Subgroups — C₂₉×#19294 #20314194

Order 7424.

694 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3115	C₂	1	2	yes	maximal, complemented
3	C₂₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#1690	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1686	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1685	C₂	1	2	yes	maximal, complemented
10	C₂₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1553	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₉×#135	—	2	1	no	—
13	C₂×C₂₉×#135	—	2	1	no	—
14	C₂₉×#532	C₂²	1	2	yes	—
15	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#495	—	2	1	no	—
17	C₂₉×#495	—	2	1	no	—
18	C₂₉×#494	C₂²	1	1	yes	characteristic
19	C₂₉×#493	C₂²	1	1	yes	characteristic
20	C₂₉×#492	C₂²	1	2	yes	—
21	C₂₉×#482	—	2	2	no	—
22	C₂₉×#475	C₂²	1	2	yes	—
23	C₂₉×#474	C₂²	1	2	yes	—
24	C₂₉×#460	C₂²	1	2	yes	—
25	C₂₉×#459	C₂²	1	2	yes	—
26	C₂₉×#449	—	2	2	no	—
27	C₂₉×#446	C₂²	1	1	yes	characteristic
28	C₂₉×#446	C₂²	1	1	yes	characteristic
29	C₂₉×#442	—	2	2	no	—
30	C₂₉×#440	—	2	2	no	—
31	C₂₉×#436	C₂²	1	1	yes	characteristic
32	C₂₉×#436	C₂²	1	1	yes	characteristic
33	C₂₉×#435	—	2	1	no	—
34	C₂₉×#435	—	2	1	no	—
35	C₂₉×#432	C₂²	1	2	yes	—
36	C₂₉×#431	—	2	1	no	—
37	C₂₉×#431	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₂₉	—	2	1	no	—
39	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic
40	C₂₉×#335	C₂²	1	2	yes	—
41	C₂₉×#334	C₂²	1	1	yes	characteristic
42	C₂₉×#334	C₂²	1	1	yes	characteristic
43	C₂₉×#332	C₂²	1	2	yes	—
44	C₂₉×#332	C₂²	1	2	yes	—
45	C₂₉×#331	C₂²	1	2	yes	—
46	C₂₉×#331	C₂²	1	2	yes	—
47	C₂×#41×C₂₉	—	2	2	no	—
48	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
49	C₂₉×#135	—	4	4	no	—
50	C₂₉×#135	—	4	4	no	—
51	C₂×Q₁₆×C₂₉	—	2	1	no	—
52	C₂×Q₁₆×C₂₉	—	2	1	no	—
53	C₂×SD₁₆×C₂₉	—	2	2	no	—
54	C₂×SD₁₆×C₂₉	—	2	2	no	—
55	C₂×SD₁₆×C₂₉	—	2	2	no	—
56	C₂×D₈×C₂₉	—	2	2	no	—
57	C₂×D₈×C₂₉	—	2	1	no	—
58	C₂×D₈×C₂₉	—	2	1	no	—
59	C₂×M₁₆×C₂₉	—	2	1	no	—
60	C₂×M₁₆×C₂₉	—	2	1	no	—
61	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₂₉	D₄	1	1	yes	characteristic
63	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₂₉×#127	C₂³	1	2	yes	—
65	C₂₉×#124	—	2	2	no	—
66	C₂₉×#121	—	2	2	no	—
67	C₂₉×#121	—	2	2	no	—
68	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₂₉	—	2	1	no	—
71	C₄×D₄×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	—	2	2	no	—
73	C₄×D₄×C₂₉	—	2	2	no	—
74	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
75	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
76	C₂₉×#117	—	2	1	no	—
77	C₂₉×#117	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₂₉	—	2	1	no	—
79	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
80	C₂₉×#107	—	2	2	no	—
81	C₂₉×#106	—	2	2	no	—
82	C₂₉×C₄⋊C₈	—	2	1	no	—
83	C₂₉×C₄⋊C₈	—	2	1	no	—
84	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
87	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
