Subgroups — C₅₉×#26259 #28438368

Order 15104.

828 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2448	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2446	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2055	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2042	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#1973	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#1971	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1968	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#1944	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₉×#1880	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#497	—	2	4	no	—
25	C₄×Q₁₆×C₅₉	—	2	4	no	—
26	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#400	—	2	1	no	—
41	C₅₉×#399	—	2	1	no	—
42	C₅₉×#398	—	2	1	no	—
43	C₅₉×#397	—	2	1	no	—
44	C₅₉×#391	C₂²	1	1	yes	characteristic
45	C₅₉×#391	C₂²	1	1	yes	characteristic
46	C₅₉×#391	C₂²	1	1	yes	characteristic
47	C₅₉×#391	C₂²	1	1	yes	characteristic
48	C₅₉×#390	C₂²	1	1	yes	characteristic
49	C₅₉×#390	C₂²	1	1	yes	characteristic
50	C₅₉×#389	C₂²	1	1	yes	characteristic
51	C₅₉×#389	C₂²	1	1	yes	characteristic
52	C₅₉×#388	—	2	1	no	—
53	C₅₉×#388	—	2	1	no	—
54	C₅₉×#387	—	2	1	no	—
55	C₅₉×#387	—	2	1	no	—
56	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₅₉×#340	C₂²	1	1	yes	characteristic
58	C₅₉×#340	C₂²	1	1	yes	characteristic
59	C₅₉×#336	C₂²	1	1	yes	characteristic
60	C₅₉×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₅₉	—	2	2	no	—
66	C₂×Q₁₆×C₅₉	—	2	2	no	—
67	C₂×Q₁₆×C₅₉	—	2	2	no	—
68	C₂×Q₁₆×C₅₉	—	2	2	no	—
69	C₂×Q₁₆×C₅₉	—	4	1	no	—
70	C₂×Q₁₆×C₅₉	D₄	1	4	yes	—
71	C₂×SD₁₆×C₅₉	—	2	2	no	—
72	C₂×SD₁₆×C₅₉	—	2	2	no	—
73	C₂×SD₁₆×C₅₉	—	2	2	no	—
74	C₂×SD₁₆×C₅₉	—	2	2	no	—
75	C₂×SD₁₆×C₅₉	—	2	2	no	—
76	C₂×SD₁₆×C₅₉	—	4	1	no	—
77	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₅₉	—	2	2	no	—
82	C₄⋊Q₈×C₅₉	—	4	1	no	—
83	#124×C₅₉	—	2	2	no	—
84	#124×C₅₉	—	4	1	no	—
85	C₄×Q₈×C₅₉	—	2	2	no	—
86	C₄×Q₈×C₅₉	—	2	2	no	—
87	C₄×Q₈×C₅₉	—	4	1	no	—
88	C₄×Q₈×C₅₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
107	C₂×C₄²×C₅₉	—	2	1	no	—
108	C₂×C₄²×C₅₉	—	2	1	no	—
109	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
112	#107×C₅₉	—	2	2	no	—
113	#106×C₅₉	—	2	2	no	—
114	C₄⋊C₈×C₅₉	—	2	2	no	—
115	#103×C₅₉	—	2	2	no	—
116	#103×C₅₉	—	2	2	no	—
117	#103×C₅₉	—	4	1	no	—
118	#103×C₅₉	—	4	1	no	—
119	#103×C₅₉	—	4	1	no	—
120	#103×C₅₉	—	4	1	no	—
121	#102×C₅₉	—	4	1	no	—
122	#102×C₅₉	—	4	1	no	—
123	#97×C₅₉	—	2	2	no	—
