Subgroups — C₂₉×#60170 #20355070

Order 7424.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#575	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#2952	C₂	1	4	yes	maximal, complemented
5	C₂₉×#2951	C₂	1	4	yes	maximal, complemented
6	C₂₉×#2947	C₂	1	4	yes	maximal, complemented
7	C₂₉×#2946	C₂	1	4	yes	maximal, complemented
8	C₄×C₂₉×#137	C₂	1	4	yes	maximal, complemented
9	C₄×C₂₉×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
10	C₂×C₂₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₉×#2873	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₂₉	C₂²	1	1	yes	characteristic
16	C₂₉×#575	C₄	1	16	yes	complemented
17	C₂×C₂₉×#137	C₂²	1	2	yes	—
18	C₂×C₂₉×#137	C₂²	1	2	yes	—
19	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₂₉×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₂₉×#135	C₂²	1	4	yes	—
22	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₂₉	C₂²	1	1	yes	characteristic
24	C₂₉×#520	—	2	2	no	—
25	C₂₉×#520	—	2	2	no	—
26	C₂₉×#520	—	2	1	no	—
27	C₂₉×#520	—	2	1	no	—
28	C₂₉×#520	C₂²	1	4	yes	—
29	C₂₉×#520	C₂²	1	2	yes	complemented
30	C₂₉×#520	C₂²	1	4	yes	complemented
31	C₂₉×#520	C₂²	1	2	yes	complemented
32	C₂₉×#519	C₂²	1	2	yes	complemented
33	C₂₉×#518	—	2	2	no	—
34	C₂₉×#518	C₂²	1	2	yes	complemented
35	C₄×#41×C₂₉	—	2	2	no	—
36	C₄×#41×C₂₉	C₂²	1	4	yes	—
37	C₂×C₄×Q₈×C₂₉	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₂₉	—	2	2	no	—
39	C₂×C₄×D₄×C₂₉	C₂²	1	2	yes	complemented
40	C₂×C₂₉×#117	—	2	2	no	—
41	C₂×C₂₉×#117	—	2	1	no	—
42	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
43	C₂×C₂₉×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₉	—	2	1	no	—
45	C₂²×C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
46	C₂₉×#442	C₂²	1	8	yes	complemented
47	C₂₉×#441	C₂²	1	8	yes	complemented
48	C₂₉×#440	C₂²	1	8	yes	complemented
49	C₂₉×#440	C₂²	1	8	yes	complemented
50	C₄×Q₁₆×C₂₉	C₂²	1	8	yes	complemented
51	C₄×SD₁₆×C₂₉	C₂²	1	8	yes	complemented
52	C₄×SD₁₆×C₂₉	C₂²	1	8	yes	complemented
53	C₄×D₈×C₂₉	C₂²	1	8	yes	complemented
54	C₂₉×#428	C₂²	1	4	yes	complemented
55	C₂₉×#428	C₂²	1	4	yes	complemented
56	C₂×C₂₉×#107	C₂²	1	2	yes	complemented
57	C₂×C₂₉×#106	C₂²	1	2	yes	complemented
58	C₂₉×#419	C₂²	1	2	yes	complemented
59	C₂₉×#418	C₂²	1	2	yes	complemented
60	C₂₉×#417	C₂²	1	4	yes	—
61	C₂₉×#417	C₂²	1	2	yes	complemented
62	C₂₉×#417	C₂²	1	4	yes	complemented
63	C₂₉×#417	C₂²	1	2	yes	complemented
64	C₂₉×#416	C₂²	1	4	yes	—
65	C₂×C₂₉×#103	C₂²	1	2	yes	complemented
66	C₂×C₂₉×#102	C₂²	1	2	yes	complemented
67	C₂₉×#405	C₂²	1	4	yes	complemented
68	C₂₉×#405	C₂²	1	4	yes	complemented
69	C₄×M₁₆×C₂₉	C₂²	1	4	yes	complemented
70	C₂×#41×C₂₉	—	2	1	no	—
71	C₂×#41×C₂₉	—	2	1	no	—
72	C₂×#41×C₂₉	—	2	1	no	—
73	C₂×#41×C₂₉	—	2	1	no	—
74	C₂×#41×C₂₉	—	2	4	no	—
75	C₂×#41×C₂₉	—	2	4	no	—
76	C₂×#41×C₂₉	C₂×C₄	1	8	yes	complemented
77	C₂×#41×C₂₉	C₂×C₄	1	8	yes	complemented
78	C₂×#41×C₂₉	C₂³	1	2	yes	—
79	C₂×#41×C₂₉	C₂³	1	2	yes	—
80	C₂×#41×C₂₉	C₂³	1	2	yes	—
81	C₂×#41×C₂₉	C₂³	1	2	yes	—
82	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
83	C₂²×Q₈×C₂₉	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₉	—	2	1	no	—
85	C₂²×D₄×C₂₉	—	2	1	no	—
86	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₂₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₉	—	2	1	no	—
89	C₂³×C₄×C₂₉	—	2	1	no	—
90	C₂³×C₄×C₂₉	—	2	1	no	—
91	C₂³×C₄×C₂₉	—	2	2	no	—
92	C₂³×C₄×C₂₉	C₂³	1	1	yes	characteristic
