Subgroups — C₅₉×#22587 #28434696

Order 15104.

906 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#416	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2880	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1937	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1929	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1866	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1826	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1789	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#1764	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₅₉	C₂²	1	2	yes	—
14	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#433	—	2	2	no	—
17	C₅₉×#432	—	2	1	no	—
18	C₅₉×#431	—	2	1	no	—
19	C₂×#108×C₅₉	C₂²	1	2	yes	complemented
20	C₅₉×#424	C₂²	1	2	yes	complemented
21	C₂×#104×C₅₉	C₂²	1	2	yes	—
22	C₂×#104×C₅₉	C₂²	1	2	yes	—
23	C₅₉×#416	C₄	1	1	yes	characteristic, complemented
24	C₅₉×#416	C₄	1	1	yes	characteristic, complemented
25	C₅₉×#416	C₄	1	1	yes	characteristic, complemented
26	C₅₉×#416	C₄	1	1	yes	characteristic, complemented
27	C₅₉×#416	C₂²	1	1	yes	characteristic
28	C₅₉×#416	C₂²	1	1	yes	characteristic
29	C₅₉×#416	C₂²	1	1	yes	characteristic
30	C₅₉×#416	C₂²	1	1	yes	characteristic
31	C₂×#103×C₅₉	C₄	1	1	yes	characteristic, complemented
32	C₂×#103×C₅₉	C₄	1	1	yes	characteristic, complemented
33	C₂×#102×C₅₉	C₄	1	1	yes	characteristic, complemented
34	C₂×#102×C₅₉	C₄	1	1	yes	characteristic, complemented
35	C₅₉×#408	—	2	2	no	—
36	C₅₉×#408	C₂²	1	2	yes	—
37	C₅₉×#407	—	2	1	no	—
38	C₅₉×#407	C₂²	1	1	yes	characteristic
39	C₅₉×#407	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
41	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#405	C₂²	1	2	yes	complemented
43	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#341	C₂²	1	2	yes	complemented
46	C₅₉×#339	C₂²	1	2	yes	complemented
47	C₅₉×#339	C₂²	1	2	yes	complemented
48	C₅₉×#336	C₂²	1	2	yes	complemented
49	C₂×#41×C₅₉	—	2	1	no	—
50	C₂×#41×C₅₉	—	2	1	no	—
51	C₂×#41×C₅₉	—	2	4	no	—
52	C₂×#41×C₅₉	—	4	2	no	—
53	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
54	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
55	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
56	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₅₉	—	2	1	no	—
59	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₅₉	—	2	1	no	—
61	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
62	#131×C₅₉	—	2	4	no	—
63	#131×C₅₉	—	4	2	no	—
64	C₂×M₁₆×C₅₉	—	2	2	no	—
65	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
66	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
67	C₂²×C₈×C₅₉	—	2	2	no	—
68	C₂²×C₈×C₅₉	—	4	2	no	—
69	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
76	#117×C₅₉	—	2	1	no	—
77	#117×C₅₉	—	2	1	no	—
78	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
79	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
80	#117×C₅₉	C₂³	1	1	yes	characteristic
81	#117×C₅₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
86	C₂×C₄²×C₅₉	—	2	1	no	—
87	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
88	#108×C₅₉	—	4	2	no	—
89	C₄⋊C₈×C₅₉	—	2	2	no	—
90	C₄⋊C₈×C₅₉	—	2	2	no	—
91	#104×C₅₉	—	2	4	no	—
92	#104×C₅₉	—	4	2	no	—
93	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
94	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
95	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
96	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
97	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
98	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
99	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
