Subgroups — C₂₉×#18931 #20313831

Order 7424.

986 conjugacy classes of subgroups.

The subgroup lattice has 788 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
2	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3233	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3208	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×#1631	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1630	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1629	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×#533	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×#499	—	2	1	no	—
35	C₂₉×#492	C₂²	1	1	yes	characteristic
36	C₂₉×#492	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×#485	—	2	1	no	—
41	C₂₉×#482	—	2	1	no	—
42	C₂₉×#479	—	2	1	no	—
43	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
45	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#470	—	2	1	no	—
50	C₂₉×#468	—	2	1	no	—
51	C₂₉×#464	—	2	1	no	—
52	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
53	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
54	C₂₉×#460	—	2	2	no	—
55	C₂₉×#450	—	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	C₂²×D₄×C₂₉	—	2	2	no	—
74	C₂²×D₄×C₂₉	—	2	1	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	D₄	1	2	yes	—
79	C₂×Q₁₆×C₂₉	—	2	1	no	—
80	C₂×SD₁₆×C₂₉	—	2	2	no	—
81	C₂×SD₁₆×C₂₉	—	2	2	no	—
82	C₂×SD₁₆×C₂₉	—	2	1	no	—
83	C₂×M₁₆×C₂₉	—	2	1	no	—
84	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₂₉×#127	—	2	1	no	—
87	C₂₉×#127	—	2	1	no	—
88	C₂₉×#127	—	2	1	no	—
89	C₂₉×#127	—	2	1	no	—
90	C₂₉×#127	D₄	1	2	yes	—
91	C₂₉×#127	C₂³	1	1	yes	characteristic
92	C₂₉×#127	C₂³	1	1	yes	characteristic
93	C₂₉×#126	—	2	1	no	—
94	C₂₉×#126	—	2	1	no	—
95	C₂₉×#125	—	2	1	no	—
96	C₂₉×#125	D₄	1	1	yes	characteristic
97	C₂₉×#125	D₄	1	1	yes	characteristic
98	C₂₉×#124	—	2	1	no	—
99	C₂₉×#124	—	2	1	no	—
100	C₂₉×#124	D₄	1	1	yes	characteristic
101	C₂₉×#124	D₄	1	1	yes	characteristic
102	C₂₉×#123	—	2	2	no	—
103	C₂₉×#123	—	2	2	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×#123	—	2	2	no	—
106	C₂₉×#123	—	2	1	no	—
107	C₂₉×#123	—	2	1	no	—
108	C₂₉×C₂²⋊Q₈	—	2	1	no	—
109	C₂₉×C₂²⋊Q₈	—	2	1	no	—
110	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
111	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
112	C₂₉×#121	—	2	2	no	—
113	C₂₉×#121	—	2	2	no	—
114	C₂₉×#121	—	2	2	no	—
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	1	no	—
121	C₂₉×#121	—	2	1	no	—
122	C₂₉×#121	—	2	1	no	—
123	C₂₉×#121	—	2	1	no	—
124	C₂₉×#121	D₄	1	1	yes	characteristic
125	C₂₉×#121	D₄	1	1	yes	characteristic
126	C₂₉×#120	—	2	2	no	—
127	C₂₉×#120	—	2	2	no	—
128	C₂₉×#120	—	2	2	no	—
129	C₂₉×#120	—	2	2	no	—
130	C₂₉×#120	—	2	2	no	—
131	C₂₉×#120	—	2	2	no	—
132	C₄×Q₈×C₂₉	—	2	1	no	—
133	C₄×Q₈×C₂₉	—	2	1	no	—
134	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
135	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₂₉	—	2	1	no	—
137	C₄×D₄×C₂₉	—	2	1	no	—