93	C₂₉×#137	C₂×C₄	1	16	yes	complemented
94	C₂₉×#137	C₂×C₄	1	16	yes	complemented
95	C₂₉×AGL(1,ℤ/8)	C₂×C₄	1	16	yes	complemented
96	C₂₉×AGL(1,ℤ/8)	C₂×C₄	1	16	yes	complemented
97	C₂₉×#135	C₂×C₄	1	32	yes	complemented
98	C₂×Q₁₆×C₂₉	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₂₉	C₂³	1	4	yes	—
101	C₂×D₈×C₂₉	C₂³	1	4	yes	—
102	C₂×M₁₆×C₂₉	—	2	4	no	—
103	C₂×M₁₆×C₂₉	C₂×C₄	1	8	yes	complemented
104	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
106	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₂₉	C₂³	1	2	yes	—
108	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
109	C₂²×C₈×C₂₉	C₂³	1	2	yes	—
110	C₄×Q₈×C₂₉	—	2	2	no	—
111	C₄×Q₈×C₂₉	—	2	2	no	—
112	C₄×Q₈×C₂₉	—	2	4	no	—
113	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
114	C₄×Q₈×C₂₉	C₂³	1	8	yes	—
115	C₄×Q₈×C₂₉	C₂³	1	4	yes	—
116	C₄×D₄×C₂₉	—	2	4	no	—
117	C₄×D₄×C₂₉	—	2	4	no	—
118	C₄×D₄×C₂₉	—	2	2	no	—
119	C₄×D₄×C₂₉	—	2	2	no	—
120	C₄×D₄×C₂₉	—	2	8	no	—
121	C₄×D₄×C₂₉	—	2	8	no	—
122	C₄×D₄×C₂₉	—	2	4	no	—
123	C₄×D₄×C₂₉	—	2	4	no	—
124	C₄×D₄×C₂₉	—	2	4	no	—
125	C₄×D₄×C₂₉	C₂³	1	4	yes	—
126	C₄×D₄×C₂₉	C₂³	1	8	yes	—
127	C₄×D₄×C₂₉	C₂³	1	4	yes	—
128	C₂₉×#117	—	2	1	no	—
129	C₂₉×#117	—	2	1	no	—
130	C₂₉×#117	—	2	4	no	—
131	C₂₉×#117	—	2	4	no	—
132	C₂₉×#117	—	2	2	no	—
133	C₂₉×#117	—	2	2	no	—
134	C₂₉×#117	—	2	4	no	—
135	C₂₉×#117	—	2	4	no	—
136	C₂₉×#117	D₄	1	2	yes	—
137	C₂₉×#117	D₄	1	2	yes	—
138	C₂₉×#117	C₂³	1	2	yes	—
139	C₂₉×#117	C₂³	1	2	yes	—
140	C₂₉×#117	C₂³	1	2	yes	—
141	C₂₉×#117	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
144	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
147	C₂×C₄⋊C₄×C₂₉	—	2	4	no	—
148	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
149	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
150	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₉	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₂₉	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₂₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₉	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₂₉	—	2	2	no	—
159	C₂×C₂²⋊C₄×C₂₉	—	2	4	no	—
160	C₂×C₂²⋊C₄×C₂₉	D₄	1	2	yes	—
161	C₂×C₄²×C₂₉	—	2	2	no	—
162	C₂×C₄²×C₂₉	—	2	1	no	—
163	C₂×C₄²×C₂₉	—	2	4	no	—
164	C₂×C₄²×C₂₉	C₂³	1	2	yes	—
165	C₂₉×#107	C₂³	1	8	yes	—
166	C₂₉×#106	C₂³	1	8	yes	—
167	C₂₉×#103	C₂³	1	4	yes	—
168	C₂₉×#103	C₂³	1	8	yes	—
169	C₂₉×#103	C₂³	1	4	yes	—
170	C₂₉×#102	C₂³	1	4	yes	—
171	C₂₉×#102	C₂³	1	8	yes	—
172	C₂₉×#102	C₂³	1	4	yes	—
173	C₂₉×#97	C₂³	1	8	yes	—
174	C₄×C₈×C₂₉	C₂³	1	8	yes	—
175	C₂⁴×C₂₉	—	2	1	no	—
176	C₂⁴×C₂₉	—	2	1	no	—
177	C₂⁴×C₂₉	C₂×D₄	1	1	yes	characteristic
178	#41×C₂₉	—	2	8	no	—
179	#41×C₂₉	—	2	8	no	—
180	#41×C₂₉	—	2	8	no	—
181	#41×C₂₉	—	2	8	no	—
182	#41×C₂₉	—	2	4	no	—
183	#41×C₂₉	—	2	4	no	—
184	#41×C₂₉	—	2	4	no	—
185	#41×C₂₉	—	2	4	no	—
186	#41×C₂₉	C₂²×C₄	1	8	yes	—
187	#41×C₂₉	C₂²×C₄	1	8	yes	—
188	#41×C₂₉	C₂²×C₄	1	8	yes	—
189	#41×C₂₉	C₂²×C₄	1	8	yes	complemented
190	C₂×Q₈×C₂₉	—	2	1	no	—
191	C₂×Q₈×C₂₉	—	2	1	no	—
192	C₂×Q₈×C₂₉	—	2	2	no	—
193	C₂×Q₈×C₂₉	—	2	2	no	—
194	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	—
195	C₂×Q₈×C₂₉	C₂²×C₄	1	4	yes	complemented
196	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₂₉	C₂⁴	1	2	yes	—
198	C₂×D₄×C₂₉	—	2	8	no	—
199	C₂×D₄×C₂₉	—	2	8	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	1	no	—
205	C₂×D₄×C₂₉	—	2	1	no	—
206	C₂×D₄×C₂₉	—	2	2	no	—
