Subgroups — C₅₉×#35494 #28447603

Order 15104.

1528 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2611	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2606	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2599	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2594	C₂	1	2	yes	maximal
5	C₅₉×#2587	C₂	1	2	yes	maximal
6	C₅₉×#2585	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2584	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2529	C₂	1	2	yes	maximal
9	C₅₉×#2528	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2528	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2519	C₂	1	2	yes	maximal
12	C₅₉×#2508	C₂	1	2	yes	maximal, complemented
13	C₅₉×#2469	C₂	1	2	yes	maximal
14	C₅₉×#2462	C₂	1	2	yes	maximal, complemented
15	C₅₉×#2336	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₉×#2334	C₂	1	2	yes	maximal
17	C₄×#125×C₅₉	C₂	1	2	yes	maximal, complemented
18	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic
19	C₅₉×#2276	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#126×C₅₉	C₂²	1	2	yes	—
21	C₂×#125×C₅₉	C₂²	1	2	yes	—
22	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
25	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#401	C₂²	1	2	yes	—
27	C₅₉×#400	C₂²	1	2	yes	—
28	C₅₉×#400	C₂²	1	2	yes	—
29	C₅₉×#400	C₂²	1	1	yes	characteristic
30	C₅₉×#400	C₂²	1	2	yes	—
31	C₅₉×#399	C₂²	1	1	yes	characteristic
32	C₅₉×#398	C₂²	1	1	yes	characteristic
33	C₅₉×#398	C₂²	1	2	yes	—
34	C₅₉×#398	C₂²	1	2	yes	—
35	C₅₉×#398	C₂²	1	2	yes	—
36	C₅₉×#398	C₂²	1	2	yes	—
37	C₅₉×#398	C₂²	1	1	yes	characteristic
38	C₅₉×#398	C₂²	1	2	yes	—
39	C₅₉×#397	C₂²	1	1	yes	characteristic
40	C₅₉×#397	C₂²	1	1	yes	characteristic
41	C₅₉×#396	C₂²	1	2	yes	—
42	C₅₉×#396	C₂²	1	2	yes	—
43	C₅₉×#395	C₂²	1	2	yes	—
44	C₅₉×#395	C₂²	1	1	yes	characteristic
45	C₅₉×#393	C₂²	1	1	yes	characteristic
46	C₅₉×#389	C₂²	1	2	yes	—
47	C₅₉×#389	C₂²	1	2	yes	—
48	C₅₉×#389	C₂²	1	2	yes	—
49	C₅₉×#389	C₂²	1	2	yes	—
50	C₅₉×#389	C₂²	1	2	yes	—
51	C₅₉×#389	C₂²	1	2	yes	—
52	C₅₉×#389	C₂²	1	2	yes	—
53	C₅₉×#389	C₂²	1	2	yes	—
54	C₅₉×#389	C₂²	1	2	yes	—
55	C₅₉×#389	C₂²	1	2	yes	—
56	C₅₉×#388	C₂²	1	2	yes	—
57	C₅₉×#388	C₂²	1	2	yes	—
58	C₅₉×#388	C₂²	1	2	yes	—
59	C₅₉×#388	C₂²	1	2	yes	—
60	C₅₉×#388	C₂²	1	2	yes	—
61	C₅₉×#388	C₂²	1	2	yes	—
62	C₅₉×#388	C₂²	1	2	yes	—
63	C₅₉×#388	C₂²	1	2	yes	—
64	C₅₉×#388	C₂²	1	2	yes	—
65	C₅₉×#387	C₂²	1	2	yes	—
66	C₅₉×#387	C₂²	1	2	yes	—
67	C₅₉×#387	C₂²	1	2	yes	—