138	C₄×D₄×C₂₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	—	2	1	no	—
146	C₂₉×#117	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
148	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
149	C₂₉×#107	—	2	1	no	—
150	C₂₉×#107	—	2	1	no	—
151	C₂₉×#107	—	2	1	no	—
152	C₂₉×#106	—	2	1	no	—
153	C₂₉×#106	—	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×#103	—	2	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#102	—	2	2	no	—
167	C₂₉×#102	—	2	2	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	C₂×Q₈×C₂₉	—	2	1	no	—
183	C₂×Q₈×C₂₉	—	2	1	no	—
184	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
185	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₂₉	—	2	1	no	—
187	C₂×D₄×C₂₉	—	2	1	no	—
188	C₂×D₄×C₂₉	—	2	2	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	1	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	—	8	1	no	—
202	C₂×D₄×C₂₉	—	8	1	no	—
203	C₂×D₄×C₂₉	—	8	1	no	—
204	C₂×D₄×C₂₉	—	8	1	no	—
205	C₂×D₄×C₂₉	—	8	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	2	no	—
210	C₂×D₄×C₂₉	—	8	4	no	—
211	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
214	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
215	C₂²×C₄×C₂₉	—	2	2	no	—
216	C₂²×C₄×C₂₉	—	2	2	no	—
217	C₂²×C₄×C₂₉	—	2	2	no	—
218	C₂²×C₄×C₂₉	—	2	1	no	—
219	C₂²×C₄×C₂₉	—	2	1	no	—
220	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
223	Q₁₆×C₂₉	—	8	1	no	—
224	SD₁₆×C₂₉	—	8	1	no	—
225	SD₁₆×C₂₉	—	8	2	no	—
226	SD₁₆×C₂₉	—	8	2	no	—
227	M₁₆×C₂₉	—	8	1	no	—
228	C₂×C₈×C₂₉	—	2	1	no	—
229	C₂×C₈×C₂₉	—	2	1	no	—
230	C₂×C₈×C₂₉	—	2	1	no	—
231	C₂×C₈×C₂₉	—	2	1	no	—
232	C₂×C₈×C₂₉	—	2	1	no	—
233	C₂×C₈×C₂₉	—	2	1	no	—
234	C₄⋊C₄×C₂₉	—	2	1	no	—
235	C₄⋊C₄×C₂₉	—	2	1	no	—
236	C₄⋊C₄×C₂₉	—	2	1	no	—
237	C₄⋊C₄×C₂₉	—	2	1	no	—
238	C₄⋊C₄×C₂₉	—	2	1	no	—
239	C₄⋊C₄×C₂₉	—	2	1	no	—
240	C₄⋊C₄×C₂₉	—	2	1	no	—
241	C₄⋊C₄×C₂₉	—	2	1	no	—
242	C₄⋊C₄×C₂₉	—	2	1	no	—
243	C₄⋊C₄×C₂₉	—	2	1	no	—
244	C₄⋊C₄×C₂₉	—	2	1	no	—
245	C₄⋊C₄×C₂₉	—	2	1	no	—
246	C₄⋊C₄×C₂₉	—	4	1	no	—
247	C₄⋊C₄×C₂₉	—	4	1	no	—
248	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
249	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
250	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
251	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
252	C₂²⋊C₄×C₂₉	—	2	2	no	—
253	C₂²⋊C₄×C₂₉	—	2	2	no	—
254	C₂²⋊C₄×C₂₉	—	2	2	no	—
255	C₂²⋊C₄×C₂₉	—	2	2	no	—
256	C₂²⋊C₄×C₂₉	—	2	2	no	—
257	C₂²⋊C₄×C₂₉	—	2	2	no	—
258	C₂²⋊C₄×C₂₉	—	2	1	no	—
259	C₂²⋊C₄×C₂₉	—	2	1	no	—
260	C₂²⋊C₄×C₂₉	—	2	1	no	—
261	C₂²⋊C₄×C₂₉	—	2	1	no	—
262	C₂²⋊C₄×C₂₉	—	2	1	no	—
263	C₂²⋊C₄×C₂₉	—	2	1	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	—	4	1	no	—
269	C₄²×C₂₉	—	2	1	no	—
270	C₄²×C₂₉	—	2	1	no	—
271	C₄²×C₂₉	—	4	1	no	—
272	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
274	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
276	#18931	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂³×C₂₉	—	2	1	no	—
278	C₂³×C₂₉	—	2	1	no	—
279	C₂³×C₂₉	—	2	2	no	—
