Subgroups — C₂₉×#24462 #20319362

Order 7424.

1302 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#578	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#473	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3046	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3011	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2052	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2047	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2005	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1908	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1876	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1866	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1793	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₂₉×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
18	C₂₉×#578	—	2	4	no	—
19	C₂₉×#578	—	2	4	no	—
20	C₂×C₂₉×#137	—	2	1	no	—
21	C₂×C₂₉×#137	—	2	1	no	—
22	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#135	—	2	1	no	—
27	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₂₉	—	2	1	no	—
29	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
30	C₂²×Q₁₆×C₂₉	C₂²	1	1	yes	characteristic
31	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
33	C₂₉×#536	C₂²	1	1	yes	characteristic
34	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂₉×#520	C₂²	1	1	yes	characteristic
36	C₂₉×#473	—	2	4	no	—
37	C₂₉×#464	—	2	1	no	—
38	C₂₉×#463	—	2	1	no	—
39	C₂₉×#462	—	2	1	no	—
40	C₂₉×#461	—	2	1	no	—
41	C₂₉×#456	—	2	4	no	—
42	C₂₉×#452	—	2	1	no	—
43	C₂₉×#452	—	2	1	no	—
44	C₂₉×#451	—	2	1	no	—
45	C₂₉×#451	—	2	1	no	—
46	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic
47	C₂₉×#424	C₂²	1	1	yes	characteristic
48	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
49	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
50	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
51	C₂₉×#419	—	2	1	no	—
52	C₂₉×#419	C₂²	1	1	yes	characteristic
53	C₂₉×#419	C₂²	1	1	yes	characteristic
54	C₂₉×#417	—	2	1	no	—
55	C₂₉×#417	C₂²	1	1	yes	characteristic
56	C₂₉×#417	C₂²	1	1	yes	characteristic
57	C₂₉×#416	—	2	1	no	—
58	C₂₉×#416	C₂²	1	1	yes	characteristic
59	C₂×C₂₉×#103	—	2	1	no	—
60	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
61	C₂×C₂₉×#103	C₂²	1	1	yes	characteristic
62	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
63	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
64	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic
65	C₂₉×#408	C₂²	1	1	yes	characteristic
66	C₂₉×#391	C₂²	1	1	yes	characteristic
67	C₂₉×#343	C₂²	1	1	yes	characteristic
68	C₂₉×#341	C₂²	1	1	yes	characteristic
69	C₂₉×#339	C₂²	1	1	yes	characteristic
70	C₂₉×#336	C₂²	1	1	yes	characteristic
71	C₂₉×2₋¹⁺⁴	—	2	2	no	—
72	C₂₉×2₋¹⁺⁴	—	2	2	no	—
73	C₂₉×2₋¹⁺⁴	—	2	2	no	—
74	C₂₉×2₋¹⁺⁴	—	2	2	no	—
75	C₂₉×2₋¹⁺⁴	—	2	2	no	—
76	C₂₉×2₋¹⁺⁴	—	4	1	no	—
77	C₂₉×2₋¹⁺⁴	—	4	1	no	—
78	C₂₉×2₋¹⁺⁴	D₄	1	4	yes	—
79	C₂×#41×C₂₉	—	2	1	no	—
80	C₂×#41×C₂₉	—	2	1	no	—
81	C₂×#41×C₂₉	—	2	1	no	—
82	C₂×#41×C₂₉	—	2	1	no	—
83	C₂×#41×C₂₉	—	4	1	no	—
84	C₂×#41×C₂₉	—	4	1	no	—
