Subgroups — C₅₉×#23583 #28435692

Order 15104.

1178 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2035	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2023	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2000	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#1999	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#102×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#542	—	2	4	no	—
19	C₅₉×#542	—	2	4	no	—
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₅₉	—	2	1	no	—
22	C₂×#124×C₅₉	—	2	1	no	—
23	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#123×C₅₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#442	—	2	4	no	—
34	C₄×SD₁₆×C₅₉	—	2	4	no	—
35	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#106×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×#102×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₅₉×#390	—	2	1	no	—
50	C₅₉×#390	C₂²	1	1	yes	characteristic
51	C₅₉×#389	C₂²	1	1	yes	characteristic
52	C₅₉×#388	—	2	1	no	—
53	C₅₉×#386	—	2	1	no	—
54	C₅₉×#385	—	2	1	no	—
55	C₅₉×#380	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₅₉×#340	C₂²	1	1	yes	characteristic
58	C₅₉×#340	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	1	no	—
64	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₅₉	—	2	1	no	—
66	C₂²×D₄×C₅₉	—	2	1	no	—
67	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₅₉	—	2	1	no	—
70	C₂³×C₄×C₅₉	—	2	1	no	—
71	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
72	C₂×SD₁₆×C₅₉	—	2	2	no	—
73	C₂×SD₁₆×C₅₉	—	2	2	no	—
74	C₂×SD₁₆×C₅₉	—	2	2	no	—
75	C₂×D₈×C₅₉	—	2	2	no	—
76	C₂×D₈×C₅₉	—	2	2	no	—
77	C₂×D₈×C₅₉	—	2	2	no	—
78	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₅₉	—	2	2	no	—
83	C₄⋊Q₈×C₅₉	—	2	2	no	—
84	#126×C₅₉	—	2	8	no	—
85	#124×C₅₉	—	2	8	no	—
86	#124×C₅₉	—	2	2	no	—
87	#124×C₅₉	—	2	2	no	—
88	#123×C₅₉	—	2	8	no	—
89	C₂²⋊Q₈×C₅₉	—	2	8	no	—
90	C₂²⋊Q₈×C₅₉	—	2	2	no	—
91	C₂²⋊Q₈×C₅₉	—	2	2	no	—
92	#121×C₅₉	—	2	2	no	—
93	#121×C₅₉	—	2	2	no	—
94	#121×C₅₉	—	2	2	no	—
95	#121×C₅₉	—	2	2	no	—
96	C₄×Q₈×C₅₉	—	2	2	no	—
97	C₄×Q₈×C₅₉	D₄	1	4	yes	complemented
98	C₄×D₄×C₅₉	—	2	2	no	—
99	C₄×D₄×C₅₉	—	2	2	no	—
100	C₄×D₄×C₅₉	—	2	2	no	—
101	C₄×D₄×C₅₉	D₄	1	4	yes	complemented
102	#117×C₅₉	—	2	2	no	—
103	#117×C₅₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
105	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
108	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
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	D₄	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₅₉	—	2	1	no	—