280	C₂³×C₂₉	—	2	2	no	—
281	C₂³×C₂₉	—	4	4	no	—
282	C₂³×C₂₉	—	8	2	no	—
283	C₂³×C₂₉	—	8	2	no	—
284	C₂³×C₂₉	—	8	2	no	—
285	C₂³×C₂₉	—	8	2	no	—
286	C₂³×C₂₉	—	8	2	no	—
287	C₂³×C₂₉	#120	1	1	yes	characteristic
288	Q₈×C₂₉	—	2	1	no	—
289	Q₈×C₂₉	—	2	1	no	—
290	Q₈×C₂₉	—	2	1	no	—
291	Q₈×C₂₉	—	2	1	no	—
292	Q₈×C₂₉	—	4	2	no	—
293	Q₈×C₂₉	—	4	1	no	—
294	Q₈×C₂₉	—	4	1	no	—
295	D₄×C₂₉	—	2	1	no	—
296	D₄×C₂₉	—	2	1	no	—
297	D₄×C₂₉	—	2	1	no	—
298	D₄×C₂₉	—	2	1	no	—
299	D₄×C₂₉	—	4	2	no	—
300	D₄×C₂₉	—	4	2	no	—
301	D₄×C₂₉	—	4	2	no	—
302	D₄×C₂₉	—	4	2	no	—
303	D₄×C₂₉	—	4	1	no	—
304	D₄×C₂₉	—	4	1	no	—
305	D₄×C₂₉	—	4	1	no	—
306	D₄×C₂₉	—	4	1	no	—
307	D₄×C₂₉	—	4	1	no	—
308	D₄×C₂₉	—	4	1	no	—
309	D₄×C₂₉	—	4	1	no	—
310	D₄×C₂₉	—	4	1	no	—
311	D₄×C₂₉	—	8	2	no	—
312	D₄×C₂₉	—	8	2	no	—
313	D₄×C₂₉	—	8	2	no	—
314	D₄×C₂₉	—	8	2	no	—
315	D₄×C₂₉	—	8	2	no	—
316	D₄×C₂₉	—	8	2	no	—
317	D₄×C₂₉	—	8	2	no	—
318	D₄×C₂₉	—	8	2	no	—
319	D₄×C₂₉	—	8	2	no	—
320	C₂×C₄×C₂₉	—	2	1	no	—
321	C₂×C₄×C₂₉	—	2	1	no	—
322	C₂×C₄×C₂₉	—	2	1	no	—
323	C₂×C₄×C₂₉	—	2	1	no	—
324	C₂×C₄×C₂₉	—	2	1	no	—
325	C₂×C₄×C₂₉	—	2	1	no	—
326	C₂×C₄×C₂₉	—	2	1	no	—
327	C₂×C₄×C₂₉	—	2	1	no	—
328	C₂×C₄×C₂₉	—	2	1	no	—
329	C₂×C₄×C₂₉	—	2	1	no	—
330	C₂×C₄×C₂₉	—	4	1	no	—
331	C₂×C₄×C₂₉	—	4	1	no	—
332	C₂×C₄×C₂₉	—	4	1	no	—
333	C₂×C₄×C₂₉	—	4	1	no	—
334	C₂×C₄×C₂₉	—	4	1	no	—
335	C₂×C₄×C₂₉	—	4	1	no	—
336	C₂×C₄×C₂₉	—	4	1	no	—
337	C₂×C₄×C₂₉	—	8	2	no	—
338	C₂×C₄×C₂₉	—	8	2	no	—
339	C₂×C₄×C₂₉	—	8	2	no	—
340	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
341	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
342	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
343	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
346	C₈×C₂₉	—	4	1	no	—
347	C₈×C₂₉	—	4	1	no	—
348	C₈×C₂₉	—	4	1	no	—
349	C₈×C₂₉	—	4	1	no	—
350	C₈×C₂₉	—	4	1	no	—
351	C₈×C₂₉	—	4	1	no	—
352	#3543	C₂×C₂₉	1	1	yes	characteristic
353	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
354	#3233	C₂×C₂₉	1	1	yes	characteristic, complemented
355	#3208	C₂×C₂₉	1	1	yes	characteristic, complemented
356	#1642	C₂×C₂₉	1	1	yes	characteristic, complemented
357	#1641	C₂×C₂₉	1	1	yes	characteristic, complemented
358	#1640	C₂×C₂₉	1	1	yes	characteristic, complemented
359	#1639	C₂×C₂₉	1	1	yes	characteristic, complemented
360	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
361	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
362	#1630	C₂×C₂₉	1	1	yes	characteristic, complemented
363	#1629	C₂×C₂₉	1	1	yes	characteristic, complemented
364	#1545	C₂×C₂₉	1	1	yes	characteristic, complemented
365	#1495	C₂×C₂₉	1	1	yes	characteristic, complemented
366	#1482	C₂×C₂₉	1	1	yes	characteristic, complemented
367	C₂²×C₂₉	—	2	1	no	—
368	C₂²×C₂₉	—	2	1	no	—
369	C₂²×C₂₉	—	2	1	no	—
370	C₂²×C₂₉	—	4	1	no	—
371	C₂²×C₂₉	—	4	2	no	—
372	C₂²×C₂₉	—	4	1	no	—
373	C₂²×C₂₉	—	4	2	no	—
374	C₂²×C₂₉	—	4	1	no	—
375	C₂²×C₂₉	—	4	2	no	—
376	C₂²×C₂₉	—	4	1	no	—
377	C₂²×C₂₉	—	4	2	no	—
378	C₂²×C₂₉	—	4	2	no	—