124	#97×C₅₉	—	2	2	no	—
125	C₄×C₈×C₅₉	—	2	2	no	—
126	#95×C₅₉	—	2	1	no	—
127	#95×C₅₉	—	2	1	no	—
128	#95×C₅₉	—	2	1	no	—
129	#95×C₅₉	—	2	1	no	—
130	#95×C₅₉	—	2	1	no	—
131	#95×C₅₉	—	2	1	no	—
132	#95×C₅₉	—	2	1	no	—
133	#95×C₅₉	—	2	1	no	—
134	#95×C₅₉	—	2	1	no	—
135	#95×C₅₉	—	2	1	no	—
136	#95×C₅₉	D₄	1	1	yes	characteristic
137	#95×C₅₉	D₄	1	1	yes	characteristic
138	C₂⁴×C₅₉	—	2	1	no	—
139	C₂×Q₈×C₅₉	—	2	1	no	—
140	C₂×Q₈×C₅₉	—	2	1	no	—
141	C₂×Q₈×C₅₉	—	2	1	no	—
142	C₂×Q₈×C₅₉	—	2	1	no	—
143	C₂×Q₈×C₅₉	—	2	1	no	—
144	C₂×Q₈×C₅₉	—	2	1	no	—
145	C₂×Q₈×C₅₉	—	2	1	no	—
146	C₂×Q₈×C₅₉	—	2	1	no	—
147	C₂×Q₈×C₅₉	—	2	1	no	—
148	C₂×Q₈×C₅₉	—	2	1	no	—
149	C₂×Q₈×C₅₉	—	2	1	no	—
150	C₂×Q₈×C₅₉	—	2	1	no	—
151	C₂×Q₈×C₅₉	—	2	1	no	—
152	C₂×Q₈×C₅₉	—	2	1	no	—
153	C₂×Q₈×C₅₉	—	2	1	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₅₉	—	2	1	no	—
158	C₂×D₄×C₅₉	—	2	1	no	—
159	C₂×D₄×C₅₉	—	2	1	no	—
160	C₂×D₄×C₅₉	—	2	1	no	—
161	C₂×D₄×C₅₉	—	2	1	no	—
162	C₂×D₄×C₅₉	—	2	1	no	—
163	C₂²×C₄×C₅₉	—	2	1	no	—
164	C₂²×C₄×C₅₉	—	2	1	no	—
165	C₂²×C₄×C₅₉	—	2	1	no	—
166	C₂²×C₄×C₅₉	—	2	1	no	—
167	C₂²×C₄×C₅₉	—	2	1	no	—
168	C₂²×C₄×C₅₉	—	2	1	no	—
169	C₂²×C₄×C₅₉	—	2	1	no	—
170	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
177	Q₁₆×C₅₉	—	2	8	no	—
178	Q₁₆×C₅₉	—	4	4	no	—
179	SD₁₆×C₅₉	—	4	4	no	—
180	SD₁₆×C₅₉	—	4	4	no	—
181	C₂×C₈×C₅₉	—	2	1	no	—
182	C₂×C₈×C₅₉	—	2	1	no	—
183	C₂×C₈×C₅₉	—	2	1	no	—
184	C₂×C₈×C₅₉	—	2	1	no	—
185	C₂×C₈×C₅₉	—	2	1	no	—
186	C₂×C₈×C₅₉	—	2	1	no	—
187	C₂×C₈×C₅₉	—	2	1	no	—
188	C₂×C₈×C₅₉	—	2	1	no	—
189	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₅₉	#41	1	2	yes	—
191	C₂×C₈×C₅₉	#41	1	2	yes	—
192	C₂×C₈×C₅₉	#41	1	2	yes	—
193	C₄⋊C₄×C₅₉	—	2	2	no	—
194	C₄⋊C₄×C₅₉	—	2	1	no	—
195	C₄⋊C₄×C₅₉	—	2	1	no	—
196	C₄⋊C₄×C₅₉	—	2	1	no	—
197	C₄⋊C₄×C₅₉	—	2	1	no	—
198	C₄⋊C₄×C₅₉	—	2	1	no	—
199	C₄⋊C₄×C₅₉	—	2	1	no	—
200	C₄⋊C₄×C₅₉	—	2	1	no	—
201	C₄⋊C₄×C₅₉	—	2	1	no	—
202	C₄⋊C₄×C₅₉	—	4	1	no	—
203	C₄⋊C₄×C₅₉	—	4	2	no	—
204	C₄⋊C₄×C₅₉	—	4	2	no	—
205	C₄⋊C₄×C₅₉	—	4	2	no	—
206	C₄⋊C₄×C₅₉	—	4	2	no	—
207	C₄⋊C₄×C₅₉	—	4	2	no	—
208	C₄⋊C₄×C₅₉	—	8	1	no	—
209	C₂²⋊C₄×C₅₉	—	4	2	no	—
210	C₂²⋊C₄×C₅₉	—	4	2	no	—
211	C₂²⋊C₄×C₅₉	—	4	2	no	—
212	C₂²⋊C₄×C₅₉	—	4	2	no	—
213	C₂²⋊C₄×C₅₉	—	8	1	no	—
214	C₂²⋊C₄×C₅₉	—	8	1	no	—
215	C₄²×C₅₉	—	2	1	no	—
216	C₄²×C₅₉	—	2	1	no	—
217	C₄²×C₅₉	—	2	1	no	—
218	C₄²×C₅₉	—	2	1	no	—
219	C₄²×C₅₉	—	2	1	no	—
220	C₄²×C₅₉	—	2	1	no	—
221	C₄²×C₅₉	—	4	2	no	—
222	C₄²×C₅₉	—	4	2	no	—
223	C₂³×C₅₉	—	4	1	no	—
224	C₂³×C₅₉	—	4	1	no	—
225	C₂³×C₅₉	—	4	1	no	—
