Subgroups — C₅₉×#24053 #28436162

Order 15104.

1284 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2485	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1870	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	D₄×Q₈×C₅₉	—	2	4	no	—
20	D₄×Q₈×C₅₉	—	2	4	no	—
21	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₅₉	—	2	1	no	—
29	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#485	—	2	4	no	—
32	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#419	—	2	4	no	—
35	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
50	C₅₉×#397	—	2	1	no	—
51	C₅₉×#394	—	2	1	no	—
52	C₅₉×#389	C₂²	1	1	yes	characteristic
53	C₅₉×#389	C₂²	1	1	yes	characteristic
54	C₅₉×#388	—	2	1	no	—
55	C₅₉×#387	—	2	1	no	—
56	C₅₉×#380	C₂²	1	1	yes	characteristic
57	C₅₉×#380	C₂²	1	1	yes	characteristic
58	C₅₉×#380	C₂²	1	1	yes	characteristic
59	C₅₉×#340	C₂²	1	1	yes	characteristic
60	C₅₉×#340	C₂²	1	1	yes	characteristic
61	C₅₉×#336	C₂²	1	1	yes	characteristic
62	C₅₉×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₅₉	—	2	2	no	—
64	C₂²×Q₈×C₅₉	—	2	2	no	—
65	C₂²×Q₈×C₅₉	—	2	1	no	—
66	C₂²×Q₈×C₅₉	—	2	1	no	—
67	C₂²×Q₈×C₅₉	—	2	2	no	—
68	C₂²×Q₈×C₅₉	—	2	2	no	—
69	C₂²×Q₈×C₅₉	—	2	2	no	—
70	C₂²×Q₈×C₅₉	—	2	2	no	—
71	C₂²×Q₈×C₅₉	—	2	2	no	—
72	C₂²×Q₈×C₅₉	—	4	1	no	—
73	C₂²×Q₈×C₅₉	—	4	1	no	—
74	C₂²×Q₈×C₅₉	—	4	1	no	—
75	C₂²×Q₈×C₅₉	—	4	1	no	—
76	C₂²×Q₈×C₅₉	D₄	1	4	yes	—
77	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₅₉	—	2	1	no	—
82	C₂³×C₄×C₅₉	—	2	1	no	—
83	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₅₉	—	2	2	no	—
86	C₂×M₁₆×C₅₉	—	4	1	no	—
87	C₂×M₁₆×C₅₉	—	4	1	no	—
88	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
92	C₄⋊Q₈×C₅₉	—	2	8	no	—
93	C₄⋊Q₈×C₅₉	—	2	2	no	—
94	C₄⋊Q₈×C₅₉	—	2	2	no	—
95	C₂²⋊Q₈×C₅₉	—	2	8	no	—
96	C₂²⋊Q₈×C₅₉	—	2	8	no	—
97	C₂²⋊Q₈×C₅₉	—	2	2	no	—
98	C₂²⋊Q₈×C₅₉	—	2	2	no	—
99	C₂²⋊Q₈×C₅₉	—	2	2	no	—
100	C₂²⋊Q₈×C₅₉	D₄	1	4	yes	—
101	C₄×Q₈×C₅₉	—	2	2	no	—
102	C₄×Q₈×C₅₉	—	2	2	no	—
103	C₄×D₄×C₅₉	—	2	8	no	—
104	C₄×D₄×C₅₉	—	2	2	no	—
105	C₄×D₄×C₅₉	—	2	2	no	—
106	#117×C₅₉	—	2	2	no	—
107	#117×C₅₉	—	2	2	no	—
108	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
109	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
111	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₅₉	—	2	1	no	—
130	C₂×C₄²×C₅₉	—	2	1	no	—
131	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
132	#107×C₅₉	—	2	2	no	—
133	#106×C₅₉	—	2	2	no	—
134	#103×C₅₉	—	2	2	no	—
135	#103×C₅₉	—	2	2	no	—
136	#103×C₅₉	—	2	2	no	—
137	#103×C₅₉	—	2	2	no	—
138	#103×C₅₉	—	2	2	no	—
139	#103×C₅₉	—	2	2	no	—
140	#103×C₅₉	—	2	2	no	—
141	#103×C₅₉	—	2	2	no	—
142	#103×C₅₉	—	4	1	no	—
