Subgroups — C₂₉×#18930 #20313830

Order 7424.

1020 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3212	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3205	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1642	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1641	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1640	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1639	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1620	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1619	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1495	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1482	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#560	—	2	2	no	—
17	C₂₉×#559	C₂²	1	1	yes	characteristic
18	C₂₉×#550	C₂²	1	1	yes	characteristic
19	C₂₉×#550	C₂²	1	1	yes	characteristic
20	C₂₉×#546	—	2	1	no	—
21	C₂₉×#546	—	2	1	no	—
22	D₄²×C₂₉	—	2	1	no	—
23	D₄²×C₂₉	—	2	1	no	—
24	D₄²×C₂₉	C₂²	1	1	yes	characteristic
25	C₂₉×#540	—	2	1	no	—
26	C₂₉×#540	—	2	1	no	—
27	C₂₉×#535	—	2	1	no	—
28	C₂₉×#535	—	2	1	no	—
29	C₂₉×#534	—	2	2	no	—
30	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
32	C₂₉×#529	C₂²	1	1	yes	characteristic
33	C₂₉×#529	C₂²	1	1	yes	characteristic
34	C₂₉×#495	—	2	1	no	—
35	C₂₉×#493	C₂²	1	1	yes	characteristic
36	C₂₉×#493	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#488	—	2	1	no	—
38	C₂₉×#486	C₂²	1	1	yes	characteristic
39	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
40	C₂₉×#478	—	2	1	no	—
41	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
42	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#469	—	2	1	no	—
44	C₂₉×#468	—	2	1	no	—
45	C₂₉×#463	—	2	1	no	—
46	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
50	C₂₉×#459	—	2	2	no	—
51	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
53	C₂₉×#452	—	2	1	no	—
54	C₂₉×#449	—	2	1	no	—
55	C₂₉×#447	—	2	2	no	—
56	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
57	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×#423	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×#331	C₂²	1	1	yes	characteristic
60	C₂₉×#331	C₂²	1	1	yes	characteristic
61	C₂₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#331	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
69	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂²×D₄×C₂₉	—	2	2	no	—
75	C₂²×D₄×C₂₉	—	2	1	no	—
76	C₂²×D₄×C₂₉	—	2	1	no	—
77	C₂²×D₄×C₂₉	—	2	1	no	—
78	C₂²×D₄×C₂₉	—	2	1	no	—
79	C₂²×D₄×C₂₉	D₄	1	2	yes	—
80	C₂×Q₁₆×C₂₉	—	2	1	no	—
81	C₂×SD₁₆×C₂₉	—	2	1	no	—
82	C₂×SD₁₆×C₂₉	—	2	1	no	—
83	C₂×SD₁₆×C₂₉	—	2	1	no	—
84	C₂×D₈×C₂₉	—	2	2	no	—
85	C₂×D₈×C₂₉	—	2	2	no	—
86	C₂×D₈×C₂₉	—	2	1	no	—
87	C₂×D₈×C₂₉	—	2	1	no	—
88	C₂×M₁₆×C₂₉	—	2	1	no	—
89	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₂₉×#127	—	2	1	no	—
91	C₂₉×#127	—	2	1	no	—
92	C₂₉×#127	—	2	1	no	—
93	C₂₉×#127	—	2	1	no	—
94	C₂₉×#127	D₄	1	2	yes	—
95	C₂₉×#127	C₂³	1	1	yes	characteristic
96	C₂₉×#127	C₂³	1	1	yes	characteristic
