Subgroups — C₂₉×#18794 #20313694

Order 7424.

1214 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#3207	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3109	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#1637	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#1635	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#1631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#1629	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#1627	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#1625	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1619	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1553	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1488	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1478	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₉	—	2	1	no	—
17	C₂₉×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₂₉	C₂²	1	1	yes	characteristic
19	C₂₉×#548	—	2	1	no	—
20	C₂₉×#547	—	2	1	no	—
21	C₂₉×#547	C₂²	1	1	yes	characteristic
22	C₂₉×#546	—	2	2	no	—
23	C₂₉×#546	—	2	1	no	—
24	D₄²×C₂₉	—	2	1	no	—
25	D₄²×C₂₉	C₂²	1	1	yes	characteristic
26	C₂₉×#532	—	2	1	no	—
27	C₂₉×#532	C₂²	1	1	yes	characteristic
28	C₂₉×#532	C₂²	1	1	yes	characteristic, complemented
29	C₂₉×#525	—	2	2	no	—
30	C₂₉×#525	—	2	1	no	—
31	C₄×#41×C₂₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₂₉	—	2	1	no	—
33	C₂×C₄×D₄×C₂₉	C₂²	1	1	yes	characteristic
34	C₂₉×#493	C₂²	1	1	yes	characteristic, complemented
35	C₂₉×#492	C₂²	1	1	yes	characteristic, complemented
36	C₂₉×#487	C₂²	1	1	yes	characteristic, complemented
37	C₂₉×#486	C₂²	1	1	yes	characteristic, complemented
38	C₂₉×#482	—	2	1	no	—
39	C₂₉×#481	—	2	1	no	—
40	C₂₉×#477	C₂²	1	1	yes	characteristic, complemented
41	C₂₉×#476	C₂²	1	1	yes	characteristic
42	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
43	C₂₉×#476	C₂²	1	1	yes	characteristic, complemented
44	C₂₉×#463	—	2	2	no	—
45	C₂₉×#460	C₂²	1	1	yes	characteristic, complemented
46	C₂₉×#459	C₂²	1	1	yes	characteristic
47	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
48	C₂₉×#459	C₂²	1	1	yes	characteristic, complemented
49	C₂₉×#449	—	2	1	no	—
50	C₂₉×#449	—	2	2	no	—
51	C₂₉×#447	—	2	1	no	—
52	C₂₉×#442	—	2	1	no	—
53	C₂₉×#442	—	2	1	no	—
54	C₄×SD₁₆×C₂₉	—	2	1	no	—
55	C₄×D₈×C₂₉	—	2	1	no	—
56	C₂₉×#432	C₂²	1	1	yes	characteristic, complemented
57	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
58	C₂₉×#431	C₂²	1	1	yes	characteristic, complemented
59	C₂₉×#332	C₂²	1	1	yes	characteristic, complemented
60	C₂₉×#332	C₂²	1	1	yes	characteristic, complemented
61	C₂₉×#331	C₂²	1	1	yes	characteristic, complemented
62	C₂₉×#331	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
69	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
71	C₂×#41×C₂₉	—	2	2	no	—
72	C₂×#41×C₂₉	—	2	2	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂×#41×C₂₉	—	2	1	no	—
75	C₂×#41×C₂₉	—	2	1	no	—
76	C₂×#41×C₂₉	—	2	1	no	—
77	C₂×#41×C₂₉	—	4	4	no	—
78	C₂×#41×C₂₉	—	4	4	no	—
79	C₂×#41×C₂₉	D₄	1	1	yes	characteristic
80	C₂²×Q₈×C₂₉	—	2	1	no	—
81	C₂²×D₄×C₂₉	—	2	2	no	—
82	C₂²×D₄×C₂₉	—	2	1	no	—
83	C₂²×D₄×C₂₉	—	2	1	no	—