143	#103×C₅₉	—	4	1	no	—
144	#103×C₅₉	—	4	1	no	—
145	#103×C₅₉	—	4	1	no	—
146	C₂²⋊C₈×C₅₉	—	2	2	no	—
147	C₂²⋊C₈×C₅₉	—	4	1	no	—
148	C₂²⋊C₈×C₅₉	—	4	1	no	—
149	#95×C₅₉	—	2	1	no	—
150	#95×C₅₉	—	2	1	no	—
151	#95×C₅₉	—	2	1	no	—
152	#95×C₅₉	—	2	1	no	—
153	#95×C₅₉	—	2	1	no	—
154	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
155	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₅₉	—	2	4	no	—
157	C₂×Q₈×C₅₉	—	2	4	no	—
158	C₂×Q₈×C₅₉	—	2	1	no	—
159	C₂×Q₈×C₅₉	—	2	1	no	—
160	C₂×Q₈×C₅₉	—	2	1	no	—
161	C₂×Q₈×C₅₉	—	2	1	no	—
162	C₂×Q₈×C₅₉	—	2	1	no	—
163	C₂×Q₈×C₅₉	—	2	8	no	—
164	C₂×Q₈×C₅₉	—	2	1	no	—
165	C₂×Q₈×C₅₉	—	2	1	no	—
166	C₂×Q₈×C₅₉	—	2	1	no	—
167	C₂×Q₈×C₅₉	—	2	1	no	—
168	C₂×Q₈×C₅₉	—	2	1	no	—
169	C₂×Q₈×C₅₉	—	2	1	no	—
170	C₂×Q₈×C₅₉	—	2	1	no	—
171	C₂×Q₈×C₅₉	—	2	1	no	—
172	C₂×Q₈×C₅₉	—	4	2	no	—
173	C₂×Q₈×C₅₉	—	4	2	no	—
174	C₂×Q₈×C₅₉	—	4	2	no	—
175	C₂×Q₈×C₅₉	—	4	2	no	—
176	C₂×Q₈×C₅₉	—	4	4	no	—
177	C₂×Q₈×C₅₉	—	4	4	no	—
178	C₂×Q₈×C₅₉	—	4	4	no	—
179	C₂×Q₈×C₅₉	—	4	4	no	—
180	C₂×Q₈×C₅₉	—	4	4	no	—
181	C₂×Q₈×C₅₉	—	4	4	no	—
182	C₂×Q₈×C₅₉	—	4	4	no	—
183	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₅₉	#41	1	2	yes	—
187	C₂×Q₈×C₅₉	#41	1	2	yes	—
188	C₂×D₄×C₅₉	—	2	2	no	—
189	C₂×D₄×C₅₉	—	2	2	no	—
190	C₂×D₄×C₅₉	—	2	2	no	—
191	C₂²×C₄×C₅₉	—	2	1	no	—
192	C₂²×C₄×C₅₉	—	2	1	no	—
193	C₂²×C₄×C₅₉	—	2	1	no	—
194	C₂²×C₄×C₅₉	—	2	1	no	—
195	C₂²×C₄×C₅₉	—	2	1	no	—
196	C₂²×C₄×C₅₉	—	2	4	no	—
197	C₂²×C₄×C₅₉	—	2	4	no	—
198	C₂²×C₄×C₅₉	—	2	1	no	—
199	C₂²×C₄×C₅₉	—	2	1	no	—
200	C₂²×C₄×C₅₉	—	2	1	no	—
201	C₂²×C₄×C₅₉	—	2	1	no	—
202	C₂²×C₄×C₅₉	—	2	1	no	—
203	C₂²×C₄×C₅₉	—	2	1	no	—
204	C₂²×C₄×C₅₉	—	2	1	no	—
205	C₂²×C₄×C₅₉	—	2	1	no	—
206	C₂²×C₄×C₅₉	—	2	1	no	—
207	C₂²×C₄×C₅₉	—	2	1	no	—
208	C₂²×C₄×C₅₉	—	2	1	no	—
209	C₂²×C₄×C₅₉	—	2	1	no	—
210	C₂²×C₄×C₅₉	—	2	1	no	—
211	C₂²×C₄×C₅₉	—	4	2	no	—
212	C₂²×C₄×C₅₉	—	4	2	no	—
213	C₂²×C₄×C₅₉	—	4	2	no	—
214	C₂²×C₄×C₅₉	—	4	2	no	—
215	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
222	M₁₆×C₅₉	—	4	4	no	—
223	C₂×C₈×C₅₉	—	2	1	no	—
224	C₂×C₈×C₅₉	—	2	1	no	—
225	C₂×C₈×C₅₉	—	2	1	no	—
226	C₂×C₈×C₅₉	—	2	1	no	—
227	C₂×C₈×C₅₉	—	2	1	no	—
228	C₂×C₈×C₅₉	—	2	1	no	—
229	C₂×C₈×C₅₉	—	2	1	no	—
230	C₂×C₈×C₅₉	—	2	1	no	—
231	C₂×C₈×C₅₉	—	2	1	no	—
232	C₂×C₈×C₅₉	—	2	1	no	—
233	C₂×C₈×C₅₉	—	2	1	no	—
234	C₂×C₈×C₅₉	—	2	1	no	—
235	C₄⋊C₄×C₅₉	—	2	4	no	—
236	C₄⋊C₄×C₅₉	—	2	4	no	—
237	C₄⋊C₄×C₅₉	—	2	4	no	—
238	C₄⋊C₄×C₅₉	—	2	4	no	—
239	C₄⋊C₄×C₅₉	—	2	4	no	—
240	C₄⋊C₄×C₅₉	—	2	2	no	—
241	C₄⋊C₄×C₅₉	—	2	1	no	—
242	C₄⋊C₄×C₅₉	—	2	1	no	—
243	C₄⋊C₄×C₅₉	—	2	1	no	—
244	C₄⋊C₄×C₅₉	—	2	1	no	—
245	C₄⋊C₄×C₅₉	—	2	1	no	—
246	C₄⋊C₄×C₅₉	—	2	1	no	—
247	C₄⋊C₄×C₅₉	—	2	1	no	—