97	C₂₉×#127	C₂³	1	1	yes	characteristic
98	C₂₉×#126	—	2	1	no	—
99	C₂₉×#126	—	2	1	no	—
100	C₂₉×#125	D₄	1	1	yes	characteristic
101	C₂₉×#125	D₄	1	1	yes	characteristic
102	C₂₉×#124	—	2	1	no	—
103	C₂₉×#124	—	2	1	no	—
104	C₂₉×#124	—	2	1	no	—
105	C₂₉×#124	D₄	1	1	yes	characteristic
106	C₂₉×#124	D₄	1	1	yes	characteristic
107	C₂₉×#123	—	2	2	no	—
108	C₂₉×#123	—	2	2	no	—
109	C₂₉×#123	—	2	2	no	—
110	C₂₉×#123	—	2	2	no	—
111	C₂₉×#123	—	2	1	no	—
112	C₂₉×#123	—	2	1	no	—
113	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
114	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
115	C₂₉×#121	—	2	2	no	—
116	C₂₉×#121	—	2	2	no	—
117	C₂₉×#121	—	2	2	no	—
118	C₂₉×#121	—	2	2	no	—
119	C₂₉×#121	—	2	2	no	—
120	C₂₉×#121	—	2	2	no	—
121	C₂₉×#121	—	2	2	no	—
122	C₂₉×#121	—	2	2	no	—
123	C₂₉×#121	—	2	1	no	—
124	C₂₉×#121	—	2	1	no	—
125	C₂₉×#121	—	2	1	no	—
126	C₂₉×#121	—	2	1	no	—
127	C₂₉×#121	—	2	1	no	—
128	C₂₉×#121	—	2	1	no	—
129	C₂₉×#121	D₄	1	1	yes	characteristic
130	C₂₉×#121	D₄	1	1	yes	characteristic
131	C₂₉×#120	—	2	2	no	—
132	C₂₉×#120	—	2	2	no	—
133	C₂₉×#120	—	2	2	no	—
134	C₂₉×#120	—	2	2	no	—
135	C₂₉×#120	—	2	2	no	—
136	C₂₉×#120	—	2	2	no	—
137	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
138	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
139	C₄×D₄×C₂₉	—	2	1	no	—
140	C₄×D₄×C₂₉	—	2	1	no	—
141	C₄×D₄×C₂₉	—	2	1	no	—
142	C₄×D₄×C₂₉	—	2	1	no	—
143	C₄×D₄×C₂₉	—	2	1	no	—
144	C₄×D₄×C₂₉	—	2	1	no	—
145	C₄×D₄×C₂₉	—	2	1	no	—
146	C₄×D₄×C₂₉	—	2	1	no	—
147	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
148	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
149	C₂₉×#117	—	2	1	no	—
150	C₂₉×#117	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
152	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
153	C₂₉×#107	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×C₄⋊C₈	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×#103	—	2	1	no	—
162	C₂₉×#103	—	2	1	no	—
163	C₂₉×#103	—	2	1	no	—
164	C₂₉×#102	—	2	2	no	—
165	C₂₉×#102	—	2	2	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	1	no	—
171	C₂₉×C₂²⋊C₈	—	2	1	no	—
172	C₂₉×C₂²⋊C₈	—	2	1	no	—
173	C₄×C₈×C₂₉	—	2	1	no	—
174	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
176	C₂⁴×C₂₉	—	2	2	no	—
177	C₂⁴×C₂₉	—	2	2	no	—
178	#41×C₂₉	—	8	1	no	—
179	#41×C₂₉	—	8	1	no	—
180	#41×C₂₉	—	8	1	no	—
181	#41×C₂₉	—	8	1	no	—
182	#41×C₂₉	—	8	1	no	—
183	#41×C₂₉	—	8	1	no	—
184	C₂×Q₈×C₂₉	—	2	1	no	—
185	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₂₉	—	2	1	no	—
188	C₂×D₄×C₂₉	—	2	1	no	—
189	C₂×D₄×C₂₉	—	2	2	no	—
190	C₂×D₄×C₂₉	—	2	2	no	—
191	C₂×D₄×C₂₉	—	2	2	no	—
192	C₂×D₄×C₂₉	—	2	2	no	—
193	C₂×D₄×C₂₉	—	2	2	no	—
194	C₂×D₄×C₂₉	—	2	2	no	—
195	C₂×D₄×C₂₉	—	2	2	no	—
196	C₂×D₄×C₂₉	—	2	2	no	—
197	C₂×D₄×C₂₉	—	2	2	no	—
198	C₂×D₄×C₂₉	—	2	1	no	—
199	C₂×D₄×C₂₉	—	2	1	no	—
200	C₂×D₄×C₂₉	—	2	1	no	—
201	C₂×D₄×C₂₉	—	2	1	no	—
202	C₂×D₄×C₂₉	—	2	1	no	—
203	C₂×D₄×C₂₉	—	2	1	no	—
204	C₂×D₄×C₂₉	—	2	1	no	—