207	C₂×D₄×C₂₉	—	2	2	no	—
208	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	—
209	C₂×D₄×C₂₉	C₂²×C₄	1	4	yes	complemented
210	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
211	C₂×D₄×C₂₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₂₉	—	2	1	no	—
213	C₂²×C₄×C₂₉	—	2	1	no	—
214	C₂²×C₄×C₂₉	—	2	8	no	—
215	C₂²×C₄×C₂₉	—	2	8	no	—
216	C₂²×C₄×C₂₉	—	2	2	no	—
217	C₂²×C₄×C₂₉	—	2	2	no	—
218	C₂²×C₄×C₂₉	—	2	2	no	—
219	C₂²×C₄×C₂₉	—	2	2	no	—
220	C₂²×C₄×C₂₉	—	2	2	no	—
221	C₂²×C₄×C₂₉	—	2	1	no	—
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	4	no	—
226	C₂²×C₄×C₂₉	—	2	4	no	—
227	C₂²×C₄×C₂₉	—	2	8	no	—
228	C₂²×C₄×C₂₉	—	8	4	no	—
229	C₂²×C₄×C₂₉	—	8	2	no	—
230	C₂²×C₄×C₂₉	C₂²×C₄	1	4	yes	—
231	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₂₉	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₉	#41	1	4	yes	—
237	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
240	Q₁₆×C₂₉	C₂²×C₄	1	16	yes	complemented
241	SD₁₆×C₂₉	C₂²×C₄	1	16	yes	complemented
242	SD₁₆×C₂₉	C₂²×C₄	1	16	yes	complemented
243	D₈×C₂₉	C₂²×C₄	1	16	yes	complemented
244	M₁₆×C₂₉	—	2	4	no	—
245	M₁₆×C₂₉	—	2	4	no	—
246	M₁₆×C₂₉	C₂²×C₄	1	8	yes	—
247	M₁₆×C₂₉	C₂²×C₄	1	8	yes	complemented
248	C₂×C₈×C₂₉	—	2	4	no	—
249	C₂×C₈×C₂₉	C₂²×C₄	1	8	yes	complemented
250	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
251	C₂×C₈×C₂₉	C₂⁴	1	4	yes	—
252	C₄⋊C₄×C₂₉	—	2	2	no	—
253	C₄⋊C₄×C₂₉	—	2	2	no	—
254	C₄⋊C₄×C₂₉	—	2	8	no	—
255	C₄⋊C₄×C₂₉	—	2	1	no	—
256	C₄⋊C₄×C₂₉	—	2	1	no	—
257	C₄⋊C₄×C₂₉	—	2	2	no	—
258	C₄⋊C₄×C₂₉	—	2	4	no	—
259	C₄⋊C₄×C₂₉	—	2	4	no	—
260	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
263	C₄⋊C₄×C₂₉	C₂×D₄	1	2	yes	—
264	C₄⋊C₄×C₂₉	C₂⁴	1	4	yes	—
265	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₂₉	C₂⁴	1	2	yes	—
267	C₂²⋊C₄×C₂₉	—	2	2	no	—
268	C₂²⋊C₄×C₂₉	—	2	2	no	—
269	C₂²⋊C₄×C₂₉	—	2	4	no	—
270	C₂²⋊C₄×C₂₉	—	2	4	no	—
271	C₂²⋊C₄×C₂₉	—	2	8	no	—
272	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
273	C₂²⋊C₄×C₂₉	C₂×D₄	1	4	yes	—
274	C₄²×C₂₉	—	2	2	no	—
275	C₄²×C₂₉	—	2	4	no	—
276	C₄²×C₂₉	—	2	4	no	—
277	C₄²×C₂₉	—	2	8	no	—
278	C₄²×C₂₉	—	2	2	no	—
279	C₄²×C₂₉	C₂×D₄	1	4	yes	—
280	C₄²×C₂₉	C₂⁴	1	4	yes	—
281	#60170	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂³×C₂₉	—	2	4	no	—
283	C₂³×C₂₉	—	2	2	no	—
284	C₂³×C₂₉	—	2	2	no	—
285	C₂³×C₂₉	—	2	4	no	—
286	C₂³×C₂₉	—	4	1	no	—
287	C₂³×C₂₉	—	4	1	no	—
288	C₂³×C₂₉	—	4	2	no	—
289	C₂³×C₂₉	—	4	2	no	—
290	C₂³×C₂₉	—	8	1	no	—
291	C₂³×C₂₉	—	8	1	no	—
292	C₂³×C₂₉	C₄×D₄	1	4	yes	—
293	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
294	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
295	C₂³×C₂₉	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₂₉	—	2	4	no	—
297	Q₈×C₂₉	—	2	4	no	—
298	Q₈×C₂₉	—	2	2	no	—
299	Q₈×C₂₉	—	2	2	no	—
300	Q₈×C₂₉	C₂³×C₄	1	4	yes	—
301	Q₈×C₂₉	C₂³×C₄	1	4	yes	—
302	D₄×C₂₉	—	2	8	no	—
303	D₄×C₂₉	—	2	8	no	—
304	D₄×C₂₉	—	2	8	no	—
305	D₄×C₂₉	—	2	8	no	—
306	D₄×C₂₉	—	2	4	no	—
307	D₄×C₂₉	—	2	4	no	—
308	D₄×C₂₉	—	2	2	no	—
309	D₄×C₂₉	—	2	2	no	—
310	D₄×C₂₉	C₂³×C₄	1	4	yes	—
311	D₄×C₂₉	C₂³×C₄	1	4	yes	—
312	C₂×C₄×C₂₉	—	2	4	no	—
313	C₂×C₄×C₂₉	—	2	4	no	—
314	C₂×C₄×C₂₉	—	2	2	no	—
315	C₂×C₄×C₂₉	—	2	2	no	—
316	C₂×C₄×C₂₉	—	2	8	no	—
317	C₂×C₄×C₂₉	—	2	8	no	—
318	C₂×C₄×C₂₉	—	2	8	no	—
319	C₂×C₄×C₂₉	—	2	8	no	—
320	C₂×C₄×C₂₉	—	2	2	no	—
321	C₂×C₄×C₂₉	—	2	2	no	—
322	C₂×C₄×C₂₉	—	2	4	no	—
323	C₂×C₄×C₂₉	—	4	2	no	—
324	C₂×C₄×C₂₉	—	4	2	no	—