248	C₄⋊C₄×C₅₉	—	2	1	no	—
249	C₄⋊C₄×C₅₉	—	2	1	no	—
250	C₄⋊C₄×C₅₉	—	4	2	no	—
251	C₄⋊C₄×C₅₉	—	8	1	no	—
252	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
253	C₂²⋊C₄×C₅₉	—	2	4	no	—
254	C₂²⋊C₄×C₅₉	—	2	4	no	—
255	C₂²⋊C₄×C₅₉	—	2	2	no	—
256	C₂²⋊C₄×C₅₉	—	2	2	no	—
257	C₂²⋊C₄×C₅₉	—	4	2	no	—
258	C₂²⋊C₄×C₅₉	—	4	2	no	—
259	C₂²⋊C₄×C₅₉	—	8	1	no	—
260	C₂²⋊C₄×C₅₉	—	8	1	no	—
261	C₄²×C₅₉	—	2	4	no	—
262	C₄²×C₅₉	—	2	1	no	—
263	C₄²×C₅₉	—	2	1	no	—
264	C₄²×C₅₉	—	4	2	no	—
265	C₂³×C₅₉	—	2	1	no	—
266	C₂³×C₅₉	—	2	1	no	—
267	C₂³×C₅₉	—	2	1	no	—
268	C₂³×C₅₉	—	2	1	no	—
269	C₂³×C₅₉	—	2	1	no	—
270	C₂³×C₅₉	—	2	1	no	—
271	C₂³×C₅₉	—	2	1	no	—
272	C₂³×C₅₉	—	2	1	no	—
273	C₂³×C₅₉	—	2	1	no	—
274	C₂³×C₅₉	—	2	1	no	—
275	C₂³×C₅₉	—	2	1	no	—
276	C₂³×C₅₉	—	2	1	no	—
277	C₂³×C₅₉	#120	1	2	yes	—
278	C₂³×C₅₉	#137	1	2	yes	—
279	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₅₉	—	2	2	no	—
281	Q₈×C₅₉	—	2	2	no	—
282	Q₈×C₅₉	—	2	2	no	—
283	Q₈×C₅₉	—	2	2	no	—
284	Q₈×C₅₉	—	2	2	no	—
285	Q₈×C₅₉	—	2	2	no	—
286	Q₈×C₅₉	—	2	2	no	—
287	Q₈×C₅₉	—	4	8	no	—
288	Q₈×C₅₉	—	4	8	no	—
289	Q₈×C₅₉	—	4	1	no	—
290	Q₈×C₅₉	—	4	1	no	—
291	Q₈×C₅₉	—	4	1	no	—
292	Q₈×C₅₉	—	4	1	no	—
293	Q₈×C₅₉	#123	1	4	yes	—
294	D₄×C₅₉	—	2	8	no	—
295	C₂×C₄×C₅₉	—	2	1	no	—
296	C₂×C₄×C₅₉	—	2	2	no	—
297	C₂×C₄×C₅₉	—	2	1	no	—
298	C₂×C₄×C₅₉	—	2	1	no	—
299	C₂×C₄×C₅₉	—	2	2	no	—
300	C₂×C₄×C₅₉	—	2	2	no	—
301	C₂×C₄×C₅₉	—	2	1	no	—
302	C₂×C₄×C₅₉	—	2	2	no	—
303	C₂×C₄×C₅₉	—	2	2	no	—
304	C₂×C₄×C₅₉	—	2	2	no	—
305	C₂×C₄×C₅₉	—	2	2	no	—
306	C₂×C₄×C₅₉	—	2	1	no	—
307	C₂×C₄×C₅₉	—	2	2	no	—
308	C₂×C₄×C₅₉	—	2	2	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	1	no	—
311	C₂×C₄×C₅₉	—	2	1	no	—
312	C₂×C₄×C₅₉	—	2	1	no	—
313	C₂×C₄×C₅₉	—	2	1	no	—
314	C₂×C₄×C₅₉	—	2	1	no	—
315	C₂×C₄×C₅₉	—	4	8	no	—
316	C₂×C₄×C₅₉	—	4	8	no	—
317	C₂×C₄×C₅₉	—	4	1	no	—
318	C₂×C₄×C₅₉	—	4	1	no	—
319	C₂×C₄×C₅₉	—	4	1	no	—
320	C₂×C₄×C₅₉	—	4	1	no	—
321	C₂×C₄×C₅₉	—	4	1	no	—
322	C₂×C₄×C₅₉	—	4	1	no	—
323	C₂×C₄×C₅₉	—	4	1	no	—
324	C₂×C₄×C₅₉	—	4	1	no	—
325	C₂×C₄×C₅₉	—	4	1	no	—
326	C₂×C₄×C₅₉	—	4	1	no	—
327	C₂×C₄×C₅₉	—	4	1	no	—
328	C₂×C₄×C₅₉	—	4	1	no	—
329	C₂×C₄×C₅₉	—	4	1	no	—
330	C₂×C₄×C₅₉	—	4	1	no	—
331	C₂×C₄×C₅₉	—	4	1	no	—
332	C₂×C₄×C₅₉	—	4	1	no	—
333	C₂×C₄×C₅₉	—	4	1	no	—
334	C₂×C₄×C₅₉	—	4	1	no	—
335	C₂×C₄×C₅₉	—	4	1	no	—
336	C₂×C₄×C₅₉	—	4	1	no	—
337	C₂×C₄×C₅₉	—	4	1	no	—
338	C₂×C₄×C₅₉	—	4	1	no	—
339	C₂×C₄×C₅₉	#120	1	2	yes	—
340	C₂×C₄×C₅₉	#137	1	2	yes	—
341	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
345	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
347	C₈×C₅₉	—	4	1	no	—
348	C₈×C₅₉	—	4	1	no	—
349	C₈×C₅₉	—	4	1	no	—
350	C₈×C₅₉	—	4	1	no	—
