Subgroups — C₅₉×#32961 #28445070

Order 15104.

1320 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1865	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1864	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1862	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#1788	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
18	C₄×#41×C₅₉	—	2	4	no	—
19	C₄×#41×C₅₉	—	2	4	no	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₅₉	—	2	1	no	—
23	C₂×C₄×D₄×C₅₉	—	2	1	no	—
24	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₅₉	—	2	1	no	—
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₅₉	—	2	1	no	—
29	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
30	C₅₉×#479	—	2	4	no	—
31	C₅₉×#478	—	2	4	no	—
32	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₅₉×#389	C₂²	1	1	yes	characteristic
49	C₅₉×#389	C₂²	1	1	yes	characteristic
50	C₅₉×#387	—	2	1	no	—
51	C₅₉×#387	—	2	1	no	—
52	C₅₉×#385	—	2	1	no	—
53	C₅₉×#385	—	2	1	no	—
54	C₅₉×#382	C₂²	1	1	yes	characteristic
55	C₅₉×#380	C₂²	1	1	yes	characteristic
56	C₅₉×#380	C₂²	1	1	yes	characteristic
57	C₅₉×#340	C₂²	1	1	yes	characteristic
58	C₅₉×#340	C₂²	1	1	yes	characteristic
59	C₅₉×#340	C₂²	1	1	yes	characteristic
60	C₅₉×#340	C₂²	1	1	yes	characteristic
61	C₅₉×#336	C₂²	1	1	yes	characteristic
62	C₅₉×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₅₉	—	2	2	no	—
64	C₂×#41×C₅₉	—	2	2	no	—
65	C₂×#41×C₅₉	—	2	2	no	—
66	C₂×#41×C₅₉	—	2	2	no	—
67	C₂×#41×C₅₉	—	2	2	no	—
68	C₂×#41×C₅₉	Q₈	1	4	yes	—
69	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₅₉	—	2	1	no	—
71	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₉	—	2	1	no	—
73	C₂³×C₄×C₅₉	—	2	1	no	—
74	C₂³×C₄×C₅₉	—	2	1	no	—
75	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
76	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
82	#125×C₅₉	—	2	2	no	—
83	#125×C₅₉	—	2	2	no	—
84	C₄×Q₈×C₅₉	—	2	2	no	—
85	C₄×Q₈×C₅₉	—	2	2	no	—
86	C₄×Q₈×C₅₉	—	2	2	no	—
87	C₄×Q₈×C₅₉	D₄	1	4	yes	—
88	C₄×D₄×C₅₉	—	2	8	no	—
89	C₄×D₄×C₅₉	—	2	8	no	—
90	C₄×D₄×C₅₉	—	2	2	no	—
91	C₄×D₄×C₅₉	—	2	2	no	—
92	C₄×D₄×C₅₉	—	2	2	no	—
93	C₄×D₄×C₅₉	D₄	1	4	yes	—
94	#117×C₅₉	—	2	8	no	—
95	#117×C₅₉	—	2	2	no	—
96	#117×C₅₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
114	C₂×C₄²×C₅₉	—	2	8	no	—
115	C₂×C₄²×C₅₉	—	2	1	no	—
116	C₂×C₄²×C₅₉	—	2	1	no	—
117	C₂×C₄²×C₅₉	—	2	1	no	—
118	C₂×C₄²×C₅₉	—	2	2	no	—
119	C₂×C₄²×C₅₉	—	2	2	no	—
120	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
122	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
124	#107×C₅₉	—	2	2	no	—
125	#107×C₅₉	—	2	2	no	—
126	#106×C₅₉	—	2	2	no	—
127	#106×C₅₉	—	2	2	no	—
128	C₄⋊C₈×C₅₉	—	2	2	no	—
129	C₄⋊C₈×C₅₉	—	2	2	no	—
130	#103×C₅₉	—	2	2	no	—