100	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
101	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
102	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
103	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
104	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
105	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
106	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
107	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
108	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊C₈×C₅₉	—	2	1	no	—
110	C₂²⋊C₈×C₅₉	—	2	1	no	—
111	C₂²⋊C₈×C₅₉	—	2	1	no	—
112	C₂²⋊C₈×C₅₉	—	2	1	no	—
113	C₂²⋊C₈×C₅₉	—	2	2	no	—
114	C₂²⋊C₈×C₅₉	—	2	2	no	—
115	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
116	C₂²⋊C₈×C₅₉	D₄	1	1	yes	characteristic
117	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
118	#97×C₅₉	—	2	2	no	—
119	C₄×C₈×C₅₉	—	2	2	no	—
120	C₄×C₈×C₅₉	—	4	2	no	—
121	#95×C₅₉	—	2	1	no	—
122	C₂⁴×C₅₉	—	2	1	no	—
123	C₂⁴×C₅₉	#41	1	1	yes	characteristic
124	#41×C₅₉	—	2	2	no	—
125	#41×C₅₉	—	2	2	no	—
126	#41×C₅₉	—	2	2	no	—
127	#41×C₅₉	—	2	2	no	—
128	#41×C₅₉	—	2	2	no	—
129	#41×C₅₉	—	4	4	no	—
130	#41×C₅₉	—	4	1	no	—
131	#41×C₅₉	—	4	1	no	—
132	#41×C₅₉	—	4	4	no	—
133	#41×C₅₉	#41	1	4	yes	—
134	C₂×Q₈×C₅₉	—	2	1	no	—
135	C₂×Q₈×C₅₉	—	2	2	no	—
136	C₂×Q₈×C₅₉	—	4	1	no	—
137	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×D₄×C₅₉	—	2	1	no	—
140	C₂×D₄×C₅₉	—	2	2	no	—
141	C₂×D₄×C₅₉	—	2	1	no	—
142	C₂×D₄×C₅₉	—	2	1	no	—
143	C₂×D₄×C₅₉	—	2	1	no	—
144	C₂×D₄×C₅₉	—	2	1	no	—
145	C₂×D₄×C₅₉	—	4	1	no	—
146	C₂×D₄×C₅₉	—	4	4	no	—
147	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	—	2	1	no	—
150	C₂²×C₄×C₅₉	—	2	2	no	—
151	C₂²×C₄×C₅₉	—	2	2	no	—
152	C₂²×C₄×C₅₉	—	2	1	no	—
153	C₂²×C₄×C₅₉	—	2	1	no	—
154	C₂²×C₄×C₅₉	—	2	2	no	—
155	C₂²×C₄×C₅₉	—	2	1	no	—
156	C₂²×C₄×C₅₉	—	2	1	no	—
157	C₂²×C₄×C₅₉	—	2	1	no	—
158	C₂²×C₄×C₅₉	—	2	1	no	—
159	C₂²×C₄×C₅₉	—	4	4	no	—
160	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
166	M₁₆×C₅₉	—	2	2	no	—
167	M₁₆×C₅₉	—	2	2	no	—
168	M₁₆×C₅₉	—	2	2	no	—
169	M₁₆×C₅₉	—	2	2	no	—
170	M₁₆×C₅₉	—	4	4	no	—
171	C₂×C₈×C₅₉	—	2	2	no	—
172	C₂×C₈×C₅₉	—	2	2	no	—
173	C₂×C₈×C₅₉	—	2	2	no	—
174	C₂×C₈×C₅₉	—	2	2	no	—
175	C₂×C₈×C₅₉	—	2	2	no	—
176	C₂×C₈×C₅₉	—	2	2	no	—
177	C₂×C₈×C₅₉	—	4	1	no	—
178	C₂×C₈×C₅₉	—	4	1	no	—
179	C₂×C₈×C₅₉	—	4	1	no	—
180	C₂×C₈×C₅₉	—	4	1	no	—
181	C₂×C₈×C₅₉	—	4	4	no	—
182	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₅₉	—	2	1	no	—
189	C₄⋊C₄×C₅₉	—	2	1	no	—
190	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₅₉	—	2	4	no	—
195	C₂²⋊C₄×C₅₉	—	2	1	no	—
196	C₂²⋊C₄×C₅₉	—	2	1	no	—
197	C₂²⋊C₄×C₅₉	—	2	1	no	—
198	C₂²⋊C₄×C₅₉	—	2	1	no	—
199	C₄²×C₅₉	—	2	1	no	—
200	C₄²×C₅₉	—	2	1	no	—
201	C₄²×C₅₉	—	2	1	no	—
202	C₄²×C₅₉	—	2	1	no	—
203	C₄²×C₅₉	—	2	2	no	—
204	C₄²×C₅₉	—	2	2	no	—
205	C₂³×C₅₉	—	2	1	no	—
206	C₂³×C₅₉	—	2	2	no	—
207	C₂³×C₅₉	—	2	2	no	—
208	C₂³×C₅₉	—	2	1	no	—
209	C₂³×C₅₉	—	4	1	no	—
210	C₂³×C₅₉	—	4	2	no	—
211	C₂³×C₅₉	—	4	2	no	—
212	C₂³×C₅₉	—	8	1	no	—
213	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
216	Q₈×C₅₉	—	2	1	no	—
217	Q₈×C₅₉	—	2	1	no	—
218	Q₈×C₅₉	—	2	1	no	—
219	Q₈×C₅₉	—	4	2	no	—
220	Q₈×C₅₉	#117	1	2	yes	—
221	D₄×C₅₉	—	2	4	no	—
222	D₄×C₅₉	—	2	1	no	—
223	D₄×C₅₉	—	2	1	no	—
224	D₄×C₅₉	—	2	1	no	—
225	D₄×C₅₉	—	4	2	no	—
226	D₄×C₅₉	—	4	2	no	—
227	D₄×C₅₉	—	4	2	no	—
228	D₄×C₅₉	—	4	2	no	—
229	D₄×C₅₉	#117	1	2	yes	—
230	C₂×C₄×C₅₉	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	2	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	4	no	—
237	C₂×C₄×C₅₉	—	2	2	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	2	4	no	—