128	C₂×C₄²×C₅₉	—	2	1	no	—
129	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
131	#106×C₅₉	—	2	2	no	—
132	#106×C₅₉	—	2	2	no	—
133	#103×C₅₉	—	2	2	no	—
134	#103×C₅₉	—	2	2	no	—
135	#103×C₅₉	—	2	2	no	—
136	#102×C₅₉	—	2	2	no	—
137	#102×C₅₉	—	2	2	no	—
138	#102×C₅₉	—	2	2	no	—
139	#102×C₅₉	—	2	2	no	—
140	#102×C₅₉	—	2	2	no	—
141	C₂²⋊C₈×C₅₉	—	2	2	no	—
142	C₂²⋊C₈×C₅₉	—	2	2	no	—
143	#97×C₅₉	—	2	2	no	—
144	C₄×C₈×C₅₉	—	2	2	no	—
145	#95×C₅₉	—	2	1	no	—
146	#95×C₅₉	—	2	1	no	—
147	#95×C₅₉	—	2	1	no	—
148	C₂⁴×C₅₉	—	2	1	no	—
149	C₂⁴×C₅₉	—	2	1	no	—
150	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₅₉	—	2	4	no	—
152	C₂×Q₈×C₅₉	—	2	1	no	—
153	C₂×Q₈×C₅₉	—	2	1	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	—	2	1	no	—
156	C₂×Q₈×C₅₉	—	2	1	no	—
157	C₂×Q₈×C₅₉	—	8	1	no	—
158	C₂×Q₈×C₅₉	—	8	1	no	—
159	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₅₉	—	2	4	no	—
161	C₂×D₄×C₅₉	—	2	4	no	—
162	C₂×D₄×C₅₉	—	2	1	no	—
163	C₂×D₄×C₅₉	—	2	1	no	—
164	C₂×D₄×C₅₉	—	2	1	no	—
165	C₂×D₄×C₅₉	—	2	1	no	—
166	C₂×D₄×C₅₉	—	2	1	no	—
167	C₂×D₄×C₅₉	—	2	1	no	—
168	C₂×D₄×C₅₉	—	2	1	no	—
169	C₂×D₄×C₅₉	—	2	1	no	—
170	C₂×D₄×C₅₉	—	2	1	no	—
171	C₂×D₄×C₅₉	—	2	1	no	—
172	C₂×D₄×C₅₉	—	8	1	no	—
173	C₂×D₄×C₅₉	—	8	1	no	—
174	C₂×D₄×C₅₉	—	8	1	no	—
175	C₂×D₄×C₅₉	—	8	1	no	—
176	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₅₉	#41	1	2	yes	—
178	C₂²×C₄×C₅₉	—	2	1	no	—
179	C₂²×C₄×C₅₉	—	2	1	no	—
180	C₂²×C₄×C₅₉	—	2	1	no	—
181	C₂²×C₄×C₅₉	—	2	1	no	—
182	C₂²×C₄×C₅₉	—	2	1	no	—
183	C₂²×C₄×C₅₉	—	2	1	no	—
184	C₂²×C₄×C₅₉	—	2	1	no	—
185	C₂²×C₄×C₅₉	—	2	1	no	—
186	C₂²×C₄×C₅₉	—	2	1	no	—
187	C₂²×C₄×C₅₉	—	2	1	no	—
188	C₂²×C₄×C₅₉	—	2	4	no	—
189	C₂²×C₄×C₅₉	—	2	1	no	—
190	C₂²×C₄×C₅₉	—	2	1	no	—
191	C₂²×C₄×C₅₉	—	4	2	no	—
192	C₂²×C₄×C₅₉	—	8	1	no	—
193	C₂²×C₄×C₅₉	—	8	1	no	—
194	C₂²×C₄×C₅₉	—	8	1	no	—
195	C₂²×C₄×C₅₉	—	8	1	no	—
196	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
202	SD₁₆×C₅₉	—	2	8	no	—
203	D₈×C₅₉	—	2	8	no	—
204	C₂×C₈×C₅₉	—	2	1	no	—
205	C₂×C₈×C₅₉	—	2	1	no	—
206	C₂×C₈×C₅₉	—	2	1	no	—
207	C₂×C₈×C₅₉	—	2	1	no	—
208	C₂×C₈×C₅₉	—	2	1	no	—
209	C₂×C₈×C₅₉	—	2	1	no	—
210	C₂×C₈×C₅₉	—	2	1	no	—
211	C₂×C₈×C₅₉	—	2	1	no	—
212	C₂×C₈×C₅₉	—	2	1	no	—
213	C₂×C₈×C₅₉	—	2	1	no	—
214	C₂×C₈×C₅₉	#41	1	2	yes	—
215	C₂×C₈×C₅₉	#41	1	2	yes	—
216	C₄⋊C₄×C₅₉	—	2	4	no	—
217	C₄⋊C₄×C₅₉	—	2	4	no	—
218	C₄⋊C₄×C₅₉	—	2	4	no	—
219	C₄⋊C₄×C₅₉	—	2	2	no	—
220	C₄⋊C₄×C₅₉	—	2	2	no	—
221	C₄⋊C₄×C₅₉	—	2	1	no	—
222	C₄⋊C₄×C₅₉	—	2	1	no	—
223	C₄⋊C₄×C₅₉	—	2	1	no	—
224	C₄⋊C₄×C₅₉	—	2	1	no	—
225	C₄⋊C₄×C₅₉	—	2	1	no	—
226	C₄⋊C₄×C₅₉	—	2	1	no	—
227	C₄⋊C₄×C₅₉	—	2	1	no	—