68	C₅₉×#387	C₂²	1	2	yes	—
69	C₅₉×#387	C₂²	1	2	yes	—
70	C₅₉×#387	C₂²	1	2	yes	—
71	C₅₉×#387	C₂²	1	2	yes	—
72	C₅₉×#387	C₂²	1	2	yes	—
73	C₅₉×#387	C₂²	1	2	yes	—
74	C₅₉×#387	C₂²	1	2	yes	—
75	C₅₉×#387	C₂²	1	2	yes	—
76	C₅₉×#387	C₂²	1	2	yes	—
77	C₅₉×#387	C₂²	1	2	yes	—
78	C₅₉×#387	C₂²	1	2	yes	—
79	C₅₉×#387	C₂²	1	2	yes	—
80	C₅₉×#387	C₂²	1	2	yes	—
81	C₅₉×#387	C₂²	1	2	yes	—
82	C₅₉×#387	C₂²	1	2	yes	—
83	C₅₉×#387	C₂²	1	2	yes	—
84	C₅₉×#385	C₂²	1	2	yes	—
85	C₅₉×#385	C₂²	1	2	yes	—
86	C₅₉×#383	C₂²	1	1	yes	characteristic
87	C₅₉×#382	C₂²	1	2	yes	—
88	C₅₉×#382	C₂²	1	2	yes	—
89	C₅₉×#382	C₂²	1	2	yes	—
90	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
103	C₅₉×#376	C₂²	1	1	yes	characteristic
104	C₅₉×#376	C₂²	1	2	yes	—
105	C₅₉×#376	C₂²	1	1	yes	characteristic
106	C₄³×C₅₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
109	#126×C₅₉	—	2	8	no	—
110	#125×C₅₉	—	2	8	no	—
111	#125×C₅₉	—	2	4	no	—
112	C₄×Q₈×C₅₉	—	2	8	no	—
113	C₄×Q₈×C₅₉	—	2	4	no	—
114	#117×C₅₉	—	2	4	no	—
115	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
151	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
154	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
156	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
159	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
164	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
167	#95×C₅₉	C₂³	1	1	yes	characteristic
168	#95×C₅₉	C₂³	1	2	yes	—
169	#95×C₅₉	C₂³	1	2	yes	—
170	#95×C₅₉	C₂³	1	2	yes	—
171	#95×C₅₉	C₂³	1	2	yes	—
172	#95×C₅₉	C₂³	1	1	yes	characteristic
173	#95×C₅₉	C₂³	1	2	yes	—
174	#95×C₅₉	C₂³	1	2	yes	—
175	#95×C₅₉	C₂³	1	2	yes	—
176	#95×C₅₉	C₂³	1	2	yes	—
177	#95×C₅₉	C₂³	1	2	yes	—
178	#95×C₅₉	C₂³	1	2	yes	—
179	#95×C₅₉	C₂³	1	2	yes	—
180	#95×C₅₉	C₂³	1	2	yes	—
181	#95×C₅₉	C₂³	1	2	yes	—
182	#95×C₅₉	C₂³	1	2	yes	—
183	#95×C₅₉	C₂³	1	2	yes	—
184	#95×C₅₉	C₂³	1	2	yes	—
185	#95×C₅₉	C₂³	1	2	yes	—
186	#95×C₅₉	C₂³	1	2	yes	—
187	#95×C₅₉	C₂³	1	2	yes	—
188	#95×C₅₉	C₂³	1	2	yes	—
189	#95×C₅₉	C₂³	1	2	yes	—
190	#95×C₅₉	C₂³	1	2	yes	—
191	#95×C₅₉	C₂³	1	2	yes	—
192	#95×C₅₉	C₂³	1	1	yes	characteristic
193	#95×C₅₉	C₂³	1	1	yes	characteristic
194	#95×C₅₉	C₂³	1	2	yes	—
195	#95×C₅₉	C₂³	1	2	yes	—
196	#95×C₅₉	C₂³	1	2	yes	—
197	#95×C₅₉	C₂³	1	2	yes	—
198	#95×C₅₉	C₂³	1	2	yes	—
199	#95×C₅₉	C₂³	1	2	yes	—
200	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₅₉	—	2	4	no	—
202	C₂×Q₈×C₅₉	—	2	2	no	—
203	C₂²×C₄×C₅₉	—	2	2	no	—
204	C₂²×C₄×C₅₉	—	4	1	no	—
205	C₂²×C₄×C₅₉	—	4	1	no	—
