Subgroups — C₂₉×#61557 #20356457

Order 7424.

1820 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3356	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#3316	C₂	1	2	yes	maximal, complemented
10	C₂₉×#3311	C₂	1	2	yes	maximal, complemented
11	C₂₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3276	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#3275	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3173	C₂	1	2	yes	maximal, complemented
17	C₂₉×#3125	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3121	C₂	1	2	yes	maximal, complemented
19	C₂₉×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₉×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#2947	C₂	1	2	yes	maximal, complemented
23	C₄×C₂₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×#137	C₂²	1	2	yes	—
25	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	Q₈²×C₂₉	C₂²	1	1	yes	characteristic, complemented
27	C₂₉×#556	—	2	2	no	—
28	C₂₉×#556	—	2	1	no	—
29	C₂₉×#556	C₂²	1	1	yes	characteristic
30	C₂₉×#556	C₂²	1	2	yes	—
31	C₂₉×#556	C₂²	1	1	yes	characteristic, complemented
32	C₂₉×#555	—	2	1	no	—
33	C₂₉×#555	C₂²	1	1	yes	characteristic, complemented
34	C₂₉×#554	C₂²	1	2	yes	—
35	C₂₉×#552	—	2	1	no	—
36	C₂₉×#551	—	2	2	no	—
37	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
39	C₂₉×#548	—	2	1	no	—
40	C₂₉×#548	C₂²	1	2	yes	—
41	C₂₉×#547	C₂²	1	1	yes	characteristic
42	C₂₉×#547	C₂²	1	1	yes	characteristic
43	C₂₉×#546	C₂²	1	2	yes	—
44	C₂₉×#542	—	2	2	no	—
45	C₂₉×#542	C₂²	1	2	yes	—
46	C₂₉×#542	C₂²	1	2	yes	complemented
47	C₂₉×#539	—	2	2	no	—
48	C₂₉×#533	—	2	1	no	—
49	C₂₉×#533	C₂²	1	1	yes	characteristic
50	C₂₉×#533	C₂²	1	1	yes	characteristic
51	C₂₉×#529	—	2	1	no	—
52	C₂₉×#529	C₂²	1	1	yes	characteristic
53	C₂₉×#525	—	2	1	no	—
54	C₂×C₂₉×C₂²⋊Q₈	—	2	1	no	—
55	C₂₉×#520	C₂²	1	2	yes	—
56	C₂₉×#519	C₂²	1	2	yes	complemented
57	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
59	C₂₉×#498	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#498	C₂²	1	2	yes	complemented
61	C₂₉×#495	C₂²	1	2	yes	—
62	C₂₉×#494	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×#489	C₂²	1	2	yes	—
64	C₂₉×#489	C₂²	1	2	yes	complemented
65	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
66	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#485	C₂²	1	2	yes	—
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#483	C₂²	1	2	yes	—
70	C₂₉×#483	C₂²	1	2	yes	complemented
71	C₂₉×#482	C₂²	1	2	yes	—
72	C₂₉×#481	C₂²	1	2	yes	complemented
73	C₂₉×#477	C₂²	1	2	yes	complemented
74	C₂₉×#476	C₂²	1	1	yes	characteristic
75	C₂₉×#476	C₂²	1	2	yes	—
76	C₂₉×#476	C₂²	1	1	yes	characteristic
77	C₂₉×#475	C₂²	1	1	yes	characteristic, complemented
78	C₂₉×#475	C₂²	1	2	yes	complemented
79	C₂₉×#475	C₂²	1	2	yes	complemented
80	C₂₉×#474	C₂²	1	1	yes	characteristic, complemented
81	C₂₉×#470	C₂²	1	2	yes	—
82	C₂₉×#470	C₂²	1	2	yes	—
83	C₂₉×#470	C₂²	1	2	yes	complemented
84	C₂₉×#469	C₂²	1	2	yes	—
85	C₂₉×#465	C₂²	1	2	yes	—
86	C₂₉×#465	C₂²	1	2	yes	complemented
87	C₂₉×#464	C₂²	1	2	yes	—
88	C₂₉×#464	C₂²	1	2	yes	—
89	C₂₉×#464	C₂²	1	2	yes	complemented
90	C₂₉×#463	C₂²	1	2	yes	—
91	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
92	C₂₉×#461	C₂²	1	1	yes	characteristic
93	C₂₉×#461	C₂²	1	1	yes	characteristic
94	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
95	C₂₉×#452	C₂²	1	2	yes	—
96	C₂₉×#452	C₂²	1	2	yes	—
97	C₂₉×#451	C₂²	1	2	yes	complemented
98	C₂₉×#450	C₂²	1	2	yes	—
99	C₂₉×#449	C₂²	1	2	yes	—
100	C₂₉×#448	C₂²	1	2	yes	—
101	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
103	C₂₉×#442	C₂²	1	1	yes	characteristic
104	C₂₉×#442	C₂²	1	1	yes	characteristic
105	C₂₉×#441	C₂²	1	2	yes	complemented
106	C₂₉×#441	C₂²	1	2	yes	complemented
107	C₂₉×#441	C₂²	1	2	yes	complemented
108	C₂₉×#440	C₂²	1	1	yes	characteristic
109	C₂₉×#440	C₂²	1	1	yes	characteristic
110	C₂₉×#440	C₂²	1	2	yes	—
111	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
112	C₄×Q₁₆×C₂₉	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
114	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
115	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
116	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	—
118	C₄×SD₁₆×C₂₉	C₂²	1	2	yes	complemented
119	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
