Subgroups — C₅₉×#8057 #28420166

Order 15104.

906 conjugacy classes of subgroups.

The subgroup lattice has 494 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	C₂×C₅₉×#407	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂²⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1298	C₂	1	4	yes	maximal, complemented
5	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₅₉	—	2	1	no	—
7	C₂²×M₁₆×C₅₉	C₄	1	2	yes	—
8	C₂³×C₈×C₅₉	—	2	1	no	—
9	C₅₉×#407	—	2	1	no	—
10	C₅₉×#407	—	2	1	no	—
11	C₅₉×#407	—	2	1	no	—
12	C₅₉×#407	—	2	1	no	—
13	C₅₉×#407	C₄	1	2	yes	—
14	C₅₉×#407	C₄	1	2	yes	—
15	C₅₉×#407	C₄	1	2	yes	—
16	C₅₉×#407	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
18	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
19	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
20	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
21	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
22	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₅₉	C₄	1	2	yes	—
24	C₂×C₂²⋊C₈×C₅₉	C₄	1	2	yes	—
25	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
27	C₂⁵×C₅₉	Q₈	1	1	yes	characteristic
28	C₂³×C₄×C₅₉	—	4	4	no	—
29	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
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	D₄	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	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₅₉	—	2	2	no	—
44	C₂×M₁₆×C₅₉	—	2	2	no	—
45	C₂×M₁₆×C₅₉	—	2	2	no	—
46	C₂×M₁₆×C₅₉	—	4	4	no	—
47	C₂×M₁₆×C₅₉	—	4	4	no	—
48	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₅₉	—	2	2	no	—
50	C₂²×C₈×C₅₉	—	2	2	no	—
51	C₂²×C₈×C₅₉	—	2	2	no	—
52	C₂²×C₈×C₅₉	—	2	2	no	—
53	C₂²×C₈×C₅₉	—	2	2	no	—
54	C₂²×C₈×C₅₉	—	4	4	no	—
55	C₂²⋊C₈×C₅₉	—	2	2	no	—
56	C₂²⋊C₈×C₅₉	—	2	2	no	—
57	C₂²⋊C₈×C₅₉	—	2	2	no	—
58	C₂²⋊C₈×C₅₉	—	2	2	no	—
59	C₂²⋊C₈×C₅₉	—	2	2	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	C₂²⋊C₈×C₅₉	—	2	2	no	—
65	C₂²⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
66	C₂²⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
67	C₂⁴×C₅₉	—	2	4	no	—
68	C₂⁴×C₅₉	—	4	2	no	—
69	C₂⁴×C₅₉	—	4	2	no	—
70	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
71	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
72	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
73	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
74	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
75	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₅₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	—	2	4	no	—
78	C₂²×C₄×C₅₉	—	2	4	no	—
79	C₂²×C₄×C₅₉	—	2	4	no	—
80	C₂²×C₄×C₅₉	—	4	2	no	—
81	C₂²×C₄×C₅₉	—	4	2	no	—
82	C₂²×C₄×C₅₉	—	4	2	no	—
83	C₂²×C₄×C₅₉	—	4	2	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	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	M₁₆×C₅₉	—	4	4	no	—
120	M₁₆×C₅₉	—	4	4	no	—
121	M₁₆×C₅₉	—	4	4	no	—
122	M₁₆×C₅₉	—	4	4	no	—
123	C₂×C₈×C₅₉	—	2	4	no	—
124	C₂×C₈×C₅₉	—	2	4	no	—
125	C₂×C₈×C₅₉	—	2	4	no	—
126	C₂×C₈×C₅₉	—	4	4	no	—
127	C₂×C₈×C₅₉	—	4	4	no	—
128	C₂×C₈×C₅₉	—	4	4	no	—
129	C₂×C₈×C₅₉	—	4	4	no	—
130	C₂×C₈×C₅₉	—	4	4	no	—
131	C₂³×C₅₉	—	2	2	no	—
132	C₂³×C₅₉	—	2	2	no	—
133	C₂³×C₅₉	—	2	2	no	—
134	C₂³×C₅₉	—	2	2	no	—
135	C₂³×C₅₉	—	2	2	no	—
136	C₂³×C₅₉	—	2	2	no	—
137	C₂³×C₅₉	—	2	2	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	—	4	1	no	—
144	C₂³×C₅₉	—	4	1	no	—
145	C₂³×C₅₉	—	4	1	no	—
146	C₂³×C₅₉	—	4	1	no	—
147	C₂³×C₅₉	—	4	1	no	—
148	C₂³×C₅₉	—	4	1	no	—
149	C₂³×C₅₉	—	4	1	no	—
150	C₂³×C₅₉	—	4	1	no	—
151	C₂³×C₅₉	—	4	16	no	—
152	C₂³×C₅₉	#95	1	1	yes	characteristic
153	C₂³×C₅₉	#95	1	1	yes	characteristic
154	C₂³×C₅₉	#95	1	1	yes	characteristic
155	C₂³×C₅₉	#95	1	1	yes	characteristic
156	C₂³×C₅₉	#108	1	4	yes	—
