Subgroups — C₅₉×#25651 #28437760

Order 15104.

1002 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#487	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#477	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2567	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2043	C₂	1	4	yes	maximal
6	C₅₉×#1984	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1981	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1863	C₂	1	4	yes	maximal
9	C₄×#103×C₅₉	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#557	—	2	4	no	—
11	C₅₉×#557	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₅₉	—	2	1	no	—
16	C₂×#125×C₅₉	—	2	2	no	—
17	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
18	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₅₉×#487	—	2	4	no	—
22	C₅₉×#477	—	2	4	no	—
23	C₂×#107×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₅₉	C₂²	1	4	yes	—
26	C₂×#103×C₅₉	C₂²	1	2	yes	—
27	C₂×#103×C₅₉	C₂²	1	2	yes	—
28	C₂×#103×C₅₉	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#395	—	2	2	no	—
31	C₅₉×#391	—	2	1	no	—
32	C₅₉×#389	C₂²	1	4	yes	—
33	C₅₉×#384	—	2	1	no	—
34	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
35	C₅₉×#340	C₂²	1	2	yes	—
36	C₅₉×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₅₉	—	2	1	no	—
38	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
40	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
42	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
43	C₄⋊Q₈×C₅₉	—	2	4	no	—
44	C₄⋊Q₈×C₅₉	—	2	4	no	—
45	C₄⋊Q₈×C₅₉	—	2	2	no	—
46	C₄⋊Q₈×C₅₉	—	2	2	no	—
47	C₄⋊Q₈×C₅₉	—	2	2	no	—
48	C₄⋊Q₈×C₅₉	D₄	1	4	yes	—
49	#125×C₅₉	—	2	16	no	—
50	#125×C₅₉	—	2	8	no	—
51	C₄×Q₈×C₅₉	—	2	8	no	—
52	C₄×Q₈×C₅₉	—	2	4	no	—
53	C₄×Q₈×C₅₉	—	2	4	no	—
54	C₄×Q₈×C₅₉	—	2	2	no	—
55	C₄×Q₈×C₅₉	—	2	2	no	—
56	C₄×Q₈×C₅₉	—	2	2	no	—
57	C₄×Q₈×C₅₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
66	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
71	C₂×C₄²×C₅₉	—	2	2	no	—
72	C₂×C₄²×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	#107×C₅₉	—	2	4	no	—
77	C₄⋊C₈×C₅₉	—	2	2	no	—
78	#103×C₅₉	—	2	4	no	—
79	#103×C₅₉	—	2	8	no	—
80	#103×C₅₉	—	2	8	no	—
81	#103×C₅₉	—	2	4	no	—
82	C₄×C₈×C₅₉	—	2	2	no	—
83	#95×C₅₉	—	2	1	no	—
84	#95×C₅₉	—	2	4	no	—
85	C₂×Q₈×C₅₉	—	2	2	no	—
86	C₂×Q₈×C₅₉	—	2	2	no	—
87	C₂×Q₈×C₅₉	—	2	2	no	—
88	C₂×Q₈×C₅₉	—	2	1	no	—
89	C₂×Q₈×C₅₉	—	2	2	no	—
90	C₂×Q₈×C₅₉	—	2	4	no	—
91	C₂×Q₈×C₅₉	—	2	2	no	—
92	C₂×Q₈×C₅₉	—	2	4	no	—
93	C₂×Q₈×C₅₉	—	4	2	no	—
94	C₂×Q₈×C₅₉	—	8	2	no	—
95	C₂×Q₈×C₅₉	Q₁₆	1	4	yes	—
96	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
97	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₅₉	—	2	2	no	—
99	C₂²×C₄×C₅₉	—	2	1	no	—
100	C₂²×C₄×C₅₉	—	2	2	no	—
101	C₂²×C₄×C₅₉	—	2	1	no	—
102	C₂²×C₄×C₅₉	—	2	2	no	—
103	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₅₉	—	2	2	no	—
109	C₂×C₈×C₅₉	—	2	2	no	—
110	C₂×C₈×C₅₉	—	2	4	no	—
111	C₂×C₈×C₅₉	—	2	2	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₄⋊C₄×C₅₉	—	2	8	no	—
114	C₄⋊C₄×C₅₉	—	2	8	no	—
115	C₄⋊C₄×C₅₉	—	2	8	no	—
116	C₄⋊C₄×C₅₉	—	2	4	no	—
117	C₄⋊C₄×C₅₉	—	2	4	no	—
118	C₄⋊C₄×C₅₉	—	2	4	no	—
119	C₄⋊C₄×C₅₉	—	2	4	no	—