121	C₂₉×#436	C₂²	1	2	yes	—
122	C₂₉×#436	C₂²	1	1	yes	characteristic, complemented
123	C₂₉×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
125	C₂₉×#433	C₂²	1	2	yes	complemented
126	C₂₉×#431	C₂²	1	1	yes	characteristic
127	C₂₉×#428	C₂²	1	1	yes	characteristic
128	C₂₉×#428	C₂²	1	2	yes	complemented
129	C₂₉×#418	C₂²	1	1	yes	characteristic
130	C₂₉×#417	C₂²	1	1	yes	characteristic
131	C₂₉×#416	C₂²	1	2	yes	—
132	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
133	C₂₉×#405	C₂²	1	2	yes	complemented
134	C₄×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	C₂³	1	2	yes	—
137	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₂₉	—	2	1	no	—
139	C₂²×Q₈×C₂₉	C₂³	1	2	yes	—
140	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₉	—	2	1	no	—
142	C₂₉×#137	—	2	8	no	—
143	C₂₉×AGL(1,ℤ/8)	—	2	4	no	—
144	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
145	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
147	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
152	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
153	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
156	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
158	C₂₉×C₄⋊Q₈	—	2	1	no	—
159	C₂₉×C₄⋊Q₈	—	2	1	no	—
160	C₂₉×C₄⋊Q₈	—	2	2	no	—
161	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₂₉×#126	—	2	2	no	—
168	C₂₉×#126	—	2	2	no	—
169	C₂₉×#126	—	2	2	no	—
170	C₂₉×#126	—	2	2	no	—
171	C₂₉×#126	—	2	2	no	—
172	C₂₉×#126	—	2	2	no	—
173	C₂₉×#126	D₄	1	2	yes	—
174	C₂₉×#125	—	2	2	no	—
175	C₂₉×#125	—	2	1	no	—
176	C₂₉×#125	—	2	1	no	—
177	C₂₉×#125	D₄	1	1	yes	characteristic
178	C₂₉×#124	—	2	2	no	—
179	C₂₉×#124	—	2	2	no	—
180	C₂₉×#124	—	2	2	no	—
181	C₂₉×#124	—	2	2	no	—
182	C₂₉×#124	—	2	2	no	—
183	C₂₉×#124	D₄	1	1	yes	characteristic
184	C₂₉×#124	C₂³	1	2	yes	—
185	C₂₉×#124	C₂³	1	2	yes	—
186	C₂₉×#123	—	2	2	no	—
187	C₂₉×#123	—	2	2	no	—
188	C₂₉×#123	—	2	2	no	—
189	C₂₉×#123	—	2	2	no	—
190	C₂₉×#123	—	2	2	no	—
191	C₂₉×#123	D₄	1	2	yes	—
192	C₂₉×C₂²⋊Q₈	—	2	1	no	—
193	C₂₉×C₂²⋊Q₈	—	2	1	no	—
194	C₂₉×C₂²⋊Q₈	—	2	1	no	—
195	C₂₉×C₂²⋊Q₈	—	2	1	no	—
196	C₂₉×C₂²⋊Q₈	—	2	2	no	—
197	C₂₉×C₂²⋊Q₈	—	2	1	no	—
198	C₂₉×C₂²⋊Q₈	—	2	1	no	—
199	C₂₉×C₂²⋊Q₈	—	2	2	no	—
200	C₂₉×C₂²⋊Q₈	—	2	2	no	—
201	C₂₉×C₂²⋊Q₈	—	2	2	no	—
202	C₂₉×C₂²⋊Q₈	—	2	2	no	—
203	C₂₉×C₂²⋊Q₈	—	2	2	no	—
204	C₂₉×C₂²⋊Q₈	—	2	2	no	—
205	C₂₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
206	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₂₉×#121	—	2	1	no	—
211	C₂₉×#121	—	2	1	no	—
212	C₂₉×#121	—	2	2	no	—
213	C₂₉×#121	—	2	2	no	—
214	C₂₉×#121	D₄	1	1	yes	characteristic
215	C₂₉×#121	C₂³	1	2	yes	—
216	C₂₉×#121	C₂³	1	2	yes	—
217	C₂₉×#120	—	2	2	no	—
218	C₄×Q₈×C₂₉	—	2	1	no	—
219	C₄×Q₈×C₂₉	—	2	2	no	—
220	C₄×Q₈×C₂₉	—	2	2	no	—
221	C₄×Q₈×C₂₉	—	2	2	no	—
222	C₄×Q₈×C₂₉	—	2	1	no	—
223	C₄×Q₈×C₂₉	—	2	1	no	—
224	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
225	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
227	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
228	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
230	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₂₉	—	2	2	no	—
233	C₄×D₄×C₂₉	—	2	1	no	—
234	C₄×D₄×C₂₉	—	2	1	no	—
235	C₄×D₄×C₂₉	—	2	1	no	—
236	C₄×D₄×C₂₉	—	2	2	no	—
237	C₄×D₄×C₂₉	—	2	2	no	—
238	C₄×D₄×C₂₉	—	2	2	no	—
239	C₄×D₄×C₂₉	—	2	1	no	—
240	C₄×D₄×C₂₉	—	2	1	no	—
241	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₂₉	C₂³	1	2	yes	—
247	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₂₉	C₂³	1	2	yes	—
250	C₂₉×#117	—	2	1	no	—
251	C₂₉×#117	—	2	1	no	—
252	C₂₉×#117	—	2	2	no	—
253	C₂₉×#117	—	2	1	no	—
254	C₂₉×#117	—	2	1	no	—
255	C₂₉×#117	—	2	1	no	—
256	C₂₉×#117	—	2	2	no	—
257	C₂₉×#117	—	2	2	no	—
258	C₂₉×#117	—	2	1	no	—
259	C₂₉×#117	C₂³	1	1	yes	characteristic
260	C₂₉×#117	C₂³	1	2	yes	—
261	C₂₉×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
263	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
264	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
266	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
267	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
268	C₂×C₄²×C₂₉	—	2	1	no	—
269	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
270	C₂₉×#107	C₂³	1	1	yes	characteristic
271	C₂₉×#107	C₂³	1	1	yes	characteristic
