Subgroups — C₅₉×#26008 #28438117

Order 15104.

712 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2439	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2345	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1949	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1854	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#1851	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#1823	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#1809	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1736	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#396	—	2	1	no	—
28	C₅₉×#393	—	2	1	no	—
29	C₅₉×#391	—	2	1	no	—
30	C₅₉×#389	C₂²	1	1	yes	characteristic
31	C₅₉×#389	C₂²	1	1	yes	characteristic
32	C₅₉×#389	C₂²	1	1	yes	characteristic
33	C₅₉×#389	C₂²	1	1	yes	characteristic
34	C₅₉×#387	—	2	1	no	—
35	C₅₉×#387	—	2	1	no	—
36	C₅₉×#387	—	2	1	no	—
37	C₅₉×#382	C₂²	1	1	yes	characteristic
38	C₅₉×#380	—	2	1	no	—
39	C₅₉×#380	C₂²	1	1	yes	characteristic
40	C₅₉×#380	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
44	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#340	C₂²	1	1	yes	characteristic
46	C₅₉×#340	C₂²	1	1	yes	characteristic
47	C₅₉×#340	C₂²	1	1	yes	characteristic
48	C₅₉×#340	C₂²	1	1	yes	characteristic
49	C₅₉×#340	C₂²	1	1	yes	characteristic
50	C₅₉×#340	C₂²	1	1	yes	characteristic
51	C₅₉×#340	C₂²	1	1	yes	characteristic
52	C₅₉×#340	C₂²	1	1	yes	characteristic
53	C₅₉×#340	C₂²	1	1	yes	characteristic
54	C₅₉×#340	C₂²	1	1	yes	characteristic
55	C₅₉×#340	C₂²	1	1	yes	characteristic
56	C₅₉×#340	C₂²	1	1	yes	characteristic
57	C₅₉×#336	C₂²	1	1	yes	characteristic
58	C₅₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₅₉	—	2	1	no	—
60	C₂³×C₄×C₅₉	—	2	1	no	—
61	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₅₉	—	2	2	no	—
63	C₂×M₁₆×C₅₉	—	2	2	no	—
64	C₂×M₁₆×C₅₉	—	4	1	no	—
65	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₄⋊Q₈×C₅₉	—	2	2	no	—
70	C₄⋊Q₈×C₅₉	—	4	1	no	—
71	#117×C₅₉	—	2	2	no	—
72	#117×C₅₉	—	4	1	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₅₉	Q₈	1	4	yes	complemented
81	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₅₉	—	2	1	no	—
95	C₂×C₄²×C₅₉	—	2	1	no	—
96	C₂×C₄²×C₅₉	—	2	1	no	—
97	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
99	#107×C₅₉	—	2	2	no	—
100	#107×C₅₉	—	4	1	no	—
101	#106×C₅₉	—	2	2	no	—
102	#106×C₅₉	—	4	1	no	—
103	C₄⋊C₈×C₅₉	—	2	2	no	—
104	C₄⋊C₈×C₅₉	—	4	1	no	—
105	C₂²⋊C₈×C₅₉	—	2	2	no	—
106	#95×C₅₉	—	2	1	no	—
107	#95×C₅₉	—	2	1	no	—
108	#95×C₅₉	—	2	1	no	—
109	#95×C₅₉	—	2	1	no	—
110	#95×C₅₉	—	2	1	no	—
111	#95×C₅₉	—	2	1	no	—
112	#95×C₅₉	—	2	1	no	—
113	#95×C₅₉	—	2	1	no	—
114	#95×C₅₉	—	2	1	no	—
115	#95×C₅₉	—	2	1	no	—
116	#95×C₅₉	D₄	1	1	yes	characteristic
117	#95×C₅₉	D₄	1	1	yes	characteristic
118	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₅₉	—	4	2	no	—