88	C₂₉×#103	—	2	2	no	—
89	C₂₉×#102	—	2	2	no	—
90	C₂₉×#102	—	2	2	no	—
91	C₂₉×#102	—	2	2	no	—
92	C₂₉×C₂²⋊C₈	—	2	1	no	—
93	C₂₉×C₂²⋊C₈	—	2	2	no	—
94	C₂₉×C₂²⋊C₈	—	2	1	no	—
95	C₂₉×C₂²⋊C₈	—	2	1	no	—
96	C₂₉×#97	—	2	1	no	—
97	C₂₉×#97	—	2	1	no	—
98	C₂₉×#97	—	2	2	no	—
99	C₄×C₈×C₂₉	—	2	1	no	—
100	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
101	C₄×C₈×C₂₉	D₄	1	1	yes	characteristic
102	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
104	#41×C₂₉	—	4	2	no	—
105	#41×C₂₉	—	4	4	no	—
106	#41×C₂₉	—	4	4	no	—
107	C₂×Q₈×C₂₉	—	2	2	no	—
108	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₂₉	—	2	1	no	—
110	C₂×D₄×C₂₉	—	2	2	no	—
111	C₂×D₄×C₂₉	—	2	2	no	—
112	C₂×D₄×C₂₉	—	2	2	no	—
113	C₂×D₄×C₂₉	—	4	2	no	—
114	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₂₉	—	2	1	no	—
116	C₂²×C₄×C₂₉	—	2	1	no	—
117	C₂²×C₄×C₂₉	—	2	1	no	—
118	C₂²×C₄×C₂₉	—	4	2	no	—
119	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
122	Q₁₆×C₂₉	—	4	2	no	—
123	Q₁₆×C₂₉	—	4	2	no	—
124	SD₁₆×C₂₉	—	4	4	no	—
125	SD₁₆×C₂₉	—	4	4	no	—
126	SD₁₆×C₂₉	—	4	4	no	—
127	D₈×C₂₉	—	4	2	no	—
128	D₈×C₂₉	—	4	4	no	—
129	D₈×C₂₉	—	4	2	no	—
130	M₁₆×C₂₉	—	4	2	no	—
131	M₁₆×C₂₉	—	4	2	no	—
132	C₂×C₈×C₂₉	—	2	2	no	—
133	C₂×C₈×C₂₉	—	2	2	no	—
134	C₂×C₈×C₂₉	—	2	1	no	—
135	C₂×C₈×C₂₉	—	2	1	no	—
136	C₂×C₈×C₂₉	—	2	2	no	—
137	C₂×C₈×C₂₉	—	2	2	no	—
138	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₄⋊C₄×C₂₉	—	2	1	no	—
144	C₄⋊C₄×C₂₉	—	2	2	no	—
145	C₄⋊C₄×C₂₉	—	2	2	no	—
146	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₂₉	—	2	1	no	—
149	C₂²⋊C₄×C₂₉	—	2	1	no	—
150	C₂²⋊C₄×C₂₉	—	2	1	no	—
151	C₂²⋊C₄×C₂₉	—	4	2	no	—
152	C₂²⋊C₄×C₂₉	—	4	2	no	—
153	C₄²×C₂₉	—	2	1	no	—
154	C₄²×C₂₉	—	2	1	no	—
155	C₄²×C₂₉	—	2	1	no	—
156	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₂₉	#41	1	1	yes	characteristic
159	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
160	#19294	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂³×C₂₉	—	2	1	no	—
162	C₂³×C₂₉	—	4	2	no	—
163	C₂³×C₂₉	#121	1	1	yes	characteristic
164	Q₈×C₂₉	—	2	2	no	—
165	Q₈×C₂₉	—	4	2	no	—
166	Q₈×C₂₉	—	4	2	no	—
167	D₄×C₂₉	—	2	2	no	—
168	D₄×C₂₉	—	4	2	no	—
169	D₄×C₂₉	—	4	2	no	—
170	D₄×C₂₉	—	4	2	no	—
171	D₄×C₂₉	—	4	2	no	—
172	D₄×C₂₉	—	4	2	no	—
173	D₄×C₂₉	—	8	2	no	—
174	D₄×C₂₉	—	8	4	no	—
175	C₂×C₄×C₂₉	—	2	1	no	—
176	C₂×C₄×C₂₉	—	2	1	no	—
177	C₂×C₄×C₂₉	—	2	2	no	—
178	C₂×C₄×C₂₉	—	2	1	no	—
179	C₂×C₄×C₂₉	—	2	1	no	—
180	C₂×C₄×C₂₉	—	2	1	no	—
181	C₂×C₄×C₂₉	—	4	1	no	—
182	C₂×C₄×C₂₉	—	4	2	no	—
183	C₂×C₄×C₂₉	—	4	2	no	—
184	C₂×C₄×C₂₉	—	4	1	no	—
185	C₂×C₄×C₂₉	—	4	1	no	—
186	C₂×C₄×C₂₉	—	4	2	no	—
187	C₂×C₄×C₂₉	—	8	4	no	—
188	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
191	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
194	C₈×C₂₉	—	2	1	no	—
195	C₈×C₂₉	—	2	1	no	—
196	C₈×C₂₉	—	4	1	no	—
197	C₈×C₂₉	—	4	1	no	—
198	C₈×C₂₉	—	4	2	no	—
199	C₈×C₂₉	—	4	2	no	—
