Subgroups — C₅₉×#25843 #28437952

Order 15104.

1046 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#478	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2058	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1864	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#1864	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#1862	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#1862	C₂	1	1	yes	maximal, characteristic
15	C₄×#102×C₅₉	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#554	—	2	4	no	—
17	C₅₉×#554	—	2	4	no	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
25	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₅₉	—	2	1	no	—
30	C₅₉×#499	—	2	4	no	—
31	C₅₉×#478	—	2	4	no	—
32	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
44	C₅₉×#398	—	2	1	no	—
45	C₅₉×#395	—	2	1	no	—
46	C₅₉×#389	—	2	1	no	—
47	C₅₉×#389	—	2	1	no	—
48	C₅₉×#389	C₂²	1	1	yes	characteristic
49	C₅₉×#389	C₂²	1	1	yes	characteristic
50	C₅₉×#389	C₂²	1	1	yes	characteristic
51	C₅₉×#389	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₅₉	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×#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	C₅₉×#336	C₂²	1	1	yes	characteristic
62	C₅₉×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₅₉	—	2	1	no	—
64	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅₉	—	2	1	no	—
67	C₂³×C₄×C₅₉	—	2	1	no	—
68	C₂³×C₄×C₅₉	—	2	1	no	—
69	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₅₉	—	2	2	no	—
74	C₄⋊Q₈×C₅₉	—	2	2	no	—
75	#125×C₅₉	—	2	2	no	—
76	#125×C₅₉	—	2	2	no	—
77	#125×C₅₉	—	2	2	no	—
78	#125×C₅₉	—	2	2	no	—
79	#125×C₅₉	—	2	2	no	—
80	#125×C₅₉	D₄	1	4	yes	—
81	C₂²⋊Q₈×C₅₉	—	2	8	no	—
82	C₂²⋊Q₈×C₅₉	—	2	8	no	—
83	C₂²⋊Q₈×C₅₉	—	2	8	no	—
84	C₄×Q₈×C₅₉	—	2	2	no	—
85	C₄×Q₈×C₅₉	—	2	2	no	—
86	C₄×D₄×C₅₉	—	2	2	no	—
87	C₄×D₄×C₅₉	—	2	2	no	—
88	C₄×D₄×C₅₉	—	2	2	no	—
89	C₄×D₄×C₅₉	—	2	2	no	—
90	C₄×D₄×C₅₉	—	2	2	no	—
91	C₄×D₄×C₅₉	D₄	1	4	yes	—
92	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
93	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
104	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
117	C₂×C₄²×C₅₉	—	2	1	no	—
118	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
121	#107×C₅₉	—	2	2	no	—
122	#107×C₅₉	—	2	2	no	—
123	#107×C₅₉	—	2	2	no	—
124	#106×C₅₉	—	2	2	no	—
125	#106×C₅₉	—	2	2	no	—
126	#106×C₅₉	—	2	2	no	—
127	C₄⋊C₈×C₅₉	—	2	2	no	—
128	#102×C₅₉	—	2	2	no	—
129	#102×C₅₉	—	2	2	no	—
130	#102×C₅₉	Q₈	1	4	yes	complemented
131	#102×C₅₉	Q₈	1	4	yes	complemented
132	C₄×C₈×C₅₉	—	2	2	no	—
133	#95×C₅₉	—	2	1	no	—
134	#95×C₅₉	—	2	1	no	—
135	#95×C₅₉	—	2	1	no	—
136	#95×C₅₉	—	2	1	no	—
137	#95×C₅₉	—	2	1	no	—
138	C₂⁴×C₅₉	—	2	1	no	—
139	C₂×Q₈×C₅₉	—	2	4	no	—
140	C₂×Q₈×C₅₉	—	2	2	no	—
141	C₂×Q₈×C₅₉	—	2	2	no	—
142	C₂×Q₈×C₅₉	—	4	1	no	—
143	C₂×Q₈×C₅₉	—	8	1	no	—
144	C₂×Q₈×C₅₉	—	8	1	no	—
145	C₂×D₄×C₅₉	—	2	1	no	—
146	C₂×D₄×C₅₉	—	2	1	no	—
147	C₂×D₄×C₅₉	—	2	1	no	—
148	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₅₉	C₂×Q₈	1	2	yes	—
