Subgroups — C₅₉×#60688 #28472797

Order 15104.

2010 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3444	C₂	1	2	yes	maximal, complemented
2	C₅₉×#3181	C₂	1	8	yes	maximal, complemented
3	C₅₉×#3180	C₂	1	8	yes	maximal, complemented
4	C₅₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#3135	C₂	1	2	yes	maximal, complemented
7	C₅₉×#3050	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2943	C₂	1	4	yes	maximal, complemented
9	C₂²×#97×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₅₉	C₂²	1	4	yes	—
11	C₂³×C₈×C₅₉	C₂²	1	2	yes	—
12	C₅₉×#533	C₂²	1	4	yes	—
13	C₅₉×#533	C₂²	1	2	yes	—
14	C₅₉×#532	C₂²	1	2	yes	—
15	C₅₉×#532	C₂²	1	4	yes	—
16	C₅₉×#529	—	2	4	no	—
17	C₅₉×#529	—	2	4	no	—
18	C₅₉×#529	C₂²	1	8	yes	—
19	C₅₉×#525	—	2	4	no	—
20	C₅₉×#525	C₂²	1	4	yes	—
21	C₄×#41×C₅₉	—	2	4	no	—
22	C₄×#41×C₅₉	C₂²	1	4	yes	—
23	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#501	C₂²	1	8	yes	complemented
25	C₅₉×#497	C₂²	1	4	yes	complemented
26	C₅₉×#496	C₂²	1	4	yes	complemented
27	C₅₉×#491	C₂²	1	4	yes	complemented
28	C₅₉×#490	C₂²	1	4	yes	complemented
29	C₅₉×#489	C₂²	1	8	yes	complemented
30	C₅₉×#467	C₂²	1	8	yes	—
31	C₅₉×#466	C₂²	1	8	yes	—
32	C₅₉×#465	C₂²	1	16	yes	—
33	C₅₉×#442	C₂²	1	8	yes	complemented
34	C₅₉×#441	C₂²	1	8	yes	complemented
35	C₅₉×#440	C₂²	1	16	yes	complemented
36	C₅₉×#427	C₂²	1	4	yes	—
37	C₅₉×#416	C₂²	1	8	yes	—
38	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#97×C₅₉	C₂²	1	8	yes	—
41	C₂×#97×C₅₉	C₂²	1	2	yes	—
42	C₂×#41×C₅₉	—	2	4	no	—
43	C₂×#41×C₅₉	C₂³	1	4	yes	—
44	C₂³×C₄×C₅₉	D₄	1	2	yes	—
45	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
46	#135×C₅₉	—	2	16	no	—
47	C₂×Q₁₆×C₅₉	C₂³	1	4	yes	—
48	C₂×SD₁₆×C₅₉	C₂³	1	8	yes	—
49	C₂×D₈×C₅₉	C₂³	1	4	yes	—
50	C₂²×C₈×C₅₉	—	2	8	no	—
51	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₅₉	C₂³	1	8	yes	—
53	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
56	#127×C₅₉	C₂³	1	2	yes	—
57	#126×C₅₉	—	2	8	no	—
58	#125×C₅₉	—	2	4	no	—
59	#125×C₅₉	C₂³	1	4	yes	—
60	#124×C₅₉	—	2	4	no	—
61	#124×C₅₉	C₂³	1	4	yes	—
62	#123×C₅₉	—	2	8	no	—
63	#123×C₅₉	—	2	4	no	—
64	C₂²⋊Q₈×C₅₉	—	2	4	no	—
65	C₂²⋊Q₈×C₅₉	—	2	4	no	—
66	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
67	#121×C₅₉	—	2	4	no	—
68	#121×C₅₉	—	2	4	no	—
69	#121×C₅₉	C₂³	1	8	yes	—
70	#120×C₅₉	—	2	4	no	—
71	C₄×Q₈×C₅₉	—	2	4	no	—
72	C₄×Q₈×C₅₉	—	2	4	no	—
73	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
74	C₄×D₄×C₅₉	—	2	8	no	—
75	C₄×D₄×C₅₉	—	2	8	no	—
76	C₄×D₄×C₅₉	—	2	8	no	—
77	C₄×D₄×C₅₉	—	2	4	no	—
78	C₄×D₄×C₅₉	—	2	4	no	—
79	C₄×D₄×C₅₉	C₂³	1	8	yes	—
80	#117×C₅₉	—	2	4	no	—
81	#117×C₅₉	—	2	8	no	—
82	#117×C₅₉	—	2	4	no	—
83	#117×C₅₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₅₉	—	2	4	no	—
85	C₂×C₄²×C₅₉	D₄	1	4	yes	—
86	C₂×C₄²×C₅₉	D₄	1	2	yes	—
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
89	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
90	#107×C₅₉	C₂³	1	8	yes	—
91	#106×C₅₉	C₂³	1	8	yes	—
92	#103×C₅₉	C₂³	1	16	yes	—
93	#102×C₅₉	C₂³	1	16	yes	—
94	#97×C₅₉	C₂³	1	8	yes	—
95	#97×C₅₉	C₂³	1	4	yes	—
96	#97×C₅₉	C₂³	1	4	yes	—