120	C₄⋊C₄×C₅₉	—	2	2	no	—
121	C₄⋊C₄×C₅₉	—	2	1	no	—
122	C₄⋊C₄×C₅₉	—	2	2	no	—
123	C₄⋊C₄×C₅₉	—	2	2	no	—
124	C₄⋊C₄×C₅₉	—	2	2	no	—
125	C₄⋊C₄×C₅₉	—	4	2	no	—
126	C₄⋊C₄×C₅₉	—	8	4	no	—
127	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₅₉	#41	1	4	yes	—
129	C₄²×C₅₉	—	2	8	no	—
130	C₄²×C₅₉	—	2	4	no	—
131	C₄²×C₅₉	—	2	2	no	—
132	C₄²×C₅₉	—	2	2	no	—
133	C₄²×C₅₉	—	4	2	no	—
134	C₄²×C₅₉	C₂×D₄	1	2	yes	—
135	C₄²×C₅₉	C₂×D₄	1	2	yes	—
136	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₅₉	—	2	8	no	—
138	Q₈×C₅₉	—	2	2	no	—
139	Q₈×C₅₉	—	2	2	no	—
140	Q₈×C₅₉	—	2	8	no	—
141	Q₈×C₅₉	—	4	2	no	—
142	Q₈×C₅₉	—	4	2	no	—
143	Q₈×C₅₉	—	4	2	no	—
144	Q₈×C₅₉	—	8	4	no	—
145	C₂×C₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	2	4	no	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	2	4	no	—
153	C₂×C₄×C₅₉	—	2	4	no	—
154	C₂×C₄×C₅₉	—	4	2	no	—
155	C₂×C₄×C₅₉	—	4	4	no	—
156	C₂×C₄×C₅₉	—	4	2	no	—
157	C₂×C₄×C₅₉	—	4	2	no	—
158	C₂×C₄×C₅₉	—	4	2	no	—
159	C₂×C₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	4	4	no	—
161	C₂×C₄×C₅₉	#120	1	2	yes	—
162	C₂×C₄×C₅₉	#120	1	2	yes	—
163	C₂×C₄×C₅₉	C₂×Q₁₆	1	4	yes	—
164	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
165	C₂×C₄×C₅₉	#137	1	2	yes	—
166	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
169	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
170	C₈×C₅₉	—	4	2	no	—
171	C₈×C₅₉	—	4	2	no	—
172	#25651	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
174	C₂²×C₅₉	#548	1	2	yes	—
175	C₂²×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
176	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
177	C₂²×C₅₉	#577	1	2	yes	—
178	C₄×C₅₉	—	2	4	no	—
179	C₄×C₅₉	—	2	2	no	—
180	C₄×C₅₉	—	4	4	no	—
181	C₄×C₅₉	—	4	2	no	—
182	C₄×C₅₉	—	4	4	no	—
183	C₄×C₅₉	—	4	2	no	—
184	C₄×C₅₉	—	4	2	no	—
185	C₄×C₅₉	—	8	2	no	—
186	C₄×C₅₉	#451	1	4	yes	—
187	C₄×C₅₉	#532	1	1	yes	characteristic
188	C₄×C₅₉	#536	1	1	yes	characteristic
189	C₄×C₅₉	#547	1	2	yes	—
190	C₂×#557	C₂×C₅₉	1	1	yes	characteristic
191	C₂×#487	C₂×C₅₉	1	1	yes	characteristic
192	C₂×#477	C₂×C₅₉	1	1	yes	characteristic
193	#2567	C₂×C₅₉	1	1	yes	characteristic
194	#2043	C₂×C₅₉	1	4	yes	—
195	#1984	C₂×C₅₉	1	1	yes	characteristic
196	#1981	C₂×C₅₉	1	1	yes	characteristic
197	#1863	C₂×C₅₉	1	4	yes	—
198	C₄×#103	C₂×C₅₉	1	1	yes	characteristic
199	C₂×C₅₉	#2432	1	1	yes	characteristic
200	C₂×C₅₉	C₂×#451	1	1	yes	characteristic
201	C₂×C₅₉	#3010	1	1	yes	characteristic
202	C₂×C₅₉	#3363	1	2	yes	—
203	C₂×C₅₉	#3372	1	2	yes	—
204	#557	—	2	4	no	—
205	#557	—	2	4	no	—
206	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
209	C₂×#125	—	2	1	no	—
210	C₂×#125	—	2	2	no	—
211	C₂×C₄×Q₈	—	2	1	no	—
212	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
214	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
215	#487	—	2	4	no	—
216	#477	—	2	4	no	—
217	C₂×#107	C₂²×C₅₉	1	2	yes	—
218	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
219	C₂×#103	C₂²×C₅₉	1	2	yes	—
220	C₂×#103	C₂²×C₅₉	1	4	yes	—
221	C₂×#103	C₂²×C₅₉	1	4	yes	—
222	C₂×#103	C₂²×C₅₉	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
224	#395	—	2	2	no	—
225	#391	—	2	1	no	—
