Subgroups — C₂₉×#61993 #20356893

Order 7424.

1870 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3317	C₂	1	2	yes	maximal, complemented
8	C₂₉×#3315	C₂	1	2	yes	maximal, complemented
9	C₂₉×#3305	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#3268	C₂	1	2	yes	maximal, complemented
14	C₂₉×#3267	C₂	1	2	yes	maximal, complemented
15	C₂₉×#3252	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₉×#3250	C₂	1	2	yes	maximal, complemented
17	C₂₉×#3219	C₂	1	2	yes	maximal, complemented
18	C₂₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₉×#3111	C₂	1	2	yes	maximal, complemented
20	C₂₉×#3105	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₉×#3036	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₉×#3035	C₂	1	2	yes	maximal, complemented
23	C₂₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
25	C₂×C₂₉×#135	C₂²	1	2	yes	—
26	C₂×C₂₉×#135	C₂²	1	2	yes	—
27	C₂₉×#557	C₂²	1	1	yes	characteristic, complemented
28	C₂₉×#556	C₂²	1	1	yes	characteristic
29	C₂₉×#555	C₂²	1	1	yes	characteristic
30	C₂₉×#554	C₂²	1	1	yes	characteristic
31	C₂₉×#553	—	2	1	no	—
32	C₂₉×#553	—	2	2	no	—
33	C₂₉×#553	—	2	1	no	—
34	C₂₉×#552	—	2	1	no	—
35	C₂₉×#552	C₂²	1	2	yes	—
36	C₂₉×#551	—	2	2	no	—
37	C₂₉×#550	—	2	1	no	—
38	C₂₉×#550	C₂²	1	2	yes	—
39	C₂₉×#550	C₂²	1	1	yes	characteristic, complemented
40	C₂₉×#550	C₂²	1	1	yes	characteristic, complemented
41	C₂₉×#547	C₂²	1	1	yes	characteristic
42	C₂₉×#547	C₂²	1	2	yes	—
43	C₂₉×#547	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#546	C₂²	1	2	yes	—
45	C₂₉×#540	—	2	1	no	—
46	C₂₉×#540	—	2	2	no	—
47	C₂₉×#533	C₂²	1	1	yes	characteristic
48	C₂₉×#532	C₂²	1	1	yes	characteristic
49	C₂₉×#532	C₂²	1	2	yes	complemented
50	C₂₉×#529	—	2	2	no	—
51	C₂₉×#529	C₂²	1	2	yes	—
52	C₂₉×#529	C₂²	1	1	yes	characteristic
53	C₂₉×#529	C₂²	1	2	yes	complemented
54	C₂₉×#525	—	2	1	no	—
55	C₂₉×#520	—	2	1	no	—
56	C₄×#41×C₂₉	C₂²	1	2	yes	—
57	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
59	C₂×C₂₉×#117	—	2	1	no	—
60	C₂₉×#497	C₂²	1	2	yes	—
61	C₂₉×#496	C₂²	1	2	yes	—
62	C₂₉×#494	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×#492	C₂²	1	1	yes	characteristic, complemented
64	C₂₉×#491	C₂²	1	2	yes	complemented
65	C₂₉×#490	C₂²	1	2	yes	complemented
66	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×#485	C₂²	1	2	yes	complemented
69	C₂₉×#484	C₂²	1	1	yes	characteristic
70	C₂₉×#482	C₂²	1	2	yes	complemented
71	C₂₉×#481	C₂²	1	1	yes	characteristic
72	C₂₉×#479	C₂²	1	2	yes	complemented
73	C₂₉×#479	C₂²	1	2	yes	complemented
74	C₂₉×#478	C₂²	1	1	yes	characteristic
75	C₂₉×#478	C₂²	1	1	yes	characteristic
76	C₂₉×#478	C₂²	1	2	yes	complemented
77	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
78	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
79	C₂₉×#470	C₂²	1	2	yes	—
80	C₂₉×#468	C₂²	1	2	yes	—
81	C₂₉×#467	C₂²	1	2	yes	complemented
82	C₂₉×#466	C₂²	1	2	yes	—
83	C₂₉×#465	C₂²	1	2	yes	—
84	C₂₉×#465	C₂²	1	2	yes	complemented
85	C₂₉×#464	C₂²	1	2	yes	—
86	C₂₉×#464	C₂²	1	2	yes	complemented
87	C₂₉×#464	C₂²	1	2	yes	complemented
88	C₂₉×#464	C₂²	1	2	yes	complemented
89	C₂₉×#463	C₂²	1	1	yes	characteristic
90	C₂₉×#463	C₂²	1	2	yes	—
91	C₂₉×#463	C₂²	1	2	yes	—
92	C₂₉×#463	C₂²	1	1	yes	characteristic
93	C₂₉×#463	C₂²	1	2	yes	—
94	C₂₉×#462	C₂²	1	1	yes	characteristic, complemented
95	C₂₉×#462	C₂²	1	2	yes	complemented
96	C₂₉×#461	C₂²	1	2	yes	—
97	C₂₉×#461	C₂²	1	1	yes	characteristic
98	C₂₉×#461	C₂²	1	1	yes	characteristic
99	C₂₉×#461	C₂²	1	1	yes	characteristic, complemented
100	C₂₉×#460	C₂²	1	2	yes	complemented
101	C₂₉×#459	C₂²	1	2	yes	—
102	C₂₉×#459	C₂²	1	1	yes	characteristic
103	C₂₉×#459	C₂²	1	1	yes	characteristic
104	C₂₉×#452	C₂²	1	2	yes	—
105	C₂₉×#452	C₂²	1	2	yes	—
106	C₂₉×#452	C₂²	1	2	yes	—
107	C₂₉×#452	C₂²	1	2	yes	complemented
108	C₂₉×#452	C₂²	1	2	yes	complemented
109	C₂₉×#450	C₂²	1	1	yes	characteristic
110	C₂₉×#449	C₂²	1	2	yes	—
111	C₂₉×#449	C₂²	1	2	yes	—
112	C₂₉×#449	C₂²	1	2	yes	—
113	C₂₉×#447	C₂²	1	1	yes	characteristic
114	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
115	C₂₉×#446	C₂²	1	1	yes	characteristic, complemented
116	C₂₉×#442	C₂²	1	2	yes	—
117	C₂₉×#441	C₂²	1	2	yes	complemented
118	C₂₉×#440	C₂²	1	2	yes	—
119	C₂₉×#440	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
122	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
123	C₄×D₈×C₂₉	C₂²	1	1	yes	characteristic
124	C₂₉×#435	C₂²	1	2	yes	—
125	C₂₉×#435	C₂²	1	2	yes	—
126	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
127	C₈×D₄×C₂₉	C₂²	1	1	yes	characteristic, complemented
128	C₂₉×#432	C₂²	1	2	yes	complemented
129	C₂₉×#431	C₂²	1	1	yes	characteristic
