Subgroups — C₂₉×#25802 #20320702

Order 7424.

1476 conjugacy classes of subgroups.

The subgroup lattice has 900 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	C₂₉×#3154	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₉×#471	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#456	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₉×#453	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₉×#3010	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₉×#3009	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₉×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2005	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₉×#2002	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#1977	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₉×#1974	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₉×#1764	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×#137	C₂²	1	1	yes	characteristic
23	C₂×C₂₉×#137	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₉×AGL(1,ℤ/8)	—	2	1	no	—
25	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
26	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
28	C₂×C₂₉×#135	—	2	1	no	—
29	C₂×C₂₉×#135	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₂₉	—	2	1	no	—
31	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
34	C₂²×SD₁₆×C₂₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₉×#131	C₂²	1	1	yes	characteristic
36	C₂₉×#536	C₂²	1	1	yes	characteristic
37	C₂₉×#535	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂₉×#127	C₂²	1	1	yes	characteristic
40	C₂₉×#497	—	2	1	no	—
41	C₂₉×#496	—	2	1	no	—
42	C₂₉×#495	—	2	1	no	—
43	C₂₉×#492	—	2	4	no	—
44	C₂₉×#492	—	2	1	no	—
45	C₂₉×#471	—	2	4	no	—
46	C₂₉×#456	—	2	4	no	—
47	C₂₉×#453	—	2	4	no	—
48	C₂₉×#452	—	2	2	no	—
49	C₂₉×#450	—	2	2	no	—
50	C₂₉×#449	—	2	2	no	—
51	C₂₉×#448	—	2	2	no	—
52	C₂×C₂₉×#108	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
54	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic
55	C₂×C₂₉×#104	C₂²	1	1	yes	characteristic, complemented
56	C₂₉×#419	C₂²	1	1	yes	characteristic, complemented
57	C₂₉×#418	C₂²	1	1	yes	characteristic
58	C₂₉×#416	C₂²	1	1	yes	characteristic
59	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₉×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic
62	C₂×C₂₉×#100	C₂²	1	1	yes	characteristic, complemented
63	C₂₉×#408	C₂²	1	1	yes	characteristic
64	C₂₉×#408	C₂²	1	1	yes	characteristic, complemented
65	C₂₉×#405	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×C₈×C₂₉	C₂²	1	1	yes	characteristic, complemented
67	C₂₉×#341	C₂²	1	1	yes	characteristic, complemented
68	C₂₉×#339	C₂²	1	1	yes	characteristic, complemented
69	C₂₉×2₋¹⁺⁴	—	2	2	no	—
70	C₂₉×2₋¹⁺⁴	—	2	2	no	—
71	C₂₉×2₋¹⁺⁴	—	2	2	no	—
72	C₂₉×2₋¹⁺⁴	—	4	1	no	—
73	C₂₉×H(5,𝔽₂)	—	2	2	no	—
74	C₂₉×H(5,𝔽₂)	—	2	2	no	—
75	C₂₉×H(5,𝔽₂)	—	2	2	no	—
76	C₂₉×H(5,𝔽₂)	—	4	1	no	—
77	C₂×#41×C₂₉	—	2	1	no	—
78	C₂×#41×C₂₉	—	2	1	no	—
79	C₂×#41×C₂₉	—	2	1	no	—
80	C₂×#41×C₂₉	—	2	1	no	—
81	C₂×#41×C₂₉	—	4	1	no	—
82	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
83	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
84	C₂×#41×C₂₉	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₂₉	—	2	1	no	—
86	C₂²×Q₈×C₂₉	—	2	1	no	—