226	#389	C₂²×C₅₉	1	4	yes	—
227	#384	—	2	1	no	—
228	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
229	#340	C₂²×C₅₉	1	2	yes	—
230	#336	C₂²×C₅₉	1	4	yes	—
231	C₅₉	#25651	1	1	yes	characteristic, direct product factor, Sylow
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
234	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
235	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
237	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	—	2	4	no	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	D₄×C₅₉	1	4	yes	—
244	#125	—	2	16	no	—
245	#125	—	2	8	no	—
246	C₄×Q₈	—	2	8	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	D₄×C₅₉	1	4	yes	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	4	no	—
261	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
262	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
270	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
271	#107	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	#103	—	2	4	no	—
274	#103	—	2	8	no	—
275	#103	—	2	8	no	—
276	#103	—	2	4	no	—
277	C₄×C₈	—	2	2	no	—
278	#95	—	2	1	no	—
279	#95	—	2	4	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×Q₈	Q₁₆×C₅₉	1	4	yes	—
291	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
292	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	8	4	no	—
322	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
323	C₄⋊C₄	#41×C₅₉	1	4	yes	—
324	C₄²	—	2	8	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	4	2	no	—
329	C₄²	C₂×D₄×C₅₉	1	2	yes	—
330	C₄²	C₂×D₄×C₅₉	1	2	yes	—
331	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
332	Q₈	—	2	8	no	—
333	Q₈	—	2	2	no	—
334	Q₈	—	2	2	no	—
335	Q₈	—	2	8	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	8	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	#120×C₅₉	1	2	yes	—
357	C₂×C₄	#120×C₅₉	1	2	yes	—
358	C₂×C₄	C₂×Q₁₆×C₅₉	1	4	yes	—
359	C₂×C₄	C₂×Q₁₆×C₅₉	1	2	yes	—
360	C₂×C₄	#137×C₅₉	1	2	yes	—
361	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
363	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
364	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
368	C₂²	C₅₉×#548	1	2	yes	—
369	C₂²	C₂²×Q₁₆×C₅₉	1	1	yes	characteristic
370	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
371	C₂²	C₅₉×#577	1	2	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	4	no	—
379	C₄	—	8	2	no	—
380	C₄	C₅₉×#451	1	4	yes	—
381	C₄	C₅₉×#532	1	1	yes	characteristic
382	C₄	C₅₉×#536	1	1	yes	characteristic
383	C₄	C₅₉×#547	1	2	yes	—
384	C₂	C₅₉×#2432	1	1	yes	characteristic
385	C₂	C₂×C₅₉×#451	1	1	yes	characteristic
386	C₂	C₅₉×#3010	1	1	yes	characteristic
387	C₂	C₅₉×#3363	1	2	yes	—
388	C₂	C₅₉×#3372	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄×Q₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
172. #25651	C₅₉	direct (N × H)
231. C₅₉	#25651	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×C₅₉×#557	2
C₂×C₅₉×#487	2
C₂×C₅₉×#477	2
C₅₉×#2567	2
C₅₉×#2043	2
C₅₉×#1984	2
C₅₉×#1981	2
C₅₉×#1863	2
C₄×#103×C₅₉	2
#25651	59

Subgroups — C59×#25651 #28437760

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25651 #28437760