130	C₂₉×#423	C₂²	1	1	yes	characteristic
131	C₂×C₂₉×C₄⋊C₈	C₂²	1	2	yes	complemented
132	C₂₉×#417	C₂²	1	2	yes	—
133	C₂₉×#416	C₂²	1	2	yes	complemented
134	C₂₉×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₂₉	—	2	1	no	—
136	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
137	C₂×#41×C₂₉	C₂³	1	2	yes	—
138	C₂×#41×C₂₉	C₂³	1	2	yes	—
139	C₂×#41×C₂₉	C₂³	1	2	yes	—
140	C₂×#41×C₂₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₂₉	—	2	1	no	—
143	C₂₉×AGL(1,ℤ/8)	—	4	4	no	—
144	C₂₉×#135	—	4	4	no	—
145	C₂₉×#135	—	4	4	no	—
146	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₂₉	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₂₉	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₂₉	C₂³	1	2	yes	—
156	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
157	C₂×D₈×C₂₉	C₂³	1	2	yes	—
158	C₂×D₈×C₂₉	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₂₉	C₂³	1	2	yes	—
160	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
161	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
162	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
163	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₂₉×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₂₉×#127	—	2	2	no	—
168	C₂₉×#127	—	2	1	no	—
169	C₂₉×#127	C₂³	1	1	yes	characteristic
170	C₂₉×#127	C₂³	1	2	yes	—
171	C₂₉×#126	—	2	2	no	—
172	C₂₉×#126	—	2	2	no	—
173	C₂₉×#126	—	2	2	no	—
174	C₂₉×#126	—	2	1	no	—
175	C₂₉×#126	—	2	2	no	—
176	C₂₉×#125	—	2	2	no	—
177	C₂₉×#125	—	2	1	no	—
178	C₂₉×#125	—	2	2	no	—
179	C₂₉×#125	—	2	1	no	—
180	C₂₉×#125	C₂³	1	1	yes	characteristic
181	C₂₉×#125	C₂³	1	2	yes	—
182	C₂₉×#124	—	2	2	no	—
183	C₂₉×#124	C₂³	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	1	no	—
188	C₂₉×#123	—	2	2	no	—
189	C₂₉×#123	—	2	2	no	—
190	C₂₉×#123	—	2	2	no	—
191	C₂₉×#123	—	2	2	no	—
192	C₂₉×#123	—	2	2	no	—
193	C₂₉×#123	—	2	2	no	—
194	C₂₉×#123	—	2	2	no	—
195	C₂₉×C₂²⋊Q₈	—	2	1	no	—
196	C₂₉×C₂²⋊Q₈	—	2	1	no	—
197	C₂₉×C₂²⋊Q₈	—	2	1	no	—
198	C₂₉×C₂²⋊Q₈	—	2	2	no	—
199	C₂₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
200	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₂₉×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₂₉×#121	—	2	1	no	—
204	C₂₉×#121	—	2	1	no	—
205	C₂₉×#121	—	2	2	no	—
206	C₂₉×#121	—	2	1	no	—
207	C₂₉×#121	—	2	1	no	—
208	C₂₉×#121	—	2	1	no	—
209	C₂₉×#121	—	2	2	no	—
210	C₂₉×#121	—	2	2	no	—
211	C₂₉×#121	—	2	1	no	—
212	C₂₉×#121	—	2	2	no	—
213	C₂₉×#121	—	2	2	no	—
214	C₂₉×#121	—	2	2	no	—
215	C₂₉×#121	—	2	2	no	—
216	C₂₉×#121	—	2	2	no	—
217	C₂₉×#121	C₂³	1	1	yes	characteristic
218	C₂₉×#121	C₂³	1	2	yes	—
219	C₂₉×#121	C₂³	1	2	yes	—
220	C₂₉×#120	—	2	2	no	—
221	C₄×Q₈×C₂₉	—	2	1	no	—
222	C₄×Q₈×C₂₉	—	2	1	no	—
223	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
224	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₂₉	C₂³	1	2	yes	—
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×D₄×C₂₉	—	2	2	no	—
230	C₄×D₄×C₂₉	—	2	2	no	—
231	C₄×D₄×C₂₉	—	2	2	no	—
232	C₄×D₄×C₂₉	—	2	1	no	—
233	C₄×D₄×C₂₉	—	2	2	no	—
234	C₄×D₄×C₂₉	—	2	2	no	—
235	C₄×D₄×C₂₉	—	2	1	no	—
236	C₄×D₄×C₂₉	—	2	1	no	—
237	C₄×D₄×C₂₉	—	2	1	no	—
238	C₄×D₄×C₂₉	—	2	1	no	—
239	C₄×D₄×C₂₉	—	2	2	no	—
240	C₄×D₄×C₂₉	—	2	1	no	—
241	C₄×D₄×C₂₉	—	2	2	no	—
242	C₄×D₄×C₂₉	D₄	1	2	yes	—
243	C₄×D₄×C₂₉	D₄	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	1	yes	characteristic
247	C₄×D₄×C₂₉	C₂³	1	2	yes	—
248	C₄×D₄×C₂₉	C₂³	1	2	yes	—
249	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₂₉	C₂³	1	2	yes	—
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	2	no	—
259	C₂₉×#117	—	2	1	no	—
260	C₂₉×#117	—	2	2	no	—
261	C₂₉×#117	D₄	1	1	yes	characteristic
262	C₂₉×#117	D₄	1	2	yes	—
263	C₂₉×#117	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
265	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
266	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
267	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
268	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
270	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
271	C₂×C₄²×C₂₉	—	2	2	no	—
272	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
274	C₂₉×#107	C₂³	1	1	yes	characteristic
275	C₂₉×#107	C₂³	1	1	yes	characteristic
276	C₂₉×#107	C₂³	1	2	yes	—
277	C₂₉×#106	C₂³	1	1	yes	characteristic
278	C₂₉×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
284	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
286	C₂₉×C₄⋊C₈	C₂³	1	2	yes	—
287	C₂₉×#103	C₂³	1	1	yes	characteristic
288	C₂₉×#103	C₂³	1	1	yes	characteristic
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×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