131	#103×C₅₉	—	2	2	no	—
132	#103×C₅₉	—	2	2	no	—
133	#103×C₅₉	—	2	2	no	—
134	#102×C₅₉	—	2	2	no	—
135	#102×C₅₉	—	2	2	no	—
136	#102×C₅₉	—	2	2	no	—
137	#102×C₅₉	—	2	2	no	—
138	C₂²⋊C₈×C₅₉	—	2	2	no	—
139	C₂²⋊C₈×C₅₉	—	2	2	no	—
140	#95×C₅₉	—	2	1	no	—
141	#95×C₅₉	—	2	1	no	—
142	#95×C₅₉	—	2	1	no	—
143	#95×C₅₉	—	2	1	no	—
144	#95×C₅₉	—	2	1	no	—
145	#95×C₅₉	—	2	1	no	—
146	C₂⁴×C₅₉	—	2	1	no	—
147	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
148	#41×C₅₉	—	2	8	no	—
149	#41×C₅₉	—	2	8	no	—
150	#41×C₅₉	—	2	8	no	—
151	#41×C₅₉	—	2	8	no	—
152	C₂×Q₈×C₅₉	—	2	1	no	—
153	C₂×Q₈×C₅₉	—	2	1	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₅₉	C₂×Q₈	1	2	yes	—
157	C₂×Q₈×C₅₉	#41	1	2	yes	—
158	C₂×D₄×C₅₉	—	2	4	no	—
159	C₂×D₄×C₅₉	—	2	4	no	—
160	C₂×D₄×C₅₉	—	2	4	no	—
161	C₂×D₄×C₅₉	—	2	1	no	—
162	C₂×D₄×C₅₉	—	2	1	no	—
163	C₂×D₄×C₅₉	—	2	1	no	—
164	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
165	C₂×D₄×C₅₉	C₂×Q₈	1	2	yes	—
166	C₂×D₄×C₅₉	#41	1	2	yes	—
167	C₂²×C₄×C₅₉	—	2	4	no	—
168	C₂²×C₄×C₅₉	—	2	4	no	—
169	C₂²×C₄×C₅₉	—	2	1	no	—
170	C₂²×C₄×C₅₉	—	2	4	no	—
171	C₂²×C₄×C₅₉	—	2	1	no	—
172	C₂²×C₄×C₅₉	—	2	1	no	—
173	C₂²×C₄×C₅₉	—	2	1	no	—
174	C₂²×C₄×C₅₉	—	2	1	no	—
175	C₂²×C₄×C₅₉	—	2	4	no	—
176	C₂²×C₄×C₅₉	—	2	1	no	—
177	C₂²×C₄×C₅₉	—	2	1	no	—
178	C₂²×C₄×C₅₉	—	2	2	no	—
179	C₂²×C₄×C₅₉	—	2	2	no	—
180	C₂²×C₄×C₅₉	—	2	4	no	—
181	C₂²×C₄×C₅₉	—	2	2	no	—
182	C₂²×C₄×C₅₉	—	2	1	no	—
183	C₂²×C₄×C₅₉	—	2	1	no	—
184	C₂²×C₄×C₅₉	—	2	1	no	—
185	C₂²×C₄×C₅₉	—	2	1	no	—
186	C₂²×C₄×C₅₉	—	4	1	no	—
187	C₂²×C₄×C₅₉	—	4	1	no	—
188	C₂²×C₄×C₅₉	—	4	1	no	—
189	C₂²×C₄×C₅₉	—	4	2	no	—
190	C₂²×C₄×C₅₉	—	4	2	no	—
191	C₂²×C₄×C₅₉	—	4	2	no	—
192	C₂²×C₄×C₅₉	—	4	2	no	—
193	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
199	C₂²×C₄×C₅₉	#41	1	2	yes	—
200	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
201	C₂×C₈×C₅₉	—	2	1	no	—
202	C₂×C₈×C₅₉	—	2	1	no	—
203	C₂×C₈×C₅₉	—	2	1	no	—
204	C₂×C₈×C₅₉	—	2	1	no	—
205	C₂×C₈×C₅₉	—	2	1	no	—
206	C₂×C₈×C₅₉	—	2	1	no	—
207	C₂×C₈×C₅₉	—	2	1	no	—
208	C₂×C₈×C₅₉	—	2	1	no	—
209	C₂×C₈×C₅₉	—	2	1	no	—
210	C₂×C₈×C₅₉	—	2	1	no	—
211	C₂×C₈×C₅₉	—	2	1	no	—
212	C₂×C₈×C₅₉	—	2	1	no	—
213	C₄⋊C₄×C₅₉	—	2	4	no	—
214	C₄⋊C₄×C₅₉	—	2	4	no	—
215	C₄⋊C₄×C₅₉	—	2	1	no	—
216	C₄⋊C₄×C₅₉	—	2	1	no	—
217	C₄⋊C₄×C₅₉	—	2	1	no	—
218	C₄⋊C₄×C₅₉	—	2	1	no	—
219	C₄⋊C₄×C₅₉	—	2	1	no	—
220	C₄⋊C₄×C₅₉	—	2	1	no	—
221	C₄⋊C₄×C₅₉	—	2	1	no	—
222	C₄⋊C₄×C₅₉	—	2	1	no	—
223	C₄⋊C₄×C₅₉	—	2	1	no	—
224	C₄⋊C₄×C₅₉	—	2	1	no	—
225	C₄⋊C₄×C₅₉	—	4	2	no	—
226	C₄⋊C₄×C₅₉	—	4	2	no	—
227	C₄⋊C₄×C₅₉	—	4	2	no	—
228	C₄⋊C₄×C₅₉	—	4	2	no	—
229	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
230	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
231	C₂²⋊C₄×C₅₉	—	2	4	no	—