87	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₂₉	—	2	1	no	—
90	C₂²×D₄×C₂₉	—	2	1	no	—
91	C₂²×D₄×C₂₉	—	4	1	no	—
92	C₂²×D₄×C₂₉	—	4	1	no	—
93	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
95	C₂₉×#137	—	2	8	no	—
96	C₂₉×#137	—	2	2	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	—	4	1	no	—
102	C₂₉×AGL(1,ℤ/8)	—	2	8	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×AGL(1,ℤ/8)	—	2	2	no	—
107	C₂₉×AGL(1,ℤ/8)	—	2	2	no	—
108	C₂₉×AGL(1,ℤ/8)	—	4	1	no	—
109	C₂₉×#135	—	2	8	no	—
110	C₂₉×#135	—	2	2	no	—
111	C₂₉×#135	—	2	2	no	—
112	C₂×Q₁₆×C₂₉	—	2	1	no	—
113	C₂×Q₁₆×C₂₉	—	2	1	no	—
114	C₂×Q₁₆×C₂₉	—	2	1	no	—
115	C₂×Q₁₆×C₂₉	D₄	1	1	yes	characteristic, complemented
116	C₂×SD₁₆×C₂₉	—	2	8	no	—
117	C₂×SD₁₆×C₂₉	—	2	1	no	—
118	C₂×SD₁₆×C₂₉	—	2	1	no	—
119	C₂×SD₁₆×C₂₉	—	2	1	no	—
120	C₂×SD₁₆×C₂₉	—	2	2	no	—
121	C₂×SD₁₆×C₂₉	—	2	1	no	—
122	C₂×SD₁₆×C₂₉	—	2	1	no	—
123	C₂×SD₁₆×C₂₉	—	2	2	no	—
124	C₂×SD₁₆×C₂₉	—	2	1	no	—
125	C₂×SD₁₆×C₂₉	—	2	1	no	—
126	C₂×SD₁₆×C₂₉	—	2	1	no	—
127	C₂×SD₁₆×C₂₉	—	2	2	no	—
128	C₂×SD₁₆×C₂₉	—	2	2	no	—
129	C₂×SD₁₆×C₂₉	—	2	2	no	—
130	C₂×SD₁₆×C₂₉	—	2	2	no	—
131	C₂×SD₁₆×C₂₉	—	2	2	no	—
132	C₂×SD₁₆×C₂₉	—	2	1	no	—
133	C₂×SD₁₆×C₂₉	—	2	1	no	—
134	C₂×SD₁₆×C₂₉	—	4	1	no	—
135	C₂×SD₁₆×C₂₉	—	4	1	no	—
136	C₂×SD₁₆×C₂₉	D₄	1	4	yes	complemented
137	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic, complemented
138	C₂×SD₁₆×C₂₉	D₄	1	1	yes	characteristic, complemented
139	C₂×D₈×C₂₉	—	2	1	no	—
140	C₂×D₈×C₂₉	—	2	1	no	—
141	C₂×D₈×C₂₉	—	2	1	no	—
142	C₂×D₈×C₂₉	D₄	1	1	yes	characteristic, complemented
143	C₂₉×#131	—	2	2	no	—
144	C₂₉×#131	D₄	1	4	yes	complemented
145	C₂×M₁₆×C₂₉	—	2	1	no	—
146	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₂₉	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₉	—	2	1	no	—
151	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₂₉	C₂³	1	1	yes	characteristic
153	C₂₉×C₄⋊Q₈	—	2	2	no	—
154	C₂₉×C₄⋊Q₈	—	2	1	no	—
155	C₂₉×C₄⋊Q₈	—	2	2	no	—
156	C₂₉×#127	—	2	2	no	—
157	C₂₉×#127	—	2	1	no	—
158	C₂₉×#127	—	2	2	no	—
159	C₂₉×#124	—	2	1	no	—
160	C₂₉×#124	—	2	1	no	—
161	C₂₉×#123	—	4	1	no	—
162	C₂₉×C₂²⋊Q₈	—	2	2	no	—
163	C₂₉×#121	—	2	2	no	—
164	C₂₉×#120	—	4	1	no	—
165	C₂₉×#117	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₂₉	—	4	1	no	—
167	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
168	C₂₉×#108	—	2	2	no	—
169	C₂₉×#104	—	2	2	no	—
170	C₂₉×#104	—	2	2	no	—
171	C₂₉×#104	D₄	1	4	yes	complemented
172	C₂₉×#103	—	2	2	no	—
173	C₂₉×#103	D₄	1	2	yes	complemented
174	C₂₉×#102	—	2	2	no	—
175	C₂₉×#102	D₄	1	2	yes	complemented
176	C₂₉×#101	—	2	2	no	—
177	C₂₉×#101	—	2	2	no	—
178	C₂₉×#100	—	2	2	no	—
179	C₂₉×#100	—	2	2	no	—
180	C₂₉×C₂²⋊C₈	—	2	2	no	—
181	C₂₉×C₂²⋊C₈	—	2	2	no	—
182	C₂₉×#97	—	2	1	no	—
183	C₄×C₈×C₂₉	—	2	2	no	—
184	C₄×C₈×C₂₉	—	2	1	no	—
185	C₂⁴×C₂₉	—	2	1	no	—
186	C₂⁴×C₂₉	—	2	1	no	—
187	C₂⁴×C₂₉	—	4	1	no	—
188	#41×C₂₉	—	2	1	no	—
189	#41×C₂₉	—	2	1	no	—
190	#41×C₂₉	—	2	4	no	—
191	#41×C₂₉	—	2	4	no	—
192	#41×C₂₉	—	2	1	no	—
193	#41×C₂₉	—	2	1	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	—	2	1	no	—
199	#41×C₂₉	—	2	1	no	—
200	#41×C₂₉	—	4	2	no	—
201	#41×C₂₉	—	4	4	no	—
202	#41×C₂₉	—	4	2	no	—
203	#41×C₂₉	—	4	2	no	—
204	#41×C₂₉	—	4	2	no	—
205	#41×C₂₉	—	4	4	no	—