205	C₂×D₄×C₂₉	—	4	1	no	—
206	C₂×D₄×C₂₉	—	8	1	no	—
207	C₂×D₄×C₂₉	—	8	1	no	—
208	C₂×D₄×C₂₉	—	8	1	no	—
209	C₂×D₄×C₂₉	—	8	1	no	—
210	C₂×D₄×C₂₉	—	8	1	no	—
211	C₂×D₄×C₂₉	—	8	1	no	—
212	C₂×D₄×C₂₉	—	8	1	no	—
213	C₂×D₄×C₂₉	—	8	1	no	—
214	C₂×D₄×C₂₉	—	8	2	no	—
215	C₂×D₄×C₂₉	—	8	4	no	—
216	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
217	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₂₉	—	2	2	no	—
221	C₂²×C₄×C₂₉	—	2	2	no	—
222	C₂²×C₄×C₂₉	—	2	2	no	—
223	C₂²×C₄×C₂₉	—	2	1	no	—
224	C₂²×C₄×C₂₉	—	2	1	no	—
225	C₂²×C₄×C₂₉	—	4	1	no	—
226	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
229	Q₁₆×C₂₉	—	8	1	no	—
230	SD₁₆×C₂₉	—	8	1	no	—
231	SD₁₆×C₂₉	—	8	1	no	—
232	SD₁₆×C₂₉	—	8	1	no	—
233	D₈×C₂₉	—	8	1	no	—
234	D₈×C₂₉	—	8	1	no	—
235	D₈×C₂₉	—	8	2	no	—
236	D₈×C₂₉	—	8	2	no	—
237	M₁₆×C₂₉	—	8	1	no	—
238	C₂×C₈×C₂₉	—	2	1	no	—
239	C₂×C₈×C₂₉	—	2	1	no	—
240	C₂×C₈×C₂₉	—	2	1	no	—
241	C₂×C₈×C₂₉	—	2	1	no	—
242	C₂×C₈×C₂₉	—	2	1	no	—
243	C₂×C₈×C₂₉	—	2	1	no	—
244	C₄⋊C₄×C₂₉	—	2	1	no	—
245	C₄⋊C₄×C₂₉	—	2	1	no	—
246	C₄⋊C₄×C₂₉	—	2	1	no	—
247	C₄⋊C₄×C₂₉	—	2	1	no	—
248	C₄⋊C₄×C₂₉	—	2	1	no	—
249	C₄⋊C₄×C₂₉	—	2	1	no	—
250	C₄⋊C₄×C₂₉	—	2	1	no	—
251	C₄⋊C₄×C₂₉	—	2	1	no	—
252	C₄⋊C₄×C₂₉	—	2	1	no	—
253	C₄⋊C₄×C₂₉	—	2	1	no	—
254	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
255	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
258	C₂²⋊C₄×C₂₉	—	2	2	no	—
259	C₂²⋊C₄×C₂₉	—	2	2	no	—
260	C₂²⋊C₄×C₂₉	—	2	2	no	—
261	C₂²⋊C₄×C₂₉	—	2	2	no	—
262	C₂²⋊C₄×C₂₉	—	2	2	no	—
263	C₂²⋊C₄×C₂₉	—	2	2	no	—
264	C₂²⋊C₄×C₂₉	—	2	1	no	—
265	C₂²⋊C₄×C₂₉	—	2	1	no	—
266	C₂²⋊C₄×C₂₉	—	2	1	no	—
267	C₂²⋊C₄×C₂₉	—	2	1	no	—
268	C₂²⋊C₄×C₂₉	—	2	1	no	—
269	C₂²⋊C₄×C₂₉	—	2	1	no	—
270	C₂²⋊C₄×C₂₉	—	2	1	no	—
271	C₂²⋊C₄×C₂₉	—	2	1	no	—
272	C₂²⋊C₄×C₂₉	—	2	1	no	—
273	C₂²⋊C₄×C₂₉	—	2	1	no	—
274	C₂²⋊C₄×C₂₉	—	4	1	no	—
275	C₂²⋊C₄×C₂₉	—	4	1	no	—
276	C₄²×C₂₉	—	2	1	no	—
277	C₄²×C₂₉	—	2	1	no	—
278	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
282	#18930	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂³×C₂₉	—	2	1	no	—
284	C₂³×C₂₉	—	2	1	no	—
285	C₂³×C₂₉	—	2	2	no	—
286	C₂³×C₂₉	—	2	2	no	—
287	C₂³×C₂₉	—	4	4	no	—
288	C₂³×C₂₉	—	4	1	no	—
289	C₂³×C₂₉	—	8	2	no	—
290	C₂³×C₂₉	—	8	2	no	—
291	C₂³×C₂₉	—	8	2	no	—
292	C₂³×C₂₉	—	8	2	no	—
293	C₂³×C₂₉	—	8	2	no	—
294	C₂³×C₂₉	#120	1	1	yes	characteristic
295	Q₈×C₂₉	—	2	1	no	—
296	Q₈×C₂₉	—	2	1	no	—
297	Q₈×C₂₉	—	2	1	no	—
298	Q₈×C₂₉	—	2	1	no	—
299	Q₈×C₂₉	—	4	1	no	—
300	Q₈×C₂₉	—	4	1	no	—
301	D₄×C₂₉	—	2	1	no	—
302	D₄×C₂₉	—	2	1	no	—
303	D₄×C₂₉	—	2	1	no	—
304	D₄×C₂₉	—	2	1	no	—
305	D₄×C₂₉	—	4	2	no	—
306	D₄×C₂₉	—	4	2	no	—
307	D₄×C₂₉	—	4	2	no	—
308	D₄×C₂₉	—	4	2	no	—
309	D₄×C₂₉	—	4	2	no	—
310	D₄×C₂₉	—	4	1	no	—
311	D₄×C₂₉	—	4	1	no	—
312	D₄×C₂₉	—	4	1	no	—
313	D₄×C₂₉	—	4	1	no	—
314	D₄×C₂₉	—	4	1	no	—
315	D₄×C₂₉	—	4	1	no	—
316	D₄×C₂₉	—	4	1	no	—
317	D₄×C₂₉	—	4	1	no	—
318	D₄×C₂₉	—	4	1	no	—
319	D₄×C₂₉	—	4	1	no	—
320	D₄×C₂₉	—	4	1	no	—
321	D₄×C₂₉	—	4	1	no	—
322	D₄×C₂₉	—	8	2	no	—
323	D₄×C₂₉	—	8	2	no	—
