Subgroups — C₅₉×#21555 #28433664

Order 15104.

938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#472	C₂	1	1	yes	maximal, characteristic
2	C₄×AGL(1,ℤ/8)×C₅₉	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2875	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1978	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1931	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1907	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1815	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#100×C₅₉	C₂	1	2	yes	maximal, complemented
12	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
16	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
18	C₅₉×#472	C₄	1	8	yes	complemented
19	C₅₉×#442	—	2	2	no	—
20	C₅₉×#442	—	2	1	no	—
21	C₅₉×#442	—	2	1	no	—
22	C₅₉×#442	—	2	1	no	—
23	C₅₉×#442	—	2	1	no	—
24	C₅₉×#440	—	2	2	no	—
25	C₄×SD₁₆×C₅₉	—	2	2	no	—
26	C₄×D₈×C₅₉	—	2	2	no	—
27	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
29	C₅₉×#428	C₂²	1	2	yes	—
30	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#418	C₂²	1	2	yes	—
32	C₅₉×#417	C₂²	1	2	yes	—
33	C₂×#102×C₅₉	C₂²	1	2	yes	—
34	C₂×#100×C₅₉	C₂²	1	2	yes	—
35	C₂×#100×C₅₉	C₂²	1	2	yes	—
36	C₅₉×#405	—	2	1	no	—
37	C₅₉×#405	—	2	1	no	—
38	C₅₉×#405	C₂²	1	1	yes	characteristic
39	C₅₉×#405	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₅₉	—	2	1	no	—
41	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
43	C₂×#97×C₅₉	—	2	1	no	—
44	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#343	C₂²	1	2	yes	—
46	C₅₉×#343	C₂²	1	2	yes	—
47	C₅₉×#341	C₂²	1	2	yes	—
48	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₅₉	—	2	2	no	—
51	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
52	AGL(1,ℤ/8)×C₅₉	C₂×C₄	1	8	yes	complemented
53	C₂×SD₁₆×C₅₉	—	2	2	no	—
54	C₂×D₈×C₅₉	—	2	2	no	—
55	C₂×D₈×C₅₉	—	2	1	no	—
56	C₂×D₈×C₅₉	—	2	1	no	—
57	C₂×D₈×C₅₉	—	2	2	no	—
58	C₂×D₈×C₅₉	C₂×C₄	1	4	yes	complemented
59	#131×C₅₉	—	2	2	no	—
60	#131×C₅₉	—	2	2	no	—
61	#131×C₅₉	—	2	2	no	—
62	#131×C₅₉	C₂×C₄	1	4	yes	complemented
63	C₂×M₁₆×C₅₉	—	2	1	no	—
64	C₂×M₁₆×C₅₉	—	2	1	no	—
65	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
66	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
67	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	—	2	1	no	—
70	C₂²×C₈×C₅₉	—	2	1	no	—
71	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
73	C₄×Q₈×C₅₉	D₄	1	2	yes	—
74	C₄×D₄×C₅₉	—	2	2	no	—
75	C₄×D₄×C₅₉	—	2	2	no	—
76	C₄×D₄×C₅₉	—	2	2	no	—
77	C₄×D₄×C₅₉	—	2	2	no	—
78	C₄×D₄×C₅₉	—	2	2	no	—
79	C₄×D₄×C₅₉	D₄	1	2	yes	—
80	#117×C₅₉	—	2	1	no	—
81	#117×C₅₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
84	C₂×C₄²×C₅₉	—	2	1	no	—
85	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
86	#108×C₅₉	—	2	2	no	—
87	#108×C₅₉	C₂×C₄	1	4	yes	complemented
88	#107×C₅₉	—	2	2	no	—