232	C₂²⋊C₄×C₅₉	—	2	4	no	—
233	C₂²⋊C₄×C₅₉	—	2	4	no	—
234	C₂²⋊C₄×C₅₉	—	4	2	no	—
235	C₂²⋊C₄×C₅₉	—	4	2	no	—
236	C₄²×C₅₉	—	2	4	no	—
237	C₄²×C₅₉	—	2	4	no	—
238	C₄²×C₅₉	—	2	2	no	—
239	C₄²×C₅₉	—	2	4	no	—
240	C₄²×C₅₉	—	2	2	no	—
241	C₄²×C₅₉	—	2	1	no	—
242	C₄²×C₅₉	—	2	1	no	—
243	C₄²×C₅₉	C₂×D₄	1	2	yes	—
244	C₄²×C₅₉	C₂×D₄	1	2	yes	—
245	C₂³×C₅₉	—	2	1	no	—
246	C₂³×C₅₉	—	2	2	no	—
247	C₂³×C₅₉	—	2	2	no	—
248	C₂³×C₅₉	—	2	1	no	—
249	C₂³×C₅₉	—	2	2	no	—
250	C₂³×C₅₉	—	2	1	no	—
251	C₂³×C₅₉	—	2	1	no	—
252	C₂³×C₅₉	—	2	1	no	—
253	C₂³×C₅₉	—	2	1	no	—
254	C₂³×C₅₉	—	4	1	no	—
255	C₂³×C₅₉	—	4	1	no	—
256	C₂³×C₅₉	—	4	1	no	—
257	C₂³×C₅₉	—	4	1	no	—
258	C₂³×C₅₉	C₂²⋊Q₈	1	2	yes	—
259	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
260	Q₈×C₅₉	—	2	2	no	—
261	Q₈×C₅₉	—	2	2	no	—
262	Q₈×C₅₉	—	2	2	no	—
263	Q₈×C₅₉	C₂²⋊Q₈	1	4	yes	—
264	D₄×C₅₉	—	2	16	no	—
265	D₄×C₅₉	—	2	2	no	—
266	D₄×C₅₉	—	2	2	no	—
267	D₄×C₅₉	—	2	2	no	—
268	D₄×C₅₉	C₂²⋊Q₈	1	4	yes	—
269	C₂×C₄×C₅₉	—	2	16	no	—
270	C₂×C₄×C₅₉	—	2	1	no	—
271	C₂×C₄×C₅₉	—	2	1	no	—
272	C₂×C₄×C₅₉	—	2	2	no	—
273	C₂×C₄×C₅₉	—	2	2	no	—
274	C₂×C₄×C₅₉	—	2	1	no	—
275	C₂×C₄×C₅₉	—	2	2	no	—
276	C₂×C₄×C₅₉	—	2	1	no	—
277	C₂×C₄×C₅₉	—	2	1	no	—
278	C₂×C₄×C₅₉	—	2	1	no	—
279	C₂×C₄×C₅₉	—	2	1	no	—
280	C₂×C₄×C₅₉	—	2	1	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	2	no	—
283	C₂×C₄×C₅₉	—	2	2	no	—
284	C₂×C₄×C₅₉	—	2	2	no	—
285	C₂×C₄×C₅₉	—	2	1	no	—
286	C₂×C₄×C₅₉	—	2	2	no	—
287	C₂×C₄×C₅₉	—	2	2	no	—
288	C₂×C₄×C₅₉	—	2	1	no	—
289	C₂×C₄×C₅₉	—	2	1	no	—
290	C₂×C₄×C₅₉	—	4	4	no	—
291	C₂×C₄×C₅₉	—	4	8	no	—
292	C₂×C₄×C₅₉	—	4	4	no	—
293	C₂×C₄×C₅₉	—	4	8	no	—
294	C₂×C₄×C₅₉	—	4	1	no	—
295	C₂×C₄×C₅₉	—	4	1	no	—
296	C₂×C₄×C₅₉	—	4	1	no	—
297	C₂×C₄×C₅₉	—	4	1	no	—
298	C₂×C₄×C₅₉	—	4	1	no	—
299	C₂×C₄×C₅₉	—	4	1	no	—
300	C₂×C₄×C₅₉	—	4	1	no	—
301	C₂×C₄×C₅₉	—	4	1	no	—
302	C₂×C₄×C₅₉	—	4	1	no	—
303	C₂×C₄×C₅₉	—	4	1	no	—
304	C₂×C₄×C₅₉	—	4	1	no	—
305	C₂×C₄×C₅₉	—	4	1	no	—
306	C₂×C₄×C₅₉	—	4	1	no	—
307	C₂×C₄×C₅₉	—	4	1	no	—
308	C₂×C₄×C₅₉	—	4	1	no	—
309	C₂×C₄×C₅₉	—	4	1	no	—
310	C₂×C₄×C₅₉	#120	1	2	yes	—
311	C₂×C₄×C₅₉	#120	1	2	yes	—
312	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
313	C₂×C₄×C₅₉	#135	1	2	yes	—
314	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
317	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
320	C₈×C₅₉	—	4	1	no	—
321	C₈×C₅₉	—	4	1	no	—
322	C₈×C₅₉	—	4	1	no	—
323	C₈×C₅₉	—	4	1	no	—
324	#32961	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
325	C₂²×C₅₉	—	2	2	no	—
326	C₂²×C₅₉	—	2	2	no	—
327	C₂²×C₅₉	—	2	2	no	—
328	C₂²×C₅₉	—	2	4	no	—
329	C₂²×C₅₉	—	4	2	no	—
330	C₂²×C₅₉	—	4	2	no	—
331	C₂²×C₅₉	—	4	1	no	—
332	C₂²×C₅₉	—	4	2	no	—
333	C₂²×C₅₉	—	4	1	no	—
334	C₂²×C₅₉	—	4	2	no	—