84	C₂²×D₄×C₂₉	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₂₉	—	2	2	no	—
86	C₂³×C₄×C₂₉	—	2	1	no	—
87	C₂×SD₁₆×C₂₉	—	2	1	no	—
88	C₂×SD₁₆×C₂₉	—	2	2	no	—
89	C₂×D₈×C₂₉	—	2	1	no	—
90	C₂×D₈×C₂₉	—	2	1	no	—
91	C₂×D₈×C₂₉	—	2	1	no	—
92	C₂×D₈×C₂₉	—	2	2	no	—
93	C₂₉×C₄⋊Q₈	—	2	1	no	—
94	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
95	C₂₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
96	C₂₉×#127	—	2	1	no	—
97	C₂₉×#127	C₂³	1	1	yes	characteristic
98	C₂₉×#127	C₂³	1	1	yes	characteristic
99	C₂₉×#124	—	2	2	no	—
100	C₂₉×#124	—	2	1	no	—
101	C₂₉×#124	—	2	1	no	—
102	C₂₉×#123	—	2	2	no	—
103	C₂₉×#123	—	2	2	no	—
104	C₂₉×#123	—	2	2	no	—
105	C₂₉×C₂²⋊Q₈	—	2	2	no	—
106	C₂₉×C₂²⋊Q₈	—	2	1	no	—
107	C₂₉×C₂²⋊Q₈	—	2	2	no	—
108	C₂₉×C₂²⋊Q₈	—	2	1	no	—
109	C₂₉×#121	—	2	2	no	—
110	C₂₉×#121	—	2	2	no	—
111	C₂₉×#121	—	2	2	no	—
112	C₂₉×#121	—	2	1	no	—
113	C₂₉×#121	—	2	1	no	—
114	C₂₉×#121	—	2	1	no	—
115	C₂₉×#121	—	2	1	no	—
116	C₂₉×#121	—	2	1	no	—
117	C₂₉×#121	—	2	1	no	—
118	C₂₉×#121	—	2	1	no	—
119	C₂₉×#121	D₄	1	2	yes	—
120	C₂₉×#120	—	2	2	no	—
121	C₂₉×#120	—	2	2	no	—
122	C₂₉×#120	—	2	2	no	—
123	C₄×Q₈×C₂₉	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₂₉	C₂³	1	1	yes	characteristic
125	C₄×D₄×C₂₉	—	2	2	no	—
126	C₄×D₄×C₂₉	—	2	2	no	—
127	C₄×D₄×C₂₉	—	2	2	no	—
128	C₄×D₄×C₂₉	—	2	1	no	—
129	C₄×D₄×C₂₉	—	2	1	no	—
130	C₄×D₄×C₂₉	—	2	1	no	—
131	C₄×D₄×C₂₉	—	2	1	no	—
132	C₄×D₄×C₂₉	—	2	1	no	—
133	C₄×D₄×C₂₉	—	2	1	no	—
134	C₄×D₄×C₂₉	—	2	1	no	—
135	C₄×D₄×C₂₉	—	2	1	no	—
136	C₄×D₄×C₂₉	—	2	1	no	—
137	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
138	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
139	C₄×D₄×C₂₉	D₄	1	1	yes	characteristic
140	C₄×D₄×C₂₉	D₄	1	2	yes	—
141	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
143	C₄×D₄×C₂₉	C₂³	1	1	yes	characteristic
144	C₂₉×#117	—	2	1	no	—
145	C₂₉×#117	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
149	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
150	C₂×C₄²×C₂₉	—	2	1	no	—
151	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
152	C₂₉×#107	—	2	1	no	—
153	C₂₉×#106	—	2	1	no	—
154	C₂₉×#106	—	2	1	no	—
155	C₂₉×#106	—	2	1	no	—
156	C₂₉×C₄⋊C₈	—	2	1	no	—
157	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₂₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₉×#103	—	2	1	no	—
162	C₂₉×#103	—	2	2	no	—
163	C₂₉×#102	—	2	1	no	—
164	C₂₉×#102	—	2	1	no	—
165	C₂₉×#102	—	2	1	no	—
166	C₂₉×#102	—	2	1	no	—
167	C₂₉×#102	—	2	1	no	—
168	C₂₉×#102	—	2	1	no	—
169	C₂₉×#102	—	2	1	no	—
170	C₂₉×#102	—	2	2	no	—
171	C₂₉×C₂²⋊C₈	—	2	1	no	—
172	C₂₉×C₂²⋊C₈	—	2	1	no	—
173	C₂₉×C₂²⋊C₈	—	2	1	no	—
174	C₂₉×#97	—	2	1	no	—
175	C₄×C₈×C₂₉	—	2	1	no	—
176	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
177	C₄×C₈×C₂₉	C₂³	1	1	yes	characteristic
178	C₂⁴×C₂₉	—	2	2	no	—
179	C₂⁴×C₂₉	—	2	1	no	—
180	#41×C₂₉	—	2	2	no	—
181	#41×C₂₉	—	2	2	no	—
182	#41×C₂₉	—	4	8	no	—
183	#41×C₂₉	—	4	2	no	—
184	#41×C₂₉	—	4	2	no	—
185	#41×C₂₉	—	4	8	no	—
186	#41×C₂₉	—	4	2	no	—
187	#41×C₂₉	—	4	2	no	—
188	#41×C₂₉	—	4	2	no	—
189	#41×C₂₉	—	4	2	no	—
190	#41×C₂₉	—	8	2	no	—
191	C₂×Q₈×C₂₉	—	2	2	no	—
192	C₂×Q₈×C₂₉	—	2	1	no	—
193	C₂×Q₈×C₂₉	—	2	1	no	—
