Subgroups — C₂₉×#24457 #20319357

Order 7424.

1376 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×#471	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#3045	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#453	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₉×#3010	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#2897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#2046	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#1907	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×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂₉×#577	—	2	4	no	—
19	C₂₉×#577	—	2	4	no	—
20	C₂×C₂₉×#137	—	2	1	no	—
21	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic
22	C₂×C₂₉×AGL(1,ℤ/8)	—	2	1	no	—
23	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×#135	—	2	1	no	—
27	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₂₉	—	2	1	no	—
29	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
32	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
33	C₂₉×#535	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
35	C₂₉×#520	C₂²	1	1	yes	characteristic
36	C₂₉×#471	—	2	4	no	—
37	C₂₉×#464	—	2	1	no	—
38	C₂₉×#463	—	2	1	no	—
39	C₂₉×#460	—	2	1	no	—
40	C₂₉×#459	—	2	1	no	—
41	C₂₉×#453	—	2	4	no	—
42	C₂₉×#449	—	2	1	no	—
43	C₂₉×#449	—	2	1	no	—
44	C₂₉×#448	—	2	1	no	—
45	C₂₉×#448	—	2	1	no	—
46	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic, complemented
47	C₂₉×#424	C₂²	1	1	yes	characteristic, complemented
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, complemented
51	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
52	C₂₉×#418	—	2	1	no	—
53	C₂₉×#418	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, complemented
57	C₂₉×#416	—	2	1	no	—
58	C₂₉×#416	C₂²	1	1	yes	characteristic
59	C₂×C₂₉×#102	—	2	1	no	—
60	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic
61	C₂×C₂₉×#102	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
64	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
66	C₂₉×#391	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#343	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×#341	C₂²	1	1	yes	characteristic, complemented
69	C₂₉×#339	C₂²	1	1	yes	characteristic, complemented
70	C₂₉×#336	C₂²	1	1	yes	characteristic, complemented
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	—	4	1	no	—
75	C₂₉×H(5,𝔽₂)	—	2	2	no	—
76	C₂₉×H(5,𝔽₂)	—	2	2	no	—
77	C₂₉×H(5,𝔽₂)	—	4	1	no	—
78	C₂₉×H(5,𝔽₂)	D₄	1	4	yes	complemented
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	C₂³	1	1	yes	characteristic
85	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
86	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₂₉	—	2	1	no	—
88	C₂²×Q₈×C₂₉	—	2	1	no	—
89	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₂₉	—	2	1	no	—
91	C₂²×D₄×C₂₉	—	2	1	no	—
92	C₂²×D₄×C₂₉	—	4	1	no	—
93	C₂²×D₄×C₂₉	—	4	1	no	—
94	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
96	C₂₉×#137	—	2	8	no	—
97	C₂₉×#137	—	2	2	no	—
98	C₂₉×#137	D₄	1	4	yes	complemented
99	C₂₉×AGL(1,ℤ/8)	—	2	8	no	—
100	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
101	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
102	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
103	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
104	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
105	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
106	C₂₉×#135	—	2	8	no	—
107	C₂₉×#135	—	2	2	no	—
108	C₂₉×#135	—	2	2	no	—