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×#102	C₂³	1	2	yes	—
305	C₂₉×#102	C₂³	1	2	yes	—
306	C₂₉×#102	C₂³	1	2	yes	—
307	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₂₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₉×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₉×#97	C₂³	1	2	yes	—
312	C₂₉×#97	C₂³	1	2	yes	—
313	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
315	C₂⁴×C₂₉	—	2	1	no	—
316	#41×C₂₉	—	2	4	no	—
317	#41×C₂₉	—	4	2	no	—
318	#41×C₂₉	—	4	2	no	—
319	#41×C₂₉	—	4	2	no	—
320	#41×C₂₉	—	4	2	no	—
321	#41×C₂₉	—	4	2	no	—
322	#41×C₂₉	—	4	2	no	—
323	#41×C₂₉	—	4	2	no	—
324	#41×C₂₉	—	4	2	no	—
325	#41×C₂₉	—	4	4	no	—
326	C₂×Q₈×C₂₉	—	2	1	no	—
327	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₂₉	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₂₉	—	2	2	no	—
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	2	no	—
338	C₂×D₄×C₂₉	—	2	2	no	—
339	C₂×D₄×C₂₉	—	2	1	no	—
340	C₂×D₄×C₂₉	—	2	2	no	—
341	C₂×D₄×C₂₉	—	2	1	no	—
342	C₂×D₄×C₂₉	—	2	2	no	—
343	C₂×D₄×C₂₉	—	2	1	no	—
344	C₂×D₄×C₂₉	—	4	1	no	—
345	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
348	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
349	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₂₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
356	C₂²×C₄×C₂₉	—	2	1	no	—
357	C₂²×C₄×C₂₉	—	2	1	no	—
358	C₂²×C₄×C₂₉	—	2	1	no	—
359	C₂²×C₄×C₂₉	—	2	2	no	—
360	C₂²×C₄×C₂₉	—	2	2	no	—
361	C₂²×C₄×C₂₉	—	2	2	no	—
362	C₂²×C₄×C₂₉	—	2	2	no	—
363	C₂²×C₄×C₂₉	—	4	4	no	—
364	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
367	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₂₉	C₂⁴	1	2	yes	—
370	Q₁₆×C₂₉	—	4	2	no	—
371	Q₁₆×C₂₉	—	4	2	no	—
372	Q₁₆×C₂₉	—	4	2	no	—
373	SD₁₆×C₂₉	—	2	2	no	—
374	SD₁₆×C₂₉	—	2	4	no	—
375	SD₁₆×C₂₉	—	4	2	no	—
376	SD₁₆×C₂₉	—	4	1	no	—
377	SD₁₆×C₂₉	—	4	2	no	—
378	SD₁₆×C₂₉	—	4	2	no	—
379	SD₁₆×C₂₉	—	4	2	no	—
380	D₈×C₂₉	—	2	2	no	—
381	D₈×C₂₉	—	2	4	no	—
382	D₈×C₂₉	—	4	1	no	—
383	D₈×C₂₉	—	4	2	no	—
384	M₁₆×C₂₉	—	4	2	no	—
385	C₂×C₈×C₂₉	—	4	2	no	—
386	C₂×C₈×C₂₉	—	4	2	no	—
387	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
390	C₂×C₈×C₂₉	C₂⁴	1	2	yes	—
391	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₂₉	C₂⁴	1	1	yes	characteristic
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	1	no	—
397	C₄⋊C₄×C₂₉	—	2	2	no	—
398	C₄⋊C₄×C₂₉	—	2	2	no	—
399	C₄⋊C₄×C₂₉	—	2	2	no	—
400	C₄⋊C₄×C₂₉	—	2	1	no	—
401	C₄⋊C₄×C₂₉	—	2	1	no	—
402	C₄⋊C₄×C₂₉	—	2	1	no	—
403	C₄⋊C₄×C₂₉	—	2	2	no	—
404	C₄⋊C₄×C₂₉	—	2	2	no	—
405	C₄⋊C₄×C₂₉	—	2	1	no	—
406	C₄⋊C₄×C₂₉	—	2	2	no	—
407	C₄⋊C₄×C₂₉	—	2	1	no	—
408	C₄⋊C₄×C₂₉	—	2	2	no	—
409	C₄⋊C₄×C₂₉	—	2	2	no	—
410	C₄⋊C₄×C₂₉	—	2	1	no	—
411	C₄⋊C₄×C₂₉	—	2	2	no	—
412	C₄⋊C₄×C₂₉	—	2	1	no	—
413	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₂₉	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₂₉	—	2	2	no	—
423	C₂²⋊C₄×C₂₉	—	2	2	no	—
424	C₂²⋊C₄×C₂₉	—	2	1	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	2	no	—
429	C₂²⋊C₄×C₂₉	—	2	2	no	—
430	C₂²⋊C₄×C₂₉	—	2	1	no	—
431	C₂²⋊C₄×C₂₉	—	2	1	no	—
432	C₂²⋊C₄×C₂₉	—	2	1	no	—
433	C₂²⋊C₄×C₂₉	—	2	2	no	—
434	C₂²⋊C₄×C₂₉	—	2	1	no	—
435	C₂²⋊C₄×C₂₉	—	2	1	no	—
436	C₂²⋊C₄×C₂₉	—	2	2	no	—
437	C₂²⋊C₄×C₂₉	—	2	2	no	—
438	C₂²⋊C₄×C₂₉	—	2	1	no	—
439	C₂²⋊C₄×C₂₉	—	2	2	no	—
440	C₂²⋊C₄×C₂₉	—	2	2	no	—
441	C₂²⋊C₄×C₂₉	—	2	2	no	—
442	C₂²⋊C₄×C₂₉	—	2	1	no	—
443	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
446	C₄²×C₂₉	—	2	2	no	—
447	C₄²×C₂₉	—	2	2	no	—
448	C₄²×C₂₉	—	2	2	no	—
449	C₄²×C₂₉	—	2	2	no	—
450	C₄²×C₂₉	—	2	1	no	—
451	C₄²×C₂₉	C₂×D₄	1	2	yes	—
452	C₄²×C₂₉	C₂×D₄	1	2	yes	—
453	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
456	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
457	C₄²×C₂₉	C₂⁴	1	2	yes	—
458	#61993	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
459	C₂³×C₂₉	—	2	1	no	—
460	C₂³×C₂₉	—	2	1	no	—
461	C₂³×C₂₉	—	2	2	no	—
462	C₂³×C₂₉	—	2	1	no	—
463	C₂³×C₂₉	—	4	2	no	—
464	C₂³×C₂₉	—	4	2	no	—
465	C₂³×C₂₉	—	8	1	no	—
466	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
467	C₂³×C₂₉	C₂²×D₄	1	2	yes	—
468	Q₈×C₂₉	—	2	2	no	—
469	Q₈×C₂₉	—	2	2	no	—
470	Q₈×C₂₉	—	2	1	no	—
471	Q₈×C₂₉	—	2	2	no	—
472	Q₈×C₂₉	—	2	2	no	—
473	Q₈×C₂₉	—	2	1	no	—
474	Q₈×C₂₉	—	2	2	no	—
475	Q₈×C₂₉	—	8	1	no	—
476	D₄×C₂₉	—	2	2	no	—
477	D₄×C₂₉	—	2	2	no	—
478	D₄×C₂₉	—	2	1	no	—
479	D₄×C₂₉	—	2	1	no	—
480	D₄×C₂₉	—	2	1	no	—
481	D₄×C₂₉	—	2	1	no	—
482	D₄×C₂₉	—	2	1	no	—
483	D₄×C₂₉	—	2	2	no	—
484	D₄×C₂₉	—	4	2	no	—
485	D₄×C₂₉	—	4	2	no	—
486	D₄×C₂₉	—	4	4	no	—
487	D₄×C₂₉	—	4	4	no	—
488	D₄×C₂₉	—	4	2	no	—
489	D₄×C₂₉	—	8	2	no	—
490	D₄×C₂₉	—	8	1	no	—