240	C₂×C₄×C₅₉	—	2	1	no	—
241	C₂×C₄×C₅₉	—	2	1	no	—
242	C₂×C₄×C₅₉	—	2	1	no	—
243	C₂×C₄×C₅₉	—	2	1	no	—
244	C₂×C₄×C₅₉	—	2	1	no	—
245	C₂×C₄×C₅₉	—	4	2	no	—
246	C₂×C₄×C₅₉	—	4	2	no	—
247	C₂×C₄×C₅₉	—	4	2	no	—
248	C₂×C₄×C₅₉	—	4	2	no	—
249	C₂×C₄×C₅₉	—	4	2	no	—
250	C₂×C₄×C₅₉	—	4	2	no	—
251	C₂×C₄×C₅₉	—	4	2	no	—
252	C₂×C₄×C₅₉	—	8	1	no	—
253	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
258	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
259	C₈×C₅₉	—	2	1	no	—
260	C₈×C₅₉	—	2	1	no	—
261	C₈×C₅₉	—	2	1	no	—
262	C₈×C₅₉	—	2	1	no	—
263	C₈×C₅₉	—	2	2	no	—
264	C₈×C₅₉	—	2	2	no	—
265	C₈×C₅₉	—	4	2	no	—
266	C₈×C₅₉	—	4	2	no	—
267	#22587	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂²×C₅₉	—	2	1	no	—
269	C₂²×C₅₉	—	2	1	no	—
270	C₂²×C₅₉	—	2	1	no	—
271	C₂²×C₅₉	—	2	1	no	—
272	C₂²×C₅₉	—	2	1	no	—
273	C₂²×C₅₉	—	2	2	no	—
274	C₂²×C₅₉	—	2	1	no	—
275	C₂²×C₅₉	—	2	1	no	—
276	C₂²×C₅₉	—	4	4	no	—
277	C₂²×C₅₉	—	4	1	no	—
278	C₂²×C₅₉	—	4	1	no	—
279	C₂²×C₅₉	—	4	1	no	—
280	C₂²×C₅₉	—	4	1	no	—
281	C₂²×C₅₉	—	4	1	no	—
282	C₂²×C₅₉	—	8	4	no	—
283	C₂²×C₅₉	#443	1	2	yes	—
284	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂²×C₅₉	#551	1	2	yes	—
286	C₄×C₅₉	—	2	1	no	—
287	C₄×C₅₉	—	2	1	no	—
288	C₄×C₅₉	—	2	2	no	—
289	C₄×C₅₉	—	4	4	no	—
290	C₄×C₅₉	—	4	1	no	—
291	C₄×C₅₉	—	4	1	no	—
292	C₄×C₅₉	—	4	1	no	—
293	C₄×C₅₉	—	4	1	no	—
294	C₄×C₅₉	—	4	1	no	—
295	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
296	C₄×C₅₉	#518	1	1	yes	characteristic
297	C₄×C₅₉	#546	1	2	yes	—
298	#2924	C₂×C₅₉	1	1	yes	characteristic, complemented
299	C₂×#416	C₂×C₅₉	1	1	yes	characteristic
300	#2880	C₂×C₅₉	1	1	yes	characteristic
301	#1937	C₂×C₅₉	1	2	yes	complemented
302	#1929	C₂×C₅₉	1	2	yes	complemented
303	#1866	C₂×C₅₉	1	2	yes	complemented
304	#1826	C₂×C₅₉	1	1	yes	characteristic, complemented
305	#1810	C₂×C₅₉	1	1	yes	characteristic, complemented
306	#1789	C₂×C₅₉	1	1	yes	characteristic
307	#1764	C₂×C₅₉	1	2	yes	complemented
308	C₈×C₂²⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
309	C₂×C₅₉	—	2	2	no	—
310	C₂×C₅₉	—	2	2	no	—
311	C₂×C₅₉	—	4	1	no	—
312	C₂×C₅₉	—	4	2	no	—
313	C₂×C₅₉	—	8	1	no	—
314	C₂×C₅₉	#2342	1	1	yes	characteristic
315	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
316	C₂×C₅₉	#2957	1	1	yes	characteristic
317	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
318	C₂×#131	C₂²×C₅₉	1	2	yes	—
319	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
320	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
321	#433	—	2	2	no	—
322	#432	—	2	1	no	—
323	#431	—	2	1	no	—
324	C₂×#108	C₂²×C₅₉	1	2	yes	complemented
325	#424	C₂²×C₅₉	1	2	yes	complemented
326	C₂×#104	C₂²×C₅₉	1	2	yes	—
327	C₂×#104	C₂²×C₅₉	1	2	yes	—
328	#416	C₄×C₅₉	1	1	yes	characteristic, complemented
329	#416	C₄×C₅₉	1	1	yes	characteristic, complemented
330	#416	C₄×C₅₉	1	1	yes	characteristic, complemented
331	#416	C₄×C₅₉	1	1	yes	characteristic, complemented
332	#416	C₂²×C₅₉	1	1	yes	characteristic
333	#416	C₂²×C₅₉	1	1	yes	characteristic
334	#416	C₂²×C₅₉	1	1	yes	characteristic
335	#416	C₂²×C₅₉	1	1	yes	characteristic
336	C₂×#103	C₄×C₅₉	1	1	yes	characteristic, complemented
337	C₂×#103	C₄×C₅₉	1	1	yes	characteristic, complemented
338	C₂×#102	C₄×C₅₉	1	1	yes	characteristic, complemented
339	C₂×#102	C₄×C₅₉	1	1	yes	characteristic, complemented
340	#408	—	2	2	no	—
341	#408	C₂²×C₅₉	1	2	yes	—
342	#407	—	2	1	no	—
343	#407	C₂²×C₅₉	1	1	yes	characteristic
344	#407	C₂²×C₅₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₈	—	2	1	no	—
346	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