194	C₂×Q₈×C₂₉	—	4	2	no	—
195	C₂×Q₈×C₂₉	—	4	2	no	—
196	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
197	C₂×D₄×C₂₉	—	2	1	no	—
198	C₂×D₄×C₂₉	—	2	2	no	—
199	C₂×D₄×C₂₉	—	2	2	no	—
200	C₂×D₄×C₂₉	—	2	2	no	—
201	C₂×D₄×C₂₉	—	2	2	no	—
202	C₂×D₄×C₂₉	—	2	2	no	—
203	C₂×D₄×C₂₉	—	2	2	no	—
204	C₂×D₄×C₂₉	—	2	2	no	—
205	C₂×D₄×C₂₉	—	2	1	no	—
206	C₂×D₄×C₂₉	—	2	1	no	—
207	C₂×D₄×C₂₉	—	2	1	no	—
208	C₂×D₄×C₂₉	—	2	1	no	—
209	C₂×D₄×C₂₉	—	2	1	no	—
210	C₂×D₄×C₂₉	—	2	1	no	—
211	C₂×D₄×C₂₉	—	4	1	no	—
212	C₂×D₄×C₂₉	—	4	2	no	—
213	C₂×D₄×C₂₉	—	4	8	no	—
214	C₂×D₄×C₂₉	—	4	2	no	—
215	C₂×D₄×C₂₉	—	4	2	no	—
216	C₂×D₄×C₂₉	—	4	2	no	—
217	C₂×D₄×C₂₉	—	4	1	no	—
218	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
220	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₂₉	—	2	1	no	—
223	C₂²×C₄×C₂₉	—	2	2	no	—
224	C₂²×C₄×C₂₉	—	2	2	no	—
225	C₂²×C₄×C₂₉	—	2	2	no	—
226	C₂²×C₄×C₂₉	—	2	1	no	—
227	C₂²×C₄×C₂₉	—	2	1	no	—
228	C₂²×C₄×C₂₉	—	2	2	no	—
229	C₂²×C₄×C₂₉	—	2	1	no	—
230	C₂²×C₄×C₂₉	—	2	1	no	—
231	C₂²×C₄×C₂₉	—	2	1	no	—
232	C₂²×C₄×C₂₉	—	2	1	no	—
233	C₂²×C₄×C₂₉	—	2	1	no	—
234	C₂²×C₄×C₂₉	—	4	8	no	—
235	C₂²×C₄×C₂₉	—	4	2	no	—
236	C₂²×C₄×C₂₉	—	4	2	no	—
237	C₂²×C₄×C₂₉	—	4	1	no	—
238	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
241	SD₁₆×C₂₉	—	4	2	no	—
242	SD₁₆×C₂₉	—	8	2	no	—
243	D₈×C₂₉	—	4	2	no	—
244	D₈×C₂₉	—	4	2	no	—
245	D₈×C₂₉	—	4	2	no	—
246	D₈×C₂₉	—	8	2	no	—
247	C₂×C₈×C₂₉	—	2	1	no	—
248	C₂×C₈×C₂₉	—	2	1	no	—
249	C₂×C₈×C₂₉	—	2	1	no	—
250	C₂×C₈×C₂₉	—	2	1	no	—
251	C₂×C₈×C₂₉	—	2	1	no	—
252	C₂×C₈×C₂₉	—	2	1	no	—
253	C₄⋊C₄×C₂₉	—	2	2	no	—
254	C₄⋊C₄×C₂₉	—	2	2	no	—
255	C₄⋊C₄×C₂₉	—	2	1	no	—
256	C₄⋊C₄×C₂₉	—	2	1	no	—
257	C₄⋊C₄×C₂₉	—	2	1	no	—
258	C₄⋊C₄×C₂₉	—	2	1	no	—
259	C₄⋊C₄×C₂₉	—	2	1	no	—
260	C₄⋊C₄×C₂₉	—	2	1	no	—
261	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
262	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
263	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
264	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
265	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
266	C₂²⋊C₄×C₂₉	—	2	2	no	—
267	C₂²⋊C₄×C₂₉	—	2	2	no	—
268	C₂²⋊C₄×C₂₉	—	2	2	no	—
269	C₂²⋊C₄×C₂₉	—	2	2	no	—
270	C₂²⋊C₄×C₂₉	—	2	1	no	—
271	C₂²⋊C₄×C₂₉	—	2	1	no	—
272	C₂²⋊C₄×C₂₉	—	2	2	no	—
273	C₂²⋊C₄×C₂₉	—	2	1	no	—
274	C₂²⋊C₄×C₂₉	—	2	1	no	—
275	C₂²⋊C₄×C₂₉	—	2	2	no	—
276	C₂²⋊C₄×C₂₉	—	2	1	no	—
277	C₂²⋊C₄×C₂₉	—	2	1	no	—
278	C₂²⋊C₄×C₂₉	—	2	1	no	—
279	C₂²⋊C₄×C₂₉	—	4	1	no	—
280	C₂²⋊C₄×C₂₉	—	4	1	no	—
281	C₄²×C₂₉	—	2	1	no	—
282	C₄²×C₂₉	—	2	1	no	—
283	C₄²×C₂₉	—	2	1	no	—
284	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₂₉	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₂₉	C₂⁴	1	1	yes	characteristic
288	#18794	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂³×C₂₉	—	2	1	no	—
290	C₂³×C₂₉	—	2	1	no	—
291	C₂³×C₂₉	—	2	1	no	—
292	C₂³×C₂₉	—	2	2	no	—
293	C₂³×C₂₉	—	4	2	no	—
294	C₂³×C₂₉	—	4	2	no	—
295	C₂³×C₂₉	—	4	4	no	—
296	C₂³×C₂₉	—	4	4	no	—
297	C₂³×C₂₉	—	4	1	no	—
298	C₂³×C₂₉	—	8	1	no	—
299	C₂³×C₂₉	—	8	2	no	—
300	C₂³×C₂₉	#120	1	1	yes	characteristic
301	Q₈×C₂₉	—	2	1	no	—
302	Q₈×C₂₉	—	4	4	no	—
303	Q₈×C₂₉	—	4	2	no	—
304	Q₈×C₂₉	—	4	1	no	—