109	C₂×Q₁₆×C₂₉	—	2	1	no	—
110	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic, complemented
111	C₂×SD₁₆×C₂₉	—	2	8	no	—
112	C₂×SD₁₆×C₂₉	—	2	1	no	—
113	C₂×SD₁₆×C₂₉	—	2	2	no	—
114	C₂×SD₁₆×C₂₉	—	2	1	no	—
115	C₂×SD₁₆×C₂₉	—	2	2	no	—
116	C₂×SD₁₆×C₂₉	—	2	1	no	—
117	C₂×SD₁₆×C₂₉	—	2	1	no	—
118	C₂×SD₁₆×C₂₉	—	2	2	no	—
119	C₂×SD₁₆×C₂₉	—	2	1	no	—
120	C₂×SD₁₆×C₂₉	—	2	1	no	—
121	C₂×SD₁₆×C₂₉	—	2	1	no	—
122	C₂×SD₁₆×C₂₉	—	2	1	no	—
123	C₂×SD₁₆×C₂₉	—	4	1	no	—
124	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic, complemented
125	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic, complemented
126	C₂×D₈×C₂₉	—	2	1	no	—
127	C₂×D₈×C₂₉	—	2	1	no	—
128	C₂×D₈×C₂₉	—	2	1	no	—
129	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic, complemented
130	C₂₉×#131	—	2	2	no	—
131	C₂₉×#131	—	2	2	no	—
132	C₂₉×#131	—	2	2	no	—
133	C₂₉×#131	—	4	1	no	—
134	C₂×M₁₆×C₂₉	—	2	1	no	—
135	C₂×M₁₆×C₂₉	—	2	1	no	—
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	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₂₉	—	2	1	no	—
141	C₂²×C₈×C₂₉	—	2	1	no	—
142	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
144	C₂₉×#127	—	2	2	no	—
145	C₂₉×#127	—	2	1	no	—
146	C₂₉×#127	—	4	1	no	—
147	C₂₉×#124	—	2	1	no	—
148	C₂₉×#121	—	2	1	no	—
149	C₂₉×#121	—	2	1	no	—
150	C₂₉×#120	—	4	1	no	—
151	C₄×Q₈×C₂₉	—	2	1	no	—
152	C₄×D₄×C₂₉	—	2	1	no	—
153	C₄×D₄×C₂₉	—	4	1	no	—
154	C₂₉×#117	—	2	1	no	—
155	C₂₉×#117	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₉	—	2	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	D₄	1	1	yes	characteristic, complemented
170	C₂₉×#103	D₄	1	1	yes	characteristic, complemented
171	C₂₉×#102	—	2	1	no	—
172	C₂₉×#102	—	2	1	no	—
173	C₂₉×#102	—	2	1	no	—
174	C₂₉×#102	—	2	1	no	—
175	C₂₉×#102	—	2	1	no	—
176	C₂₉×#102	—	2	1	no	—
177	C₂₉×#102	—	2	1	no	—
178	C₂₉×#102	—	2	1	no	—
179	C₂₉×#102	D₄	1	1	yes	characteristic, complemented
180	C₂₉×#102	D₄	1	1	yes	characteristic, complemented
181	C₂₉×#101	—	2	2	no	—
182	C₂₉×#100	—	2	2	no	—
183	C₂₉×#100	—	2	2	no	—
184	C₂₉×C₂²⋊C₈	—	2	1	no	—
185	C₂₉×C₂²⋊C₈	—	2	1	no	—
186	C₂₉×#95	—	4	1	no	—
187	C₂⁴×C₂₉	—	2	1	no	—
188	C₂⁴×C₂₉	—	2	1	no	—
189	C₂⁴×C₂₉	—	4	1	no	—
190	#41×C₂₉	—	2	1	no	—
191	#41×C₂₉	—	2	1	no	—
192	#41×C₂₉	—	2	1	no	—
193	#41×C₂₉	—	2	1	no	—
194	#41×C₂₉	—	2	4	no	—
195	#41×C₂₉	—	2	4	no	—
196	#41×C₂₉	—	2	4	no	—
197	#41×C₂₉	—	2	1	no	—
198	#41×C₂₉	—	2	1	no	—
199	#41×C₂₉	—	2	1	no	—
200	#41×C₂₉	—	2	1	no	—
201	#41×C₂₉	—	4	2	no	—
202	#41×C₂₉	—	4	4	no	—
203	#41×C₂₉	—	4	2	no	—
204	#41×C₂₉	—	4	2	no	—
205	#41×C₂₉	—	4	2	no	—
206	#41×C₂₉	—	4	4	no	—
207	#41×C₂₉	—	4	2	no	—
208	#41×C₂₉	C₂×D₄	1	2	yes	—
209	#41×C₂₉	C₂×D₄	1	2	yes	—
210	#41×C₂₉	C₂×D₄	1	2	yes	—
211	#41×C₂₉	#41	1	2	yes	—
212	C₂×Q₈×C₂₉	—	2	1	no	—
213	C₂×Q₈×C₂₉	—	2	4	no	—
214	C₂×Q₈×C₂₉	—	2	1	no	—
215	C₂×Q₈×C₂₉	—	2	1	no	—
216	C₂×Q₈×C₂₉	—	2	1	no	—
217	C₂×Q₈×C₂₉	—	2	1	no	—
218	C₂×Q₈×C₂₉	—	4	1	no	—
219	C₂×Q₈×C₂₉	—	4	2	no	—
220	C₂×Q₈×C₂₉	—	4	2	no	—
221	C₂×Q₈×C₂₉	—	4	2	no	—
222	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
223	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
225	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
226	C₂×D₄×C₂₉	—	2	1	no	—
227	C₂×D₄×C₂₉	—	2	1	no	—
228	C₂×D₄×C₂₉	—	2	4	no	—
229	C₂×D₄×C₂₉	—	2	4	no	—
230	C₂×D₄×C₂₉	—	2	1	no	—
231	C₂×D₄×C₂₉	—	2	1	no	—
232	C₂×D₄×C₂₉	—	2	1	no	—
233	C₂×D₄×C₂₉	—	2	1	no	—
234	C₂×D₄×C₂₉	—	2	1	no	—
235	C₂×D₄×C₂₉	—	2	1	no	—
236	C₂×D₄×C₂₉	—	2	1	no	—
237	C₂×D₄×C₂₉	—	2	1	no	—
238	C₂×D₄×C₂₉	—	2	1	no	—
239	C₂×D₄×C₂₉	—	2	1	no	—