226	C₂³×C₅₉	—	4	1	no	—
227	C₂³×C₅₉	—	4	1	no	—
228	C₂³×C₅₉	—	4	1	no	—
229	C₂³×C₅₉	—	4	1	no	—
230	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₅₉	—	2	2	no	—
232	Q₈×C₅₉	—	2	2	no	—
233	Q₈×C₅₉	—	2	2	no	—
234	Q₈×C₅₉	—	2	2	no	—
235	Q₈×C₅₉	—	4	1	no	—
236	Q₈×C₅₉	—	4	1	no	—
237	Q₈×C₅₉	—	4	1	no	—
238	Q₈×C₅₉	—	4	1	no	—
239	Q₈×C₅₉	—	4	1	no	—
240	Q₈×C₅₉	—	4	1	no	—
241	Q₈×C₅₉	—	4	1	no	—
242	Q₈×C₅₉	—	4	1	no	—
243	D₄×C₅₉	—	4	1	no	—
244	D₄×C₅₉	—	4	1	no	—
245	D₄×C₅₉	—	4	1	no	—
246	D₄×C₅₉	—	4	1	no	—
247	C₂×C₄×C₅₉	—	2	1	no	—
248	C₂×C₄×C₅₉	—	2	1	no	—
249	C₂×C₄×C₅₉	—	2	1	no	—
250	C₂×C₄×C₅₉	—	2	1	no	—
251	C₂×C₄×C₅₉	—	2	1	no	—
252	C₂×C₄×C₅₉	—	2	1	no	—
253	C₂×C₄×C₅₉	—	2	1	no	—
254	C₂×C₄×C₅₉	—	2	2	no	—
255	C₂×C₄×C₅₉	—	2	2	no	—
256	C₂×C₄×C₅₉	—	2	1	no	—
257	C₂×C₄×C₅₉	—	2	1	no	—
258	C₂×C₄×C₅₉	—	2	1	no	—
259	C₂×C₄×C₅₉	—	2	1	no	—
260	C₂×C₄×C₅₉	—	2	1	no	—
261	C₂×C₄×C₅₉	—	2	1	no	—
262	C₂×C₄×C₅₉	—	2	1	no	—
263	C₂×C₄×C₅₉	—	2	1	no	—
264	C₂×C₄×C₅₉	—	2	1	no	—
265	C₂×C₄×C₅₉	—	2	1	no	—
266	C₂×C₄×C₅₉	—	4	1	no	—
267	C₂×C₄×C₅₉	—	4	1	no	—
268	C₂×C₄×C₅₉	—	4	1	no	—
269	C₂×C₄×C₅₉	—	4	1	no	—
270	C₂×C₄×C₅₉	—	4	1	no	—
271	C₂×C₄×C₅₉	—	4	1	no	—
272	C₂×C₄×C₅₉	—	4	1	no	—
273	C₂×C₄×C₅₉	—	4	1	no	—
274	C₂×C₄×C₅₉	—	4	1	no	—
275	C₂×C₄×C₅₉	—	4	1	no	—
276	C₂×C₄×C₅₉	—	4	1	no	—
277	C₂×C₄×C₅₉	—	4	1	no	—
278	C₂×C₄×C₅₉	—	4	1	no	—
279	C₂×C₄×C₅₉	—	4	1	no	—
280	C₂×C₄×C₅₉	—	4	1	no	—
281	C₂×C₄×C₅₉	—	4	1	no	—
282	C₂×C₄×C₅₉	—	4	1	no	—
283	C₂×C₄×C₅₉	—	4	1	no	—
284	C₂×C₄×C₅₉	—	4	1	no	—
285	C₂×C₄×C₅₉	#137	1	2	yes	—
286	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
292	C₈×C₅₉	—	2	2	no	—
293	C₈×C₅₉	—	4	1	no	—
294	C₈×C₅₉	—	4	1	no	—
295	C₈×C₅₉	#123	1	4	yes	—
296	#26259	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
297	C₂²×C₅₉	—	8	1	no	—
298	C₂²×C₅₉	—	8	1	no	—
299	C₂²×C₅₉	—	8	1	no	—
300	C₂²×C₅₉	—	8	1	no	—
301	C₂²×C₅₉	—	8	1	no	—
302	C₂²×C₅₉	—	8	1	no	—
303	C₂²×C₅₉	—	8	1	no	—
304	C₂²×C₅₉	#532	1	1	yes	characteristic
305	C₂²×C₅₉	D₄²	1	1	yes	characteristic
306	C₂²×C₅₉	#550	1	1	yes	characteristic
307	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
308	C₂²×C₅₉	#575	1	1	yes	characteristic
309	C₂²×C₅₉	#577	1	1	yes	characteristic
310	C₂²×C₅₉	#578	1	1	yes	characteristic
311	C₄×C₅₉	—	2	2	no	—
312	C₄×C₅₉	—	4	1	no	—
313	C₄×C₅₉	—	4	1	no	—
314	C₄×C₅₉	—	4	2	no	—
315	C₄×C₅₉	—	4	2	no	—
316	C₄×C₅₉	—	4	1	no	—
317	C₄×C₅₉	—	4	1	no	—
318	C₄×C₅₉	—	4	1	no	—
319	C₄×C₅₉	—	8	1	no	—
320	C₄×C₅₉	—	8	1	no	—
321	C₄×C₅₉	—	8	1	no	—
322	C₄×C₅₉	—	8	1	no	—