200	C₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
201	C₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
202	#3147	C₂×C₂₉	1	1	yes	characteristic, complemented
203	#3115	C₂×C₂₉	1	2	yes	complemented
204	#2965	C₂×C₂₉	1	1	yes	characteristic, complemented
205	#1690	C₂×C₂₉	1	1	yes	characteristic, complemented
206	#1689	C₂×C₂₉	1	1	yes	characteristic, complemented
207	#1688	C₂×C₂₉	1	1	yes	characteristic, complemented
208	#1687	C₂×C₂₉	1	1	yes	characteristic, complemented
209	#1686	C₂×C₂₉	1	2	yes	complemented
210	#1685	C₂×C₂₉	1	2	yes	complemented
211	#1568	C₂×C₂₉	1	1	yes	characteristic, complemented
212	#1553	C₂×C₂₉	1	2	yes	complemented
213	C₂²×C₂₉	—	2	1	no	—
214	C₂²×C₂₉	—	2	1	no	—
215	C₂²×C₂₉	—	2	1	no	—
216	C₂²×C₂₉	—	4	1	no	—
217	C₂²×C₂₉	—	4	1	no	—
218	C₂²×C₂₉	—	4	1	no	—
219	C₂²×C₂₉	—	8	2	no	—
220	C₂²×C₂₉	—	8	2	no	—
221	C₂²×C₂₉	—	8	2	no	—
222	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
223	C₄×C₂₉	—	2	1	no	—
224	C₄×C₂₉	—	2	1	no	—
225	C₄×C₂₉	—	2	1	no	—
226	C₄×C₂₉	—	2	1	no	—
227	C₄×C₂₉	—	4	1	no	—
228	C₄×C₂₉	—	4	1	no	—
229	C₄×C₂₉	—	4	1	no	—
230	C₄×C₂₉	—	8	2	no	—
231	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₄×C₂₉	#575	1	2	yes	—
234	C₂×#135	—	2	1	no	—
235	C₂×#135	—	2	1	no	—
236	#532	C₂²×C₂₉	1	2	yes	—
237	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
238	#495	—	2	1	no	—
239	#495	—	2	1	no	—
240	#494	C₂²×C₂₉	1	1	yes	characteristic
241	#493	C₂²×C₂₉	1	1	yes	characteristic
242	#492	C₂²×C₂₉	1	2	yes	—
243	#482	—	2	2	no	—
244	#475	C₂²×C₂₉	1	2	yes	—
245	#474	C₂²×C₂₉	1	2	yes	—
246	#460	C₂²×C₂₉	1	2	yes	—
247	#459	C₂²×C₂₉	1	2	yes	—
248	#449	—	2	2	no	—
249	#446	C₂²×C₂₉	1	1	yes	characteristic
250	#446	C₂²×C₂₉	1	1	yes	characteristic
251	#442	—	2	2	no	—
252	#440	—	2	2	no	—
253	#436	C₂²×C₂₉	1	1	yes	characteristic
254	#436	C₂²×C₂₉	1	1	yes	characteristic
255	#435	—	2	1	no	—
256	#435	—	2	1	no	—
257	#432	C₂²×C₂₉	1	2	yes	—
258	#431	—	2	1	no	—
259	#431	C₂²×C₂₉	1	1	yes	characteristic
260	C₄×M₁₆	—	2	1	no	—
261	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic
262	#335	C₂²×C₂₉	1	2	yes	—
263	#334	C₂²×C₂₉	1	1	yes	characteristic
264	#334	C₂²×C₂₉	1	1	yes	characteristic
265	#332	C₂²×C₂₉	1	2	yes	—
266	#332	C₂²×C₂₉	1	2	yes	—
267	#331	C₂²×C₂₉	1	2	yes	—
268	#331	C₂²×C₂₉	1	2	yes	—
269	C₂×C₂₉	—	4	1	no	—
270	C₂×C₂₉	—	8	1	no	—
271	C₂×C₂₉	—	16	2	no	—
272	C₂×C₂₉	#3038	1	1	yes	characteristic
273	C₂×C₂₉	#3054	1	1	yes	characteristic
274	C₂×C₂₉	#3067	1	1	yes	characteristic
275	C₂×#41	—	2	2	no	—
276	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
277	#135	—	4	4	no	—
278	#135	—	4	4	no	—
279	C₂×Q₁₆	—	2	1	no	—
280	C₂×Q₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
290	C₂²×C₈	D₄×C₂₉	1	1	yes	characteristic
291	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
292	#127	C₂³×C₂₉	1	2	yes	—
293	#124	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	—	2	2	no	—