240	C₂×D₄×C₂₉	—	2	1	no	—
241	C₂×D₄×C₂₉	—	2	1	no	—
242	C₂×D₄×C₂₉	—	4	2	no	—
243	C₂×D₄×C₂₉	—	4	2	no	—
244	C₂×D₄×C₂₉	—	4	1	no	—
245	C₂×D₄×C₂₉	—	4	1	no	—
246	C₂×D₄×C₂₉	—	4	1	no	—
247	C₂×D₄×C₂₉	—	4	1	no	—
248	C₂×D₄×C₂₉	—	4	4	no	—
249	C₂×D₄×C₂₉	—	4	4	no	—
250	C₂×D₄×C₂₉	—	4	1	no	—
251	C₂×D₄×C₂₉	—	4	4	no	—
252	C₂×D₄×C₂₉	—	8	2	no	—
253	C₂×D₄×C₂₉	—	8	2	no	—
254	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
256	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₉	—	2	1	no	—
259	C₂²×C₄×C₂₉	—	2	1	no	—
260	C₂²×C₄×C₂₉	—	2	1	no	—
261	C₂²×C₄×C₂₉	—	2	1	no	—
262	C₂²×C₄×C₂₉	—	2	1	no	—
263	C₂²×C₄×C₂₉	—	2	1	no	—
264	C₂²×C₄×C₂₉	—	4	1	no	—
265	C₂²×C₄×C₂₉	—	4	1	no	—
266	C₂²×C₄×C₂₉	—	4	1	no	—
267	C₂²×C₄×C₂₉	—	4	1	no	—
268	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
269	Q₁₆×C₂₉	—	2	4	no	—
270	Q₁₆×C₂₉	—	2	2	no	—
271	SD₁₆×C₂₉	—	2	4	no	—
272	SD₁₆×C₂₉	—	2	4	no	—
273	SD₁₆×C₂₉	—	2	4	no	—
274	SD₁₆×C₂₉	—	2	2	no	—
275	SD₁₆×C₂₉	—	2	2	no	—
276	SD₁₆×C₂₉	—	2	4	no	—
277	SD₁₆×C₂₉	—	4	2	no	—
278	SD₁₆×C₂₉	—	4	2	no	—
279	SD₁₆×C₂₉	—	4	2	no	—
280	SD₁₆×C₂₉	—	4	2	no	—
281	D₈×C₂₉	—	2	4	no	—
282	D₈×C₂₉	—	2	2	no	—
283	D₈×C₂₉	—	4	2	no	—
284	D₈×C₂₉	—	4	2	no	—
285	M₁₆×C₂₉	—	2	4	no	—
286	M₁₆×C₂₉	—	2	1	no	—
287	M₁₆×C₂₉	—	2	1	no	—
288	M₁₆×C₂₉	—	2	1	no	—
289	M₁₆×C₂₉	—	2	1	no	—
290	M₁₆×C₂₉	—	2	1	no	—
291	M₁₆×C₂₉	—	2	1	no	—
292	M₁₆×C₂₉	—	2	1	no	—
293	M₁₆×C₂₉	—	4	2	no	—
294	M₁₆×C₂₉	C₂×D₄	1	2	yes	—
295	C₂×C₈×C₂₉	—	2	4	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	—	2	1	no	—
300	C₂×C₈×C₂₉	—	2	1	no	—
301	C₂×C₈×C₂₉	—	2	1	no	—
302	C₂×C₈×C₂₉	—	2	1	no	—
303	C₂×C₈×C₂₉	—	2	1	no	—
304	C₂×C₈×C₂₉	—	4	2	no	—
305	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
306	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
307	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
308	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₂₉	—	2	1	no	—
310	C₄⋊C₄×C₂₉	—	2	1	no	—
311	C₄⋊C₄×C₂₉	—	4	1	no	—
312	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
314	C₂²⋊C₄×C₂₉	—	2	1	no	—
315	C₂²⋊C₄×C₂₉	—	4	1	no	—
316	C₂²⋊C₄×C₂₉	—	4	1	no	—
317	C₂²⋊C₄×C₂₉	—	4	1	no	—
318	C₄²×C₂₉	—	2	1	no	—
319	C₄²×C₂₉	—	2	1	no	—
320	C₄²×C₂₉	—	2	1	no	—
321	C₄²×C₂₉	—	4	1	no	—
322	#24457	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂³×C₂₉	—	2	1	no	—
324	C₂³×C₂₉	—	2	1	no	—
325	C₂³×C₂₉	—	2	1	no	—
326	C₂³×C₂₉	—	2	2	no	—
327	C₂³×C₂₉	—	4	4	no	—
328	C₂³×C₂₉	—	4	1	no	—
329	C₂³×C₂₉	—	4	1	no	—
330	C₂³×C₂₉	—	4	1	no	—
331	C₂³×C₂₉	—	4	1	no	—
332	C₂³×C₂₉	—	4	1	no	—
333	C₂³×C₂₉	—	8	1	no	—
334	C₂³×C₂₉	—	8	1	no	—
335	C₂³×C₂₉	—	8	1	no	—
336	C₂³×C₂₉	—	8	1	no	—
337	C₂³×C₂₉	—	16	1	no	—
338	C₂³×C₂₉	—	16	1	no	—
339	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
340	Q₈×C₂₉	—	2	1	no	—
341	Q₈×C₂₉	—	2	1	no	—
342	Q₈×C₂₉	—	2	2	no	—
343	Q₈×C₂₉	—	2	1	no	—
344	Q₈×C₂₉	—	2	2	no	—
345	Q₈×C₂₉	—	2	1	no	—
346	Q₈×C₂₉	—	4	4	no	—
347	Q₈×C₂₉	—	4	1	no	—
348	Q₈×C₂₉	—	4	1	no	—
349	Q₈×C₂₉	#120	1	2	yes	—
350	Q₈×C₂₉	#121	1	2	yes	—
351	D₄×C₂₉	—	2	2	no	—
352	D₄×C₂₉	—	2	2	no	—
353	D₄×C₂₉	—	2	2	no	—
354	D₄×C₂₉	—	2	2	no	—
355	D₄×C₂₉	—	2	1	no	—
356	D₄×C₂₉	—	2	2	no	—
357	D₄×C₂₉	—	2	2	no	—
358	D₄×C₂₉	—	2	1	no	—
359	D₄×C₂₉	—	2	1	no	—
360	D₄×C₂₉	—	2	1	no	—
361	D₄×C₂₉	—	4	4	no	—
362	D₄×C₂₉	—	4	4	no	—
363	D₄×C₂₉	—	4	4	no	—
364	D₄×C₂₉	—	4	1	no	—
365	D₄×C₂₉	—	4	1	no	—
366	D₄×C₂₉	—	4	1	no	—
367	D₄×C₂₉	—	4	1	no	—
368	D₄×C₂₉	—	4	1	no	—
369	D₄×C₂₉	—	4	1	no	—
370	D₄×C₂₉	—	4	1	no	—
371	D₄×C₂₉	—	4	1	no	—
372	D₄×C₂₉	—	8	8	no	—
373	D₄×C₂₉	—	16	1	no	—
