Subgroups — C₅₉×#24311 #28436420

Order 15104.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#544	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2323	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2024	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1989	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1873	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#1872	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#1854	C₂	1	1	yes	maximal, characteristic
14	C₅₉×#1852	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1798	C₂	1	1	yes	maximal, characteristic
16	C₅₉×#544	—	2	4	no	—
17	C₅₉×#544	—	2	4	no	—
18	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
19	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×#125×C₅₉	—	2	1	no	—
22	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
25	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#479	—	2	4	no	—
32	C₅₉×#477	—	2	4	no	—
33	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#391	C₂²	1	1	yes	characteristic
46	C₅₉×#389	—	2	1	no	—
47	C₅₉×#389	C₂²	1	1	yes	characteristic
48	C₅₉×#388	—	2	1	no	—
49	C₅₉×#388	—	2	1	no	—
50	C₅₉×#387	—	2	1	no	—
51	C₅₉×#380	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×#340	C₂²	1	1	yes	characteristic
60	C₅₉×#340	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	—	2	1	no	—
65	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₅₉	—	2	1	no	—
67	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₅₉	—	2	8	no	—
73	C₄⋊Q₈×C₅₉	—	2	2	no	—
74	C₄⋊Q₈×C₅₉	—	2	2	no	—
75	C₄⋊Q₈×C₅₉	—	2	2	no	—
76	C₄⋊Q₈×C₅₉	D₄	1	4	yes	—
77	#125×C₅₉	—	2	8	no	—
78	#125×C₅₉	—	2	2	no	—
79	#125×C₅₉	—	2	2	no	—
80	#125×C₅₉	—	2	2	no	—
81	#125×C₅₉	D₄	1	4	yes	—
82	C₂²⋊Q₈×C₅₉	—	2	8	no	—
83	C₂²⋊Q₈×C₅₉	—	2	8	no	—
84	C₂²⋊Q₈×C₅₉	—	2	2	no	—
85	C₂²⋊Q₈×C₅₉	Q₈	1	4	yes	complemented
86	C₄×Q₈×C₅₉	—	2	2	no	—
87	C₄×Q₈×C₅₉	—	2	2	no	—
88	#117×C₅₉	—	2	2	no	—
89	#117×C₅₉	—	2	2	no	—
90	#117×C₅₉	—	2	2	no	—
91	#117×C₅₉	—	2	2	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	—	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	2	no	—
101	C₂×C₄⋊C₄×C₅₉	—	2	2	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	C₂³	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×C₂²⋊C₄×C₅₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
116	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅₉	—	2	1	no	—
119	C₂×C₄²×C₅₉	—	2	1	no	—
120	C₂×C₄²×C₅₉	—	2	1	no	—
121	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
123	#107×C₅₉	—	2	2	no	—
124	#107×C₅₉	—	2	2	no	—
125	#107×C₅₉	—	2	2	no	—
126	#106×C₅₉	—	2	2	no	—
127	C₄⋊C₈×C₅₉	—	2	2	no	—
128	C₄⋊C₈×C₅₉	—	2	2	no	—
129	#103×C₅₉	—	2	2	no	—
130	#103×C₅₉	—	2	2	no	—
131	#103×C₅₉	—	2	2	no	—
132	#103×C₅₉	—	2	2	no	—
133	C₂²⋊C₈×C₅₉	—	2	2	no	—
134	C₂²⋊C₈×C₅₉	—	2	2	no	—
135	#95×C₅₉	—	2	1	no	—
136	#95×C₅₉	—	2	1	no	—
137	#95×C₅₉	—	2	1	no	—
138	#95×C₅₉	—	2	1	no	—
139	#95×C₅₉	—	2	1	no	—
140	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Q₈×C₅₉	—	2	4	no	—
142	C₂×Q₈×C₅₉	—	2	4	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	—	8	1	no	—
149	C₂×Q₈×C₅₉	—	8	1	no	—
150	C₂×Q₈×C₅₉	—	8	1	no	—
151	C₂×Q₈×C₅₉	—	8	1	no	—
152	C₂×Q₈×C₅₉	C₂×Q₈	1	2	yes	—
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	1	no	—
158	C₂²×C₄×C₅₉	—	2	1	no	—
159	C₂²×C₄×C₅₉	—	2	1	no	—
160	C₂²×C₄×C₅₉	—	2	1	no	—
161	C₂²×C₄×C₅₉	—	2	1	no	—
162	C₂²×C₄×C₅₉	—	2	1	no	—
163	C₂²×C₄×C₅₉	—	2	4	no	—
164	C₂²×C₄×C₅₉	—	2	1	no	—
165	C₂²×C₄×C₅₉	—	2	1	no	—
166	C₂²×C₄×C₅₉	—	8	1	no	—
167	C₂²×C₄×C₅₉	—	8	1	no	—
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	C₂×Q₈	1	2	yes	—
174	C₂²×C₄×C₅₉	#41	1	2	yes	—
175	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
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	—	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	C₄⋊C₄×C₅₉	—	2	4	no	—
