Subgroups — C₅₉×#10774 #28422883

Order 15104.

1230 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#417	C₂	1	2	yes	maximal
3	C₂×C₅₉×#343	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₉×#340	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
7	C₂×#131×C₅₉	—	2	4	no	—
8	C₂×#131×C₅₉	—	2	4	no	—
9	C₂×#131×C₅₉	—	2	2	no	—
10	C₂×#131×C₅₉	C₄	1	4	yes	complemented
11	C₂²×M₁₆×C₅₉	—	2	1	no	—
12	C₂²×M₁₆×C₅₉	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₅₉	—	2	1	no	—
15	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
17	C₅₉×#417	—	2	4	no	—
18	C₅₉×#417	C₄	1	8	yes	complemented
19	C₂×#103×C₅₉	—	2	2	no	—
20	C₂×#102×C₅₉	—	2	2	no	—
21	C₅₉×#343	—	2	4	no	—
22	C₅₉×#341	—	2	2	no	—
23	C₅₉×#340	—	2	1	no	—
24	C₅₉×#340	—	2	1	no	—
25	C₂×#41×C₅₉	—	2	1	no	—
26	C₂×#41×C₅₉	—	2	2	no	—
27	C₂×#41×C₅₉	—	2	2	no	—
28	C₂×#41×C₅₉	—	2	1	no	—
29	C₂×#41×C₅₉	C₂×C₄	1	4	yes	—
30	C₂×#41×C₅₉	C₂×C₄	1	2	yes	—
31	C₂×#41×C₅₉	D₄	1	4	yes	—
32	C₂×#41×C₅₉	Q₈	1	2	yes	—
33	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₅₉	—	2	1	no	—
35	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₉	—	2	1	no	—
37	C₂³×C₄×C₅₉	—	2	2	no	—
38	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
39	#131×C₅₉	—	2	16	no	—
40	#131×C₅₉	—	2	8	no	—
41	#131×C₅₉	—	2	8	no	—
42	C₂×M₁₆×C₅₉	—	2	8	no	—
43	C₂×M₁₆×C₅₉	—	2	1	no	—
44	C₂×M₁₆×C₅₉	—	2	2	no	—
45	C₂×M₁₆×C₅₉	—	2	2	no	—
46	C₂×M₁₆×C₅₉	—	2	4	no	—
47	C₂×M₁₆×C₅₉	—	2	2	no	—
48	C₂×M₁₆×C₅₉	—	2	2	no	—
49	C₂×M₁₆×C₅₉	—	2	2	no	—
50	C₂×M₁₆×C₅₉	—	2	2	no	—
51	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
52	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
53	C₂×M₁₆×C₅₉	D₄	1	4	yes	—
54	C₂²×C₈×C₅₉	—	2	8	no	—
55	C₂²×C₈×C₅₉	—	2	1	no	—
56	C₂²×C₈×C₅₉	—	2	2	no	—
57	C₂²×C₈×C₅₉	—	2	2	no	—
58	C₂²×C₈×C₅₉	—	2	4	no	—
59	C₂²×C₈×C₅₉	—	2	2	no	—
60	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₅₉	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	4	yes	—
70	#103×C₅₉	—	2	8	no	—
71	#102×C₅₉	—	2	8	no	—
72	C₂⁴×C₅₉	—	2	1	no	—
73	C₂⁴×C₅₉	#41	1	1	yes	characteristic
74	#41×C₅₉	—	2	2	no	—
75	#41×C₅₉	—	2	2	no	—
76	#41×C₅₉	—	2	4	no	—
77	#41×C₅₉	—	2	4	no	—
78	#41×C₅₉	—	2	4	no	—
79	#41×C₅₉	—	2	4	no	—
80	#41×C₅₉	—	2	4	no	—
81	#41×C₅₉	C₄²	1	4	yes	—
82	#41×C₅₉	C₂²⋊C₄	1	4	yes	—
83	#41×C₅₉	C₄⋊C₄	1	8	yes	—
84	C₂×Q₈×C₅₉	—	2	1	no	—
85	C₂×Q₈×C₅₉	—	2	2	no	—
86	C₂×Q₈×C₅₉	C₂²⋊C₄	1	4	yes	—
87	C₂×Q₈×C₅₉	C₄⋊C₄	1	2	yes	—
88	C₂×D₄×C₅₉	—	2	2	no	—
89	C₂×D₄×C₅₉	—	2	4	no	—
90	C₂×D₄×C₅₉	—	2	2	no	—
91	C₂×D₄×C₅₉	—	2	4	no	—
92	C₂×D₄×C₅₉	—	2	2	no	—
93	C₂×D₄×C₅₉	—	2	1	no	—
94	C₂×D₄×C₅₉	C₂²⋊C₄	1	4	yes	—
95	C₂×D₄×C₅₉	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₅₉	—	2	1	no	—
97	C₂²×C₄×C₅₉	—	2	2	no	—
98	C₂²×C₄×C₅₉	—	2	4	no	—
99	C₂²×C₄×C₅₉	—	2	4	no	—
100	C₂²×C₄×C₅₉	—	2	2	no	—
101	C₂²×C₄×C₅₉	—	2	4	no	—
102	C₂²×C₄×C₅₉	—	4	2	no	—
103	C₂²×C₄×C₅₉	—	4	2	no	—
104	C₂²×C₄×C₅₉	—	8	2	no	—
105	C₂²×C₄×C₅₉	—	8	2	no	—
106	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
114	C₂²×C₄×C₅₉	#41	1	2	yes	—