351	#24053	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂²×C₅₉	—	2	2	no	—
353	C₂²×C₅₉	—	2	2	no	—
354	C₂²×C₅₉	—	2	2	no	—
355	C₂²×C₅₉	—	2	2	no	—
356	C₂²×C₅₉	—	2	2	no	—
357	C₂²×C₅₉	—	2	2	no	—
358	C₂²×C₅₉	—	4	1	no	—
359	C₂²×C₅₉	—	4	1	no	—
360	C₂²×C₅₉	—	4	1	no	—
361	C₂²×C₅₉	—	4	1	no	—
362	C₂²×C₅₉	—	4	1	no	—
363	C₂²×C₅₉	—	4	1	no	—
364	C₂²×C₅₉	—	4	1	no	—
365	C₂²×C₅₉	—	4	1	no	—
366	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
367	C₂²×C₅₉	#546	1	1	yes	characteristic
368	C₂²×C₅₉	#546	1	1	yes	characteristic
369	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
370	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
371	C₂²×C₅₉	#577	1	1	yes	characteristic
372	C₂²×C₅₉	#578	1	1	yes	characteristic
373	C₄×C₅₉	—	2	2	no	—
374	C₄×C₅₉	—	2	4	no	—
375	C₄×C₅₉	—	2	2	no	—
376	C₄×C₅₉	—	4	1	no	—
377	C₄×C₅₉	—	4	2	no	—
378	C₄×C₅₉	—	4	2	no	—
379	C₄×C₅₉	—	4	1	no	—
380	C₄×C₅₉	—	4	2	no	—
381	C₄×C₅₉	—	8	1	no	—
382	C₄×C₅₉	—	8	1	no	—
383	C₄×C₅₉	—	8	1	no	—
384	C₄×C₅₉	—	8	1	no	—
385	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
386	C₄×C₅₉	#534	1	1	yes	characteristic
387	C₄×C₅₉	#546	1	1	yes	characteristic
388	C₄×C₅₉	#546	1	1	yes	characteristic
389	C₂×D₄×Q₈	C₂×C₅₉	1	1	yes	characteristic
390	C₂×#485	C₂×C₅₉	1	1	yes	characteristic, complemented
391	C₂×#419	C₂×C₅₉	1	1	yes	characteristic, complemented
392	#2485	C₂×C₅₉	1	1	yes	characteristic
393	#2043	C₂×C₅₉	1	1	yes	characteristic, complemented
394	#2043	C₂×C₅₉	1	1	yes	characteristic, complemented
395	#2036	C₂×C₅₉	1	1	yes	characteristic, complemented
396	#2035	C₂×C₅₉	1	1	yes	characteristic, complemented
397	#1894	C₂×C₅₉	1	1	yes	characteristic, complemented
398	#1870	C₂×C₅₉	1	1	yes	characteristic
399	#1865	C₂×C₅₉	1	1	yes	characteristic, complemented
400	#1863	C₂×C₅₉	1	1	yes	characteristic, complemented
401	#1787	C₂×C₅₉	1	1	yes	characteristic, complemented
402	#1787	C₂×C₅₉	1	1	yes	characteristic, complemented
403	#1787	C₂×C₅₉	1	1	yes	characteristic, complemented
404	C₂×C₅₉	—	4	2	no	—
405	C₂×C₅₉	—	4	2	no	—
406	C₂×C₅₉	#2405	1	1	yes	characteristic
407	C₂×C₅₉	#3004	1	1	yes	characteristic
408	C₂×C₅₉	#3013	1	1	yes	characteristic
409	C₂×C₅₉	#3312	1	1	yes	characteristic
410	C₂×C₅₉	#3320	1	1	yes	characteristic
411	C₂×C₅₉	#3328	1	1	yes	characteristic
412	C₂×C₅₉	#3329	1	1	yes	characteristic
413	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
414	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
415	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
416	D₄×Q₈	—	2	4	no	—
417	D₄×Q₈	—	2	4	no	—
418	C₂×C₄⋊Q₈	—	2	1	no	—
419	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
420	C₂×C₂²⋊Q₈	—	2	1	no	—