374	D₄×C₂₉	—	16	1	no	—
375	D₄×C₂₉	#120	1	2	yes	—
376	D₄×C₂₉	#121	1	2	yes	—
377	C₂×C₄×C₂₉	—	2	1	no	—
378	C₂×C₄×C₂₉	—	2	1	no	—
379	C₂×C₄×C₂₉	—	2	2	no	—
380	C₂×C₄×C₂₉	—	2	2	no	—
381	C₂×C₄×C₂₉	—	2	2	no	—
382	C₂×C₄×C₂₉	—	2	2	no	—
383	C₂×C₄×C₂₉	—	2	2	no	—
384	C₂×C₄×C₂₉	—	2	1	no	—
385	C₂×C₄×C₂₉	—	2	1	no	—
386	C₂×C₄×C₂₉	—	2	1	no	—
387	C₂×C₄×C₂₉	—	2	2	no	—
388	C₂×C₄×C₂₉	—	4	4	no	—
389	C₂×C₄×C₂₉	—	4	4	no	—
390	C₂×C₄×C₂₉	—	4	1	no	—
391	C₂×C₄×C₂₉	—	4	4	no	—
392	C₂×C₄×C₂₉	—	4	1	no	—
393	C₂×C₄×C₂₉	—	4	1	no	—
394	C₂×C₄×C₂₉	—	4	1	no	—
395	C₂×C₄×C₂₉	—	4	1	no	—
396	C₂×C₄×C₂₉	—	4	1	no	—
397	C₂×C₄×C₂₉	—	4	1	no	—
398	C₂×C₄×C₂₉	—	8	1	no	—
399	C₂×C₄×C₂₉	—	16	1	no	—
400	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₂₉	C₂×#41	1	1	yes	characteristic
405	C₂×C₄×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
406	C₈×C₂₉	—	2	1	no	—
407	C₈×C₂₉	—	2	2	no	—
408	C₈×C₂₉	—	2	1	no	—
409	C₈×C₂₉	—	2	1	no	—
410	C₈×C₂₉	—	2	1	no	—
411	C₈×C₂₉	—	4	1	no	—
412	C₈×C₂₉	—	4	1	no	—
413	C₈×C₂₉	—	4	1	no	—
414	C₂×#577	C₂×C₂₉	1	1	yes	characteristic, complemented
415	C₂×#471	C₂×C₂₉	1	1	yes	characteristic, complemented
416	#3045	C₂×C₂₉	1	1	yes	characteristic, complemented
417	C₂×#453	C₂×C₂₉	1	1	yes	characteristic, complemented
418	#3010	C₂×C₂₉	1	1	yes	characteristic, complemented
419	#2897	C₂×C₂₉	1	1	yes	characteristic, complemented
420	#2051	C₂×C₂₉	1	1	yes	characteristic, complemented
421	#2046	C₂×C₂₉	1	1	yes	characteristic, complemented
422	#2014	C₂×C₂₉	1	1	yes	characteristic, complemented
423	#2002	C₂×C₂₉	1	1	yes	characteristic, complemented
424	#1907	C₂×C₂₉	1	1	yes	characteristic, complemented
425	#1882	C₂×C₂₉	1	1	yes	characteristic, complemented
426	#1876	C₂×C₂₉	1	1	yes	characteristic, complemented
427	#1866	C₂×C₂₉	1	1	yes	characteristic, complemented
428	#1793	C₂×C₂₉	1	1	yes	characteristic, complemented
429	C₂²×C₂₉	—	2	1	no	—
430	C₂²×C₂₉	—	2	1	no	—
431	C₂²×C₂₉	—	2	2	no	—
432	C₂²×C₂₉	—	2	2	no	—
433	C₂²×C₂₉	—	4	1	no	—
434	C₂²×C₂₉	—	4	1	no	—
435	C₂²×C₂₉	—	4	1	no	—
436	C₂²×C₂₉	—	4	1	no	—
437	C₂²×C₂₉	—	4	1	no	—
438	C₂²×C₂₉	—	4	2	no	—
439	C₂²×C₂₉	—	4	1	no	—
440	C₂²×C₂₉	—	4	1	no	—
441	C₂²×C₂₉	—	8	2	no	—
442	C₂²×C₂₉	—	8	2	no	—
443	C₂²×C₂₉	—	8	1	no	—
444	C₂²×C₂₉	—	8	1	no	—
445	C₂²×C₂₉	—	8	1	no	—
446	C₂²×C₂₉	—	8	1	no	—
447	C₂²×C₂₉	—	8	1	no	—
448	C₂²×C₂₉	—	16	1	no	—
449	C₂²×C₂₉	—	16	1	no	—
450	C₂²×C₂₉	—	16	4	no	—
451	C₂²×C₂₉	#534	1	1	yes	characteristic
452	C₂²×C₂₉	D₄²	1	1	yes	characteristic
453	C₂²×C₂₉	#546	1	1	yes	characteristic
454	C₄×C₂₉	—	2	2	no	—
455	C₄×C₂₉	—	2	2	no	—
456	C₄×C₂₉	—	4	2	no	—
457	C₄×C₂₉	—	4	1	no	—
458	C₄×C₂₉	—	4	2	no	—
459	C₄×C₂₉	—	4	1	no	—
460	C₄×C₂₉	—	4	1	no	—
461	C₄×C₂₉	—	8	1	no	—
462	C₄×C₂₉	C₂×#120	1	1	yes	characteristic
463	C₄×C₂₉	C₂×#121	1	1	yes	characteristic
464	C₄×C₂₉	D₄²	1	1	yes	characteristic
465	C₄×C₂₉	#546	1	1	yes	characteristic
466	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
467	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic
468	#577	—	2	4	no	—
469	#577	—	2	4	no	—
470	C₂×#137	—	2	1	no	—
471	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
472	C₂×AGL(1,ℤ/8)	—	2	1	no	—
473	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
474	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
475	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
476	C₂×#135	—	2	1	no	—
477	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
478	C₂²×SD₁₆	—	2	1	no	—
479	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