189	C₄⋊C₄×C₅₉	—	2	4	no	—
190	C₄⋊C₄×C₅₉	—	2	4	no	—
191	C₄⋊C₄×C₅₉	—	2	4	no	—
192	C₄⋊C₄×C₅₉	—	2	4	no	—
193	C₄⋊C₄×C₅₉	—	2	4	no	—
194	C₄⋊C₄×C₅₉	—	2	4	no	—
195	C₄⋊C₄×C₅₉	—	2	2	no	—
196	C₄⋊C₄×C₅₉	—	2	2	no	—
197	C₄⋊C₄×C₅₉	—	2	4	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	—	2	1	no	—
204	C₄⋊C₄×C₅₉	—	2	1	no	—
205	C₄⋊C₄×C₅₉	—	2	1	no	—
206	C₄⋊C₄×C₅₉	—	2	1	no	—
207	C₄⋊C₄×C₅₉	—	4	2	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×D₄	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	2	no	—
217	C₂²⋊C₄×C₅₉	—	2	2	no	—
218	C₂²⋊C₄×C₅₉	—	8	1	no	—
219	C₄²×C₅₉	—	2	4	no	—
220	C₄²×C₅₉	—	2	1	no	—
221	C₄²×C₅₉	—	2	1	no	—
222	C₄²×C₅₉	—	4	2	no	—
223	C₄²×C₅₉	—	8	1	no	—
224	C₄²×C₅₉	C₂×D₄	1	2	yes	—
225	C₄²×C₅₉	C₂×D₄	1	2	yes	—
226	C₂³×C₅₉	—	2	1	no	—
227	C₂³×C₅₉	—	2	1	no	—
228	C₂³×C₅₉	—	2	1	no	—
229	C₂³×C₅₉	—	2	1	no	—
230	C₂³×C₅₉	—	2	1	no	—
231	C₂³×C₅₉	—	2	1	no	—
232	C₂³×C₅₉	C₂²⋊Q₈	1	2	yes	—
233	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₅₉	—	2	2	no	—
235	Q₈×C₅₉	—	2	2	no	—
236	Q₈×C₅₉	—	4	1	no	—
237	Q₈×C₅₉	—	4	1	no	—
238	Q₈×C₅₉	—	8	4	no	—
239	Q₈×C₅₉	—	8	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	—	2	1	no	—
246	C₂×C₄×C₅₉	—	2	2	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	1	no	—
251	C₂×C₄×C₅₉	—	2	2	no	—
252	C₂×C₄×C₅₉	—	2	1	no	—
253	C₂×C₄×C₅₉	—	2	2	no	—
254	C₂×C₄×C₅₉	—	2	2	no	—
255	C₂×C₄×C₅₉	—	2	2	no	—
256	C₂×C₄×C₅₉	—	2	2	no	—
257	C₂×C₄×C₅₉	—	2	2	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	—	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	—	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	—	8	4	no	—
281	C₂×C₄×C₅₉	#120	1	2	yes	—
282	C₂×C₄×C₅₉	#120	1	2	yes	—
283	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
284	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
287	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
289	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
290	C₈×C₅₉	—	4	1	no	—
291	C₈×C₅₉	—	4	1	no	—
292	C₈×C₅₉	—	4	1	no	—
293	C₈×C₅₉	—	4	1	no	—
294	#24311	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂²×C₅₉	—	2	2	no	—
296	C₂²×C₅₉	—	2	2	no	—
297	C₂²×C₅₉	—	2	2	no	—
298	C₂²×C₅₉	—	4	1	no	—
299	C₂²×C₅₉	—	4	1	no	—
300	C₂²×C₅₉	—	4	1	no	—
301	C₂²×C₅₉	—	4	1	no	—
302	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
303	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₅₉	#536	1	1	yes	characteristic
305	C₂²×C₅₉	#576	1	1	yes	characteristic
306	C₂²×C₅₉	#577	1	1	yes	characteristic
307	C₂²×C₅₉	#578	1	1	yes	characteristic
308	C₂²×C₅₉	#578	1	1	yes	characteristic
309	C₄×C₅₉	—	2	2	no	—
310	C₄×C₅₉	—	2	2	no	—
311	C₄×C₅₉	—	2	2	no	—
312	C₄×C₅₉	—	4	2	no	—
313	C₄×C₅₉	—	4	2	no	—
314	C₄×C₅₉	—	4	1	no	—
315	C₄×C₅₉	—	4	2	no	—
316	C₄×C₅₉	—	4	1	no	—
317	C₄×C₅₉	—	4	2	no	—
318	C₄×C₅₉	—	4	2	no	—
319	C₄×C₅₉	—	4	2	no	—
320	C₄×C₅₉	—	8	1	no	—
321	C₄×C₅₉	—	8	1	no	—
322	C₄×C₅₉	#548	1	1	yes	characteristic
323	C₄×C₅₉	#548	1	1	yes	characteristic
324	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
325	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
326	C₂×#544	C₂×C₅₉	1	1	yes	characteristic
327	C₂×#479	C₂×C₅₉	1	1	yes	characteristic, complemented
328	C₂×#477	C₂×C₅₉	1	1	yes	characteristic, complemented
329	#2323	C₂×C₅₉	1	1	yes	characteristic
330	#2059	C₂×C₅₉	1	1	yes	characteristic, complemented
331	#2057	C₂×C₅₉	1	1	yes	characteristic, complemented
332	#2026	C₂×C₅₉	1	1	yes	characteristic, complemented
333	#2024	C₂×C₅₉	1	1	yes	characteristic, complemented
334	#1989	C₂×C₅₉	1	1	yes	characteristic, complemented
335	#1988	C₂×C₅₉	1	1	yes	characteristic, complemented
336	#1873	C₂×C₅₉	1	1	yes	characteristic
337	#1872	C₂×C₅₉	1	1	yes	characteristic
338	#1854	C₂×C₅₉	1	1	yes	characteristic
339	#1852	C₂×C₅₉	1	1	yes	characteristic
