Subgroups — C₂₉×#60708 #20355608

Order 7424.

1860 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3495	C₂	1	2	yes	maximal, complemented
2	C₂₉×#3181	C₂	1	4	yes	maximal, complemented
3	C₂₉×#3178	C₂	1	4	yes	maximal, complemented
4	C₂₉×#3177	C₂	1	2	yes	maximal, complemented
5	C₂₉×#3175	C₂	1	2	yes	maximal, complemented
6	C₂₉×#3170	C₂	1	2	yes	maximal, complemented
7	C₂₉×#3168	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3156	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#3137	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3056	C₂	1	2	yes	maximal, complemented
12	C₂₉×#3050	C₂	1	1	yes	maximal, characteristic
13	C₂×C₂₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#2951	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#2950	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₂₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₉×#137	C₂²	1	2	yes	—
19	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₂₉	C₂²	1	1	yes	characteristic
23	C₂₉×#556	—	2	2	no	—
24	C₂₉×#554	—	2	2	no	—
25	C₂₉×#552	—	2	4	no	—
26	C₂₉×#552	—	2	2	no	—
27	C₂₉×#552	—	2	2	no	—
28	C₂₉×#551	—	2	4	no	—
29	C₂₉×#544	C₂²	1	2	yes	—
30	C₂₉×#542	C₂²	1	4	yes	—
31	C₂₉×#541	C₂²	1	4	yes	—
32	C₂₉×#536	C₂²	1	2	yes	—
33	C₂₉×#533	C₂²	1	4	yes	—
34	C₂₉×#529	C₂²	1	4	yes	—
35	C₂₉×#525	C₂²	1	2	yes	—
36	C₂×C₂₉×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂₉×#520	C₂²	1	2	yes	—
38	C₂₉×#519	C₂²	1	2	yes	—
39	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
40	C₂₉×#501	C₂²	1	4	yes	complemented
41	C₂₉×#500	C₂²	1	2	yes	complemented
42	C₂₉×#499	C₂²	1	2	yes	complemented
43	C₂₉×#497	C₂²	1	4	yes	complemented
44	C₂₉×#495	C₂²	1	2	yes	complemented
45	C₂₉×#494	C₂²	1	2	yes	complemented
46	C₂₉×#491	C₂²	1	4	yes	complemented
47	C₂₉×#489	C₂²	1	4	yes	complemented
48	C₂₉×#488	C₂²	1	4	yes	complemented
49	C₂₉×#487	C₂²	1	4	yes	complemented
50	C₂₉×#470	C₂²	1	4	yes	—
51	C₂₉×#468	C₂²	1	4	yes	—
52	C₂₉×#467	C₂²	1	2	yes	—
53	C₂₉×#467	C₂²	1	2	yes	—
54	C₂₉×#467	C₂²	1	2	yes	—
55	C₂₉×#467	C₂²	1	2	yes	—
56	C₂₉×#467	C₂²	1	1	yes	characteristic
57	C₂₉×#467	C₂²	1	1	yes	characteristic
58	C₂₉×#467	C₂²	1	4	yes	—
59	C₂₉×#466	C₂²	1	1	yes	characteristic
60	C₂₉×#466	C₂²	1	1	yes	characteristic
61	C₂₉×#465	C₂²	1	2	yes	—
62	C₂₉×#465	C₂²	1	2	yes	—
63	C₂₉×#465	C₂²	1	4	yes	—
64	C₂₉×#441	C₂²	1	4	yes	complemented
65	C₂₉×#441	C₂²	1	4	yes	complemented
66	C₂₉×#440	C₂²	1	4	yes	complemented
67	C₂₉×#440	C₂²	1	4	yes	complemented
68	C₄×Q₁₆×C₂₉	C₂²	1	4	yes	complemented
69	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
70	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
71	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
72	C₄×SD₁₆×C₂₉	C₂²	1	4	yes	complemented
73	C₄×D₈×C₂₉	C₂²	1	2	yes	complemented
74	C₂₉×#428	C₂²	1	2	yes	—
75	C₂₉×#427	C₂²	1	1	yes	characteristic
76	C₂×C₂₉×#107	C₂²	1	1	yes	characteristic
77	C₂₉×#419	C₂²	1	2	yes	—
78	C₂₉×#417	C₂²	1	2	yes	—
79	C₂₉×#416	C₂²	1	2	yes	—
80	C₂×C₂₉×#103	C₂²	1	2	yes	—
81	C₂₉×#405	C₂²	1	1	yes	characteristic