150	C₂×D₄×C₅₉	C₂×Q₈	1	2	yes	—
151	C₂²×C₄×C₅₉	—	2	4	no	—
152	C₂²×C₄×C₅₉	—	2	1	no	—
153	C₂²×C₄×C₅₉	—	2	1	no	—
154	C₂²×C₄×C₅₉	—	2	1	no	—
155	C₂²×C₄×C₅₉	—	2	1	no	—
156	C₂²×C₄×C₅₉	—	2	1	no	—
157	C₂²×C₄×C₅₉	—	2	4	no	—
158	C₂²×C₄×C₅₉	—	2	4	no	—
159	C₂²×C₄×C₅₉	—	2	1	no	—
160	C₂²×C₄×C₅₉	—	2	1	no	—
161	C₂²×C₄×C₅₉	—	4	2	no	—
162	C₂²×C₄×C₅₉	—	4	2	no	—
163	C₂²×C₄×C₅₉	—	8	1	no	—
164	C₂²×C₄×C₅₉	—	8	1	no	—
165	C₂²×C₄×C₅₉	—	8	1	no	—
166	C₂²×C₄×C₅₉	—	8	1	no	—
167	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
174	C₂×C₈×C₅₉	—	2	1	no	—
175	C₂×C₈×C₅₉	—	2	1	no	—
176	C₂×C₈×C₅₉	—	2	1	no	—
177	C₂×C₈×C₅₉	—	2	1	no	—
178	C₂×C₈×C₅₉	—	2	1	no	—
179	C₂×C₈×C₅₉	—	2	1	no	—
180	C₂×C₈×C₅₉	—	2	1	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	C₂×Q₈	1	2	yes	—
185	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
186	C₄⋊C₄×C₅₉	—	2	4	no	—
187	C₄⋊C₄×C₅₉	—	2	4	no	—
188	C₄⋊C₄×C₅₉	—	2	4	no	—
189	C₄⋊C₄×C₅₉	—	2	2	no	—
190	C₄⋊C₄×C₅₉	—	2	4	no	—
191	C₄⋊C₄×C₅₉	—	2	4	no	—
192	C₄⋊C₄×C₅₉	—	2	2	no	—
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	—	2	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	—	8	1	no	—
208	C₄⋊C₄×C₅₉	—	8	1	no	—
209	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
210	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
211	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
213	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
214	C₂²⋊C₄×C₅₉	—	2	4	no	—
215	C₂²⋊C₄×C₅₉	—	2	4	no	—
216	C₂²⋊C₄×C₅₉	—	2	4	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	—	8	1	no	—
222	C₄²×C₅₉	C₂×D₄	1	2	yes	—
223	C₄²×C₅₉	C₂×D₄	1	2	yes	—
224	C₂³×C₅₉	—	2	2	no	—
225	C₂³×C₅₉	—	2	2	no	—
226	C₂³×C₅₉	—	2	2	no	—
227	C₂³×C₅₉	—	4	1	no	—
228	C₂³×C₅₉	—	4	1	no	—
229	C₂³×C₅₉	—	4	1	no	—
230	C₂³×C₅₉	—	4	1	no	—
231	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₅₉	—	4	4	no	—
233	Q₈×C₅₉	—	8	4	no	—
234	D₄×C₅₉	—	2	2	no	—
235	D₄×C₅₉	—	2	2	no	—
236	D₄×C₅₉	—	2	2	no	—
237	D₄×C₅₉	C₄⋊Q₈	1	4	yes	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	1	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	—	2	1	no	—
246	C₂×C₄×C₅₉	—	2	1	no	—
247	C₂×C₄×C₅₉	—	2	2	no	—
248	C₂×C₄×C₅₉	—	2	2	no	—
249	C₂×C₄×C₅₉	—	2	2	no	—
250	C₂×C₄×C₅₉	—	2	2	no	—
251	C₂×C₄×C₅₉	—	2	2	no	—
252	C₂×C₄×C₅₉	—	2	1	no	—
253	C₂×C₄×C₅₉	—	2	1	no	—
254	C₂×C₄×C₅₉	—	2	1	no	—
255	C₂×C₄×C₅₉	—	2	1	no	—
256	C₂×C₄×C₅₉	—	2	1	no	—
257	C₂×C₄×C₅₉	—	2	1	no	—
258	C₂×C₄×C₅₉	—	4	8	no	—
259	C₂×C₄×C₅₉	—	4	1	no	—
260	C₂×C₄×C₅₉	—	4	1	no	—
261	C₂×C₄×C₅₉	—	4	1	no	—
262	C₂×C₄×C₅₉	—	4	1	no	—
263	C₂×C₄×C₅₉	—	4	1	no	—
264	C₂×C₄×C₅₉	—	4	1	no	—
265	C₂×C₄×C₅₉	—	4	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	—	8	4	no	—
276	C₂×C₄×C₅₉	—	8	4	no	—
277	C₂×C₄×C₅₉	#120	1	2	yes	—
278	C₂×C₄×C₅₉	#120	1	2	yes	—
279	C₂×C₄×C₅₉	#135	1	2	yes	—
280	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
283	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
284	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
285	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