480	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
481	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
482	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
483	#535	C₂²×C₂₉	1	1	yes	characteristic, complemented
484	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
485	#520	C₂²×C₂₉	1	1	yes	characteristic
486	#471	—	2	4	no	—
487	#464	—	2	1	no	—
488	#463	—	2	1	no	—
489	#460	—	2	1	no	—
490	#459	—	2	1	no	—
491	#453	—	2	4	no	—
492	#449	—	2	1	no	—
493	#449	—	2	1	no	—
494	#448	—	2	1	no	—
495	#448	—	2	1	no	—
496	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic, complemented
497	#424	C₂²×C₂₉	1	1	yes	characteristic, complemented
498	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
499	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
500	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic, complemented
501	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
502	#418	—	2	1	no	—
503	#418	C₂²×C₂₉	1	1	yes	characteristic
504	#417	—	2	1	no	—
505	#417	C₂²×C₂₉	1	1	yes	characteristic
506	#417	C₂²×C₂₉	1	1	yes	characteristic, complemented
507	#416	—	2	1	no	—
508	#416	C₂²×C₂₉	1	1	yes	characteristic
509	C₂×#102	—	2	1	no	—
510	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic
511	C₂×#102	C₂²×C₂₉	1	1	yes	characteristic, complemented
512	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic, complemented
513	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
514	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic, complemented
515	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
516	#391	C₂²×C₂₉	1	1	yes	characteristic, complemented
517	#343	C₂²×C₂₉	1	1	yes	characteristic, complemented
518	#341	C₂²×C₂₉	1	1	yes	characteristic, complemented
519	#339	C₂²×C₂₉	1	1	yes	characteristic, complemented
520	#336	C₂²×C₂₉	1	1	yes	characteristic, complemented
521	C₂×C₂₉	—	2	1	no	—
522	C₂×C₂₉	—	2	1	no	—
523	C₂×C₂₉	—	4	2	no	—
524	C₂×C₂₉	—	4	2	no	—
525	C₂×C₂₉	—	8	1	no	—
526	C₂×C₂₉	—	8	2	no	—
527	C₂×C₂₉	—	16	1	no	—
528	C₂×C₂₉	#2410	1	1	yes	characteristic
529	C₂×C₂₉	#3288	1	1	yes	characteristic
530	C₂×C₂₉	#3291	1	1	yes	characteristic
531	2₋¹⁺⁴	—	2	2	no	—
532	2₋¹⁺⁴	—	2	2	no	—
533	2₋¹⁺⁴	—	2	2	no	—
534	2₋¹⁺⁴	—	4	1	no	—
535	H(5,𝔽₂)	—	2	2	no	—
536	H(5,𝔽₂)	—	2	2	no	—
537	H(5,𝔽₂)	—	4	1	no	—
538	H(5,𝔽₂)	D₄×C₂₉	1	4	yes	complemented
539	C₂×#41	—	2	1	no	—
540	C₂×#41	—	2	1	no	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	—	4	1	no	—
544	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
545	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
546	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
547	C₂²×Q₈	—	2	1	no	—
548	C₂²×Q₈	—	2	1	no	—
549	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	4	1	no	—
553	C₂²×D₄	—	4	1	no	—
554	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
556	#137	—	2	8	no	—
557	#137	—	2	2	no	—
558	#137	D₄×C₂₉	1	4	yes	complemented
559	AGL(1,ℤ/8)	—	2	8	no	—
560	AGL(1,ℤ/8)	—	2	2	no	—
561	AGL(1,ℤ/8)	—	2	2	no	—
562	AGL(1,ℤ/8)	—	2	2	no	—
563	AGL(1,ℤ/8)	—	2	2	no	—
564	AGL(1,ℤ/8)	—	2	2	no	—
565	AGL(1,ℤ/8)	—	2	2	no	—
566	#135	—	2	8	no	—
567	#135	—	2	2	no	—
568	#135	—	2	2	no	—
569	C₂×Q₁₆	—	2	1	no	—
570	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic, complemented
571	C₂×SD₁₆	—	2	8	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	2	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	2	no	—
576	C₂×SD₁₆	—	2	2	no	—
577	C₂×SD₁₆	—	2	1	no	—
578	C₂×SD₁₆	—	2	1	no	—
579	C₂×SD₁₆	—	2	1	no	—