206	#41×C₂₉	—	4	2	no	—
207	#41×C₂₉	—	4	2	no	—
208	#41×C₂₉	C₂×D₄	1	2	yes	—
209	#41×C₂₉	C₂×D₄	1	2	yes	—
210	C₂×Q₈×C₂₉	—	2	1	no	—
211	C₂×Q₈×C₂₉	—	2	4	no	—
212	C₂×Q₈×C₂₉	—	2	1	no	—
213	C₂×Q₈×C₂₉	—	2	1	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	—	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	—	4	1	no	—
223	C₂×Q₈×C₂₉	—	4	2	no	—
224	C₂×Q₈×C₂₉	—	4	2	no	—
225	C₂×Q₈×C₂₉	—	4	2	no	—
226	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
227	C₂×Q₈×C₂₉	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
229	C₂×Q₈×C₂₉	C₂×D₄	1	1	yes	characteristic
230	C₂×D₄×C₂₉	—	2	1	no	—
231	C₂×D₄×C₂₉	—	2	4	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	—	2	1	no	—
243	C₂×D₄×C₂₉	—	2	1	no	—
244	C₂×D₄×C₂₉	—	2	1	no	—
245	C₂×D₄×C₂₉	—	4	2	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	2	no	—
250	C₂×D₄×C₂₉	—	4	2	no	—
251	C₂×D₄×C₂₉	—	4	4	no	—
252	C₂×D₄×C₂₉	—	4	4	no	—
253	C₂×D₄×C₂₉	—	4	1	no	—
254	C₂×D₄×C₂₉	—	4	2	no	—
255	C₂×D₄×C₂₉	—	8	4	no	—
256	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₂₉	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₂₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
265	C₂²×C₄×C₂₉	—	2	1	no	—
266	C₂²×C₄×C₂₉	—	4	1	no	—
267	C₂²×C₄×C₂₉	—	4	1	no	—
268	C₂²×C₄×C₂₉	—	4	1	no	—
269	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
270	Q₁₆×C₂₉	—	2	4	no	—
271	Q₁₆×C₂₉	—	2	2	no	—
272	Q₁₆×C₂₉	—	4	2	no	—
273	Q₁₆×C₂₉	—	4	2	no	—
274	SD₁₆×C₂₉	—	2	4	no	—
275	SD₁₆×C₂₉	—	2	4	no	—
276	SD₁₆×C₂₉	—	2	2	no	—
277	SD₁₆×C₂₉	—	2	4	no	—
278	SD₁₆×C₂₉	—	2	4	no	—
279	SD₁₆×C₂₉	—	2	2	no	—
280	SD₁₆×C₂₉	—	4	4	no	—
281	SD₁₆×C₂₉	—	4	2	no	—
282	SD₁₆×C₂₉	—	4	4	no	—
283	SD₁₆×C₂₉	—	4	2	no	—
284	SD₁₆×C₂₉	—	4	2	no	—
285	SD₁₆×C₂₉	—	4	2	no	—
286	SD₁₆×C₂₉	—	4	2	no	—
287	SD₁₆×C₂₉	—	4	2	no	—
288	D₈×C₂₉	—	2	4	no	—
289	D₈×C₂₉	—	2	2	no	—
290	D₈×C₂₉	—	4	2	no	—
291	D₈×C₂₉	—	4	2	no	—
292	M₁₆×C₂₉	—	2	1	no	—
293	M₁₆×C₂₉	—	2	1	no	—
294	M₁₆×C₂₉	—	2	4	no	—
295	M₁₆×C₂₉	—	2	1	no	—
296	M₁₆×C₂₉	—	2	1	no	—
297	M₁₆×C₂₉	—	2	1	no	—
298	M₁₆×C₂₉	—	2	1	no	—
299	M₁₆×C₂₉	C₂×D₄	1	2	yes	—
300	M₁₆×C₂₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
305	C₂×C₈×C₂₉	—	2	4	no	—
306	C₂×C₈×C₂₉	—	2	1	no	—
307	C₂×C₈×C₂₉	—	2	1	no	—
308	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
309	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
310	C₂×C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
311	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
312	C₂×C₈×C₂₉	C₂×D₄	1	2	yes	—
313	C₄⋊C₄×C₂₉	—	4	4	no	—
314	C₄⋊C₄×C₂₉	—	4	2	no	—
315	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
316	C₂²⋊C₄×C₂₉	—	2	1	no	—
317	C₂²⋊C₄×C₂₉	—	4	2	no	—
318	C₂²⋊C₄×C₂₉	—	4	2	no	—
319	C₄²×C₂₉	—	2	1	no	—
320	C₄²×C₂₉	—	2	1	no	—
321	C₄²×C₂₉	C₂×D₄	1	2	yes	—
322	#25802	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	2	no	—
334	C₂³×C₂₉	—	8	2	no	—
335	C₂³×C₂₉	—	16	2	no	—
336	C₂³×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
337	Q₈×C₂₉	—	2	1	no	—
338	Q₈×C₂₉	—	2	1	no	—
339	Q₈×C₂₉	—	2	2	no	—
340	Q₈×C₂₉	—	2	1	no	—
341	Q₈×C₂₉	—	2	2	no	—
342	Q₈×C₂₉	—	2	1	no	—
343	Q₈×C₂₉	—	2	1	no	—
344	Q₈×C₂₉	—	4	4	no	—
345	Q₈×C₂₉	—	4	1	no	—
346	Q₈×C₂₉	—	4	1	no	—
347	Q₈×C₂₉	—	4	1	no	—
348	Q₈×C₂₉	—	4	1	no	—
349	Q₈×C₂₉	—	4	1	no	—
350	Q₈×C₂₉	—	4	1	no	—