97	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
98	#41×C₅₉	—	2	16	no	—
99	#41×C₅₉	—	4	16	no	—
100	C₂×Q₈×C₅₉	—	2	4	no	—
101	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
102	C₂×D₄×C₅₉	—	2	4	no	—
103	C₂×D₄×C₅₉	—	2	8	no	—
104	C₂×D₄×C₅₉	—	2	4	no	—
105	C₂×D₄×C₅₉	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₅₉	—	2	4	no	—
107	C₂²×C₄×C₅₉	—	2	8	no	—
108	C₂²×C₄×C₅₉	—	2	4	no	—
109	C₂²×C₄×C₅₉	—	4	4	no	—
110	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₅₉	—	2	8	no	—
119	SD₁₆×C₅₉	—	2	16	no	—
120	D₈×C₅₉	—	2	8	no	—
121	C₂×C₈×C₅₉	—	2	4	no	—
122	C₂×C₈×C₅₉	—	2	16	no	—
123	C₂×C₈×C₅₉	#41	1	8	yes	complemented
124	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
125	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
126	C₄⋊C₄×C₅₉	—	2	4	no	—
127	C₄⋊C₄×C₅₉	—	2	4	no	—
128	C₄⋊C₄×C₅₉	—	2	8	no	—
129	C₄⋊C₄×C₅₉	—	2	8	no	—
130	C₄⋊C₄×C₅₉	—	2	8	no	—
131	C₄⋊C₄×C₅₉	C₂⁴	1	8	yes	—
132	C₂²⋊C₄×C₅₉	—	2	8	no	—
133	C₂²⋊C₄×C₅₉	—	2	4	no	—
134	C₂²⋊C₄×C₅₉	—	2	8	no	—
135	C₂²⋊C₄×C₅₉	—	2	8	no	—
136	C₂²⋊C₄×C₅₉	—	2	8	no	—
137	C₄²×C₅₉	—	2	8	no	—
138	C₄²×C₅₉	—	2	4	no	—
139	C₄²×C₅₉	C₂×D₄	1	4	yes	—
140	C₄²×C₅₉	C₂×D₄	1	4	yes	—
141	C₄²×C₅₉	C₂×D₄	1	2	yes	—
142	C₄²×C₅₉	C₂×D₄	1	2	yes	—
143	C₄²×C₅₉	C₂⁴	1	2	yes	—
144	C₄²×C₅₉	C₂⁴	1	2	yes	—
145	C₂³×C₅₉	—	2	2	no	—
146	C₂³×C₅₉	—	2	4	no	—
147	C₂³×C₅₉	—	2	4	no	—
148	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
149	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
150	Q₈×C₅₉	—	2	8	no	—
151	Q₈×C₅₉	—	4	8	no	—
152	D₄×C₅₉	—	2	8	no	—
153	D₄×C₅₉	—	4	8	no	—
154	D₄×C₅₉	—	4	8	no	—
155	D₄×C₅₉	—	4	16	no	—
156	C₂×C₄×C₅₉	—	2	2	no	—
157	C₂×C₄×C₅₉	—	2	8	no	—
158	C₂×C₄×C₅₉	—	2	4	no	—
159	C₂×C₄×C₅₉	—	2	4	no	—
160	C₂×C₄×C₅₉	—	2	4	no	—
161	C₂×C₄×C₅₉	—	2	8	no	—
162	C₂×C₄×C₅₉	—	4	2	no	—
163	C₂×C₄×C₅₉	—	4	4	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	16	no	—
166	C₂×C₄×C₅₉	—	4	8	no	—
167	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
172	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
173	C₈×C₅₉	—	2	4	no	—
174	C₈×C₅₉	C₂×#41	1	8	yes	—
175	#60688	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₅₉	—	2	8	no	—
177	C₂²×C₅₉	—	2	2	no	—
178	C₂²×C₅₉	—	2	2	no	—
179	C₂²×C₅₉	—	2	2	no	—
180	C₂²×C₅₉	—	4	4	no	—
181	C₂²×C₅₉	—	4	8	no	—
182	C₂²×C₅₉	#532	1	2	yes	—
183	C₂²×C₅₉	#575	1	4	yes	—
184	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
185	C₄×C₅₉	—	2	2	no	—
186	C₄×C₅₉	—	2	4	no	—
187	C₄×C₅₉	—	2	4	no	—
188	C₄×C₅₉	—	4	4	no	—
189	C₄×C₅₉	—	4	8	no	—
190	C₄×C₅₉	#532	1	2	yes	—
191	C₄×C₅₉	C₂²×#41	1	2	yes	—
192	#3444	C₂×C₅₉	1	2	yes	complemented
193	#3181	C₂×C₅₉	1	8	yes	complemented
194	#3180	C₂×C₅₉	1	8	yes	complemented
195	#3162	C₂×C₅₉	1	1	yes	characteristic, complemented
196	#3150	C₂×C₅₉	1	1	yes	characteristic, complemented
197	#3135	C₂×C₅₉	1	2	yes	complemented
198	#3050	C₂×C₅₉	1	4	yes	complemented
199	#2943	C₂×C₅₉	1	4	yes	complemented
200	C₂²×#97	C₂×C₅₉	1	1	yes	characteristic, complemented
201	C₂×C₅₉	—	2	2	no	—
202	C₂×C₅₉	—	2	4	no	—
203	C₂×C₅₉	—	8	4	no	—
204	C₂×C₅₉	C₂×#532	1	1	yes	characteristic