325	C₂×C₄×C₂₉	—	4	4	no	—
326	C₂×C₄×C₂₉	—	8	4	no	—
327	C₂×C₄×C₂₉	—	8	4	no	—
328	C₂×C₄×C₂₉	—	8	8	no	—
329	C₂×C₄×C₂₉	—	8	1	no	—
330	C₂×C₄×C₂₉	—	8	1	no	—
331	C₂×C₄×C₂₉	—	8	2	no	—
332	C₂×C₄×C₂₉	—	8	2	no	—
333	C₂×C₄×C₂₉	C₄×D₄	1	4	yes	—
334	C₂×C₄×C₂₉	C₄×D₄	1	4	yes	—
335	C₂×C₄×C₂₉	C₄×D₄	1	4	yes	—
336	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
337	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
338	C₂×C₄×C₂₉	C₂³×C₄	1	2	yes	—
339	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₂₉	C₂²×D₄	1	4	yes	—
341	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₉	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
345	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
346	C₂×C₄×C₂₉	C₂×#41	1	2	yes	—
347	C₂×C₄×C₂₉	C₂⁵	1	1	yes	characteristic
348	C₈×C₂₉	—	2	4	no	—
349	C₈×C₂₉	C₂³×C₄	1	8	yes	—
350	C₂×#575	C₂×C₂₉	1	1	yes	characteristic
351	#3428	C₂×C₂₉	1	1	yes	characteristic, complemented
352	C₂×#520	C₂×C₂₉	1	1	yes	characteristic, complemented
353	#2952	C₂×C₂₉	1	4	yes	complemented
354	#2951	C₂×C₂₉	1	4	yes	complemented
355	#2947	C₂×C₂₉	1	4	yes	complemented
356	#2946	C₂×C₂₉	1	4	yes	complemented
357	C₄×#137	C₂×C₂₉	1	4	yes	complemented
358	C₄×AGL(1,ℤ/8)	C₂×C₂₉	1	4	yes	complemented
359	C₂×#428	C₂×C₂₉	1	1	yes	characteristic, complemented
360	#2896	C₂×C₂₉	1	1	yes	characteristic, complemented
361	C₂×#417	C₂×C₂₉	1	1	yes	characteristic, complemented
362	#2873	C₂×C₂₉	1	1	yes	characteristic, complemented
363	C₂²×C₂₉	—	2	1	no	—
364	C₂²×C₂₉	—	2	1	no	—
365	C₂²×C₂₉	—	2	1	no	—
366	C₂²×C₂₉	—	2	1	no	—
367	C₂²×C₂₉	—	2	1	no	—
368	C₂²×C₂₉	—	2	1	no	—
369	C₂²×C₂₉	—	2	4	no	—
370	C₂²×C₂₉	—	2	4	no	—
371	C₂²×C₂₉	—	4	4	no	—
372	C₂²×C₂₉	—	4	8	no	—
373	C₂²×C₂₉	—	4	2	no	—
374	C₂²×C₂₉	—	4	2	no	—
375	C₂²×C₂₉	—	4	2	no	—
376	C₂²×C₂₉	—	4	2	no	—
377	C₂²×C₂₉	—	8	4	no	—
378	C₂²×C₂₉	C₂×C₄×D₄	1	2	yes	—
379	C₂²×C₂₉	C₂×C₄×D₄	1	2	yes	—
380	C₂²×C₂₉	C₂×C₄×D₄	1	2	yes	—
381	C₂²×C₂₉	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₂₉	—	2	4	no	—
383	C₄×C₂₉	—	2	4	no	—
384	C₄×C₂₉	—	2	4	no	—
385	C₄×C₂₉	—	2	4	no	—
386	C₄×C₂₉	—	4	4	no	—
387	C₄×C₂₉	—	4	2	no	—
388	C₄×C₂₉	—	4	2	no	—
389	C₄×C₂₉	C₂×C₄×D₄	1	2	yes	—
390	C₄×C₂₉	C₂×C₄×D₄	1	2	yes	—
391	C₄×C₂₉	C₂×C₄×D₄	1	2	yes	—
392	C₄×C₂₉	C₂⁴×C₄	1	1	yes	characteristic
393	C₄×C₂₉	C₂²×#41	1	1	yes	characteristic
394	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
395	C₂²×#41	C₂²×C₂₉	1	1	yes	characteristic
396	#575	C₄×C₂₉	1	16	yes	complemented
397	C₂×#137	C₂²×C₂₉	1	2	yes	—
398	C₂×#137	C₂²×C₂₉	1	2	yes	—
399	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
400	C₂×AGL(1,ℤ/8)	C₂²×C₂₉	1	2	yes	—
401	C₂×#135	C₂²×C₂₉	1	4	yes	—
402	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
403	C₂²×M₁₆	C₂²×C₂₉	1	1	yes	characteristic
404	#520	—	2	2	no	—
405	#520	—	2	2	no	—
406	#520	—	2	1	no	—
407	#520	—	2	1	no	—
408	#520	C₂²×C₂₉	1	4	yes	—
409	#520	C₂²×C₂₉	1	4	yes	complemented
410	#520	C₂²×C₂₉	1	2	yes	complemented
411	#520	C₂²×C₂₉	1	2	yes	complemented
412	#519	C₂²×C₂₉	1	2	yes	complemented
413	#518	—	2	2	no	—
414	#518	C₂²×C₂₉	1	2	yes	complemented
415	C₄×#41	—	2	2	no	—
416	C₄×#41	C₂²×C₂₉	1	4	yes	—
417	C₂×C₄×Q₈	C₂²×C₂₉	1	2	yes	complemented
418	C₂×C₄×D₄	—	2	2	no	—
419	C₂×C₄×D₄	C₂²×C₂₉	1	2	yes	complemented
420	C₂×#117	—	2	2	no	—
421	C₂×#117	—	2	1	no	—
422	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