206	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
224	C₄⋊C₄×C₅₉	—	2	2	no	—
225	C₄⋊C₄×C₅₉	—	2	2	no	—
226	C₄⋊C₄×C₅₉	—	2	4	no	—
227	C₄⋊C₄×C₅₉	—	2	4	no	—
228	C₄⋊C₄×C₅₉	—	2	4	no	—
229	C₄⋊C₄×C₅₉	—	2	2	no	—
230	C₄⋊C₄×C₅₉	—	2	4	no	—
231	C₄⋊C₄×C₅₉	—	2	4	no	—
232	C₄⋊C₄×C₅₉	—	2	4	no	—
233	C₄⋊C₄×C₅₉	—	2	4	no	—
234	C₄⋊C₄×C₅₉	—	2	4	no	—
235	C₄⋊C₄×C₅₉	—	2	2	no	—
236	C₄⋊C₄×C₅₉	—	2	2	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	4	no	—
241	C₄⋊C₄×C₅₉	—	2	4	no	—
242	C₄⋊C₄×C₅₉	—	2	4	no	—
243	C₄⋊C₄×C₅₉	—	2	4	no	—
244	C₄⋊C₄×C₅₉	—	4	2	no	—
245	C₄⋊C₄×C₅₉	—	4	2	no	—
246	C₄⋊C₄×C₅₉	—	4	2	no	—
247	C₄⋊C₄×C₅₉	—	4	2	no	—
248	C₄⋊C₄×C₅₉	—	4	2	no	—
249	C₄⋊C₄×C₅₉	—	4	2	no	—
250	C₄⋊C₄×C₅₉	—	4	2	no	—
251	C₄⋊C₄×C₅₉	#41	1	8	yes	—
252	C₂²⋊C₄×C₅₉	—	2	2	no	—
253	C₂²⋊C₄×C₅₉	—	2	2	no	—
254	C₂²⋊C₄×C₅₉	—	2	4	no	—
255	C₂²⋊C₄×C₅₉	—	2	4	no	—
256	C₂²⋊C₄×C₅₉	—	2	4	no	—
257	C₂²⋊C₄×C₅₉	—	2	4	no	—
258	C₂²⋊C₄×C₅₉	—	4	2	no	—
259	C₂²⋊C₄×C₅₉	—	4	2	no	—
260	C₄²×C₅₉	—	2	2	no	—
261	C₄²×C₅₉	—	2	4	no	—
262	C₄²×C₅₉	—	2	4	no	—
263	C₄²×C₅₉	—	2	4	no	—
264	C₄²×C₅₉	—	2	4	no	—
265	C₄²×C₅₉	—	2	4	no	—
266	C₄²×C₅₉	—	2	4	no	—
267	C₄²×C₅₉	—	2	4	no	—
268	C₄²×C₅₉	—	4	1	no	—
269	C₄²×C₅₉	—	4	2	no	—
270	C₄²×C₅₉	—	4	2	no	—
271	C₄²×C₅₉	—	4	2	no	—
272	C₄²×C₅₉	—	4	1	no	—
273	C₄²×C₅₉	—	4	1	no	—
274	C₄²×C₅₉	—	4	1	no	—
275	C₄²×C₅₉	#41	1	4	yes	—
276	C₂³×C₅₉	—	2	2	no	—
277	C₂³×C₅₉	—	2	1	no	—
278	C₂³×C₅₉	—	2	2	no	—
279	C₂³×C₅₉	—	2	1	no	—
280	C₂³×C₅₉	—	2	1	no	—
281	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
282	Q₈×C₅₉	—	2	8	no	—
283	C₂×C₄×C₅₉	—	2	2	no	—
284	C₂×C₄×C₅₉	—	2	2	no	—
285	C₂×C₄×C₅₉	—	2	2	no	—
286	C₂×C₄×C₅₉	—	2	2	no	—
287	C₂×C₄×C₅₉	—	2	2	no	—
288	C₂×C₄×C₅₉	—	2	2	no	—
289	C₂×C₄×C₅₉	—	2	2	no	—
290	C₂×C₄×C₅₉	—	2	2	no	—
291	C₂×C₄×C₅₉	—	2	2	no	—
292	C₂×C₄×C₅₉	—	2	1	no	—
293	C₂×C₄×C₅₉	—	2	1	no	—
294	C₂×C₄×C₅₉	—	2	2	no	—
295	C₂×C₄×C₅₉	—	2	2	no	—
296	C₂×C₄×C₅₉	—	2	1	no	—
297	C₂×C₄×C₅₉	—	2	2	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	2	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	2	no	—
307	C₂×C₄×C₅₉	—	2	2	no	—
308	C₂×C₄×C₅₉	—	2	1	no	—
309	C₂×C₄×C₅₉	—	2	2	no	—
310	C₂×C₄×C₅₉	—	2	2	no	—
311	C₂×C₄×C₅₉	—	2	2	no	—
312	C₂×C₄×C₅₉	—	2	2	no	—
313	C₂×C₄×C₅₉	—	2	2	no	—
314	C₂×C₄×C₅₉	—	2	2	no	—
315	C₂×C₄×C₅₉	—	2	2	no	—
316	C₂×C₄×C₅₉	—	2	2	no	—
317	C₂×C₄×C₅₉	—	2	2	no	—
318	C₂×C₄×C₅₉	—	2	2	no	—
319	C₂×C₄×C₅₉	—	2	2	no	—
320	C₂×C₄×C₅₉	—	2	2	no	—
321	C₂×C₄×C₅₉	—	2	2	no	—
322	C₂×C₄×C₅₉	—	2	2	no	—