324	D₄×C₂₉	—	8	2	no	—
325	D₄×C₂₉	—	8	2	no	—
326	D₄×C₂₉	—	8	2	no	—
327	D₄×C₂₉	—	8	2	no	—
328	D₄×C₂₉	—	8	2	no	—
329	D₄×C₂₉	—	8	2	no	—
330	D₄×C₂₉	—	8	2	no	—
331	D₄×C₂₉	—	8	2	no	—
332	C₂×C₄×C₂₉	—	2	1	no	—
333	C₂×C₄×C₂₉	—	2	1	no	—
334	C₂×C₄×C₂₉	—	2	1	no	—
335	C₂×C₄×C₂₉	—	2	1	no	—
336	C₂×C₄×C₂₉	—	2	1	no	—
337	C₂×C₄×C₂₉	—	2	1	no	—
338	C₂×C₄×C₂₉	—	2	1	no	—
339	C₂×C₄×C₂₉	—	2	1	no	—
340	C₂×C₄×C₂₉	—	2	1	no	—
341	C₂×C₄×C₂₉	—	2	1	no	—
342	C₂×C₄×C₂₉	—	4	1	no	—
343	C₂×C₄×C₂₉	—	4	1	no	—
344	C₂×C₄×C₂₉	—	4	1	no	—
345	C₂×C₄×C₂₉	—	4	1	no	—
346	C₂×C₄×C₂₉	—	4	1	no	—
347	C₂×C₄×C₂₉	—	4	1	no	—
348	C₂×C₄×C₂₉	—	8	2	no	—
349	C₂×C₄×C₂₉	—	8	2	no	—
350	C₂×C₄×C₂₉	—	8	2	no	—
351	C₂×C₄×C₂₉	—	8	2	no	—
352	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
353	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
354	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
355	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
358	C₈×C₂₉	—	4	1	no	—
359	C₈×C₂₉	—	4	1	no	—
360	C₈×C₂₉	—	4	1	no	—
361	C₈×C₂₉	—	4	1	no	—
362	C₈×C₂₉	—	4	1	no	—
363	C₈×C₂₉	—	4	1	no	—
364	#3543	C₂×C₂₉	1	1	yes	characteristic, complemented
365	#3251	C₂×C₂₉	1	1	yes	characteristic, complemented
366	#3212	C₂×C₂₉	1	1	yes	characteristic, complemented
367	#3205	C₂×C₂₉	1	1	yes	characteristic, complemented
368	#1642	C₂×C₂₉	1	1	yes	characteristic, complemented
369	#1641	C₂×C₂₉	1	1	yes	characteristic, complemented
370	#1640	C₂×C₂₉	1	1	yes	characteristic, complemented
371	#1639	C₂×C₂₉	1	1	yes	characteristic, complemented
372	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
373	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
374	#1620	C₂×C₂₉	1	1	yes	characteristic, complemented
375	#1619	C₂×C₂₉	1	1	yes	characteristic, complemented
376	#1545	C₂×C₂₉	1	1	yes	characteristic, complemented
377	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
378	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
379	C₂²×C₂₉	—	2	1	no	—
380	C₂²×C₂₉	—	2	1	no	—
381	C₂²×C₂₉	—	2	1	no	—
382	C₂²×C₂₉	—	4	1	no	—
383	C₂²×C₂₉	—	4	2	no	—
384	C₂²×C₂₉	—	4	1	no	—
385	C₂²×C₂₉	—	4	2	no	—
386	C₂²×C₂₉	—	4	1	no	—
387	C₂²×C₂₉	—	4	2	no	—
388	C₂²×C₂₉	—	4	1	no	—
389	C₂²×C₂₉	—	4	2	no	—
390	C₂²×C₂₉	—	4	2	no	—
391	C₂²×C₂₉	—	4	1	no	—
392	C₂²×C₂₉	—	4	1	no	—
393	C₂²×C₂₉	—	4	2	no	—
394	C₂²×C₂₉	—	8	1	no	—
395	C₂²×C₂₉	—	8	1	no	—
396	C₂²×C₂₉	—	8	1	no	—
397	C₂²×C₂₉	—	16	4	no	—
398	C₂²×C₂₉	—	16	4	no	—
399	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
400	C₄×C₂₉	—	2	1	no	—
401	C₄×C₂₉	—	2	1	no	—
402	C₄×C₂₉	—	2	1	no	—
403	C₄×C₂₉	—	2	1	no	—
404	C₄×C₂₉	—	4	1	no	—
405	C₄×C₂₉	—	4	1	no	—
406	C₄×C₂₉	—	4	1	no	—
407	C₄×C₂₉	—	4	1	no	—
408	C₄×C₂₉	—	4	1	no	—
409	C₄×C₂₉	—	4	1	no	—
410	C₄×C₂₉	—	8	1	no	—
411	C₄×C₂₉	#576	1	1	yes	characteristic
412	C₄×C₂₉	#576	1	1	yes	characteristic
413	C₄×C₂₉	#576	1	1	yes	characteristic
414	C₄×C₂₉	#577	1	1	yes	characteristic
415	#560	—	2	2	no	—
416	#559	C₂²×C₂₉	1	1	yes	characteristic
417	#550	C₂²×C₂₉	1	1	yes	characteristic
