Subgroups — C₅₉×#24430 #28436539

Order 15104.

1448 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₉×#416	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2415	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#547	—	2	4	no	—
23	C₅₉×#547	—	2	4	no	—
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₅₉	—	2	1	no	—
26	C₂×#123×C₅₉	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#121×C₅₉	—	2	1	no	—
32	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
36	C₅₉×#467	—	2	4	no	—
37	C₅₉×#452	—	2	4	no	—
38	C₅₉×#452	—	2	4	no	—
39	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#416	—	2	4	no	—
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×#103×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#397	—	2	1	no	—
55	C₅₉×#394	—	2	1	no	—
56	C₅₉×#391	C₂²	1	1	yes	characteristic
57	C₅₉×#389	—	2	1	no	—
58	C₅₉×#389	C₂²	1	1	yes	characteristic
59	C₅₉×#388	—	2	1	no	—
60	C₅₉×#380	C₂²	1	1	yes	characteristic
61	C₅₉×#340	C₂²	1	1	yes	characteristic
62	C₅₉×#340	C₂²	1	1	yes	characteristic
63	C₅₉×#336	C₂²	1	1	yes	characteristic
64	C₅₉×#336	C₂²	1	1	yes	characteristic
65	C₂×#41×C₅₉	—	2	2	no	—
66	C₂×#41×C₅₉	—	2	2	no	—
67	C₂×#41×C₅₉	—	2	2	no	—
68	C₂×#41×C₅₉	—	2	2	no	—
69	C₂×#41×C₅₉	—	2	2	no	—
70	C₂×#41×C₅₉	—	2	2	no	—
71	C₂×#41×C₅₉	—	2	2	no	—
72	C₂×#41×C₅₉	—	4	1	no	—
73	C₂×#41×C₅₉	—	4	1	no	—
74	C₂×#41×C₅₉	—	4	1	no	—
75	C₂×#41×C₅₉	—	4	1	no	—
76	C₂×#41×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	—	2	1	no	—
81	C₂²×D₄×C₅₉	—	2	1	no	—
82	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅₉	—	2	1	no	—
85	C₂³×C₄×C₅₉	—	2	1	no	—
86	C₂³×C₄×C₅₉	—	2	1	no	—
87	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
89	C₂×Q₁₆×C₅₉	—	2	2	no	—
90	C₂×Q₁₆×C₅₉	—	2	2	no	—
91	C₂×Q₁₆×C₅₉	—	2	2	no	—
92	C₂×Q₁₆×C₅₉	—	4	1	no	—
93	C₂×Q₁₆×C₅₉	—	4	1	no	—
94	C₂×Q₁₆×C₅₉	—	4	1	no	—
95	C₂×SD₁₆×C₅₉	—	2	2	no	—
96	C₂×SD₁₆×C₅₉	—	2	2	no	—
97	C₂×SD₁₆×C₅₉	—	2	2	no	—
98	C₂²×C₈×C₅₉	—	2	2	no	—
99	C₂²×C₈×C₅₉	—	2	2	no	—
100	C₂²×C₈×C₅₉	—	4	1	no	—
101	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₅₉	—	2	2	no	—
106	C₄⋊Q₈×C₅₉	—	2	2	no	—
107	#123×C₅₉	—	2	8	no	—
108	#123×C₅₉	—	2	8	no	—
109	C₂²⋊Q₈×C₅₉	—	2	2	no	—
110	C₂²⋊Q₈×C₅₉	—	2	2	no	—
111	C₂²⋊Q₈×C₅₉	—	2	2	no	—
112	C₂²⋊Q₈×C₅₉	—	2	2	no	—
113	C₂²⋊Q₈×C₅₉	—	2	2	no	—
114	C₂²⋊Q₈×C₅₉	—	2	2	no	—
115	C₂²⋊Q₈×C₅₉	—	4	1	no	—
116	C₂²⋊Q₈×C₅₉	D₄	1	4	yes	—
117	#121×C₅₉	—	2	8	no	—
118	C₄×D₄×C₅₉	—	2	2	no	—
119	C₄×D₄×C₅₉	—	2	2	no	—
120	C₄×D₄×C₅₉	—	2	2	no	—
121	C₄×D₄×C₅₉	—	2	2	no	—
122	#117×C₅₉	—	2	2	no	—
123	#117×C₅₉	—	4	1	no	—
124	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