421	C₂×C₂²⋊Q₈	—	2	1	no	—
422	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
423	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
424	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
425	C₂×C₄×D₄	—	2	1	no	—
426	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
427	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
428	#485	—	2	4	no	—
429	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
430	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
431	#419	—	2	4	no	—
432	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
433	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
434	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
435	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
436	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
437	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
438	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
439	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
440	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
441	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
442	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
443	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
447	#397	—	2	1	no	—
448	#394	—	2	1	no	—
449	#389	C₂²×C₅₉	1	1	yes	characteristic
450	#389	C₂²×C₅₉	1	1	yes	characteristic
451	#388	—	2	1	no	—
452	#387	—	2	1	no	—
453	#380	C₂²×C₅₉	1	1	yes	characteristic
454	#380	C₂²×C₅₉	1	1	yes	characteristic
455	#380	C₂²×C₅₉	1	1	yes	characteristic
456	#340	C₂²×C₅₉	1	1	yes	characteristic
457	#340	C₂²×C₅₉	1	1	yes	characteristic
458	#336	C₂²×C₅₉	1	1	yes	characteristic
459	#336	C₂²×C₅₉	1	1	yes	characteristic
460	C₅₉	#24053	1	1	yes	characteristic, direct product factor, Sylow
461	C₂²×Q₈	—	2	2	no	—
462	C₂²×Q₈	—	2	2	no	—
463	C₂²×Q₈	—	2	1	no	—
464	C₂²×Q₈	—	2	1	no	—
465	C₂²×Q₈	—	2	2	no	—
466	C₂²×Q₈	—	2	2	no	—
467	C₂²×Q₈	—	2	2	no	—
468	C₂²×Q₈	—	2	2	no	—
469	C₂²×Q₈	—	2	2	no	—
470	C₂²×Q₈	—	4	1	no	—
471	C₂²×Q₈	—	4	1	no	—
472	C₂²×Q₈	—	4	1	no	—
473	C₂²×Q₈	—	4	1	no	—
474	C₂²×Q₈	D₄×C₅₉	1	4	yes	—
475	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
478	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
483	C₂×M₁₆	—	2	2	no	—
484	C₂×M₁₆	—	4	1	no	—
485	C₂×M₁₆	—	4	1	no	—
486	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
487	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
489	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
490	C₄⋊Q₈	—	2	8	no	—
491	C₄⋊Q₈	—	2	2	no	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	8	no	—
494	C₂²⋊Q₈	—	2	8	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	D₄×C₅₉	1	4	yes	—