115	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
116	M₁₆×C₅₉	—	2	16	no	—
117	M₁₆×C₅₉	—	2	2	no	—
118	M₁₆×C₅₉	—	2	4	no	—
119	M₁₆×C₅₉	—	2	4	no	—
120	M₁₆×C₅₉	—	2	4	no	—
121	M₁₆×C₅₉	—	4	2	no	—
122	M₁₆×C₅₉	—	4	2	no	—
123	M₁₆×C₅₉	C₂²⋊C₄	1	4	yes	—
124	C₂×C₈×C₅₉	—	2	16	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₂×C₈×C₅₉	—	2	2	no	—
127	C₂×C₈×C₅₉	—	2	2	no	—
128	C₂×C₈×C₅₉	—	2	2	no	—
129	C₂×C₈×C₅₉	—	2	4	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₂×C₈×C₅₉	—	2	4	no	—
132	C₂×C₈×C₅₉	—	2	4	no	—
133	C₂×C₈×C₅₉	—	4	2	no	—
134	C₂×C₈×C₅₉	—	4	2	no	—
135	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
136	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
137	C₄⋊C₄×C₅₉	—	2	4	no	—
138	C₄⋊C₄×C₅₉	—	2	4	no	—
139	C₄⋊C₄×C₅₉	—	4	2	no	—
140	C₄⋊C₄×C₅₉	—	4	2	no	—
141	C₂³×C₅₉	—	2	2	no	—
142	C₂³×C₅₉	—	2	1	no	—
143	C₂³×C₅₉	—	2	1	no	—
144	C₂³×C₅₉	—	2	2	no	—
145	C₂³×C₅₉	—	2	4	no	—
146	C₂³×C₅₉	—	4	2	no	—
147	C₂³×C₅₉	—	4	1	no	—
148	C₂³×C₅₉	—	4	1	no	—
149	C₂³×C₅₉	#117	1	1	yes	characteristic
150	C₂³×C₅₉	C₄×D₄	1	2	yes	—
151	C₂³×C₅₉	#121	1	1	yes	characteristic
152	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂³×C₅₉	#123	1	2	yes	—
154	Q₈×C₅₉	—	2	2	no	—
155	Q₈×C₅₉	—	2	4	no	—
156	Q₈×C₅₉	#95	1	4	yes	—
157	D₄×C₅₉	—	2	4	no	—
158	D₄×C₅₉	—	2	4	no	—
159	D₄×C₅₉	—	2	8	no	—
160	D₄×C₅₉	—	2	2	no	—
161	D₄×C₅₉	—	2	4	no	—
162	D₄×C₅₉	#95	1	4	yes	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	—	2	4	no	—
165	C₂×C₄×C₅₉	—	2	4	no	—
166	C₂×C₄×C₅₉	—	2	4	no	—
167	C₂×C₄×C₅₉	—	2	8	no	—
168	C₂×C₄×C₅₉	—	4	4	no	—
169	C₂×C₄×C₅₉	—	8	4	no	—
170	C₂×C₄×C₅₉	—	8	2	no	—
171	C₂×C₄×C₅₉	—	8	2	no	—
172	C₂×C₄×C₅₉	—	8	4	no	—
173	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
180	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
181	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₅₉	#120	1	2	yes	—
185	C₂×C₄×C₅₉	#120	1	2	yes	—
186	C₂×C₄×C₅₉	#121	1	2	yes	—
187	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
189	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
190	C₂×C₄×C₅₉	#123	1	2	yes	—
191	C₈×C₅₉	—	2	2	no	—
192	C₈×C₅₉	—	2	4	no	—
193	C₈×C₅₉	—	2	2	no	—
194	C₈×C₅₉	—	4	4	no	—
195	#10774	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂²×C₅₉	—	2	1	no	—
197	C₂²×C₅₉	—	2	1	no	—
198	C₂²×C₅₉	—	2	1	no	—
199	C₂²×C₅₉	—	2	1	no	—
200	C₂²×C₅₉	—	2	2	no	—
201	C₂²×C₅₉	—	2	2	no	—
202	C₂²×C₅₉	—	2	2	no	—
203	C₂²×C₅₉	—	2	2	no	—
204	C₂²×C₅₉	—	2	4	no	—
205	C₂²×C₅₉	—	4	2	no	—
206	C₂²×C₅₉	—	4	2	no	—
207	C₂²×C₅₉	—	4	4	no	—
208	C₂²×C₅₉	—	4	4	no	—
209	C₂²×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₅₉	#380	1	1	yes	characteristic
211	C₂²×C₅₉	#381	1	1	yes	characteristic
212	C₂²×C₅₉	#385	1	2	yes	—
213	C₂²×C₅₉	#386	1	2	yes	—
214	C₂²×C₅₉	#471	1	2	yes	—
215	C₂²×C₅₉	#472	1	1	yes	characteristic
216	C₂²×C₅₉	#473	1	1	yes	characteristic
217	C₄×C₅₉	—	2	4	no	—
218	C₄×C₅₉	—	8	4	no	—
219	C₄×C₅₉	C₂×#95	1	1	yes	characteristic
220	C₄×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
221	C₄×C₅₉	#379	1	1	yes	characteristic