120	C₂×Q₈×C₅₉	—	4	2	no	—
121	C₂×Q₈×C₅₉	—	8	1	no	—
122	C₂²×C₄×C₅₉	—	2	1	no	—
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	1	no	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	—	2	4	no	—
130	C₂²×C₄×C₅₉	—	2	1	no	—
131	C₂²×C₄×C₅₉	—	2	1	no	—
132	C₂²×C₄×C₅₉	—	2	1	no	—
133	C₂²×C₄×C₅₉	—	2	1	no	—
134	C₂²×C₄×C₅₉	—	2	1	no	—
135	C₂²×C₄×C₅₉	—	8	1	no	—
136	C₂²×C₄×C₅₉	—	8	1	no	—
137	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
143	C₂²×C₄×C₅₉	#41	1	2	yes	—
144	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
145	M₁₆×C₅₉	—	4	4	no	—
146	C₂×C₈×C₅₉	—	2	1	no	—
147	C₂×C₈×C₅₉	—	2	1	no	—
148	C₂×C₈×C₅₉	—	2	1	no	—
149	C₂×C₈×C₅₉	—	2	1	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	1	no	—
154	C₂×C₈×C₅₉	—	2	1	no	—
155	C₂×C₈×C₅₉	—	2	1	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	#41	1	2	yes	—
158	C₄⋊C₄×C₅₉	—	2	4	no	—
159	C₄⋊C₄×C₅₉	—	2	1	no	—
160	C₄⋊C₄×C₅₉	—	2	1	no	—
161	C₄⋊C₄×C₅₉	—	2	1	no	—
162	C₄⋊C₄×C₅₉	—	2	1	no	—
163	C₄⋊C₄×C₅₉	—	2	1	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	1	no	—
168	C₄⋊C₄×C₅₉	—	2	1	no	—
169	C₄⋊C₄×C₅₉	—	2	1	no	—
170	C₄⋊C₄×C₅₉	—	2	1	no	—
171	C₄⋊C₄×C₅₉	—	2	1	no	—
172	C₄⋊C₄×C₅₉	—	4	2	no	—
173	C₄⋊C₄×C₅₉	—	4	2	no	—
174	C₄⋊C₄×C₅₉	—	8	1	no	—
175	C₄⋊C₄×C₅₉	—	8	1	no	—
176	C₄⋊C₄×C₅₉	—	8	1	no	—
177	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
178	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
179	C₄⋊C₄×C₅₉	#41	1	2	yes	—
180	C₂²⋊C₄×C₅₉	—	2	2	no	—
181	C₂²⋊C₄×C₅₉	—	4	1	no	—
182	C₂²⋊C₄×C₅₉	—	4	2	no	—
183	C₂²⋊C₄×C₅₉	—	4	2	no	—
184	C₂²⋊C₄×C₅₉	—	8	1	no	—
185	C₄²×C₅₉	—	2	1	no	—
186	C₄²×C₅₉	—	2	1	no	—
187	C₄²×C₅₉	—	2	1	no	—
188	C₄²×C₅₉	—	2	1	no	—
189	C₄²×C₅₉	—	4	2	no	—
190	C₄²×C₅₉	—	8	1	no	—
191	C₄²×C₅₉	—	8	1	no	—
192	C₂³×C₅₉	—	2	1	no	—
193	C₂³×C₅₉	—	2	1	no	—
194	C₂³×C₅₉	—	2	1	no	—
195	C₂³×C₅₉	—	2	1	no	—
196	C₂³×C₅₉	—	2	1	no	—
197	C₂³×C₅₉	—	2	1	no	—
198	C₂³×C₅₉	C₂²⋊Q₈	1	2	yes	—
199	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₅₉	—	8	4	no	—
201	C₂×C₄×C₅₉	—	2	1	no	—
202	C₂×C₄×C₅₉	—	2	1	no	—
203	C₂×C₄×C₅₉	—	2	1	no	—
204	C₂×C₄×C₅₉	—	2	1	no	—
205	C₂×C₄×C₅₉	—	2	2	no	—
206	C₂×C₄×C₅₉	—	2	2	no	—
207	C₂×C₄×C₅₉	—	2	2	no	—
208	C₂×C₄×C₅₉	—	2	2	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	2	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	2	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	—	2	1	no	—
218	C₂×C₄×C₅₉	—	2	1	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	4	1	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	1	no	—
224	C₂×C₄×C₅₉	—	4	1	no	—
225	C₂×C₄×C₅₉	—	4	1	no	—
226	C₂×C₄×C₅₉	—	4	1	no	—
227	C₂×C₄×C₅₉	—	4	1	no	—
228	C₂×C₄×C₅₉	—	4	1	no	—
229	C₂×C₄×C₅₉	—	4	1	no	—
230	C₂×C₄×C₅₉	—	4	1	no	—
231	C₂×C₄×C₅₉	—	4	1	no	—
232	C₂×C₄×C₅₉	—	4	1	no	—
233	C₂×C₄×C₅₉	—	4	1	no	—
234	C₂×C₄×C₅₉	—	4	1	no	—
