Subgroups — C₅₉×#8051 #28420160

Order 15104.

1090 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#407	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1297	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₅₉	C₄	1	2	yes	complemented
7	C₂×#117×C₅₉	—	2	1	no	—
8	C₂²×C₂²⋊C₄×C₅₉	—	2	1	no	—
9	C₂²×C₄²×C₅₉	—	2	1	no	—
10	C₅₉×#407	—	2	1	no	—
11	C₅₉×#407	—	2	1	no	—
12	C₅₉×#407	C₄	1	2	yes	complemented
13	C₅₉×#407	C₂²	1	2	yes	—
14	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
15	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
16	C₅₉×#381	C₄	1	2	yes	complemented
17	C₅₉×#380	—	2	1	no	—
18	C₅₉×#380	C₄	1	2	yes	complemented
19	C₅₉×#379	—	2	1	no	—
20	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
21	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
22	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₅₉	C₄	1	2	yes	complemented
24	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
25	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
26	C₂×#95×C₅₉	C₄	1	2	yes	complemented
27	C₂⁵×C₅₉	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₅₉	—	2	2	no	—
29	C₂³×C₄×C₅₉	—	4	4	no	—
30	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₅₉	Q₈	1	1	yes	characteristic
42	C₂³×C₄×C₅₉	Q₈	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₅₉	—	2	2	no	—
45	C₂×M₁₆×C₅₉	—	4	4	no	—
46	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	complemented
47	C₂²×C₈×C₅₉	—	2	2	no	—
48	#117×C₅₉	—	4	4	no	—
49	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
51	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
56	C₂×C₄²×C₅₉	—	2	2	no	—
57	C₂×C₄²×C₅₉	—	2	2	no	—
58	C₂×C₄²×C₅₉	—	2	2	no	—
59	C₂×C₄²×C₅₉	—	4	4	no	—
60	C₂²⋊C₈×C₅₉	—	2	2	no	—
61	C₂²⋊C₈×C₅₉	—	2	2	no	—
62	C₂²⋊C₈×C₅₉	—	2	2	no	—
63	C₂²⋊C₈×C₅₉	—	2	2	no	—
64	#95×C₅₉	—	2	2	no	—
65	#95×C₅₉	—	2	2	no	—
66	#95×C₅₉	C₂×C₄	1	4	yes	—
67	#95×C₅₉	C₂×C₄	1	4	yes	complemented
68	C₂⁴×C₅₉	—	2	4	no	—
69	C₂⁴×C₅₉	—	4	2	no	—
70	C₂⁴×C₅₉	—	4	2	no	—
71	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	—	2	4	no	—
79	C₂²×C₄×C₅₉	—	2	4	no	—
80	C₂²×C₄×C₅₉	—	2	4	no	—
81	C₂²×C₄×C₅₉	—	2	8	no	—
82	C₂²×C₄×C₅₉	—	2	4	no	—
83	C₂²×C₄×C₅₉	—	2	4	no	—
84	C₂²×C₄×C₅₉	—	4	2	no	—
85	C₂²×C₄×C₅₉	—	4	2	no	—
86	C₂²×C₄×C₅₉	—	4	2	no	—
87	C₂²×C₄×C₅₉	—	4	2	no	—
88	C₂²×C₄×C₅₉	—	4	2	no	—
89	C₂²×C₄×C₅₉	—	4	2	no	—
90	C₂²×C₄×C₅₉	—	4	2	no	—
91	C₂²×C₄×C₅₉	—	4	2	no	—
92	C₂²×C₄×C₅₉	—	4	2	no	—
93	C₂²×C₄×C₅₉	—	4	2	no	—
94	C₂²×C₄×C₅₉	—	4	2	no	—
95	C₂²×C₄×C₅₉	—	4	4	no	—
96	C₂²×C₄×C₅₉	—	4	4	no	—
97	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
125	M₁₆×C₅₉	—	4	4	no	—
126	M₁₆×C₅₉	—	4	4	no	—
127	C₂×C₈×C₅₉	—	2	4	no	—
128	C₂×C₈×C₅₉	—	4	4	no	—
129	C₄⋊C₄×C₅₉	—	4	4	no	—
130	C₂²⋊C₄×C₅₉	—	2	8	no	—
131	C₂²⋊C₄×C₅₉	—	2	8	no	—
132	C₂²⋊C₄×C₅₉	—	4	4	no	—
133	C₂²⋊C₄×C₅₉	—	4	4	no	—
134	C₂²⋊C₄×C₅₉	—	4	4	no	—
135	C₄²×C₅₉	—	4	4	no	—
136	C₄²×C₅₉	—	4	4	no	—
137	C₄²×C₅₉	—	4	4	no	—
138	C₂³×C₅₉	—	2	2	no	—
139	C₂³×C₅₉	—	2	2	no	—
140	C₂³×C₅₉	—	2	2	no	—
141	C₂³×C₅₉	—	2	2	no	—
142	C₂³×C₅₉	—	2	2	no	—
143	C₂³×C₅₉	—	2	2	no	—
144	C₂³×C₅₉	—	2	2	no	—
145	C₂³×C₅₉	—	2	2	no	—
146	C₂³×C₅₉	—	2	2	no	—
147	C₂³×C₅₉	—	2	2	no	—