125	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
131	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₅₉	—	2	1	no	—
147	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
148	#107×C₅₉	—	2	2	no	—
149	#103×C₅₉	—	2	2	no	—
150	#103×C₅₉	—	2	2	no	—
151	#103×C₅₉	—	2	2	no	—
152	#103×C₅₉	—	2	2	no	—
153	#103×C₅₉	—	2	2	no	—
154	#103×C₅₉	—	2	2	no	—
155	#103×C₅₉	—	4	1	no	—
156	#102×C₅₉	—	2	2	no	—
157	#102×C₅₉	—	2	2	no	—
158	#102×C₅₉	D₄	1	4	yes	complemented
159	C₂²⋊C₈×C₅₉	—	2	2	no	—
160	C₂²⋊C₈×C₅₉	—	2	2	no	—
161	C₂²⋊C₈×C₅₉	—	4	1	no	—
162	#95×C₅₉	—	2	1	no	—
163	#95×C₅₉	—	2	1	no	—
164	#95×C₅₉	—	2	1	no	—
165	#95×C₅₉	—	2	1	no	—
166	C₂⁴×C₅₉	—	2	1	no	—
167	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
169	#41×C₅₉	—	2	8	no	—
170	#41×C₅₉	—	4	4	no	—
171	#41×C₅₉	—	4	4	no	—
172	#41×C₅₉	—	4	4	no	—
173	#41×C₅₉	—	4	4	no	—
174	#41×C₅₉	—	4	4	no	—
175	#41×C₅₉	—	4	4	no	—
176	#41×C₅₉	—	4	4	no	—
177	C₂×Q₈×C₅₉	—	2	1	no	—
178	C₂×Q₈×C₅₉	—	2	1	no	—
179	C₂×Q₈×C₅₉	—	2	1	no	—
180	C₂×Q₈×C₅₉	—	2	1	no	—
181	C₂×Q₈×C₅₉	—	2	1	no	—
182	C₂×Q₈×C₅₉	—	2	1	no	—
183	C₂×Q₈×C₅₉	—	2	1	no	—
184	C₂×Q₈×C₅₉	—	2	1	no	—
185	C₂×Q₈×C₅₉	—	2	1	no	—
186	C₂×Q₈×C₅₉	—	2	1	no	—
187	C₂×Q₈×C₅₉	—	2	1	no	—
188	C₂×Q₈×C₅₉	—	2	1	no	—
189	C₂×Q₈×C₅₉	—	2	1	no	—
190	C₂×Q₈×C₅₉	—	2	1	no	—
191	C₂×Q₈×C₅₉	—	2	1	no	—
192	C₂×Q₈×C₅₉	—	2	1	no	—
193	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
194	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₅₉	—	2	4	no	—
196	C₂×D₄×C₅₉	—	2	2	no	—
197	C₂×D₄×C₅₉	—	2	4	no	—
198	C₂×D₄×C₅₉	—	2	2	no	—
199	C₂×D₄×C₅₉	—	2	1	no	—
200	C₂×D₄×C₅₉	—	2	1	no	—
201	C₂×D₄×C₅₉	—	2	1	no	—
202	C₂×D₄×C₅₉	—	4	1	no	—
203	C₂×D₄×C₅₉	—	4	2	no	—
204	C₂×D₄×C₅₉	—	4	2	no	—
205	C₂×D₄×C₅₉	—	4	2	no	—
206	C₂×D₄×C₅₉	—	4	2	no	—
207	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
208	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
209	C₂×D₄×C₅₉	#41	1	2	yes	—
210	C₂²×C₄×C₅₉	—	2	1	no	—
211	C₂²×C₄×C₅₉	—	2	1	no	—
212	C₂²×C₄×C₅₉	—	2	1	no	—
213	C₂²×C₄×C₅₉	—	2	1	no	—
214	C₂²×C₄×C₅₉	—	2	4	no	—
215	C₂²×C₄×C₅₉	—	2	4	no	—
216	C₂²×C₄×C₅₉	—	2	1	no	—
217	C₂²×C₄×C₅₉	—	2	1	no	—
218	C₂²×C₄×C₅₉	—	2	1	no	—
219	C₂²×C₄×C₅₉	—	2	1	no	—
220	C₂²×C₄×C₅₉	—	2	4	no	—
221	C₂²×C₄×C₅₉	—	2	1	no	—
222	C₂²×C₄×C₅₉	—	2	1	no	—
223	C₂²×C₄×C₅₉	—	2	1	no	—
224	C₂²×C₄×C₅₉	—	2	1	no	—
225	C₂²×C₄×C₅₉	—	2	1	no	—
226	C₂²×C₄×C₅₉	—	2	1	no	—
227	C₂²×C₄×C₅₉	—	2	1	no	—
228	C₂²×C₄×C₅₉	—	2	1	no	—
229	C₂²×C₄×C₅₉	—	2	1	no	—
230	C₂²×C₄×C₅₉	—	4	2	no	—
231	C₂²×C₄×C₅₉	—	4	2	no	—
232	C₂²×C₄×C₅₉	—	4	2	no	—
233	C₂²×C₄×C₅₉	—	4	2	no	—
234	C₂²×C₄×C₅₉	—	4	2	no	—