323	C₄×C₅₉	—	8	1	no	—
324	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
325	C₄×C₅₉	#540	1	1	yes	characteristic
326	C₄×C₅₉	#546	1	1	yes	characteristic
327	C₄×C₅₉	#559	1	1	yes	characteristic
328	C₂×#497	C₂×C₅₉	1	1	yes	characteristic
329	C₂×C₄×Q₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
330	#2448	C₂×C₅₉	1	1	yes	characteristic
331	#2446	C₂×C₅₉	1	1	yes	characteristic, complemented
332	#2056	C₂×C₅₉	1	1	yes	characteristic, complemented
333	#2055	C₂×C₅₉	1	1	yes	characteristic
334	#2043	C₂×C₅₉	1	1	yes	characteristic, complemented
335	#2042	C₂×C₅₉	1	1	yes	characteristic
336	#1973	C₂×C₅₉	1	1	yes	characteristic
337	#1971	C₂×C₅₉	1	1	yes	characteristic, complemented
338	#1968	C₂×C₅₉	1	1	yes	characteristic
339	#1944	C₂×C₅₉	1	1	yes	characteristic, complemented
340	#1880	C₂×C₅₉	1	1	yes	characteristic
341	#1878	C₂×C₅₉	1	1	yes	characteristic, complemented
342	#1771	C₂×C₅₉	1	1	yes	characteristic, complemented
343	C₂×C₅₉	—	16	1	no	—
344	C₂×C₅₉	#2445	1	1	yes	characteristic
345	C₂×C₅₉	#3172	1	1	yes	characteristic
346	C₂×C₅₉	#3178	1	1	yes	characteristic
347	C₂×C₅₉	#3270	1	1	yes	characteristic
348	C₂×C₅₉	#3271	1	1	yes	characteristic
349	C₂×C₅₉	#3400	1	1	yes	characteristic
350	C₂×C₅₉	#3402	1	1	yes	characteristic
351	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
352	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
353	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
354	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
355	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
356	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
357	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
358	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
359	#497	—	2	4	no	—
360	C₄×Q₁₆	—	2	4	no	—
361	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
362	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
363	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
364	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
365	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
366	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
367	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
368	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
370	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
371	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
372	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
373	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