82	C₂₉×#405	C₂²	1	1	yes	characteristic
83	C₂₉×#405	C₂²	1	1	yes	characteristic
84	C₂₉×#405	C₂²	1	1	yes	characteristic
85	C₂₉×#405	C₂²	1	2	yes	—
86	C₂₉×#405	C₂²	1	2	yes	—
87	C₂×C₂₉×#97	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₂₉	C₂²	1	2	yes	—
89	C₂×#41×C₂₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
92	C₂₉×#137	—	2	8	no	—
93	C₂₉×#135	—	2	4	no	—
94	C₂×Q₁₆×C₂₉	—	2	4	no	—
95	C₂×Q₁₆×C₂₉	C₂³	1	1	yes	characteristic
96	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
97	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
98	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
99	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
101	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₂₉	—	2	4	no	—
103	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
104	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₉	—	2	4	no	—
107	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
110	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
114	C₂₉×C₄⋊Q₈	—	2	2	no	—
115	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₂₉×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₂₉×#126	—	2	4	no	—
118	C₂₉×#126	—	2	4	no	—
119	C₂₉×#126	—	2	4	no	—
120	C₂₉×#126	—	2	4	no	—
121	C₂₉×#125	—	2	4	no	—
122	C₂₉×#125	—	2	4	no	—
123	C₂₉×#125	—	2	2	no	—
124	C₂₉×#125	—	2	4	no	—
125	C₂₉×#125	C₂³	1	4	yes	—
126	C₂₉×#124	—	2	4	no	—
127	C₂₉×#124	C₂³	1	4	yes	—
128	C₂₉×#123	—	2	2	no	—
129	C₂₉×#123	—	2	4	no	—
130	C₂₉×#123	—	2	4	no	—
131	C₂₉×#123	—	2	4	no	—
132	C₂₉×C₂²⋊Q₈	—	2	2	no	—
133	C₂₉×C₂²⋊Q₈	—	2	2	no	—
134	C₂₉×C₂²⋊Q₈	—	2	4	no	—
135	C₂₉×C₂²⋊Q₈	—	2	2	no	—
136	C₂₉×C₂²⋊Q₈	—	2	2	no	—
137	C₂₉×C₂²⋊Q₈	—	2	4	no	—
138	C₂₉×C₂²⋊Q₈	—	2	4	no	—
139	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
140	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₉×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₂₉×#121	C₂³	1	2	yes	—
144	C₂₉×#121	C₂³	1	2	yes	—
145	C₂₉×#120	—	2	2	no	—
146	C₄×Q₈×C₂₉	—	2	2	no	—
147	C₄×Q₈×C₂₉	—	2	2	no	—
148	C₄×Q₈×C₂₉	—	2	4	no	—
149	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
150	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
151	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
152	C₄×D₄×C₂₉	—	2	2	no	—
153	C₄×D₄×C₂₉	—	2	2	no	—
154	C₄×D₄×C₂₉	—	2	4	no	—
155	C₄×D₄×C₂₉	—	2	4	no	—
156	C₄×D₄×C₂₉	C₂³	1	4	yes	—
157	C₂₉×#117	—	2	4	no	—
158	C₂₉×#117	—	2	2	no	—
159	C₂₉×#117	—	2	4	no	—
160	C₂₉×#117	—	2	4	no	—
161	C₂₉×#117	D₄	1	1	yes	characteristic
162	C₂₉×#117	D₄	1	2	yes	—
163	C₂₉×#117	D₄	1	1	yes	characteristic
164	C₂₉×#117	C₂³	1	2	yes	—
165	C₂₉×#117	C₂³	1	1	yes	characteristic
166	C₂₉×#117	C₂³	1	1	yes	characteristic
167	C₂₉×#117	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
169	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
170	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
174	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
175	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
176	C₂₉×#107	C₂³	1	2	yes	—
177	C₂₉×#107	C₂³	1	2	yes	—
178	C₂₉×#107	C₂³	1	1	yes	characteristic
