Subgroups — C₂₉×#19415 #20314315

Order 7424.

640 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3076	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#3039	C₂	1	1	yes	maximal, characteristic
4	C₂₉×#2988	C₂	1	1	yes	maximal, characteristic
5	C₂₉×#1680	C₂	1	2	yes	maximal, complemented
6	C₂₉×#1679	C₂	1	2	yes	maximal, complemented
7	C₂₉×#1672	C₂	1	2	yes	maximal, complemented
8	C₂₉×#1671	C₂	1	2	yes	maximal, complemented
9	C₂₉×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₉×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#137	—	2	1	no	—
13	C₂₉×#533	C₂²	1	1	yes	characteristic
14	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#498	C₂²	1	2	yes	—
17	C₂₉×#487	C₂²	1	2	yes	—
18	C₂₉×#483	—	2	2	no	—
19	C₂₉×#479	—	2	1	no	—
20	C₂₉×#478	—	2	1	no	—
21	C₂₉×#477	C₂²	1	1	yes	characteristic
22	C₂₉×#476	C₂²	1	1	yes	characteristic
23	C₂₉×#475	—	2	1	no	—
24	C₂₉×#475	—	2	1	no	—
25	C₂₉×#475	C₂²	1	1	yes	characteristic
26	C₂₉×#474	C₂²	1	1	yes	characteristic
27	C₂₉×#462	—	2	1	no	—
28	C₂₉×#462	C₂²	1	2	yes	—
29	C₂₉×#461	—	2	1	no	—
30	C₂₉×#461	C₂²	1	2	yes	—
31	C₈×Q₈×C₂₉	C₂²	1	2	yes	—
32	C₈×D₄×C₂₉	—	2	2	no	—
33	C₈×D₄×C₂₉	C₂²	1	2	yes	—
34	C₂₉×#431	—	2	1	no	—
35	C₂₉×#431	C₂²	1	1	yes	characteristic
36	C₂₉×#427	—	2	1	no	—
37	C₂₉×#423	C₂²	1	1	yes	characteristic
38	C₂×C₂₉×C₄⋊C₈	—	2	1	no	—
39	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂₉×#419	—	2	1	no	—
42	C₂₉×#416	—	2	1	no	—
43	C₂₉×#334	C₂²	1	2	yes	—
44	C₂₉×#334	C₂²	1	2	yes	—
45	C₂₉×#333	C₂²	1	2	yes	—
46	C₂₉×#332	C₂²	1	2	yes	—
47	C₂₉×#332	C₂²	1	2	yes	—
48	C₂₉×#332	C₂²	1	2	yes	—
49	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₂₉	—	2	1	no	—
51	C₂₉×#137	—	4	4	no	—
52	C₂×Q₁₆×C₂₉	—	2	2	no	—
53	C₂×SD₁₆×C₂₉	—	2	2	no	—
54	C₂×M₁₆×C₂₉	—	2	1	no	—
55	C₂²×C₈×C₂₉	—	2	1	no	—
56	C₂²×C₈×C₂₉	—	2	1	no	—
57	C₂²×C₈×C₂₉	—	2	2	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	C₂³	1	2	yes	—
62	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₂₉×#125	—	2	1	no	—
65	C₂₉×C₂²⋊Q₈	—	2	1	no	—
66	C₂₉×C₂²⋊Q₈	—	2	1	no	—
67	C₄×Q₈×C₂₉	—	2	1	no	—
68	C₄×Q₈×C₂₉	—	2	1	no	—
69	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
70	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₂₉	—	2	1	no	—
72	C₄×D₄×C₂₉	—	2	1	no	—
73	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
74	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
75	C₂₉×#117	—	2	1	no	—
76	C₂₉×#117	—	2	1	no	—
77	C₂₉×#117	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
80	C₂×C₄²×C₂₉	—	2	1	no	—
81	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
82	C₂₉×#107	—	2	1	no	—
83	C₂₉×#107	—	2	1	no	—
84	C₂₉×#106	—	2	2	no	—
85	C₂₉×#106	—	2	2	no	—
86	C₂₉×#106	—	2	1	no	—
87	C₂₉×#106	—	2	1	no	—
88	C₂₉×C₄⋊C₈	—	2	2	no	—
89	C₂₉×C₄⋊C₈	—	2	1	no	—
90	C₂₉×C₄⋊C₈	—	2	1	no	—
91	C₂₉×C₄⋊C₈	—	2	1	no	—
92	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₂₉×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
95	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
96	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₂₉×#103	—	2	1	no	—
99	C₂₉×#103	—	2	1	no	—
100	C₂₉×#103	—	2	2	no	—
101	C₂₉×#103	—	2	2	no	—