305	Q₈×C₂₉	—	4	1	no	—
306	Q₈×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
307	D₄×C₂₉	—	2	4	no	—
308	D₄×C₂₉	—	2	1	no	—
309	D₄×C₂₉	—	2	1	no	—
310	D₄×C₂₉	—	2	1	no	—
311	D₄×C₂₉	—	2	1	no	—
312	D₄×C₂₉	—	4	2	no	—
313	D₄×C₂₉	—	4	2	no	—
314	D₄×C₂₉	—	4	4	no	—
315	D₄×C₂₉	—	4	2	no	—
316	D₄×C₂₉	—	4	4	no	—
317	D₄×C₂₉	—	4	4	no	—
318	D₄×C₂₉	—	4	4	no	—
319	D₄×C₂₉	—	4	4	no	—
320	D₄×C₂₉	—	4	1	no	—
321	D₄×C₂₉	—	4	1	no	—
322	D₄×C₂₉	—	4	1	no	—
323	D₄×C₂₉	—	4	1	no	—
324	D₄×C₂₉	—	4	1	no	—
325	D₄×C₂₉	—	4	1	no	—
326	D₄×C₂₉	—	4	1	no	—
327	D₄×C₂₉	—	4	1	no	—
328	D₄×C₂₉	—	8	2	no	—
329	D₄×C₂₉	—	8	2	no	—
330	D₄×C₂₉	#135	1	2	yes	—
331	D₄×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
332	C₂×C₄×C₂₉	—	2	4	no	—
333	C₂×C₄×C₂₉	—	2	1	no	—
334	C₂×C₄×C₂₉	—	2	1	no	—
335	C₂×C₄×C₂₉	—	2	1	no	—
336	C₂×C₄×C₂₉	—	2	1	no	—
337	C₂×C₄×C₂₉	—	2	1	no	—
338	C₂×C₄×C₂₉	—	2	1	no	—
339	C₂×C₄×C₂₉	—	2	1	no	—
340	C₂×C₄×C₂₉	—	2	1	no	—
341	C₂×C₄×C₂₉	—	2	2	no	—
342	C₂×C₄×C₂₉	—	2	1	no	—
343	C₂×C₄×C₂₉	—	4	1	no	—
344	C₂×C₄×C₂₉	—	4	2	no	—
345	C₂×C₄×C₂₉	—	4	4	no	—
346	C₂×C₄×C₂₉	—	4	4	no	—
347	C₂×C₄×C₂₉	—	4	2	no	—
348	C₂×C₄×C₂₉	—	4	4	no	—
349	C₂×C₄×C₂₉	—	4	2	no	—
350	C₂×C₄×C₂₉	—	4	4	no	—
351	C₂×C₄×C₂₉	—	4	1	no	—
352	C₂×C₄×C₂₉	—	4	1	no	—
353	C₂×C₄×C₂₉	—	4	1	no	—
354	C₂×C₄×C₂₉	—	4	1	no	—
355	C₂×C₄×C₂₉	—	4	1	no	—
356	C₂×C₄×C₂₉	—	4	1	no	—
357	C₂×C₄×C₂₉	—	4	1	no	—
358	C₂×C₄×C₂₉	—	8	1	no	—
359	C₂×C₄×C₂₉	—	8	2	no	—
360	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
361	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
362	C₂×C₄×C₂₉	#120	1	1	yes	characteristic
363	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
366	C₈×C₂₉	—	4	1	no	—
367	C₈×C₂₉	—	4	1	no	—
368	C₈×C₂₉	—	4	1	no	—
369	C₈×C₂₉	—	4	1	no	—
370	C₈×C₂₉	—	4	1	no	—
371	C₈×C₂₉	—	4	1	no	—
372	D₄×#41	C₂×C₂₉	1	1	yes	characteristic, complemented
373	#3207	C₂×C₂₉	1	1	yes	characteristic, complemented
374	#3109	C₂×C₂₉	1	1	yes	characteristic, complemented
375	#3106	C₂×C₂₉	1	1	yes	characteristic, complemented
376	#1637	C₂×C₂₉	1	1	yes	characteristic, complemented
377	#1635	C₂×C₂₉	1	1	yes	characteristic, complemented
378	#1631	C₂×C₂₉	1	1	yes	characteristic, complemented
379	#1629	C₂×C₂₉	1	1	yes	characteristic, complemented
380	#1627	C₂×C₂₉	1	1	yes	characteristic, complemented
381	#1625	C₂×C₂₉	1	1	yes	characteristic, complemented
382	#1621	C₂×C₂₉	1	1	yes	characteristic, complemented
383	#1619	C₂×C₂₉	1	1	yes	characteristic, complemented
384	#1553	C₂×C₂₉	1	1	yes	characteristic, complemented
385	#1488	C₂×C₂₉	1	1	yes	characteristic, complemented
386	#1478	C₂×C₂₉	1	1	yes	characteristic, complemented
387	C₂²×C₂₉	—	2	1	no	—
388	C₂²×C₂₉	—	2	2	no	—
389	C₂²×C₂₉	—	2	1	no	—
390	C₂²×C₂₉	—	2	2	no	—
391	C₂²×C₂₉	—	2	1	no	—
392	C₂²×C₂₉	—	4	1	no	—
393	C₂²×C₂₉	—	4	1	no	—
394	C₂²×C₂₉	—	4	1	no	—
395	C₂²×C₂₉	—	4	1	no	—
396	C₂²×C₂₉	—	4	1	no	—
397	C₂²×C₂₉	—	4	2	no	—
398	C₂²×C₂₉	—	4	2	no	—
399	C₂²×C₂₉	—	4	1	no	—
400	C₂²×C₂₉	—	4	2	no	—
401	C₂²×C₂₉	—	4	1	no	—
402	C₂²×C₂₉	—	8	4	no	—
403	C₂²×C₂₉	—	8	8	no	—
404	C₂²×C₂₉	—	8	1	no	—
405	C₂²×C₂₉	—	8	1	no	—
406	C₂²×C₂₉	—	8	1	no	—
407	C₂²×C₂₉	C₂×#120	1	1	yes	characteristic