85	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₂₉	—	2	1	no	—
89	C₂²×Q₈×C₂₉	—	2	1	no	—
90	C₂²×Q₈×C₂₉	—	2	1	no	—
91	C₂²×Q₈×C₂₉	—	2	1	no	—
92	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
95	C₂₉×#137	—	2	8	no	—
96	C₂₉×#137	—	2	8	no	—
97	C₂₉×#137	—	2	2	no	—
98	C₂₉×#137	—	2	2	no	—
99	C₂₉×#137	—	2	2	no	—
100	C₂₉×#137	—	2	2	no	—
101	C₂₉×#137	—	2	2	no	—
102	C₂₉×#137	—	2	2	no	—
103	C₂₉×#137	—	2	2	no	—
104	C₂₉×#137	D₄	1	4	yes	—
105	C₂₉×#135	—	2	8	no	—
106	C₂₉×#135	—	2	2	no	—
107	C₂₉×#135	—	2	2	no	—
108	C₂×Q₁₆×C₂₉	—	2	8	no	—
109	C₂×Q₁₆×C₂₉	—	2	1	no	—
110	C₂×Q₁₆×C₂₉	—	2	1	no	—
111	C₂×Q₁₆×C₂₉	—	2	2	no	—
112	C₂×Q₁₆×C₂₉	—	2	2	no	—
113	C₂×Q₁₆×C₂₉	—	2	1	no	—
114	C₂×Q₁₆×C₂₉	—	2	1	no	—
115	C₂×Q₁₆×C₂₉	—	2	2	no	—
116	C₂×Q₁₆×C₂₉	—	2	1	no	—
117	C₂×Q₁₆×C₂₉	—	2	1	no	—
118	C₂×Q₁₆×C₂₉	—	2	1	no	—
119	C₂×Q₁₆×C₂₉	—	2	1	no	—
120	C₂×Q₁₆×C₂₉	—	4	1	no	—
121	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic
122	C₂×SD₁₆×C₂₉	—	2	1	no	—
123	C₂×SD₁₆×C₂₉	—	2	1	no	—
124	C₂×SD₁₆×C₂₉	—	2	1	no	—
125	C₂×SD₁₆×C₂₉	—	2	1	no	—
126	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
127	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic
128	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic
129	C₂₉×#131	—	2	2	no	—
130	C₂₉×#131	—	2	2	no	—
131	C₂₉×#131	—	2	2	no	—
132	C₂₉×#131	—	4	1	no	—
133	C₂×M₁₆×C₂₉	—	2	1	no	—
134	C₂×M₁₆×C₂₉	—	2	1	no	—
135	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₂₉	—	2	1	no	—
140	C₂²×C₈×C₂₉	—	2	1	no	—
141	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₂₉×C₄⋊Q₈	—	2	2	no	—
144	C₂₉×C₄⋊Q₈	—	2	1	no	—
145	C₂₉×C₄⋊Q₈	—	4	1	no	—
146	C₂₉×#124	—	2	1	no	—
147	C₂₉×#123	—	4	1	no	—
148	C₂₉×C₂²⋊Q₈	—	2	1	no	—
149	C₂₉×C₂²⋊Q₈	—	2	1	no	—
150	C₄×Q₈×C₂₉	—	2	1	no	—
151	C₄×D₄×C₂₉	—	2	1	no	—
152	C₄×D₄×C₂₉	—	4	1	no	—
153	C₂₉×#117	—	2	1	no	—
154	C₂₉×#117	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
156	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
157	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
159	C₂₉×#108	—	2	2	no	—
160	C₂₉×C₄⋊C₈	—	2	1	no	—
161	C₂₉×C₄⋊C₈	—	2	1	no	—
162	C₂₉×#104	—	2	2	no	—
163	C₂₉×#104	—	2	2	no	—
164	C₂₉×#104	—	4	1	no	—
165	C₂₉×#103	—	2	1	no	—
166	C₂₉×#103	—	2	1	no	—
167	C₂₉×#103	—	2	1	no	—
168	C₂₉×#103	—	2	1	no	—
169	C₂₉×#103	—	2	1	no	—
170	C₂₉×#103	—	2	1	no	—
171	C₂₉×#103	—	2	1	no	—
172	C₂₉×#103	—	2	1	no	—
173	C₂₉×#103	—	2	1	no	—
174	C₂₉×#103	—	2	1	no	—
175	C₂₉×#103	D₄	1	1	yes	characteristic
176	C₂₉×#103	D₄	1	1	yes	characteristic
177	C₂₉×#102	—	2	1	no	—
178	C₂₉×#102	—	2	1	no	—
179	C₂₉×#102	D₄	1	1	yes	characteristic
180	C₂₉×#102	D₄	1	1	yes	characteristic
181	C₂₉×#101	—	2	2	no	—
182	C₂₉×#101	—	2	2	no	—
183	C₂₉×#101	—	2	2	no	—
184	C₂₉×C₂²⋊C₈	—	2	1	no	—
185	C₂₉×C₂²⋊C₈	—	2	1	no	—
186	C₂₉×#95	—	4	1	no	—
187	#41×C₂₉	—	2	1	no	—
188	#41×C₂₉	—	2	1	no	—
189	#41×C₂₉	—	2	1	no	—
190	#41×C₂₉	—	2	1	no	—
191	#41×C₂₉	—	2	4	no	—
192	#41×C₂₉	—	2	4	no	—
193	#41×C₂₉	—	2	4	no	—
194	#41×C₂₉	—	2	1	no	—
195	#41×C₂₉	—	2	1	no	—
196	#41×C₂₉	—	2	1	no	—
197	#41×C₂₉	—	2	1	no	—
198	#41×C₂₉	—	4	4	no	—
199	#41×C₂₉	—	4	2	no	—
200	#41×C₂₉	—	4	2	no	—