205	C₂×C₅₉	C₂×#575	1	2	yes	—
206	C₂×#135	C₂²×C₅₉	1	4	yes	—
207	C₂³×C₈	C₂²×C₅₉	1	2	yes	—
208	#533	C₂²×C₅₉	1	4	yes	—
209	#533	C₂²×C₅₉	1	2	yes	—
210	#532	C₂²×C₅₉	1	2	yes	—
211	#532	C₂²×C₅₉	1	4	yes	—
212	#529	—	2	4	no	—
213	#529	—	2	4	no	—
214	#529	C₂²×C₅₉	1	8	yes	—
215	#525	—	2	4	no	—
216	#525	C₂²×C₅₉	1	4	yes	—
217	C₄×#41	—	2	4	no	—
218	C₄×#41	C₂²×C₅₉	1	4	yes	—
219	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
220	#501	C₂²×C₅₉	1	8	yes	complemented
221	#497	C₂²×C₅₉	1	4	yes	complemented
222	#496	C₂²×C₅₉	1	4	yes	complemented
223	#491	C₂²×C₅₉	1	4	yes	complemented
224	#490	C₂²×C₅₉	1	4	yes	complemented
225	#489	C₂²×C₅₉	1	8	yes	complemented
226	#467	C₂²×C₅₉	1	8	yes	—
227	#466	C₂²×C₅₉	1	8	yes	—
228	#465	C₂²×C₅₉	1	16	yes	—
229	#442	C₂²×C₅₉	1	8	yes	complemented
230	#441	C₂²×C₅₉	1	8	yes	complemented
231	#440	C₂²×C₅₉	1	16	yes	complemented
232	#427	C₂²×C₅₉	1	4	yes	—
233	#416	C₂²×C₅₉	1	8	yes	—
234	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
235	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
236	C₂×#97	C₂²×C₅₉	1	8	yes	—
237	C₂×#97	C₂²×C₅₉	1	2	yes	—
238	C₅₉	#60688	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	—	2	4	no	—
240	C₂×#41	C₂³×C₅₉	1	4	yes	—
241	C₂³×C₄	D₄×C₅₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
243	#135	—	2	16	no	—
244	C₂×Q₁₆	C₂³×C₅₉	1	4	yes	—
245	C₂×SD₁₆	C₂³×C₅₉	1	8	yes	—
246	C₂×D₈	C₂³×C₅₉	1	4	yes	—
247	C₂²×C₈	—	2	8	no	—
248	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
249	C₂²×C₈	C₂³×C₅₉	1	8	yes	—
250	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
252	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
253	#127	C₂³×C₅₉	1	2	yes	—
254	#126	—	2	8	no	—
255	#125	—	2	4	no	—
256	#125	C₂³×C₅₉	1	4	yes	—
257	#124	—	2	4	no	—
258	#124	C₂³×C₅₉	1	4	yes	—
259	#123	—	2	8	no	—
260	#123	—	2	4	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
264	#121	—	2	4	no	—
265	#121	—	2	4	no	—
266	#121	C₂³×C₅₉	1	8	yes	—
267	#120	—	2	4	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	2	4	no	—
270	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
271	C₄×D₄	—	2	8	no	—
272	C₄×D₄	—	2	8	no	—
273	C₄×D₄	—	2	8	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	C₄×D₄	C₂³×C₅₉	1	8	yes	—
277	#117	—	2	4	no	—
278	#117	—	2	8	no	—
279	#117	—	2	4	no	—
280	#117	C₂³×C₅₉	1	4	yes	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	D₄×C₅₉	1	4	yes	—
283	C₂×C₄²	D₄×C₅₉	1	2	yes	—
284	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
286	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
287	#107	C₂³×C₅₉	1	8	yes	—
288	#106	C₂³×C₅₉	1	8	yes	—
289	#103	C₂³×C₅₉	1	16	yes	—
290	#102	C₂³×C₅₉	1	16	yes	—
291	#97	C₂³×C₅₉	1	8	yes	—
292	#97	C₂³×C₅₉	1	4	yes	—
293	#97	C₂³×C₅₉	1	4	yes	—
294	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
295	#41	—	2	16	no	—
296	#41	—	4	16	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	C₂⁴×C₅₉	1	4	yes	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
312	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
315	Q₁₆	—	2	8	no	—
316	SD₁₆	—	2	16	no	—