235	C₂²×C₄×C₅₉	—	4	2	no	—
236	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₅₉	—	4	4	no	—
244	Q₁₆×C₅₉	—	4	4	no	—
245	SD₁₆×C₅₉	—	4	4	no	—
246	C₂×C₈×C₅₉	—	2	1	no	—
247	C₂×C₈×C₅₉	—	2	1	no	—
248	C₂×C₈×C₅₉	—	2	1	no	—
249	C₂×C₈×C₅₉	—	2	1	no	—
250	C₂×C₈×C₅₉	—	2	1	no	—
251	C₂×C₈×C₅₉	—	2	1	no	—
252	C₂×C₈×C₅₉	—	2	1	no	—
253	C₂×C₈×C₅₉	—	2	1	no	—
254	C₂×C₈×C₅₉	—	2	1	no	—
255	C₂×C₈×C₅₉	—	2	1	no	—
256	C₂×C₈×C₅₉	—	2	1	no	—
257	C₂×C₈×C₅₉	—	4	4	no	—
258	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₅₉	—	2	4	no	—
260	C₄⋊C₄×C₅₉	—	2	4	no	—
261	C₄⋊C₄×C₅₉	—	2	4	no	—
262	C₄⋊C₄×C₅₉	—	2	2	no	—
263	C₄⋊C₄×C₅₉	—	2	4	no	—
264	C₄⋊C₄×C₅₉	—	2	1	no	—
265	C₄⋊C₄×C₅₉	—	2	1	no	—
266	C₄⋊C₄×C₅₉	—	2	1	no	—
267	C₄⋊C₄×C₅₉	—	2	1	no	—
268	C₄⋊C₄×C₅₉	—	2	1	no	—
269	C₄⋊C₄×C₅₉	—	2	1	no	—
270	C₄⋊C₄×C₅₉	—	4	2	no	—
271	C₄⋊C₄×C₅₉	—	4	2	no	—
272	C₄⋊C₄×C₅₉	—	4	2	no	—
273	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
274	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₅₉	—	2	4	no	—
276	C₂²⋊C₄×C₅₉	—	2	4	no	—
277	C₂²⋊C₄×C₅₉	—	2	4	no	—
278	C₂²⋊C₄×C₅₉	—	2	2	no	—
279	C₂²⋊C₄×C₅₉	—	2	2	no	—
280	C₂²⋊C₄×C₅₉	—	4	2	no	—
281	C₂²⋊C₄×C₅₉	—	4	2	no	—
282	C₂²⋊C₄×C₅₉	—	4	2	no	—
283	C₂²⋊C₄×C₅₉	—	4	2	no	—
284	C₄²×C₅₉	—	2	1	no	—
285	C₄²×C₅₉	—	2	1	no	—
286	C₄²×C₅₉	—	4	2	no	—
287	C₂³×C₅₉	—	2	2	no	—
288	C₂³×C₅₉	—	2	1	no	—
289	C₂³×C₅₉	—	2	2	no	—
290	C₂³×C₅₉	—	2	1	no	—
291	C₂³×C₅₉	—	2	2	no	—
292	C₂³×C₅₉	—	2	1	no	—
293	C₂³×C₅₉	—	2	1	no	—
294	C₂³×C₅₉	—	2	1	no	—
295	C₂³×C₅₉	—	2	1	no	—
296	C₂³×C₅₉	—	2	1	no	—
297	C₂³×C₅₉	—	2	1	no	—
298	C₂³×C₅₉	—	2	1	no	—
299	C₂³×C₅₉	—	2	1	no	—
300	C₂³×C₅₉	—	2	1	no	—
301	C₂³×C₅₉	—	2	1	no	—
302	C₂³×C₅₉	—	2	1	no	—
303	C₂³×C₅₉	—	4	1	no	—
304	C₂³×C₅₉	—	4	1	no	—
305	C₂³×C₅₉	—	4	1	no	—
306	C₂³×C₅₉	—	4	1	no	—
307	C₂³×C₅₉	#120	1	2	yes	—
308	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₅₉	—	2	2	no	—
310	Q₈×C₅₉	—	2	2	no	—
311	Q₈×C₅₉	—	2	2	no	—
312	Q₈×C₅₉	—	2	2	no	—
313	Q₈×C₅₉	—	4	1	no	—
314	Q₈×C₅₉	—	4	1	no	—
315	Q₈×C₅₉	—	4	1	no	—
316	Q₈×C₅₉	—	4	1	no	—
317	Q₈×C₅₉	—	4	1	no	—
318	Q₈×C₅₉	—	4	1	no	—
319	Q₈×C₅₉	—	4	1	no	—
320	Q₈×C₅₉	—	4	1	no	—
321	D₄×C₅₉	—	2	2	no	—
322	D₄×C₅₉	—	2	2	no	—
323	D₄×C₅₉	—	2	2	no	—
324	D₄×C₅₉	—	4	4	no	—
325	D₄×C₅₉	—	4	8	no	—
326	D₄×C₅₉	—	4	8	no	—
327	D₄×C₅₉	#121	1	4	yes	—
328	C₂×C₄×C₅₉	—	2	1	no	—
329	C₂×C₄×C₅₉	—	2	1	no	—
330	C₂×C₄×C₅₉	—	2	1	no	—
331	C₂×C₄×C₅₉	—	2	1	no	—
332	C₂×C₄×C₅₉	—	2	2	no	—
333	C₂×C₄×C₅₉	—	2	2	no	—
334	C₂×C₄×C₅₉	—	2	2	no	—
335	C₂×C₄×C₅₉	—	2	2	no	—
336	C₂×C₄×C₅₉	—	2	1	no	—
337	C₂×C₄×C₅₉	—	2	2	no	—
338	C₂×C₄×C₅₉	—	2	1	no	—
339	C₂×C₄×C₅₉	—	2	2	no	—
340	C₂×C₄×C₅₉	—	2	2	no	—