228	C₄⋊C₄×C₅₉	—	8	1	no	—
229	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
231	C₄⋊C₄×C₅₉	#41	1	2	yes	—
232	C₂²⋊C₄×C₅₉	—	2	4	no	—
233	C₂²⋊C₄×C₅₉	—	2	4	no	—
234	C₂²⋊C₄×C₅₉	—	2	4	no	—
235	C₂²⋊C₄×C₅₉	—	2	4	no	—
236	C₂²⋊C₄×C₅₉	—	2	4	no	—
237	C₂²⋊C₄×C₅₉	—	2	4	no	—
238	C₂²⋊C₄×C₅₉	—	2	2	no	—
239	C₂²⋊C₄×C₅₉	—	2	2	no	—
240	C₂²⋊C₄×C₅₉	—	4	2	no	—
241	C₂²⋊C₄×C₅₉	—	8	1	no	—
242	C₂²⋊C₄×C₅₉	—	8	1	no	—
243	C₂²⋊C₄×C₅₉	—	8	1	no	—
244	C₄²×C₅₉	—	2	4	no	—
245	C₄²×C₅₉	—	2	1	no	—
246	C₄²×C₅₉	—	2	1	no	—
247	C₄²×C₅₉	—	8	1	no	—
248	C₄²×C₅₉	C₂×D₄	1	2	yes	—
249	C₄²×C₅₉	C₂×D₄	1	2	yes	—
250	C₂³×C₅₉	—	2	1	no	—
251	C₂³×C₅₉	—	2	2	no	—
252	C₂³×C₅₉	—	2	2	no	—
253	C₂³×C₅₉	—	2	1	no	—
254	C₂³×C₅₉	—	2	1	no	—
255	C₂³×C₅₉	—	2	1	no	—
256	C₂³×C₅₉	—	2	1	no	—
257	C₂³×C₅₉	—	2	1	no	—
258	C₂³×C₅₉	—	2	1	no	—
259	C₂³×C₅₉	—	4	1	no	—
260	C₂³×C₅₉	—	4	1	no	—
261	C₂³×C₅₉	—	4	1	no	—
262	C₂³×C₅₉	—	4	1	no	—
263	C₂³×C₅₉	—	4	1	no	—
264	C₂³×C₅₉	—	4	1	no	—
265	C₂³×C₅₉	—	4	1	no	—
266	C₂³×C₅₉	—	4	1	no	—
267	C₂³×C₅₉	—	4	1	no	—
268	C₂³×C₅₉	—	4	1	no	—
269	C₂³×C₅₉	—	4	1	no	—
270	C₂³×C₅₉	—	4	1	no	—
271	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
272	Q₈×C₅₉	—	2	2	no	—
273	Q₈×C₅₉	—	2	2	no	—
274	Q₈×C₅₉	—	4	1	no	—
275	Q₈×C₅₉	—	4	1	no	—
276	Q₈×C₅₉	—	8	4	no	—
277	D₄×C₅₉	—	2	2	no	—
278	D₄×C₅₉	—	2	2	no	—
279	D₄×C₅₉	—	2	2	no	—
280	D₄×C₅₉	—	2	2	no	—
281	D₄×C₅₉	—	4	1	no	—
282	D₄×C₅₉	—	4	1	no	—
283	D₄×C₅₉	—	4	1	no	—
284	D₄×C₅₉	—	4	1	no	—
285	D₄×C₅₉	—	8	4	no	—
286	D₄×C₅₉	—	8	4	no	—
287	C₂×C₄×C₅₉	—	2	1	no	—
288	C₂×C₄×C₅₉	—	2	1	no	—
289	C₂×C₄×C₅₉	—	2	1	no	—
290	C₂×C₄×C₅₉	—	2	1	no	—
291	C₂×C₄×C₅₉	—	2	1	no	—
292	C₂×C₄×C₅₉	—	2	2	no	—
293	C₂×C₄×C₅₉	—	2	1	no	—
294	C₂×C₄×C₅₉	—	2	2	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	2	no	—
299	C₂×C₄×C₅₉	—	2	1	no	—
300	C₂×C₄×C₅₉	—	2	1	no	—
301	C₂×C₄×C₅₉	—	2	1	no	—
302	C₂×C₄×C₅₉	—	2	1	no	—
303	C₂×C₄×C₅₉	—	2	1	no	—
304	C₂×C₄×C₅₉	—	4	1	no	—
305	C₂×C₄×C₅₉	—	4	1	no	—
306	C₂×C₄×C₅₉	—	4	1	no	—
307	C₂×C₄×C₅₉	—	4	1	no	—
308	C₂×C₄×C₅₉	—	4	1	no	—
309	C₂×C₄×C₅₉	—	4	1	no	—
310	C₂×C₄×C₅₉	—	4	1	no	—
311	C₂×C₄×C₅₉	—	4	1	no	—
312	C₂×C₄×C₅₉	—	4	1	no	—
313	C₂×C₄×C₅₉	—	4	1	no	—
314	C₂×C₄×C₅₉	—	4	1	no	—
315	C₂×C₄×C₅₉	—	4	1	no	—
316	C₂×C₄×C₅₉	—	4	1	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	—	8	4	no	—
323	C₂×C₄×C₅₉	—	8	4	no	—
324	C₂×C₄×C₅₉	#120	1	2	yes	—
325	C₂×C₄×C₅₉	#120	1	2	yes	—
326	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
330	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
331	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
332	C₈×C₅₉	—	2	2	no	—