272	C₂₉×#107	C₂³	1	2	yes	—
273	C₂₉×#106	C₂³	1	1	yes	characteristic
274	C₂₉×#106	C₂³	1	1	yes	characteristic
275	C₂₉×#106	C₂³	1	2	yes	—
276	C₂₉×#106	C₂³	1	2	yes	—
277	C₂₉×#106	C₂³	1	2	yes	—
278	C₂₉×#106	C₂³	1	2	yes	—
279	C₂₉×#106	C₂³	1	2	yes	—
280	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₉×#103	C₂³	1	2	yes	—
285	C₂₉×#103	C₂³	1	2	yes	—
286	C₂₉×#103	C₂³	1	1	yes	characteristic
287	C₂₉×#103	C₂³	1	1	yes	characteristic
288	C₂₉×#103	C₂³	1	2	yes	—
289	C₂₉×#103	C₂³	1	2	yes	—
290	C₂₉×#103	C₂³	1	2	yes	—
291	C₂₉×#103	C₂³	1	2	yes	—
292	C₂₉×#103	C₂³	1	2	yes	—
293	C₂₉×#103	C₂³	1	2	yes	—
294	C₂₉×#103	C₂³	1	2	yes	—
295	C₂₉×#102	C₂³	1	1	yes	characteristic
296	C₂₉×#102	C₂³	1	1	yes	characteristic
297	C₂₉×#102	C₂³	1	1	yes	characteristic
298	C₂₉×#102	C₂³	1	1	yes	characteristic
299	C₂₉×#102	C₂³	1	2	yes	—
300	C₂₉×#102	C₂³	1	1	yes	characteristic
301	C₂₉×#102	C₂³	1	1	yes	characteristic
302	C₂₉×#102	C₂³	1	2	yes	—
303	C₂₉×#102	C₂³	1	2	yes	—
304	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₉×#97	C₂³	1	1	yes	characteristic
308	C₂₉×#97	C₂³	1	2	yes	—
309	C₂₉×#97	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₉	C₂³	1	2	yes	—
311	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₂₉	C₂³	1	2	yes	—
313	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
314	C₂⁴×C₂₉	—	2	1	no	—
315	#41×C₂₉	—	2	2	no	—
316	#41×C₂₉	—	2	4	no	—
317	#41×C₂₉	—	4	2	no	—
318	#41×C₂₉	—	4	1	no	—
319	#41×C₂₉	—	8	2	no	—
320	C₂×Q₈×C₂₉	—	2	2	no	—
321	C₂×Q₈×C₂₉	—	2	1	no	—
322	C₂×Q₈×C₂₉	—	2	1	no	—
323	C₂×Q₈×C₂₉	—	2	2	no	—
324	C₂×Q₈×C₂₉	—	2	2	no	—
325	C₂×Q₈×C₂₉	—	2	4	no	—
326	C₂×Q₈×C₂₉	—	4	2	no	—
327	C₂×Q₈×C₂₉	—	8	2	no	—
328	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₂₉	—	2	2	no	—
333	C₂×D₄×C₂₉	—	2	2	no	—
334	C₂×D₄×C₂₉	—	2	1	no	—
335	C₂×D₄×C₂₉	—	2	2	no	—
336	C₂×D₄×C₂₉	—	2	2	no	—
337	C₂×D₄×C₂₉	—	2	1	no	—
338	C₂×D₄×C₂₉	—	4	1	no	—
339	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
340	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
341	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₂₉	—	2	2	no	—
345	C₂²×C₄×C₂₉	—	2	1	no	—
346	C₂²×C₄×C₂₉	—	2	2	no	—
347	C₂²×C₄×C₂₉	—	2	1	no	—
348	C₂²×C₄×C₂₉	—	2	1	no	—
349	C₂²×C₄×C₂₉	—	2	2	no	—
350	C₂²×C₄×C₂₉	—	2	1	no	—
351	C₂²×C₄×C₂₉	—	2	1	no	—
352	C₂²×C₄×C₂₉	—	2	1	no	—
353	C₂²×C₄×C₂₉	—	2	2	no	—
354	C₂²×C₄×C₂₉	—	2	1	no	—
355	C₂²×C₄×C₂₉	—	2	1	no	—
356	C₂²×C₄×C₂₉	—	8	2	no	—
357	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
361	Q₁₆×C₂₉	—	2	4	no	—
362	Q₁₆×C₂₉	—	2	4	no	—
363	Q₁₆×C₂₉	—	4	2	no	—
364	SD₁₆×C₂₉	—	2	2	no	—
365	SD₁₆×C₂₉	—	2	4	no	—
366	SD₁₆×C₂₉	—	4	2	no	—
367	SD₁₆×C₂₉	—	4	2	no	—
368	SD₁₆×C₂₉	#41	1	4	yes	complemented
369	D₈×C₂₉	—	2	2	no	—
370	D₈×C₂₉	—	2	2	no	—
371	M₁₆×C₂₉	—	2	2	no	—
372	M₁₆×C₂₉	—	2	4	no	—
373	M₁₆×C₂₉	—	4	1	no	—
374	C₂×C₈×C₂₉	—	4	2	no	—
375	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
377	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
379	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₂₉	—	2	2	no	—
382	C₄⋊C₄×C₂₉	—	2	1	no	—
383	C₄⋊C₄×C₂₉	—	2	2	no	—
384	C₄⋊C₄×C₂₉	—	2	2	no	—
385	C₄⋊C₄×C₂₉	—	2	2	no	—
386	C₄⋊C₄×C₂₉	—	2	1	no	—
387	C₄⋊C₄×C₂₉	—	2	1	no	—
388	C₄⋊C₄×C₂₉	—	2	1	no	—
389	C₄⋊C₄×C₂₉	—	2	1	no	—
390	C₄⋊C₄×C₂₉	—	2	1	no	—
391	C₄⋊C₄×C₂₉	—	2	2	no	—
392	C₄⋊C₄×C₂₉	—	2	2	no	—
393	C₄⋊C₄×C₂₉	—	2	2	no	—
394	C₄⋊C₄×C₂₉	—	2	1	no	—
395	C₄⋊C₄×C₂₉	—	2	1	no	—
396	C₄⋊C₄×C₂₉	—	2	2	no	—
397	C₄⋊C₄×C₂₉	—	2	2	no	—
398	C₄⋊C₄×C₂₉	—	2	2	no	—
399	C₄⋊C₄×C₂₉	—	2	1	no	—
400	C₄⋊C₄×C₂₉	—	2	2	no	—
401	C₄⋊C₄×C₂₉	—	2	2	no	—
402	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
403	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
404	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
406	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
407	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
408	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
410	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
411	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
414	C₂²⋊C₄×C₂₉	—	2	2	no	—
415	C₂²⋊C₄×C₂₉	—	2	2	no	—
416	C₂²⋊C₄×C₂₉	—	2	2	no	—
417	C₂²⋊C₄×C₂₉	—	2	1	no	—
418	C₂²⋊C₄×C₂₉	—	2	2	no	—
419	C₂²⋊C₄×C₂₉	—	2	2	no	—
420	C₂²⋊C₄×C₂₉	—	2	1	no	—
421	C₂²⋊C₄×C₂₉	—	2	1	no	—
422	C₂²⋊C₄×C₂₉	—	2	1	no	—
423	C₂²⋊C₄×C₂₉	—	2	1	no	—
424	C₂²⋊C₄×C₂₉	—	2	2	no	—