418	#550	C₂²×C₂₉	1	1	yes	characteristic
419	#546	—	2	1	no	—
420	#546	—	2	1	no	—
421	D₄²	—	2	1	no	—
422	D₄²	—	2	1	no	—
423	D₄²	C₂²×C₂₉	1	1	yes	characteristic
424	#540	—	2	1	no	—
425	#540	—	2	1	no	—
426	#535	—	2	1	no	—
427	#535	—	2	1	no	—
428	#534	—	2	2	no	—
429	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
430	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
431	#529	C₂²×C₂₉	1	1	yes	characteristic
432	#529	C₂²×C₂₉	1	1	yes	characteristic
433	#495	—	2	1	no	—
434	#493	C₂²×C₂₉	1	1	yes	characteristic
435	#493	C₂²×C₂₉	1	1	yes	characteristic, complemented
436	#488	—	2	1	no	—
437	#486	C₂²×C₂₉	1	1	yes	characteristic
438	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
439	#478	—	2	1	no	—
440	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
441	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
442	#469	—	2	1	no	—
443	#468	—	2	1	no	—
444	#463	—	2	1	no	—
445	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
446	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
447	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
448	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
449	#459	—	2	2	no	—
450	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
451	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
452	#452	—	2	1	no	—
453	#449	—	2	1	no	—
454	#447	—	2	2	no	—
455	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
456	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
457	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
458	#331	C₂²×C₂₉	1	1	yes	characteristic
459	#331	C₂²×C₂₉	1	1	yes	characteristic
460	#331	C₂²×C₂₉	1	1	yes	characteristic, complemented
461	#331	C₂²×C₂₉	1	1	yes	characteristic, complemented
462	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
463	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
464	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
465	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
466	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
467	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
468	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
469	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
470	C₂×C₂₉	—	4	1	no	—
471	C₂×C₂₉	—	8	2	no	—
472	C₂×C₂₉	—	8	1	no	—
473	C₂×C₂₉	—	8	1	no	—
474	C₂×C₂₉	—	8	2	no	—
475	C₂×C₂₉	—	16	1	no	—
476	C₂×C₂₉	#3008	1	1	yes	characteristic
477	C₂×C₂₉	#3012	1	1	yes	characteristic
478	C₂×C₂₉	#3019	1	1	yes	characteristic
479	C₂×#41	—	2	1	no	—
480	C₂×#41	—	2	1	no	—
481	C₂×#41	—	2	1	no	—
482	C₂²×D₄	—	2	2	no	—
483	C₂²×D₄	—	2	1	no	—
484	C₂²×D₄	—	2	1	no	—
485	C₂²×D₄	—	2	1	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	D₄×C₂₉	1	2	yes	—
488	C₂×Q₁₆	—	2	1	no	—
489	C₂×SD₁₆	—	2	1	no	—
490	C₂×SD₁₆	—	2	1	no	—
491	C₂×SD₁₆	—	2	1	no	—
492	C₂×D₈	—	2	2	no	—
493	C₂×D₈	—	2	2	no	—
494	C₂×D₈	—	2	1	no	—
495	C₂×D₈	—	2	1	no	—
496	C₂×M₁₆	—	2	1	no	—
497	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