333	C₈×C₅₉	—	2	2	no	—
334	C₈×C₅₉	—	4	1	no	—
335	C₈×C₅₉	—	4	1	no	—
336	#23583	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂²×C₅₉	—	4	1	no	—
338	C₂²×C₅₉	—	4	2	no	—
339	C₂²×C₅₉	—	4	1	no	—
340	C₂²×C₅₉	—	4	2	no	—
341	C₂²×C₅₉	—	4	1	no	—
342	C₂²×C₅₉	—	4	2	no	—
343	C₂²×C₅₉	—	4	2	no	—
344	C₂²×C₅₉	—	4	1	no	—
345	C₂²×C₅₉	—	4	1	no	—
346	C₂²×C₅₉	—	4	1	no	—
347	C₂²×C₅₉	—	4	2	no	—
348	C₂²×C₅₉	—	4	2	no	—
349	C₂²×C₅₉	—	4	1	no	—
350	C₂²×C₅₉	—	8	1	no	—
351	C₂²×C₅₉	—	8	1	no	—
352	C₂²×C₅₉	—	8	1	no	—
353	C₂²×C₅₉	—	8	1	no	—
354	C₂²×C₅₉	—	8	1	no	—
355	C₂²×C₅₉	—	8	1	no	—
356	C₂²×C₅₉	—	8	1	no	—
357	C₂²×C₅₉	—	8	1	no	—
358	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
359	C₂²×C₅₉	#525	1	1	yes	characteristic
360	C₂²×C₅₉	#532	1	1	yes	characteristic
361	C₂²×C₅₉	#576	1	1	yes	characteristic
362	C₂²×C₅₉	#577	1	1	yes	characteristic
363	C₂²×C₅₉	#577	1	1	yes	characteristic
364	C₂²×C₅₉	#577	1	1	yes	characteristic
365	C₄×C₅₉	—	2	2	no	—
366	C₄×C₅₉	—	2	2	no	—
367	C₄×C₅₉	—	4	2	no	—
368	C₄×C₅₉	—	4	1	no	—
369	C₄×C₅₉	—	4	2	no	—
370	C₄×C₅₉	—	4	1	no	—
371	C₄×C₅₉	—	4	1	no	—
372	C₄×C₅₉	—	4	2	no	—
373	C₄×C₅₉	—	4	2	no	—
374	C₄×C₅₉	—	8	1	no	—
375	C₄×C₅₉	—	8	1	no	—
376	C₄×C₅₉	#525	1	1	yes	characteristic
377	C₄×C₅₉	#525	1	1	yes	characteristic
378	C₄×C₅₉	#532	1	1	yes	characteristic
379	C₄×C₅₉	#532	1	1	yes	characteristic
380	C₂×#542	C₂×C₅₉	1	1	yes	characteristic, complemented
381	C₂×#442	C₂×C₅₉	1	1	yes	characteristic, complemented
382	C₂×C₄×SD₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
383	#2324	C₂×C₅₉	1	1	yes	characteristic, complemented
384	#2058	C₂×C₅₉	1	1	yes	characteristic, complemented
385	#2042	C₂×C₅₉	1	1	yes	characteristic, complemented
386	#2035	C₂×C₅₉	1	1	yes	characteristic, complemented
387	#2034	C₂×C₅₉	1	1	yes	characteristic, complemented
388	#2023	C₂×C₅₉	1	1	yes	characteristic, complemented
389	#2012	C₂×C₅₉	1	1	yes	characteristic, complemented
390	#2000	C₂×C₅₉	1	1	yes	characteristic, complemented
391	#1999	C₂×C₅₉	1	1	yes	characteristic
392	#1763	C₂×C₅₉	1	1	yes	characteristic, complemented
393	C₄×#102	C₂×C₅₉	1	1	yes	characteristic, complemented
394	#1750	C₂×C₅₉	1	1	yes	characteristic, complemented
395	C₂×C₅₉	—	8	1	no	—
396	C₂×C₅₉	—	8	2	no	—
397	C₂×C₅₉	—	8	2	no	—
398	C₂×C₅₉	#2388	1	1	yes	characteristic
399	C₂×C₅₉	#3010	1	1	yes	characteristic
400	C₂×C₅₉	#3012	1	1	yes	characteristic
401	C₂×C₅₉	#3118	1	1	yes	characteristic
402	C₂×C₅₉	#3125	1	1	yes	characteristic
403	C₂×C₅₉	#3173	1	1	yes	characteristic
404	C₂×C₅₉	#3179	1	1	yes	characteristic