425	C₂²⋊C₄×C₂₉	—	2	2	no	—
426	C₂²⋊C₄×C₂₉	—	2	2	no	—
427	C₂²⋊C₄×C₂₉	—	2	1	no	—
428	C₂²⋊C₄×C₂₉	—	2	1	no	—
429	C₂²⋊C₄×C₂₉	—	2	2	no	—
430	C₂²⋊C₄×C₂₉	—	2	2	no	—
431	C₂²⋊C₄×C₂₉	—	2	2	no	—
432	C₂²⋊C₄×C₂₉	—	2	2	no	—
433	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
434	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
435	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
436	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
437	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
438	C₄²×C₂₉	—	2	1	no	—
439	C₄²×C₂₉	—	2	1	no	—
440	C₄²×C₂₉	—	2	1	no	—
441	C₄²×C₂₉	—	2	2	no	—
442	C₄²×C₂₉	—	2	2	no	—
443	C₄²×C₂₉	—	2	2	no	—
444	C₄²×C₂₉	—	2	2	no	—
445	C₄²×C₂₉	—	2	2	no	—
446	C₄²×C₂₉	—	2	2	no	—
447	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
450	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
451	C₄²×C₂₉	C₂⁴	1	2	yes	—
452	#61557	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
453	C₂³×C₂₉	—	2	1	no	—
454	C₂³×C₂₉	—	2	1	no	—
455	C₂³×C₂₉	—	2	1	no	—
456	C₂³×C₂₉	—	4	2	no	—
457	C₂³×C₂₉	—	4	2	no	—
458	C₂³×C₂₉	—	8	1	no	—
459	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
460	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
461	Q₈×C₂₉	—	2	2	no	—
462	Q₈×C₂₉	—	2	1	no	—
463	Q₈×C₂₉	—	2	2	no	—
464	Q₈×C₂₉	—	2	2	no	—
465	Q₈×C₂₉	—	2	2	no	—
466	Q₈×C₂₉	—	2	2	no	—
467	Q₈×C₂₉	—	4	4	no	—
468	Q₈×C₂₉	—	4	2	no	—
469	Q₈×C₂₉	—	8	1	no	—
470	Q₈×C₂₉	—	8	2	no	—
471	Q₈×C₂₉	—	8	2	no	—
472	Q₈×C₂₉	C₂×#41	1	2	yes	—
473	D₄×C₂₉	—	2	2	no	—
474	D₄×C₂₉	—	2	1	no	—
475	D₄×C₂₉	—	2	1	no	—
476	D₄×C₂₉	—	2	1	no	—
477	D₄×C₂₉	—	2	1	no	—
478	D₄×C₂₉	—	2	1	no	—
479	D₄×C₂₉	—	4	2	no	—
480	D₄×C₂₉	—	4	2	no	—
481	D₄×C₂₉	—	4	2	no	—
482	D₄×C₂₉	—	4	4	no	—
483	D₄×C₂₉	—	8	2	no	—
484	D₄×C₂₉	—	8	2	no	—
485	D₄×C₂₉	C₂×#41	1	2	yes	—
486	C₂×C₄×C₂₉	—	2	1	no	—
487	C₂×C₄×C₂₉	—	2	2	no	—
488	C₂×C₄×C₂₉	—	2	1	no	—
489	C₂×C₄×C₂₉	—	2	2	no	—
490	C₂×C₄×C₂₉	—	2	2	no	—
491	C₂×C₄×C₂₉	—	2	1	no	—
492	C₂×C₄×C₂₉	—	2	1	no	—
493	C₂×C₄×C₂₉	—	2	2	no	—
494	C₂×C₄×C₂₉	—	2	2	no	—
495	C₂×C₄×C₂₉	—	2	2	no	—
496	C₂×C₄×C₂₉	—	2	1	no	—
497	C₂×C₄×C₂₉	—	2	1	no	—
498	C₂×C₄×C₂₉	—	2	2	no	—
499	C₂×C₄×C₂₉	—	2	1	no	—
500	C₂×C₄×C₂₉	—	4	1	no	—
501	C₂×C₄×C₂₉	—	4	2	no	—
502	C₂×C₄×C₂₉	—	4	4	no	—
503	C₂×C₄×C₂₉	—	4	4	no	—
504	C₂×C₄×C₂₉	—	4	2	no	—
505	C₂×C₄×C₂₉	—	4	2	no	—
506	C₂×C₄×C₂₉	—	4	2	no	—
507	C₂×C₄×C₂₉	—	8	1	no	—
508	C₂×C₄×C₂₉	—	8	1	no	—
509	C₂×C₄×C₂₉	—	8	1	no	—
510	C₂×C₄×C₂₉	—	8	2	no	—
511	C₂×C₄×C₂₉	—	8	1	no	—
512	C₂×C₄×C₂₉	—	8	2	no	—
513	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
519	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
522	C₈×C₂₉	—	2	1	no	—
523	C₈×C₂₉	—	2	2	no	—
524	C₈×C₂₉	—	2	1	no	—
525	C₈×C₂₉	—	2	2	no	—
526	C₈×C₂₉	—	2	1	no	—
527	C₈×C₂₉	C₂×#41	1	2	yes	—
528	#3520	C₂×C₂₉	1	1	yes	characteristic, complemented
529	#3518	C₂×C₂₉	1	1	yes	characteristic, complemented
530	#3393	C₂×C₂₉	1	1	yes	characteristic, complemented
531	Q₈×SD₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
532	#3369	C₂×C₂₉	1	1	yes	characteristic, complemented
533	#3367	C₂×C₂₉	1	1	yes	characteristic, complemented
534	#3356	C₂×C₂₉	1	2	yes	complemented
535	#3354	C₂×C₂₉	1	1	yes	characteristic, complemented
536	#3316	C₂×C₂₉	1	2	yes	complemented
537	#3311	C₂×C₂₉	1	2	yes	complemented
538	#3303	C₂×C₂₉	1	1	yes	characteristic, complemented
539	#3298	C₂×C₂₉	1	1	yes	characteristic, complemented
540	#3276	C₂×C₂₉	1	1	yes	characteristic, complemented
541	#3275	C₂×C₂₉	1	2	yes	complemented
542	#3185	C₂×C₂₉	1	1	yes	characteristic, complemented
543	#3173	C₂×C₂₉	1	2	yes	complemented
544	#3125	C₂×C₂₉	1	2	yes	complemented
545	#3121	C₂×C₂₉	1	2	yes	complemented
546	#3107	C₂×C₂₉	1	1	yes	characteristic, complemented
547	#3101	C₂×C₂₉	1	1	yes	characteristic, complemented
548	#2969	C₂×C₂₉	1	1	yes	characteristic, complemented
549	#2947	C₂×C₂₉	1	2	yes	complemented
550	C₄×AGL(1,ℤ/8)	C₂×C₂₉	1	1	yes	characteristic, complemented
551	C₂²×C₂₉	—	2	1	no	—
552	C₂²×C₂₉	—	2	2	no	—
553	C₂²×C₂₉	—	2	2	no	—
554	C₂²×C₂₉	—	2	1	no	—
555	C₂²×C₂₉	—	2	2	no	—
556	C₂²×C₂₉	—	2	1	no	—
557	C₂²×C₂₉	—	2	2	no	—
558	C₂²×C₂₉	—	4	1	no	—
559	C₂²×C₂₉	—	4	1	no	—
560	C₂²×C₂₉	—	4	1	no	—
561	C₂²×C₂₉	—	4	1	no	—
562	C₂²×C₂₉	—	4	1	no	—
563	C₂²×C₂₉	—	4	1	no	—
564	C₂²×C₂₉	—	4	1	no	—
565	C₂²×C₂₉	—	4	1	no	—