379	C₂²×C₂₉	—	4	1	no	—
380	C₂²×C₂₉	—	4	1	no	—
381	C₂²×C₂₉	—	4	2	no	—
382	C₂²×C₂₉	—	16	4	no	—
383	C₂²×C₂₉	—	16	4	no	—
384	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
385	C₄×C₂₉	—	2	1	no	—
386	C₄×C₂₉	—	2	1	no	—
387	C₄×C₂₉	—	2	1	no	—
388	C₄×C₂₉	—	2	1	no	—
389	C₄×C₂₉	—	4	1	no	—
390	C₄×C₂₉	—	4	1	no	—
391	C₄×C₂₉	—	4	1	no	—
392	C₄×C₂₉	—	4	1	no	—
393	C₄×C₂₉	—	4	1	no	—
394	C₄×C₂₉	—	4	1	no	—
395	C₄×C₂₉	—	8	1	no	—
396	C₄×C₂₉	—	8	1	no	—
397	C₄×C₂₉	#576	1	1	yes	characteristic
398	C₄×C₂₉	#577	1	1	yes	characteristic
399	C₄×C₂₉	#577	1	1	yes	characteristic
400	C₄×C₂₉	#577	1	1	yes	characteristic
401	#560	—	2	2	no	—
402	#559	C₂²×C₂₉	1	1	yes	characteristic
403	#550	C₂²×C₂₉	1	1	yes	characteristic
404	#550	C₂²×C₂₉	1	1	yes	characteristic
405	#546	—	2	1	no	—
406	#546	—	2	1	no	—
407	D₄²	—	2	1	no	—
408	D₄²	—	2	1	no	—
409	D₄²	C₂²×C₂₉	1	1	yes	characteristic
410	#540	—	2	1	no	—
411	#540	—	2	1	no	—
412	#535	—	2	1	no	—
413	#535	—	2	1	no	—
414	#534	—	2	2	no	—
415	#533	C₂²×C₂₉	1	1	yes	characteristic, complemented
416	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
417	#529	C₂²×C₂₉	1	1	yes	characteristic
418	#529	C₂²×C₂₉	1	1	yes	characteristic
419	#499	—	2	1	no	—
420	#492	C₂²×C₂₉	1	1	yes	characteristic
421	#492	C₂²×C₂₉	1	1	yes	characteristic, complemented
422	#488	—	2	1	no	—
423	#486	C₂²×C₂₉	1	1	yes	characteristic
424	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
425	#485	—	2	1	no	—
426	#482	—	2	1	no	—
427	#479	—	2	1	no	—
428	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
429	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
430	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
431	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
432	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
433	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
434	#470	—	2	1	no	—
435	#468	—	2	1	no	—
436	#464	—	2	1	no	—
437	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
438	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
439	#460	—	2	2	no	—
440	#450	—	2	2	no	—
441	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
442	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
443	#423	C₂²×C₂₉	1	1	yes	characteristic, complemented
444	#331	C₂²×C₂₉	1	1	yes	characteristic
445	#331	C₂²×C₂₉	1	1	yes	characteristic
446	#331	C₂²×C₂₉	1	1	yes	characteristic, complemented
447	#331	C₂²×C₂₉	1	1	yes	characteristic, complemented
448	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
449	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
450	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
451	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
452	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
453	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
454	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
455	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
456	C₂×C₂₉	—	4	1	no	—
457	C₂×C₂₉	—	8	2	no	—