179	C₂₉×#107	C₂³	1	1	yes	characteristic
180	C₂₉×#107	C₂³	1	4	yes	—
181	C₂₉×#106	C₂³	1	2	yes	—
182	C₂₉×#106	C₂³	1	4	yes	—
183	C₂₉×#103	C₂³	1	4	yes	—
184	C₂₉×#103	C₂³	1	2	yes	—
185	C₂₉×#103	C₂³	1	4	yes	—
186	C₂₉×#103	C₂³	1	4	yes	—
187	C₂₉×#103	C₂³	1	4	yes	—
188	C₂₉×#103	C₂³	1	4	yes	—
189	C₂₉×#103	C₂³	1	2	yes	—
190	C₂₉×#102	C₂³	1	4	yes	—
191	C₂₉×#102	C₂³	1	2	yes	—
192	C₂₉×#102	C₂³	1	2	yes	—
193	C₂₉×#97	C₂³	1	2	yes	—
194	C₂₉×#97	C₂³	1	2	yes	—
195	C₂₉×#97	C₂³	1	2	yes	—
196	C₂₉×#97	C₂³	1	2	yes	—
197	C₄×C₈×C₂₉	C₂³	1	2	yes	—
198	C₄×C₈×C₂₉	C₂³	1	2	yes	—
199	C₄×C₈×C₂₉	C₂³	1	2	yes	—
200	C₄×C₈×C₂₉	C₂³	1	2	yes	—
201	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
202	#41×C₂₉	—	2	4	no	—
203	#41×C₂₉	—	2	4	no	—
204	C₂×Q₈×C₂₉	—	2	2	no	—
205	C₂×Q₈×C₂₉	—	2	4	no	—
206	C₂×Q₈×C₂₉	—	2	4	no	—
207	C₂×Q₈×C₂₉	—	2	4	no	—
208	C₂×Q₈×C₂₉	C₂⁴	1	4	yes	—
209	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
210	C₂×D₄×C₂₉	—	2	2	no	—
211	C₂×D₄×C₂₉	—	2	2	no	—
212	C₂×D₄×C₂₉	—	2	2	no	—
213	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₉	—	2	2	no	—
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	2	no	—
219	C₂²×C₄×C₂₉	—	2	4	no	—
220	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
228	Q₁₆×C₂₉	—	2	4	no	—
229	Q₁₆×C₂₉	—	2	4	no	—
230	Q₁₆×C₂₉	—	2	2	no	—
231	Q₁₆×C₂₉	—	2	8	no	—
232	SD₁₆×C₂₉	—	2	4	no	—
233	SD₁₆×C₂₉	—	2	8	no	—
234	D₈×C₂₉	—	2	2	no	—
235	M₁₆×C₂₉	—	2	2	no	—
236	M₁₆×C₂₉	—	2	4	no	—
237	M₁₆×C₂₉	#41	1	4	yes	—
238	C₂×C₈×C₂₉	—	2	2	no	—
239	C₂×C₈×C₂₉	—	2	2	no	—
240	C₂×C₈×C₂₉	—	2	2	no	—
241	C₂×C₈×C₂₉	—	2	2	no	—
242	C₂×C₈×C₂₉	—	2	2	no	—
243	C₂×C₈×C₂₉	—	2	4	no	—
244	C₂×C₈×C₂₉	#41	1	4	yes	—
245	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
248	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₂₉	—	2	2	no	—
252	C₄⋊C₄×C₂₉	—	2	4	no	—
253	C₄⋊C₄×C₂₉	—	2	4	no	—
254	C₄⋊C₄×C₂₉	—	2	4	no	—
255	C₄⋊C₄×C₂₉	—	2	4	no	—
256	C₄⋊C₄×C₂₉	—	2	4	no	—
257	C₄⋊C₄×C₂₉	—	2	4	no	—
258	C₄⋊C₄×C₂₉	—	2	4	no	—
259	C₄⋊C₄×C₂₉	—	2	4	no	—
260	C₄⋊C₄×C₂₉	—	2	2	no	—
261	C₄⋊C₄×C₂₉	—	2	4	no	—
262	C₄⋊C₄×C₂₉	—	2	2	no	—
263	C₄⋊C₄×C₂₉	—	2	4	no	—
264	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
267	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
269	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
270	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
271	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
273	C₂²⋊C₄×C₂₉	—	2	4	no	—
274	C₂²⋊C₄×C₂₉	—	2	4	no	—
275	C₂²⋊C₄×C₂₉	—	2	2	no	—
276	C₂²⋊C₄×C₂₉	—	2	2	no	—
277	C₂²⋊C₄×C₂₉	—	2	2	no	—
278	C₂²⋊C₄×C₂₉	—	2	2	no	—
279	C₂²⋊C₄×C₂₉	—	2	4	no	—
280	C₂²⋊C₄×C₂₉	—	2	4	no	—
281	C₂²⋊C₄×C₂₉	—	2	2	no	—
282	C₂²⋊C₄×C₂₉	—	2	4	no	—
283	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
284	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
285	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
286	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
287	C₄²×C₂₉	—	2	4	no	—
288	C₄²×C₂₉	—	2	4	no	—
289	C₄²×C₂₉	—	2	4	no	—
290	C₄²×C₂₉	—	2	2	no	—
291	C₄²×C₂₉	C₂×D₄	1	2	yes	—