405	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
406	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
407	#542	—	2	4	no	—
408	#542	—	2	4	no	—
409	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
410	C₂×#126	—	2	1	no	—
411	C₂×#124	—	2	1	no	—
412	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
413	C₂×#123	—	2	1	no	—
414	C₂×C₂²⋊Q₈	—	2	1	no	—
415	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
416	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
417	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
418	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
422	#442	—	2	4	no	—
423	C₄×SD₁₆	—	2	4	no	—
424	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
425	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
426	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
427	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
428	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
429	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
430	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
431	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
432	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
433	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
436	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
437	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
438	#390	—	2	1	no	—
439	#390	C₂²×C₅₉	1	1	yes	characteristic
440	#389	C₂²×C₅₉	1	1	yes	characteristic
441	#388	—	2	1	no	—
442	#386	—	2	1	no	—
443	#385	—	2	1	no	—
444	#380	C₂²×C₅₉	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
446	#340	C₂²×C₅₉	1	1	yes	characteristic
447	#340	C₂²×C₅₉	1	1	yes	characteristic
448	#340	C₂²×C₅₉	1	1	yes	characteristic
449	#340	C₂²×C₅₉	1	1	yes	characteristic
450	#336	C₂²×C₅₉	1	1	yes	characteristic
451	#336	C₂²×C₅₉	1	1	yes	characteristic
452	C₅₉	#23583	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²×Q₈	—	2	1	no	—
454	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
458	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
459	C₂³×C₄	—	2	1	no	—
460	C₂³×C₄	—	2	1	no	—
461	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
462	C₂×SD₁₆	—	2	2	no	—
463	C₂×SD₁₆	—	2	2	no	—
464	C₂×SD₁₆	—	2	2	no	—
465	C₂×D₈	—	2	2	no	—
466	C₂×D₈	—	2	2	no	—
467	C₂×D₈	—	2	2	no	—
468	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
469	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
472	C₄⋊Q₈	—	2	2	no	—
473	C₄⋊Q₈	—	2	2	no	—
474	#126	—	2	8	no	—
475	#124	—	2	8	no	—
476	#124	—	2	2	no	—
477	#124	—	2	2	no	—