89	#106×C₅₉	—	2	1	no	—
90	#106×C₅₉	—	2	1	no	—
91	#106×C₅₉	—	2	2	no	—
92	#103×C₅₉	—	2	2	no	—
93	#102×C₅₉	—	2	2	no	—
94	#102×C₅₉	—	2	2	no	—
95	#102×C₅₉	—	2	2	no	—
96	#102×C₅₉	—	2	2	no	—
97	#102×C₅₉	—	2	2	no	—
98	#100×C₅₉	—	2	4	no	—
99	#100×C₅₉	C₂×C₄	1	8	yes	complemented
100	#97×C₅₉	—	2	1	no	—
101	#97×C₅₉	—	2	1	no	—
102	#97×C₅₉	—	2	1	no	—
103	#97×C₅₉	—	2	2	no	—
104	#97×C₅₉	D₄	1	1	yes	characteristic
105	#97×C₅₉	D₄	1	1	yes	characteristic
106	#97×C₅₉	D₄	1	1	yes	characteristic
107	#97×C₅₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₅₉	—	2	1	no	—
109	C₄×C₈×C₅₉	—	2	1	no	—
110	C₄×C₈×C₅₉	—	2	1	no	—
111	C₄×C₈×C₅₉	—	2	2	no	—
112	C₂⁴×C₅₉	—	2	2	no	—
113	#41×C₅₉	—	2	1	no	—
114	#41×C₅₉	—	2	1	no	—
115	#41×C₅₉	C₂²×C₄	1	2	yes	—
116	#41×C₅₉	#41	1	2	yes	—
117	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₅₉	—	2	1	no	—
119	C₂×D₄×C₅₉	—	2	2	no	—
120	C₂×D₄×C₅₉	—	2	2	no	—
121	C₂×D₄×C₅₉	—	2	2	no	—
122	C₂×D₄×C₅₉	—	2	2	no	—
123	C₂×D₄×C₅₉	—	2	2	no	—
124	C₂×D₄×C₅₉	C₂²×C₄	1	4	yes	—
125	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	—	2	1	no	—
127	C₂²×C₄×C₅₉	—	2	2	no	—
128	C₂²×C₄×C₅₉	—	2	2	no	—
129	C₂²×C₄×C₅₉	—	4	2	no	—
130	C₂²×C₄×C₅₉	—	4	2	no	—
131	C₂²×C₄×C₅₉	—	8	4	no	—
132	C₂²×C₄×C₅₉	#41	1	2	yes	—
133	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
134	SD₁₆×C₅₉	—	2	8	no	—
135	D₈×C₅₉	—	2	8	no	—
136	D₈×C₅₉	—	2	4	no	—
137	D₈×C₅₉	—	2	4	no	—
138	M₁₆×C₅₉	—	2	4	no	—
139	M₁₆×C₅₉	—	2	1	no	—
140	M₁₆×C₅₉	—	2	1	no	—
141	M₁₆×C₅₉	—	2	2	no	—
142	M₁₆×C₅₉	—	2	4	no	—
143	M₁₆×C₅₉	—	2	2	no	—
144	M₁₆×C₅₉	—	2	2	no	—
145	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
146	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
147	M₁₆×C₅₉	#41	1	2	yes	—
148	C₂×C₈×C₅₉	—	2	4	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	1	no	—
154	C₂×C₈×C₅₉	—	2	4	no	—
155	C₂×C₈×C₅₉	—	2	2	no	—
156	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₅₉	#41	1	2	yes	—
162	C₄⋊C₄×C₅₉	—	2	2	no	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	2	no	—
165	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₅₉	—	2	1	no	—
167	C₂²⋊C₄×C₅₉	—	2	2	no	—
168	C₂²⋊C₄×C₅₉	—	4	2	no	—
169	C₂²⋊C₄×C₅₉	—	4	2	no	—
170	C₄²×C₅₉	—	2	2	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	C₂×D₄	1	2	yes	—
173	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₅₉	—	2	1	no	—
176	C₂³×C₅₉	—	2	4	no	—
177	C₂³×C₅₉	—	4	2	no	—
178	C₂³×C₅₉	—	4	2	no	—
179	C₂³×C₅₉	—	8	2	no	—
180	C₂³×C₅₉	—	8	2	no	—
181	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
182	Q₈×C₅₉	—	2	1	no	—
183	Q₈×C₅₉	C₄×D₄	1	2	yes	—
184	D₄×C₅₉	—	2	2	no	—
185	D₄×C₅₉	—	2	2	no	—
186	D₄×C₅₉	—	2	4	no	—
187	D₄×C₅₉	—	2	4	no	—
188	D₄×C₅₉	—	2	1	no	—
189	D₄×C₅₉	—	4	2	no	—
190	D₄×C₅₉	—	4	2	no	—
191	D₄×C₅₉	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₅₉	—	2	1	no	—
193	C₂×C₄×C₅₉	—	2	2	no	—