491	D₄×C₂₉	—	8	2	no	—
492	D₄×C₂₉	—	8	2	no	—
493	D₄×C₂₉	—	8	1	no	—
494	D₄×C₂₉	—	8	2	no	—
495	D₄×C₂₉	—	8	2	no	—
496	D₄×C₂₉	—	8	2	no	—
497	D₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
498	C₂×C₄×C₂₉	—	2	2	no	—
499	C₂×C₄×C₂₉	—	2	2	no	—
500	C₂×C₄×C₂₉	—	2	1	no	—
501	C₂×C₄×C₂₉	—	2	1	no	—
502	C₂×C₄×C₂₉	—	2	2	no	—
503	C₂×C₄×C₂₉	—	2	1	no	—
504	C₂×C₄×C₂₉	—	2	1	no	—
505	C₂×C₄×C₂₉	—	2	2	no	—
506	C₂×C₄×C₂₉	—	2	2	no	—
507	C₂×C₄×C₂₉	—	2	2	no	—
508	C₂×C₄×C₂₉	—	2	1	no	—
509	C₂×C₄×C₂₉	—	2	1	no	—
510	C₂×C₄×C₂₉	—	2	1	no	—
511	C₂×C₄×C₂₉	—	4	2	no	—
512	C₂×C₄×C₂₉	—	4	1	no	—
513	C₂×C₄×C₂₉	—	4	2	no	—
514	C₂×C₄×C₂₉	—	4	4	no	—
515	C₂×C₄×C₂₉	—	4	2	no	—
516	C₂×C₄×C₂₉	—	4	2	no	—
517	C₂×C₄×C₂₉	—	4	4	no	—
518	C₂×C₄×C₂₉	—	4	2	no	—
519	C₂×C₄×C₂₉	—	4	2	no	—
520	C₂×C₄×C₂₉	—	4	2	no	—
521	C₂×C₄×C₂₉	—	4	2	no	—
522	C₂×C₄×C₂₉	—	8	2	no	—
523	C₂×C₄×C₂₉	—	8	2	no	—
524	C₂×C₄×C₂₉	—	8	2	no	—
525	C₂×C₄×C₂₉	—	8	2	no	—
526	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₂₉	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
533	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
535	C₈×C₂₉	—	2	1	no	—
536	C₈×C₂₉	—	2	1	no	—
537	C₈×C₂₉	—	2	2	no	—
538	C₈×C₂₉	—	2	2	no	—
539	C₈×C₂₉	—	2	1	no	—
540	C₈×C₂₉	—	2	1	no	—
541	#3517	C₂×C₂₉	1	1	yes	characteristic, complemented
542	#3475	C₂×C₂₉	1	1	yes	characteristic, complemented
543	#3398	C₂×C₂₉	1	1	yes	characteristic, complemented
544	#3397	C₂×C₂₉	1	1	yes	characteristic, complemented
545	#3372	C₂×C₂₉	1	1	yes	characteristic, complemented
546	#3366	C₂×C₂₉	1	1	yes	characteristic, complemented
547	#3317	C₂×C₂₉	1	2	yes	complemented
548	#3315	C₂×C₂₉	1	2	yes	complemented
549	#3305	C₂×C₂₉	1	1	yes	characteristic, complemented
550	#3303	C₂×C₂₉	1	1	yes	characteristic, complemented
551	#3284	C₂×C₂₉	1	1	yes	characteristic, complemented
552	#3283	C₂×C₂₉	1	1	yes	characteristic, complemented
553	#3268	C₂×C₂₉	1	2	yes	complemented
554	#3267	C₂×C₂₉	1	2	yes	complemented
555	#3252	C₂×C₂₉	1	1	yes	characteristic, complemented
556	#3250	C₂×C₂₉	1	2	yes	complemented
557	#3219	C₂×C₂₉	1	2	yes	complemented
558	#3210	C₂×C₂₉	1	1	yes	characteristic, complemented
559	#3111	C₂×C₂₉	1	2	yes	complemented
560	#3105	C₂×C₂₉	1	1	yes	characteristic, complemented
561	#3036	C₂×C₂₉	1	1	yes	characteristic, complemented
562	#3035	C₂×C₂₉	1	2	yes	complemented
563	#2990	C₂×C₂₉	1	1	yes	characteristic, complemented
564	C₂²×C₂₉	—	2	2	no	—
565	C₂²×C₂₉	—	2	1	no	—
566	C₂²×C₂₉	—	2	2	no	—
567	C₂²×C₂₉	—	2	1	no	—
568	C₂²×C₂₉	—	2	2	no	—
569	C₂²×C₂₉	—	2	1	no	—
570	C₂²×C₂₉	—	2	2	no	—
571	C₂²×C₂₉	—	4	1	no	—
572	C₂²×C₂₉	—	4	1	no	—
573	C₂²×C₂₉	—	4	1	no	—
574	C₂²×C₂₉	—	4	2	no	—
575	C₂²×C₂₉	—	4	1	no	—
576	C₂²×C₂₉	—	4	2	no	—
577	C₂²×C₂₉	—	4	1	no	—
578	C₂²×C₂₉	—	4	1	no	—
579	C₂²×C₂₉	—	4	1	no	—
580	C₂²×C₂₉	—	4	2	no	—
581	C₂²×C₂₉	—	4	1	no	—
582	C₂²×C₂₉	—	8	4	no	—
583	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
584	C₄×C₂₉	—	2	1	no	—
585	C₄×C₂₉	—	2	2	no	—
586	C₄×C₂₉	—	2	1	no	—
587	C₄×C₂₉	—	2	2	no	—
588	C₄×C₂₉	—	2	1	no	—
589	C₄×C₂₉	—	2	1	no	—
590	C₄×C₂₉	—	2	2	no	—
591	C₄×C₂₉	—	4	2	no	—
592	C₄×C₂₉	—	4	1	no	—
593	C₄×C₂₉	—	4	2	no	—
594	C₄×C₂₉	—	4	2	no	—
595	C₄×C₂₉	—	4	1	no	—
596	C₄×C₂₉	—	4	1	no	—
597	C₄×C₂₉	—	4	1	no	—
598	C₄×C₂₉	—	4	1	no	—
599	C₄×C₂₉	#575	1	2	yes	—
600	C₄×C₂₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	C₄×C₂₉	#585	1	1	yes	characteristic
602	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
603	C₂×#135	C₂²×C₂₉	1	2	yes	—
604	C₂×#135	C₂²×C₂₉	1	2	yes	—
605	#557	C₂²×C₂₉	1	1	yes	characteristic, complemented
606	#556	C₂²×C₂₉	1	1	yes	characteristic
607	#555	C₂²×C₂₉	1	1	yes	characteristic
608	#554	C₂²×C₂₉	1	1	yes	characteristic
609	#553	—	2	1	no	—
610	#553	—	2	2	no	—
611	#553	—	2	1	no	—
612	#552	—	2	1	no	—
613	#552	C₂²×C₂₉	1	2	yes	—
614	#551	—	2	2	no	—
615	#550	—	2	1	no	—
616	#550	C₂²×C₂₉	1	2	yes	—
617	#550	C₂²×C₂₉	1	1	yes	characteristic, complemented
618	#550	C₂²×C₂₉	1	1	yes	characteristic, complemented
619	#547	C₂²×C₂₉	1	1	yes	characteristic
620	#547	C₂²×C₂₉	1	2	yes	—
621	#547	C₂²×C₂₉	1	1	yes	characteristic, complemented
622	#546	C₂²×C₂₉	1	2	yes	—
623	#540	—	2	1	no	—
624	#540	—	2	2	no	—
625	#533	C₂²×C₂₉	1	1	yes	characteristic
626	#532	C₂²×C₂₉	1	1	yes	characteristic
627	#532	C₂²×C₂₉	1	2	yes	complemented
628	#529	—	2	2	no	—
629	#529	C₂²×C₂₉	1	1	yes	characteristic
630	#529	C₂²×C₂₉	1	2	yes	—
631	#529	C₂²×C₂₉	1	2	yes	complemented
632	#525	—	2	1	no	—
633	#520	—	2	1	no	—
634	C₄×#41	C₂²×C₂₉	1	2	yes	—
635	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
636	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
637	C₂×#117	—	2	1	no	—