351	Q₈×C₂₉	#127	1	2	yes	—
352	D₄×C₂₉	—	2	2	no	—
353	D₄×C₂₉	—	2	2	no	—
354	D₄×C₂₉	—	2	1	no	—
355	D₄×C₂₉	—	2	2	no	—
356	D₄×C₂₉	—	2	1	no	—
357	D₄×C₂₉	—	2	1	no	—
358	D₄×C₂₉	—	2	1	no	—
359	D₄×C₂₉	—	2	2	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	—	4	1	no	—
373	D₄×C₂₉	—	4	1	no	—
374	D₄×C₂₉	—	8	8	no	—
375	D₄×C₂₉	—	16	2	no	—
376	D₄×C₂₉	#127	1	2	yes	—
377	C₂×C₄×C₂₉	—	2	4	no	—
378	C₂×C₄×C₂₉	—	2	2	no	—
379	C₂×C₄×C₂₉	—	2	1	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	—	4	4	no	—
387	C₂×C₄×C₂₉	—	4	4	no	—
388	C₂×C₄×C₂₉	—	4	4	no	—
389	C₂×C₄×C₂₉	—	4	1	no	—
390	C₂×C₄×C₂₉	—	4	1	no	—
391	C₂×C₄×C₂₉	—	4	1	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	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
404	C₈×C₂₉	—	2	2	no	—
405	C₈×C₂₉	—	2	2	no	—
406	C₈×C₂₉	—	2	2	no	—
407	C₈×C₂₉	—	4	1	no	—
408	C₈×C₂₉	—	4	1	no	—
409	C₈×C₂₉	#120	1	2	yes	—
410	C₈×C₂₉	#120	1	2	yes	—
411	C₂×#577	C₂×C₂₉	1	1	yes	characteristic, complemented
412	#3154	C₂×C₂₉	1	1	yes	characteristic, complemented
413	C₂×#492	C₂×C₂₉	1	1	yes	characteristic, complemented
414	C₂×#471	C₂×C₂₉	1	1	yes	characteristic, complemented
415	C₂×#456	C₂×C₂₉	1	1	yes	characteristic, complemented
416	C₂×#453	C₂×C₂₉	1	1	yes	characteristic, complemented
417	#3010	C₂×C₂₉	1	1	yes	characteristic, complemented
418	#3009	C₂×C₂₉	1	1	yes	characteristic, complemented
419	#2019	C₂×C₂₉	1	1	yes	characteristic, complemented
420	#2019	C₂×C₂₉	1	1	yes	characteristic, complemented
421	#2005	C₂×C₂₉	1	1	yes	characteristic, complemented
422	#2002	C₂×C₂₉	1	1	yes	characteristic, complemented
423	#1977	C₂×C₂₉	1	1	yes	characteristic, complemented
424	#1974	C₂×C₂₉	1	1	yes	characteristic, complemented
425	#1764	C₂×C₂₉	1	1	yes	characteristic, complemented
426	C₂²×C₂₉	—	2	2	no	—
427	C₂²×C₂₉	—	2	2	no	—
428	C₂²×C₂₉	—	4	2	no	—
429	C₂²×C₂₉	—	4	1	no	—
430	C₂²×C₂₉	—	4	1	no	—
431	C₂²×C₂₉	—	4	2	no	—
432	C₂²×C₂₉	—	4	2	no	—
433	C₂²×C₂₉	—	4	2	no	—
434	C₂²×C₂₉	—	8	2	no	—
435	C₂²×C₂₉	—	8	2	no	—
436	C₂²×C₂₉	—	8	2	no	—
437	C₂²×C₂₉	—	8	1	no	—
438	C₂²×C₂₉	—	8	2	no	—
439	C₂²×C₂₉	—	16	1	no	—
440	C₂²×C₂₉	—	16	1	no	—
441	C₂²×C₂₉	—	16	4	no	—
442	C₂²×C₂₉	#535	1	1	yes	characteristic
443	C₂²×C₂₉	D₄²	1	1	yes	characteristic
444	C₂²×C₂₉	D₄²	1	1	yes	characteristic
445	C₄×C₂₉	—	2	4	no	—
446	C₄×C₂₉	—	2	2	no	—
447	C₄×C₂₉	—	4	1	no	—
448	C₄×C₂₉	—	4	2	no	—
449	C₄×C₂₉	—	4	1	no	—
450	C₄×C₂₉	—	4	2	no	—
451	C₄×C₂₉	—	8	1	no	—
452	C₄×C₂₉	C₂×#120	1	1	yes	characteristic
453	C₄×C₂₉	C₂×#127	1	1	yes	characteristic
454	C₄×C₂₉	D₄²	1	1	yes	characteristic
455	C₄×C₂₉	D₄²	1	1	yes	characteristic
456	C₂×2₋¹⁺⁴	C₂²×C₂₉	1	1	yes	characteristic
457	C₂×H(5,𝔽₂)	C₂²×C₂₉	1	1	yes	characteristic
458	#577	—	2	4	no	—
459	#577	—	2	4	no	—
460	C₂×#137	—	2	1	no	—
461	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
462	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic
463	C₂×#137	C₂²×C₂₉	1	1	yes	characteristic, complemented
464	C₂×AGL(1,ℤ/8)	—	2	1	no	—
465	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
466	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
467	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	1	yes	characteristic
468	C₂×#135	—	2	1	no	—
469	C₂×#135	C₂²×C₂₉	1	1	yes	characteristic
470	C₂²×SD₁₆	—	2	1	no	—
