Subgroups — C₅₉×#29131 #28441240

Order 15104.

742 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2101	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2042	C₂	1	2	yes	maximal
5	C₅₉×#1936	C₂	1	2	yes	maximal
6	C₅₉×#1935	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1802	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#1802	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₅₉	—	2	1	no	—
13	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#103×C₅₉	C₂²	1	2	yes	—
19	C₂×#103×C₅₉	C₂²	1	2	yes	—
20	C₂×#102×C₅₉	C₂²	1	2	yes	—
21	C₂×#102×C₅₉	C₂²	1	2	yes	—
22	C₂×#97×C₅₉	C₂²	1	2	yes	—
23	C₅₉×#391	C₂²	1	1	yes	characteristic
24	C₅₉×#390	C₂²	1	1	yes	characteristic
25	C₅₉×#389	—	2	1	no	—
26	C₅₉×#389	—	2	1	no	—
27	C₅₉×#389	C₂²	1	2	yes	—
28	C₅₉×#389	C₂²	1	2	yes	—
29	C₅₉×#388	—	2	1	no	—
30	C₅₉×#388	—	2	1	no	—
31	C₅₉×#384	C₂²	1	1	yes	characteristic
32	C₅₉×#384	C₂²	1	1	yes	characteristic
33	C₅₉×#382	—	2	1	no	—
34	C₅₉×#382	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
37	C₄³×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#340	C₂²	1	2	yes	—
39	C₅₉×#340	C₂²	1	2	yes	—
40	C₅₉×#340	C₂²	1	2	yes	—
41	C₅₉×#340	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₅₉	—	2	1	no	—
46	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
47	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
48	#125×C₅₉	—	4	4	no	—
49	#124×C₅₉	—	2	2	no	—
50	#124×C₅₉	—	2	2	no	—
51	C₄×Q₈×C₅₉	—	2	2	no	—
52	C₄×Q₈×C₅₉	—	2	2	no	—
53	C₄×D₄×C₅₉	—	2	2	no	—
54	C₄×D₄×C₅₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₄²×C₅₉	—	2	1	no	—
72	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₅₉	—	2	2	no	—
80	C₄⋊C₈×C₅₉	—	2	2	no	—
81	#103×C₅₉	—	2	4	no	—
82	#103×C₅₉	—	4	2	no	—
83	#102×C₅₉	—	2	4	no	—
84	#102×C₅₉	—	4	2	no	—
85	#97×C₅₉	—	4	2	no	—
86	#95×C₅₉	—	2	1	no	—
87	#95×C₅₉	—	2	1	no	—
88	#95×C₅₉	—	2	1	no	—
89	#95×C₅₉	—	2	1	no	—
90	#95×C₅₉	—	2	2	no	—
91	#95×C₅₉	—	2	2	no	—
92	C₂⁴×C₅₉	—	2	1	no	—
93	C₂×Q₈×C₅₉	—	2	1	no	—
94	C₂×Q₈×C₅₉	—	2	1	no	—
95	C₂×Q₈×C₅₉	—	2	1	no	—
96	C₂×Q₈×C₅₉	—	2	1	no	—
97	C₂×Q₈×C₅₉	—	2	1	no	—
98	C₂×Q₈×C₅₉	#41	1	2	yes	—
99	C₂×D₄×C₅₉	—	2	1	no	—
100	C₂×D₄×C₅₉	—	2	1	no	—
101	C₂×D₄×C₅₉	—	2	1	no	—
102	C₂×D₄×C₅₉	—	2	1	no	—
103	C₂×D₄×C₅₉	—	2	1	no	—
104	C₂×D₄×C₅₉	#41	1	2	yes	—
105	C₂²×C₄×C₅₉	—	2	1	no	—
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	—	2	2	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	4	2	no	—
111	C₂²×C₄×C₅₉	—	4	2	no	—
112	C₂²×C₄×C₅₉	—	4	2	no	—
113	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂×D₄	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	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₅₉	—	2	2	no	—