566	C₂²×C₂₉	—	8	4	no	—
567	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₂₉	—	2	1	no	—
569	C₄×C₂₉	—	2	1	no	—
570	C₄×C₂₉	—	2	2	no	—
571	C₄×C₂₉	—	2	1	no	—
572	C₄×C₂₉	—	2	2	no	—
573	C₄×C₂₉	—	2	2	no	—
574	C₄×C₂₉	—	2	1	no	—
575	C₄×C₂₉	—	2	2	no	—
576	C₄×C₂₉	—	4	1	no	—
577	C₄×C₂₉	—	4	2	no	—
578	C₄×C₂₉	—	4	2	no	—
579	C₄×C₂₉	—	4	2	no	—
580	C₄×C₂₉	—	4	1	no	—
581	C₄×C₂₉	—	4	1	no	—
582	C₄×C₂₉	—	4	1	no	—
583	C₄×C₂₉	—	4	2	no	—
584	C₄×C₂₉	#577	1	2	yes	—
585	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
586	C₄×C₂₉	#585	1	1	yes	characteristic
587	C₂×#137	C₂²×C₂₉	1	2	yes	—
588	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
589	Q₈²	C₂²×C₂₉	1	1	yes	characteristic, complemented
590	#556	—	2	2	no	—
591	#556	—	2	1	no	—
592	#556	C₂²×C₂₉	1	1	yes	characteristic
593	#556	C₂²×C₂₉	1	2	yes	—
594	#556	C₂²×C₂₉	1	1	yes	characteristic, complemented
595	#555	—	2	1	no	—
596	#555	C₂²×C₂₉	1	1	yes	characteristic, complemented
597	#554	C₂²×C₂₉	1	2	yes	—
598	#552	—	2	1	no	—
599	#551	—	2	2	no	—
600	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
601	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
602	#548	—	2	1	no	—
603	#548	C₂²×C₂₉	1	2	yes	—
604	#547	C₂²×C₂₉	1	1	yes	characteristic
605	#547	C₂²×C₂₉	1	1	yes	characteristic
606	#546	C₂²×C₂₉	1	2	yes	—
607	#542	—	2	2	no	—
608	#542	C₂²×C₂₉	1	2	yes	—
609	#542	C₂²×C₂₉	1	2	yes	complemented
610	#539	—	2	2	no	—
611	#533	—	2	1	no	—
612	#533	C₂²×C₂₉	1	1	yes	characteristic
613	#533	C₂²×C₂₉	1	1	yes	characteristic
614	#529	—	2	1	no	—
615	#529	C₂²×C₂₉	1	1	yes	characteristic
616	#525	—	2	1	no	—
617	C₂×C₂²⋊Q₈	—	2	1	no	—
618	#520	C₂²×C₂₉	1	2	yes	—
619	#519	C₂²×C₂₉	1	2	yes	complemented
620	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
621	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
622	#498	C₂²×C₂₉	1	1	yes	characteristic, complemented
623	#498	C₂²×C₂₉	1	2	yes	complemented
624	#495	C₂²×C₂₉	1	2	yes	—
625	#494	C₂²×C₂₉	1	1	yes	characteristic, complemented
626	#489	C₂²×C₂₉	1	2	yes	—
627	#489	C₂²×C₂₉	1	2	yes	complemented
628	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
629	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
630	#485	C₂²×C₂₉	1	2	yes	—
631	#485	C₂²×C₂₉	1	2	yes	complemented
632	#483	C₂²×C₂₉	1	2	yes	—
633	#483	C₂²×C₂₉	1	2	yes	complemented
634	#482	C₂²×C₂₉	1	2	yes	—
635	#481	C₂²×C₂₉	1	2	yes	complemented
636	#477	C₂²×C₂₉	1	2	yes	complemented
637	#476	C₂²×C₂₉	1	1	yes	characteristic
638	#476	C₂²×C₂₉	1	1	yes	characteristic
639	#476	C₂²×C₂₉	1	2	yes	—
640	#475	C₂²×C₂₉	1	2	yes	complemented
641	#475	C₂²×C₂₉	1	1	yes	characteristic, complemented
642	#475	C₂²×C₂₉	1	2	yes	complemented
643	#474	C₂²×C₂₉	1	1	yes	characteristic, complemented
644	#470	C₂²×C₂₉	1	2	yes	—
645	#470	C₂²×C₂₉	1	2	yes	—
646	#470	C₂²×C₂₉	1	2	yes	complemented
647	#469	C₂²×C₂₉	1	2	yes	—
648	#465	C₂²×C₂₉	1	2	yes	—
649	#465	C₂²×C₂₉	1	2	yes	complemented
650	#464	C₂²×C₂₉	1	2	yes	—
651	#464	C₂²×C₂₉	1	2	yes	—
652	#464	C₂²×C₂₉	1	2	yes	complemented
653	#463	C₂²×C₂₉	1	2	yes	—
654	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
655	#461	C₂²×C₂₉	1	1	yes	characteristic
656	#461	C₂²×C₂₉	1	1	yes	characteristic
657	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
658	#452	C₂²×C₂₉	1	2	yes	—
659	#452	C₂²×C₂₉	1	2	yes	—
660	#451	C₂²×C₂₉	1	2	yes	complemented
661	#450	C₂²×C₂₉	1	2	yes	—
662	#449	C₂²×C₂₉	1	2	yes	—
663	#448	C₂²×C₂₉	1	2	yes	—
664	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
665	C₈×Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
666	#442	C₂²×C₂₉	1	1	yes	characteristic
667	#442	C₂²×C₂₉	1	1	yes	characteristic
668	#441	C₂²×C₂₉	1	2	yes	complemented
669	#441	C₂²×C₂₉	1	2	yes	complemented
670	#441	C₂²×C₂₉	1	2	yes	complemented
671	#440	C₂²×C₂₉	1	2	yes	—
672	#440	C₂²×C₂₉	1	1	yes	characteristic
673	#440	C₂²×C₂₉	1	1	yes	characteristic
674	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
675	C₄×Q₁₆	C₂²×C₂₉	1	2	yes	complemented
676	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
677	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
678	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
679	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
680	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	—
681	C₄×SD₁₆	C₂²×C₂₉	1	2	yes	complemented
