Subgroups — C₅₉×#33282 #28445391

Order 15104.

720 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2861	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1959	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#1959	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1936	C₂	1	2	yes	maximal
8	C₅₉×#1935	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1934	C₂	1	2	yes	maximal
10	C₅₉×#1933	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₅₉	—	2	1	no	—
13	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#103×C₅₉	C₂²	1	2	yes	—
16	C₂×#103×C₅₉	C₂²	1	2	yes	—
17	C₂×#102×C₅₉	C₂²	1	2	yes	—
18	C₂×#102×C₅₉	C₂²	1	2	yes	—
19	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#97×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
23	C₅₉×#391	C₂²	1	1	yes	characteristic
24	C₅₉×#391	C₂²	1	1	yes	characteristic
25	C₅₉×#390	C₂²	1	1	yes	characteristic
26	C₅₉×#390	C₂²	1	1	yes	characteristic
27	C₅₉×#389	—	2	1	no	—
28	C₅₉×#389	—	2	1	no	—
29	C₅₉×#389	C₂²	1	2	yes	—
30	C₅₉×#389	C₂²	1	2	yes	—
31	C₅₉×#388	—	2	1	no	—
32	C₅₉×#388	—	2	1	no	—
33	C₅₉×#388	—	2	1	no	—
34	C₅₉×#388	—	2	1	no	—
35	C₅₉×#384	C₂²	1	1	yes	characteristic
36	C₅₉×#384	C₂²	1	1	yes	characteristic
37	C₅₉×#382	—	2	1	no	—
38	C₄³×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#340	C₂²	1	2	yes	—
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₅₉×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
47	#125×C₅₉	—	2	2	no	—
48	#125×C₅₉	—	2	2	no	—
49	#125×C₅₉	—	4	4	no	—
50	#124×C₅₉	—	2	2	no	—
51	#124×C₅₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
77	#103×C₅₉	—	2	4	no	—
78	#103×C₅₉	—	2	4	no	—
79	#102×C₅₉	—	2	4	no	—
80	#102×C₅₉	—	2	4	no	—
81	#97×C₅₉	—	2	4	no	—
82	#97×C₅₉	—	2	2	no	—
83	#97×C₅₉	—	2	2	no	—
84	C₄×C₈×C₅₉	—	2	4	no	—
85	#95×C₅₉	—	2	2	no	—
86	#95×C₅₉	—	2	2	no	—
87	#95×C₅₉	—	2	1	no	—
88	#95×C₅₉	—	2	1	no	—
89	#95×C₅₉	—	2	1	no	—
90	#95×C₅₉	—	2	1	no	—
91	C₂⁴×C₅₉	—	2	1	no	—
92	C₂×Q₈×C₅₉	—	2	2	no	—
93	C₂×Q₈×C₅₉	—	2	2	no	—
94	C₂×Q₈×C₅₉	—	2	1	no	—
95	C₂×Q₈×C₅₉	—	2	1	no	—
96	C₂×D₄×C₅₉	—	2	2	no	—
97	C₂×D₄×C₅₉	—	2	2	no	—
98	C₂×D₄×C₅₉	—	2	1	no	—
99	C₂×D₄×C₅₉	—	2	1	no	—
100	C₂²×C₄×C₅₉	—	2	1	no	—
101	C₂²×C₄×C₅₉	—	2	1	no	—
102	C₂²×C₄×C₅₉	—	2	1	no	—
103	C₂²×C₄×C₅₉	—	2	2	no	—
104	C₂²×C₄×C₅₉	—	2	2	no	—
105	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	2	no	—
114	C₂×C₈×C₅₉	—	2	2	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	#41	1	4	yes	—
117	C₂×C₈×C₅₉	#41	1	4	yes	—
118	C₄⋊C₄×C₅₉	—	2	2	no	—
119	C₄⋊C₄×C₅₉	—	2	2	no	—
120	C₄⋊C₄×C₅₉	—	2	2	no	—
121	C₄⋊C₄×C₅₉	—	2	2	no	—
122	C₄⋊C₄×C₅₉	—	2	1	no	—
123	C₄⋊C₄×C₅₉	—	2	1	no	—
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	—	4	2	no	—
127	C₄⋊C₄×C₅₉	—	4	2	no	—
128	C₄⋊C₄×C₅₉	—	4	2	no	—
129	C₄⋊C₄×C₅₉	—	4	2	no	—
130	C₄⋊C₄×C₅₉	—	4	4	no	—
131	C₄⋊C₄×C₅₉	—	4	2	no	—
132	C₄⋊C₄×C₅₉	—	4	2	no	—
133	C₄⋊C₄×C₅₉	—	4	4	no	—
134	C₂²⋊C₄×C₅₉	—	4	2	no	—
135	C₂²⋊C₄×C₅₉	—	4	2	no	—
136	C₂²⋊C₄×C₅₉	—	4	2	no	—
137	C₂²⋊C₄×C₅₉	—	4	2	no	—
138	C₂²⋊C₄×C₅₉	—	4	2	no	—
139	C₂²⋊C₄×C₅₉	—	4	2	no	—
140	C₄²×C₅₉	—	2	2	no	—
141	C₄²×C₅₉	—	2	2	no	—
142	C₄²×C₅₉	—	2	2	no	—
143	C₄²×C₅₉	—	2	2	no	—
144	C₄²×C₅₉	—	4	1	no	—
145	C₄²×C₅₉	—	4	1	no	—
146	C₄²×C₅₉	#41	1	2	yes	—
147	C₄²×C₅₉	#41	1	2	yes	—
148	C₂³×C₅₉	—	4	1	no	—
149	C₂³×C₅₉	—	4	1	no	—
150	C₂³×C₅₉	—	4	1	no	—
151	C₂³×C₅₉	—	4	1	no	—
152	C₂³×C₅₉	—	4	1	no	—
153	C₂³×C₅₉	—	4	1	no	—
154	C₂³×C₅₉	—	4	1	no	—