335	C₂²×C₅₉	—	4	1	no	—
336	C₂²×C₅₉	—	4	2	no	—
337	C₂²×C₅₉	—	4	1	no	—
338	C₂²×C₅₉	—	4	2	no	—
339	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
340	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
341	C₂²×C₅₉	#525	1	1	yes	characteristic
342	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
343	C₂²×C₅₉	#575	1	1	yes	characteristic
344	C₂²×C₅₉	#575	1	1	yes	characteristic
345	C₂²×C₅₉	#575	1	1	yes	characteristic
346	C₄×C₅₉	—	2	2	no	—
347	C₄×C₅₉	—	2	4	no	—
348	C₄×C₅₉	—	2	2	no	—
349	C₄×C₅₉	—	2	2	no	—
350	C₄×C₅₉	—	2	2	no	—
351	C₄×C₅₉	—	4	2	no	—
352	C₄×C₅₉	—	4	1	no	—
353	C₄×C₅₉	—	4	2	no	—
354	C₄×C₅₉	—	8	1	no	—
355	C₄×C₅₉	—	8	1	no	—
356	C₄×C₅₉	—	8	1	no	—
357	C₄×C₅₉	—	8	1	no	—
358	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
359	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
360	C₄×C₅₉	#525	1	1	yes	characteristic
361	C₄×C₅₉	#525	1	1	yes	characteristic
362	C₂×C₄×#41	C₂×C₅₉	1	1	yes	characteristic
363	C₂×#479	C₂×C₅₉	1	1	yes	characteristic, complemented
364	C₂×#478	C₂×C₅₉	1	1	yes	characteristic, complemented
365	#2851	C₂×C₅₉	1	1	yes	characteristic, complemented
366	#1865	C₂×C₅₉	1	1	yes	characteristic, complemented
367	#1864	C₂×C₅₉	1	1	yes	characteristic, complemented
368	#1863	C₂×C₅₉	1	1	yes	characteristic, complemented
369	#1862	C₂×C₅₉	1	1	yes	characteristic, complemented
370	#1854	C₂×C₅₉	1	1	yes	characteristic, complemented
371	#1854	C₂×C₅₉	1	1	yes	characteristic, complemented
372	#1805	C₂×C₅₉	1	1	yes	characteristic, complemented
373	#1804	C₂×C₅₉	1	1	yes	characteristic, complemented
374	#1797	C₂×C₅₉	1	1	yes	characteristic, complemented
375	#1788	C₂×C₅₉	1	1	yes	characteristic
376	#1788	C₂×C₅₉	1	1	yes	characteristic
377	C₂×C₅₉	—	4	2	no	—
378	C₂×C₅₉	—	4	4	no	—
379	C₂×C₅₉	#2848	1	1	yes	characteristic
380	C₂×C₅₉	#3002	1	1	yes	characteristic
381	C₂×C₅₉	#3005	1	1	yes	characteristic
382	C₂×C₅₉	#3076	1	1	yes	characteristic
383	C₂×C₅₉	#3080	1	1	yes	characteristic
384	C₂×C₅₉	#3102	1	1	yes	characteristic
385	C₂×C₅₉	#3111	1	1	yes	characteristic
386	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
387	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
388	C₄×#41	—	2	4	no	—
389	C₄×#41	—	2	4	no	—
390	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
391	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
392	C₂×C₄×D₄	—	2	1	no	—
393	C₂×C₄×D₄	—	2	1	no	—
394	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
395	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
396	C₂×#117	—	2	1	no	—
397	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
398	C₂²×C₄²	—	2	1	no	—
399	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
400	#479	—	2	4	no	—