682	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
683	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
684	#436	C₂²×C₂₉	1	2	yes	—
685	#436	C₂²×C₂₉	1	1	yes	characteristic, complemented
686	#435	C₂²×C₂₉	1	2	yes	—
687	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
688	#433	C₂²×C₂₉	1	2	yes	complemented
689	#431	C₂²×C₂₉	1	1	yes	characteristic
690	#428	C₂²×C₂₉	1	1	yes	characteristic
691	#428	C₂²×C₂₉	1	2	yes	complemented
692	#418	C₂²×C₂₉	1	1	yes	characteristic
693	#417	C₂²×C₂₉	1	1	yes	characteristic
694	#416	C₂²×C₂₉	1	2	yes	—
695	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
696	#405	C₂²×C₂₉	1	2	yes	complemented
697	C₄×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
698	C₂×C₂₉	—	4	2	no	—
699	C₂×C₂₉	—	4	1	no	—
700	C₂×C₂₉	—	4	2	no	—
701	C₂×C₂₉	—	8	1	no	—
702	C₂×C₂₉	—	8	1	no	—
703	C₂×C₂₉	D₄×#41	1	1	yes	characteristic
704	C₂×C₂₉	C₂×#577	1	1	yes	characteristic
705	C₂×C₂₉	#3586	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
708	C₂×#41	C₂³×C₂₉	1	2	yes	—
709	C₂²×Q₈	—	2	1	no	—
710	C₂²×Q₈	C₂³×C₂₉	1	2	yes	—
711	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
712	C₂³×C₄	—	2	1	no	—
713	#137	—	2	8	no	—
714	AGL(1,ℤ/8)	—	2	4	no	—
715	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
716	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
717	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
720	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
723	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
724	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
725	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
726	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
727	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
728	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
729	C₄⋊Q₈	—	2	1	no	—
730	C₄⋊Q₈	—	2	1	no	—
731	C₄⋊Q₈	—	2	2	no	—
732	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
733	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
734	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
737	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	D₄×C₂₉	1	2	yes	—
745	#125	—	2	2	no	—
746	#125	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	D₄×C₂₉	1	1	yes	characteristic
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	2	2	no	—
754	#124	D₄×C₂₉	1	1	yes	characteristic
755	#124	C₂³×C₂₉	1	2	yes	—
756	#124	C₂³×C₂₉	1	2	yes	—
757	#123	—	2	2	no	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	D₄×C₂₉	1	2	yes	—
763	C₂²⋊Q₈	—	2	1	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	2	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	D₄×C₂₉	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
778	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
781	#121	—	2	1	no	—
782	#121	—	2	1	no	—
783	#121	—	2	2	no	—
784	#121	—	2	2	no	—
785	#121	D₄×C₂₉	1	1	yes	characteristic
786	#121	C₂³×C₂₉	1	2	yes	—
787	#121	C₂³×C₂₉	1	2	yes	—
788	#120	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	2	no	—
791	C₄×Q₈	—	2	2	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
798	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
799	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
800	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
801	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
802	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
814	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₂₉	1	2	yes	—
819	C₄×D₄	C₂³×C₂₉	1	2	yes	—
820	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
821	#117	—	2	1	no	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	2	no	—
829	#117	—	2	1	no	—
830	#117	C₂³×C₂₉	1	1	yes	characteristic
831	#117	C₂³×C₂₉	1	2	yes	—
832	#117	C₂³×C₂₉	1	2	yes	—
833	C₂×C₄⋊C₄	—	2	2	no	—
834	C₂×C₄⋊C₄	—	2	1	no	—
835	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
836	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
837	C₂×C₂²⋊C₄	—	2	1	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
841	#107	C₂³×C₂₉	1	1	yes	characteristic
842	#107	C₂³×C₂₉	1	1	yes	characteristic
843	#107	C₂³×C₂₉	1	2	yes	—
844	#106	C₂³×C₂₉	1	1	yes	characteristic
845	#106	C₂³×C₂₉	1	1	yes	characteristic
846	#106	C₂³×C₂₉	1	2	yes	—
847	#106	C₂³×C₂₉	1	2	yes	—
848	#106	C₂³×C₂₉	1	2	yes	—