235	C₂×C₄×C₅₉	—	4	1	no	—
236	C₂×C₄×C₅₉	—	4	1	no	—
237	C₂×C₄×C₅₉	—	4	1	no	—
238	C₂×C₄×C₅₉	—	4	1	no	—
239	C₂×C₄×C₅₉	—	4	1	no	—
240	C₂×C₄×C₅₉	—	4	1	no	—
241	C₂×C₄×C₅₉	—	4	1	no	—
242	C₂×C₄×C₅₉	—	8	4	no	—
243	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
244	C₂×C₄×C₅₉	#137	1	2	yes	—
245	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
246	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
251	C₈×C₅₉	—	2	2	no	—
252	C₈×C₅₉	—	4	1	no	—
253	C₈×C₅₉	—	4	1	no	—
254	C₈×C₅₉	—	4	1	no	—
255	#26008	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₅₉	—	2	2	no	—
257	C₂²×C₅₉	—	2	2	no	—
258	C₂²×C₅₉	—	2	2	no	—
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	—	4	1	no	—
262	C₂²×C₅₉	—	4	1	no	—
263	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂²×C₅₉	#546	1	1	yes	characteristic
265	C₂²×C₅₉	#547	1	1	yes	characteristic
266	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
267	C₂²×C₅₉	#575	1	1	yes	characteristic
268	C₂²×C₅₉	#576	1	1	yes	characteristic
269	C₂²×C₅₉	#577	1	1	yes	characteristic
270	C₄×C₅₉	—	2	2	no	—
271	C₄×C₅₉	—	2	2	no	—
272	C₄×C₅₉	—	4	2	no	—
273	C₄×C₅₉	—	4	2	no	—
274	C₄×C₅₉	—	4	1	no	—
275	C₄×C₅₉	—	4	1	no	—
276	C₄×C₅₉	—	4	2	no	—
277	C₄×C₅₉	—	4	1	no	—
278	C₄×C₅₉	—	8	1	no	—
279	C₄×C₅₉	—	8	1	no	—
280	C₄×C₅₉	—	8	1	no	—
281	C₄×C₅₉	—	8	1	no	—
282	C₄×C₅₉	—	8	1	no	—
283	C₄×C₅₉	#533	1	1	yes	characteristic
284	C₄×C₅₉	#544	1	1	yes	characteristic
285	C₄×C₅₉	#551	1	1	yes	characteristic
286	C₄×C₅₉	#552	1	1	yes	characteristic
287	#2439	C₂×C₅₉	1	1	yes	characteristic
288	#2345	C₂×C₅₉	1	1	yes	characteristic
289	#2101	C₂×C₅₉	1	1	yes	characteristic, complemented
290	#2087	C₂×C₅₉	1	1	yes	characteristic, complemented
291	#2086	C₂×C₅₉	1	1	yes	characteristic, complemented
292	#2058	C₂×C₅₉	1	1	yes	characteristic, complemented
293	#1988	C₂×C₅₉	1	1	yes	characteristic, complemented
294	#1949	C₂×C₅₉	1	1	yes	characteristic, complemented
295	#1921	C₂×C₅₉	1	1	yes	characteristic, complemented
296	#1920	C₂×C₅₉	1	1	yes	characteristic, complemented
297	#1854	C₂×C₅₉	1	1	yes	characteristic
298	#1851	C₂×C₅₉	1	1	yes	characteristic
299	#1823	C₂×C₅₉	1	1	yes	characteristic
300	#1809	C₂×C₅₉	1	1	yes	characteristic
301	#1736	C₂×C₅₉	1	1	yes	characteristic
302	C₂×C₅₉	—	4	2	no	—
303	C₂×C₅₉	#2438	1	1	yes	characteristic
304	C₂×C₅₉	#3078	1	1	yes	characteristic
305	C₂×C₅₉	#3081	1	1	yes	characteristic
306	C₂×C₅₉	#3314	1	1	yes	characteristic
307	C₂×C₅₉	#3326	1	1	yes	characteristic
308	C₂×C₅₉	#3347	1	1	yes	characteristic
309	C₂×C₅₉	#3356	1	1	yes	characteristic
310	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
311	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
312	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
313	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