292	C₄²×C₂₉	C₂×D₄	1	2	yes	—
293	C₄²×C₂₉	C₂⁴	1	2	yes	—
294	C₄²×C₂₉	C₂⁴	1	2	yes	—
295	#60708	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂³×C₂₉	—	2	2	no	—
297	C₂³×C₂₉	—	2	2	no	—
298	C₂³×C₂₉	—	2	2	no	—
299	C₂³×C₂₉	—	4	1	no	—
300	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
301	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
302	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
303	Q₈×C₂₉	—	2	4	no	—
304	Q₈×C₂₉	—	2	2	no	—
305	Q₈×C₂₉	—	2	4	no	—
306	Q₈×C₂₉	—	2	2	no	—
307	Q₈×C₂₉	—	4	4	no	—
308	Q₈×C₂₉	—	8	4	no	—
309	D₄×C₂₉	—	2	2	no	—
310	D₄×C₂₉	—	2	2	no	—
311	D₄×C₂₉	—	4	4	no	—
312	D₄×C₂₉	—	4	4	no	—
313	D₄×C₂₉	—	8	2	no	—
314	C₂×C₄×C₂₉	—	2	2	no	—
315	C₂×C₄×C₂₉	—	2	4	no	—
316	C₂×C₄×C₂₉	—	2	2	no	—
317	C₂×C₄×C₂₉	—	2	2	no	—
318	C₂×C₄×C₂₉	—	2	1	no	—
319	C₂×C₄×C₂₉	—	2	1	no	—
320	C₂×C₄×C₂₉	—	2	1	no	—
321	C₂×C₄×C₂₉	—	2	1	no	—
322	C₂×C₄×C₂₉	—	2	2	no	—
323	C₂×C₄×C₂₉	—	2	2	no	—
324	C₂×C₄×C₂₉	—	2	4	no	—
325	C₂×C₄×C₂₉	—	2	2	no	—
326	C₂×C₄×C₂₉	—	2	4	no	—
327	C₂×C₄×C₂₉	—	4	2	no	—
328	C₂×C₄×C₂₉	—	4	4	no	—
329	C₂×C₄×C₂₉	—	4	4	no	—
330	C₂×C₄×C₂₉	—	8	4	no	—
331	C₂×C₄×C₂₉	—	8	2	no	—
332	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
336	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
340	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
341	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
342	C₈×C₂₉	—	2	1	no	—
343	C₈×C₂₉	—	2	1	no	—
344	C₈×C₂₉	—	2	2	no	—
345	C₈×C₂₉	C₂×#41	1	2	yes	—
346	C₈×C₂₉	C₂×#41	1	2	yes	—
347	C₈×C₂₉	C₂×#41	1	4	yes	—
348	#3495	C₂×C₂₉	1	2	yes	complemented
349	#3181	C₂×C₂₉	1	4	yes	complemented
350	#3178	C₂×C₂₉	1	4	yes	complemented
351	#3177	C₂×C₂₉	1	2	yes	complemented
352	#3175	C₂×C₂₉	1	2	yes	complemented
353	#3170	C₂×C₂₉	1	2	yes	complemented
354	#3168	C₂×C₂₉	1	2	yes	complemented
355	#3164	C₂×C₂₉	1	1	yes	characteristic, complemented
356	#3156	C₂×C₂₉	1	1	yes	characteristic, complemented
357	#3137	C₂×C₂₉	1	2	yes	complemented
358	#3056	C₂×C₂₉	1	2	yes	complemented
359	#3050	C₂×C₂₉	1	1	yes	characteristic
360	C₂×#467	C₂×C₂₉	1	1	yes	characteristic, complemented
361	#2951	C₂×C₂₉	1	1	yes	characteristic, complemented
362	#2950	C₂×C₂₉	1	1	yes	characteristic, complemented
363	#2947	C₂×C₂₉	1	2	yes	complemented
364	C₂×#405	C₂×C₂₉	1	1	yes	characteristic, complemented
365	C₂²×C₂₉	—	2	1	no	—
366	C₂²×C₂₉	—	2	1	no	—
367	C₂²×C₂₉	—	2	1	no	—
368	C₂²×C₂₉	—	2	1	no	—
369	C₂²×C₂₉	—	2	1	no	—
370	C₂²×C₂₉	—	2	1	no	—
371	C₂²×C₂₉	—	2	1	no	—
372	C₂²×C₂₉	—	4	4	no	—
373	C₂²×C₂₉	—	4	2	no	—
374	C₂²×C₂₉	—	4	2	no	—
375	C₂²×C₂₉	—	4	2	no	—
376	C₂²×C₂₉	#532	1	2	yes	—
377	C₂²×C₂₉	#578	1	2	yes	—
378	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₂₉	—	2	2	no	—
380	C₄×C₂₉	—	2	2	no	—
381	C₄×C₂₉	—	2	1	no	—
382	C₄×C₂₉	—	2	1	no	—
383	C₄×C₂₉	—	2	2	no	—
384	C₄×C₂₉	—	2	2	no	—
385	C₄×C₂₉	—	4	4	no	—
386	C₄×C₂₉	—	4	2	no	—
387	C₄×C₂₉	—	4	2	no	—
388	C₄×C₂₉	—	4	4	no	—
389	C₄×C₂₉	—	4	2	no	—
390	C₄×C₂₉	#532	1	2	yes	—
391	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
392	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