499	C₄×Q₈	—	2	2	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×D₄	—	2	8	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	#117	—	2	2	no	—
505	#117	—	2	2	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	1	no	—
513	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
530	#107	—	2	2	no	—
531	#106	—	2	2	no	—
532	#103	—	2	2	no	—
533	#103	—	2	2	no	—
534	#103	—	2	2	no	—
535	#103	—	2	2	no	—
536	#103	—	2	2	no	—
537	#103	—	2	2	no	—
538	#103	—	2	2	no	—
539	#103	—	2	2	no	—
540	#103	—	4	1	no	—
541	#103	—	4	1	no	—
542	#103	—	4	1	no	—
543	#103	—	4	1	no	—
544	C₂²⋊C₈	—	2	2	no	—
545	C₂²⋊C₈	—	4	1	no	—
546	C₂²⋊C₈	—	4	1	no	—
547	#95	—	2	1	no	—
548	#95	—	2	1	no	—
549	#95	—	2	1	no	—
550	#95	—	2	1	no	—
551	#95	—	2	1	no	—
552	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
553	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	8	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	1	no	—
567	C₂×Q₈	—	2	1	no	—
568	C₂×Q₈	—	2	1	no	—
569	C₂×Q₈	—	2	1	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	—	4	2	no	—
573	C₂×Q₈	—	4	2	no	—
574	C₂×Q₈	—	4	4	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×Q₈	—	4	4	no	—
577	C₂×Q₈	—	4	4	no	—
578	C₂×Q₈	—	4	4	no	—
579	C₂×Q₈	—	4	4	no	—
580	C₂×Q₈	—	4	4	no	—
581	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
582	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
583	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
584	C₂×Q₈	#41×C₅₉	1	2	yes	—
585	C₂×Q₈	#41×C₅₉	1	2	yes	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	4	2	no	—
610	C₂²×C₄	—	4	2	no	—
611	C₂²×C₄	—	4	2	no	—
612	C₂²×C₄	—	4	2	no	—
613	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
616	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
617	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
618	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
620	M₁₆	—	4	4	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	1	no	—
642	C₄⋊C₄	—	2	1	no	—
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₄⋊C₄	—	8	1	no	—
650	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	4	2	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	8	1	no	—
658	C₂²⋊C₄	—	8	1	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	4	2	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	#120×C₅₉	1	2	yes	—
676	C₂³	#137×C₅₉	1	2	yes	—
677	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	2	2	no	—
681	Q₈	—	2	2	no	—
682	Q₈	—	2	2	no	—
683	Q₈	—	2	2	no	—
684	Q₈	—	2	2	no	—
685	Q₈	—	4	8	no	—
686	Q₈	—	4	8	no	—
687	Q₈	—	4	1	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	1	no	—
690	Q₈	—	4	1	no	—