408	C₄×C₂₉	—	2	1	no	—
409	C₄×C₂₉	—	2	1	no	—
410	C₄×C₂₉	—	2	2	no	—
411	C₄×C₂₉	—	2	1	no	—
412	C₄×C₂₉	—	2	1	no	—
413	C₄×C₂₉	—	4	1	no	—
414	C₄×C₂₉	—	4	1	no	—
415	C₄×C₂₉	—	4	2	no	—
416	C₄×C₂₉	—	4	1	no	—
417	C₄×C₂₉	—	4	1	no	—
418	C₄×C₂₉	—	8	1	no	—
419	C₄×C₂₉	C₂×#135	1	1	yes	characteristic
420	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₄×C₂₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
422	C₄×C₂₉	#575	1	1	yes	characteristic
423	C₂²×#41	—	2	1	no	—
424	#550	C₂²×C₂₉	1	1	yes	characteristic
425	D₄×Q₈	C₂²×C₂₉	1	1	yes	characteristic
426	#548	—	2	1	no	—
427	#547	—	2	1	no	—
428	#547	C₂²×C₂₉	1	1	yes	characteristic
429	#546	—	2	2	no	—
430	#546	—	2	1	no	—
431	D₄²	—	2	1	no	—
432	D₄²	C₂²×C₂₉	1	1	yes	characteristic
433	#532	—	2	1	no	—
434	#532	C₂²×C₂₉	1	1	yes	characteristic
435	#532	C₂²×C₂₉	1	1	yes	characteristic, complemented
436	#525	—	2	2	no	—
437	#525	—	2	1	no	—
438	C₄×#41	C₂²×C₂₉	1	1	yes	characteristic
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	C₂²×C₂₉	1	1	yes	characteristic
441	#493	C₂²×C₂₉	1	1	yes	characteristic, complemented
442	#492	C₂²×C₂₉	1	1	yes	characteristic, complemented
443	#487	C₂²×C₂₉	1	1	yes	characteristic, complemented
444	#486	C₂²×C₂₉	1	1	yes	characteristic, complemented
445	#482	—	2	1	no	—
446	#481	—	2	1	no	—
447	#477	C₂²×C₂₉	1	1	yes	characteristic, complemented
448	#476	C₂²×C₂₉	1	1	yes	characteristic
449	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
450	#476	C₂²×C₂₉	1	1	yes	characteristic, complemented
451	#463	—	2	2	no	—
452	#460	C₂²×C₂₉	1	1	yes	characteristic, complemented
453	#459	C₂²×C₂₉	1	1	yes	characteristic
454	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
455	#459	C₂²×C₂₉	1	1	yes	characteristic, complemented
456	#449	—	2	1	no	—
457	#449	—	2	2	no	—
458	#447	—	2	1	no	—
459	#442	—	2	1	no	—
460	#442	—	2	1	no	—
461	C₄×SD₁₆	—	2	1	no	—
462	C₄×D₈	—	2	1	no	—
463	#432	C₂²×C₂₉	1	1	yes	characteristic, complemented
464	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
465	#431	C₂²×C₂₉	1	1	yes	characteristic, complemented
466	#332	C₂²×C₂₉	1	1	yes	characteristic, complemented
467	#332	C₂²×C₂₉	1	1	yes	characteristic, complemented
468	#331	C₂²×C₂₉	1	1	yes	characteristic, complemented
469	#331	C₂²×C₂₉	1	1	yes	characteristic, complemented
470	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
471	Q₈⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
472	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
473	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic
474	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
475	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
476	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
477	D₄⋊C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
478	C₂×C₂₉	—	4	1	no	—
479	C₂×C₂₉	—	4	2	no	—
480	C₂×C₂₉	—	4	2	no	—
481	C₂×C₂₉	—	8	1	no	—
482	C₂×C₂₉	—	8	2	no	—
483	C₂×C₂₉	—	16	1	no	—
484	C₂×C₂₉	#3002	1	1	yes	characteristic
485	C₂×C₂₉	#3003	1	1	yes	characteristic
486	C₂×C₂₉	#3021	1	1	yes	characteristic
487	C₂×#41	—	2	2	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	1	no	—