201	#41×C₂₉	—	4	2	no	—
202	#41×C₂₉	—	4	4	no	—
203	#41×C₂₉	—	4	4	no	—
204	#41×C₂₉	—	4	2	no	—
205	#41×C₂₉	—	4	4	no	—
206	#41×C₂₉	—	4	2	no	—
207	#41×C₂₉	C₂×D₄	1	2	yes	—
208	#41×C₂₉	C₂×D₄	1	2	yes	—
209	#41×C₂₉	C₂×D₄	1	2	yes	—
210	#41×C₂₉	#41	1	2	yes	—
211	C₂×Q₈×C₂₉	—	2	1	no	—
212	C₂×Q₈×C₂₉	—	2	1	no	—
213	C₂×Q₈×C₂₉	—	2	4	no	—
214	C₂×Q₈×C₂₉	—	2	4	no	—
215	C₂×Q₈×C₂₉	—	2	4	no	—
216	C₂×Q₈×C₂₉	—	2	1	no	—
217	C₂×Q₈×C₂₉	—	2	1	no	—
218	C₂×Q₈×C₂₉	—	2	1	no	—
219	C₂×Q₈×C₂₉	—	2	1	no	—
220	C₂×Q₈×C₂₉	—	2	1	no	—
221	C₂×Q₈×C₂₉	—	2	1	no	—
222	C₂×Q₈×C₂₉	—	2	1	no	—
223	C₂×Q₈×C₂₉	—	2	1	no	—
224	C₂×Q₈×C₂₉	—	2	1	no	—
225	C₂×Q₈×C₂₉	—	2	1	no	—
226	C₂×Q₈×C₂₉	—	2	1	no	—
227	C₂×Q₈×C₂₉	—	2	1	no	—
228	C₂×Q₈×C₂₉	—	2	1	no	—
229	C₂×Q₈×C₂₉	—	2	1	no	—
230	C₂×Q₈×C₂₉	—	4	1	no	—
231	C₂×Q₈×C₂₉	—	4	1	no	—
232	C₂×Q₈×C₂₉	—	4	2	no	—
233	C₂×Q₈×C₂₉	—	4	2	no	—
234	C₂×Q₈×C₂₉	—	4	2	no	—
235	C₂×Q₈×C₂₉	—	4	2	no	—
236	C₂×Q₈×C₂₉	—	4	2	no	—
237	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
239	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
241	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
242	C₂×D₄×C₂₉	—	2	1	no	—
243	C₂×D₄×C₂₉	—	2	1	no	—
244	C₂×D₄×C₂₉	—	2	1	no	—
245	C₂×D₄×C₂₉	—	4	1	no	—
246	C₂×D₄×C₂₉	—	4	1	no	—
247	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₂₉	—	2	1	no	—
251	C₂²×C₄×C₂₉	—	2	1	no	—
252	C₂²×C₄×C₂₉	—	2	1	no	—
253	C₂²×C₄×C₂₉	—	2	1	no	—
254	C₂²×C₄×C₂₉	—	2	1	no	—
255	C₂²×C₄×C₂₉	—	2	1	no	—
256	C₂²×C₄×C₂₉	—	2	1	no	—
257	C₂²×C₄×C₂₉	—	2	1	no	—
258	C₂²×C₄×C₂₉	—	4	1	no	—
259	C₂²×C₄×C₂₉	—	4	1	no	—
260	C₂²×C₄×C₂₉	—	4	1	no	—
261	C₂²×C₄×C₂₉	—	4	1	no	—
262	C₂²×C₄×C₂₉	—	4	1	no	—
263	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₂₉	—	2	4	no	—
265	Q₁₆×C₂₉	—	2	4	no	—
266	Q₁₆×C₂₉	—	2	4	no	—
267	Q₁₆×C₂₉	—	2	2	no	—
268	Q₁₆×C₂₉	—	2	4	no	—
269	Q₁₆×C₂₉	—	4	2	no	—
270	Q₁₆×C₂₉	—	4	2	no	—
271	Q₁₆×C₂₉	—	4	2	no	—
272	Q₁₆×C₂₉	—	4	2	no	—
273	SD₁₆×C₂₉	—	2	4	no	—
274	SD₁₆×C₂₉	—	2	2	no	—
275	SD₁₆×C₂₉	—	2	4	no	—
276	SD₁₆×C₂₉	—	2	2	no	—
277	SD₁₆×C₂₉	—	4	2	no	—
278	SD₁₆×C₂₉	—	4	2	no	—
279	D₈×C₂₉	—	2	2	no	—
280	M₁₆×C₂₉	—	2	4	no	—
281	M₁₆×C₂₉	—	2	1	no	—
282	M₁₆×C₂₉	—	2	1	no	—
283	M₁₆×C₂₉	—	2	1	no	—
284	M₁₆×C₂₉	—	2	1	no	—
285	M₁₆×C₂₉	—	2	1	no	—
286	M₁₆×C₂₉	—	2	1	no	—
287	M₁₆×C₂₉	—	2	1	no	—
288	M₁₆×C₂₉	—	4	2	no	—
289	M₁₆×C₂₉	C₂×D₄	1	2	yes	—
290	C₂×C₈×C₂₉	—	2	4	no	—
291	C₂×C₈×C₂₉	—	2	1	no	—
292	C₂×C₈×C₂₉	—	2	1	no	—
293	C₂×C₈×C₂₉	—	2	1	no	—
294	C₂×C₈×C₂₉	—	2	1	no	—
295	C₂×C₈×C₂₉	—	2	1	no	—
296	C₂×C₈×C₂₉	—	2	1	no	—
297	C₂×C₈×C₂₉	—	2	1	no	—
298	C₂×C₈×C₂₉	—	2	1	no	—
299	C₂×C₈×C₂₉	—	4	2	no	—
300	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
301	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
302	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
303	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
304	C₄⋊C₄×C₂₉	—	2	1	no	—
305	C₄⋊C₄×C₂₉	—	2	1	no	—
306	C₄⋊C₄×C₂₉	—	4	1	no	—
307	C₄⋊C₄×C₂₉	—	4	1	no	—
308	C₄⋊C₄×C₂₉	—	4	1	no	—
309	C₄⋊C₄×C₂₉	—	4	4	no	—
310	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
311	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