458	C₂×C₂₉	—	8	1	no	—
459	C₂×C₂₉	—	8	1	no	—
460	C₂×C₂₉	—	8	2	no	—
461	C₂×C₂₉	#3009	1	1	yes	characteristic
462	C₂×C₂₉	#3012	1	1	yes	characteristic
463	C₂×C₂₉	#3019	1	1	yes	characteristic
464	C₂×#41	—	2	1	no	—
465	C₂×#41	—	2	1	no	—
466	C₂²×D₄	—	2	2	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	D₄×C₂₉	1	2	yes	—
472	C₂×Q₁₆	—	2	1	no	—
473	C₂×SD₁₆	—	2	2	no	—
474	C₂×SD₁₆	—	2	2	no	—
475	C₂×SD₁₆	—	2	1	no	—
476	C₂×M₁₆	—	2	1	no	—
477	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
479	#127	—	2	1	no	—
480	#127	—	2	1	no	—
481	#127	—	2	1	no	—
482	#127	—	2	1	no	—
483	#127	D₄×C₂₉	1	2	yes	—
484	#127	C₂³×C₂₉	1	1	yes	characteristic
485	#127	C₂³×C₂₉	1	1	yes	characteristic
486	#126	—	2	1	no	—
487	#126	—	2	1	no	—
488	#125	—	2	1	no	—
489	#125	D₄×C₂₉	1	1	yes	characteristic
490	#125	D₄×C₂₉	1	1	yes	characteristic
491	#124	—	2	1	no	—
492	#124	—	2	1	no	—
493	#124	D₄×C₂₉	1	1	yes	characteristic
494	#124	D₄×C₂₉	1	1	yes	characteristic
495	#123	—	2	2	no	—
496	#123	—	2	2	no	—
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	#123	—	2	1	no	—
500	#123	—	2	1	no	—
501	C₂²⋊Q₈	—	2	1	no	—
502	C₂²⋊Q₈	—	2	1	no	—
503	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
504	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
505	#121	—	2	2	no	—
506	#121	—	2	2	no	—
507	#121	—	2	2	no	—
508	#121	—	2	2	no	—
509	#121	—	2	2	no	—
510	#121	—	2	2	no	—
511	#121	—	2	2	no	—
512	#121	—	2	2	no	—
513	#121	—	2	1	no	—
514	#121	—	2	1	no	—
515	#121	—	2	1	no	—
516	#121	—	2	1	no	—
517	#121	D₄×C₂₉	1	1	yes	characteristic
518	#121	D₄×C₂₉	1	1	yes	characteristic
519	#120	—	2	2	no	—
520	#120	—	2	2	no	—
521	#120	—	2	2	no	—
522	#120	—	2	2	no	—
523	#120	—	2	2	no	—
524	#120	—	2	2	no	—
525	C₄×Q₈	—	2	1	no	—
526	C₄×Q₈	—	2	1	no	—
527	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
528	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
529	C₄×D₄	—	2	1	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
536	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
537	#117	—	2	1	no	—
538	#117	—	2	1	no	—
539	#117	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
542	#107	—	2	1	no	—
543	#107	—	2	1	no	—
544	#107	—	2	1	no	—
545	#106	—	2	1	no	—
546	#106	—	2	1	no	—
547	#106	—	2	1	no	—
548	C₄⋊C₈	—	2	1	no	—
549	C₄⋊C₈	—	2	1	no	—
550	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
553	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
554	#103	—	2	1	no	—
555	#103	—	2	1	no	—
556	#103	—	2	1	no	—
557	#103	—	2	1	no	—
558	#103	—	2	1	no	—
559	#102	—	2	2	no	—
560	#102	—	2	2	no	—
561	#102	—	2	1	no	—
562	#102	—	2	1	no	—
563	#102	—	2	1	no	—
564	C₂²⋊C₈	—	2	1	no	—
565	C₂²⋊C₈	—	2	1	no	—
566	C₄×C₈	—	2	1	no	—
567	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
568	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
569	C₂₉	#18931	1	1	yes	characteristic, direct product factor, Sylow
570	C₂⁴	—	2	2	no	—
571	C₂⁴	—	2	2	no	—
572	#41	—	8	1	no	—
573	#41	—	8	1	no	—
574	#41	—	8	1	no	—