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	—	2	2	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	—	2	2	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₄⋊C₄×C₅₉	—	2	2	no	—
127	C₄⋊C₄×C₅₉	—	2	2	no	—
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	—	2	1	no	—
131	C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	4	2	no	—
135	C₄⋊C₄×C₅₉	—	4	2	no	—
136	C₄⋊C₄×C₅₉	—	4	4	no	—
137	C₄⋊C₄×C₅₉	—	4	4	no	—
138	C₄⋊C₄×C₅₉	—	4	2	no	—
139	C₄⋊C₄×C₅₉	—	4	2	no	—
140	C₄⋊C₄×C₅₉	—	4	2	no	—
141	C₂²⋊C₄×C₅₉	—	2	4	no	—
142	C₂²⋊C₄×C₅₉	—	2	4	no	—
143	C₂²⋊C₄×C₅₉	—	4	2	no	—
144	C₂²⋊C₄×C₅₉	—	4	2	no	—
145	C₂²⋊C₄×C₅₉	—	4	2	no	—
146	C₄²×C₅₉	—	2	2	no	—
147	C₄²×C₅₉	—	2	2	no	—
148	C₄²×C₅₉	—	2	1	no	—
149	C₄²×C₅₉	—	2	1	no	—
150	C₄²×C₅₉	—	2	1	no	—
151	C₄²×C₅₉	—	2	1	no	—
152	C₄²×C₅₉	—	4	1	no	—
153	C₄²×C₅₉	—	4	1	no	—
154	C₄²×C₅₉	—	4	2	no	—
155	C₄²×C₅₉	#41	1	2	yes	—
156	C₄²×C₅₉	#41	1	2	yes	—
157	C₂³×C₅₉	—	2	2	no	—
158	C₂³×C₅₉	—	4	1	no	—
159	C₂³×C₅₉	—	4	1	no	—
160	C₂³×C₅₉	—	4	1	no	—
161	C₂³×C₅₉	—	4	1	no	—
162	C₂³×C₅₉	—	4	1	no	—
163	C₂³×C₅₉	—	4	1	no	—
164	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₅₉	—	2	2	no	—
166	Q₈×C₅₉	—	2	2	no	—
167	Q₈×C₅₉	—	4	1	no	—
168	Q₈×C₅₉	—	4	1	no	—
169	D₄×C₅₉	—	2	2	no	—
170	D₄×C₅₉	—	2	2	no	—
171	D₄×C₅₉	—	4	1	no	—
172	D₄×C₅₉	—	4	1	no	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	2	1	no	—
175	C₂×C₄×C₅₉	—	2	1	no	—
176	C₂×C₄×C₅₉	—	2	1	no	—
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	2	1	no	—
179	C₂×C₄×C₅₉	—	2	1	no	—
180	C₂×C₄×C₅₉	—	2	1	no	—
181	C₂×C₄×C₅₉	—	2	1	no	—
182	C₂×C₄×C₅₉	—	2	1	no	—
183	C₂×C₄×C₅₉	—	2	1	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	1	no	—
186	C₂×C₄×C₅₉	—	2	1	no	—
187	C₂×C₄×C₅₉	—	2	1	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	1	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	—	4	1	no	—
192	C₂×C₄×C₅₉	—	4	1	no	—
193	C₂×C₄×C₅₉	—	4	2	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	4	2	no	—
196	C₂×C₄×C₅₉	—	4	1	no	—
197	C₂×C₄×C₅₉	—	4	1	no	—
198	C₂×C₄×C₅₉	—	4	1	no	—
199	C₂×C₄×C₅₉	—	4	1	no	—
200	C₂×C₄×C₅₉	—	4	2	no	—
201	C₂×C₄×C₅₉	—	4	2	no	—
202	C₂×C₄×C₅₉	—	8	4	no	—
203	C₂×C₄×C₅₉	#124	1	2	yes	—
204	C₂×C₄×C₅₉	#124	1	2	yes	—
205	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
206	C₂×C₄×C₅₉	#137	1	2	yes	—
207	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₅₉	—	4	2	no	—
214	C₈×C₅₉	—	4	2	no	—
215	#29131	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₅₉	—	4	2	no	—
217	C₂²×C₅₉	—	4	2	no	—
218	C₂²×C₅₉	—	4	2	no	—
219	C₂²×C₅₉	—	8	1	no	—
220	C₂²×C₅₉	—	8	1	no	—
221	C₂²×C₅₉	—	8	1	no	—
222	C₂²×C₅₉	—	8	1	no	—
223	C₂²×C₅₉	#525	1	1	yes	characteristic
224	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