148	C₂³×C₅₉	—	2	2	no	—
149	C₂³×C₅₉	—	2	2	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	—	4	1	no	—
156	C₂³×C₅₉	—	4	1	no	—
157	C₂³×C₅₉	—	4	1	no	—
158	C₂³×C₅₉	—	4	16	no	—
159	C₂³×C₅₉	#95	1	1	yes	characteristic
160	C₂³×C₅₉	#95	1	1	yes	characteristic
161	C₂³×C₅₉	#95	1	1	yes	characteristic
162	C₂³×C₅₉	#95	1	1	yes	characteristic
163	C₂³×C₅₉	#104	1	4	yes	—
164	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	—	2	2	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	2	2	no	—
170	C₂×C₄×C₅₉	—	2	2	no	—
171	C₂×C₄×C₅₉	—	2	2	no	—
172	C₂×C₄×C₅₉	—	2	2	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	2	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	2	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	2	2	no	—
182	C₂×C₄×C₅₉	—	2	8	no	—
183	C₂×C₄×C₅₉	—	4	1	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	1	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	1	no	—
190	C₂×C₄×C₅₉	—	4	1	no	—
191	C₂×C₄×C₅₉	—	4	1	no	—
192	C₂×C₄×C₅₉	—	4	1	no	—
193	C₂×C₄×C₅₉	—	4	1	no	—
194	C₂×C₄×C₅₉	—	4	1	no	—
195	C₂×C₄×C₅₉	—	4	4	no	—
196	C₂×C₄×C₅₉	—	4	16	no	—
197	C₂×C₄×C₅₉	—	4	4	no	—
198	C₂×C₄×C₅₉	—	4	4	no	—
199	C₂×C₄×C₅₉	—	4	4	no	—
200	C₂×C₄×C₅₉	—	4	4	no	—
201	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
202	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
203	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
204	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
205	C₂×C₄×C₅₉	#99	1	4	yes	—
206	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₈×C₅₉	—	4	4	no	—
211	#8051	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₅₉	—	2	8	no	—
213	C₂²×C₅₉	—	2	1	no	—
214	C₂²×C₅₉	—	2	1	no	—
215	C₂²×C₅₉	—	2	1	no	—
216	C₂²×C₅₉	—	2	1	no	—
217	C₂²×C₅₉	—	2	1	no	—
218	C₂²×C₅₉	—	2	1	no	—
219	C₂²×C₅₉	—	2	1	no	—
220	C₂²×C₅₉	—	2	1	no	—
221	C₂²×C₅₉	—	2	1	no	—
222	C₂²×C₅₉	—	2	1	no	—
223	C₂²×C₅₉	—	2	1	no	—
224	C₂²×C₅₉	—	2	1	no	—
225	C₂²×C₅₉	—	2	1	no	—
226	C₂²×C₅₉	—	2	1	no	—
227	C₂²×C₅₉	—	2	1	no	—
228	C₂²×C₅₉	—	2	1	no	—
229	C₂²×C₅₉	—	4	4	no	—
230	C₂²×C₅₉	—	4	4	no	—
231	C₂²×C₅₉	—	4	4	no	—
232	C₂²×C₅₉	—	4	4	no	—
233	C₂²×C₅₉	—	4	4	no	—
234	C₂²×C₅₉	—	4	4	no	—
235	C₂²×C₅₉	#339	1	2	yes	—
236	C₂²×C₅₉	#339	1	2	yes	—
237	C₂²×C₅₉	#342	1	2	yes	—
238	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
239	C₂²×C₅₉	C₂×#104	1	2	yes	—
240	C₂²×C₅₉	#421	1	2	yes	—
241	C₄×C₅₉	—	2	1	no	—
242	C₄×C₅₉	—	2	1	no	—
243	C₄×C₅₉	—	2	1	no	—
244	C₄×C₅₉	—	2	1	no	—
245	C₄×C₅₉	—	2	1	no	—
246	C₄×C₅₉	—	2	1	no	—
247	C₄×C₅₉	—	4	8	no	—
248	C₄×C₅₉	—	8	4	no	—
249	C₄×C₅₉	#342	1	2	yes	—
250	C₄×C₅₉	C₂×#99	1	2	yes	—
251	C₂×#407	C₂×C₅₉	1	1	yes	characteristic
252	#2280	C₂×C₅₉	1	1	yes	characteristic
253	C₂×C₄×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic
254	#1297	C₂×C₅₉	1	4	yes	complemented
255	C₂×C₅₉	—	2	2	no	—
256	C₂×C₅₉	—	2	2	no	—
257	C₂×C₅₉	—	2	2	no	—
258	C₂×C₅₉	—	2	2	no	—
259	C₂×C₅₉	—	2	2	no	—
260	C₂×C₅₉	—	4	1	no	—
261	C₂×C₅₉	—	4	1	no	—
262	C₂×C₅₉	C₂×#339	1	1	yes	characteristic
263	C₂×C₅₉	#1733	1	1	yes	characteristic
264	C₂×C₅₉	C₂×#342	1	1	yes	characteristic
265	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