478	#123	—	2	8	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	2	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	D₄×C₅₉	1	4	yes	complemented
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	D₄×C₅₉	1	4	yes	complemented
492	#117	—	2	2	no	—
493	#117	—	2	2	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
520	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
521	#106	—	2	2	no	—
522	#106	—	2	2	no	—
523	#103	—	2	2	no	—
524	#103	—	2	2	no	—
525	#103	—	2	2	no	—
526	#102	—	2	2	no	—
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	#102	—	2	2	no	—
531	C₂²⋊C₈	—	2	2	no	—
532	C₂²⋊C₈	—	2	2	no	—
533	#97	—	2	2	no	—
534	C₄×C₈	—	2	2	no	—
535	#95	—	2	1	no	—
536	#95	—	2	1	no	—
537	#95	—	2	1	no	—
538	C₂⁴	—	2	1	no	—
539	C₂⁴	—	2	1	no	—
540	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
541	C₂×Q₈	—	2	4	no	—
542	C₂×Q₈	—	2	1	no	—
543	C₂×Q₈	—	2	1	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	8	1	no	—
548	C₂×Q₈	—	8	1	no	—
549	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	8	1	no	—
563	C₂×D₄	—	8	1	no	—
564	C₂×D₄	—	8	1	no	—
565	C₂×D₄	—	8	1	no	—
566	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
567	C₂×D₄	#41×C₅₉	1	2	yes	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	4	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	8	1	no	—
583	C₂²×C₄	—	8	1	no	—
584	C₂²×C₄	—	8	1	no	—
585	C₂²×C₄	—	8	1	no	—
586	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
592	SD₁₆	—	2	8	no	—
593	D₈	—	2	8	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	#41×C₅₉	1	2	yes	—
605	C₂×C₈	#41×C₅₉	1	2	yes	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	8	1	no	—
619	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
620	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
621	C₄⋊C₄	#41×C₅₉	1	2	yes	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	8	1	no	—
632	C₂²⋊C₄	—	8	1	no	—
633	C₂²⋊C₄	—	8	1	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₄²	—	8	1	no	—
638	C₄²	C₂×D₄×C₅₉	1	2	yes	—
639	C₄²	C₂×D₄×C₅₉	1	2	yes	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
662	Q₈	—	2	2	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	4	1	no	—
665	Q₈	—	4	1	no	—
666	Q₈	—	8	4	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	4	1	no	—
675	D₄	—	8	4	no	—
676	D₄	—	8	4	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	8	4	no	—
713	C₂×C₄	—	8	4	no	—
714	C₂×C₄	#120×C₅₉	1	2	yes	—
715	C₂×C₄	#120×C₅₉	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
718	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