225	C₂²×C₅₉	#537	1	1	yes	characteristic
226	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
228	C₂²×C₅₉	#575	1	1	yes	characteristic
229	C₂²×C₅₉	#575	1	1	yes	characteristic
230	C₄×C₅₉	—	2	2	no	—
231	C₄×C₅₉	—	4	2	no	—
232	C₄×C₅₉	—	4	1	no	—
233	C₄×C₅₉	—	4	1	no	—
234	C₄×C₅₉	—	4	1	no	—
235	C₄×C₅₉	—	4	1	no	—
236	C₄×C₅₉	—	8	2	no	—
237	C₄×C₅₉	—	8	1	no	—
238	C₄×C₅₉	—	8	1	no	—
239	C₄×C₅₉	—	8	2	no	—
240	C₄×C₅₉	#489	1	4	yes	—
241	C₄×C₅₉	#552	1	1	yes	characteristic
242	C₄×C₅₉	#552	1	1	yes	characteristic
243	C₄×C₅₉	#553	1	1	yes	characteristic
244	C₄×C₅₉	#553	1	1	yes	characteristic
245	#2859	C₂×C₅₉	1	1	yes	characteristic, complemented
246	C₄×#124	C₂×C₅₉	1	1	yes	characteristic
247	#2101	C₂×C₅₉	1	2	yes	complemented
248	#2042	C₂×C₅₉	1	2	yes	—
249	#1936	C₂×C₅₉	1	2	yes	—
250	#1935	C₂×C₅₉	1	2	yes	complemented
251	#1803	C₂×C₅₉	1	1	yes	characteristic, complemented
252	#1803	C₂×C₅₉	1	1	yes	characteristic, complemented
253	#1802	C₂×C₅₉	1	1	yes	characteristic
254	#1802	C₂×C₅₉	1	1	yes	characteristic
255	#1767	C₂×C₅₉	1	1	yes	characteristic, complemented
256	C₂×C₅₉	—	8	2	no	—
257	C₂×C₅₉	#2562	1	1	yes	characteristic
258	C₂×C₅₉	#3115	1	1	yes	characteristic
259	C₂×C₅₉	#3116	1	1	yes	characteristic
260	C₂×C₅₉	C₂×#489	1	1	yes	characteristic
261	C₂×C₅₉	#3142	1	1	yes	characteristic
262	C₂×C₅₉	#3251	1	1	yes	characteristic
263	C₂×C₅₉	#3252	1	1	yes	characteristic
264	C₂×#125	—	2	1	no	—
265	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
266	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
270	C₂×#103	C₂²×C₅₉	1	2	yes	—
271	C₂×#103	C₂²×C₅₉	1	2	yes	—
272	C₂×#102	C₂²×C₅₉	1	2	yes	—
273	C₂×#102	C₂²×C₅₉	1	2	yes	—
274	C₂×#97	C₂²×C₅₉	1	2	yes	—
275	#391	C₂²×C₅₉	1	1	yes	characteristic
276	#390	C₂²×C₅₉	1	1	yes	characteristic
277	#389	—	2	1	no	—
278	#389	—	2	1	no	—
279	#389	C₂²×C₅₉	1	2	yes	—
280	#389	C₂²×C₅₉	1	2	yes	—
281	#388	—	2	1	no	—
282	#388	—	2	1	no	—
283	#384	C₂²×C₅₉	1	1	yes	characteristic
284	#384	C₂²×C₅₉	1	1	yes	characteristic
285	#382	—	2	1	no	—
286	#382	C₂²×C₅₉	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	—	2	1	no	—
288	C₄×C₂²⋊C₄	—	2	1	no	—
289	C₄³	C₂²×C₅₉	1	1	yes	characteristic
290	#340	C₂²×C₅₉	1	2	yes	—
291	#340	C₂²×C₅₉	1	2	yes	—
292	#340	C₂²×C₅₉	1	2	yes	—
293	#340	C₂²×C₅₉	1	2	yes	—
294	#336	C₂²×C₅₉	1	2	yes	—
295	C₅₉	#29131	1	1	yes	characteristic, direct product factor, Sylow
296	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
297	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
300	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
301	#125	—	4	4	no	—
302	#124	—	2	2	no	—
303	#124	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