155	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₅₉	—	4	2	no	—
157	Q₈×C₅₉	—	4	2	no	—
158	D₄×C₅₉	—	4	2	no	—
159	D₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	2	1	no	—
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	1	no	—
169	C₂×C₄×C₅₉	—	2	1	no	—
170	C₂×C₄×C₅₉	—	2	1	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	1	no	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	4	1	no	—
175	C₂×C₄×C₅₉	—	4	1	no	—
176	C₂×C₄×C₅₉	—	4	1	no	—
177	C₂×C₄×C₅₉	—	4	2	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	4	1	no	—
180	C₂×C₄×C₅₉	—	4	1	no	—
181	C₂×C₄×C₅₉	—	4	1	no	—
182	C₂×C₄×C₅₉	—	4	2	no	—
183	C₂×C₄×C₅₉	—	4	2	no	—
184	C₂×C₄×C₅₉	—	4	1	no	—
185	C₂×C₄×C₅₉	—	4	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	2	no	—
188	C₂×C₄×C₅₉	—	4	2	no	—
189	C₂×C₄×C₅₉	#124	1	2	yes	—
190	C₂×C₄×C₅₉	#124	1	2	yes	—
191	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₅₉	#137	1	2	yes	—
193	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
196	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
197	C₈×C₅₉	—	2	4	no	—
198	C₈×C₅₉	—	2	4	no	—
199	#33282	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₅₉	—	8	1	no	—
201	C₂²×C₅₉	—	8	1	no	—
202	C₂²×C₅₉	—	8	1	no	—
203	C₂²×C₅₉	—	8	1	no	—
204	C₂²×C₅₉	—	8	1	no	—
205	C₂²×C₅₉	—	8	1	no	—
206	C₂²×C₅₉	—	8	1	no	—
207	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
208	C₂²×C₅₉	#532	1	1	yes	characteristic
209	C₂²×C₅₉	#532	1	1	yes	characteristic
210	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
212	C₂²×C₅₉	#575	1	1	yes	characteristic
213	C₂²×C₅₉	#575	1	1	yes	characteristic
214	C₄×C₅₉	—	2	2	no	—
215	C₄×C₅₉	—	2	2	no	—
216	C₄×C₅₉	—	2	2	no	—
217	C₄×C₅₉	—	2	2	no	—
218	C₄×C₅₉	—	4	1	no	—
219	C₄×C₅₉	—	4	1	no	—
220	C₄×C₅₉	—	8	1	no	—
221	C₄×C₅₉	—	8	1	no	—
222	C₄×C₅₉	—	8	1	no	—
223	C₄×C₅₉	—	8	2	no	—
224	C₄×C₅₉	—	8	2	no	—
225	C₄×C₅₉	#529	1	2	yes	—
226	C₄×C₅₉	#529	1	2	yes	—
227	#2861	C₂×C₅₉	1	1	yes	characteristic
228	#2859	C₂×C₅₉	1	1	yes	characteristic, complemented
229	#1992	C₂×C₅₉	1	1	yes	characteristic, complemented
230	#1992	C₂×C₅₉	1	1	yes	characteristic, complemented
231	#1959	C₂×C₅₉	1	1	yes	characteristic
232	#1959	C₂×C₅₉	1	1	yes	characteristic
233	#1936	C₂×C₅₉	1	2	yes	—
234	#1935	C₂×C₅₉	1	2	yes	complemented
235	#1934	C₂×C₅₉	1	2	yes	—
236	#1933	C₂×C₅₉	1	2	yes	complemented
237	C₄×#97	C₂×C₅₉	1	1	yes	characteristic, complemented
238	C₂×C₅₉	—	16	1	no	—
239	C₂×C₅₉	#2861	1	1	yes	characteristic
240	C₂×C₅₉	#3141	1	1	yes	characteristic
241	C₂×C₅₉	#3142	1	1	yes	characteristic
242	C₂×C₅₉	#3171	1	1	yes	characteristic
243	C₂×C₅₉	#3172	1	1	yes	characteristic
244	C₂×C₅₉	#3180	1	1	yes	characteristic
245	C₂×C₅₉	#3181	1	1	yes	characteristic
246	C₂×#125	—	2	1	no	—
247	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
248	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
249	C₂×#103	C₂²×C₅₉	1	2	yes	—
250	C₂×#103	C₂²×C₅₉	1	2	yes	—
251	C₂×#102	C₂²×C₅₉	1	2	yes	—
252	C₂×#102	C₂²×C₅₉	1	2	yes	—
253	C₂×#97	C₂²×C₅₉	1	2	yes	—
254	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
255	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
256	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
257	#391	C₂²×C₅₉	1	1	yes	characteristic
258	#391	C₂²×C₅₉	1	1	yes	characteristic
259	#390	C₂²×C₅₉	1	1	yes	characteristic
260	#390	C₂²×C₅₉	1	1	yes	characteristic
261	#389	—	2	1	no	—