194	C₂×C₄×C₅₉	—	2	2	no	—
195	C₂×C₄×C₅₉	—	2	2	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	—	4	2	no	—
198	C₂×C₄×C₅₉	—	8	2	no	—
199	C₂×C₄×C₅₉	—	8	4	no	—
200	C₂×C₄×C₅₉	—	8	4	no	—
201	C₂×C₄×C₅₉	—	8	2	no	—
202	C₂×C₄×C₅₉	#121	1	2	yes	—
203	C₂×C₄×C₅₉	#121	1	2	yes	—
204	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
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	C₈×C₅₉	—	2	2	no	—
211	C₈×C₅₉	—	2	4	no	—
212	C₈×C₅₉	—	2	1	no	—
213	C₈×C₅₉	—	2	2	no	—
214	C₈×C₅₉	—	2	1	no	—
215	C₈×C₅₉	—	4	2	no	—
216	C₈×C₅₉	C₄×D₄	1	2	yes	—
217	C₈×C₅₉	C₄×D₄	1	2	yes	—
218	#21555	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₅₉	—	2	2	no	—
220	C₂²×C₅₉	—	2	2	no	—
221	C₂²×C₅₉	—	4	2	no	—
222	C₂²×C₅₉	—	4	4	no	—
223	C₂²×C₅₉	—	8	4	no	—
224	C₂²×C₅₉	—	8	4	no	—
225	C₂²×C₅₉	—	8	2	no	—
226	C₂²×C₅₉	—	8	2	no	—
227	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
228	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
229	C₂²×C₅₉	#529	1	1	yes	characteristic
230	C₄×C₅₉	—	2	2	no	—
231	C₄×C₅₉	—	2	2	no	—
232	C₄×C₅₉	—	2	2	no	—
233	C₄×C₅₉	—	4	2	no	—
234	C₄×C₅₉	—	8	2	no	—
235	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
237	C₄×C₅₉	#525	1	1	yes	characteristic
238	C₄×C₅₉	#532	1	1	yes	characteristic
239	C₂×#472	C₂×C₅₉	1	1	yes	characteristic
240	C₄×AGL(1,ℤ/8)	C₂×C₅₉	1	2	yes	complemented
241	C₂×#442	C₂×C₅₉	1	1	yes	characteristic, complemented
242	#2875	C₂×C₅₉	1	1	yes	characteristic, complemented
243	#1978	C₂×C₅₉	1	1	yes	characteristic, complemented
244	#1951	C₂×C₅₉	1	1	yes	characteristic, complemented
245	#1931	C₂×C₅₉	1	2	yes	complemented
246	#1907	C₂×C₅₉	1	2	yes	complemented
247	#1815	C₂×C₅₉	1	1	yes	characteristic, complemented
248	#1778	C₂×C₅₉	1	1	yes	characteristic, complemented
249	C₄×#100	C₂×C₅₉	1	2	yes	complemented
250	C₂×C₅₉	—	2	1	no	—
251	C₂×C₅₉	—	2	1	no	—
252	C₂×C₅₉	—	4	2	no	—
253	C₂×C₅₉	—	8	4	no	—
254	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
255	C₂×C₅₉	#3068	1	2	yes	—
256	C₂×AGL(1,ℤ/8)	C₂²×C₅₉	1	2	yes	—
257	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
258	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
259	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
260	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
262	#472	C₄×C₅₉	1	8	yes	complemented
263	#442	—	2	2	no	—
264	#442	—	2	1	no	—
265	#442	—	2	1	no	—
266	#442	—	2	1	no	—
267	#442	—	2	1	no	—
268	#440	—	2	2	no	—
269	C₄×SD₁₆	—	2	2	no	—
270	C₄×D₈	—	2	2	no	—
271	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
272	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
273	#428	C₂²×C₅₉	1	2	yes	—
274	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
275	#418	C₂²×C₅₉	1	2	yes	—
276	#417	C₂²×C₅₉	1	2	yes	—
277	C₂×#102	C₂²×C₅₉	1	2	yes	—
278	C₂×#100	C₂²×C₅₉	1	2	yes	—
279	C₂×#100	C₂²×C₅₉	1	2	yes	—