490	C₂×#41	—	2	1	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	4	4	no	—
494	C₂×#41	—	4	4	no	—
495	C₂×#41	D₄×C₂₉	1	1	yes	characteristic
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	D₄×C₂₉	1	1	yes	characteristic
501	C₂³×C₄	—	2	2	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂×SD₁₆	—	2	1	no	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×D₈	—	2	1	no	—
506	C₂×D₈	—	2	1	no	—
507	C₂×D₈	—	2	1	no	—
508	C₂×D₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	1	no	—
510	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₂₉	1	1	yes	characteristic
512	#127	—	2	1	no	—
513	#127	C₂³×C₂₉	1	1	yes	characteristic
514	#127	C₂³×C₂₉	1	1	yes	characteristic
515	#124	—	2	2	no	—
516	#124	—	2	1	no	—
517	#124	—	2	1	no	—
518	#123	—	2	2	no	—
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	C₂²⋊Q₈	—	2	2	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	#121	—	2	2	no	—
526	#121	—	2	2	no	—
527	#121	—	2	2	no	—
528	#121	—	2	1	no	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	D₄×C₂₉	1	2	yes	—
536	#120	—	2	2	no	—
537	#120	—	2	2	no	—
538	#120	—	2	2	no	—
539	C₄×Q₈	D₄×C₂₉	1	1	yes	characteristic
540	C₄×Q₈	C₂³×C₂₉	1	1	yes	characteristic
541	C₄×D₄	—	2	2	no	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	2	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	1	no	—
552	C₄×D₄	—	2	1	no	—
553	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
554	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
555	C₄×D₄	D₄×C₂₉	1	1	yes	characteristic
556	C₄×D₄	D₄×C₂₉	1	2	yes	—
557	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
558	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
559	C₄×D₄	C₂³×C₂₉	1	1	yes	characteristic
560	#117	—	2	1	no	—
561	#117	D₄×C₂₉	1	1	yes	characteristic
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
564	C₂×C₂²⋊C₄	—	2	2	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
568	#107	—	2	1	no	—
569	#106	—	2	1	no	—
570	#106	—	2	1	no	—
571	#106	—	2	1	no	—
572	C₄⋊C₈	—	2	1	no	—
573	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
574	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
575	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
576	C₄⋊C₈	C₂³×C₂₉	1	1	yes	characteristic
577	#103	—	2	1	no	—
578	#103	—	2	2	no	—
579	#102	—	2	1	no	—
580	#102	—	2	1	no	—
581	#102	—	2	1	no	—
582	#102	—	2	1	no	—
583	#102	—	2	1	no	—
584	#102	—	2	1	no	—
585	#102	—	2	1	no	—
586	#102	—	2	2	no	—
587	C₂²⋊C₈	—	2	1	no	—
588	C₂²⋊C₈	—	2	1	no	—
589	C₂²⋊C₈	—	2	1	no	—
590	#97	—	2	1	no	—
591	C₄×C₈	—	2	1	no	—
592	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
593	C₄×C₈	C₂³×C₂₉	1	1	yes	characteristic
594	C₂₉	#18794	1	1	yes	characteristic, direct product factor, Sylow
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	1	no	—
597	#41	—	2	2	no	—
598	#41	—	2	2	no	—
599	#41	—	4	8	no	—
600	#41	—	4	2	no	—
601	#41	—	4	2	no	—
602	#41	—	4	8	no	—
603	#41	—	4	2	no	—
604	#41	—	4	2	no	—
605	#41	—	4	2	no	—
606	#41	—	4	2	no	—
607	#41	—	8	2	no	—
608	C₂×Q₈	—	2	2	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	2	2	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	4	1	no	—
629	C₂×D₄	—	4	8	no	—
630	C₂×D₄	—	4	2	no	—