401	#478	—	2	4	no	—
402	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
403	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
404	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
405	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
406	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
407	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
408	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
409	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
410	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
411	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
412	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
413	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
414	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
415	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
417	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
418	#389	C₂²×C₅₉	1	1	yes	characteristic
419	#389	C₂²×C₅₉	1	1	yes	characteristic
420	#387	—	2	1	no	—
421	#387	—	2	1	no	—
422	#385	—	2	1	no	—
423	#385	—	2	1	no	—
424	#382	C₂²×C₅₉	1	1	yes	characteristic
425	#380	C₂²×C₅₉	1	1	yes	characteristic
426	#380	C₂²×C₅₉	1	1	yes	characteristic
427	#340	C₂²×C₅₉	1	1	yes	characteristic
428	#340	C₂²×C₅₉	1	1	yes	characteristic
429	#340	C₂²×C₅₉	1	1	yes	characteristic
430	#340	C₂²×C₅₉	1	1	yes	characteristic
431	#336	C₂²×C₅₉	1	1	yes	characteristic
432	#336	C₂²×C₅₉	1	1	yes	characteristic
433	C₅₉	#32961	1	1	yes	characteristic, direct product factor, Sylow
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	2	no	—
436	C₂×#41	—	2	2	no	—
437	C₂×#41	—	2	2	no	—
438	C₂×#41	—	2	2	no	—
439	C₂×#41	Q₈×C₅₉	1	4	yes	—
440	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
447	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
448	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
453	#125	—	2	2	no	—
454	#125	—	2	2	no	—
455	C₄×Q₈	—	2	2	no	—
456	C₄×Q₈	—	2	2	no	—
457	C₄×Q₈	—	2	2	no	—
458	C₄×Q₈	D₄×C₅₉	1	4	yes	—
459	C₄×D₄	—	2	8	no	—
460	C₄×D₄	—	2	8	no	—
461	C₄×D₄	—	2	2	no	—
462	C₄×D₄	—	2	2	no	—
463	C₄×D₄	—	2	2	no	—
464	C₄×D₄	D₄×C₅₉	1	4	yes	—
465	#117	—	2	8	no	—
466	#117	—	2	2	no	—
467	#117	—	2	2	no	—
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	—	2	1	no	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	—	2	1	no	—
474	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
477	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
478	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
479	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	—	2	1	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	—	2	1	no	—
483	C₂×C₂²⋊C₄	—	2	1	no	—
484	C₂×C₂²⋊C₄	—	2	1	no	—