262	#389	—	2	1	no	—
263	#389	C₂²×C₅₉	1	2	yes	—
264	#389	C₂²×C₅₉	1	2	yes	—
265	#388	—	2	1	no	—
266	#388	—	2	1	no	—
267	#388	—	2	1	no	—
268	#388	—	2	1	no	—
269	#384	C₂²×C₅₉	1	1	yes	characteristic
270	#384	C₂²×C₅₉	1	1	yes	characteristic
271	#382	—	2	1	no	—
272	C₄³	C₂²×C₅₉	1	1	yes	characteristic
273	#340	C₂²×C₅₉	1	2	yes	—
274	#340	C₂²×C₅₉	1	2	yes	—
275	#340	C₂²×C₅₉	1	2	yes	—
276	#340	C₂²×C₅₉	1	2	yes	—
277	C₅₉	#33282	1	1	yes	characteristic, direct product factor, Sylow
278	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
279	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
281	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
282	#125	—	2	2	no	—
283	#125	—	2	2	no	—
284	#125	—	4	4	no	—
285	#124	—	2	2	no	—
286	#124	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
306	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
307	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
312	#103	—	2	4	no	—
313	#103	—	2	4	no	—
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#97	—	2	4	no	—
317	#97	—	2	2	no	—
318	#97	—	2	2	no	—
319	C₄×C₈	—	2	4	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	1	no	—
323	#95	—	2	1	no	—
324	#95	—	2	1	no	—
325	#95	—	2	1	no	—
326	C₂⁴	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
346	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	#41×C₅₉	1	4	yes	—
352	C₂×C₈	#41×C₅₉	1	4	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	4	2	no	—
370	C₂²⋊C₄	—	4	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	4	1	no	—
380	C₄²	—	4	1	no	—
381	C₄²	#41×C₅₉	1	2	yes	—
382	C₄²	#41×C₅₉	1	2	yes	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	#124×C₅₉	1	2	yes	—
425	C₂×C₄	#124×C₅₉	1	2	yes	—
426	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
427	C₂×C₄	#137×C₅₉	1	2	yes	—
428	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
431	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
432	C₈	—	2	4	no	—
433	C₈	—	2	4	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
442	C₂²	C₅₉×#532	1	1	yes	characteristic
443	C₂²	C₅₉×#532	1	1	yes	characteristic
444	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
445	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
446	C₂²	C₅₉×#575	1	1	yes	characteristic
447	C₂²	C₅₉×#575	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	2	no	—
459	C₄	C₅₉×#529	1	2	yes	—
460	C₄	C₅₉×#529	1	2	yes	—
461	C₂	—	16	1	no	—
462	C₂	C₅₉×#2861	1	1	yes	characteristic
463	C₂	C₅₉×#3141	1	1	yes	characteristic
464	C₂	C₅₉×#3142	1	1	yes	characteristic
465	C₂	C₅₉×#3171	1	1	yes	characteristic
466	C₂	C₅₉×#3172	1	1	yes	characteristic
467	C₂	C₅₉×#3180	1	1	yes	characteristic
468	C₂	C₅₉×#3181	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2859	C₂	semidirect
3. C₅₉×#1992	C₂	semidirect
4. C₅₉×#1992	C₂	semidirect
8. C₅₉×#1935	C₂	semidirect
10. C₅₉×#1933	C₂	semidirect
11. C₄×#97×C₅₉	C₂	semidirect
199. #33282	C₅₉	direct (N × H)
228. #2859	C₂×C₅₉	semidirect
229. #1992	C₂×C₅₉	semidirect
230. #1992	C₂×C₅₉	semidirect
234. #1935	C₂×C₅₉	semidirect
236. #1933	C₂×C₅₉	semidirect
237. C₄×#97	C₂×C₅₉	semidirect
277. C₅₉	#33282	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×#2861	2
C₅₉×#2859	2
C₅₉×#1992	2
C₅₉×#1959	2
C₅₉×#1936	2
C₅₉×#1935	2
C₅₉×#1934	2
C₅₉×#1933	2
C₄×#97×C₅₉	2
#33282	59

Subgroups — C59×#33282 #28445391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33282 #28445391