341	C₂×C₄×C₅₉	—	2	2	no	—
342	C₂×C₄×C₅₉	—	2	1	no	—
343	C₂×C₄×C₅₉	—	2	1	no	—
344	C₂×C₄×C₅₉	—	2	1	no	—
345	C₂×C₄×C₅₉	—	2	1	no	—
346	C₂×C₄×C₅₉	—	4	8	no	—
347	C₂×C₄×C₅₉	—	4	8	no	—
348	C₂×C₄×C₅₉	—	4	8	no	—
349	C₂×C₄×C₅₉	—	4	1	no	—
350	C₂×C₄×C₅₉	—	4	1	no	—
351	C₂×C₄×C₅₉	—	4	1	no	—
352	C₂×C₄×C₅₉	—	4	1	no	—
353	C₂×C₄×C₅₉	—	4	1	no	—
354	C₂×C₄×C₅₉	—	4	1	no	—
355	C₂×C₄×C₅₉	—	4	1	no	—
356	C₂×C₄×C₅₉	—	4	1	no	—
357	C₂×C₄×C₅₉	—	4	1	no	—
358	C₂×C₄×C₅₉	—	4	1	no	—
359	C₂×C₄×C₅₉	—	4	1	no	—
360	C₂×C₄×C₅₉	—	4	1	no	—
361	C₂×C₄×C₅₉	—	4	1	no	—
362	C₂×C₄×C₅₉	—	4	1	no	—
363	C₂×C₄×C₅₉	—	4	1	no	—
364	C₂×C₄×C₅₉	—	4	1	no	—
365	C₂×C₄×C₅₉	—	4	1	no	—
366	C₂×C₄×C₅₉	—	4	1	no	—
367	C₂×C₄×C₅₉	—	4	1	no	—
368	C₂×C₄×C₅₉	—	4	1	no	—
369	C₂×C₄×C₅₉	—	4	1	no	—
370	C₂×C₄×C₅₉	#120	1	2	yes	—
371	C₂×C₄×C₅₉	#135	1	2	yes	—
372	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
376	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
377	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
378	C₈×C₅₉	—	2	2	no	—
379	C₈×C₅₉	—	4	1	no	—
380	C₈×C₅₉	—	4	1	no	—
381	C₈×C₅₉	—	4	1	no	—
382	#24430	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂²×C₅₉	—	2	2	no	—
384	C₂²×C₅₉	—	2	4	no	—
385	C₂²×C₅₉	—	2	2	no	—
386	C₂²×C₅₉	—	2	2	no	—
387	C₂²×C₅₉	—	4	2	no	—
388	C₂²×C₅₉	—	4	2	no	—
389	C₂²×C₅₉	—	4	1	no	—
390	C₂²×C₅₉	—	4	2	no	—
391	C₂²×C₅₉	—	4	1	no	—
392	C₂²×C₅₉	—	4	2	no	—
393	C₂²×C₅₉	—	4	1	no	—
394	C₂²×C₅₉	—	4	2	no	—
395	C₂²×C₅₉	—	4	1	no	—
396	C₂²×C₅₉	—	4	2	no	—
397	C₂²×C₅₉	—	4	1	no	—
398	C₂²×C₅₉	—	4	1	no	—
399	C₂²×C₅₉	—	4	1	no	—
400	C₂²×C₅₉	—	4	1	no	—
401	C₂²×C₅₉	—	4	1	no	—
402	C₂²×C₅₉	—	4	1	no	—
403	C₂²×C₅₉	—	4	1	no	—
404	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
405	C₂²×C₅₉	D₄²	1	1	yes	characteristic
406	C₂²×C₅₉	#546	1	1	yes	characteristic
407	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
408	C₂²×C₅₉	#575	1	1	yes	characteristic
409	C₂²×C₅₉	#578	1	1	yes	characteristic
410	C₂²×C₅₉	#578	1	1	yes	characteristic
411	C₄×C₅₉	—	2	2	no	—
412	C₄×C₅₉	—	2	2	no	—
413	C₄×C₅₉	—	4	1	no	—
414	C₄×C₅₉	—	4	2	no	—
415	C₄×C₅₉	—	4	2	no	—
416	C₄×C₅₉	—	4	2	no	—
417	C₄×C₅₉	—	4	1	no	—
418	C₄×C₅₉	—	4	2	no	—
419	C₄×C₅₉	—	8	1	no	—
420	C₄×C₅₉	—	8	1	no	—
421	C₄×C₅₉	—	8	1	no	—
422	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
423	C₄×C₅₉	#534	1	1	yes	characteristic
424	C₄×C₅₉	D₄²	1	1	yes	characteristic
425	C₄×C₅₉	#546	1	1	yes	characteristic
426	C₂×#547	C₂×C₅₉	1	1	yes	characteristic
427	C₂×#467	C₂×C₅₉	1	1	yes	characteristic, complemented
428	C₂×#452	C₂×C₅₉	1	1	yes	characteristic, complemented
429	C₂×#452	C₂×C₅₉	1	1	yes	characteristic, complemented