471	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
472	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic
473	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
474	C₂²×SD₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
475	C₂×#131	C₂²×C₂₉	1	1	yes	characteristic
476	#536	C₂²×C₂₉	1	1	yes	characteristic
477	#535	C₂²×C₂₉	1	1	yes	characteristic, complemented
478	C₂×C₄⋊Q₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
479	C₂×#127	C₂²×C₂₉	1	1	yes	characteristic
480	#497	—	2	1	no	—
481	#496	—	2	1	no	—
482	#495	—	2	1	no	—
483	#492	—	2	4	no	—
484	#492	—	2	1	no	—
485	#471	—	2	4	no	—
486	#456	—	2	4	no	—
487	#453	—	2	4	no	—
488	#452	—	2	2	no	—
489	#450	—	2	2	no	—
490	#449	—	2	2	no	—
491	#448	—	2	2	no	—
492	C₂×#108	C₂²×C₂₉	1	1	yes	characteristic, complemented
493	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
494	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic
495	C₂×#104	C₂²×C₂₉	1	1	yes	characteristic, complemented
496	#419	C₂²×C₂₉	1	1	yes	characteristic, complemented
497	#418	C₂²×C₂₉	1	1	yes	characteristic
498	#416	C₂²×C₂₉	1	1	yes	characteristic
499	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic, complemented
500	C₂×#101	C₂²×C₂₉	1	1	yes	characteristic, complemented
501	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic
502	C₂×#100	C₂²×C₂₉	1	1	yes	characteristic, complemented
503	#408	C₂²×C₂₉	1	1	yes	characteristic
504	#408	C₂²×C₂₉	1	1	yes	characteristic, complemented
505	#405	C₂²×C₂₉	1	1	yes	characteristic, complemented
506	C₂×C₄×C₈	C₂²×C₂₉	1	1	yes	characteristic, complemented
507	#341	C₂²×C₂₉	1	1	yes	characteristic, complemented
508	#339	C₂²×C₂₉	1	1	yes	characteristic, complemented
509	C₂×C₂₉	—	2	1	no	—
510	C₂×C₂₉	—	2	1	no	—
511	C₂×C₂₉	—	4	2	no	—
512	C₂×C₂₉	—	8	1	no	—
513	C₂×C₂₉	—	8	1	no	—
514	C₂×C₂₉	—	8	2	no	—
515	C₂×C₂₉	—	16	1	no	—
516	C₂×C₂₉	#2433	1	1	yes	characteristic
517	C₂×C₂₉	#3291	1	2	yes	—
518	2₋¹⁺⁴	—	2	2	no	—
519	2₋¹⁺⁴	—	2	2	no	—
520	2₋¹⁺⁴	—	2	2	no	—
521	2₋¹⁺⁴	—	4	1	no	—
522	H(5,𝔽₂)	—	2	2	no	—
523	H(5,𝔽₂)	—	2	2	no	—
524	H(5,𝔽₂)	—	2	2	no	—
525	H(5,𝔽₂)	—	4	1	no	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	1	no	—
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	4	1	no	—
531	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
532	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
533	C₂×#41	C₂³×C₂₉	1	1	yes	characteristic
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	—	4	1	no	—
541	C₂²×D₄	—	4	1	no	—
542	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
543	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
544	#137	—	2	8	no	—
545	#137	—	2	2	no	—
546	#137	—	2	2	no	—
547	#137	—	2	2	no	—
548	#137	—	2	2	no	—
549	#137	—	2	2	no	—
550	#137	—	4	1	no	—
551	AGL(1,ℤ/8)	—	2	8	no	—
552	AGL(1,ℤ/8)	—	2	2	no	—
553	AGL(1,ℤ/8)	—	2	2	no	—
554	AGL(1,ℤ/8)	—	2	2	no	—
555	AGL(1,ℤ/8)	—	2	2	no	—
556	AGL(1,ℤ/8)	—	2	2	no	—
557	AGL(1,ℤ/8)	—	4	1	no	—
558	#135	—	2	8	no	—
559	#135	—	2	2	no	—
560	#135	—	2	2	no	—
561	C₂×Q₁₆	—	2	1	no	—
562	C₂×Q₁₆	—	2	1	no	—
563	C₂×Q₁₆	—	2	1	no	—
564	C₂×Q₁₆	D₄×C₂₉	1	1	yes	characteristic, complemented
565	C₂×SD₁₆	—	2	8	no	—
566	C₂×SD₁₆	—	2	1	no	—
567	C₂×SD₁₆	—	2	1	no	—
568	C₂×SD₁₆	—	2	2	no	—