374	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
375	#400	—	2	1	no	—
376	#399	—	2	1	no	—
377	#398	—	2	1	no	—
378	#397	—	2	1	no	—
379	#391	C₂²×C₅₉	1	1	yes	characteristic
380	#391	C₂²×C₅₉	1	1	yes	characteristic
381	#391	C₂²×C₅₉	1	1	yes	characteristic
382	#391	C₂²×C₅₉	1	1	yes	characteristic
383	#390	C₂²×C₅₉	1	1	yes	characteristic
384	#390	C₂²×C₅₉	1	1	yes	characteristic
385	#389	C₂²×C₅₉	1	1	yes	characteristic
386	#389	C₂²×C₅₉	1	1	yes	characteristic
387	#388	—	2	1	no	—
388	#388	—	2	1	no	—
389	#387	—	2	1	no	—
390	#387	—	2	1	no	—
391	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
392	#340	C₂²×C₅₉	1	1	yes	characteristic
393	#340	C₂²×C₅₉	1	1	yes	characteristic
394	#336	C₂²×C₅₉	1	1	yes	characteristic
395	#336	C₂²×C₅₉	1	1	yes	characteristic
396	C₅₉	#26259	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
401	C₂×Q₁₆	—	2	2	no	—
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×Q₁₆	—	2	2	no	—
405	C₂×Q₁₆	—	4	1	no	—
406	C₂×Q₁₆	D₄×C₅₉	1	4	yes	—
407	C₂×SD₁₆	—	2	2	no	—
408	C₂×SD₁₆	—	2	2	no	—
409	C₂×SD₁₆	—	2	2	no	—
410	C₂×SD₁₆	—	2	2	no	—
411	C₂×SD₁₆	—	2	2	no	—
412	C₂×SD₁₆	—	4	1	no	—
413	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
416	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
417	C₄⋊Q₈	—	2	2	no	—
418	C₄⋊Q₈	—	4	1	no	—
419	#124	—	2	2	no	—
420	#124	—	4	1	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	—	4	1	no	—
424	C₄×Q₈	—	4	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
432	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
448	#107	—	2	2	no	—
449	#106	—	2	2	no	—
450	C₄⋊C₈	—	2	2	no	—
451	#103	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	—	4	1	no	—
454	#103	—	4	1	no	—
455	#103	—	4	1	no	—
456	#103	—	4	1	no	—
457	#102	—	4	1	no	—
458	#102	—	4	1	no	—
459	#97	—	2	2	no	—
460	#97	—	2	2	no	—
461	C₄×C₈	—	2	2	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	D₄×C₅₉	1	1	yes	characteristic
473	#95	D₄×C₅₉	1	1	yes	characteristic
474	C₂⁴	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
492	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	1	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	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	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
513	Q₁₆	—	2	8	no	—
514	Q₁₆	—	4	4	no	—
515	SD₁₆	—	4	4	no	—
516	SD₁₆	—	4	4	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
526	C₂×C₈	#41×C₅₉	1	2	yes	—
527	C₂×C₈	#41×C₅₉	1	2	yes	—