498	#127	—	2	1	no	—
499	#127	—	2	1	no	—
500	#127	—	2	1	no	—
501	#127	—	2	1	no	—
502	#127	D₄×C₂₉	1	2	yes	—
503	#127	C₂³×C₂₉	1	1	yes	characteristic
504	#127	C₂³×C₂₉	1	1	yes	characteristic
505	#127	C₂³×C₂₉	1	1	yes	characteristic
506	#126	—	2	1	no	—
507	#126	—	2	1	no	—
508	#125	D₄×C₂₉	1	1	yes	characteristic
509	#125	D₄×C₂₉	1	1	yes	characteristic
510	#124	—	2	1	no	—
511	#124	—	2	1	no	—
512	#124	—	2	1	no	—
513	#124	D₄×C₂₉	1	1	yes	characteristic
514	#124	D₄×C₂₉	1	1	yes	characteristic
515	#123	—	2	2	no	—
516	#123	—	2	2	no	—
517	#123	—	2	2	no	—
518	#123	—	2	2	no	—
519	#123	—	2	1	no	—
520	#123	—	2	1	no	—
521	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
522	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
523	#121	—	2	2	no	—
524	#121	—	2	2	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	—	2	2	no	—
530	#121	—	2	2	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	1	no	—
536	#121	—	2	1	no	—
537	#121	D₄×C₂₉	1	1	yes	characteristic
538	#121	D₄×C₂₉	1	1	yes	characteristic
539	#120	—	2	2	no	—
540	#120	—	2	2	no	—
541	#120	—	2	2	no	—
542	#120	—	2	2	no	—
543	#120	—	2	2	no	—
544	#120	—	2	2	no	—
545	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
546	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
556	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
557	#117	—	2	1	no	—
558	#117	—	2	1	no	—
559	C₂×C₂²⋊C₄	—	2	2	no	—
560	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
561	#107	—	2	1	no	—
562	#106	—	2	1	no	—
563	C₄⋊C₈	—	2	1	no	—
564	C₄⋊C₈	—	2	1	no	—
565	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
566	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
567	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
568	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
569	#103	—	2	1	no	—
570	#103	—	2	1	no	—
571	#103	—	2	1	no	—
572	#102	—	2	2	no	—
573	#102	—	2	2	no	—
574	#102	—	2	1	no	—
575	#102	—	2	1	no	—
576	#102	—	2	1	no	—
577	#102	—	2	1	no	—
578	#102	—	2	1	no	—
579	C₂²⋊C₈	—	2	1	no	—
580	C₂²⋊C₈	—	2	1	no	—
581	C₄×C₈	—	2	1	no	—
582	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
583	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
584	C₂₉	#18930	1	1	yes	characteristic, direct product factor, Sylow
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	#41	—	8	1	no	—
588	#41	—	8	1	no	—
589	#41	—	8	1	no	—
590	#41	—	8	1	no	—
591	#41	—	8	1	no	—
592	#41	—	8	1	no	—
593	C₂×Q₈	—	2	1	no	—
594	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
595	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	2	no	—
607	C₂×D₄	—	2	1	no	—
608	C₂×D₄	—	2	1	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	4	1	no	—
615	C₂×D₄	—	8	1	no	—
616	C₂×D₄	—	8	1	no	—
617	C₂×D₄	—	8	1	no	—
618	C₂×D₄	—	8	1	no	—
619	C₂×D₄	—	8	1	no	—
620	C₂×D₄	—	8	1	no	—
621	C₂×D₄	—	8	1	no	—
622	C₂×D₄	—	8	1	no	—
623	C₂×D₄	—	8	2	no	—
624	C₂×D₄	—	8	4	no	—
625	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