485	C₂×C₄²	—	2	8	no	—
486	C₂×C₄²	—	2	1	no	—
487	C₂×C₄²	—	2	1	no	—
488	C₂×C₄²	—	2	1	no	—
489	C₂×C₄²	—	2	2	no	—
490	C₂×C₄²	—	2	2	no	—
491	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
492	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
495	#107	—	2	2	no	—
496	#107	—	2	2	no	—
497	#106	—	2	2	no	—
498	#106	—	2	2	no	—
499	C₄⋊C₈	—	2	2	no	—
500	C₄⋊C₈	—	2	2	no	—
501	#103	—	2	2	no	—
502	#103	—	2	2	no	—
503	#103	—	2	2	no	—
504	#103	—	2	2	no	—
505	#102	—	2	2	no	—
506	#102	—	2	2	no	—
507	#102	—	2	2	no	—
508	#102	—	2	2	no	—
509	C₂²⋊C₈	—	2	2	no	—
510	C₂²⋊C₈	—	2	2	no	—
511	#95	—	2	1	no	—
512	#95	—	2	1	no	—
513	#95	—	2	1	no	—
514	#95	—	2	1	no	—
515	#95	—	2	1	no	—
516	#95	—	2	1	no	—
517	C₂⁴	—	2	1	no	—
518	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
519	#41	—	2	8	no	—
520	#41	—	2	8	no	—
521	#41	—	2	8	no	—
522	#41	—	2	8	no	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
527	C₂×Q₈	C₂×Q₈×C₅₉	1	2	yes	—
528	C₂×Q₈	#41×C₅₉	1	2	yes	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	1	no	—
535	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
536	C₂×D₄	C₂×Q₈×C₅₉	1	2	yes	—
537	C₂×D₄	#41×C₅₉	1	2	yes	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	4	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	—	4	1	no	—
560	C₂²×C₄	—	4	2	no	—
561	C₂²×C₄	—	4	2	no	—
562	C₂²×C₄	—	4	2	no	—
563	C₂²×C₄	—	4	2	no	—
564	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
570	C₂²×C₄	#41×C₅₉	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
572	C₂×C₈	—	2	1	no	—
573	C₂×C₈	—	2	1	no	—
574	C₂×C₈	—	2	1	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	4	2	no	—
597	C₄⋊C₄	—	4	2	no	—
598	C₄⋊C₄	—	4	2	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
601	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	4	2	no	—
606	C₂²⋊C₄	—	4	2	no	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	4	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	4	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	C₂×D₄×C₅₉	1	2	yes	—
615	C₄²	C₂×D₄×C₅₉	1	2	yes	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	4	1	no	—
626	C₂³	—	4	1	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	C₂²⋊Q₈×C₅₉	1	2	yes	—
630	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
631	Q₈	—	2	2	no	—
632	Q₈	—	2	2	no	—
633	Q₈	—	2	2	no	—
634	Q₈	C₂²⋊Q₈×C₅₉	1	4	yes	—
635	D₄	—	2	16	no	—
636	D₄	—	2	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	C₂²⋊Q₈×C₅₉	1	4	yes	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	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	1	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	8	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	8	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	#120×C₅₉	1	2	yes	—