580	C₂×SD₁₆	—	2	1	no	—
581	C₂×SD₁₆	—	2	1	no	—
582	C₂×SD₁₆	—	2	1	no	—
583	C₂×SD₁₆	—	4	1	no	—
584	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic, complemented
585	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic, complemented
586	C₂×D₈	—	2	1	no	—
587	C₂×D₈	—	2	1	no	—
588	C₂×D₈	—	2	1	no	—
589	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic, complemented
590	#131	—	2	2	no	—
591	#131	—	2	2	no	—
592	#131	—	2	2	no	—
593	#131	—	4	1	no	—
594	C₂×M₁₆	—	2	1	no	—
595	C₂×M₁₆	—	2	1	no	—
596	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
598	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
599	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
600	C₂²×C₈	—	2	1	no	—
601	C₂²×C₈	—	2	1	no	—
602	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
603	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
604	#127	—	2	2	no	—
605	#127	—	2	1	no	—
606	#127	—	4	1	no	—
607	#124	—	2	1	no	—
608	#121	—	2	1	no	—
609	#121	—	2	1	no	—
610	#120	—	4	1	no	—
611	C₄×Q₈	—	2	1	no	—
612	C₄×D₄	—	2	1	no	—
613	C₄×D₄	—	4	1	no	—
614	#117	—	2	1	no	—
615	#117	C₂³×C₂₉	1	1	yes	characteristic
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
618	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
619	#108	—	2	2	no	—
620	C₄⋊C₈	—	2	1	no	—
621	C₄⋊C₈	—	2	1	no	—
622	#104	—	2	2	no	—
623	#104	—	2	2	no	—
624	#104	—	4	1	no	—
625	#103	—	2	1	no	—
626	#103	—	2	1	no	—
627	#103	—	2	1	no	—
628	#103	—	2	1	no	—
629	#103	D₄×C₂₉	1	1	yes	characteristic, complemented
630	#103	D₄×C₂₉	1	1	yes	characteristic, complemented
631	#102	—	2	1	no	—
632	#102	—	2	1	no	—
633	#102	—	2	1	no	—
634	#102	—	2	1	no	—
635	#102	—	2	1	no	—
636	#102	—	2	1	no	—
637	#102	—	2	1	no	—
638	#102	—	2	1	no	—
639	#102	D₄×C₂₉	1	1	yes	characteristic, complemented
640	#102	D₄×C₂₉	1	1	yes	characteristic, complemented
641	#101	—	2	2	no	—
642	#100	—	2	2	no	—
643	#100	—	2	2	no	—
644	C₂²⋊C₈	—	2	1	no	—
645	C₂²⋊C₈	—	2	1	no	—
646	#95	—	4	1	no	—
647	C₂₉	#24457	1	1	yes	characteristic, direct product factor, Sylow
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	4	1	no	—
651	#41	—	2	1	no	—
652	#41	—	2	1	no	—
653	#41	—	2	1	no	—
654	#41	—	2	1	no	—
655	#41	—	2	4	no	—
656	#41	—	2	4	no	—
657	#41	—	2	4	no	—
658	#41	—	2	1	no	—
659	#41	—	2	1	no	—
660	#41	—	2	1	no	—
661	#41	—	2	1	no	—
662	#41	—	4	2	no	—
663	#41	—	4	4	no	—
664	#41	—	4	2	no	—
665	#41	—	4	2	no	—
666	#41	—	4	2	no	—
667	#41	—	4	4	no	—
668	#41	—	4	2	no	—
669	#41	C₂×D₄×C₂₉	1	2	yes	—
670	#41	C₂×D₄×C₂₉	1	2	yes	—
671	#41	C₂×D₄×C₂₉	1	2	yes	—
672	#41	#41×C₂₉	1	2	yes	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	2	1	no	—
676	C₂×Q₈	—	2	1	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	4	1	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	2	no	—
683	C₂×Q₈	C₂×D₄×C₂₉	1	2	yes	—
684	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
685	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
686	C₂×Q₈	C₂×D₄×C₂₉	1	1	yes	characteristic
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	4	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	1	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	1	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	4	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	4	no	—
713	C₂×D₄	—	8	2	no	—
714	C₂×D₄	—	8	2	no	—
715	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
716	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
717	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