528	C₂×C₈	#41×C₅₉	1	2	yes	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	8	1	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₂²⋊C₄	—	8	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	4	2	no	—
558	C₄²	—	4	2	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	#137×C₅₉	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
625	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
626	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
627	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
628	C₈	—	2	2	no	—
629	C₈	—	4	1	no	—
630	C₈	—	4	1	no	—
631	C₈	#123×C₅₉	1	4	yes	—
632	C₂²	—	8	1	no	—
633	C₂²	—	8	1	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	—	8	1	no	—
638	C₂²	—	8	1	no	—
639	C₂²	C₅₉×#532	1	1	yes	characteristic
640	C₂²	D₄²×C₅₉	1	1	yes	characteristic
641	C₂²	C₅₉×#550	1	1	yes	characteristic
642	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
643	C₂²	C₅₉×#575	1	1	yes	characteristic
644	C₂²	C₅₉×#577	1	1	yes	characteristic
645	C₂²	C₅₉×#578	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	1	no	—
649	C₄	—	4	1	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
660	C₄	C₅₉×#540	1	1	yes	characteristic
661	C₄	C₅₉×#546	1	1	yes	characteristic
662	C₄	C₅₉×#559	1	1	yes	characteristic
663	C₂	—	16	1	no	—
664	C₂	C₅₉×#2445	1	1	yes	characteristic
665	C₂	C₅₉×#3172	1	1	yes	characteristic
666	C₂	C₅₉×#3178	1	1	yes	characteristic
667	C₂	C₅₉×#3270	1	1	yes	characteristic
668	C₂	C₅₉×#3271	1	1	yes	characteristic
669	C₂	C₅₉×#3400	1	1	yes	characteristic
670	C₂	C₅₉×#3402	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 ◁ C₄×C₄⋊C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₅₉	C₂	semidirect
4. C₅₉×#2446	C₂	semidirect
5. C₅₉×#2056	C₂	semidirect
7. C₅₉×#2043	C₂	semidirect
10. C₅₉×#1971	C₂	semidirect
12. C₅₉×#1944	C₂	semidirect
14. C₅₉×#1878	C₂	semidirect
15. C₅₉×#1771	C₂	semidirect
296. #26259	C₅₉	direct (N × H)
329. C₂×C₄×Q₁₆	C₂×C₅₉	semidirect
331. #2446	C₂×C₅₉	semidirect
332. #2056	C₂×C₅₉	semidirect
334. #2043	C₂×C₅₉	semidirect
337. #1971	C₂×C₅₉	semidirect
339. #1944	C₂×C₅₉	semidirect
341. #1878	C₂×C₅₉	semidirect
342. #1771	C₂×C₅₉	semidirect
396. C₅₉	#26259	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×#497	2
C₂×C₄×Q₁₆×C₅₉	2
C₅₉×#2448	2
C₅₉×#2446	2
C₅₉×#2056	2
C₅₉×#2055	2
C₅₉×#2043	2
C₅₉×#2042	2
C₅₉×#1973	2
C₅₉×#1971	2
C₅₉×#1968	2
C₅₉×#1944	2
C₅₉×#1880	2
C₅₉×#1878	2
C₅₉×#1771	2
#26259	59

Subgroups — C59×#26259 #28438368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26259 #28438368