626	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
627	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
628	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	4	1	no	—
635	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
637	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
638	Q₁₆	—	8	1	no	—
639	SD₁₆	—	8	1	no	—
640	SD₁₆	—	8	1	no	—
641	SD₁₆	—	8	1	no	—
642	D₈	—	8	1	no	—
643	D₈	—	8	1	no	—
644	D₈	—	8	2	no	—
645	D₈	—	8	2	no	—
646	M₁₆	—	8	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₄⋊C₄	—	2	1	no	—
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	—	2	1	no	—
658	C₄⋊C₄	—	2	1	no	—
659	C₄⋊C₄	—	2	1	no	—
660	C₄⋊C₄	—	2	1	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
665	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
666	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	1	no	—
676	C₂²⋊C₄	—	2	1	no	—
677	C₂²⋊C₄	—	2	1	no	—
678	C₂²⋊C₄	—	2	1	no	—
679	C₂²⋊C₄	—	2	1	no	—
680	C₂²⋊C₄	—	2	1	no	—
681	C₂²⋊C₄	—	2	1	no	—
682	C₂²⋊C₄	—	2	1	no	—
683	C₂²⋊C₄	—	4	1	no	—
684	C₂²⋊C₄	—	4	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
688	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
690	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	4	4	no	—
696	C₂³	—	4	1	no	—
697	C₂³	—	8	2	no	—
698	C₂³	—	8	2	no	—
699	C₂³	—	8	2	no	—
700	C₂³	—	8	2	no	—
701	C₂³	—	8	2	no	—
702	C₂³	C₂₉×#120	1	1	yes	characteristic
703	Q₈	—	2	1	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	1	no	—
706	Q₈	—	2	1	no	—
707	Q₈	—	4	1	no	—
708	Q₈	—	4	1	no	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	2	1	no	—
713	D₄	—	4	2	no	—
714	D₄	—	4	2	no	—
715	D₄	—	4	2	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	4	1	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	4	1	no	—
722	D₄	—	4	1	no	—
723	D₄	—	4	1	no	—
724	D₄	—	4	1	no	—
725	D₄	—	4	1	no	—
726	D₄	—	4	1	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	8	2	no	—
731	D₄	—	8	2	no	—
732	D₄	—	8	2	no	—
733	D₄	—	8	2	no	—
734	D₄	—	8	2	no	—
735	D₄	—	8	2	no	—
736	D₄	—	8	2	no	—
737	D₄	—	8	2	no	—
738	D₄	—	8	2	no	—
739	D₄	—	8	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	8	2	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	2	no	—
759	C₂×C₄	—	8	2	no	—
760	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
761	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
762	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
766	C₈	—	4	1	no	—
767	C₈	—	4	1	no	—
768	C₈	—	4	1	no	—
769	C₈	—	4	1	no	—
770	C₈	—	4	1	no	—
771	C₈	—	4	1	no	—
772	C₂²	—	2	1	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	2	no	—
787	C₂²	—	8	1	no	—
788	C₂²	—	8	1	no	—
789	C₂²	—	8	1	no	—
790	C₂²	—	16	4	no	—
791	C₂²	—	16	4	no	—
792	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	8	1	no	—
804	C₄	C₂₉×#576	1	1	yes	characteristic
805	C₄	C₂₉×#576	1	1	yes	characteristic
806	C₄	C₂₉×#576	1	1	yes	characteristic
807	C₄	C₂₉×#577	1	1	yes	characteristic
808	C₂	—	4	1	no	—
809	C₂	—	8	1	no	—