347	#405	C₂²×C₅₉	1	2	yes	complemented
348	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	complemented
349	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
350	#341	C₂²×C₅₉	1	2	yes	complemented
351	#339	C₂²×C₅₉	1	2	yes	complemented
352	#339	C₂²×C₅₉	1	2	yes	complemented
353	#336	C₂²×C₅₉	1	2	yes	complemented
354	C₅₉	#22587	1	1	yes	characteristic, direct product factor, Sylow
355	C₂×#41	—	2	1	no	—
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	4	no	—
358	C₂×#41	—	4	2	no	—
359	C₂×#41	C₂×C₄×C₅₉	1	1	yes	characteristic
360	C₂×#41	C₂×C₄×C₅₉	1	1	yes	characteristic
361	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
362	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
363	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
368	#131	—	2	4	no	—
369	#131	—	4	2	no	—
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
372	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	4	2	no	—
375	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
376	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
377	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
378	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	#117	C₂×C₄×C₅₉	1	1	yes	characteristic
385	#117	C₂×C₄×C₅₉	1	1	yes	characteristic
386	#117	C₂³×C₅₉	1	1	yes	characteristic
387	#117	C₂³×C₅₉	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
394	#108	—	4	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	C₄⋊C₈	—	2	2	no	—
397	#104	—	2	4	no	—
398	#104	—	4	2	no	—
399	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
400	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
401	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
402	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
403	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
404	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
405	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
406	#103	C₂×C₄×C₅₉	1	1	yes	characteristic
407	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
408	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
409	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
410	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
411	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
412	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
413	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
414	#102	C₂×C₄×C₅₉	1	1	yes	characteristic
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	2	no	—
420	C₂²⋊C₈	—	2	2	no	—
421	C₂²⋊C₈	D₄×C₅₉	1	1	yes	characteristic
422	C₂²⋊C₈	D₄×C₅₉	1	1	yes	characteristic
423	C₂²⋊C₈	D₄×C₅₉	1	2	yes	—
424	#97	—	2	2	no	—
425	C₄×C₈	—	2	2	no	—
426	C₄×C₈	—	4	2	no	—
427	#95	—	2	1	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	#41×C₅₉	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	4	4	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	4	4	no	—
439	#41	#41×C₅₉	1	4	yes	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	4	1	no	—
443	C₂×Q₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
444	C₂×Q₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	4	no	—
453	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
454	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
470	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	4	4	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	4	no	—
488	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
489	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
490	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
491	C₂×C₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