575	#41	—	8	1	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
579	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
580	C₂×D₄	—	2	1	no	—
581	C₂×D₄	—	2	1	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	8	1	no	—
596	C₂×D₄	—	8	1	no	—
597	C₂×D₄	—	8	1	no	—
598	C₂×D₄	—	8	1	no	—
599	C₂×D₄	—	8	1	no	—
600	C₂×D₄	—	8	1	no	—
601	C₂×D₄	—	8	1	no	—
602	C₂×D₄	—	8	1	no	—
603	C₂×D₄	—	8	2	no	—
604	C₂×D₄	—	8	4	no	—
605	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
606	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
607	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
608	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	2	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
617	Q₁₆	—	8	1	no	—
618	SD₁₆	—	8	1	no	—
619	SD₁₆	—	8	2	no	—
620	SD₁₆	—	8	2	no	—
621	M₁₆	—	8	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	4	1	no	—
641	C₄⋊C₄	—	4	1	no	—
642	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
643	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
645	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	—	2	1	no	—
654	C₂²⋊C₄	—	2	1	no	—
655	C₂²⋊C₄	—	2	1	no	—
656	C₂²⋊C₄	—	2	1	no	—
657	C₂²⋊C₄	—	2	1	no	—
658	C₂²⋊C₄	—	2	1	no	—
659	C₂²⋊C₄	—	2	1	no	—
660	C₂²⋊C₄	—	2	1	no	—
661	C₂²⋊C₄	—	2	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	4	1	no	—
666	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
667	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
668	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
669	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	8	2	no	—
676	C₂³	—	8	2	no	—
677	C₂³	—	8	2	no	—
678	C₂³	—	8	2	no	—
679	C₂³	—	8	2	no	—
680	C₂³	C₂₉×#120	1	1	yes	characteristic
681	Q₈	—	2	1	no	—
682	Q₈	—	2	1	no	—
683	Q₈	—	2	1	no	—
684	Q₈	—	2	1	no	—
685	Q₈	—	4	2	no	—
686	Q₈	—	4	1	no	—
687	Q₈	—	4	1	no	—
688	D₄	—	2	1	no	—
689	D₄	—	2	1	no	—
690	D₄	—	2	1	no	—
691	D₄	—	2	1	no	—
692	D₄	—	4	2	no	—
693	D₄	—	4	2	no	—
694	D₄	—	4	2	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	1	no	—
703	D₄	—	4	1	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	2	no	—
706	D₄	—	8	2	no	—
707	D₄	—	8	2	no	—
708	D₄	—	8	2	no	—
709	D₄	—	8	2	no	—
710	D₄	—	8	2	no	—
711	D₄	—	8	2	no	—
712	D₄	—	8	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	8	2	no	—
731	C₂×C₄	—	8	2	no	—
732	C₂×C₄	—	8	2	no	—
733	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
734	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
735	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
736	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
737	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
738	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₈	—	4	1	no	—
742	C₈	—	4	1	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	4	1	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	2	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	2	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	16	4	no	—