317	D₈	—	2	8	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	16	no	—
320	C₂×C₈	#41×C₅₉	1	8	yes	complemented
321	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
322	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	C₂⁴×C₅₉	1	8	yes	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₄²	—	2	8	no	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂×D₄×C₅₉	1	2	yes	—
337	C₄²	C₂×D₄×C₅₉	1	4	yes	—
338	C₄²	C₂×D₄×C₅₉	1	2	yes	—
339	C₄²	C₂×D₄×C₅₉	1	4	yes	—
340	C₄²	C₂⁴×C₅₉	1	2	yes	—
341	C₄²	C₂⁴×C₅₉	1	2	yes	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
346	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
347	Q₈	—	2	8	no	—
348	Q₈	—	4	8	no	—
349	D₄	—	2	8	no	—
350	D₄	—	4	8	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	16	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	16	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
365	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
366	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
369	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	C₂×#41×C₅₉	1	8	yes	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₅₉×#532	1	2	yes	—
379	C₂²	C₅₉×#575	1	4	yes	—
380	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
381	C₄	—	2	4	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	4	8	no	—
385	C₄	—	4	4	no	—
386	C₄	C₅₉×#532	1	2	yes	—
387	C₄	C₂²×#41×C₅₉	1	2	yes	—
388	C₂	—	2	2	no	—
389	C₂	—	2	4	no	—
390	C₂	—	8	4	no	—
391	C₂	C₂×C₅₉×#532	1	1	yes	characteristic
392	C₂	C₂×C₅₉×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
socle	C₂²×C₅₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3444	C₂	semidirect
2. C₅₉×#3181	C₂	semidirect
3. C₅₉×#3180	C₂	semidirect
4. C₅₉×#3162	C₂	semidirect
5. C₅₉×#3150	C₂	semidirect
6. C₅₉×#3135	C₂	semidirect
7. C₅₉×#3050	C₂	semidirect
8. C₅₉×#2943	C₂	semidirect
9. C₂²×#97×C₅₉	C₂	semidirect
24. C₅₉×#501	C₂²	semidirect
25. C₅₉×#497	C₂²	semidirect
26. C₅₉×#496	C₂²	semidirect
27. C₅₉×#491	C₂²	semidirect
28. C₅₉×#490	C₂²	semidirect
29. C₅₉×#489	C₂²	semidirect
33. C₅₉×#442	C₂²	semidirect
34. C₅₉×#441	C₂²	semidirect
35. C₅₉×#440	C₂²	semidirect
123. C₂×C₈×C₅₉	#41	semidirect
175. #60688	C₅₉	direct (N × H)
192. #3444	C₂×C₅₉	semidirect
193. #3181	C₂×C₅₉	semidirect
194. #3180	C₂×C₅₉	semidirect
195. #3162	C₂×C₅₉	semidirect
196. #3150	C₂×C₅₉	semidirect
197. #3135	C₂×C₅₉	semidirect
198. #3050	C₂×C₅₉	semidirect
199. #2943	C₂×C₅₉	semidirect
200. C₂²×#97	C₂×C₅₉	semidirect
220. #501	C₂²×C₅₉	semidirect
221. #497	C₂²×C₅₉	semidirect
222. #496	C₂²×C₅₉	semidirect
223. #491	C₂²×C₅₉	semidirect
224. #490	C₂²×C₅₉	semidirect
225. #489	C₂²×C₅₉	semidirect
229. #442	C₂²×C₅₉	semidirect
230. #441	C₂²×C₅₉	semidirect
231. #440	C₂²×C₅₉	semidirect
238. C₅₉	#60688	direct (N × H)
320. C₂×C₈	#41×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3444	2
C₅₉×#3181	2
C₅₉×#3180	2
C₅₉×#3162	2
C₅₉×#3150	2
C₅₉×#3135	2
C₅₉×#3050	2
C₅₉×#2943	2
C₂²×#97×C₅₉	2
#60688	59

Subgroups — C59×#60688 #28472797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#60688 #28472797