312	C₂²⋊C₄×C₂₉	—	2	1	no	—
313	C₂²⋊C₄×C₂₉	—	4	1	no	—
314	C₂²⋊C₄×C₂₉	—	4	1	no	—
315	C₂²⋊C₄×C₂₉	—	4	1	no	—
316	C₄²×C₂₉	—	2	1	no	—
317	C₄²×C₂₉	—	2	1	no	—
318	C₄²×C₂₉	—	2	1	no	—
319	C₄²×C₂₉	—	4	1	no	—
320	#24462	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
321	C₂³×C₂₉	—	2	1	no	—
322	C₂³×C₂₉	—	2	1	no	—
323	C₂³×C₂₉	—	2	1	no	—
324	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
325	Q₈×C₂₉	—	2	1	no	—
326	Q₈×C₂₉	—	2	1	no	—
327	Q₈×C₂₉	—	2	2	no	—
328	Q₈×C₂₉	—	2	2	no	—
329	Q₈×C₂₉	—	2	1	no	—
330	Q₈×C₂₉	—	2	2	no	—
331	Q₈×C₂₉	—	2	2	no	—
332	Q₈×C₂₉	—	2	1	no	—
333	Q₈×C₂₉	—	4	4	no	—
334	Q₈×C₂₉	—	4	4	no	—
335	Q₈×C₂₉	—	4	1	no	—
336	Q₈×C₂₉	—	4	1	no	—
337	Q₈×C₂₉	—	4	1	no	—
338	Q₈×C₂₉	—	4	1	no	—
339	Q₈×C₂₉	—	4	1	no	—
340	Q₈×C₂₉	—	4	1	no	—
341	Q₈×C₂₉	—	4	1	no	—
342	Q₈×C₂₉	—	4	1	no	—
343	Q₈×C₂₉	#120	1	2	yes	—
344	Q₈×C₂₉	#121	1	2	yes	—
345	D₄×C₂₉	—	2	2	no	—
346	D₄×C₂₉	—	2	2	no	—
347	D₄×C₂₉	—	2	2	no	—
348	D₄×C₂₉	—	2	2	no	—
349	D₄×C₂₉	—	2	1	no	—
350	D₄×C₂₉	—	2	1	no	—
351	D₄×C₂₉	—	2	1	no	—
352	D₄×C₂₉	—	2	1	no	—
353	D₄×C₂₉	—	4	4	no	—
354	D₄×C₂₉	—	4	4	no	—
355	D₄×C₂₉	—	4	1	no	—
356	D₄×C₂₉	—	4	1	no	—
357	D₄×C₂₉	#120	1	2	yes	—
358	D₄×C₂₉	#121	1	2	yes	—
359	C₂×C₄×C₂₉	—	2	1	no	—
360	C₂×C₄×C₂₉	—	2	1	no	—
361	C₂×C₄×C₂₉	—	2	2	no	—
362	C₂×C₄×C₂₉	—	2	2	no	—
363	C₂×C₄×C₂₉	—	2	2	no	—
364	C₂×C₄×C₂₉	—	2	2	no	—
365	C₂×C₄×C₂₉	—	2	2	no	—
366	C₂×C₄×C₂₉	—	2	2	no	—
367	C₂×C₄×C₂₉	—	2	1	no	—
368	C₂×C₄×C₂₉	—	2	1	no	—
369	C₂×C₄×C₂₉	—	2	1	no	—
370	C₂×C₄×C₂₉	—	2	2	no	—
371	C₂×C₄×C₂₉	—	4	4	no	—
372	C₂×C₄×C₂₉	—	4	4	no	—
373	C₂×C₄×C₂₉	—	4	4	no	—
374	C₂×C₄×C₂₉	—	4	1	no	—
375	C₂×C₄×C₂₉	—	4	4	no	—
376	C₂×C₄×C₂₉	—	4	1	no	—
377	C₂×C₄×C₂₉	—	4	1	no	—
378	C₂×C₄×C₂₉	—	4	1	no	—
379	C₂×C₄×C₂₉	—	4	1	no	—
380	C₂×C₄×C₂₉	—	4	1	no	—
381	C₂×C₄×C₂₉	—	4	1	no	—
382	C₂×C₄×C₂₉	—	4	1	no	—
383	C₂×C₄×C₂₉	—	4	1	no	—
384	C₂×C₄×C₂₉	—	4	1	no	—
385	C₂×C₄×C₂₉	—	4	1	no	—
386	C₂×C₄×C₂₉	—	4	1	no	—
387	C₂×C₄×C₂₉	—	8	1	no	—
388	C₂×C₄×C₂₉	—	16	1	no	—
389	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
394	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
395	C₈×C₂₉	—	2	1	no	—
396	C₈×C₂₉	—	2	2	no	—
397	C₈×C₂₉	—	2	1	no	—
398	C₈×C₂₉	—	2	1	no	—
399	C₈×C₂₉	—	2	1	no	—
400	C₈×C₂₉	—	4	1	no	—
401	C₈×C₂₉	—	4	1	no	—
402	C₈×C₂₉	—	4	1	no	—
403	C₂×#578	C₂×C₂₉	1	1	yes	characteristic
404	C₂×#473	C₂×C₂₉	1	1	yes	characteristic, complemented
405	#3046	C₂×C₂₉	1	1	yes	characteristic, complemented
406	C₂×#456	C₂×C₂₉	1	1	yes	characteristic, complemented
407	#3011	C₂×C₂₉	1	1	yes	characteristic, complemented
408	#2898	C₂×C₂₉	1	1	yes	characteristic, complemented
409	#2052	C₂×C₂₉	1	1	yes	characteristic, complemented
410	#2047	C₂×C₂₉	1	1	yes	characteristic, complemented
411	#2016	C₂×C₂₉	1	1	yes	characteristic, complemented
412	#2005	C₂×C₂₉	1	1	yes	characteristic, complemented
413	#1908	C₂×C₂₉	1	1	yes	characteristic, complemented
414	#1882	C₂×C₂₉	1	1	yes	characteristic, complemented
415	#1876	C₂×C₂₉	1	1	yes	characteristic, complemented
416	#1866	C₂×C₂₉	1	1	yes	characteristic, complemented
417	#1793	C₂×C₂₉	1	1	yes	characteristic, complemented