638	#497	C₂²×C₂₉	1	2	yes	—
639	#496	C₂²×C₂₉	1	2	yes	—
640	#494	C₂²×C₂₉	1	1	yes	characteristic, complemented
641	#492	C₂²×C₂₉	1	1	yes	characteristic, complemented
642	#491	C₂²×C₂₉	1	2	yes	complemented
643	#490	C₂²×C₂₉	1	2	yes	complemented
644	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
645	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
646	#485	C₂²×C₂₉	1	2	yes	complemented
647	#484	C₂²×C₂₉	1	1	yes	characteristic
648	#482	C₂²×C₂₉	1	2	yes	complemented
649	#481	C₂²×C₂₉	1	1	yes	characteristic
650	#479	C₂²×C₂₉	1	2	yes	complemented
651	#479	C₂²×C₂₉	1	2	yes	complemented
652	#478	C₂²×C₂₉	1	1	yes	characteristic
653	#478	C₂²×C₂₉	1	1	yes	characteristic
654	#478	C₂²×C₂₉	1	2	yes	complemented
655	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
656	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
657	#470	C₂²×C₂₉	1	2	yes	—
658	#468	C₂²×C₂₉	1	2	yes	—
659	#467	C₂²×C₂₉	1	2	yes	complemented
660	#466	C₂²×C₂₉	1	2	yes	—
661	#465	C₂²×C₂₉	1	2	yes	—
662	#465	C₂²×C₂₉	1	2	yes	complemented
663	#464	C₂²×C₂₉	1	2	yes	—
664	#464	C₂²×C₂₉	1	2	yes	complemented
665	#464	C₂²×C₂₉	1	2	yes	complemented
666	#464	C₂²×C₂₉	1	2	yes	complemented
667	#463	C₂²×C₂₉	1	1	yes	characteristic
668	#463	C₂²×C₂₉	1	1	yes	characteristic
669	#463	C₂²×C₂₉	1	2	yes	—
670	#463	C₂²×C₂₉	1	2	yes	—
671	#463	C₂²×C₂₉	1	2	yes	—
672	#462	C₂²×C₂₉	1	1	yes	characteristic, complemented
673	#462	C₂²×C₂₉	1	2	yes	complemented
674	#461	C₂²×C₂₉	1	2	yes	—
675	#461	C₂²×C₂₉	1	1	yes	characteristic
676	#461	C₂²×C₂₉	1	1	yes	characteristic
677	#461	C₂²×C₂₉	1	1	yes	characteristic, complemented
678	#460	C₂²×C₂₉	1	2	yes	complemented
679	#459	C₂²×C₂₉	1	2	yes	—
680	#459	C₂²×C₂₉	1	1	yes	characteristic
681	#459	C₂²×C₂₉	1	1	yes	characteristic
682	#452	C₂²×C₂₉	1	2	yes	—
683	#452	C₂²×C₂₉	1	2	yes	—
684	#452	C₂²×C₂₉	1	2	yes	—
685	#452	C₂²×C₂₉	1	2	yes	complemented
686	#452	C₂²×C₂₉	1	2	yes	complemented
687	#450	C₂²×C₂₉	1	1	yes	characteristic
688	#449	C₂²×C₂₉	1	2	yes	—
689	#449	C₂²×C₂₉	1	2	yes	—
690	#449	C₂²×C₂₉	1	2	yes	—
691	#447	C₂²×C₂₉	1	1	yes	characteristic
692	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
693	#446	C₂²×C₂₉	1	1	yes	characteristic, complemented
694	#442	C₂²×C₂₉	1	2	yes	—
695	#441	C₂²×C₂₉	1	2	yes	complemented
696	#440	C₂²×C₂₉	1	2	yes	—
697	#440	C₂²×C₂₉	1	2	yes	complemented
698	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
700	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
701	C₄×D₈	C₂²×C₂₉	1	1	yes	characteristic
702	#435	C₂²×C₂₉	1	2	yes	—
703	#435	C₂²×C₂₉	1	2	yes	—
704	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
705	C₈×D₄	C₂²×C₂₉	1	1	yes	characteristic, complemented
706	#432	C₂²×C₂₉	1	2	yes	complemented
707	#431	C₂²×C₂₉	1	1	yes	characteristic
708	#423	C₂²×C₂₉	1	1	yes	characteristic
709	C₂×C₄⋊C₈	C₂²×C₂₉	1	2	yes	complemented
710	#417	C₂²×C₂₉	1	2	yes	—
711	#416	C₂²×C₂₉	1	2	yes	complemented
712	#416	C₂²×C₂₉	1	2	yes	complemented
713	C₂×C₂₉	—	4	2	no	—
714	C₂×C₂₉	—	4	1	no	—
715	C₂×C₂₉	—	4	2	no	—
716	C₂×C₂₉	—	8	2	no	—
717	C₂×C₂₉	—	8	1	no	—
718	C₂×C₂₉	—	8	1	no	—
719	C₂×C₂₉	#3488	1	1	yes	characteristic
720	C₂×C₂₉	C₂×#575	1	1	yes	characteristic
721	C₂×C₂₉	#3584	1	1	yes	characteristic
722	C₂×#41	—	2	1	no	—
723	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
724	C₂×#41	C₂³×C₂₉	1	2	yes	—
725	C₂×#41	C₂³×C₂₉	1	2	yes	—
726	C₂×#41	C₂³×C₂₉	1	2	yes	—
727	C₂×#41	C₂³×C₂₉	1	2	yes	—
728	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
729	C₂³×C₄	—	2	1	no	—
730	AGL(1,ℤ/8)	—	4	4	no	—
731	#135	—	4	4	no	—
732	#135	—	4	4	no	—
733	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
734	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
735	C₂×Q₁₆	C₂³×C₂₉	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
738	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
740	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
741	C₂×SD₁₆	C₂³×C₂₉	1	1	yes	characteristic
742	C₂×SD₁₆	C₂³×C₂₉	1	2	yes	—
743	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
744	C₂×D₈	C₂³×C₂₉	1	2	yes	—
745	C₂×D₈	C₂³×C₂₉	1	2	yes	—
746	C₂×D₈	C₂³×C₂₉	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
748	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
749	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₂₉	1	2	yes	—
752	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
753	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
754	#127	—	2	2	no	—
755	#127	—	2	1	no	—
756	#127	C₂³×C₂₉	1	1	yes	characteristic
757	#127	C₂³×C₂₉	1	2	yes	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	2	2	no	—
761	#126	—	2	1	no	—