286	C₈×C₅₉	—	2	2	no	—
287	C₈×C₅₉	—	2	2	no	—
288	C₈×C₅₉	—	4	1	no	—
289	C₈×C₅₉	—	4	1	no	—
290	#25843	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
291	C₂²×C₅₉	—	2	4	no	—
292	C₂²×C₅₉	—	4	2	no	—
293	C₂²×C₅₉	—	4	2	no	—
294	C₂²×C₅₉	—	4	2	no	—
295	C₂²×C₅₉	—	4	2	no	—
296	C₂²×C₅₉	—	4	2	no	—
297	C₂²×C₅₉	—	4	2	no	—
298	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
299	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
300	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
301	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
302	C₂²×C₅₉	#575	1	1	yes	characteristic
303	C₂²×C₅₉	#576	1	1	yes	characteristic
304	C₂²×C₅₉	#577	1	1	yes	characteristic
305	C₄×C₅₉	—	2	2	no	—
306	C₄×C₅₉	—	2	2	no	—
307	C₄×C₅₉	—	2	2	no	—
308	C₄×C₅₉	—	4	2	no	—
309	C₄×C₅₉	—	4	2	no	—
310	C₄×C₅₉	—	4	1	no	—
311	C₄×C₅₉	—	4	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	—	8	1	no	—
317	C₄×C₅₉	—	8	1	no	—
318	C₄×C₅₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
319	C₄×C₅₉	#536	1	1	yes	characteristic
320	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
321	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
322	C₂×#554	C₂×C₅₉	1	1	yes	characteristic
323	C₂×#499	C₂×C₅₉	1	1	yes	characteristic, complemented
324	C₂×#478	C₂×C₅₉	1	1	yes	characteristic
325	#2584	C₂×C₅₉	1	1	yes	characteristic, complemented
326	#2059	C₂×C₅₉	1	1	yes	characteristic, complemented
327	#2059	C₂×C₅₉	1	1	yes	characteristic, complemented
328	#2058	C₂×C₅₉	1	1	yes	characteristic, complemented
329	#2057	C₂×C₅₉	1	1	yes	characteristic, complemented
330	#1989	C₂×C₅₉	1	1	yes	characteristic, complemented
331	#1984	C₂×C₅₉	1	1	yes	characteristic, complemented
332	#1864	C₂×C₅₉	1	1	yes	characteristic
333	#1864	C₂×C₅₉	1	1	yes	characteristic
334	#1862	C₂×C₅₉	1	1	yes	characteristic
335	#1862	C₂×C₅₉	1	1	yes	characteristic
336	C₄×#102	C₂×C₅₉	1	1	yes	characteristic
337	C₂×C₅₉	—	4	4	no	—
338	C₂×C₅₉	#2434	1	1	yes	characteristic
339	C₂×C₅₉	#3002	1	1	yes	characteristic
340	C₂×C₅₉	#3012	1	1	yes	characteristic
341	C₂×C₅₉	#3380	1	1	yes	characteristic
342	C₂×C₅₉	#3381	1	1	yes	characteristic
343	C₂×C₅₉	#3388	1	1	yes	characteristic
344	C₂×C₅₉	#3389	1	1	yes	characteristic
345	#554	—	2	4	no	—
346	#554	—	2	4	no	—
347	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
348	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
349	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
350	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	—	2	1	no	—
352	C₂×C₂²⋊Q₈	—	2	1	no	—
353	C₂×C₂²⋊Q₈	—	2	1	no	—
354	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
358	C₂²×C₄⋊C₄	—	2	1	no	—
359	#499	—	2	4	no	—
360	#478	—	2	4	no	—
361	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
362	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
363	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
364	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
365	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