493	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	1	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	2	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	2	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	8	1	no	—
519	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
520	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
521	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
522	Q₈	—	2	1	no	—
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	4	2	no	—
526	Q₈	#117×C₅₉	1	2	yes	—
527	D₄	—	2	4	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	#117×C₅₉	1	2	yes	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	8	1	no	—
559	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
560	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
561	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
564	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	—	2	1	no	—
568	C₈	—	2	1	no	—
569	C₈	—	2	2	no	—
570	C₈	—	2	2	no	—
571	C₈	—	4	2	no	—
572	C₈	—	4	2	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	8	4	no	—
588	C₂²	C₅₉×#443	1	2	yes	—
589	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
590	C₂²	C₅₉×#551	1	2	yes	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	2	no	—
594	C₄	—	4	4	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	1	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	C₂×#117×C₅₉	1	1	yes	characteristic
601	C₄	C₅₉×#518	1	1	yes	characteristic
602	C₄	C₅₉×#546	1	2	yes	—
603	C₂	—	2	2	no	—
604	C₂	—	2	2	no	—
605	C₂	—	4	1	no	—
606	C₂	—	4	2	no	—
607	C₂	—	8	1	no	—
608	C₂	C₅₉×#2342	1	1	yes	characteristic
609	C₂	C₂×C₅₉×#443	1	1	yes	characteristic
610	C₂	C₅₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₂²⋊C₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2924	C₂	semidirect
4. C₅₉×#1937	C₂	semidirect
5. C₅₉×#1929	C₂	semidirect
6. C₅₉×#1866	C₂	semidirect
7. C₅₉×#1826	C₂	semidirect
8. C₅₉×#1810	C₂	semidirect
10. C₅₉×#1764	C₂	semidirect
11. C₈×C₂²⋊C₄×C₅₉	C₂	semidirect
19. C₂×#108×C₅₉	C₂²	semidirect
20. C₅₉×#424	C₂²	semidirect
23. C₅₉×#416	C₄	semidirect
24. C₅₉×#416	C₄	semidirect
25. C₅₉×#416	C₄	semidirect
26. C₅₉×#416	C₄	semidirect
31. C₂×#103×C₅₉	C₄	semidirect
32. C₂×#103×C₅₉	C₄	semidirect
33. C₂×#102×C₅₉	C₄	semidirect
34. C₂×#102×C₅₉	C₄	semidirect
42. C₅₉×#405	C₂²	semidirect
43. C₂×C₄×C₈×C₅₉	C₂²	semidirect
45. C₅₉×#341	C₂²	semidirect
46. C₅₉×#339	C₂²	semidirect
47. C₅₉×#339	C₂²	semidirect
48. C₅₉×#336	C₂²	semidirect
267. #22587	C₅₉	direct (N × H)
298. #2924	C₂×C₅₉	semidirect
301. #1937	C₂×C₅₉	semidirect
302. #1929	C₂×C₅₉	semidirect
303. #1866	C₂×C₅₉	semidirect
304. #1826	C₂×C₅₉	semidirect
305. #1810	C₂×C₅₉	semidirect
307. #1764	C₂×C₅₉	semidirect
308. C₈×C₂²⋊C₄	C₂×C₅₉	semidirect
324. C₂×#108	C₂²×C₅₉	semidirect
325. #424	C₂²×C₅₉	semidirect
328. #416	C₄×C₅₉	semidirect
329. #416	C₄×C₅₉	semidirect
330. #416	C₄×C₅₉	semidirect
331. #416	C₄×C₅₉	semidirect
336. C₂×#103	C₄×C₅₉	semidirect
337. C₂×#103	C₄×C₅₉	semidirect
338. C₂×#102	C₄×C₅₉	semidirect
339. C₂×#102	C₄×C₅₉	semidirect
347. #405	C₂²×C₅₉	semidirect
348. C₂×C₄×C₈	C₂²×C₅₉	semidirect
350. #341	C₂²×C₅₉	semidirect
351. #339	C₂²×C₅₉	semidirect
352. #339	C₂²×C₅₉	semidirect
353. #336	C₂²×C₅₉	semidirect
354. C₅₉	#22587	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×#2924	2
C₂×C₅₉×#416	2
C₅₉×#2880	2
C₅₉×#1937	2
C₅₉×#1929	2
C₅₉×#1866	2
C₅₉×#1826	2
C₅₉×#1810	2
C₅₉×#1789	2
C₅₉×#1764	2
C₈×C₂²⋊C₄×C₅₉	2
#22587	59

Subgroups — C59×#22587 #28434696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#22587 #28434696