393	C₂×#137	C₂²×C₂₉	1	2	yes	—
394	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
395	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
396	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
397	C₂³×C₈	C₂²×C₂₉	1	1	yes	characteristic
398	#556	—	2	2	no	—
399	#554	—	2	2	no	—
400	#552	—	2	4	no	—
401	#552	—	2	2	no	—
402	#552	—	2	2	no	—
403	#551	—	2	4	no	—
404	#544	C₂²×C₂₉	1	2	yes	—
405	#542	C₂²×C₂₉	1	4	yes	—
406	#541	C₂²×C₂₉	1	4	yes	—
407	#536	C₂²×C₂₉	1	2	yes	—
408	#533	C₂²×C₂₉	1	4	yes	—
409	#529	C₂²×C₂₉	1	4	yes	—
410	#525	C₂²×C₂₉	1	2	yes	—
411	C₂×C₂²⋊Q₈	C₂²×C₂₉	1	2	yes	—
412	#520	C₂²×C₂₉	1	2	yes	—
413	#519	C₂²×C₂₉	1	2	yes	—
414	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
415	#501	C₂²×C₂₉	1	4	yes	complemented
416	#500	C₂²×C₂₉	1	2	yes	complemented
417	#499	C₂²×C₂₉	1	2	yes	complemented
418	#497	C₂²×C₂₉	1	4	yes	complemented
419	#495	C₂²×C₂₉	1	2	yes	complemented
420	#494	C₂²×C₂₉	1	2	yes	complemented
421	#491	C₂²×C₂₉	1	4	yes	complemented
422	#489	C₂²×C₂₉	1	4	yes	complemented
423	#488	C₂²×C₂₉	1	4	yes	complemented
424	#487	C₂²×C₂₉	1	4	yes	complemented
425	#470	C₂²×C₂₉	1	4	yes	—
426	#468	C₂²×C₂₉	1	4	yes	—
427	#467	C₂²×C₂₉	1	2	yes	—
428	#467	C₂²×C₂₉	1	1	yes	characteristic
429	#467	C₂²×C₂₉	1	4	yes	—
430	#467	C₂²×C₂₉	1	2	yes	—
431	#467	C₂²×C₂₉	1	1	yes	characteristic
432	#467	C₂²×C₂₉	1	2	yes	—
433	#467	C₂²×C₂₉	1	2	yes	—
434	#466	C₂²×C₂₉	1	1	yes	characteristic
435	#466	C₂²×C₂₉	1	1	yes	characteristic
436	#465	C₂²×C₂₉	1	4	yes	—
437	#465	C₂²×C₂₉	1	2	yes	—
438	#465	C₂²×C₂₉	1	2	yes	—
439	#441	C₂²×C₂₉	1	4	yes	complemented
440	#441	C₂²×C₂₉	1	4	yes	complemented
441	#440	C₂²×C₂₉	1	4	yes	complemented
442	#440	C₂²×C₂₉	1	4	yes	complemented
443	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
444	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
445	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
446	C₄×Q₁₆	C₂²×C₂₉	1	4	yes	complemented
447	C₄×SD₁₆	C₂²×C₂₉	1	4	yes	complemented
448	C₄×D₈	C₂²×C₂₉	1	2	yes	complemented
449	#428	C₂²×C₂₉	1	2	yes	—
450	#427	C₂²×C₂₉	1	1	yes	characteristic
451	C₂×#107	C₂²×C₂₉	1	1	yes	characteristic
452	#419	C₂²×C₂₉	1	2	yes	—
453	#417	C₂²×C₂₉	1	2	yes	—
454	#416	C₂²×C₂₉	1	2	yes	—
455	C₂×#103	C₂²×C₂₉	1	2	yes	—
456	#405	C₂²×C₂₉	1	1	yes	characteristic
457	#405	C₂²×C₂₉	1	1	yes	characteristic
458	#405	C₂²×C₂₉	1	2	yes	—
459	#405	C₂²×C₂₉	1	2	yes	—
460	#405	C₂²×C₂₉	1	1	yes	characteristic
461	#405	C₂²×C₂₉	1	1	yes	characteristic
462	C₂×#97	C₂²×C₂₉	1	2	yes	—
463	C₂×C₄×C₈	C₂²×C₂₉	1	2	yes	—
464	C₂×C₂₉	—	2	2	no	—
465	C₂×C₂₉	—	2	2	no	—
466	C₂×C₂₉	—	4	1	no	—
467	C₂×C₂₉	—	8	2	no	—
468	C₂×C₂₉	C₂×#532	1	1	yes	characteristic
469	C₂×C₂₉	C₂×#578	1	1	yes	characteristic
470	C₂×C₂₉	#3584	1	1	yes	characteristic
471	C₂×#41	C₂³×C₂₉	1	2	yes	—
472	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
473	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
474	#137	—	2	8	no	—
475	#135	—	2	4	no	—
476	C₂×Q₁₆	—	2	4	no	—
477	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