296	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
303	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	#117	D₄×C₂₉	1	1	yes	characteristic
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
308	#107	—	2	2	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
315	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
316	#103	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	#97	—	2	1	no	—
325	#97	—	2	1	no	—
326	#97	—	2	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
329	C₄×C₈	D₄×C₂₉	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
332	C₂₉	#19294	1	1	yes	characteristic, direct product factor, Sylow
333	#41	—	4	2	no	—
334	#41	—	4	4	no	—
335	#41	—	4	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
350	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
351	Q₁₆	—	4	2	no	—
352	Q₁₆	—	4	2	no	—
353	SD₁₆	—	4	4	no	—
354	SD₁₆	—	4	4	no	—
355	SD₁₆	—	4	4	no	—
356	D₈	—	4	2	no	—
357	D₈	—	4	4	no	—
358	D₈	—	4	2	no	—
359	M₁₆	—	4	2	no	—
360	M₁₆	—	4	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
386	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
387	C₄²	#41×C₂₉	1	1	yes	characteristic
388	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₂₉×#121	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
417	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
418	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	—	4	2	no	—
428	C₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
429	C₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
449	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
450	C₄	C₂₉×#575	1	2	yes	—
451	C₂	—	4	1	no	—
452	C₂	—	8	1	no	—
453	C₂	—	16	2	no	—
454	C₂	C₂₉×#3038	1	1	yes	characteristic
455	C₂	C₂₉×#3054	1	1	yes	characteristic
456	C₂	C₂₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
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×#3147	C₂	semidirect
2. C₂₉×#3115	C₂	semidirect
3. C₂₉×#2965	C₂	semidirect
4. C₂₉×#1690	C₂	semidirect
5. C₂₉×#1689	C₂	semidirect
6. C₂₉×#1688	C₂	semidirect
7. C₂₉×#1687	C₂	semidirect
8. C₂₉×#1686	C₂	semidirect
9. C₂₉×#1685	C₂	semidirect
10. C₂₉×#1568	C₂	semidirect
11. C₂₉×#1553	C₂	semidirect
160. #19294	C₂₉	direct (N × H)
202. #3147	C₂×C₂₉	semidirect
203. #3115	C₂×C₂₉	semidirect
204. #2965	C₂×C₂₉	semidirect
205. #1690	C₂×C₂₉	semidirect
206. #1689	C₂×C₂₉	semidirect
207. #1688	C₂×C₂₉	semidirect
208. #1687	C₂×C₂₉	semidirect
209. #1686	C₂×C₂₉	semidirect
210. #1685	C₂×C₂₉	semidirect
211. #1568	C₂×C₂₉	semidirect
212. #1553	C₂×C₂₉	semidirect
332. C₂₉	#19294	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×#3147	2
C₂₉×#3115	2
C₂₉×#2965	2
C₂₉×#1690	2
C₂₉×#1689	2
C₂₉×#1688	2
C₂₉×#1687	2
C₂₉×#1686	2
C₂₉×#1685	2
C₂₉×#1568	2
C₂₉×#1553	2
#19294	29

Subgroups — C29×#19294 #20314194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19294 #20314194