423	C₂×#117	C₂²×C₂₉	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	—	2	1	no	—
425	C₂²×C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
426	#442	C₂²×C₂₉	1	8	yes	complemented
427	#441	C₂²×C₂₉	1	8	yes	complemented
428	#440	C₂²×C₂₉	1	8	yes	complemented
429	#440	C₂²×C₂₉	1	8	yes	complemented
430	C₄×Q₁₆	C₂²×C₂₉	1	8	yes	complemented
431	C₄×SD₁₆	C₂²×C₂₉	1	8	yes	complemented
432	C₄×SD₁₆	C₂²×C₂₉	1	8	yes	complemented
433	C₄×D₈	C₂²×C₂₉	1	8	yes	complemented
434	#428	C₂²×C₂₉	1	4	yes	complemented
435	#428	C₂²×C₂₉	1	4	yes	complemented
436	C₂×#107	C₂²×C₂₉	1	2	yes	complemented
437	C₂×#106	C₂²×C₂₉	1	2	yes	complemented
438	#419	C₂²×C₂₉	1	2	yes	complemented
439	#418	C₂²×C₂₉	1	2	yes	complemented
440	#417	C₂²×C₂₉	1	4	yes	—
441	#417	C₂²×C₂₉	1	4	yes	complemented
442	#417	C₂²×C₂₉	1	2	yes	complemented
443	#417	C₂²×C₂₉	1	2	yes	complemented
444	#416	C₂²×C₂₉	1	4	yes	—
445	C₂×#103	C₂²×C₂₉	1	2	yes	complemented
446	C₂×#102	C₂²×C₂₉	1	2	yes	complemented
447	#405	C₂²×C₂₉	1	4	yes	complemented
448	#405	C₂²×C₂₉	1	4	yes	complemented
449	C₄×M₁₆	C₂²×C₂₉	1	4	yes	complemented
450	C₂×C₂₉	—	2	2	no	—
451	C₂×C₂₉	—	2	2	no	—
452	C₂×C₂₉	—	2	2	no	—
453	C₂×C₂₉	—	4	4	no	—
454	C₂×C₂₉	—	4	4	no	—
455	C₂×C₂₉	C₂²×C₄×D₄	1	1	yes	characteristic
456	C₂×C₂₉	#3585	1	1	yes	characteristic
457	C₂×C₂₉	#3586	1	1	yes	characteristic
458	C₂×#41	—	2	1	no	—
459	C₂×#41	—	2	1	no	—
460	C₂×#41	—	2	1	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	4	no	—
463	C₂×#41	—	2	4	no	—
464	C₂×#41	C₂×C₄×C₂₉	1	8	yes	complemented
465	C₂×#41	C₂×C₄×C₂₉	1	8	yes	complemented
466	C₂×#41	C₂³×C₂₉	1	2	yes	—
467	C₂×#41	C₂³×C₂₉	1	2	yes	—
468	C₂×#41	C₂³×C₂₉	1	2	yes	—
469	C₂×#41	C₂³×C₂₉	1	2	yes	—
470	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
471	C₂²×Q₈	C₂³×C₂₉	1	1	yes	characteristic
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₂₉	1	1	yes	characteristic
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	2	no	—
480	C₂³×C₄	C₂³×C₂₉	1	1	yes	characteristic
481	#137	C₂×C₄×C₂₉	1	16	yes	complemented
482	#137	C₂×C₄×C₂₉	1	16	yes	complemented
483	AGL(1,ℤ/8)	C₂×C₄×C₂₉	1	16	yes	complemented
484	AGL(1,ℤ/8)	C₂×C₄×C₂₉	1	16	yes	complemented
485	#135	C₂×C₄×C₂₉	1	32	yes	complemented
486	C₂×Q₁₆	C₂³×C₂₉	1	4	yes	—
487	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
488	C₂×SD₁₆	C₂³×C₂₉	1	4	yes	—
489	C₂×D₈	C₂³×C₂₉	1	4	yes	—
490	C₂×M₁₆	—	2	4	no	—
491	C₂×M₁₆	C₂×C₄×C₂₉	1	8	yes	complemented
492	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
493	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
494	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
495	C₂×M₁₆	C₂³×C₂₉	1	2	yes	—
496	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
497	C₂²×C₈	C₂³×C₂₉	1	2	yes	—
498	C₄×Q₈	—	2	2	no	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	4	no	—
501	C₄×Q₈	C₂³×C₂₉	1	8	yes	—
502	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
503	C₄×Q₈	C₂³×C₂₉	1	4	yes	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	4	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	8	no	—
509	C₄×D₄	—	2	8	no	—
510	C₄×D₄	—	2	4	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	C₂³×C₂₉	1	8	yes	—
514	C₄×D₄	C₂³×C₂₉	1	4	yes	—
515	C₄×D₄	C₂³×C₂₉	1	4	yes	—
516	#117	—	2	1	no	—
517	#117	—	2	1	no	—
518	#117	—	2	4	no	—
519	#117	—	2	4	no	—
520	#117	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	—	2	4	no	—
523	#117	—	2	4	no	—
524	#117	D₄×C₂₉	1	2	yes	—