222	C₄×C₅₉	#380	1	1	yes	characteristic
223	C₄×C₅₉	#385	1	2	yes	—
224	C₄×C₅₉	#386	1	2	yes	—
225	C₂²×#131	C₂×C₅₉	1	1	yes	characteristic
226	C₂×#417	C₂×C₅₉	1	2	yes	—
227	C₂×#343	C₂×C₅₉	1	2	yes	complemented
228	C₂×#341	C₂×C₅₉	1	1	yes	characteristic, complemented
229	C₂×#340	C₂×C₅₉	1	1	yes	characteristic, complemented
230	C₂×C₅₉	—	2	1	no	—
231	C₂×C₅₉	—	2	1	no	—
232	C₂×C₅₉	—	2	2	no	—
233	C₂×C₅₉	—	4	4	no	—
234	C₂×C₅₉	C₂²⋊#95	1	1	yes	characteristic
235	C₂×C₅₉	#1815	1	1	yes	characteristic
236	C₂×C₅₉	#1816	1	1	yes	characteristic
237	C₂×C₅₉	#1907	1	2	yes	—
238	C₂×C₅₉	#1908	1	2	yes	—
239	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
240	C₂×#131	—	2	4	no	—
241	C₂×#131	—	2	4	no	—
242	C₂×#131	—	2	2	no	—
243	C₂×#131	C₄×C₅₉	1	4	yes	complemented
244	C₂²×M₁₆	—	2	1	no	—
245	C₂²×M₁₆	C₂²×C₅₉	1	2	yes	—
246	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
247	C₂³×C₈	—	2	1	no	—
248	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
250	#417	—	2	4	no	—
251	#417	C₄×C₅₉	1	8	yes	complemented
252	C₂×#103	—	2	2	no	—
253	C₂×#102	—	2	2	no	—
254	#343	—	2	4	no	—
255	#341	—	2	2	no	—
256	#340	—	2	1	no	—
257	#340	—	2	1	no	—
258	C₅₉	#10774	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	1	no	—
263	C₂×#41	C₂×C₄×C₅₉	1	4	yes	—
264	C₂×#41	C₂×C₄×C₅₉	1	2	yes	—
265	C₂×#41	D₄×C₅₉	1	4	yes	—
266	C₂×#41	Q₈×C₅₉	1	2	yes	—
267	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
273	#131	—	2	16	no	—
274	#131	—	2	8	no	—
275	#131	—	2	8	no	—
276	C₂×M₁₆	—	2	8	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	C₂×C₄×C₅₉	1	4	yes	—
286	C₂×M₁₆	C₂×C₄×C₅₉	1	2	yes	—
287	C₂×M₁₆	D₄×C₅₉	1	4	yes	—
288	C₂²×C₈	—	2	8	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	4	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	C₂×C₄×C₅₉	1	2	yes	—
295	C₂²×C₈	D₄×C₅₉	1	1	yes	characteristic
296	C₂²×C₈	D₄×C₅₉	1	1	yes	characteristic
297	C₂²×C₈	D₄×C₅₉	1	2	yes	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	4	yes	—
304	#103	—	2	8	no	—
305	#102	—	2	8	no	—
306	C₂⁴	—	2	1	no	—
307	C₂⁴	#41×C₅₉	1	1	yes	characteristic
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	2	4	no	—
311	#41	—	2	4	no	—
312	#41	—	2	4	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	C₄²×C₅₉	1	4	yes	—
316	#41	C₂²⋊C₄×C₅₉	1	4	yes	—
317	#41	C₄⋊C₄×C₅₉	1	8	yes	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	C₂²⋊C₄×C₅₉	1	4	yes	—
321	C₂×Q₈	C₄⋊C₄×C₅₉	1	2	yes	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	C₂²⋊C₄×C₅₉	1	4	yes	—
329	C₂×D₄	C₄⋊C₄×C₅₉	1	2	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
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	C₂×D₄×C₅₉	1	2	yes	—
347	C₂²×C₄	C₂×Q₈×C₅₉	1	1	yes	characteristic
348	C₂²×C₄	#41×C₅₉	1	2	yes	—
349	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
350	M₁₆	—	2	16	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	2	4	no	—
355	M₁₆	—	4	2	no	—
356	M₁₆	—	4	2	no	—
357	M₁₆	C₂²⋊C₄×C₅₉	1	4	yes	—
358	C₂×C₈	—	2	16	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	C₂²⋊C₄×C₅₉	1	2	yes	—