326	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
327	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	—	2	2	no	—
334	#103	—	2	4	no	—
335	#103	—	4	2	no	—
336	#102	—	2	4	no	—
337	#102	—	4	2	no	—
338	#97	—	4	2	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	#41×C₅₉	1	2	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	#41×C₅₉	1	2	yes	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	1	no	—
406	C₄²	—	4	1	no	—
407	C₄²	—	4	2	no	—
408	C₄²	#41×C₅₉	1	2	yes	—
409	C₄²	#41×C₅₉	1	2	yes	—
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	C₂²×D₄×C₅₉	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	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	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	#124×C₅₉	1	2	yes	—
457	C₂×C₄	#124×C₅₉	1	2	yes	—
458	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
459	C₂×C₄	#137×C₅₉	1	2	yes	—
460	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
464	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
465	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₅₉×#525	1	1	yes	characteristic
476	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
477	C₂²	C₅₉×#537	1	1	yes	characteristic
478	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
479	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
480	C₂²	C₅₉×#575	1	1	yes	characteristic
481	C₂²	C₅₉×#575	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	C₅₉×#489	1	4	yes	—
493	C₄	C₅₉×#552	1	1	yes	characteristic
494	C₄	C₅₉×#552	1	1	yes	characteristic
495	C₄	C₅₉×#553	1	1	yes	characteristic
496	C₄	C₅₉×#553	1	1	yes	characteristic
497	C₂	—	8	2	no	—
498	C₂	C₅₉×#2562	1	1	yes	characteristic
499	C₂	C₅₉×#3115	1	1	yes	characteristic
500	C₂	C₅₉×#3116	1	1	yes	characteristic
501	C₂	C₂×C₅₉×#489	1	1	yes	characteristic
502	C₂	C₅₉×#3142	1	1	yes	characteristic
503	C₂	C₅₉×#3251	1	1	yes	characteristic
504	C₂	C₅₉×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×D₄×C₅₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2859	C₂	semidirect
3. C₅₉×#2101	C₂	semidirect
6. C₅₉×#1935	C₂	semidirect
7. C₅₉×#1803	C₂	semidirect
8. C₅₉×#1803	C₂	semidirect
11. C₅₉×#1767	C₂	semidirect
215. #29131	C₅₉	direct (N × H)
245. #2859	C₂×C₅₉	semidirect
247. #2101	C₂×C₅₉	semidirect
250. #1935	C₂×C₅₉	semidirect
251. #1803	C₂×C₅₉	semidirect
252. #1803	C₂×C₅₉	semidirect
255. #1767	C₂×C₅₉	semidirect
295. C₅₉	#29131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2859	2
C₄×#124×C₅₉	2
C₅₉×#2101	2
C₅₉×#2042	2
C₅₉×#1936	2
C₅₉×#1935	2
C₅₉×#1803	2
C₅₉×#1802	2
C₅₉×#1767	2
#29131	59

Subgroups — C59×#29131 #28441240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#29131 #28441240