418	C₂²×C₂₉	—	2	1	no	—
419	C₂²×C₂₉	—	2	1	no	—
420	C₂²×C₂₉	—	2	2	no	—
421	C₂²×C₂₉	—	2	2	no	—
422	C₂²×C₂₉	—	4	1	no	—
423	C₂²×C₂₉	—	4	1	no	—
424	C₂²×C₂₉	—	4	1	no	—
425	C₂²×C₂₉	—	4	1	no	—
426	C₂²×C₂₉	—	4	1	no	—
427	C₂²×C₂₉	—	4	1	no	—
428	C₂²×C₂₉	—	4	1	no	—
429	C₂²×C₂₉	#534	1	1	yes	characteristic
430	C₂²×C₂₉	D₄²	1	1	yes	characteristic
431	C₂²×C₂₉	#546	1	1	yes	characteristic
432	C₄×C₂₉	—	2	2	no	—
433	C₄×C₂₉	—	2	2	no	—
434	C₄×C₂₉	—	4	2	no	—
435	C₄×C₂₉	—	4	2	no	—
436	C₄×C₂₉	—	4	1	no	—
437	C₄×C₂₉	—	4	2	no	—
438	C₄×C₂₉	—	4	1	no	—
439	C₄×C₂₉	—	4	1	no	—
440	C₄×C₂₉	—	8	1	no	—
441	C₄×C₂₉	—	8	1	no	—
442	C₄×C₂₉	C₂×#120	1	1	yes	characteristic
443	C₄×C₂₉	C₂×#121	1	1	yes	characteristic
444	C₄×C₂₉	D₄²	1	1	yes	characteristic
445	C₄×C₂₉	#546	1	1	yes	characteristic
446	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
447	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
448	#578	—	2	4	no	—
449	#578	—	2	4	no	—
450	C₂×#137	—	2	1	no	—
451	C₂×#137	—	2	1	no	—
452	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
453	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
454	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
455	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
456	C₂×#135	—	2	1	no	—
457	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
458	C₂²×Q₁₆	—	2	1	no	—
459	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
460	C₂²×Q₁₆	C₂²×C₂₉	1	1	yes	characteristic
461	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
462	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
463	#536	C₂²×C₂₉	1	1	yes	characteristic
464	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic
465	#520	C₂²×C₂₉	1	1	yes	characteristic
466	#473	—	2	4	no	—
467	#464	—	2	1	no	—
468	#463	—	2	1	no	—
469	#462	—	2	1	no	—
470	#461	—	2	1	no	—
471	#456	—	2	4	no	—
472	#452	—	2	1	no	—
473	#452	—	2	1	no	—
474	#451	—	2	1	no	—
475	#451	—	2	1	no	—
476	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic
477	#424	C₂²×C₂₉	1	1	yes	characteristic
478	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
479	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
480	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
481	#419	—	2	1	no	—
482	#419	C₂²×C₂₉	1	1	yes	characteristic
483	#419	C₂²×C₂₉	1	1	yes	characteristic
484	#417	—	2	1	no	—
485	#417	C₂²×C₂₉	1	1	yes	characteristic
486	#417	C₂²×C₂₉	1	1	yes	characteristic
487	#416	—	2	1	no	—
488	#416	C₂²×C₂₉	1	1	yes	characteristic
489	C₂×#103	—	2	1	no	—
490	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
491	C₂×#103	C₂²×C₂₉	1	1	yes	characteristic
492	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
493	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
494	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic
495	#408	C₂²×C₂₉	1	1	yes	characteristic
496	#391	C₂²×C₂₉	1	1	yes	characteristic
497	#343	C₂²×C₂₉	1	1	yes	characteristic
498	#341	C₂²×C₂₉	1	1	yes	characteristic
499	#339	C₂²×C₂₉	1	1	yes	characteristic
500	#336	C₂²×C₂₉	1	1	yes	characteristic
501	C₂×C₂₉	—	2	1	no	—
502	C₂×C₂₉	—	2	1	no	—
503	C₂×C₂₉	—	4	2	no	—