157	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	—	2	2	no	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	2	no	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	—	2	2	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	2	2	no	—
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	—	4	1	no	—
176	C₂×C₄×C₅₉	—	4	1	no	—
177	C₂×C₄×C₅₉	—	4	1	no	—
178	C₂×C₄×C₅₉	—	4	1	no	—
179	C₂×C₄×C₅₉	—	4	1	no	—
180	C₂×C₄×C₅₉	—	4	1	no	—
181	C₂×C₄×C₅₉	—	4	1	no	—
182	C₂×C₄×C₅₉	—	4	1	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	#95	1	1	yes	characteristic
188	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
189	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
190	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
191	C₂×C₄×C₅₉	#99	1	4	yes	—
192	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₈×C₅₉	—	4	4	no	—
197	C₈×C₅₉	—	4	4	no	—
198	C₈×C₅₉	—	4	4	no	—
199	#8057	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₅₉	—	2	8	no	—
201	C₂²×C₅₉	—	2	1	no	—
202	C₂²×C₅₉	—	2	1	no	—
203	C₂²×C₅₉	—	2	1	no	—
204	C₂²×C₅₉	—	2	1	no	—
205	C₂²×C₅₉	—	2	1	no	—
206	C₂²×C₅₉	—	2	1	no	—
207	C₂²×C₅₉	—	2	1	no	—
208	C₂²×C₅₉	—	2	1	no	—
209	C₂²×C₅₉	—	2	1	no	—
210	C₂²×C₅₉	—	2	1	no	—
211	C₂²×C₅₉	—	2	1	no	—
212	C₂²×C₅₉	—	2	1	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	—	4	4	no	—
218	C₂²×C₅₉	—	4	4	no	—
219	C₂²×C₅₉	—	4	4	no	—
220	C₂²×C₅₉	—	4	4	no	—
221	C₂²×C₅₉	—	4	4	no	—
222	C₂²×C₅₉	—	4	4	no	—
223	C₂²×C₅₉	#341	1	2	yes	—
224	C₂²×C₅₉	#341	1	2	yes	—
225	C₂²×C₅₉	#342	1	2	yes	—
226	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
227	C₂²×C₅₉	C₂×#108	1	2	yes	—
228	C₂²×C₅₉	#430	1	2	yes	—
229	C₄×C₅₉	—	2	1	no	—
230	C₄×C₅₉	—	2	1	no	—
231	C₄×C₅₉	—	2	1	no	—
232	C₄×C₅₉	—	2	1	no	—
233	C₄×C₅₉	—	2	1	no	—
234	C₄×C₅₉	—	2	1	no	—
235	C₄×C₅₉	#342	1	2	yes	—
236	C₄×C₅₉	C₂×#99	1	2	yes	—
237	C₂×#407	C₂×C₅₉	1	1	yes	characteristic
238	C₂×#407	C₂×C₅₉	1	1	yes	characteristic
239	C₂²×C₂²⋊C₈	C₂×C₅₉	1	1	yes	characteristic
240	#1298	C₂×C₅₉	1	4	yes	complemented
241	C₂×C₅₉	—	2	2	no	—
242	C₂×C₅₉	—	2	2	no	—
243	C₂×C₅₉	—	2	2	no	—
244	C₂×C₅₉	—	2	2	no	—
245	C₂×C₅₉	—	2	2	no	—
246	C₂×C₅₉	—	4	1	no	—
247	C₂×C₅₉	—	4	1	no	—
248	C₂×C₅₉	C₂×#341	1	1	yes	characteristic
249	C₂×C₅₉	#1738	1	1	yes	characteristic
250	C₂×C₅₉	C₂×#342	1	1	yes	characteristic
251	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
252	C₂²×M₁₆	—	2	1	no	—
253	C₂²×M₁₆	C₄×C₅₉	1	2	yes	—
254	C₂³×C₈	—	2	1	no	—
255	#407	—	2	1	no	—
256	#407	—	2	1	no	—
257	#407	—	2	1	no	—
258	#407	—	2	1	no	—
259	#407	C₄×C₅₉	1	2	yes	—
260	#407	C₄×C₅₉	1	2	yes	—
261	#407	C₄×C₅₉	1	2	yes	—
262	#407	C₂²×C₅₉	1	2	yes	—
263	C₂×C₂²⋊C₈	—	2	1	no	—
264	C₂×C₂²⋊C₈	—	2	1	no	—
265	C₂×C₂²⋊C₈	—	2	1	no	—
266	C₂×C₂²⋊C₈	—	2	1	no	—
267	C₂×C₂²⋊C₈	—	2	1	no	—
268	C₂×C₂²⋊C₈	—	2	1	no	—
269	C₂×C₂²⋊C₈	C₄×C₅₉	1	2	yes	—
270	C₂×C₂²⋊C₈	C₄×C₅₉	1	2	yes	—
271	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
273	C₅₉	#8057	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁵	Q₈×C₅₉	1	1	yes	characteristic
275	C₂³×C₄	—	4	4	no	—
276	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
278	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
279	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
280	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
281	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
282	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
283	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
284	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
286	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
288	C₂³×C₄	Q₈×C₅₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	4	4	no	—
294	C₂×M₁₆	—	4	4	no	—
295	C₂×M₁₆	C₂×C₄×C₅₉	1	4	yes	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	4	4	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	2	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	C₂×C₄×C₅₉	1	4	yes	—