370	C₂×C₈	C₂²⋊C₄×C₅₉	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	#117×C₅₉	1	1	yes	characteristic
384	C₂³	C₄×D₄×C₅₉	1	2	yes	—
385	C₂³	#121×C₅₉	1	1	yes	characteristic
386	C₂³	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
387	C₂³	#123×C₅₉	1	2	yes	—
388	Q₈	—	2	2	no	—
389	Q₈	—	2	4	no	—
390	Q₈	#95×C₅₉	1	4	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	8	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	4	no	—
396	D₄	#95×C₅₉	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	8	4	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	8	4	no	—
407	C₂×C₄	C₂×C₄²×C₅₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
409	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	2	yes	—
414	C₂×C₄	#117×C₅₉	1	1	yes	characteristic
415	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
416	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
417	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
418	C₂×C₄	#120×C₅₉	1	2	yes	—
419	C₂×C₄	#120×C₅₉	1	2	yes	—
420	C₂×C₄	#121×C₅₉	1	2	yes	—
421	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
422	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
423	C₂×C₄	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
424	C₂×C₄	#123×C₅₉	1	2	yes	—
425	C₈	—	2	2	no	—
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₈	—	4	4	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	C₄×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
443	C₂²	C₅₉×#380	1	1	yes	characteristic
444	C₂²	C₅₉×#381	1	1	yes	characteristic
445	C₂²	C₅₉×#385	1	2	yes	—
446	C₂²	C₅₉×#386	1	2	yes	—
447	C₂²	C₅₉×#471	1	2	yes	—
448	C₂²	C₅₉×#472	1	1	yes	characteristic
449	C₂²	C₅₉×#473	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	8	4	no	—
452	C₄	C₂×#95×C₅₉	1	1	yes	characteristic
453	C₄	C₄×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
454	C₄	C₅₉×#379	1	1	yes	characteristic
455	C₄	C₅₉×#380	1	1	yes	characteristic
456	C₄	C₅₉×#385	1	2	yes	—
457	C₄	C₅₉×#386	1	2	yes	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	4	4	no	—
462	C₂	C₅₉×C₂²⋊#95	1	1	yes	characteristic
463	C₂	C₅₉×#1815	1	1	yes	characteristic
464	C₂	C₅₉×#1816	1	1	yes	characteristic
465	C₂	C₅₉×#1907	1	2	yes	—
466	C₂	C₅₉×#1908	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	#121
commutator	C₂×C₄	C₂×C₄²×C₅₉
Frattini, cosocle	C₂³×C₄	C₂³×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₅₉×#343	C₂	semidirect
4. C₂×C₅₉×#341	C₂	semidirect
5. C₂×C₅₉×#340	C₂	semidirect
10. C₂×#131×C₅₉	C₄	semidirect
18. C₅₉×#417	C₄	semidirect
195. #10774	C₅₉	direct (N × H)
227. C₂×#343	C₂×C₅₉	semidirect
228. C₂×#341	C₂×C₅₉	semidirect
229. C₂×#340	C₂×C₅₉	semidirect
243. C₂×#131	C₄×C₅₉	semidirect
251. #417	C₄×C₅₉	semidirect
258. C₅₉	#10774	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#131×C₅₉	2
C₂×C₅₉×#417	2
C₂×C₅₉×#343	2
C₂×C₅₉×#341	2
C₂×C₅₉×#340	2
#10774	59

Subgroups — C59×#10774 #28422883

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#10774 #28422883