849	#106	C₂³×C₂₉	1	2	yes	—
850	#106	C₂³×C₂₉	1	2	yes	—
851	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
854	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
855	#103	C₂³×C₂₉	1	1	yes	characteristic
856	#103	C₂³×C₂₉	1	2	yes	—
857	#103	C₂³×C₂₉	1	2	yes	—
858	#103	C₂³×C₂₉	1	2	yes	—
859	#103	C₂³×C₂₉	1	2	yes	—
860	#103	C₂³×C₂₉	1	2	yes	—
861	#103	C₂³×C₂₉	1	1	yes	characteristic
862	#103	C₂³×C₂₉	1	2	yes	—
863	#103	C₂³×C₂₉	1	2	yes	—
864	#103	C₂³×C₂₉	1	2	yes	—
865	#103	C₂³×C₂₉	1	2	yes	—
866	#102	C₂³×C₂₉	1	1	yes	characteristic
867	#102	C₂³×C₂₉	1	2	yes	—
868	#102	C₂³×C₂₉	1	1	yes	characteristic
869	#102	C₂³×C₂₉	1	1	yes	characteristic
870	#102	C₂³×C₂₉	1	1	yes	characteristic
871	#102	C₂³×C₂₉	1	1	yes	characteristic
872	#102	C₂³×C₂₉	1	1	yes	characteristic
873	#102	C₂³×C₂₉	1	2	yes	—
874	#102	C₂³×C₂₉	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
878	#97	C₂³×C₂₉	1	1	yes	characteristic
879	#97	C₂³×C₂₉	1	1	yes	characteristic
880	#97	C₂³×C₂₉	1	2	yes	—
881	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₂₉	1	2	yes	—
884	C₄×C₈	C₂³×C₂₉	1	2	yes	—
885	C₂₉	#61557	1	1	yes	characteristic, direct product factor, Sylow
886	C₂⁴	—	2	1	no	—
887	#41	—	2	2	no	—
888	#41	—	2	4	no	—
889	#41	—	4	2	no	—
890	#41	—	4	1	no	—
891	#41	—	8	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	2	4	no	—
898	C₂×Q₈	—	4	2	no	—
899	C₂×Q₈	—	8	2	no	—
900	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
903	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	4	1	no	—
911	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
912	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
913	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
914	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	2	1	no	—
928	C₂²×C₄	—	8	2	no	—
929	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
930	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
932	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
933	Q₁₆	—	2	4	no	—
934	Q₁₆	—	2	4	no	—
935	Q₁₆	—	4	2	no	—
936	SD₁₆	—	2	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	SD₁₆	#41×C₂₉	1	4	yes	complemented
941	D₈	—	2	2	no	—
942	D₈	—	2	2	no	—
943	M₁₆	—	2	2	no	—
944	M₁₆	—	2	4	no	—
945	M₁₆	—	4	1	no	—
946	C₂×C₈	—	4	2	no	—
947	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
948	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
951	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
975	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
976	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
977	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
978	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
980	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
981	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	—	2	2	no	—
1019	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1020	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₂₉	1	2	yes	—
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	4	4	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	1	no	—
1042	Q₈	—	8	2	no	—
1043	Q₈	C₂×#41×C₂₉	1	2	yes	—
1044	D₄	—	2	2	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	4	no	—
1054	D₄	—	8	2	no	—
1055	D₄	—	8	2	no	—
1056	D₄	C₂×#41×C₂₉	1	2	yes	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	4	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	1	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	1	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1090	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	2	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	C₂×#41×C₂₉	1	2	yes	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	1	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	8	4	no	—
1115	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	2	no	—
1125	C₄	—	4	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	C₂₉×#577	1	2	yes	—
1133	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
1134	C₄	C₂₉×#585	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	D₄×#41×C₂₉	1	1	yes	characteristic
1141	C₂	C₂×C₂₉×#577	1	1	yes	characteristic
1142	C₂	C₂₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂₉×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3520	C₂	semidirect
2. C₂₉×#3518	C₂	semidirect