761	C₂²	—	16	4	no	—
762	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	2	1	no	—
766	C₄	—	2	1	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	8	1	no	—
774	C₄	—	8	1	no	—
775	C₄	C₂₉×#576	1	1	yes	characteristic
776	C₄	C₂₉×#577	1	1	yes	characteristic
777	C₄	C₂₉×#577	1	1	yes	characteristic
778	C₄	C₂₉×#577	1	1	yes	characteristic
779	C₂	—	4	1	no	—
780	C₂	—	8	1	no	—
781	C₂	—	8	1	no	—
782	C₂	—	8	2	no	—
783	C₂	—	8	2	no	—
784	C₂	C₂₉×#3009	1	1	yes	characteristic
785	C₂	C₂₉×#3012	1	1	yes	characteristic
786	C₂	C₂₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
prime radical	C₂₉×#3543	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
2. C₂₉×#3252	C₂	semidirect
3. C₂₉×#3233	C₂	semidirect
4. C₂₉×#3208	C₂	semidirect
5. C₂₉×#1642	C₂	semidirect
6. C₂₉×#1641	C₂	semidirect
7. C₂₉×#1640	C₂	semidirect
8. C₂₉×#1639	C₂	semidirect
9. C₂₉×#1631	C₂	semidirect
10. C₂₉×#1631	C₂	semidirect
11. C₂₉×#1630	C₂	semidirect
12. C₂₉×#1629	C₂	semidirect
13. C₂₉×#1545	C₂	semidirect
14. C₂₉×#1495	C₂	semidirect
15. C₂₉×#1482	C₂	semidirect
30. C₂₉×#533	C₂²	semidirect
36. C₂₉×#492	C₂²	semidirect
39. C₂₉×#486	C₂²	semidirect
43. C₂₉×#477	C₂²	semidirect
44. C₂₉×#477	C₂²	semidirect
45. C₂₉×#476	C₂²	semidirect
46. C₂₉×#476	C₂²	semidirect
47. C₂₉×#475	C₂²	semidirect
48. C₂₉×#474	C₂²	semidirect
52. C₂₉×#462	C₂²	semidirect
53. C₂₉×#461	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
276. #18931	C₂₉	direct (N × H)
353. #3252	C₂×C₂₉	semidirect
354. #3233	C₂×C₂₉	semidirect
355. #3208	C₂×C₂₉	semidirect
356. #1642	C₂×C₂₉	semidirect
357. #1641	C₂×C₂₉	semidirect
358. #1640	C₂×C₂₉	semidirect
359. #1639	C₂×C₂₉	semidirect
360. #1631	C₂×C₂₉	semidirect
361. #1631	C₂×C₂₉	semidirect
362. #1630	C₂×C₂₉	semidirect
363. #1629	C₂×C₂₉	semidirect
364. #1545	C₂×C₂₉	semidirect
365. #1495	C₂×C₂₉	semidirect
366. #1482	C₂×C₂₉	semidirect
415. #533	C₂²×C₂₉	semidirect
421. #492	C₂²×C₂₉	semidirect
424. #486	C₂²×C₂₉	semidirect
428. #477	C₂²×C₂₉	semidirect
429. #477	C₂²×C₂₉	semidirect
430. #476	C₂²×C₂₉	semidirect
431. #476	C₂²×C₂₉	semidirect
432. #475	C₂²×C₂₉	semidirect
433. #474	C₂²×C₂₉	semidirect
437. #462	C₂²×C₂₉	semidirect
438. #461	C₂²×C₂₉	semidirect
441. #431	C₂²×C₂₉	semidirect
442. #431	C₂²×C₂₉	semidirect
443. #423	C₂²×C₂₉	semidirect
446. #331	C₂²×C₂₉	semidirect
447. #331	C₂²×C₂₉	semidirect
448. Q₈⋊C₈	C₂²×C₂₉	semidirect
449. Q₈⋊C₈	C₂²×C₂₉	semidirect
450. Q₈⋊C₈	C₂²×C₂₉	semidirect
451. Q₈⋊C₈	C₂²×C₂₉	semidirect
452. D₄⋊C₈	C₂²×C₂₉	semidirect
453. D₄⋊C₈	C₂²×C₂₉	semidirect
454. D₄⋊C₈	C₂²×C₂₉	semidirect
455. D₄⋊C₈	C₂²×C₂₉	semidirect
569. C₂₉	#18931	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×#3252	2
C₂₉×#3233	2
C₂₉×#3208	2
C₂₉×#1642	2
C₂₉×#1641	2
C₂₉×#1640	2
C₂₉×#1639	2
C₂₉×#1631	2
C₂₉×#1630	2
C₂₉×#1629	2
C₂₉×#1545	2
C₂₉×#1495	2
C₂₉×#1482	2
#18931	29

Subgroups — C29×#18931 #20313831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18931 #20313831