718	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	4	1	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	—	4	1	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
730	Q₁₆	—	2	4	no	—
731	Q₁₆	—	2	2	no	—
732	SD₁₆	—	2	4	no	—
733	SD₁₆	—	2	4	no	—
734	SD₁₆	—	2	4	no	—
735	SD₁₆	—	2	2	no	—
736	SD₁₆	—	2	2	no	—
737	SD₁₆	—	2	4	no	—
738	SD₁₆	—	4	2	no	—
739	SD₁₆	—	4	2	no	—
740	SD₁₆	—	4	2	no	—
741	SD₁₆	—	4	2	no	—
742	D₈	—	2	4	no	—
743	D₈	—	2	2	no	—
744	D₈	—	4	2	no	—
745	D₈	—	4	2	no	—
746	M₁₆	—	2	4	no	—
747	M₁₆	—	2	1	no	—
748	M₁₆	—	2	1	no	—
749	M₁₆	—	2	1	no	—
750	M₁₆	—	2	1	no	—
751	M₁₆	—	2	1	no	—
752	M₁₆	—	2	1	no	—
753	M₁₆	—	2	1	no	—
754	M₁₆	—	4	2	no	—
755	M₁₆	C₂×D₄×C₂₉	1	2	yes	—
756	C₂×C₈	—	2	4	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	—	2	1	no	—
759	C₂×C₈	—	2	1	no	—
760	C₂×C₈	—	2	1	no	—
761	C₂×C₈	—	2	1	no	—
762	C₂×C₈	—	2	1	no	—
763	C₂×C₈	—	2	1	no	—
764	C₂×C₈	—	2	1	no	—
765	C₂×C₈	—	4	2	no	—
766	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
767	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
768	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
769	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	4	1	no	—
773	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
774	C₄⋊C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	4	1	no	—
777	C₂²⋊C₄	—	4	1	no	—
778	C₂²⋊C₄	—	4	1	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	1	no	—
782	C₄²	—	4	1	no	—
783	C₂³	—	2	1	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	4	4	no	—
788	C₂³	—	4	1	no	—
789	C₂³	—	4	1	no	—
790	C₂³	—	4	1	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	1	no	—
793	C₂³	—	8	1	no	—
794	C₂³	—	8	1	no	—
795	C₂³	—	8	1	no	—
796	C₂³	—	8	1	no	—
797	C₂³	—	16	1	no	—
798	C₂³	—	16	1	no	—
799	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
800	Q₈	—	2	1	no	—
801	Q₈	—	2	1	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	2	1	no	—
804	Q₈	—	2	2	no	—
805	Q₈	—	2	1	no	—
806	Q₈	—	4	4	no	—
807	Q₈	—	4	1	no	—
808	Q₈	—	4	1	no	—
809	Q₈	C₂₉×#120	1	2	yes	—
810	Q₈	C₂₉×#121	1	2	yes	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	1	no	—
816	D₄	—	2	2	no	—
817	D₄	—	2	2	no	—
818	D₄	—	2	1	no	—
819	D₄	—	2	1	no	—
820	D₄	—	2	1	no	—
821	D₄	—	4	4	no	—
822	D₄	—	4	4	no	—
823	D₄	—	4	4	no	—
824	D₄	—	4	1	no	—
825	D₄	—	4	1	no	—
826	D₄	—	4	1	no	—
827	D₄	—	4	1	no	—
828	D₄	—	4	1	no	—
829	D₄	—	4	1	no	—
830	D₄	—	4	1	no	—
831	D₄	—	4	1	no	—
832	D₄	—	8	8	no	—
833	D₄	—	16	1	no	—
834	D₄	—	16	1	no	—
835	D₄	C₂₉×#120	1	2	yes	—
836	D₄	C₂₉×#121	1	2	yes	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	4	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	8	1	no	—
859	C₂×C₄	—	16	1	no	—
860	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
861	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
864	C₂×C₄	C₂×#41×C₂₉	1	1	yes	characteristic
865	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
866	C₈	—	2	1	no	—
867	C₈	—	2	2	no	—
868	C₈	—	2	1	no	—
869	C₈	—	2	1	no	—
870	C₈	—	2	1	no	—
871	C₈	—	4	1	no	—
872	C₈	—	4	1	no	—
873	C₈	—	4	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	1	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	8	2	no	—
887	C₂²	—	8	2	no	—
888	C₂²	—	8	1	no	—
889	C₂²	—	8	1	no	—
890	C₂²	—	8	1	no	—
891	C₂²	—	8	1	no	—
892	C₂²	—	8	1	no	—
893	C₂²	—	16	1	no	—
894	C₂²	—	16	1	no	—
895	C₂²	—	16	4	no	—
896	C₂²	C₂₉×#534	1	1	yes	characteristic
897	C₂²	D₄²×C₂₉	1	1	yes	characteristic
898	C₂²	C₂₉×#546	1	1	yes	characteristic