323	C₂×C₄×C₅₉	—	2	2	no	—
324	C₂×C₄×C₅₉	—	2	1	no	—
325	C₂×C₄×C₅₉	—	2	1	no	—
326	C₂×C₄×C₅₉	—	4	4	no	—
327	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
328	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
329	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
331	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
332	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
333	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
334	#35494	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂²×C₅₉	—	4	1	no	—
336	C₂²×C₅₉	—	4	1	no	—
337	C₂²×C₅₉	—	4	1	no	—
338	C₂²×C₅₉	—	4	2	no	—
339	C₂²×C₅₉	—	4	2	no	—
340	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
341	C₂²×C₅₉	C₂²×#41	1	2	yes	—
342	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
343	C₂²×C₅₉	#585	1	1	yes	characteristic
344	C₂²×C₅₉	#585	1	1	yes	characteristic
345	C₄×C₅₉	—	2	4	no	—
346	C₄×C₅₉	—	2	2	no	—
347	C₄×C₅₉	—	2	2	no	—
348	C₄×C₅₉	—	2	2	no	—
349	C₄×C₅₉	—	2	4	no	—
350	C₄×C₅₉	—	2	4	no	—
351	C₄×C₅₉	—	2	4	no	—
352	C₄×C₅₉	—	4	1	no	—
353	C₄×C₅₉	—	4	2	no	—
354	C₄×C₅₉	—	4	2	no	—
355	C₄×C₅₉	—	4	2	no	—
356	C₄×C₅₉	—	4	1	no	—
357	C₄×C₅₉	—	4	1	no	—
358	C₄×C₅₉	—	4	2	no	—
359	C₄×C₅₉	—	4	2	no	—
360	C₄×C₅₉	—	4	2	no	—
361	C₄×C₅₉	—	4	2	no	—
362	C₄×C₅₉	—	4	2	no	—
363	#2611	C₂×C₅₉	1	1	yes	characteristic
364	#2606	C₂×C₅₉	1	1	yes	characteristic, complemented
365	#2599	C₂×C₅₉	1	1	yes	characteristic
366	#2594	C₂×C₅₉	1	2	yes	—
367	#2587	C₂×C₅₉	1	2	yes	—
368	#2585	C₂×C₅₉	1	2	yes	complemented
369	#2584	C₂×C₅₉	1	1	yes	characteristic, complemented
370	#2529	C₂×C₅₉	1	2	yes	—
371	#2528	C₂×C₅₉	1	2	yes	complemented
372	#2528	C₂×C₅₉	1	2	yes	complemented
373	#2519	C₂×C₅₉	1	2	yes	—
374	#2508	C₂×C₅₉	1	2	yes	complemented
375	#2469	C₂×C₅₉	1	2	yes	—
376	#2462	C₂×C₅₉	1	2	yes	complemented
377	#2336	C₂×C₅₉	1	1	yes	characteristic, complemented
378	#2334	C₂×C₅₉	1	2	yes	—
379	C₄×#125	C₂×C₅₉	1	2	yes	complemented
380	#2298	C₂×C₅₉	1	1	yes	characteristic
381	#2276	C₂×C₅₉	1	1	yes	characteristic, complemented
382	C₂×C₅₉	—	8	1	no	—
383	C₂×C₅₉	#3444	1	1	yes	characteristic
384	C₂×C₅₉	#3493	1	1	yes	characteristic
385	C₂×C₅₉	#3509	1	1	yes	characteristic
386	C₂×C₅₉	#3515	1	2	yes	—
387	C₂×C₅₉	#3516	1	2	yes	—
388	C₂×#126	C₂²×C₅₉	1	2	yes	—
389	C₂×#125	C₂²×C₅₉	1	2	yes	—
390	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
392	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
393	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