280	#405	—	2	1	no	—
281	#405	—	2	1	no	—
282	#405	C₂²×C₅₉	1	1	yes	characteristic
283	#405	C₂²×C₅₉	1	1	yes	characteristic
284	C₄×M₁₆	—	2	1	no	—
285	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
286	C₄×M₁₆	C₂²×C₅₉	1	2	yes	—
287	C₂×#97	—	2	1	no	—
288	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
289	#343	C₂²×C₅₉	1	2	yes	—
290	#343	C₂²×C₅₉	1	2	yes	—
291	#341	C₂²×C₅₉	1	2	yes	—
292	C₅₉	#21555	1	1	yes	characteristic, direct product factor, Sylow
293	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
294	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	AGL(1,ℤ/8)	—	2	4	no	—
297	AGL(1,ℤ/8)	C₂×C₄×C₅₉	1	8	yes	complemented
298	C₂×SD₁₆	—	2	2	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	—	2	1	no	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	C₂×C₄×C₅₉	1	4	yes	complemented
304	#131	—	2	2	no	—
305	#131	—	2	2	no	—
306	#131	—	2	2	no	—
307	#131	C₂×C₄×C₅₉	1	4	yes	complemented
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
311	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
312	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
313	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
318	C₄×Q₈	D₄×C₅₉	1	2	yes	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	D₄×C₅₉	1	2	yes	—
325	#117	—	2	1	no	—
326	#117	C₂³×C₅₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
331	#108	—	2	2	no	—
332	#108	C₂×C₄×C₅₉	1	4	yes	complemented
333	#107	—	2	2	no	—
334	#106	—	2	1	no	—
335	#106	—	2	1	no	—
336	#106	—	2	2	no	—
337	#103	—	2	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	2	2	no	—
343	#100	—	2	4	no	—
344	#100	C₂×C₄×C₅₉	1	8	yes	complemented
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	#97	—	2	1	no	—
348	#97	—	2	2	no	—
349	#97	D₄×C₅₉	1	1	yes	characteristic
350	#97	D₄×C₅₉	1	1	yes	characteristic
351	#97	D₄×C₅₉	1	1	yes	characteristic
352	#97	D₄×C₅₉	1	1	yes	characteristic
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	C₂²×C₄×C₅₉	1	2	yes	—
361	#41	#41×C₅₉	1	2	yes	—
362	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₂²×C₄×C₅₉	1	4	yes	—
370	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	8	4	no	—
377	C₂²×C₄	#41×C₅₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
379	SD₁₆	—	2	8	no	—
380	D₈	—	2	8	no	—
381	D₈	—	2	4	no	—
382	D₈	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	4	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	C₂²×C₄×C₅₉	1	2	yes	—
391	M₁₆	C₂²×C₄×C₅₉	1	4	yes	—
392	M₁₆	#41×C₅₉	1	2	yes	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
403	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
404	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
405	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
406	C₂×C₈	#41×C₅₉	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	1	no	—
417	C₄²	C₂×D₄×C₅₉	1	2	yes	—