569	C₂×SD₁₆	—	2	1	no	—
570	C₂×SD₁₆	—	2	1	no	—
571	C₂×SD₁₆	—	2	2	no	—
572	C₂×SD₁₆	—	2	1	no	—
573	C₂×SD₁₆	—	2	1	no	—
574	C₂×SD₁₆	—	2	1	no	—
575	C₂×SD₁₆	—	2	1	no	—
576	C₂×SD₁₆	—	2	2	no	—
577	C₂×SD₁₆	—	2	2	no	—
578	C₂×SD₁₆	—	2	2	no	—
579	C₂×SD₁₆	—	2	2	no	—
580	C₂×SD₁₆	—	2	2	no	—
581	C₂×SD₁₆	—	2	1	no	—
582	C₂×SD₁₆	—	2	1	no	—
583	C₂×SD₁₆	—	4	1	no	—
584	C₂×SD₁₆	—	4	1	no	—
585	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic, complemented
586	C₂×SD₁₆	D₄×C₂₉	1	4	yes	complemented
587	C₂×SD₁₆	D₄×C₂₉	1	1	yes	characteristic, complemented
588	C₂×D₈	—	2	1	no	—
589	C₂×D₈	—	2	1	no	—
590	C₂×D₈	—	2	1	no	—
591	C₂×D₈	D₄×C₂₉	1	1	yes	characteristic, complemented
592	#131	—	2	2	no	—
593	#131	D₄×C₂₉	1	4	yes	complemented
594	C₂×M₁₆	—	2	1	no	—
595	C₂×M₁₆	C₂³×C₂₉	1	1	yes	characteristic
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	C₂²×C₈	—	2	1	no	—
600	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
601	C₂²×C₈	C₂³×C₂₉	1	1	yes	characteristic
602	C₄⋊Q₈	—	2	2	no	—
603	C₄⋊Q₈	—	2	1	no	—
604	C₄⋊Q₈	—	2	2	no	—
605	#127	—	2	2	no	—
606	#127	—	2	1	no	—
607	#127	—	2	2	no	—
608	#124	—	2	1	no	—
609	#124	—	2	1	no	—
610	#123	—	4	1	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	#121	—	2	2	no	—
613	#120	—	4	1	no	—
614	#117	C₂³×C₂₉	1	1	yes	characteristic
615	C₂×C₄⋊C₄	—	4	1	no	—
616	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
617	#108	—	2	2	no	—
618	#104	—	2	2	no	—
619	#104	—	2	2	no	—
620	#104	D₄×C₂₉	1	4	yes	complemented
621	#103	—	2	2	no	—
622	#103	D₄×C₂₉	1	2	yes	complemented
623	#102	—	2	2	no	—
624	#102	D₄×C₂₉	1	2	yes	complemented
625	#101	—	2	2	no	—
626	#101	—	2	2	no	—
627	#100	—	2	2	no	—
628	#100	—	2	2	no	—
629	C₂²⋊C₈	—	2	2	no	—
630	C₂²⋊C₈	—	2	2	no	—
631	#97	—	2	1	no	—
632	C₄×C₈	—	2	2	no	—
633	C₄×C₈	—	2	1	no	—
634	C₂₉	#25802	1	1	yes	characteristic, direct product factor, Sylow
635	C₂⁴	—	2	1	no	—
636	C₂⁴	—	2	1	no	—
637	C₂⁴	—	4	1	no	—
638	#41	—	2	1	no	—
639	#41	—	2	1	no	—
640	#41	—	2	4	no	—
641	#41	—	2	4	no	—
642	#41	—	2	1	no	—
643	#41	—	2	1	no	—
644	#41	—	2	1	no	—
645	#41	—	2	1	no	—
646	#41	—	2	1	no	—
647	#41	—	2	1	no	—
648	#41	—	2	1	no	—
649	#41	—	2	1	no	—
650	#41	—	4	2	no	—
651	#41	—	4	4	no	—
652	#41	—	4	2	no	—
653	#41	—	4	2	no	—
654	#41	—	4	2	no	—
655	#41	—	4	4	no	—
656	#41	—	4	2	no	—
657	#41	—	4	2	no	—
658	#41	C₂×D₄×C₂₉	1	2	yes	—
659	#41	C₂×D₄×C₂₉	1	2	yes	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	4	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	—	2	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	4	1	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	1	yes	characteristic
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×D₄	—	2	1	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	2	1	no	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	1	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	—	4	2	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	—	4	1	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	4	no	—
702	C₂×D₄	—	4	4	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	8	4	no	—
706	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
707	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
708	C₂×D₄	C₂×D₄×C₂₉	1	2	yes	—
709	C₂×D₄	C₂×D₄×C₂₉	1	1	yes	characteristic
