	#3208	C₂×C₂₉	1	1	yes	characteristic, complemented
197	#3205	C₂×C₂₉	1	1	yes	characteristic
198	#2981	C₂×C₂₉	1	1	yes	characteristic, complemented
199	#1697	C₂×C₂₉	1	2	yes	complemented
200	#1685	C₂×C₂₉	1	2	yes	complemented
201	#1677	C₂×C₂₉	1	2	yes	complemented
202	#1665	C₂×C₂₉	1	2	yes	complemented
203	#1572	C₂×C₂₉	1	1	yes	characteristic, complemented
204	#1555	C₂×C₂₉	1	1	yes	characteristic, complemented
205	#1554	C₂×C₂₉	1	1	yes	characteristic, complemented
206	C₂²×C₂₉	—	2	1	no	—
207	C₂²×C₂₉	—	2	1	no	—
208	C₂²×C₂₉	—	2	1	no	—
209	C₂²×C₂₉	—	4	2	no	—
210	C₂²×C₂₉	—	4	2	no	—
211	C₂²×C₂₉	—	4	2	no	—
212	C₂²×C₂₉	—	8	1	no	—
213	C₂²×C₂₉	—	8	1	no	—
214	C₂²×C₂₉	—	8	1	no	—
215	C₂²×C₂₉	—	8	1	no	—
216	C₂²×C₂₉	—	8	1	no	—
217	C₂²×C₂₉	—	8	1	no	—
218	C₂²×C₂₉	—	16	4	no	—
219	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
220	C₄×C₂₉	—	2	1	no	—
221	C₄×C₂₉	—	2	1	no	—
222	C₄×C₂₉	—	2	1	no	—
223	C₄×C₂₉	—	2	1	no	—
224	C₄×C₂₉	—	4	2	no	—
225	C₄×C₂₉	—	8	1	no	—
226	C₄×C₂₉	—	8	1	no	—
227	C₄×C₂₉	#576	1	2	yes	—
228	C₄×C₂₉	#577	1	2	yes	—
229	#533	C₂²×C₂₉	1	1	yes	characteristic
230	#532	C₂²×C₂₉	1	1	yes	characteristic
231	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
232	#501	—	2	1	no	—
233	#493	—	2	1	no	—
234	#492	C₂²×C₂₉	1	1	yes	characteristic
235	#492	C₂²×C₂₉	1	1	yes	characteristic
236	#490	—	2	1	no	—
237	#486	—	2	1	no	—
238	#486	C₂²×C₂₉	1	1	yes	characteristic
239	#486	C₂²×C₂₉	1	1	yes	characteristic
240	#482	—	2	2	no	—
241	#476	C₂²×C₂₉	1	2	yes	complemented
242	#474	C₂²×C₂₉	1	2	yes	complemented
243	#460	—	2	2	no	—
244	#459	C₂²×C₂₉	1	2	yes	—
245	#459	C₂²×C₂₉	1	2	yes	—
246	#450	—	2	2	no	—
247	#447	—	2	2	no	—
248	#436	C₂²×C₂₉	1	2	yes	complemented
249	#435	—	2	2	no	—
250	C₈×D₄	C₂²×C₂₉	1	2	yes	complemented
251	#432	C₂²×C₂₉	1	1	yes	characteristic
252	#432	C₂²×C₂₉	1	1	yes	characteristic
253	#431	C₂²×C₂₉	1	1	yes	characteristic
254	#431	C₂²×C₂₉	1	1	yes	characteristic
255	#408	—	2	2	no	—
256	#335	C₂²×C₂₉	1	2	yes	complemented
257	#334	C₂²×C₂₉	1	2	yes	complemented
258	#333	C₂²×C₂₉	1	2	yes	complemented
259	#332	C₂²×C₂₉	1	2	yes	complemented
260	#331	C₂²×C₂₉	1	2	yes	—
261	#331	C₂²×C₂₉	1	2	yes	—
262	C₂×C₂₉	—	4	1	no	—
263	C₂×C₂₉	—	8	2	no	—
264	C₂×C₂₉	—	16	1	no	—
265	C₂×C₂₉	—	16	1	no	—
266	C₂×C₂₉	#3041	1	1	yes	characteristic
267	C₂×C₂₉	#3057	1	1	yes	characteristic
268	C₂×C₂₉	#3068	1	1	yes	characteristic
269	C₂×#41	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₄⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	D₄×C₂₉	1	1	yes	characteristic
286	#127	C₂³×C₂₉	1	1	yes	characteristic
287	#127	C₂³×C₂₉	1	1	yes	characteristic
288	#125	—	2	1	no	—
289	#124	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	D₄×C₂₉	1	2	yes	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	C₂³×C₂₉	1	2	yes	—
298	#117	—	2	1	no	—
299	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	#106	—	2	2	no	—
302	C₄⋊C₈	D₄×C₂₉	1	2	yes	—
303	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
304	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