504	C₂×C₂₉	—	4	2	no	—
505	C₂×C₂₉	—	8	1	no	—
506	C₂×C₂₉	#2410	1	1	yes	characteristic
507	C₂×C₂₉	#3289	1	1	yes	characteristic
508	C₂×C₂₉	#3293	1	1	yes	characteristic
509	2₋¹⁺⁴	—	2	2	no	—
510	2₋¹⁺⁴	—	2	2	no	—
511	2₋¹⁺⁴	—	2	2	no	—
512	2₋¹⁺⁴	—	2	2	no	—
513	2₋¹⁺⁴	—	2	2	no	—
514	2₋¹⁺⁴	—	4	1	no	—
515	2₋¹⁺⁴	—	4	1	no	—
516	2₋¹⁺⁴	D₄×C₂₉	1	4	yes	—
517	C₂×#41	—	2	1	no	—
518	C₂×#41	—	2	1	no	—
519	C₂×#41	—	2	1	no	—
520	C₂×#41	—	2	1	no	—
521	C₂×#41	—	4	1	no	—
522	C₂×#41	—	4	1	no	—
523	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
524	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
525	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
526	C₂²×Q₈	—	2	1	no	—
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	—	2	1	no	—
529	C₂²×Q₈	—	2	1	no	—
530	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
532	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
533	#137	—	2	8	no	—
534	#137	—	2	8	no	—
535	#137	—	2	2	no	—
536	#137	—	2	2	no	—
537	#137	—	2	2	no	—
538	#137	—	2	2	no	—
539	#137	—	2	2	no	—
540	#137	—	2	2	no	—
541	#137	—	2	2	no	—
542	#137	D₄×C₂₉	1	4	yes	—
543	#135	—	2	8	no	—
544	#135	—	2	2	no	—
545	#135	—	2	2	no	—
546	C₂×Q₁₆	—	2	8	no	—
547	C₂×Q₁₆	—	2	1	no	—
548	C₂×Q₁₆	—	2	1	no	—
549	C₂×Q₁₆	—	2	2	no	—
550	C₂×Q₁₆	—	2	2	no	—
551	C₂×Q₁₆	—	2	2	no	—
552	C₂×Q₁₆	—	2	1	no	—
553	C₂×Q₁₆	—	2	1	no	—
554	C₂×Q₁₆	—	2	1	no	—
555	C₂×Q₁₆	—	2	1	no	—
556	C₂×Q₁₆	—	2	1	no	—
557	C₂×Q₁₆	—	2	1	no	—
558	C₂×Q₁₆	—	4	1	no	—
559	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic
560	C₂×SD₁₆	—	2	1	no	—
561	C₂×SD₁₆	—	2	1	no	—
562	C₂×SD₁₆	—	2	1	no	—
563	C₂×SD₁₆	—	2	1	no	—
564	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
565	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic
566	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic
567	#131	—	2	2	no	—
568	#131	—	2	2	no	—
569	#131	—	2	2	no	—
570	#131	—	4	1	no	—
571	C₂×M₁₆	—	2	1	no	—
572	C₂×M₁₆	—	2	1	no	—
573	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
574	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
575	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
576	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
577	C₂²×C₈	—	2	1	no	—
578	C₂²×C₈	—	2	1	no	—
579	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
580	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
581	C₄⋊Q₈	—	2	2	no	—
582	C₄⋊Q₈	—	2	1	no	—
583	C₄⋊Q₈	—	4	1	no	—
584	#124	—	2	1	no	—
585	#123	—	4	1	no	—
586	C₂²⋊Q₈	—	2	1	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×D₄	—	2	1	no	—
590	C₄×D₄	—	4	1	no	—
591	#117	—	2	1	no	—
592	#117	C₂³×C₂₉	1	1	yes	characteristic
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	4	1	no	—
595	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
597	#108	—	2	2	no	—
598	C₄⋊C₈	—	2	1	no	—
599	C₄⋊C₈	—	2	1	no	—
600	#104	—	2	2	no	—
601	#104	—	2	2	no	—
602	#104	—	4	1	no	—
603	#103	—	2	1	no	—
604	#103	—	2	1	no	—
605	#103	—	2	1	no	—
606	#103	—	2	1	no	—
607	#103	—	2	1	no	—
608	#103	—	2	1	no	—
609	#103	—	2	1	no	—
610	#103	—	2	1	no	—
611	#103	—	2	1	no	—
612	#103	—	2	1	no	—