102	C₂₉×#103	—	2	2	no	—
103	C₂₉×#103	—	2	2	no	—
104	C₂₉×#102	—	2	1	no	—
105	C₂₉×#102	—	2	1	no	—
106	C₂₉×C₂²⋊C₈	—	2	2	no	—
107	C₂₉×C₂²⋊C₈	D₄	1	2	yes	—
108	C₄×C₈×C₂₉	—	2	2	no	—
109	C₄×C₈×C₂₉	C₂³	1	2	yes	—
110	#41×C₂₉	—	2	2	no	—
111	#41×C₂₉	SD₁₆	1	4	yes	—
112	C₂×Q₈×C₂₉	—	2	1	no	—
113	C₂×Q₈×C₂₉	—	2	2	no	—
114	C₂×Q₈×C₂₉	—	2	1	no	—
115	C₂×Q₈×C₂₉	—	4	1	no	—
116	C₂×Q₈×C₂₉	—	4	2	no	—
117	C₂×Q₈×C₂₉	—	4	2	no	—
118	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
119	C₂×D₄×C₂₉	—	2	1	no	—
120	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₂₉	—	2	1	no	—
122	C₂²×C₄×C₂₉	—	2	1	no	—
123	C₂²×C₄×C₂₉	—	2	1	no	—
124	C₂²×C₄×C₂₉	—	4	1	no	—
125	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₂₉	#41	1	1	yes	characteristic
128	Q₁₆×C₂₉	—	4	4	no	—
129	SD₁₆×C₂₉	—	4	4	no	—
130	M₁₆×C₂₉	—	4	2	no	—
131	C₂×C₈×C₂₉	—	2	2	no	—
132	C₂×C₈×C₂₉	—	2	1	no	—
133	C₂×C₈×C₂₉	—	2	1	no	—
134	C₂×C₈×C₂₉	—	2	2	no	—
135	C₂×C₈×C₂₉	—	4	2	no	—
136	C₂×C₈×C₂₉	—	8	2	no	—
137	C₂×C₈×C₂₉	—	8	1	no	—
138	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₂₉	—	2	1	no	—
141	C₄⋊C₄×C₂₉	—	2	1	no	—
142	C₄⋊C₄×C₂₉	—	2	2	no	—
143	C₄⋊C₄×C₂₉	—	2	1	no	—
144	C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₄⋊C₄×C₂₉	—	2	1	no	—
146	C₄⋊C₄×C₂₉	—	2	2	no	—
147	C₄⋊C₄×C₂₉	—	2	1	no	—
148	C₄⋊C₄×C₂₉	—	4	1	no	—
149	C₄⋊C₄×C₂₉	—	4	1	no	—
150	C₄⋊C₄×C₂₉	—	4	1	no	—
151	C₄⋊C₄×C₂₉	—	4	1	no	—
152	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
153	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₂₉	—	2	1	no	—
155	C₂²⋊C₄×C₂₉	—	2	1	no	—
156	C₂²⋊C₄×C₂₉	—	2	1	no	—
157	C₂²⋊C₄×C₂₉	—	4	1	no	—
158	C₄²×C₂₉	—	2	1	no	—
159	C₄²×C₂₉	—	2	1	no	—
160	C₄²×C₂₉	—	2	1	no	—
161	C₄²×C₂₉	—	4	1	no	—
162	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₂₉	#41	1	1	yes	characteristic
165	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
166	#19415	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂³×C₂₉	—	2	1	no	—
168	C₂³×C₂₉	#121	1	1	yes	characteristic
169	Q₈×C₂₉	—	2	1	no	—
170	Q₈×C₂₉	—	4	2	no	—
171	Q₈×C₂₉	—	4	2	no	—
172	Q₈×C₂₉	—	4	1	no	—
173	Q₈×C₂₉	—	4	1	no	—
174	Q₈×C₂₉	—	8	1	no	—
175	Q₈×C₂₉	—	8	2	no	—
176	Q₈×C₂₉	C₂×SD₁₆	1	2	yes	—
177	D₄×C₂₉	—	2	4	no	—
178	D₄×C₂₉	—	2	1	no	—
179	D₄×C₂₉	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₂₉	—	2	1	no	—
181	C₂×C₄×C₂₉	—	2	1	no	—
182	C₂×C₄×C₂₉	—	2	1	no	—
183	C₂×C₄×C₂₉	—	2	4	no	—
184	C₂×C₄×C₂₉	—	2	1	no	—
185	C₂×C₄×C₂₉	—	2	1	no	—
186	C₂×C₄×C₂₉	—	4	1	no	—
187	C₂×C₄×C₂₉	—	4	1	no	—
188	C₂×C₄×C₂₉	—	4	1	no	—
189	C₂×C₄×C₂₉	—	4	1	no	—
190	C₂×C₄×C₂₉	—	4	1	no	—
191	C₂×C₄×C₂₉	—	4	2	no	—
192	C₂×C₄×C₂₉	—	8	1	no	—
193	C₂×C₄×C₂₉	—	8	2	no	—
194	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₂₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₂₉	C₂×SD₁₆	1	2	yes	—
198	C₂×C₄×C₂₉	#135	1	2	yes	—
199	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
202	C₈×C₂₉	—	2	2	no	—
203	C₈×C₂₉	—	2	2	no	—
204	C₈×C₂₉	—	4	2	no	—
205	C₈×C₂₉	—	4	1	no	—
206	C₈×C₂₉	—	4	1	no	—
207	C₈×C₂₉	—	4	2	no	—
208	#3229	C₂×C₂₉	1	1	yes	characteristic, complemented
209	#3076	C₂×C₂₉	1	1	yes	characteristic
210	#3039	C₂×C₂₉	1	1	yes	characteristic
211	#2988	C₂×C₂₉	1	1	yes	characteristic