691	Q₈	#123×C₅₉	1	4	yes	—
692	D₄	—	2	8	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	8	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	#120×C₅₉	1	2	yes	—
738	C₂×C₄	#137×C₅₉	1	2	yes	—
739	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
743	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
744	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
745	C₈	—	4	1	no	—
746	C₈	—	4	1	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
764	C₂²	C₅₉×#546	1	1	yes	characteristic
765	C₂²	C₅₉×#546	1	1	yes	characteristic
766	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
767	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
768	C₂²	C₅₉×#577	1	1	yes	characteristic
769	C₂²	C₅₉×#578	1	1	yes	characteristic
770	C₄	—	2	2	no	—
771	C₄	—	2	2	no	—
772	C₄	—	2	4	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	1	no	—
776	C₄	—	4	2	no	—
777	C₄	—	4	2	no	—
778	C₄	—	8	1	no	—
779	C₄	—	8	1	no	—
780	C₄	—	8	1	no	—
781	C₄	—	8	1	no	—
782	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
783	C₄	C₅₉×#534	1	1	yes	characteristic
784	C₄	C₅₉×#546	1	1	yes	characteristic
785	C₄	C₅₉×#546	1	1	yes	characteristic
786	C₂	—	4	2	no	—
787	C₂	—	4	2	no	—
788	C₂	C₅₉×#2405	1	1	yes	characteristic
789	C₂	C₅₉×#3004	1	1	yes	characteristic
790	C₂	C₅₉×#3013	1	1	yes	characteristic
791	C₂	C₅₉×#3312	1	1	yes	characteristic
792	C₂	C₅₉×#3320	1	1	yes	characteristic
793	C₂	C₅₉×#3328	1	1	yes	characteristic
794	C₂	C₅₉×#3329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×D₄×C₅₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#485	C₂	semidirect
3. C₂×C₅₉×#419	C₂	semidirect
5. C₅₉×#2043	C₂	semidirect
6. C₅₉×#2043	C₂	semidirect
7. C₅₉×#2036	C₂	semidirect
8. C₅₉×#2035	C₂	semidirect
9. C₅₉×#1894	C₂	semidirect
11. C₅₉×#1865	C₂	semidirect
12. C₅₉×#1863	C₂	semidirect
13. C₅₉×#1787	C₂	semidirect
14. C₅₉×#1787	C₂	semidirect
15. C₅₉×#1787	C₂	semidirect
351. #24053	C₅₉	direct (N × H)
390. C₂×#485	C₂×C₅₉	semidirect
391. C₂×#419	C₂×C₅₉	semidirect
393. #2043	C₂×C₅₉	semidirect
394. #2043	C₂×C₅₉	semidirect
395. #2036	C₂×C₅₉	semidirect
396. #2035	C₂×C₅₉	semidirect
397. #1894	C₂×C₅₉	semidirect
399. #1865	C₂×C₅₉	semidirect
400. #1863	C₂×C₅₉	semidirect
401. #1787	C₂×C₅₉	semidirect
402. #1787	C₂×C₅₉	semidirect
403. #1787	C₂×C₅₉	semidirect
460. C₅₉	#24053	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×D₄×Q₈×C₅₉	2
C₂×C₅₉×#485	2
C₂×C₅₉×#419	2
C₅₉×#2485	2
C₅₉×#2043	2
C₅₉×#2036	2
C₅₉×#2035	2
C₅₉×#1894	2
C₅₉×#1870	2
C₅₉×#1865	2
C₅₉×#1863	2
C₅₉×#1787	2
#24053	59

Subgroups — C59×#24053 #28436162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24053 #28436162