340	#1798	C₂×C₅₉	1	1	yes	characteristic
341	C₂×C₅₉	—	4	2	no	—
342	C₂×C₅₉	#2409	1	1	yes	characteristic
343	C₂×C₅₉	#3011	1	1	yes	characteristic
344	C₂×C₅₉	#3012	1	1	yes	characteristic
345	C₂×C₅₉	#3082	1	1	yes	characteristic
346	C₂×C₅₉	#3083	1	1	yes	characteristic
347	C₂×C₅₉	#3242	1	1	yes	characteristic
348	C₂×C₅₉	#3243	1	1	yes	characteristic
349	#544	—	2	4	no	—
350	#544	—	2	4	no	—
351	C₂×C₄⋊Q₈	—	2	1	no	—
352	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
353	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
354	C₂×#125	—	2	1	no	—
355	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
356	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	—	2	1	no	—
358	C₂×C₂²⋊Q₈	—	2	1	no	—
359	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
361	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
362	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
364	#479	—	2	4	no	—
365	#477	—	2	4	no	—
366	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
367	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
368	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
369	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
370	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
371	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
374	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
375	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
376	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
378	#391	C₂²×C₅₉	1	1	yes	characteristic
379	#389	—	2	1	no	—
380	#389	C₂²×C₅₉	1	1	yes	characteristic
381	#388	—	2	1	no	—
382	#388	—	2	1	no	—
383	#387	—	2	1	no	—
384	#380	C₂²×C₅₉	1	1	yes	characteristic
385	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
386	#340	C₂²×C₅₉	1	1	yes	characteristic
387	#340	C₂²×C₅₉	1	1	yes	characteristic
388	#340	C₂²×C₅₉	1	1	yes	characteristic
389	#340	C₂²×C₅₉	1	1	yes	characteristic
390	#340	C₂²×C₅₉	1	1	yes	characteristic
391	#340	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	#24311	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²×Q₈	—	2	1	no	—
398	C₂²×Q₈	—	2	1	no	—
399	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
402	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
403	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
406	C₄⋊Q₈	—	2	8	no	—
407	C₄⋊Q₈	—	2	2	no	—
408	C₄⋊Q₈	—	2	2	no	—
409	C₄⋊Q₈	—	2	2	no	—
410	C₄⋊Q₈	D₄×C₅₉	1	4	yes	—
411	#125	—	2	8	no	—
412	#125	—	2	2	no	—
413	#125	—	2	2	no	—
414	#125	—	2	2	no	—
415	#125	D₄×C₅₉	1	4	yes	—
416	C₂²⋊Q₈	—	2	8	no	—
417	C₂²⋊Q₈	—	2	8	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	Q₈×C₅₉	1	4	yes	complemented
420	C₄×Q₈	—	2	2	no	—
421	C₄×Q₈	—	2	2	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	—	2	2	no	—
425	#117	—	2	2	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	—	2	2	no	—
435	C₂×C₄⋊C₄	—	2	2	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₂²⋊C₄	—	2	1	no	—
450	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	D₄×C₅₉	1	1	yes	characteristic
452	C₂×C₄²	—	2	1	no	—
453	C₂×C₄²	—	2	1	no	—
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
457	#107	—	2	2	no	—
458	#107	—	2	2	no	—
459	#107	—	2	2	no	—
460	#106	—	2	2	no	—
461	C₄⋊C₈	—	2	2	no	—
462	C₄⋊C₈	—	2	2	no	—
463	#103	—	2	2	no	—
464	#103	—	2	2	no	—
465	#103	—	2	2	no	—
466	#103	—	2	2	no	—
467	C₂²⋊C₈	—	2	2	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	—	2	4	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	—	8	1	no	—
483	C₂×Q₈	—	8	1	no	—
484	C₂×Q₈	—	8	1	no	—
485	C₂×Q₈	—	8	1	no	—
486	C₂×Q₈	C₂×Q₈×C₅₉	1	2	yes	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	8	1	no	—
501	C₂²×C₄	—	8	1	no	—
502	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
507	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
508	C₂²×C₄	#41×C₅₉	1	2	yes	—