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
720	Q₁₆	—	2	4	no	—
721	Q₁₆	—	2	2	no	—
722	Q₁₆	—	4	2	no	—
723	Q₁₆	—	4	2	no	—
724	SD₁₆	—	2	4	no	—
725	SD₁₆	—	2	4	no	—
726	SD₁₆	—	2	2	no	—
727	SD₁₆	—	2	4	no	—
728	SD₁₆	—	2	4	no	—
729	SD₁₆	—	2	2	no	—
730	SD₁₆	—	4	4	no	—
731	SD₁₆	—	4	2	no	—
732	SD₁₆	—	4	4	no	—
733	SD₁₆	—	4	2	no	—
734	SD₁₆	—	4	2	no	—
735	SD₁₆	—	4	2	no	—
736	SD₁₆	—	4	2	no	—
737	SD₁₆	—	4	2	no	—
738	D₈	—	2	4	no	—
739	D₈	—	2	2	no	—
740	D₈	—	4	2	no	—
741	D₈	—	4	2	no	—
742	M₁₆	—	2	1	no	—
743	M₁₆	—	2	1	no	—
744	M₁₆	—	2	4	no	—
745	M₁₆	—	2	1	no	—
746	M₁₆	—	2	1	no	—
747	M₁₆	—	2	1	no	—
748	M₁₆	—	2	1	no	—
749	M₁₆	C₂×D₄×C₂₉	1	2	yes	—
750	M₁₆	C₂×D₄×C₂₉	1	2	yes	—
751	C₂×C₈	—	2	1	no	—
752	C₂×C₈	—	2	1	no	—
753	C₂×C₈	—	2	1	no	—
754	C₂×C₈	—	2	1	no	—
755	C₂×C₈	—	2	4	no	—
756	C₂×C₈	—	2	1	no	—
757	C₂×C₈	—	2	1	no	—
758	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
759	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
760	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
761	C₂×C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
762	C₂×C₈	C₂×D₄×C₂₉	1	2	yes	—
763	C₄⋊C₄	—	4	4	no	—
764	C₄⋊C₄	—	4	2	no	—
765	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₄²	—	2	1	no	—
770	C₄²	—	2	1	no	—
771	C₄²	C₂×D₄×C₂₉	1	2	yes	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	1	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	1	no	—
780	C₂³	—	4	1	no	—
781	C₂³	—	4	1	no	—
782	C₂³	—	8	2	no	—
783	C₂³	—	8	2	no	—
784	C₂³	—	16	2	no	—
785	C₂³	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
786	Q₈	—	2	1	no	—
787	Q₈	—	2	1	no	—
788	Q₈	—	2	2	no	—
789	Q₈	—	2	1	no	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	1	no	—
793	Q₈	—	4	4	no	—
794	Q₈	—	4	1	no	—
795	Q₈	—	4	1	no	—
796	Q₈	—	4	1	no	—
797	Q₈	—	4	1	no	—
798	Q₈	—	4	1	no	—
799	Q₈	—	4	1	no	—
800	Q₈	C₂₉×#127	1	2	yes	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	1	no	—
806	D₄	—	2	1	no	—
807	D₄	—	2	1	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	1	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	1	no	—
814	D₄	—	4	1	no	—
815	D₄	—	4	1	no	—
816	D₄	—	4	1	no	—
817	D₄	—	4	1	no	—
818	D₄	—	4	1	no	—
819	D₄	—	4	1	no	—
820	D₄	—	4	1	no	—
821	D₄	—	4	1	no	—
822	D₄	—	4	1	no	—
823	D₄	—	8	8	no	—
824	D₄	—	16	2	no	—
825	D₄	C₂₉×#127	1	2	yes	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	4	4	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	4	1	no	—
843	C₂×C₄	—	4	1	no	—
844	C₂×C₄	—	4	1	no	—
845	C₂×C₄	—	4	1	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
851	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
852	C₂×C₄	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	—	4	1	no	—
857	C₈	—	4	1	no	—
858	C₈	C₂₉×#120	1	2	yes	—
859	C₈	C₂₉×#120	1	2	yes	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	1	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	8	2	no	—
869	C₂²	—	8	2	no	—
870	C₂²	—	8	2	no	—
871	C₂²	—	8	1	no	—
872	C₂²	—	8	2	no	—
873	C₂²	—	16	1	no	—
874	C₂²	—	16	1	no	—
875	C₂²	—	16	4	no	—
876	C₂²	C₂₉×#535	1	1	yes	characteristic
877	C₂²	D₄²×C₂₉	1	1	yes	characteristic
878	C₂²	D₄²×C₂₉	1	1	yes	characteristic
879	C₄	—	2	4	no	—
880	C₄	—	2	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	8	1	no	—