631	C₂×D₄	—	4	2	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	—	4	1	no	—
635	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
636	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
637	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
638	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	4	8	no	—
652	C₂²×C₄	—	4	2	no	—
653	C₂²×C₄	—	4	2	no	—
654	C₂²×C₄	—	4	1	no	—
655	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
658	SD₁₆	—	4	2	no	—
659	SD₁₆	—	8	2	no	—
660	D₈	—	4	2	no	—
661	D₈	—	4	2	no	—
662	D₈	—	4	2	no	—
663	D₈	—	8	2	no	—
664	C₂×C₈	—	2	1	no	—
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
679	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
680	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
681	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
682	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
683	C₂²⋊C₄	—	2	2	no	—
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	1	no	—
688	C₂²⋊C₄	—	2	1	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	no	—
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	4	1	no	—
697	C₂²⋊C₄	—	4	1	no	—
698	C₄²	—	2	1	no	—
699	C₄²	—	2	1	no	—
700	C₄²	—	2	1	no	—
701	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
702	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₂₉	1	1	yes	characteristic
704	C₄²	C₂⁴×C₂₉	1	1	yes	characteristic
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	4	no	—
712	C₂³	—	4	4	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	8	1	no	—
715	C₂³	—	8	2	no	—
716	C₂³	C₂₉×#120	1	1	yes	characteristic
717	Q₈	—	2	1	no	—
718	Q₈	—	4	4	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	4	1	no	—
721	Q₈	—	4	1	no	—
722	Q₈	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
723	D₄	—	2	4	no	—
724	D₄	—	2	1	no	—
725	D₄	—	2	1	no	—
726	D₄	—	2	1	no	—
727	D₄	—	2	1	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	D₄	—	4	4	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	4	no	—
735	D₄	—	4	4	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	8	2	no	—
745	D₄	—	8	2	no	—
746	D₄	C₂₉×#135	1	2	yes	—
747	D₄	C₂₉×AGL(1,ℤ/8)	1	2	yes	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	2	no	—
766	C₂×C₄	—	4	4	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	2	no	—
776	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
777	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
778	C₂×C₄	C₂₉×#120	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
782	C₈	—	4	1	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₈	—	4	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	2	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	8	4	no	—
804	C₂²	—	8	8	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	C₂×C₂₉×#120	1	1	yes	characteristic
809	C₄	—	2	1	no	—
810	C₄	—	2	1	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	1	no	—
813	C₄	—	2	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	1	no	—
818	C₄	—	4	1	no	—
819	C₄	—	8	1	no	—
820	C₄	C₂×C₂₉×#135	1	1	yes	characteristic
821	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
822	C₄	C₂×C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