509	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
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	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	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	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	2	4	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	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
544	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
545	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
546	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
547	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₄²	—	2	4	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	4	2	no	—
557	C₄²	—	8	1	no	—
558	C₄²	C₂×D₄×C₅₉	1	2	yes	—
559	C₄²	C₂×D₄×C₅₉	1	2	yes	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	C₂²⋊Q₈×C₅₉	1	2	yes	—
567	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	8	4	no	—
573	Q₈	—	8	4	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	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	—	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	—	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	—	8	4	no	—
615	C₂×C₄	#120×C₅₉	1	2	yes	—
616	C₂×C₄	#120×C₅₉	1	2	yes	—
617	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
618	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
619	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
620	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
621	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
622	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
623	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
624	C₈	—	4	1	no	—
625	C₈	—	4	1	no	—
626	C₈	—	4	1	no	—
627	C₈	—	4	1	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
636	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
637	C₂²	C₅₉×#536	1	1	yes	characteristic
638	C₂²	C₅₉×#576	1	1	yes	characteristic
639	C₂²	C₅₉×#577	1	1	yes	characteristic
640	C₂²	C₅₉×#578	1	1	yes	characteristic
641	C₂²	C₅₉×#578	1	1	yes	characteristic
642	C₄	—	2	2	no	—
643	C₄	—	2	2	no	—
644	C₄	—	2	2	no	—
645	C₄	—	4	1	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	2	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	8	1	no	—
654	C₄	—	8	1	no	—
655	C₄	C₅₉×#548	1	1	yes	characteristic
656	C₄	C₅₉×#548	1	1	yes	characteristic
657	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
658	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
659	C₂	—	4	2	no	—
660	C₂	C₅₉×#2409	1	1	yes	characteristic
661	C₂	C₅₉×#3011	1	1	yes	characteristic
662	C₂	C₅₉×#3012	1	1	yes	characteristic
663	C₂	C₅₉×#3082	1	1	yes	characteristic
664	C₂	C₅₉×#3083	1	1	yes	characteristic
665	C₂	C₅₉×#3242	1	1	yes	characteristic
666	C₂	C₅₉×#3243	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 ◁ C₂×#117×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#479	C₂	semidirect
3. C₂×C₅₉×#477	C₂	semidirect
5. C₅₉×#2059	C₂	semidirect
6. C₅₉×#2057	C₂	semidirect
7. C₅₉×#2026	C₂	semidirect
8. C₅₉×#2024	C₂	semidirect
9. C₅₉×#1989	C₂	semidirect
10. C₅₉×#1988	C₂	semidirect
85. C₂²⋊Q₈×C₅₉	Q₈	semidirect
294. #24311	C₅₉	direct (N × H)
327. C₂×#479	C₂×C₅₉	semidirect
328. C₂×#477	C₂×C₅₉	semidirect
330. #2059	C₂×C₅₉	semidirect
331. #2057	C₂×C₅₉	semidirect
332. #2026	C₂×C₅₉	semidirect
333. #2024	C₂×C₅₉	semidirect
334. #1989	C₂×C₅₉	semidirect
335. #1988	C₂×C₅₉	semidirect
396. C₅₉	#24311	direct (N × H)
419. C₂²⋊Q₈	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×#544	2
C₂×C₅₉×#479	2
C₂×C₅₉×#477	2
C₅₉×#2323	2
C₅₉×#2059	2
C₅₉×#2057	2
C₅₉×#2026	2
C₅₉×#2024	2
C₅₉×#1989	2
C₅₉×#1988	2
C₅₉×#1873	2
C₅₉×#1872	2
C₅₉×#1854	2
C₅₉×#1852	2
C₅₉×#1798	2
#24311	59

Subgroups — C59×#24311 #28436420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24311 #28436420