613	#103	D₄×C₂₉	1	1	yes	characteristic
614	#103	D₄×C₂₉	1	1	yes	characteristic
615	#102	—	2	1	no	—
616	#102	—	2	1	no	—
617	#102	D₄×C₂₉	1	1	yes	characteristic
618	#102	D₄×C₂₉	1	1	yes	characteristic
619	#101	—	2	2	no	—
620	#101	—	2	2	no	—
621	#101	—	2	2	no	—
622	C₂²⋊C₈	—	2	1	no	—
623	C₂²⋊C₈	—	2	1	no	—
624	#95	—	4	1	no	—
625	C₂₉	#24462	1	1	yes	characteristic, direct product factor, Sylow
626	#41	—	2	1	no	—
627	#41	—	2	1	no	—
628	#41	—	2	1	no	—
629	#41	—	2	1	no	—
630	#41	—	2	4	no	—
631	#41	—	2	4	no	—
632	#41	—	2	4	no	—
633	#41	—	2	1	no	—
634	#41	—	2	1	no	—
635	#41	—	2	1	no	—
636	#41	—	2	1	no	—
637	#41	—	4	4	no	—
638	#41	—	4	2	no	—
639	#41	—	4	2	no	—
640	#41	—	4	2	no	—
641	#41	—	4	4	no	—
642	#41	—	4	4	no	—
643	#41	—	4	2	no	—
644	#41	—	4	4	no	—
645	#41	—	4	2	no	—
646	#41	C₂×D₄×C₂₉	1	2	yes	—
647	#41	C₂×D₄×C₂₉	1	2	yes	—
648	#41	C₂×D₄×C₂₉	1	2	yes	—
649	#41	#41×C₂₉	1	2	yes	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	2	4	no	—
655	C₂×Q₈	—	2	1	no	—
656	C₂×Q₈	—	2	1	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	1	no	—
659	C₂×Q₈	—	2	1	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	4	1	no	—
670	C₂×Q₈	—	4	1	no	—
671	C₂×Q₈	—	4	2	no	—
672	C₂×Q₈	—	4	2	no	—
673	C₂×Q₈	—	4	2	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
677	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
678	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
679	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
680	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	4	1	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
687	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
688	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	1	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	1	no	—
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	—	2	1	no	—
697	C₂²×C₄	—	4	1	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	1	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
703	Q₁₆	—	2	4	no	—
704	Q₁₆	—	2	4	no	—
705	Q₁₆	—	2	4	no	—
706	Q₁₆	—	2	2	no	—
707	Q₁₆	—	2	4	no	—
708	Q₁₆	—	4	2	no	—
709	Q₁₆	—	4	2	no	—
710	Q₁₆	—	4	2	no	—
711	Q₁₆	—	4	2	no	—
712	SD₁₆	—	2	4	no	—
713	SD₁₆	—	2	2	no	—
714	SD₁₆	—	2	4	no	—
715	SD₁₆	—	2	2	no	—
716	SD₁₆	—	4	2	no	—
717	SD₁₆	—	4	2	no	—
718	D₈	—	2	2	no	—
719	M₁₆	—	2	4	no	—
720	M₁₆	—	2	1	no	—
721	M₁₆	—	2	1	no	—
722	M₁₆	—	2	1	no	—
723	M₁₆	—	2	1	no	—
724	M₁₆	—	2	1	no	—
725	M₁₆	—	2	1	no	—
726	M₁₆	—	2	1	no	—
727	M₁₆	—	4	2	no	—
728	M₁₆	C₂×D₄×C₂₉	1	2	yes	—
729	C₂×C₈	—	2	4	no	—
730	C₂×C₈	—	2	1	no	—
731	C₂×C₈	—	2	1	no	—
732	C₂×C₈	—	2	1	no	—
733	C₂×C₈	—	2	1	no	—
734	C₂×C₈	—	2	1	no	—
735	C₂×C₈	—	2	1	no	—
736	C₂×C₈	—	2	1	no	—
737	C₂×C₈	—	2	1	no	—
738	C₂×C₈	—	4	2	no	—
739	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
740	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
741	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
742	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	4	1	no	—
746	C₄⋊C₄	—	4	1	no	—
747	C₄⋊C₄	—	4	1	no	—
748	C₄⋊C₄	—	4	4	no	—
749	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₄²	—	2	1	no	—