3. C₂₉×#3393	C₂	semidirect
4. Q₈×SD₁₆×C₂₉	C₂	semidirect
5. C₂₉×#3369	C₂	semidirect
6. C₂₉×#3367	C₂	semidirect
7. C₂₉×#3356	C₂	semidirect
8. C₂₉×#3354	C₂	semidirect
9. C₂₉×#3316	C₂	semidirect
10. C₂₉×#3311	C₂	semidirect
11. C₂₉×#3303	C₂	semidirect
12. C₂₉×#3298	C₂	semidirect
13. C₂₉×#3276	C₂	semidirect
14. C₂₉×#3275	C₂	semidirect
15. C₂₉×#3185	C₂	semidirect
16. C₂₉×#3173	C₂	semidirect
17. C₂₉×#3125	C₂	semidirect
18. C₂₉×#3121	C₂	semidirect
19. C₂₉×#3107	C₂	semidirect
20. C₂₉×#3101	C₂	semidirect
21. C₂₉×#2969	C₂	semidirect
22. C₂₉×#2947	C₂	semidirect
23. C₄×C₂₉×AGL(1,ℤ/8)	C₂	semidirect
26. Q₈²×C₂₉	C₂²	semidirect
31. C₂₉×#556	C₂²	semidirect
33. C₂₉×#555	C₂²	semidirect
38. D₄×Q₈×C₂₉	C₂²	semidirect
46. C₂₉×#542	C₂²	semidirect
56. C₂₉×#519	C₂²	semidirect
59. C₂₉×#498	C₂²	semidirect
60. C₂₉×#498	C₂²	semidirect
62. C₂₉×#494	C₂²	semidirect
64. C₂₉×#489	C₂²	semidirect
65. C₂₉×#487	C₂²	semidirect
66. C₂₉×#487	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
70. C₂₉×#483	C₂²	semidirect
72. C₂₉×#481	C₂²	semidirect
73. C₂₉×#477	C₂²	semidirect
77. C₂₉×#475	C₂²	semidirect
78. C₂₉×#475	C₂²	semidirect
79. C₂₉×#475	C₂²	semidirect
80. C₂₉×#474	C₂²	semidirect
83. C₂₉×#470	C₂²	semidirect
86. C₂₉×#465	C₂²	semidirect
89. C₂₉×#464	C₂²	semidirect
91. C₂₉×#462	C₂²	semidirect
94. C₂₉×#461	C₂²	semidirect
97. C₂₉×#451	C₂²	semidirect
101. C₂₉×#446	C₂²	semidirect
102. C₈×Q₈×C₂₉	C₂²	semidirect
105. C₂₉×#441	C₂²	semidirect
106. C₂₉×#441	C₂²	semidirect
107. C₂₉×#441	C₂²	semidirect
111. C₄×Q₁₆×C₂₉	C₂²	semidirect
112. C₄×Q₁₆×C₂₉	C₂²	semidirect
118. C₄×SD₁₆×C₂₉	C₂²	semidirect
122. C₂₉×#436	C₂²	semidirect
124. C₈×D₄×C₂₉	C₂²	semidirect
125. C₂₉×#433	C₂²	semidirect
128. C₂₉×#428	C₂²	semidirect
132. C₂×C₂₉×#103	C₂²	semidirect
133. C₂₉×#405	C₂²	semidirect
368. SD₁₆×C₂₉	#41	semidirect
452. #61557	C₂₉	direct (N × H)
528. #3520	C₂×C₂₉	semidirect
529. #3518	C₂×C₂₉	semidirect
530. #3393	C₂×C₂₉	semidirect
531. Q₈×SD₁₆	C₂×C₂₉	semidirect
532. #3369	C₂×C₂₉	semidirect
533. #3367	C₂×C₂₉	semidirect
534. #3356	C₂×C₂₉	semidirect
535. #3354	C₂×C₂₉	semidirect
536. #3316	C₂×C₂₉	semidirect
537. #3311	C₂×C₂₉	semidirect
538. #3303	C₂×C₂₉	semidirect
539. #3298	C₂×C₂₉	semidirect
540. #3276	C₂×C₂₉	semidirect
541. #3275	C₂×C₂₉	semidirect
542. #3185	C₂×C₂₉	semidirect
543. #3173	C₂×C₂₉	semidirect
544. #3125	C₂×C₂₉	semidirect
545. #3121	C₂×C₂₉	semidirect
546. #3107	C₂×C₂₉	semidirect
547. #3101	C₂×C₂₉	semidirect
548. #2969	C₂×C₂₉	semidirect
549. #2947	C₂×C₂₉	semidirect
550. C₄×AGL(1,ℤ/8)	C₂×C₂₉	semidirect
589. Q₈²	C₂²×C₂₉	semidirect
594. #556	C₂²×C₂₉	semidirect
596. #555	C₂²×C₂₉	semidirect
601. D₄×Q₈	C₂²×C₂₉	semidirect
609. #542	C₂²×C₂₉	semidirect
619. #519	C₂²×C₂₉	semidirect
622. #498	C₂²×C₂₉	semidirect
623. #498	C₂²×C₂₉	semidirect
625. #494	C₂²×C₂₉	semidirect
627. #489	C₂²×C₂₉	semidirect
628. #487	C₂²×C₂₉	semidirect
629. #487	C₂²×C₂₉	semidirect
631. #485	C₂²×C₂₉	semidirect
633. #483	C₂²×C₂₉	semidirect
635. #481	C₂²×C₂₉	semidirect
636. #477	C₂²×C₂₉	semidirect
640. #475	C₂²×C₂₉	semidirect
641. #475	C₂²×C₂₉	semidirect
642. #475	C₂²×C₂₉	semidirect
643. #474	C₂²×C₂₉	semidirect
646. #470	C₂²×C₂₉	semidirect
649. #465	C₂²×C₂₉	semidirect
652. #464	C₂²×C₂₉	semidirect
654. #462	C₂²×C₂₉	semidirect
657. #461	C₂²×C₂₉	semidirect
660. #451	C₂²×C₂₉	semidirect
664. #446	C₂²×C₂₉	semidirect
665. C₈×Q₈	C₂²×C₂₉	semidirect
668. #441	C₂²×C₂₉	semidirect
669. #441	C₂²×C₂₉	semidirect
670. #441	C₂²×C₂₉	semidirect
674. C₄×Q₁₆	C₂²×C₂₉	semidirect
675. C₄×Q₁₆	C₂²×C₂₉	semidirect
681. C₄×SD₁₆	C₂²×C₂₉	semidirect
685. #436	C₂²×C₂₉	semidirect
687. C₈×D₄	C₂²×C₂₉	semidirect
688. #433	C₂²×C₂₉	semidirect
691. #428	C₂²×C₂₉	semidirect
695. C₂×#103	C₂²×C₂₉	semidirect
696. #405	C₂²×C₂₉	semidirect
885. C₂₉	#61557	direct (N × H)
940. SD₁₆	#41×C₂₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₉×#3520	2
C₂₉×#3518	2
C₂₉×#3393	2
Q₈×SD₁₆×C₂₉	2
C₂₉×#3369	2
C₂₉×#3367	2
C₂₉×#3356	2
C₂₉×#3354	2
C₂₉×#3316	2
C₂₉×#3311	2
C₂₉×#3303	2
C₂₉×#3298	2
C₂₉×#3276	2
C₂₉×#3275	2
C₂₉×#3185	2
C₂₉×#3173	2
C₂₉×#3125	2
C₂₉×#3121	2
C₂₉×#3107	2
C₂₉×#3101	2
C₂₉×#2969	2
C₂₉×#2947	2
C₄×C₂₉×AGL(1,ℤ/8)	2
#61557	29

Subgroups — C29×#61557 #20356457

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61557 #20356457