394	#401	C₂²×C₅₉	1	2	yes	—
395	#400	C₂²×C₅₉	1	2	yes	—
396	#400	C₂²×C₅₉	1	2	yes	—
397	#400	C₂²×C₅₉	1	1	yes	characteristic
398	#400	C₂²×C₅₉	1	2	yes	—
399	#399	C₂²×C₅₉	1	1	yes	characteristic
400	#398	C₂²×C₅₉	1	2	yes	—
401	#398	C₂²×C₅₉	1	1	yes	characteristic
402	#398	C₂²×C₅₉	1	2	yes	—
403	#398	C₂²×C₅₉	1	2	yes	—
404	#398	C₂²×C₅₉	1	1	yes	characteristic
405	#398	C₂²×C₅₉	1	2	yes	—
406	#398	C₂²×C₅₉	1	2	yes	—
407	#397	C₂²×C₅₉	1	1	yes	characteristic
408	#397	C₂²×C₅₉	1	1	yes	characteristic
409	#396	C₂²×C₅₉	1	2	yes	—
410	#396	C₂²×C₅₉	1	2	yes	—
411	#395	C₂²×C₅₉	1	2	yes	—
412	#395	C₂²×C₅₉	1	1	yes	characteristic
413	#393	C₂²×C₅₉	1	1	yes	characteristic
414	#389	C₂²×C₅₉	1	2	yes	—
415	#389	C₂²×C₅₉	1	2	yes	—
416	#389	C₂²×C₅₉	1	2	yes	—
417	#389	C₂²×C₅₉	1	2	yes	—
418	#389	C₂²×C₅₉	1	2	yes	—
419	#389	C₂²×C₅₉	1	2	yes	—
420	#389	C₂²×C₅₉	1	2	yes	—
421	#389	C₂²×C₅₉	1	2	yes	—
422	#389	C₂²×C₅₉	1	2	yes	—
423	#389	C₂²×C₅₉	1	2	yes	—
424	#388	C₂²×C₅₉	1	2	yes	—
425	#388	C₂²×C₅₉	1	2	yes	—
426	#388	C₂²×C₅₉	1	2	yes	—
427	#388	C₂²×C₅₉	1	2	yes	—
428	#388	C₂²×C₅₉	1	2	yes	—
429	#388	C₂²×C₅₉	1	2	yes	—
430	#388	C₂²×C₅₉	1	2	yes	—
431	#388	C₂²×C₅₉	1	2	yes	—
432	#388	C₂²×C₅₉	1	2	yes	—
433	#387	C₂²×C₅₉	1	2	yes	—
434	#387	C₂²×C₅₉	1	2	yes	—
435	#387	C₂²×C₅₉	1	2	yes	—
436	#387	C₂²×C₅₉	1	2	yes	—
437	#387	C₂²×C₅₉	1	2	yes	—
438	#387	C₂²×C₅₉	1	2	yes	—
439	#387	C₂²×C₅₉	1	2	yes	—
440	#387	C₂²×C₅₉	1	2	yes	—
441	#387	C₂²×C₅₉	1	2	yes	—
442	#387	C₂²×C₅₉	1	2	yes	—
443	#387	C₂²×C₅₉	1	2	yes	—
444	#387	C₂²×C₅₉	1	2	yes	—
445	#387	C₂²×C₅₉	1	2	yes	—
446	#387	C₂²×C₅₉	1	2	yes	—
447	#387	C₂²×C₅₉	1	2	yes	—
448	#387	C₂²×C₅₉	1	2	yes	—
449	#387	C₂²×C₅₉	1	2	yes	—
450	#387	C₂²×C₅₉	1	2	yes	—
451	#387	C₂²×C₅₉	1	2	yes	—
452	#385	C₂²×C₅₉	1	2	yes	—
453	#385	C₂²×C₅₉	1	2	yes	—
454	#383	C₂²×C₅₉	1	1	yes	characteristic
455	#382	C₂²×C₅₉	1	2	yes	—
456	#382	C₂²×C₅₉	1	2	yes	—
457	#382	C₂²×C₅₉	1	2	yes	—
458	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
459	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
460	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
462	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
465	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
467	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
470	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
471	#376	C₂²×C₅₉	1	1	yes	characteristic
472	#376	C₂²×C₅₉	1	1	yes	characteristic
473	#376	C₂²×C₅₉	1	2	yes	—