478	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
479	C₂×Q₁₆	C₂³×C₂₉	1	1	yes	characteristic
480	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
481	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
482	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
483	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
484	C₂×M₁₆	—	2	4	no	—
485	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
486	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
487	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
488	C₂²×C₈	—	2	4	no	—
489	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
494	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
495	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
496	C₄⋊Q₈	—	2	2	no	—
497	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
498	C₄⋊Q₈	C₂³×C₂₉	1	4	yes	—
499	#126	—	2	4	no	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#126	—	2	4	no	—
503	#125	—	2	4	no	—
504	#125	—	2	4	no	—
505	#125	—	2	2	no	—
506	#125	—	2	4	no	—
507	#125	C₂³×C₂₉	1	4	yes	—
508	#124	—	2	4	no	—
509	#124	C₂³×C₂₉	1	4	yes	—
510	#123	—	2	2	no	—
511	#123	—	2	4	no	—
512	#123	—	2	4	no	—
513	#123	—	2	4	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	2	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
522	C₂²⋊Q₈	C₂³×C₂₉	1	4	yes	—
523	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
524	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
525	#121	C₂³×C₂₉	1	2	yes	—
526	#121	C₂³×C₂₉	1	2	yes	—
527	#120	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	4	no	—
531	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
532	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
533	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	4	no	—
537	C₄×D₄	—	2	4	no	—
538	C₄×D₄	C₂³×C₂₉	1	4	yes	—
539	#117	—	2	4	no	—
540	#117	—	2	2	no	—
541	#117	—	2	4	no	—
542	#117	—	2	4	no	—
543	#117	D₄×C₂₉	1	1	yes	characteristic
544	#117	D₄×C₂₉	1	2	yes	—
545	#117	D₄×C₂₉	1	1	yes	characteristic
546	#117	C₂³×C₂₉	1	2	yes	—
547	#117	C₂³×C₂₉	1	1	yes	characteristic
548	#117	C₂³×C₂₉	1	1	yes	characteristic
549	#117	C₂³×C₂₉	1	2	yes	—
550	C₂×C₄⋊C₄	—	2	2	no	—
551	C₂×C₄⋊C₄	—	2	2	no	—
552	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
555	C₂×C₂²⋊C₄	—	2	2	no	—
556	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
557	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
558	#107	C₂³×C₂₉	1	2	yes	—
559	#107	C₂³×C₂₉	1	2	yes	—
560	#107	C₂³×C₂₉	1	1	yes	characteristic
561	#107	C₂³×C₂₉	1	1	yes	characteristic
562	#107	C₂³×C₂₉	1	4	yes	—
563	#106	C₂³×C₂₉	1	2	yes	—
564	#106	C₂³×C₂₉	1	4	yes	—
565	#103	C₂³×C₂₉	1	4	yes	—
566	#103	C₂³×C₂₉	1	4	yes	—
567	#103	C₂³×C₂₉	1	2	yes	—
568	#103	C₂³×C₂₉	1	2	yes	—
569	#103	C₂³×C₂₉	1	4	yes	—
570	#103	C₂³×C₂₉	1	4	yes	—
571	#103	C₂³×C₂₉	1	4	yes	—
572	#102	C₂³×C₂₉	1	2	yes	—
573	#102	C₂³×C₂₉	1	2	yes	—
574	#102	C₂³×C₂₉	1	4	yes	—
575	#97	C₂³×C₂₉	1	2	yes	—
576	#97	C₂³×C₂₉	1	2	yes	—
577	#97	C₂³×C₂₉	1	2	yes	—
578	#97	C₂³×C₂₉	1	2	yes	—
579	C₄×C₈	C₂³×C₂₉	1	2	yes	—
580	C₄×C₈	C₂³×C₂₉	1	2	yes	—