762	#126	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	—	2	2	no	—
766	#125	—	2	1	no	—
767	#125	C₂³×C₂₉	1	1	yes	characteristic
768	#125	C₂³×C₂₉	1	2	yes	—
769	#124	—	2	2	no	—
770	#124	C₂³×C₂₉	1	1	yes	characteristic
771	#124	C₂³×C₂₉	1	2	yes	—
772	#124	C₂³×C₂₉	1	2	yes	—
773	#123	—	2	2	no	—
774	#123	—	2	1	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
787	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
788	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
789	C₂²⋊Q₈	C₂³×C₂₉	1	2	yes	—
790	#121	—	2	1	no	—
791	#121	—	2	1	no	—
792	#121	—	2	2	no	—
793	#121	—	2	1	no	—
794	#121	—	2	1	no	—
795	#121	—	2	1	no	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	C₂³×C₂₉	1	2	yes	—
805	#121	C₂³×C₂₉	1	1	yes	characteristic
806	#121	C₂³×C₂₉	1	2	yes	—
807	#120	—	2	2	no	—
808	C₄×Q₈	—	2	1	no	—
809	C₄×Q₈	—	2	1	no	—
810	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
811	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
812	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
813	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
814	C₄×Q₈	C₂³×C₂₉	1	2	yes	—
815	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	1	no	—
820	C₄×D₄	—	2	2	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	D₄×C₂₉	1	2	yes	—
830	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
831	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
835	C₄×D₄	C₂³×C₂₉	1	2	yes	—
836	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₂₉	1	2	yes	—
838	C₄×D₄	C₂³×C₂₉	1	2	yes	—
839	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	2	1	no	—
847	#117	—	2	2	no	—
848	#117	D₄×C₂₉	1	1	yes	characteristic
849	#117	D₄×C₂₉	1	2	yes	—
850	#117	C₂³×C₂₉	1	2	yes	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	2	no	—
854	C₂×C₄⋊C₄	—	2	1	no	—
855	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
856	C₂×C₂²⋊C₄	—	2	1	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₄²	—	2	2	no	—
859	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
860	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
861	#107	C₂³×C₂₉	1	1	yes	characteristic
862	#107	C₂³×C₂₉	1	1	yes	characteristic
863	#107	C₂³×C₂₉	1	2	yes	—
864	#106	C₂³×C₂₉	1	1	yes	characteristic
865	#106	C₂³×C₂₉	1	1	yes	characteristic
866	#106	C₂³×C₂₉	1	2	yes	—
867	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
868	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
869	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
870	C₄⋊C₈	C₂³×C₂₉	1	2	yes	—
871	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
872	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
873	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
874	#103	C₂³×C₂₉	1	1	yes	characteristic
875	#103	C₂³×C₂₉	1	2	yes	—
876	#103	C₂³×C₂₉	1	2	yes	—
877	#103	C₂³×C₂₉	1	2	yes	—
878	#103	C₂³×C₂₉	1	2	yes	—
879	#103	C₂³×C₂₉	1	1	yes	characteristic
880	#103	C₂³×C₂₉	1	2	yes	—
881	#103	C₂³×C₂₉	1	2	yes	—
882	#103	C₂³×C₂₉	1	2	yes	—
883	#102	C₂³×C₂₉	1	1	yes	characteristic
884	#102	C₂³×C₂₉	1	2	yes	—
885	#102	C₂³×C₂₉	1	2	yes	—
886	#102	C₂³×C₂₉	1	2	yes	—
887	#102	C₂³×C₂₉	1	2	yes	—
888	#102	C₂³×C₂₉	1	1	yes	characteristic
889	#102	C₂³×C₂₉	1	1	yes	characteristic
890	#102	C₂³×C₂₉	1	1	yes	characteristic
891	#102	C₂³×C₂₉	1	1	yes	characteristic
892	#102	C₂³×C₂₉	1	1	yes	characteristic
893	#102	C₂³×C₂₉	1	2	yes	—
894	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
895	C₂²⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
896	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
897	C₂²⋊C₈	C₂³×C₂₉	1	2	yes	—
898	#97	C₂³×C₂₉	1	2	yes	—
899	#97	C₂³×C₂₉	1	2	yes	—
900	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
902	C₂₉	#61993	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	—	2	1	no	—
904	#41	—	2	4	no	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	4	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	2	no	—
912	#41	—	4	2	no	—
913	#41	—	4	4	no	—
914	C₂×Q₈	—	2	1	no	—
915	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
917	C₂×Q₈	C₂⁴×C₂₉	1	1	yes	characteristic
918	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	2	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	—	2	2	no	—
926	C₂×D₄	—	2	2	no	—
927	C₂×D₄	—	2	1	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	4	1	no	—
933	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
934	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
935	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
936	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
937	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
938	C₂×D₄	C₂⁴×C₂₉	1	1	yes	characteristic