430	C₂×#416	C₂×C₅₉	1	1	yes	characteristic, complemented
431	#2415	C₂×C₅₉	1	1	yes	characteristic, complemented
432	#2043	C₂×C₅₉	1	1	yes	characteristic, complemented
433	#2036	C₂×C₅₉	1	1	yes	characteristic, complemented
434	#2016	C₂×C₅₉	1	1	yes	characteristic, complemented
435	#2001	C₂×C₅₉	1	1	yes	characteristic, complemented
436	#1877	C₂×C₅₉	1	1	yes	characteristic, complemented
437	#1873	C₂×C₅₉	1	1	yes	characteristic, complemented
438	#1869	C₂×C₅₉	1	1	yes	characteristic, complemented
439	#1862	C₂×C₅₉	1	1	yes	characteristic, complemented
440	#1788	C₂×C₅₉	1	1	yes	characteristic, complemented
441	C₂×C₅₉	—	4	2	no	—
442	C₂×C₅₉	—	4	4	no	—
443	C₂×C₅₉	—	8	1	no	—
444	C₂×C₅₉	#2410	1	1	yes	characteristic
445	C₂×C₅₉	#3002	1	1	yes	characteristic
446	C₂×C₅₉	#3011	1	1	yes	characteristic
447	C₂×C₅₉	#3269	1	1	yes	characteristic
448	C₂×C₅₉	#3283	1	1	yes	characteristic
449	C₂×C₅₉	#3302	1	1	yes	characteristic
450	C₂×C₅₉	#3315	1	1	yes	characteristic
451	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
452	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
453	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
454	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
455	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
456	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
457	#547	—	2	4	no	—
458	#547	—	2	4	no	—
459	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
460	C₂×#123	—	2	1	no	—
461	C₂×#123	—	2	1	no	—
462	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
465	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
466	C₂×#121	—	2	1	no	—
467	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
469	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
470	C₂²×C₄⋊C₄	—	2	1	no	—
471	#467	—	2	4	no	—
472	#452	—	2	4	no	—
473	#452	—	2	4	no	—
474	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
475	#416	—	2	4	no	—
476	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
477	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
478	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
479	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
480	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
481	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
482	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
483	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
484	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
485	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
486	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