581	C₄×C₈	C₂³×C₂₉	1	2	yes	—
582	C₄×C₈	C₂³×C₂₉	1	2	yes	—
583	C₂₉	#60708	1	1	yes	characteristic, direct product factor, Sylow
584	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
585	#41	—	2	4	no	—
586	#41	—	2	4	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	4	no	—
589	C₂×Q₈	—	2	4	no	—
590	C₂×Q₈	—	2	4	no	—
591	C₂×Q₈	C₂⁴×C₂₉	1	4	yes	—
592	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
597	C₂²×C₄	—	2	2	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
604	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
611	Q₁₆	—	2	4	no	—
612	Q₁₆	—	2	4	no	—
613	Q₁₆	—	2	2	no	—
614	Q₁₆	—	2	8	no	—
615	SD₁₆	—	2	4	no	—
616	SD₁₆	—	2	8	no	—
617	D₈	—	2	2	no	—
618	M₁₆	—	2	2	no	—
619	M₁₆	—	2	4	no	—
620	M₁₆	#41×C₂₉	1	4	yes	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	2	2	no	—
626	C₂×C₈	—	2	4	no	—
627	C₂×C₈	#41×C₂₉	1	4	yes	—
628	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
630	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
633	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	—	2	4	no	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
648	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
649	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
651	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
652	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
655	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
667	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
668	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
669	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	4	no	—
672	C₄²	—	2	4	no	—
673	C₄²	—	2	2	no	—
674	C₄²	C₂×D₄×C₂₉	1	2	yes	—
675	C₄²	C₂×D₄×C₂₉	1	2	yes	—
676	C₄²	C₂⁴×C₂₉	1	2	yes	—
677	C₄²	C₂⁴×C₂₉	1	2	yes	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	1	no	—
682	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
683	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
684	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
685	Q₈	—	2	4	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	4	no	—
688	Q₈	—	2	2	no	—
689	Q₈	—	4	4	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	8	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	4	2	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	2	no	—
714	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
718	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
720	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
721	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
722	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
723	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
724	C₈	—	2	1	no	—
725	C₈	—	2	1	no	—
726	C₈	—	2	2	no	—
727	C₈	C₂×#41×C₂₉	1	2	yes	—
728	C₈	C₂×#41×C₂₉	1	2	yes	—
729	C₈	C₂×#41×C₂₉	1	4	yes	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	2	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₂₉×#532	1	2	yes	—
742	C₂²	C₂₉×#578	1	2	yes	—
743	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	1	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	4	no	—