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	2	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	1	no	—
946	C₂²×C₄	—	2	1	no	—
947	C₂²×C₄	—	2	2	no	—
948	C₂²×C₄	—	2	2	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	4	4	no	—
952	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
953	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
954	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
955	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
956	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
957	C₂²×C₄	C₂⁴×C₂₉	1	2	yes	—
958	Q₁₆	—	4	2	no	—
959	Q₁₆	—	4	2	no	—
960	Q₁₆	—	4	2	no	—
961	SD₁₆	—	2	2	no	—
962	SD₁₆	—	2	4	no	—
963	SD₁₆	—	4	2	no	—
964	SD₁₆	—	4	2	no	—
965	SD₁₆	—	4	2	no	—
966	SD₁₆	—	4	2	no	—
967	SD₁₆	—	4	1	no	—
968	D₈	—	2	2	no	—
969	D₈	—	2	4	no	—
970	D₈	—	4	2	no	—
971	D₈	—	4	1	no	—
972	M₁₆	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	2	no	—
975	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₂₉	1	1	yes	characteristic
979	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
980	C₂×C₈	C₂⁴×C₂₉	1	2	yes	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	2	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
1003	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1004	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1005	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1006	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1007	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
1008	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1009	C₄⋊C₄	C₂⁴×C₂₉	1	1	yes	characteristic
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	1	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	1	no	—
1031	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1032	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1033	C₂²⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
1034	C₄²	—	2	2	no	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	C₂×D₄×C₂₉	1	2	yes	—
1040	C₄²	C₂×D₄×C₂₉	1	2	yes	—
1041	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1042	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1044	C₄²	C₂⁴×C₂₉	1	2	yes	—
1045	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
1046	C₂³	—	2	1	no	—
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	1	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	—	8	1	no	—
1053	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
1054	C₂³	C₂²×D₄×C₂₉	1	2	yes	—
1055	Q₈	—	2	2	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	2	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	8	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	1	no	—
1067	D₄	—	2	1	no	—
1068	D₄	—	2	1	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	4	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	4	2	no	—
1076	D₄	—	8	2	no	—
1077	D₄	—	8	1	no	—
1078	D₄	—	8	2	no	—
1079	D₄	—	8	2	no	—
1080	D₄	—	8	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	8	1	no	—
1084	D₄	C₂₉×H(5,𝔽₂)	1	2	yes	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	2	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	4	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	4	no	—
1105	C₂×C₄	—	4	2	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	8	2	no	—
1110	C₂×C₄	—	8	2	no	—
1111	C₂×C₄	—	8	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1114	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1115	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1116	C₂×C₄	C₂²×D₄×C₂₉	1	2	yes	—
1117	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1118	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1119	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1120	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
1121	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
1122	C₈	—	2	1	no	—
1123	C₈	—	2	1	no	—
1124	C₈	—	2	2	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	2	1	no	—
1127	C₈	—	2	1	no	—
1128	C₂²	—	2	2	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	4	1	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	2	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	2	no	—
1142	C₂²	—	4	1	no	—
1143	C₂²	—	4	1	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	8	4	no	—
1147	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	4	2	no	—
1156	C₄	—	4	2	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	1	no	—
1160	C₄	—	4	1	no	—
1161	C₄	—	4	2	no	—
1162	C₄	—	4	1	no	—
1163	C₄	C₂₉×#575	1	2	yes	—
1164	C₄	C₂×C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₂₉×#585	1	1	yes	characteristic