886	C₄	C₂×C₂₉×#120	1	1	yes	characteristic
887	C₄	C₂×C₂₉×#127	1	1	yes	characteristic
888	C₄	D₄²×C₂₉	1	1	yes	characteristic
889	C₄	D₄²×C₂₉	1	1	yes	characteristic
890	C₂	—	2	1	no	—
891	C₂	—	2	1	no	—
892	C₂	—	4	2	no	—
893	C₂	—	8	1	no	—
894	C₂	—	8	1	no	—
895	C₂	—	8	2	no	—
896	C₂	—	16	1	no	—
897	C₂	C₂₉×#2433	1	1	yes	characteristic
898	C₂	C₂₉×#3291	1	2	yes	—

	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. C₂₉×#3154	C₂	semidirect
3. C₂×C₂₉×#492	C₂	semidirect
4. C₂×C₂₉×#471	C₂	semidirect
5. C₂×C₂₉×#456	C₂	semidirect
6. C₂×C₂₉×#453	C₂	semidirect
7. C₂₉×#3010	C₂	semidirect
8. C₂₉×#3009	C₂	semidirect
9. C₂₉×#2019	C₂	semidirect
10. C₂₉×#2019	C₂	semidirect
11. C₂₉×#2005	C₂	semidirect
12. C₂₉×#2002	C₂	semidirect
13. C₂₉×#1977	C₂	semidirect
14. C₂₉×#1974	C₂	semidirect
15. C₂₉×#1764	C₂	semidirect
23. C₂×C₂₉×#137	C₂²	semidirect
33. C₂²×SD₁₆×C₂₉	C₂²	semidirect
34. C₂²×SD₁₆×C₂₉	C₂²	semidirect
37. C₂₉×#535	C₂²	semidirect
38. C₂×C₂₉×C₄⋊Q₈	C₂²	semidirect
52. C₂×C₂₉×#108	C₂²	semidirect
55. C₂×C₂₉×#104	C₂²	semidirect
56. C₂₉×#419	C₂²	semidirect
59. C₂×C₂₉×#101	C₂²	semidirect
60. C₂×C₂₉×#101	C₂²	semidirect
62. C₂×C₂₉×#100	C₂²	semidirect
64. C₂₉×#408	C₂²	semidirect
65. C₂₉×#405	C₂²	semidirect
66. C₂×C₄×C₈×C₂₉	C₂²	semidirect
67. C₂₉×#341	C₂²	semidirect
68. C₂₉×#339	C₂²	semidirect
115. C₂×Q₁₆×C₂₉	D₄	semidirect
136. C₂×SD₁₆×C₂₉	D₄	semidirect
137. C₂×SD₁₆×C₂₉	D₄	semidirect
138. C₂×SD₁₆×C₂₉	D₄	semidirect
142. C₂×D₈×C₂₉	D₄	semidirect
144. C₂₉×#131	D₄	semidirect
171. C₂₉×#104	D₄	semidirect
173. C₂₉×#103	D₄	semidirect
175. C₂₉×#102	D₄	semidirect
322. #25802	C₂₉	direct (N × H)
411. C₂×#577	C₂×C₂₉	semidirect
412. #3154	C₂×C₂₉	semidirect
413. C₂×#492	C₂×C₂₉	semidirect
414. C₂×#471	C₂×C₂₉	semidirect
415. C₂×#456	C₂×C₂₉	semidirect
416. C₂×#453	C₂×C₂₉	semidirect
417. #3010	C₂×C₂₉	semidirect
418. #3009	C₂×C₂₉	semidirect
419. #2019	C₂×C₂₉	semidirect
420. #2019	C₂×C₂₉	semidirect
421. #2005	C₂×C₂₉	semidirect
422. #2002	C₂×C₂₉	semidirect
423. #1977	C₂×C₂₉	semidirect
424. #1974	C₂×C₂₉	semidirect
425. #1764	C₂×C₂₉	semidirect
463. C₂×#137	C₂²×C₂₉	semidirect
473. C₂²×SD₁₆	C₂²×C₂₉	semidirect
474. C₂²×SD₁₆	C₂²×C₂₉	semidirect
477. #535	C₂²×C₂₉	semidirect
478. C₂×C₄⋊Q₈	C₂²×C₂₉	semidirect
492. C₂×#108	C₂²×C₂₉	semidirect
495. C₂×#104	C₂²×C₂₉	semidirect
496. #419	C₂²×C₂₉	semidirect
499. C₂×#101	C₂²×C₂₉	semidirect
500. C₂×#101	C₂²×C₂₉	semidirect
502. C₂×#100	C₂²×C₂₉	semidirect
504. #408	C₂²×C₂₉	semidirect
505. #405	C₂²×C₂₉	semidirect
506. C₂×C₄×C₈	C₂²×C₂₉	semidirect
507. #341	C₂²×C₂₉	semidirect
508. #339	C₂²×C₂₉	semidirect
564. C₂×Q₁₆	D₄×C₂₉	semidirect
585. C₂×SD₁₆	D₄×C₂₉	semidirect
586. C₂×SD₁₆	D₄×C₂₉	semidirect
587. C₂×SD₁₆	D₄×C₂₉	semidirect
591. C₂×D₈	D₄×C₂₉	semidirect
593. #131	D₄×C₂₉	semidirect
620. #104	D₄×C₂₉	semidirect
622. #103	D₄×C₂₉	semidirect
624. #102	D₄×C₂₉	semidirect
634. C₂₉	#25802	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
C₂₉×#3154	2
C₂×C₂₉×#492	2
C₂×C₂₉×#471	2
C₂×C₂₉×#456	2
C₂×C₂₉×#453	2
C₂₉×#3010	2
C₂₉×#3009	2
C₂₉×#2019	2
C₂₉×#2005	2
C₂₉×#2002	2
C₂₉×#1977	2
C₂₉×#1974	2
C₂₉×#1764	2
#25802	29

Subgroups — C29×#25802 #20320702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#25802 #20320702