474	C₄³	C₂²×C₅₉	1	1	yes	characteristic
475	C₅₉	#35494	1	1	yes	characteristic, direct product factor, Sylow
476	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
478	#126	—	2	8	no	—
479	#125	—	2	8	no	—
480	#125	—	2	4	no	—
481	C₄×Q₈	—	2	8	no	—
482	C₄×Q₈	—	2	4	no	—
483	#117	—	2	4	no	—
484	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
492	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
521	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
522	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
523	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
524	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
525	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
526	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
527	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
528	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
533	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
534	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
536	#95	C₂³×C₅₉	1	1	yes	characteristic
537	#95	C₂³×C₅₉	1	2	yes	—
538	#95	C₂³×C₅₉	1	2	yes	—
539	#95	C₂³×C₅₉	1	2	yes	—
540	#95	C₂³×C₅₉	1	2	yes	—
541	#95	C₂³×C₅₉	1	1	yes	characteristic
542	#95	C₂³×C₅₉	1	2	yes	—
543	#95	C₂³×C₅₉	1	2	yes	—
544	#95	C₂³×C₅₉	1	2	yes	—
545	#95	C₂³×C₅₉	1	2	yes	—
546	#95	C₂³×C₅₉	1	2	yes	—
547	#95	C₂³×C₅₉	1	2	yes	—
548	#95	C₂³×C₅₉	1	2	yes	—
549	#95	C₂³×C₅₉	1	2	yes	—
550	#95	C₂³×C₅₉	1	2	yes	—
551	#95	C₂³×C₅₉	1	2	yes	—
552	#95	C₂³×C₅₉	1	2	yes	—
553	#95	C₂³×C₅₉	1	2	yes	—
554	#95	C₂³×C₅₉	1	2	yes	—
555	#95	C₂³×C₅₉	1	2	yes	—
556	#95	C₂³×C₅₉	1	2	yes	—
557	#95	C₂³×C₅₉	1	2	yes	—
558	#95	C₂³×C₅₉	1	2	yes	—
559	#95	C₂³×C₅₉	1	2	yes	—
560	#95	C₂³×C₅₉	1	2	yes	—
561	#95	C₂³×C₅₉	1	1	yes	characteristic
562	#95	C₂³×C₅₉	1	1	yes	characteristic
563	#95	C₂³×C₅₉	1	2	yes	—
564	#95	C₂³×C₅₉	1	2	yes	—
565	#95	C₂³×C₅₉	1	2	yes	—
566	#95	C₂³×C₅₉	1	2	yes	—
567	#95	C₂³×C₅₉	1	2	yes	—
568	#95	C₂³×C₅₉	1	2	yes	—
569	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
570	C₂×Q₈	—	2	4	no	—
571	C₂×Q₈	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	4	1	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
576	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
577	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	4	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	#41×C₅₉	1	8	yes	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	2	2	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	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	4	no	—