525	#117	D₄×C₂₉	1	2	yes	—
526	#117	C₂³×C₂₉	1	2	yes	—
527	#117	C₂³×C₂₉	1	2	yes	—
528	#117	C₂³×C₂₉	1	2	yes	—
529	#117	C₂³×C₂₉	1	2	yes	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	4	no	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
539	C₂×C₄⋊C₄	D₄×C₂₉	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₂₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₂₉	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	2	no	—
547	C₂×C₂²⋊C₄	—	2	4	no	—
548	C₂×C₂²⋊C₄	D₄×C₂₉	1	2	yes	—
549	C₂×C₄²	—	2	2	no	—
550	C₂×C₄²	—	2	1	no	—
551	C₂×C₄²	—	2	4	no	—
552	C₂×C₄²	C₂³×C₂₉	1	2	yes	—
553	#107	C₂³×C₂₉	1	8	yes	—
554	#106	C₂³×C₂₉	1	8	yes	—
555	#103	C₂³×C₂₉	1	8	yes	—
556	#103	C₂³×C₂₉	1	4	yes	—
557	#103	C₂³×C₂₉	1	4	yes	—
558	#102	C₂³×C₂₉	1	8	yes	—
559	#102	C₂³×C₂₉	1	4	yes	—
560	#102	C₂³×C₂₉	1	4	yes	—
561	#97	C₂³×C₂₉	1	8	yes	—
562	C₄×C₈	C₂³×C₂₉	1	8	yes	—
563	C₂₉	#60170	1	1	yes	characteristic, direct product factor, Sylow
564	C₂⁴	—	2	1	no	—
565	C₂⁴	—	2	1	no	—
566	C₂⁴	C₂×D₄×C₂₉	1	1	yes	characteristic
567	#41	—	2	8	no	—
568	#41	—	2	8	no	—
569	#41	—	2	8	no	—
570	#41	—	2	8	no	—
571	#41	—	2	4	no	—
572	#41	—	2	4	no	—
573	#41	—	2	4	no	—
574	#41	—	2	4	no	—
575	#41	C₂²×C₄×C₂₉	1	8	yes	—
576	#41	C₂²×C₄×C₂₉	1	8	yes	—
577	#41	C₂²×C₄×C₂₉	1	8	yes	—
578	#41	C₂²×C₄×C₂₉	1	8	yes	complemented
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	—
584	C₂×Q₈	C₂²×C₄×C₂₉	1	4	yes	complemented
585	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
586	C₂×Q₈	C₂⁴×C₂₉	1	2	yes	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	—
598	C₂×D₄	C₂²×C₄×C₂₉	1	4	yes	complemented
599	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
600	C₂×D₄	C₂⁴×C₂₉	1	2	yes	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	8	no	—
604	C₂²×C₄	—	2	8	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	2	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	8	4	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	C₂²×C₄×C₂₉	1	4	yes	—
620	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
621	C₂²×C₄	C₂×D₄×C₂₉	1	2	yes	—
622	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₂₉	1	1	yes	characteristic
625	C₂²×C₄	#41×C₂₉	1	4	yes	—
626	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
627	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
628	C₂²×C₄	C₂⁴×C₂₉	1	1	yes	characteristic
629	Q₁₆	C₂²×C₄×C₂₉	1	16	yes	complemented
630	SD₁₆	C₂²×C₄×C₂₉	1	16	yes	complemented
631	SD₁₆	C₂²×C₄×C₂₉	1	16	yes	complemented
632	D₈	C₂²×C₄×C₂₉	1	16	yes	complemented
633	M₁₆	—	2	4	no	—
634	M₁₆	—	2	4	no	—
635	M₁₆	C₂²×C₄×C₂₉	1	8	yes	—
636	M₁₆	C₂²×C₄×C₂₉	1	8	yes	complemented
637	C₂×C₈	—	2	4	no	—
638	C₂×C₈	C₂²×C₄×C₂₉	1	8	yes	complemented
639	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
640	C₂×C₈	C₂⁴×C₂₉	1	4	yes	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
650	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
651	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
652	C₄⋊C₄	C₂×D₄×C₂₉	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₂₉	1	4	yes	—
655	C₄⋊C₄	C₂⁴×C₂₉	1	2	yes	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	2	2	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
662	C₂²⋊C₄	C₂×D₄×C₂₉	1	4	yes	—
663	C₄²	—	2	2	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	2	4	no	—
666	C₄²	—	2	8	no	—
667	C₄²	—	2	2	no	—
668	C₄²	C₂×D₄×C₂₉	1	4	yes	—