367	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
368	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
369	C₂×#102	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×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
373	#398	—	2	1	no	—
374	#395	—	2	1	no	—
375	#389	—	2	1	no	—
376	#389	—	2	1	no	—
377	#389	C₂²×C₅₉	1	1	yes	characteristic
378	#389	C₂²×C₅₉	1	1	yes	characteristic
379	#389	C₂²×C₅₉	1	1	yes	characteristic
380	#389	C₂²×C₅₉	1	1	yes	characteristic
381	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
382	#340	C₂²×C₅₉	1	1	yes	characteristic
383	#340	C₂²×C₅₉	1	1	yes	characteristic
384	#340	C₂²×C₅₉	1	1	yes	characteristic
385	#340	C₂²×C₅₉	1	1	yes	characteristic
386	#340	C₂²×C₅₉	1	1	yes	characteristic
387	#340	C₂²×C₅₉	1	1	yes	characteristic
388	#336	C₂²×C₅₉	1	1	yes	characteristic
389	#336	C₂²×C₅₉	1	1	yes	characteristic
390	#336	C₂²×C₅₉	1	1	yes	characteristic
391	#336	C₂²×C₅₉	1	1	yes	characteristic
392	C₅₉	#25843	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²×Q₈	—	2	1	no	—
394	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	—	2	1	no	—
399	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
401	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	2	no	—
405	#125	—	2	2	no	—
406	#125	—	2	2	no	—
407	#125	—	2	2	no	—
408	#125	—	2	2	no	—
409	#125	—	2	2	no	—
410	#125	D₄×C₅₉	1	4	yes	—
411	C₂²⋊Q₈	—	2	8	no	—
412	C₂²⋊Q₈	—	2	8	no	—
413	C₂²⋊Q₈	—	2	8	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	D₄×C₅₉	1	4	yes	—
422	C₂×C₄⋊C₄	—	2	8	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	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	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₄²	—	2	1	no	—
448	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
451	#107	—	2	2	no	—
452	#107	—	2	2	no	—
453	#107	—	2	2	no	—
454	#106	—	2	2	no	—
455	#106	—	2	2	no	—
456	#106	—	2	2	no	—
457	C₄⋊C₈	—	2	2	no	—
458	#102	—	2	2	no	—
459	#102	—	2	2	no	—
460	#102	Q₈×C₅₉	1	4	yes	complemented
461	#102	Q₈×C₅₉	1	4	yes	complemented
462	C₄×C₈	—	2	2	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	C₂⁴	—	2	1	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	4	1	no	—
473	C₂×Q₈	—	8	1	no	—
474	C₂×Q₈	—	8	1	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
479	C₂×D₄	C₂×Q₈×C₅₉	1	2	yes	—
480	C₂×D₄	C₂×Q₈×C₅₉	1	2	yes	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	8	1	no	—
494	C₂²×C₄	—	8	1	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	—
515	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	—
516	C₄⋊C₄	—	2	4	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	2	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	2	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	8	1	no	—
538	C₄⋊C₄	—	8	1	no	—
539	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
540	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
541	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