631	C₄²	—	2	4	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	4	1	no	—
638	C₄²	—	4	2	no	—
639	C₄²	—	4	2	no	—
640	C₄²	—	4	2	no	—
641	C₄²	—	4	1	no	—
642	C₄²	—	4	1	no	—
643	C₄²	—	4	1	no	—
644	C₄²	#41×C₅₉	1	4	yes	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
651	Q₈	—	2	8	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
697	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
698	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
699	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
700	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
701	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
702	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
709	C₂²	C₂²×#41×C₅₉	1	2	yes	—
710	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
711	C₂²	C₅₉×#585	1	1	yes	characteristic
712	C₂²	C₅₉×#585	1	1	yes	characteristic
713	C₄	—	2	2	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	4	no	—
716	C₄	—	2	4	no	—
717	C₄	—	2	4	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	2	no	—
731	C₂	—	8	1	no	—
732	C₂	C₅₉×#3444	1	1	yes	characteristic
733	C₂	C₅₉×#3493	1	1	yes	characteristic
734	C₂	C₅₉×#3509	1	1	yes	characteristic
735	C₂	C₅₉×#3515	1	2	yes	—
736	C₂	C₅₉×#3516	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁴×C₅₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2606	C₂	semidirect
6. C₅₉×#2585	C₂	semidirect
7. C₅₉×#2584	C₂	semidirect
9. C₅₉×#2528	C₂	semidirect
10. C₅₉×#2528	C₂	semidirect
12. C₅₉×#2508	C₂	semidirect
14. C₅₉×#2462	C₂	semidirect
15. C₅₉×#2336	C₂	semidirect
17. C₄×#125×C₅₉	C₂	semidirect
19. C₅₉×#2276	C₂	semidirect
334. #35494	C₅₉	direct (N × H)
364. #2606	C₂×C₅₉	semidirect
368. #2585	C₂×C₅₉	semidirect
369. #2584	C₂×C₅₉	semidirect
371. #2528	C₂×C₅₉	semidirect
372. #2528	C₂×C₅₉	semidirect
374. #2508	C₂×C₅₉	semidirect
376. #2462	C₂×C₅₉	semidirect
377. #2336	C₂×C₅₉	semidirect
379. C₄×#125	C₂×C₅₉	semidirect
381. #2276	C₂×C₅₉	semidirect
475. C₅₉	#35494	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2611	2
C₅₉×#2606	2
C₅₉×#2599	2
C₅₉×#2594	2
C₅₉×#2587	2
C₅₉×#2585	2
C₅₉×#2584	2
C₅₉×#2529	2
C₅₉×#2528	2
C₅₉×#2519	2
C₅₉×#2508	2
C₅₉×#2469	2
C₅₉×#2462	2
C₅₉×#2336	2
C₅₉×#2334	2
C₄×#125×C₅₉	2
C₅₉×#2298	2
C₅₉×#2276	2
#35494	59

Subgroups — C59×#35494 #28447603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35494 #28447603