1166	C₂	—	4	1	no	—
1167	C₂	—	4	2	no	—
1168	C₂	—	4	2	no	—
1169	C₂	—	8	1	no	—
1170	C₂	—	8	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	C₂₉×#3488	1	1	yes	characteristic
1173	C₂	C₂×C₂₉×#575	1	1	yes	characteristic
1174	C₂	C₂₉×#3584	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 ◁ C₄×#41×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#3517	C₂	semidirect
2. C₂₉×#3475	C₂	semidirect
3. C₂₉×#3398	C₂	semidirect
4. C₂₉×#3397	C₂	semidirect
5. C₂₉×#3372	C₂	semidirect
6. C₂₉×#3366	C₂	semidirect
7. C₂₉×#3317	C₂	semidirect
8. C₂₉×#3315	C₂	semidirect
9. C₂₉×#3305	C₂	semidirect
10. C₂₉×#3303	C₂	semidirect
11. C₂₉×#3284	C₂	semidirect
12. C₂₉×#3283	C₂	semidirect
13. C₂₉×#3268	C₂	semidirect
14. C₂₉×#3267	C₂	semidirect
15. C₂₉×#3252	C₂	semidirect
16. C₂₉×#3250	C₂	semidirect
17. C₂₉×#3219	C₂	semidirect
18. C₂₉×#3210	C₂	semidirect
19. C₂₉×#3111	C₂	semidirect
20. C₂₉×#3105	C₂	semidirect
21. C₂₉×#3036	C₂	semidirect
22. C₂₉×#3035	C₂	semidirect
23. C₂₉×#2990	C₂	semidirect
27. C₂₉×#557	C₂²	semidirect
39. C₂₉×#550	C₂²	semidirect
40. C₂₉×#550	C₂²	semidirect
43. C₂₉×#547	C₂²	semidirect
49. C₂₉×#532	C₂²	semidirect
53. C₂₉×#529	C₂²	semidirect
62. C₂₉×#494	C₂²	semidirect
63. C₂₉×#492	C₂²	semidirect
64. C₂₉×#491	C₂²	semidirect
65. C₂₉×#490	C₂²	semidirect
66. C₂₉×#487	C₂²	semidirect
67. C₂₉×#486	C₂²	semidirect
68. C₂₉×#485	C₂²	semidirect
70. C₂₉×#482	C₂²	semidirect
72. C₂₉×#479	C₂²	semidirect
73. C₂₉×#479	C₂²	semidirect
76. C₂₉×#478	C₂²	semidirect
77. C₂₉×#477	C₂²	semidirect
78. C₂₉×#476	C₂²	semidirect
81. C₂₉×#467	C₂²	semidirect
84. C₂₉×#465	C₂²	semidirect
86. C₂₉×#464	C₂²	semidirect
87. C₂₉×#464	C₂²	semidirect
88. C₂₉×#464	C₂²	semidirect
94. C₂₉×#462	C₂²	semidirect
95. C₂₉×#462	C₂²	semidirect
99. C₂₉×#461	C₂²	semidirect
100. C₂₉×#460	C₂²	semidirect
107. C₂₉×#452	C₂²	semidirect
108. C₂₉×#452	C₂²	semidirect
114. C₂₉×#446	C₂²	semidirect
115. C₂₉×#446	C₂²	semidirect
117. C₂₉×#441	C₂²	semidirect
119. C₂₉×#440	C₂²	semidirect
126. C₈×D₄×C₂₉	C₂²	semidirect
127. C₈×D₄×C₂₉	C₂²	semidirect
128. C₂₉×#432	C₂²	semidirect
131. C₂×C₂₉×C₄⋊C₈	C₂²	semidirect
133. C₂₉×#416	C₂²	semidirect
134. C₂₉×#416	C₂²	semidirect
458. #61993	C₂₉	direct (N × H)
541. #3517	C₂×C₂₉	semidirect
542. #3475	C₂×C₂₉	semidirect
543. #3398	C₂×C₂₉	semidirect
544. #3397	C₂×C₂₉	semidirect
545. #3372	C₂×C₂₉	semidirect
546. #3366	C₂×C₂₉	semidirect
547. #3317	C₂×C₂₉	semidirect
548. #3315	C₂×C₂₉	semidirect
549. #3305	C₂×C₂₉	semidirect
550. #3303	C₂×C₂₉	semidirect
551. #3284	C₂×C₂₉	semidirect
552. #3283	C₂×C₂₉	semidirect
553. #3268	C₂×C₂₉	semidirect
554. #3267	C₂×C₂₉	semidirect
555. #3252	C₂×C₂₉	semidirect
556. #3250	C₂×C₂₉	semidirect
557. #3219	C₂×C₂₉	semidirect
558. #3210	C₂×C₂₉	semidirect
559. #3111	C₂×C₂₉	semidirect
560. #3105	C₂×C₂₉	semidirect
561. #3036	C₂×C₂₉	semidirect
562. #3035	C₂×C₂₉	semidirect
563. #2990	C₂×C₂₉	semidirect
605. #557	C₂²×C₂₉	semidirect
617. #550	C₂²×C₂₉	semidirect
618. #550	C₂²×C₂₉	semidirect
621. #547	C₂²×C₂₉	semidirect
627. #532	C₂²×C₂₉	semidirect
631. #529	C₂²×C₂₉	semidirect
640. #494	C₂²×C₂₉	semidirect
641. #492	C₂²×C₂₉	semidirect
642. #491	C₂²×C₂₉	semidirect
643. #490	C₂²×C₂₉	semidirect
644. #487	C₂²×C₂₉	semidirect
645. #486	C₂²×C₂₉	semidirect
646. #485	C₂²×C₂₉	semidirect
648. #482	C₂²×C₂₉	semidirect
650. #479	C₂²×C₂₉	semidirect
651. #479	C₂²×C₂₉	semidirect
654. #478	C₂²×C₂₉	semidirect
655. #477	C₂²×C₂₉	semidirect
656. #476	C₂²×C₂₉	semidirect
659. #467	C₂²×C₂₉	semidirect
662. #465	C₂²×C₂₉	semidirect
664. #464	C₂²×C₂₉	semidirect
665. #464	C₂²×C₂₉	semidirect
666. #464	C₂²×C₂₉	semidirect
672. #462	C₂²×C₂₉	semidirect
673. #462	C₂²×C₂₉	semidirect
677. #461	C₂²×C₂₉	semidirect
678. #460	C₂²×C₂₉	semidirect
685. #452	C₂²×C₂₉	semidirect
686. #452	C₂²×C₂₉	semidirect
692. #446	C₂²×C₂₉	semidirect
693. #446	C₂²×C₂₉	semidirect
695. #441	C₂²×C₂₉	semidirect
697. #440	C₂²×C₂₉	semidirect
704. C₈×D₄	C₂²×C₂₉	semidirect
705. C₈×D₄	C₂²×C₂₉	semidirect
706. #432	C₂²×C₂₉	semidirect
709. C₂×C₄⋊C₈	C₂²×C₂₉	semidirect
711. #416	C₂²×C₂₉	semidirect
712. #416	C₂²×C₂₉	semidirect
902. C₂₉	#61993	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×#3517	2
C₂₉×#3475	2
C₂₉×#3398	2
C₂₉×#3397	2
C₂₉×#3372	2
C₂₉×#3366	2
C₂₉×#3317	2
C₂₉×#3315	2
C₂₉×#3305	2
C₂₉×#3303	2
C₂₉×#3284	2
C₂₉×#3283	2
C₂₉×#3268	2
C₂₉×#3267	2
C₂₉×#3252	2
C₂₉×#3250	2
C₂₉×#3219	2
C₂₉×#3210	2
C₂₉×#3111	2
C₂₉×#3105	2
C₂₉×#3036	2
C₂₉×#3035	2
C₂₉×#2990	2
#61993	29

Subgroups — C29×#61993 #20356893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#61993 #20356893