823	C₄	C₂₉×#575	1	1	yes	characteristic
824	C₂	—	4	1	no	—
825	C₂	—	4	2	no	—
826	C₂	—	4	2	no	—
827	C₂	—	8	1	no	—
828	C₂	—	8	2	no	—
829	C₂	—	16	1	no	—
830	C₂	C₂₉×#3002	1	1	yes	characteristic
831	C₂	C₂₉×#3003	1	1	yes	characteristic
832	C₂	C₂₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₂₉
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. D₄×#41×C₂₉	C₂	semidirect
2. C₂₉×#3207	C₂	semidirect
3. C₂₉×#3109	C₂	semidirect
4. C₂₉×#3106	C₂	semidirect
5. C₂₉×#1637	C₂	semidirect
6. C₂₉×#1635	C₂	semidirect
7. C₂₉×#1631	C₂	semidirect
8. C₂₉×#1629	C₂	semidirect
9. C₂₉×#1627	C₂	semidirect
10. C₂₉×#1625	C₂	semidirect
11. C₂₉×#1621	C₂	semidirect
12. C₂₉×#1619	C₂	semidirect
13. C₂₉×#1553	C₂	semidirect
14. C₂₉×#1488	C₂	semidirect
15. C₂₉×#1478	C₂	semidirect
28. C₂₉×#532	C₂²	semidirect
34. C₂₉×#493	C₂²	semidirect
35. C₂₉×#492	C₂²	semidirect
36. C₂₉×#487	C₂²	semidirect
37. C₂₉×#486	C₂²	semidirect
40. C₂₉×#477	C₂²	semidirect
42. C₂₉×#476	C₂²	semidirect
43. C₂₉×#476	C₂²	semidirect
45. C₂₉×#460	C₂²	semidirect
47. C₂₉×#459	C₂²	semidirect
48. C₂₉×#459	C₂²	semidirect
56. C₂₉×#432	C₂²	semidirect
57. C₂₉×#431	C₂²	semidirect
58. C₂₉×#431	C₂²	semidirect
59. C₂₉×#332	C₂²	semidirect
60. C₂₉×#332	C₂²	semidirect
61. C₂₉×#331	C₂²	semidirect
62. C₂₉×#331	C₂²	semidirect
63. C₂₉×Q₈⋊C₈	C₂²	semidirect
64. C₂₉×Q₈⋊C₈	C₂²	semidirect
67. C₂₉×D₄⋊C₈	C₂²	semidirect
68. C₂₉×D₄⋊C₈	C₂²	semidirect
69. C₂₉×D₄⋊C₈	C₂²	semidirect
70. C₂₉×D₄⋊C₈	C₂²	semidirect
288. #18794	C₂₉	direct (N × H)
372. D₄×#41	C₂×C₂₉	semidirect
373. #3207	C₂×C₂₉	semidirect
374. #3109	C₂×C₂₉	semidirect
375. #3106	C₂×C₂₉	semidirect
376. #1637	C₂×C₂₉	semidirect
377. #1635	C₂×C₂₉	semidirect
378. #1631	C₂×C₂₉	semidirect
379. #1629	C₂×C₂₉	semidirect
380. #1627	C₂×C₂₉	semidirect
381. #1625	C₂×C₂₉	semidirect
382. #1621	C₂×C₂₉	semidirect
383. #1619	C₂×C₂₉	semidirect
384. #1553	C₂×C₂₉	semidirect
385. #1488	C₂×C₂₉	semidirect
386. #1478	C₂×C₂₉	semidirect
435. #532	C₂²×C₂₉	semidirect
441. #493	C₂²×C₂₉	semidirect
442. #492	C₂²×C₂₉	semidirect
443. #487	C₂²×C₂₉	semidirect
444. #486	C₂²×C₂₉	semidirect
447. #477	C₂²×C₂₉	semidirect
449. #476	C₂²×C₂₉	semidirect
450. #476	C₂²×C₂₉	semidirect
452. #460	C₂²×C₂₉	semidirect
454. #459	C₂²×C₂₉	semidirect
455. #459	C₂²×C₂₉	semidirect
463. #432	C₂²×C₂₉	semidirect
464. #431	C₂²×C₂₉	semidirect
465. #431	C₂²×C₂₉	semidirect
466. #332	C₂²×C₂₉	semidirect
467. #332	C₂²×C₂₉	semidirect
468. #331	C₂²×C₂₉	semidirect
469. #331	C₂²×C₂₉	semidirect
470. Q₈⋊C₈	C₂²×C₂₉	semidirect
471. Q₈⋊C₈	C₂²×C₂₉	semidirect
474. D₄⋊C₈	C₂²×C₂₉	semidirect
475. D₄⋊C₈	C₂²×C₂₉	semidirect
476. D₄⋊C₈	C₂²×C₂₉	semidirect
477. D₄⋊C₈	C₂²×C₂₉	semidirect
594. C₂₉	#18794	direct (N × H)

Maximal subgroups

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

subgroup	index
D₄×#41×C₂₉	2
C₂₉×#3207	2
C₂₉×#3109	2
C₂₉×#3106	2
C₂₉×#1637	2
C₂₉×#1635	2
C₂₉×#1631	2
C₂₉×#1629	2
C₂₉×#1627	2
C₂₉×#1625	2
C₂₉×#1621	2
C₂₉×#1619	2
C₂₉×#1553	2
C₂₉×#1488	2
C₂₉×#1478	2
#18794	29

Subgroups — C29×#18794 #20313694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#18794 #20313694