669	C₄²	C₂⁴×C₂₉	1	4	yes	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	4	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	8	1	no	—
679	C₂³	—	8	1	no	—
680	C₂³	C₄×D₄×C₂₉	1	4	yes	—
681	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
682	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
683	C₂³	C₂²×D₄×C₂₉	1	1	yes	characteristic
684	Q₈	—	2	4	no	—
685	Q₈	—	2	4	no	—
686	Q₈	—	2	2	no	—
687	Q₈	—	2	2	no	—
688	Q₈	C₂³×C₄×C₂₉	1	4	yes	—
689	Q₈	C₂³×C₄×C₂₉	1	4	yes	—
690	D₄	—	2	8	no	—
691	D₄	—	2	8	no	—
692	D₄	—	2	8	no	—
693	D₄	—	2	8	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	C₂³×C₄×C₂₉	1	4	yes	—
699	D₄	C₂³×C₄×C₂₉	1	4	yes	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	8	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	8	no	—
707	C₂×C₄	—	2	8	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	8	8	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	1	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	C₄×D₄×C₂₉	1	4	yes	—
722	C₂×C₄	C₄×D₄×C₂₉	1	4	yes	—
723	C₂×C₄	C₄×D₄×C₂₉	1	4	yes	—
724	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
725	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
726	C₂×C₄	C₂³×C₄×C₂₉	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
728	C₂×C₄	C₂²×D₄×C₂₉	1	4	yes	—
729	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
730	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
731	C₂×C₄	C₂²×D₄×C₂₉	1	1	yes	characteristic
732	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
733	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
734	C₂×C₄	C₂×#41×C₂₉	1	2	yes	—
735	C₂×C₄	C₂⁵×C₂₉	1	1	yes	characteristic
736	C₈	—	2	4	no	—
737	C₈	C₂³×C₄×C₂₉	1	8	yes	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	4	4	no	—
747	C₂²	—	4	8	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	8	4	no	—
753	C₂²	C₂×C₄×D₄×C₂₉	1	2	yes	—
754	C₂²	C₂×C₄×D₄×C₂₉	1	2	yes	—
755	C₂²	C₂×C₄×D₄×C₂₉	1	2	yes	—
756	C₂²	C₂³×D₄×C₂₉	1	1	yes	characteristic
757	C₄	—	2	4	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	4	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	C₂×C₄×D₄×C₂₉	1	2	yes	—
765	C₄	C₂×C₄×D₄×C₂₉	1	2	yes	—
766	C₄	C₂×C₄×D₄×C₂₉	1	2	yes	—
767	C₄	C₂⁴×C₄×C₂₉	1	1	yes	characteristic
768	C₄	C₂²×#41×C₂₉	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	2	2	no	—
772	C₂	—	4	4	no	—
773	C₂	—	4	4	no	—
774	C₂	C₂²×C₄×D₄×C₂₉	1	1	yes	characteristic
775	C₂	C₂₉×#3585	1	1	yes	characteristic
776	C₂	C₂₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂³×D₄
commutator	C₄	C₂⁴×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₉
prime radical	C₂×C₂₉×#575	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₂₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#3428	C₂	semidirect
3. C₂×C₂₉×#520	C₂	semidirect
4. C₂₉×#2952	C₂	semidirect
5. C₂₉×#2951	C₂	semidirect
6. C₂₉×#2947	C₂	semidirect
7. C₂₉×#2946	C₂	semidirect
8. C₄×C₂₉×#137	C₂	semidirect
9. C₄×C₂₉×AGL(1,ℤ/8)	C₂	semidirect
10. C₂×C₂₉×#428	C₂	semidirect
11. C₂₉×#2896	C₂	semidirect
12. C₂×C₂₉×#417	C₂	semidirect
13. C₂₉×#2873	C₂	semidirect
16. C₂₉×#575	C₄	semidirect
29. C₂₉×#520	C₂²	semidirect
30. C₂₉×#520	C₂²	semidirect
31. C₂₉×#520	C₂²	semidirect
32. C₂₉×#519	C₂²	semidirect
34. C₂₉×#518	C₂²	semidirect
37. C₂×C₄×Q₈×C₂₉	C₂²	semidirect
39. C₂×C₄×D₄×C₂₉	C₂²	semidirect
46. C₂₉×#442	C₂²	semidirect
47. C₂₉×#441	C₂²	semidirect
48. C₂₉×#440	C₂²	semidirect
49. C₂₉×#440	C₂²	semidirect