212	#1680	C₂×C₂₉	1	2	yes	complemented
213	#1679	C₂×C₂₉	1	2	yes	complemented
214	#1672	C₂×C₂₉	1	2	yes	complemented
215	#1671	C₂×C₂₉	1	2	yes	complemented
216	#1570	C₂×C₂₉	1	1	yes	characteristic, complemented
217	#1550	C₂×C₂₉	1	1	yes	characteristic, complemented
218	C₂×#332	C₂×C₂₉	1	1	yes	characteristic, complemented
219	C₂²×C₂₉	—	2	1	no	—
220	C₂²×C₂₉	—	2	1	no	—
221	C₂²×C₂₉	—	2	2	no	—
222	C₂²×C₂₉	—	4	1	no	—
223	C₂²×C₂₉	—	4	1	no	—
224	C₂²×C₂₉	#465	1	2	yes	—
225	C₂²×C₂₉	C₂×#121	1	1	yes	characteristic
226	C₄×C₂₉	—	2	1	no	—
227	C₄×C₂₉	—	2	2	no	—
228	C₄×C₂₉	—	2	1	no	—
229	C₄×C₂₉	—	2	1	no	—
230	C₄×C₂₉	—	4	1	no	—
231	C₄×C₂₉	—	4	1	no	—
232	C₄×C₂₉	—	8	1	no	—
233	C₄×C₂₉	—	8	2	no	—
234	C₄×C₂₉	—	8	1	no	—
235	C₄×C₂₉	#465	1	2	yes	—
236	C₄×C₂₉	C₂²×SD₁₆	1	1	yes	characteristic
237	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
238	C₄×C₂₉	#577	1	1	yes	characteristic
239	C₄×C₂₉	#578	1	1	yes	characteristic
240	C₂×#137	—	2	1	no	—
241	#533	C₂²×C₂₉	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
243	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
244	#498	C₂²×C₂₉	1	2	yes	—
245	#487	C₂²×C₂₉	1	2	yes	—
246	#483	—	2	2	no	—
247	#479	—	2	1	no	—
248	#478	—	2	1	no	—
249	#477	C₂²×C₂₉	1	1	yes	characteristic
250	#476	C₂²×C₂₉	1	1	yes	characteristic
251	#475	—	2	1	no	—
252	#475	—	2	1	no	—
253	#475	C₂²×C₂₉	1	1	yes	characteristic
254	#474	C₂²×C₂₉	1	1	yes	characteristic
255	#462	—	2	1	no	—
256	#462	C₂²×C₂₉	1	2	yes	—
257	#461	—	2	1	no	—
258	#461	C₂²×C₂₉	1	2	yes	—
259	C₈×Q₈	C₂²×C₂₉	1	2	yes	—
260	C₈×D₄	—	2	2	no	—
261	C₈×D₄	C₂²×C₂₉	1	2	yes	—
262	#431	—	2	1	no	—
263	#431	C₂²×C₂₉	1	1	yes	characteristic
264	#427	—	2	1	no	—
265	#423	C₂²×C₂₉	1	1	yes	characteristic
266	C₂×C₄⋊C₈	—	2	1	no	—
267	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
269	#419	—	2	1	no	—
270	#416	—	2	1	no	—
271	#334	C₂²×C₂₉	1	2	yes	—
272	#334	C₂²×C₂₉	1	2	yes	—
273	#333	C₂²×C₂₉	1	2	yes	—
274	#332	C₂²×C₂₉	1	2	yes	—
275	#332	C₂²×C₂₉	1	2	yes	—
276	#332	C₂²×C₂₉	1	2	yes	—
277	C₂×C₂₉	—	2	2	no	—
278	C₂×C₂₉	—	4	2	no	—
279	C₂×C₂₉	#3046	1	1	yes	characteristic
280	C₂×C₂₉	C₂×#465	1	1	yes	characteristic
281	C₂×C₂₉	#3069	1	1	yes	characteristic
282	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
283	C₂²×Q₈	—	2	1	no	—
284	#137	—	4	4	no	—
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
295	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
296	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
297	#125	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
303	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
307	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
308	#117	—	2	1	no	—
309	#117	—	2	1	no	—
310	#117	D₄×C₂₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
315	#107	—	2	1	no	—
316	#107	—	2	1	no	—
317	#106	—	2	2	no	—
318	#106	—	2	2	no	—
319	#106	—	2	1	no	—
320	#106	—	2	1	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
326	C₄⋊C₈	D₄×C₂₉	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
328	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
331	#103	—	2	1	no	—
332	#103	—	2	1	no	—
333	#103	—	2	2	no	—
334	#103	—	2	2	no	—