756	C₄²	—	2	1	no	—
757	C₄²	—	2	1	no	—
758	C₄²	—	4	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	2	1	no	—
762	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
763	Q₈	—	2	1	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	1	no	—
771	Q₈	—	4	4	no	—
772	Q₈	—	4	4	no	—
773	Q₈	—	4	1	no	—
774	Q₈	—	4	1	no	—
775	Q₈	—	4	1	no	—
776	Q₈	—	4	1	no	—
777	Q₈	—	4	1	no	—
778	Q₈	—	4	1	no	—
779	Q₈	—	4	1	no	—
780	Q₈	—	4	1	no	—
781	Q₈	C₂₉×#120	1	2	yes	—
782	Q₈	C₂₉×#121	1	2	yes	—
783	D₄	—	2	2	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	4	no	—
793	D₄	—	4	1	no	—
794	D₄	—	4	1	no	—
795	D₄	C₂₉×#120	1	2	yes	—
796	D₄	C₂₉×#121	1	2	yes	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	8	1	no	—
826	C₂×C₄	—	16	1	no	—
827	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
831	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
832	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
833	C₈	—	2	1	no	—
834	C₈	—	2	2	no	—
835	C₈	—	2	1	no	—
836	C₈	—	2	1	no	—
837	C₈	—	2	1	no	—
838	C₈	—	4	1	no	—
839	C₈	—	4	1	no	—
840	C₈	—	4	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	4	1	no	—
852	C₂²	C₂₉×#534	1	1	yes	characteristic
853	C₂²	D₄²×C₂₉	1	1	yes	characteristic
854	C₂²	C₂₉×#546	1	1	yes	characteristic
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	8	1	no	—
864	C₄	—	8	1	no	—
865	C₄	C₂×C₂₉×#120	1	1	yes	characteristic
866	C₄	C₂×C₂₉×#121	1	1	yes	characteristic
867	C₄	D₄²×C₂₉	1	1	yes	characteristic
868	C₄	C₂₉×#546	1	1	yes	characteristic
869	C₂	—	2	1	no	—
870	C₂	—	2	1	no	—
871	C₂	—	4	2	no	—
872	C₂	—	4	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂₉×#2410	1	1	yes	characteristic
875	C₂	C₂₉×#3289	1	1	yes	characteristic
876	C₂	C₂₉×#3293	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
prime radical	C₂×C₂₉×#578	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₉×#473	C₂	semidirect
3. C₂₉×#3046	C₂	semidirect
4. C₂×C₂₉×#456	C₂	semidirect
5. C₂₉×#3011	C₂	semidirect
6. C₂₉×#2898	C₂	semidirect
7. C₂₉×#2052	C₂	semidirect
8. C₂₉×#2047	C₂	semidirect
9. C₂₉×#2016	C₂	semidirect
10. C₂₉×#2005	C₂	semidirect
11. C₂₉×#1908	C₂	semidirect
12. C₂₉×#1882	C₂	semidirect
13. C₂₉×#1876	C₂	semidirect
14. C₂₉×#1866	C₂	semidirect
15. C₂₉×#1793	C₂	semidirect
320. #24462	C₂₉	direct (N × H)
404. C₂×#473	C₂×C₂₉	semidirect
405. #3046	C₂×C₂₉	semidirect
406. C₂×#456	C₂×C₂₉	semidirect
407. #3011	C₂×C₂₉	semidirect
408. #2898	C₂×C₂₉	semidirect
409. #2052	C₂×C₂₉	semidirect
410. #2047	C₂×C₂₉	semidirect
411. #2016	C₂×C₂₉	semidirect
412. #2005	C₂×C₂₉	semidirect
413. #1908	C₂×C₂₉	semidirect
414. #1882	C₂×C₂₉	semidirect
415. #1876	C₂×C₂₉	semidirect
416. #1866	C₂×C₂₉	semidirect
417. #1793	C₂×C₂₉	semidirect
625. C₂₉	#24462	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#578	2
C₂×C₂₉×#473	2
C₂₉×#3046	2
C₂×C₂₉×#456	2
C₂₉×#3011	2
C₂₉×#2898	2
C₂₉×#2052	2
C₂₉×#2047	2
C₂₉×#2016	2
C₂₉×#2005	2
C₂₉×#1908	2
C₂₉×#1882	2
C₂₉×#1876	2
C₂₉×#1866	2
C₂₉×#1793	2
#24462	29

Subgroups — C29×#24462 #20319362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24462 #20319362