313	C₂²⋊C₈	C₂×C₄×C₅₉	1	4	yes	—
314	C₂⁴	—	2	4	no	—
315	C₂⁴	—	4	2	no	—
316	C₂⁴	—	4	2	no	—
317	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
318	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
319	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
320	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
321	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
322	C₂⁴	C₄⋊C₄×C₅₉	1	1	yes	characteristic
323	C₂⁴	C₂×Q₈×C₅₉	1	1	yes	characteristic
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
339	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
340	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
341	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
342	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
343	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
344	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
345	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
347	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
348	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
349	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
350	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
352	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
354	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
355	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
356	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
357	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
358	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
359	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
362	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
366	M₁₆	—	4	4	no	—
367	M₁₆	—	4	4	no	—
368	M₁₆	—	4	4	no	—
369	M₁₆	—	4	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	4	4	no	—
374	C₂×C₈	—	4	4	no	—
375	C₂×C₈	—	4	4	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	—	4	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	16	no	—
399	C₂³	#95×C₅₉	1	1	yes	characteristic
400	C₂³	#95×C₅₉	1	1	yes	characteristic
401	C₂³	#95×C₅₉	1	1	yes	characteristic
402	C₂³	#95×C₅₉	1	1	yes	characteristic
403	C₂³	#108×C₅₉	1	4	yes	—
404	C₂³	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
405	C₂³	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
406	C₂³	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
435	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
436	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
437	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
438	C₂×C₄	#99×C₅₉	1	4	yes	—
439	C₂×C₄	C₂×C₄²×C₅₉	1	1	yes	characteristic
440	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
441	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
442	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
443	C₈	—	4	4	no	—
444	C₈	—	4	4	no	—
445	C₈	—	4	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	C₅₉×#341	1	2	yes	—
470	C₂²	C₅₉×#341	1	2	yes	—
471	C₂²	C₅₉×#342	1	2	yes	—
472	C₂²	C₂×#95×C₅₉	1	1	yes	characteristic
473	C₂²	C₂×#108×C₅₉	1	2	yes	—
474	C₂²	C₅₉×#430	1	2	yes	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	C₅₉×#342	1	2	yes	—
482	C₄	C₂×#99×C₅₉	1	2	yes	—
483	C₂	—	2	2	no	—
484	C₂	—	2	2	no	—
485	C₂	—	2	2	no	—
486	C₂	—	2	2	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	4	1	no	—
490	C₂	C₂×C₅₉×#341	1	1	yes	characteristic
491	C₂	C₅₉×#1738	1	1	yes	characteristic
492	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	Q₈
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×#1298	C₂	semidirect
199. #8057	C₅₉	direct (N × H)
240. #1298	C₂×C₅₉	semidirect
273. C₅₉	#8057	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×#407	2
C₂²×C₂²⋊C₈×C₅₉	2
C₅₉×#1298	2
#8057	59

Subgroups — C59×#8057 #28420166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#8057 #28420166