314	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
315	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
316	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
317	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
318	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
320	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
321	#396	—	2	1	no	—
322	#393	—	2	1	no	—
323	#391	—	2	1	no	—
324	#389	C₂²×C₅₉	1	1	yes	characteristic
325	#389	C₂²×C₅₉	1	1	yes	characteristic
326	#389	C₂²×C₅₉	1	1	yes	characteristic
327	#389	C₂²×C₅₉	1	1	yes	characteristic
328	#387	—	2	1	no	—
329	#387	—	2	1	no	—
330	#387	—	2	1	no	—
331	#382	C₂²×C₅₉	1	1	yes	characteristic
332	#380	—	2	1	no	—
333	#380	C₂²×C₅₉	1	1	yes	characteristic
334	#380	C₂²×C₅₉	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
336	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
337	C₄×C₂²⋊C₄	—	2	1	no	—
338	C₄×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
339	#340	C₂²×C₅₉	1	1	yes	characteristic
340	#340	C₂²×C₅₉	1	1	yes	characteristic
341	#340	C₂²×C₅₉	1	1	yes	characteristic
342	#340	C₂²×C₅₉	1	1	yes	characteristic
343	#340	C₂²×C₅₉	1	1	yes	characteristic
344	#340	C₂²×C₅₉	1	1	yes	characteristic
345	#340	C₂²×C₅₉	1	1	yes	characteristic
346	#340	C₂²×C₅₉	1	1	yes	characteristic
347	#340	C₂²×C₅₉	1	1	yes	characteristic
348	#340	C₂²×C₅₉	1	1	yes	characteristic
349	#340	C₂²×C₅₉	1	1	yes	characteristic
350	#340	C₂²×C₅₉	1	1	yes	characteristic
351	#336	C₂²×C₅₉	1	1	yes	characteristic
352	#336	C₂²×C₅₉	1	1	yes	characteristic
353	C₅₉	#26008	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²×Q₈	—	2	1	no	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	4	1	no	—
360	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
361	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
362	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
364	C₄⋊Q₈	—	2	2	no	—
365	C₄⋊Q₈	—	4	1	no	—
366	#117	—	2	2	no	—
367	#117	—	4	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	Q₈×C₅₉	1	4	yes	complemented
376	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
394	#107	—	2	2	no	—
395	#107	—	4	1	no	—
396	#106	—	2	2	no	—
397	#106	—	4	1	no	—
398	C₄⋊C₈	—	2	2	no	—
399	C₄⋊C₈	—	4	1	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	#95	—	2	1	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	D₄×C₅₉	1	1	yes	characteristic
412	#95	D₄×C₅₉	1	1	yes	characteristic
413	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
414	C₂×Q₈	—	4	2	no	—
415	C₂×Q₈	—	4	2	no	—
416	C₂×Q₈	—	8	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	8	1	no	—
431	C₂²×C₄	—	8	1	no	—
432	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
437	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
438	C₂²×C₄	#41×C₅₉	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