754	C₄	—	4	2	no	—
755	C₄	C₂₉×#532	1	2	yes	—
756	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
757	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
758	C₂	—	2	2	no	—
759	C₂	—	2	2	no	—
760	C₂	—	4	1	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₂₉×#532	1	1	yes	characteristic
763	C₂	C₂×C₂₉×#578	1	1	yes	characteristic
764	C₂	C₂₉×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂₉×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₉×#3495	C₂	semidirect
2. C₂₉×#3181	C₂	semidirect
3. C₂₉×#3178	C₂	semidirect
4. C₂₉×#3177	C₂	semidirect
5. C₂₉×#3175	C₂	semidirect
6. C₂₉×#3170	C₂	semidirect
7. C₂₉×#3168	C₂	semidirect
8. C₂₉×#3164	C₂	semidirect
9. C₂₉×#3156	C₂	semidirect
10. C₂₉×#3137	C₂	semidirect
11. C₂₉×#3056	C₂	semidirect
13. C₂×C₂₉×#467	C₂	semidirect
14. C₂₉×#2951	C₂	semidirect
15. C₂₉×#2950	C₂	semidirect
16. C₂₉×#2947	C₂	semidirect
17. C₂×C₂₉×#405	C₂	semidirect
40. C₂₉×#501	C₂²	semidirect
41. C₂₉×#500	C₂²	semidirect
42. C₂₉×#499	C₂²	semidirect
43. C₂₉×#497	C₂²	semidirect
44. C₂₉×#495	C₂²	semidirect
45. C₂₉×#494	C₂²	semidirect
46. C₂₉×#491	C₂²	semidirect
47. C₂₉×#489	C₂²	semidirect
48. C₂₉×#488	C₂²	semidirect
49. C₂₉×#487	C₂²	semidirect
64. C₂₉×#441	C₂²	semidirect
65. C₂₉×#441	C₂²	semidirect
66. C₂₉×#440	C₂²	semidirect
67. C₂₉×#440	C₂²	semidirect
68. C₄×Q₁₆×C₂₉	C₂²	semidirect
69. C₄×Q₁₆×C₂₉	C₂²	semidirect
70. C₄×Q₁₆×C₂₉	C₂²	semidirect
71. C₄×Q₁₆×C₂₉	C₂²	semidirect
72. C₄×SD₁₆×C₂₉	C₂²	semidirect
73. C₄×D₈×C₂₉	C₂²	semidirect
295. #60708	C₂₉	direct (N × H)
348. #3495	C₂×C₂₉	semidirect
349. #3181	C₂×C₂₉	semidirect
350. #3178	C₂×C₂₉	semidirect
351. #3177	C₂×C₂₉	semidirect
352. #3175	C₂×C₂₉	semidirect
353. #3170	C₂×C₂₉	semidirect
354. #3168	C₂×C₂₉	semidirect
355. #3164	C₂×C₂₉	semidirect
356. #3156	C₂×C₂₉	semidirect
357. #3137	C₂×C₂₉	semidirect
358. #3056	C₂×C₂₉	semidirect
360. C₂×#467	C₂×C₂₉	semidirect
361. #2951	C₂×C₂₉	semidirect
362. #2950	C₂×C₂₉	semidirect
363. #2947	C₂×C₂₉	semidirect
364. C₂×#405	C₂×C₂₉	semidirect
415. #501	C₂²×C₂₉	semidirect
416. #500	C₂²×C₂₉	semidirect
417. #499	C₂²×C₂₉	semidirect
418. #497	C₂²×C₂₉	semidirect
419. #495	C₂²×C₂₉	semidirect
420. #494	C₂²×C₂₉	semidirect
421. #491	C₂²×C₂₉	semidirect
422. #489	C₂²×C₂₉	semidirect
423. #488	C₂²×C₂₉	semidirect
424. #487	C₂²×C₂₉	semidirect
439. #441	C₂²×C₂₉	semidirect
440. #441	C₂²×C₂₉	semidirect
441. #440	C₂²×C₂₉	semidirect
442. #440	C₂²×C₂₉	semidirect
443. C₄×Q₁₆	C₂²×C₂₉	semidirect
444. C₄×Q₁₆	C₂²×C₂₉	semidirect
445. C₄×Q₁₆	C₂²×C₂₉	semidirect
446. C₄×Q₁₆	C₂²×C₂₉	semidirect
447. C₄×SD₁₆	C₂²×C₂₉	semidirect
448. C₄×D₈	C₂²×C₂₉	semidirect
583. C₂₉	#60708	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×#3495	2
C₂₉×#3181	2
C₂₉×#3178	2
C₂₉×#3177	2
C₂₉×#3175	2
C₂₉×#3170	2
C₂₉×#3168	2
C₂₉×#3164	2
C₂₉×#3156	2
C₂₉×#3137	2
C₂₉×#3056	2
C₂₉×#3050	2
C₂×C₂₉×#467	2
C₂₉×#2951	2
C₂₉×#2950	2
C₂₉×#2947	2
C₂×C₂₉×#405	2
#60708	29

Subgroups — C29×#60708 #20355608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60708 #20355608