487	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
488	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
489	#397	—	2	1	no	—
490	#394	—	2	1	no	—
491	#391	C₂²×C₅₉	1	1	yes	characteristic
492	#389	—	2	1	no	—
493	#389	C₂²×C₅₉	1	1	yes	characteristic
494	#388	—	2	1	no	—
495	#380	C₂²×C₅₉	1	1	yes	characteristic
496	#340	C₂²×C₅₉	1	1	yes	characteristic
497	#340	C₂²×C₅₉	1	1	yes	characteristic
498	#336	C₂²×C₅₉	1	1	yes	characteristic
499	#336	C₂²×C₅₉	1	1	yes	characteristic
500	C₅₉	#24430	1	1	yes	characteristic, direct product factor, Sylow
501	C₂×#41	—	2	2	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	2	no	—
504	C₂×#41	—	2	2	no	—
505	C₂×#41	—	2	2	no	—
506	C₂×#41	—	2	2	no	—
507	C₂×#41	—	2	2	no	—
508	C₂×#41	—	4	1	no	—
509	C₂×#41	—	4	1	no	—
510	C₂×#41	—	4	1	no	—
511	C₂×#41	—	4	1	no	—
512	C₂×#41	D₄×C₅₉	1	4	yes	—
513	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
515	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	2	1	no	—
518	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
519	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
520	C₂³×C₄	—	2	1	no	—
521	C₂³×C₄	—	2	1	no	—
522	C₂³×C₄	—	2	1	no	—
523	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
525	C₂×Q₁₆	—	2	2	no	—
526	C₂×Q₁₆	—	2	2	no	—
527	C₂×Q₁₆	—	2	2	no	—
528	C₂×Q₁₆	—	4	1	no	—
529	C₂×Q₁₆	—	4	1	no	—
530	C₂×Q₁₆	—	4	1	no	—
531	C₂×SD₁₆	—	2	2	no	—
532	C₂×SD₁₆	—	2	2	no	—
533	C₂×SD₁₆	—	2	2	no	—
534	C₂²×C₈	—	2	2	no	—
535	C₂²×C₈	—	2	2	no	—
536	C₂²×C₈	—	4	1	no	—
537	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
539	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
540	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
541	C₄⋊Q₈	—	2	2	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	#123	—	2	8	no	—
544	#123	—	2	8	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	4	1	no	—
552	C₂²⋊Q₈	D₄×C₅₉	1	4	yes	—
553	#121	—	2	8	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	#117	—	2	2	no	—
559	#117	—	4	1	no	—
560	C₂×C₄⋊C₄	—	2	8	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	—	2	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	1	no	—
568	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
581	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
582	C₂×C₄²	—	2	1	no	—
583	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
584	#107	—	2	2	no	—
585	#103	—	2	2	no	—
586	#103	—	2	2	no	—
587	#103	—	2	2	no	—
588	#103	—	2	2	no	—
589	#103	—	2	2	no	—
590	#103	—	2	2	no	—
591	#103	—	4	1	no	—
592	#102	—	2	2	no	—
593	#102	—	2	2	no	—
594	#102	D₄×C₅₉	1	4	yes	complemented