266	C₂²×M₁₆	C₄×C₅₉	1	2	yes	complemented
267	C₂×#117	—	2	1	no	—
268	C₂²×C₂²⋊C₄	—	2	1	no	—
269	C₂²×C₄²	—	2	1	no	—
270	#407	—	2	1	no	—
271	#407	—	2	1	no	—
272	#407	C₄×C₅₉	1	2	yes	complemented
273	#407	C₂²×C₅₉	1	2	yes	—
274	C₂×C₂²⋊C₈	—	2	1	no	—
275	C₂×C₂²⋊C₈	—	2	1	no	—
276	#381	C₄×C₅₉	1	2	yes	complemented
277	#380	—	2	1	no	—
278	#380	C₄×C₅₉	1	2	yes	complemented
279	#379	—	2	1	no	—
280	C₄×C₂²⋊C₄	—	2	1	no	—
281	C₄×C₂²⋊C₄	—	2	1	no	—
282	C₄×C₂²⋊C₄	—	2	1	no	—
283	C₄×C₂²⋊C₄	C₄×C₅₉	1	2	yes	complemented
284	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
285	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
286	C₂×#95	C₄×C₅₉	1	2	yes	complemented
287	C₅₉	#8051	1	1	yes	characteristic, direct product factor, Sylow
288	C₂⁵	D₄×C₅₉	1	1	yes	characteristic
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	4	4	no	—
291	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
292	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
293	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
294	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
295	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
296	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
298	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
300	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
301	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
302	C₂³×C₄	Q₈×C₅₉	1	1	yes	characteristic
303	C₂³×C₄	Q₈×C₅₉	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	4	4	no	—
307	C₂×M₁₆	C₂×C₄×C₅₉	1	4	yes	complemented
308	C₂²×C₈	—	2	2	no	—
309	#117	—	4	4	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	8	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	4	4	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	C₂×C₄×C₅₉	1	4	yes	—
328	#95	C₂×C₄×C₅₉	1	4	yes	complemented
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	4	2	no	—
331	C₂⁴	—	4	2	no	—
332	C₂⁴	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
333	C₂⁴	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
334	C₂⁴	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
335	C₂⁴	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
336	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
337	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
338	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	4	no	—
357	C₂²×C₄	—	4	4	no	—
358	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
359	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
360	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
361	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
363	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
364	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
369	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
370	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
371	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
372	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
373	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
374	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
375	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