50. C₄×Q₁₆×C₂₉	C₂²	semidirect
51. C₄×SD₁₆×C₂₉	C₂²	semidirect
52. C₄×SD₁₆×C₂₉	C₂²	semidirect
53. C₄×D₈×C₂₉	C₂²	semidirect
54. C₂₉×#428	C₂²	semidirect
55. C₂₉×#428	C₂²	semidirect
56. C₂×C₂₉×#107	C₂²	semidirect
57. C₂×C₂₉×#106	C₂²	semidirect
58. C₂₉×#419	C₂²	semidirect
59. C₂₉×#418	C₂²	semidirect
61. C₂₉×#417	C₂²	semidirect
62. C₂₉×#417	C₂²	semidirect
63. C₂₉×#417	C₂²	semidirect
65. C₂×C₂₉×#103	C₂²	semidirect
66. C₂×C₂₉×#102	C₂²	semidirect
67. C₂₉×#405	C₂²	semidirect
68. C₂₉×#405	C₂²	semidirect
69. C₄×M₁₆×C₂₉	C₂²	semidirect
76. C₂×#41×C₂₉	C₂×C₄	semidirect
77. C₂×#41×C₂₉	C₂×C₄	semidirect
93. C₂₉×#137	C₂×C₄	semidirect
94. C₂₉×#137	C₂×C₄	semidirect
95. C₂₉×AGL(1,ℤ/8)	C₂×C₄	semidirect
96. C₂₉×AGL(1,ℤ/8)	C₂×C₄	semidirect
97. C₂₉×#135	C₂×C₄	semidirect
103. C₂×M₁₆×C₂₉	C₂×C₄	semidirect
189. #41×C₂₉	C₂²×C₄	semidirect
195. C₂×Q₈×C₂₉	C₂²×C₄	semidirect
209. C₂×D₄×C₂₉	C₂²×C₄	semidirect
240. Q₁₆×C₂₉	C₂²×C₄	semidirect
241. SD₁₆×C₂₉	C₂²×C₄	semidirect
242. SD₁₆×C₂₉	C₂²×C₄	semidirect
243. D₈×C₂₉	C₂²×C₄	semidirect
247. M₁₆×C₂₉	C₂²×C₄	semidirect
249. C₂×C₈×C₂₉	C₂²×C₄	semidirect
281. #60170	C₂₉	direct (N × H)
351. #3428	C₂×C₂₉	semidirect
352. C₂×#520	C₂×C₂₉	semidirect
353. #2952	C₂×C₂₉	semidirect
354. #2951	C₂×C₂₉	semidirect
355. #2947	C₂×C₂₉	semidirect
356. #2946	C₂×C₂₉	semidirect
357. C₄×#137	C₂×C₂₉	semidirect
358. C₄×AGL(1,ℤ/8)	C₂×C₂₉	semidirect
359. C₂×#428	C₂×C₂₉	semidirect
360. #2896	C₂×C₂₉	semidirect
361. C₂×#417	C₂×C₂₉	semidirect
362. #2873	C₂×C₂₉	semidirect
396. #575	C₄×C₂₉	semidirect
409. #520	C₂²×C₂₉	semidirect
410. #520	C₂²×C₂₉	semidirect
411. #520	C₂²×C₂₉	semidirect
412. #519	C₂²×C₂₉	semidirect
414. #518	C₂²×C₂₉	semidirect
417. C₂×C₄×Q₈	C₂²×C₂₉	semidirect
419. C₂×C₄×D₄	C₂²×C₂₉	semidirect
426. #442	C₂²×C₂₉	semidirect
427. #441	C₂²×C₂₉	semidirect
428. #440	C₂²×C₂₉	semidirect
429. #440	C₂²×C₂₉	semidirect
430. C₄×Q₁₆	C₂²×C₂₉	semidirect
431. C₄×SD₁₆	C₂²×C₂₉	semidirect
432. C₄×SD₁₆	C₂²×C₂₉	semidirect
433. C₄×D₈	C₂²×C₂₉	semidirect
434. #428	C₂²×C₂₉	semidirect
435. #428	C₂²×C₂₉	semidirect
436. C₂×#107	C₂²×C₂₉	semidirect
437. C₂×#106	C₂²×C₂₉	semidirect
438. #419	C₂²×C₂₉	semidirect
439. #418	C₂²×C₂₉	semidirect
441. #417	C₂²×C₂₉	semidirect
442. #417	C₂²×C₂₉	semidirect
443. #417	C₂²×C₂₉	semidirect
445. C₂×#103	C₂²×C₂₉	semidirect
446. C₂×#102	C₂²×C₂₉	semidirect
447. #405	C₂²×C₂₉	semidirect
448. #405	C₂²×C₂₉	semidirect
449. C₄×M₁₆	C₂²×C₂₉	semidirect
464. C₂×#41	C₂×C₄×C₂₉	semidirect
465. C₂×#41	C₂×C₄×C₂₉	semidirect
481. #137	C₂×C₄×C₂₉	semidirect
482. #137	C₂×C₄×C₂₉	semidirect
483. AGL(1,ℤ/8)	C₂×C₄×C₂₉	semidirect
484. AGL(1,ℤ/8)	C₂×C₄×C₂₉	semidirect
485. #135	C₂×C₄×C₂₉	semidirect
491. C₂×M₁₆	C₂×C₄×C₂₉	semidirect
563. C₂₉	#60170	direct (N × H)
578. #41	C₂²×C₄×C₂₉	semidirect
584. C₂×Q₈	C₂²×C₄×C₂₉	semidirect
598. C₂×D₄	C₂²×C₄×C₂₉	semidirect
629. Q₁₆	C₂²×C₄×C₂₉	semidirect
630. SD₁₆	C₂²×C₄×C₂₉	semidirect
631. SD₁₆	C₂²×C₄×C₂₉	semidirect
632. D₈	C₂²×C₄×C₂₉	semidirect
636. M₁₆	C₂²×C₄×C₂₉	semidirect
638. C₂×C₈	C₂²×C₄×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#575	2
C₂₉×#3428	2
C₂×C₂₉×#520	2
C₂₉×#2952	2
C₂₉×#2951	2
C₂₉×#2947	2
C₂₉×#2946	2
C₄×C₂₉×#137	2
C₄×C₂₉×AGL(1,ℤ/8)	2
C₂×C₂₉×#428	2
C₂₉×#2896	2
C₂×C₂₉×#417	2
C₂₉×#2873	2
#60170	29

Subgroups — C29×#60170 #20355070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#60170 #20355070