440	M₁₆	—	4	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	#41×C₅₉	1	2	yes	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	8	1	no	—
470	C₄⋊C₄	—	8	1	no	—
471	C₄⋊C₄	—	8	1	no	—
472	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
473	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
474	C₄⋊C₄	#41×C₅₉	1	2	yes	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	8	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	4	2	no	—
485	C₄²	—	8	1	no	—
486	C₄²	—	8	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	2	1	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	1	no	—
493	C₂³	C₂²⋊Q₈×C₅₉	1	2	yes	—
494	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
495	Q₈	—	8	4	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	4	no	—
538	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
539	C₂×C₄	#137×C₅₉	1	2	yes	—
540	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
544	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
545	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
546	C₈	—	2	2	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
558	C₂²	C₅₉×#546	1	1	yes	characteristic
559	C₂²	C₅₉×#547	1	1	yes	characteristic
560	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
561	C₂²	C₅₉×#575	1	1	yes	characteristic
562	C₂²	C₅₉×#576	1	1	yes	characteristic
563	C₂²	C₅₉×#577	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₅₉×#533	1	1	yes	characteristic
578	C₄	C₅₉×#544	1	1	yes	characteristic
579	C₄	C₅₉×#551	1	1	yes	characteristic
580	C₄	C₅₉×#552	1	1	yes	characteristic
581	C₂	—	4	2	no	—
582	C₂	C₅₉×#2438	1	1	yes	characteristic
583	C₂	C₅₉×#3078	1	1	yes	characteristic
584	C₂	C₅₉×#3081	1	1	yes	characteristic
585	C₂	C₅₉×#3314	1	1	yes	characteristic
586	C₂	C₅₉×#3326	1	1	yes	characteristic
587	C₂	C₅₉×#3347	1	1	yes	characteristic
588	C₂	C₅₉×#3356	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₅₉×#2101	C₂	semidirect
4. C₅₉×#2087	C₂	semidirect
5. C₅₉×#2086	C₂	semidirect
6. C₅₉×#2058	C₂	semidirect
7. C₅₉×#1988	C₂	semidirect
8. C₅₉×#1949	C₂	semidirect
9. C₅₉×#1921	C₂	semidirect
10. C₅₉×#1920	C₂	semidirect
80. C₂×C₄⋊C₄×C₅₉	Q₈	semidirect
255. #26008	C₅₉	direct (N × H)
289. #2101	C₂×C₅₉	semidirect
290. #2087	C₂×C₅₉	semidirect
291. #2086	C₂×C₅₉	semidirect
292. #2058	C₂×C₅₉	semidirect
293. #1988	C₂×C₅₉	semidirect
294. #1949	C₂×C₅₉	semidirect
295. #1921	C₂×C₅₉	semidirect
296. #1920	C₂×C₅₉	semidirect
353. C₅₉	#26008	direct (N × H)
375. C₂×C₄⋊C₄	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2439	2
C₅₉×#2345	2
C₅₉×#2101	2
C₅₉×#2087	2
C₅₉×#2086	2
C₅₉×#2058	2
C₅₉×#1988	2
C₅₉×#1949	2
C₅₉×#1921	2
C₅₉×#1920	2
C₅₉×#1854	2
C₅₉×#1851	2
C₅₉×#1823	2
C₅₉×#1809	2
C₅₉×#1736	2
#26008	59

Subgroups — C59×#26008 #28438117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26008 #28438117