376	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
377	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
378	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
379	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
380	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
381	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×Q₈×C₅₉	1	1	yes	characteristic
386	M₁₆	—	4	4	no	—
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	4	4	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₂²⋊C₄	—	4	4	no	—
396	C₄²	—	4	4	no	—
397	C₄²	—	4	4	no	—
398	C₄²	—	4	4	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	16	no	—
420	C₂³	#95×C₅₉	1	1	yes	characteristic
421	C₂³	#95×C₅₉	1	1	yes	characteristic
422	C₂³	#95×C₅₉	1	1	yes	characteristic
423	C₂³	#95×C₅₉	1	1	yes	characteristic
424	C₂³	#104×C₅₉	1	4	yes	—
425	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
426	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
427	C₂³	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
463	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
464	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
465	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
466	C₂×C₄	#99×C₅₉	1	4	yes	—
467	C₂×C₄	C₂×C₄²×C₅₉	1	1	yes	characteristic
468	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
469	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
470	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
471	C₈	—	4	4	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	C₅₉×#339	1	2	yes	—
496	C₂²	C₅₉×#339	1	2	yes	—
497	C₂²	C₅₉×#342	1	2	yes	—
498	C₂²	C₂×#95×C₅₉	1	1	yes	characteristic
499	C₂²	C₂×#104×C₅₉	1	2	yes	—
500	C₂²	C₅₉×#421	1	2	yes	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	4	8	no	—
508	C₄	—	8	4	no	—
509	C₄	C₅₉×#342	1	2	yes	—
510	C₄	C₂×#99×C₅₉	1	2	yes	—
511	C₂	—	2	2	no	—
512	C₂	—	2	2	no	—
513	C₂	—	2	2	no	—
514	C₂	—	2	2	no	—
515	C₂	—	2	2	no	—
516	C₂	—	4	1	no	—
517	C₂	—	4	1	no	—
518	C₂	C₂×C₅₉×#339	1	1	yes	characteristic
519	C₂	C₅₉×#1733	1	1	yes	characteristic
520	C₂	C₂×C₅₉×#342	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅₉
Frattini, cosocle	C₂³×C₄	C₂³×C₅₉
socle	C₂²×C₅₉	C₂×#95
prime radical	C₂⁵×C₅₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂⁴×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₉×#1297	C₂	semidirect
6. C₂²×M₁₆×C₅₉	C₄	semidirect
12. C₅₉×#407	C₄	semidirect
16. C₅₉×#381	C₄	semidirect
18. C₅₉×#380	C₄	semidirect
23. C₄×C₂²⋊C₄×C₅₉	C₄	semidirect
26. C₂×#95×C₅₉	C₄	semidirect
46. C₂×M₁₆×C₅₉	C₂×C₄	semidirect
67. #95×C₅₉	C₂×C₄	semidirect
211. #8051	C₅₉	direct (N × H)
254. #1297	C₂×C₅₉	semidirect
266. C₂²×M₁₆	C₄×C₅₉	semidirect
272. #407	C₄×C₅₉	semidirect
276. #381	C₄×C₅₉	semidirect
278. #380	C₄×C₅₉	semidirect
283. C₄×C₂²⋊C₄	C₄×C₅₉	semidirect
286. C₂×#95	C₄×C₅₉	semidirect
287. C₅₉	#8051	direct (N × H)
307. C₂×M₁₆	C₂×C₄×C₅₉	semidirect
328. #95	C₂×C₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#407	2
C₅₉×#2280	2
C₂×C₄×C₂²⋊C₄×C₅₉	2
C₅₉×#1297	2
#8051	59

Subgroups — C59×#8051 #28420160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#8051 #28420160