418	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
420	C₂³	—	2	1	no	—
421	C₂³	—	2	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	8	2	no	—
426	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	C₄×D₄×C₅₉	1	2	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	4	no	—
432	D₄	—	2	4	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	C₄×D₄×C₅₉	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	8	2	no	—
444	C₂×C₄	—	8	4	no	—
445	C₂×C₄	—	8	4	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	#121×C₅₉	1	2	yes	—
448	C₂×C₄	#121×C₅₉	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	4	no	—
457	C₈	—	2	1	no	—
458	C₈	—	2	2	no	—
459	C₈	—	2	1	no	—
460	C₈	—	4	2	no	—
461	C₈	C₄×D₄×C₅₉	1	2	yes	—
462	C₈	C₄×D₄×C₅₉	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	—	8	4	no	—
469	C₂²	—	8	2	no	—
470	C₂²	—	8	2	no	—
471	C₂²	C₄×#41×C₅₉	1	1	yes	characteristic
472	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
473	C₂²	C₅₉×#529	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	2	no	—
479	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
480	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
481	C₄	C₅₉×#525	1	1	yes	characteristic
482	C₄	C₅₉×#532	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	—	8	4	no	—
487	C₂	C₄×#121×C₅₉	1	1	yes	characteristic
488	C₂	C₅₉×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×C₅₉×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×AGL(1,ℤ/8)×C₅₉	C₂	semidirect
3. C₂×C₅₉×#442	C₂	semidirect
4. C₅₉×#2875	C₂	semidirect
5. C₅₉×#1978	C₂	semidirect
6. C₅₉×#1951	C₂	semidirect
7. C₅₉×#1931	C₂	semidirect
8. C₅₉×#1907	C₂	semidirect
9. C₅₉×#1815	C₂	semidirect
10. C₅₉×#1778	C₂	semidirect
11. C₄×#100×C₅₉	C₂	semidirect
18. C₅₉×#472	C₄	semidirect
52. AGL(1,ℤ/8)×C₅₉	C₂×C₄	semidirect
58. C₂×D₈×C₅₉	C₂×C₄	semidirect
62. #131×C₅₉	C₂×C₄	semidirect
87. #108×C₅₉	C₂×C₄	semidirect
99. #100×C₅₉	C₂×C₄	semidirect
218. #21555	C₅₉	direct (N × H)
240. C₄×AGL(1,ℤ/8)	C₂×C₅₉	semidirect
241. C₂×#442	C₂×C₅₉	semidirect
242. #2875	C₂×C₅₉	semidirect
243. #1978	C₂×C₅₉	semidirect
244. #1951	C₂×C₅₉	semidirect
245. #1931	C₂×C₅₉	semidirect
246. #1907	C₂×C₅₉	semidirect
247. #1815	C₂×C₅₉	semidirect
248. #1778	C₂×C₅₉	semidirect
249. C₄×#100	C₂×C₅₉	semidirect
262. #472	C₄×C₅₉	semidirect
292. C₅₉	#21555	direct (N × H)
297. AGL(1,ℤ/8)	C₂×C₄×C₅₉	semidirect
303. C₂×D₈	C₂×C₄×C₅₉	semidirect
307. #131	C₂×C₄×C₅₉	semidirect
332. #108	C₂×C₄×C₅₉	semidirect
344. #100	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×#472	2
C₄×AGL(1,ℤ/8)×C₅₉	2
C₂×C₅₉×#442	2
C₅₉×#2875	2
C₅₉×#1978	2
C₅₉×#1951	2
C₅₉×#1931	2
C₅₉×#1907	2
C₅₉×#1815	2
C₅₉×#1778	2
C₄×#100×C₅₉	2
#21555	59

Subgroups — C59×#21555 #28433664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21555 #28433664