542	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
543	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	8	1	no	—
552	C₄²	C₂×D₄×C₅₉	1	2	yes	—
553	C₄²	C₂×D₄×C₅₉	1	2	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
562	Q₈	—	4	4	no	—
563	Q₈	—	8	4	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	2	no	—
567	D₄	C₄⋊Q₈×C₅₉	1	4	yes	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	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	—	4	8	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	8	4	no	—
606	C₂×C₄	—	8	4	no	—
607	C₂×C₄	#120×C₅₉	1	2	yes	—
608	C₂×C₄	#120×C₅₉	1	2	yes	—
609	C₂×C₄	#135×C₅₉	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
611	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
612	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
613	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
614	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
615	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
616	C₈	—	2	2	no	—
617	C₈	—	2	2	no	—
618	C₈	—	4	1	no	—
619	C₈	—	4	1	no	—
620	C₂²	—	2	4	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
628	C₂²	D₄×Q₈×C₅₉	1	1	yes	characteristic
629	C₂²	D₄×Q₈×C₅₉	1	1	yes	characteristic
630	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
631	C₂²	C₅₉×#575	1	1	yes	characteristic
632	C₂²	C₅₉×#576	1	1	yes	characteristic
633	C₂²	C₅₉×#577	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	8	1	no	—
646	C₄	—	8	1	no	—
647	C₄	C₂×C₄⋊Q₈×C₅₉	1	1	yes	characteristic
648	C₄	C₅₉×#536	1	1	yes	characteristic
649	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
650	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
651	C₂	—	4	4	no	—
652	C₂	C₅₉×#2434	1	1	yes	characteristic
653	C₂	C₅₉×#3002	1	1	yes	characteristic
654	C₂	C₅₉×#3012	1	1	yes	characteristic
655	C₂	C₅₉×#3380	1	1	yes	characteristic
656	C₂	C₅₉×#3381	1	1	yes	characteristic
657	C₂	C₅₉×#3388	1	1	yes	characteristic
658	C₂	C₅₉×#3389	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 ◁ C₂×C₄×Q₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#499	C₂	semidirect
4. C₅₉×#2584	C₂	semidirect
5. C₅₉×#2059	C₂	semidirect
6. C₅₉×#2059	C₂	semidirect
7. C₅₉×#2058	C₂	semidirect
8. C₅₉×#2057	C₂	semidirect
9. C₅₉×#1989	C₂	semidirect
10. C₅₉×#1984	C₂	semidirect
130. #102×C₅₉	Q₈	semidirect
131. #102×C₅₉	Q₈	semidirect
290. #25843	C₅₉	direct (N × H)
323. C₂×#499	C₂×C₅₉	semidirect
325. #2584	C₂×C₅₉	semidirect
326. #2059	C₂×C₅₉	semidirect
327. #2059	C₂×C₅₉	semidirect
328. #2058	C₂×C₅₉	semidirect
329. #2057	C₂×C₅₉	semidirect
330. #1989	C₂×C₅₉	semidirect
331. #1984	C₂×C₅₉	semidirect
392. C₅₉	#25843	direct (N × H)
460. #102	Q₈×C₅₉	semidirect
461. #102	Q₈×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×#554	2
C₂×C₅₉×#499	2
C₂×C₅₉×#478	2
C₅₉×#2584	2
C₅₉×#2059	2
C₅₉×#2058	2
C₅₉×#2057	2
C₅₉×#1989	2
C₅₉×#1984	2
C₅₉×#1864	2
C₅₉×#1862	2
C₄×#102×C₅₉	2
#25843	59

Subgroups — C59×#25843 #28437952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25843 #28437952