595	C₂²⋊C₈	—	2	2	no	—
596	C₂²⋊C₈	—	2	2	no	—
597	C₂²⋊C₈	—	4	1	no	—
598	#95	—	2	1	no	—
599	#95	—	2	1	no	—
600	#95	—	2	1	no	—
601	#95	—	2	1	no	—
602	C₂⁴	—	2	1	no	—
603	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
604	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
605	#41	—	2	8	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
630	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	4	1	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
644	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
645	C₂×D₄	#41×C₅₉	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	2	1	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	1	no	—
658	C₂²×C₄	—	2	1	no	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	2	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
676	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
677	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
679	Q₁₆	—	4	4	no	—
680	Q₁₆	—	4	4	no	—
681	SD₁₆	—	4	4	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	4	4	no	—
694	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	4	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
710	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	4	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	1	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	1	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	2	1	no	—
733	C₂³	—	2	1	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	#120×C₅₉	1	2	yes	—
744	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
745	Q₈	—	2	2	no	—
746	Q₈	—	2	2	no	—
747	Q₈	—	2	2	no	—
748	Q₈	—	2	2	no	—
749	Q₈	—	4	1	no	—
750	Q₈	—	4	1	no	—
751	Q₈	—	4	1	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	4	1	no	—
754	Q₈	—	4	1	no	—
755	Q₈	—	4	1	no	—
756	Q₈	—	4	1	no	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	4	4	no	—
761	D₄	—	4	8	no	—
762	D₄	—	4	8	no	—
763	D₄	#121×C₅₉	1	4	yes	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	4	8	no	—
783	C₂×C₄	—	4	8	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	4	1	no	—
799	C₂×C₄	—	4	1	no	—
800	C₂×C₄	—	4	1	no	—
801	C₂×C₄	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	4	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	#120×C₅₉	1	2	yes	—
807	C₂×C₄	#135×C₅₉	1	2	yes	—
808	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
810	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
811	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
812	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
813	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
814	C₈	—	2	2	no	—