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	1	no	—
903	C₄	—	4	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	8	1	no	—
907	C₄	C₂×C₂₉×#120	1	1	yes	characteristic
908	C₄	C₂×C₂₉×#121	1	1	yes	characteristic
909	C₄	D₄²×C₂₉	1	1	yes	characteristic
910	C₄	C₂₉×#546	1	1	yes	characteristic
911	C₂	—	2	1	no	—
912	C₂	—	2	1	no	—
913	C₂	—	4	2	no	—
914	C₂	—	4	2	no	—
915	C₂	—	8	1	no	—
916	C₂	—	8	2	no	—
917	C₂	—	16	1	no	—
918	C₂	C₂₉×#2410	1	1	yes	characteristic
919	C₂	C₂₉×#3288	1	1	yes	characteristic
920	C₂	C₂₉×#3291	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₉
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
1. C₂×C₂₉×#577	C₂	semidirect
2. C₂×C₂₉×#471	C₂	semidirect
3. C₂₉×#3045	C₂	semidirect
4. C₂×C₂₉×#453	C₂	semidirect
5. C₂₉×#3010	C₂	semidirect
6. C₂₉×#2897	C₂	semidirect
7. C₂₉×#2051	C₂	semidirect
8. C₂₉×#2046	C₂	semidirect
9. C₂₉×#2014	C₂	semidirect
10. C₂₉×#2002	C₂	semidirect
11. C₂₉×#1907	C₂	semidirect
12. C₂₉×#1882	C₂	semidirect
13. C₂₉×#1876	C₂	semidirect
14. C₂₉×#1866	C₂	semidirect
15. C₂₉×#1793	C₂	semidirect
30. C₂²×SD₁₆×C₂₉	C₂²	semidirect
33. C₂₉×#535	C₂²	semidirect
46. C₂×C₂₉×#108	C₂²	semidirect
47. C₂₉×#424	C₂²	semidirect
50. C₂×C₂₉×#104	C₂²	semidirect
51. C₂₉×#419	C₂²	semidirect
56. C₂₉×#417	C₂²	semidirect
61. C₂×C₂₉×#102	C₂²	semidirect
62. C₂×C₂₉×#101	C₂²	semidirect
64. C₂×C₂₉×#100	C₂²	semidirect
65. C₂₉×#408	C₂²	semidirect
66. C₂₉×#391	C₂²	semidirect
67. C₂₉×#343	C₂²	semidirect
68. C₂₉×#341	C₂²	semidirect
69. C₂₉×#339	C₂²	semidirect
70. C₂₉×#336	C₂²	semidirect
78. C₂₉×H(5,𝔽₂)	D₄	semidirect
98. C₂₉×#137	D₄	semidirect
110. C₂×Q₁₆×C₂₉	D₄	semidirect
124. C₂×SD₁₆×C₂₉	D₄	semidirect
125. C₂×SD₁₆×C₂₉	D₄	semidirect
129. C₂×D₈×C₂₉	D₄	semidirect
169. C₂₉×#103	D₄	semidirect
170. C₂₉×#103	D₄	semidirect
179. C₂₉×#102	D₄	semidirect
180. C₂₉×#102	D₄	semidirect
322. #24457	C₂₉	direct (N × H)
414. C₂×#577	C₂×C₂₉	semidirect
415. C₂×#471	C₂×C₂₉	semidirect
416. #3045	C₂×C₂₉	semidirect
417. C₂×#453	C₂×C₂₉	semidirect
418. #3010	C₂×C₂₉	semidirect
419. #2897	C₂×C₂₉	semidirect
420. #2051	C₂×C₂₉	semidirect
421. #2046	C₂×C₂₉	semidirect
422. #2014	C₂×C₂₉	semidirect
423. #2002	C₂×C₂₉	semidirect
424. #1907	C₂×C₂₉	semidirect
425. #1882	C₂×C₂₉	semidirect
426. #1876	C₂×C₂₉	semidirect
427. #1866	C₂×C₂₉	semidirect
428. #1793	C₂×C₂₉	semidirect
480. C₂²×SD₁₆	C₂²×C₂₉	semidirect
483. #535	C₂²×C₂₉	semidirect
496. C₂×#108	C₂²×C₂₉	semidirect
497. #424	C₂²×C₂₉	semidirect
500. C₂×#104	C₂²×C₂₉	semidirect
501. #419	C₂²×C₂₉	semidirect
506. #417	C₂²×C₂₉	semidirect
511. C₂×#102	C₂²×C₂₉	semidirect
512. C₂×#101	C₂²×C₂₉	semidirect
514. C₂×#100	C₂²×C₂₉	semidirect
515. #408	C₂²×C₂₉	semidirect
516. #391	C₂²×C₂₉	semidirect
517. #343	C₂²×C₂₉	semidirect
518. #341	C₂²×C₂₉	semidirect
519. #339	C₂²×C₂₉	semidirect
520. #336	C₂²×C₂₉	semidirect
538. H(5,𝔽₂)	D₄×C₂₉	semidirect
558. #137	D₄×C₂₉	semidirect
570. C₂×Q₁₆	D₄×C₂₉	semidirect
584. C₂×SD₁₆	D₄×C₂₉	semidirect
585. C₂×SD₁₆	D₄×C₂₉	semidirect
589. C₂×D₈	D₄×C₂₉	semidirect
629. #103	D₄×C₂₉	semidirect
630. #103	D₄×C₂₉	semidirect
639. #102	D₄×C₂₉	semidirect
640. #102	D₄×C₂₉	semidirect
647. C₂₉	#24457	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×#577	2
C₂×C₂₉×#471	2
C₂₉×#3045	2
C₂×C₂₉×#453	2
C₂₉×#3010	2
C₂₉×#2897	2
C₂₉×#2051	2
C₂₉×#2046	2
C₂₉×#2014	2
C₂₉×#2002	2
C₂₉×#1907	2
C₂₉×#1882	2
C₂₉×#1876	2
C₂₉×#1866	2
C₂₉×#1793	2
#24457	29

Subgroups — C29×#24457 #20319357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#24457 #20319357