335	#103	—	2	2	no	—
336	#103	—	2	2	no	—
337	#102	—	2	1	no	—
338	#102	—	2	1	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	D₄×C₂₉	1	2	yes	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	C₂³×C₂₉	1	2	yes	—
343	C₂₉	#19415	1	1	yes	characteristic, direct product factor, Sylow
344	#41	—	2	2	no	—
345	#41	SD₁₆×C₂₉	1	4	yes	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	4	1	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	—	4	2	no	—
352	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
361	C₂²×C₄	#41×C₂₉	1	1	yes	characteristic
362	Q₁₆	—	4	4	no	—
363	SD₁₆	—	4	4	no	—
364	M₁₆	—	4	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	8	2	no	—
371	C₂×C₈	—	8	1	no	—
372	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
373	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
387	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	4	1	no	—
396	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
398	C₄²	#41×C₂₉	1	1	yes	characteristic
399	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
400	C₂³	—	2	1	no	—
401	C₂³	C₂₉×#121	1	1	yes	characteristic
402	Q₈	—	2	1	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	1	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	8	1	no	—
408	Q₈	—	8	2	no	—
409	Q₈	C₂×SD₁₆×C₂₉	1	2	yes	—
410	D₄	—	2	4	no	—
411	D₄	—	2	1	no	—
412	D₄	C₂×SD₁₆×C₂₉	1	2	yes	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	1	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
428	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
429	C₂×C₄	C₂₉×#121	1	1	yes	characteristic
430	C₂×C₄	C₂×SD₁₆×C₂₉	1	2	yes	—
431	C₂×C₄	C₂₉×#135	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	2	2	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	C₂₉×#465	1	2	yes	—
447	C₂²	C₂×C₂₉×#121	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	2	no	—
456	C₄	—	8	1	no	—
457	C₄	C₂₉×#465	1	2	yes	—
458	C₄	C₂²×SD₁₆×C₂₉	1	1	yes	characteristic
459	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
460	C₄	C₂₉×#577	1	1	yes	characteristic
461	C₄	C₂₉×#578	1	1	yes	characteristic
462	C₂	—	2	2	no	—
463	C₂	—	4	2	no	—
464	C₂	C₂₉×#3046	1	1	yes	characteristic
465	C₂	C₂×C₂₉×#465	1	1	yes	characteristic
466	C₂	C₂₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	D₄
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×#3229	C₂	semidirect
5. C₂₉×#1680	C₂	semidirect
6. C₂₉×#1679	C₂	semidirect
7. C₂₉×#1672	C₂	semidirect
8. C₂₉×#1671	C₂	semidirect
9. C₂₉×#1570	C₂	semidirect
10. C₂₉×#1550	C₂	semidirect
11. C₂×C₂₉×#332	C₂	semidirect
166. #19415	C₂₉	direct (N × H)
208. #3229	C₂×C₂₉	semidirect
212. #1680	C₂×C₂₉	semidirect
213. #1679	C₂×C₂₉	semidirect
214. #1672	C₂×C₂₉	semidirect
215. #1671	C₂×C₂₉	semidirect
216. #1570	C₂×C₂₉	semidirect
217. #1550	C₂×C₂₉	semidirect
218. C₂×#332	C₂×C₂₉	semidirect
343. C₂₉	#19415	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×#3229	2
C₂₉×#3076	2
C₂₉×#3039	2
C₂₉×#2988	2
C₂₉×#1680	2
C₂₉×#1679	2
C₂₉×#1672	2
C₂₉×#1671	2
C₂₉×#1570	2
C₂₉×#1550	2
C₂×C₂₉×#332	2
#19415	29

Subgroups — C29×#19415 #20314315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#19415 #20314315