815	C₈	—	4	1	no	—
816	C₈	—	4	1	no	—
817	C₈	—	4	1	no	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	4	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	1	no	—
839	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
840	C₂²	D₄²×C₅₉	1	1	yes	characteristic
841	C₂²	C₅₉×#546	1	1	yes	characteristic
842	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
843	C₂²	C₅₉×#575	1	1	yes	characteristic
844	C₂²	C₅₉×#578	1	1	yes	characteristic
845	C₂²	C₅₉×#578	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	2	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	1	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	8	1	no	—
855	C₄	—	8	1	no	—
856	C₄	—	8	1	no	—
857	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
858	C₄	C₅₉×#534	1	1	yes	characteristic
859	C₄	D₄²×C₅₉	1	1	yes	characteristic
860	C₄	C₅₉×#546	1	1	yes	characteristic
861	C₂	—	4	2	no	—
862	C₂	—	4	4	no	—
863	C₂	—	8	1	no	—
864	C₂	C₅₉×#2410	1	1	yes	characteristic
865	C₂	C₅₉×#3002	1	1	yes	characteristic
866	C₂	C₅₉×#3011	1	1	yes	characteristic
867	C₂	C₅₉×#3269	1	1	yes	characteristic
868	C₂	C₅₉×#3283	1	1	yes	characteristic
869	C₂	C₅₉×#3302	1	1	yes	characteristic
870	C₂	C₅₉×#3315	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×C₅₉×#547	C₂
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×#467	C₂	semidirect
3. C₂×C₅₉×#452	C₂	semidirect
4. C₂×C₅₉×#452	C₂	semidirect
5. C₂×C₅₉×#416	C₂	semidirect
6. C₅₉×#2415	C₂	semidirect
7. C₅₉×#2043	C₂	semidirect
8. C₅₉×#2036	C₂	semidirect
9. C₅₉×#2016	C₂	semidirect
10. C₅₉×#2001	C₂	semidirect
11. C₅₉×#1877	C₂	semidirect
12. C₅₉×#1873	C₂	semidirect
13. C₅₉×#1869	C₂	semidirect
14. C₅₉×#1862	C₂	semidirect
15. C₅₉×#1788	C₂	semidirect
158. #102×C₅₉	D₄	semidirect
382. #24430	C₅₉	direct (N × H)
427. C₂×#467	C₂×C₅₉	semidirect
428. C₂×#452	C₂×C₅₉	semidirect
429. C₂×#452	C₂×C₅₉	semidirect
430. C₂×#416	C₂×C₅₉	semidirect
431. #2415	C₂×C₅₉	semidirect
432. #2043	C₂×C₅₉	semidirect
433. #2036	C₂×C₅₉	semidirect
434. #2016	C₂×C₅₉	semidirect
435. #2001	C₂×C₅₉	semidirect
436. #1877	C₂×C₅₉	semidirect
437. #1873	C₂×C₅₉	semidirect
438. #1869	C₂×C₅₉	semidirect
439. #1862	C₂×C₅₉	semidirect
440. #1788	C₂×C₅₉	semidirect
500. C₅₉	#24430	direct (N × H)
594. #102	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#547	2
C₂×C₅₉×#467	2
C₂×C₅₉×#452	2
C₂×C₅₉×#416	2
C₅₉×#2415	2
C₅₉×#2043	2
C₅₉×#2036	2
C₅₉×#2016	2
C₅₉×#2001	2
C₅₉×#1877	2
C₅₉×#1873	2
C₅₉×#1869	2
C₅₉×#1862	2
C₅₉×#1788	2
#24430	59

Subgroups — C59×#24430 #28436539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24430 #28436539