810	C₂	—	8	1	no	—
811	C₂	—	8	2	no	—
812	C₂	—	8	2	no	—
813	C₂	—	16	1	no	—
814	C₂	C₂₉×#3008	1	1	yes	characteristic
815	C₂	C₂₉×#3012	1	1	yes	characteristic
816	C₂	C₂₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
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×#3543	C₂	semidirect
2. C₂₉×#3251	C₂	semidirect
3. C₂₉×#3212	C₂	semidirect
4. C₂₉×#3205	C₂	semidirect
5. C₂₉×#1642	C₂	semidirect
6. C₂₉×#1641	C₂	semidirect
7. C₂₉×#1640	C₂	semidirect
8. C₂₉×#1639	C₂	semidirect
9. C₂₉×#1621	C₂	semidirect
10. C₂₉×#1621	C₂	semidirect
11. C₂₉×#1620	C₂	semidirect
12. C₂₉×#1619	C₂	semidirect
13. C₂₉×#1545	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1482	C₂	semidirect
30. C₂₉×#532	C₂²	semidirect
36. C₂₉×#493	C₂²	semidirect
39. C₂₉×#486	C₂²	semidirect
41. C₂₉×#475	C₂²	semidirect
42. C₂₉×#474	C₂²	semidirect
46. C₂₉×#462	C₂²	semidirect
47. C₂₉×#461	C₂²	semidirect
48. C₂₉×#460	C₂²	semidirect
49. C₂₉×#460	C₂²	semidirect
51. C₂₉×#459	C₂²	semidirect
52. C₂₉×#459	C₂²	semidirect
56. C₂₉×#431	C₂²	semidirect
57. C₂₉×#431	C₂²	semidirect
58. C₂₉×#423	C₂²	semidirect
61. C₂₉×#331	C₂²	semidirect
62. C₂₉×#331	C₂²	semidirect
63. C₂₉×Q₈⋊C₈	C₂²	semidirect
64. C₂₉×Q₈⋊C₈	C₂²	semidirect
65. C₂₉×Q₈⋊C₈	C₂²	semidirect
66. C₂₉×Q₈⋊C₈	C₂²	semidirect
67. C₂₉×D₄⋊C₈	C₂²	semidirect
68. C₂₉×D₄⋊C₈	C₂²	semidirect
69. C₂₉×D₄⋊C₈	C₂²	semidirect
70. C₂₉×D₄⋊C₈	C₂²	semidirect
282. #18930	C₂₉	direct (N × H)
364. #3543	C₂×C₂₉	semidirect
365. #3251	C₂×C₂₉	semidirect
366. #3212	C₂×C₂₉	semidirect
367. #3205	C₂×C₂₉	semidirect
368. #1642	C₂×C₂₉	semidirect
369. #1641	C₂×C₂₉	semidirect
370. #1640	C₂×C₂₉	semidirect
371. #1639	C₂×C₂₉	semidirect
372. #1621	C₂×C₂₉	semidirect
373. #1621	C₂×C₂₉	semidirect
374. #1620	C₂×C₂₉	semidirect
375. #1619	C₂×C₂₉	semidirect
376. #1545	C₂×C₂₉	semidirect
377. #1495	C₂×C₂₉	semidirect
378. #1482	C₂×C₂₉	semidirect
429. #532	C₂²×C₂₉	semidirect
435. #493	C₂²×C₂₉	semidirect
438. #486	C₂²×C₂₉	semidirect
440. #475	C₂²×C₂₉	semidirect
441. #474	C₂²×C₂₉	semidirect
445. #462	C₂²×C₂₉	semidirect
446. #461	C₂²×C₂₉	semidirect
447. #460	C₂²×C₂₉	semidirect
448. #460	C₂²×C₂₉	semidirect
450. #459	C₂²×C₂₉	semidirect
451. #459	C₂²×C₂₉	semidirect
455. #431	C₂²×C₂₉	semidirect
456. #431	C₂²×C₂₉	semidirect
457. #423	C₂²×C₂₉	semidirect
460. #331	C₂²×C₂₉	semidirect
461. #331	C₂²×C₂₉	semidirect
462. Q₈⋊C₈	C₂²×C₂₉	semidirect
463. Q₈⋊C₈	C₂²×C₂₉	semidirect
464. Q₈⋊C₈	C₂²×C₂₉	semidirect
465. Q₈⋊C₈	C₂²×C₂₉	semidirect
466. D₄⋊C₈	C₂²×C₂₉	semidirect
467. D₄⋊C₈	C₂²×C₂₉	semidirect
468. D₄⋊C₈	C₂²×C₂₉	semidirect
469. D₄⋊C₈	C₂²×C₂₉	semidirect
584. C₂₉	#18930	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×#3543	2
C₂₉×#3251	2
C₂₉×#3212	2
C₂₉×#3205	2
C₂₉×#1642	2
C₂₉×#1641	2
C₂₉×#1640	2
C₂₉×#1639	2
C₂₉×#1621	2
C₂₉×#1620	2
C₂₉×#1619	2
C₂₉×#1545	2
C₂₉×#1495	2
C₂₉×#1482	2
#18930	29

Subgroups — C29×#18930 #20313830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18930 #20313830