682	C₂×C₄	#120×C₅₉	1	2	yes	—
683	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
684	C₂×C₄	#135×C₅₉	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
687	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
688	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
689	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
690	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
691	C₈	—	4	1	no	—
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
710	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
711	C₂²	C₅₉×#525	1	1	yes	characteristic
712	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
713	C₂²	C₅₉×#575	1	1	yes	characteristic
714	C₂²	C₅₉×#575	1	1	yes	characteristic
715	C₂²	C₅₉×#575	1	1	yes	characteristic
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	4	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	1	no	—
723	C₄	—	4	2	no	—
724	C₄	—	8	1	no	—
725	C₄	—	8	1	no	—
726	C₄	—	8	1	no	—
727	C₄	—	8	1	no	—
728	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
729	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
730	C₄	C₅₉×#525	1	1	yes	characteristic
731	C₄	C₅₉×#525	1	1	yes	characteristic
732	C₂	—	4	2	no	—
733	C₂	—	4	4	no	—
734	C₂	C₅₉×#2848	1	1	yes	characteristic
735	C₂	C₅₉×#3002	1	1	yes	characteristic
736	C₂	C₅₉×#3005	1	1	yes	characteristic
737	C₂	C₅₉×#3076	1	1	yes	characteristic
738	C₂	C₅₉×#3080	1	1	yes	characteristic
739	C₂	C₅₉×#3102	1	1	yes	characteristic
740	C₂	C₅₉×#3111	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#479	C₂	semidirect
3. C₂×C₅₉×#478	C₂	semidirect
4. C₅₉×#2851	C₂	semidirect
5. C₅₉×#1865	C₂	semidirect
6. C₅₉×#1864	C₂	semidirect
7. C₅₉×#1863	C₂	semidirect
8. C₅₉×#1862	C₂	semidirect
9. C₅₉×#1854	C₂	semidirect
10. C₅₉×#1854	C₂	semidirect
11. C₅₉×#1805	C₂	semidirect
12. C₅₉×#1804	C₂	semidirect
13. C₅₉×#1797	C₂	semidirect
324. #32961	C₅₉	direct (N × H)
363. C₂×#479	C₂×C₅₉	semidirect
364. C₂×#478	C₂×C₅₉	semidirect
365. #2851	C₂×C₅₉	semidirect
366. #1865	C₂×C₅₉	semidirect
367. #1864	C₂×C₅₉	semidirect
368. #1863	C₂×C₅₉	semidirect
369. #1862	C₂×C₅₉	semidirect
370. #1854	C₂×C₅₉	semidirect
371. #1854	C₂×C₅₉	semidirect
372. #1805	C₂×C₅₉	semidirect
373. #1804	C₂×C₅₉	semidirect
374. #1797	C₂×C₅₉	semidirect
433. C₅₉	#32961	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×C₄×#41×C₅₉	2
C₂×C₅₉×#479	2
C₂×C₅₉×#478	2
C₅₉×#2851	2
C₅₉×#1865	2
C₅₉×#1864	2
C₅₉×#1863	2
C₅₉×#1862	2
C₅₉×#1854	2
C₅₉×#1805	2
C₅₉×#1804	2
C₅₉×#1797	2
C₅₉×#1788	2
#32961	59

Subgroups — C59×#32961 #28445070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#32961 #28445070