305	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
318	#97	—	2	1	no	—
319	#97	—	2	1	no	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
322	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
323	C₂₉	#19504	1	1	yes	characteristic, direct product factor, Sylow
324	C₂⁴	—	4	1	no	—
325	#41	—	8	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	8	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
348	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
349	SD₁₆	—	8	2	no	—
350	SD₁₆	—	8	2	no	—
351	D₈	—	8	2	no	—
352	D₈	—	8	2	no	—
353	M₁₆	—	8	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	8	2	no	—
358	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₄²	—	4	1	no	—
372	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
374	C₄²	#41×C₂₉	1	1	yes	characteristic
375	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
376	C₂³	—	2	2	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	—	8	2	no	—
382	C₂³	C₂₉×#121	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	8	1	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
409	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
410	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	4	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	16	4	no	—
432	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	C₂₉×#576	1	2	yes	—
441	C₄	C₂₉×#577	1	2	yes	—
442	C₂	—	4	1	no	—
443	C₂	—	8	2	no	—
444	C₂	—	16	1	no	—
445	C₂	—	16	1	no	—
446	C₂	C₂₉×#3041	1	1	yes	characteristic
447	C₂	C₂₉×#3057	1	1	yes	characteristic
448	C₂	C₂₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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
1. C₂₉×#3235	C₂	semidirect
2. C₂₉×#3208	C₂	semidirect
4. C₂₉×#2981	C₂	semidirect
5. C₂₉×#1697	C₂	semidirect
6. C₂₉×#1685	C₂	semidirect
7. C₂₉×#1677	C₂	semidirect
8. C₂₉×#1665	C₂	semidirect
9. C₂₉×#1572	C₂	semidirect
10. C₂₉×#1555	C₂	semidirect
11. C₂₉×#1554	C₂	semidirect
24. C₂₉×#476	C₂²	semidirect
25. C₂₉×#474	C₂²	semidirect
31. C₂₉×#436	C₂²	semidirect
33. C₈×D₄×C₂₉	C₂²	semidirect
39. C₂₉×#335	C₂²	semidirect
40. C₂₉×#334	C₂²	semidirect
41. C₂₉×#333	C₂²	semidirect
42. C₂₉×#332	C₂²	semidirect
151. #19504	C₂₉	direct (N × H)
195. #3235	C₂×C₂₉	semidirect
196. #3208	C₂×C₂₉	semidirect
198. #2981	C₂×C₂₉	semidirect
199. #1697	C₂×C₂₉	semidirect
200. #1685	C₂×C₂₉	semidirect
201. #1677	C₂×C₂₉	semidirect
202. #1665	C₂×C₂₉	semidirect
203. #1572	C₂×C₂₉	semidirect
204. #1555	C₂×C₂₉	semidirect
205. #1554	C₂×C₂₉	semidirect
241. #476	C₂²×C₂₉	semidirect
242. #474	C₂²×C₂₉	semidirect
248. #436	C₂²×C₂₉	semidirect
250. C₈×D₄	C₂²×C₂₉	semidirect
256. #335	C₂²×C₂₉	semidirect
257. #334	C₂²×C₂₉	semidirect
258. #333	C₂²×C₂₉	semidirect
259. #332	C₂²×C₂₉	semidirect
323. C₂₉	#19504	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×#3235	2
C₂₉×#3208	2
C₂₉×#3205	2
C₂₉×#2981	2
C₂₉×#1697	2
C₂₉×#1685	2
C₂₉×#1677	2
C₂₉×#1665	2
C₂₉×#1572	2
C₂₉×#1555	2
C₂₉×#1554	2
#19504	29

Subgroups — C29×#19504 #20314404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19504 #20314404