719	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
721	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
722	C₈	—	2	2	no	—
723	C₈	—	2	2	no	—
724	C₈	—	4	1	no	—
725	C₈	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
748	C₂²	C₅₉×#525	1	1	yes	characteristic
749	C₂²	C₅₉×#532	1	1	yes	characteristic
750	C₂²	C₅₉×#576	1	1	yes	characteristic
751	C₂²	C₅₉×#577	1	1	yes	characteristic
752	C₂²	C₅₉×#577	1	1	yes	characteristic
753	C₂²	C₅₉×#577	1	1	yes	characteristic
754	C₄	—	2	2	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	1	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	8	1	no	—
764	C₄	—	8	1	no	—
765	C₄	C₅₉×#525	1	1	yes	characteristic
766	C₄	C₅₉×#525	1	1	yes	characteristic
767	C₄	C₅₉×#532	1	1	yes	characteristic
768	C₄	C₅₉×#532	1	1	yes	characteristic
769	C₂	—	8	1	no	—
770	C₂	—	8	2	no	—
771	C₂	—	8	2	no	—
772	C₂	C₅₉×#2388	1	1	yes	characteristic
773	C₂	C₅₉×#3010	1	1	yes	characteristic
774	C₂	C₅₉×#3012	1	1	yes	characteristic
775	C₂	C₅₉×#3118	1	1	yes	characteristic
776	C₂	C₅₉×#3125	1	1	yes	characteristic
777	C₂	C₅₉×#3173	1	1	yes	characteristic
778	C₂	C₅₉×#3179	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#1999	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#542	C₂	semidirect
2. C₂×C₅₉×#442	C₂	semidirect
3. C₂×C₄×SD₁₆×C₅₉	C₂	semidirect
4. C₅₉×#2324	C₂	semidirect
5. C₅₉×#2058	C₂	semidirect
6. C₅₉×#2042	C₂	semidirect
7. C₅₉×#2035	C₂	semidirect
8. C₅₉×#2034	C₂	semidirect
9. C₅₉×#2023	C₂	semidirect
10. C₅₉×#2012	C₂	semidirect
11. C₅₉×#2000	C₂	semidirect
13. C₅₉×#1763	C₂	semidirect
14. C₄×#102×C₅₉	C₂	semidirect
15. C₅₉×#1750	C₂	semidirect
97. C₄×Q₈×C₅₉	D₄	semidirect
101. C₄×D₄×C₅₉	D₄	semidirect
336. #23583	C₅₉	direct (N × H)
380. C₂×#542	C₂×C₅₉	semidirect
381. C₂×#442	C₂×C₅₉	semidirect
382. C₂×C₄×SD₁₆	C₂×C₅₉	semidirect
383. #2324	C₂×C₅₉	semidirect
384. #2058	C₂×C₅₉	semidirect
385. #2042	C₂×C₅₉	semidirect
386. #2035	C₂×C₅₉	semidirect
387. #2034	C₂×C₅₉	semidirect
388. #2023	C₂×C₅₉	semidirect
389. #2012	C₂×C₅₉	semidirect
390. #2000	C₂×C₅₉	semidirect
392. #1763	C₂×C₅₉	semidirect
393. C₄×#102	C₂×C₅₉	semidirect
394. #1750	C₂×C₅₉	semidirect
452. C₅₉	#23583	direct (N × H)
487. C₄×Q₈	D₄×C₅₉	semidirect
491. C₄×D₄	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×#542	2
C₂×C₅₉×#442	2
C₂×C₄×SD₁₆×C₅₉	2
C₅₉×#2324	2
C₅₉×#2058	2
C₅₉×#2042	2
C₅₉×#2035	2
C₅₉×#2034	2
C₅₉×#2023	2
C₅₉×#2012	2
C₅₉×#2000	2
C₅₉×#1999	2
C₅₉×#1763	2
C₄×#102×C₅₉	2
C₅₉×#1750	2
#23583	59

Subgroups — C59×#23583 #28435692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23583 #28435692