Subgroups — C₅₉×#24239 #28436348

Order 15104.

1490 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#448	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2537	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#2035	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2000	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1787	C₂	1	2	yes	maximal, complemented
12	C₂³×Q₈×C₅₉	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	D₄×Q₈×C₅₉	—	2	4	no	—
16	D₄×Q₈×C₅₉	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₅₉	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
21	C₂×#121×C₅₉	—	2	1	no	—
22	C₂×#121×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₅₉	—	2	1	no	—
25	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#461	—	2	4	no	—
28	C₅₉×#448	—	2	8	no	—
29	C₄×SD₁₆×C₅₉	—	2	4	no	—
30	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₅₉	C₂²	1	2	yes	—
33	C₂×#103×C₅₉	C₂²	1	2	yes	—
34	C₂×#103×C₅₉	C₂²	1	2	yes	—
35	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₅₉	C₂²	1	2	yes	—
37	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#394	—	2	2	no	—
42	C₅₉×#384	C₂²	1	1	yes	characteristic
43	C₅₉×#380	—	2	1	no	—
44	C₅₉×#380	C₂²	1	2	yes	—
45	C₅₉×#340	C₂²	1	2	yes	—
46	C₂²×Q₈×C₅₉	—	2	4	no	—
47	C₂²×Q₈×C₅₉	—	2	4	no	—
48	C₂²×Q₈×C₅₉	—	2	2	no	—
49	C₂²×Q₈×C₅₉	—	2	4	no	—
50	C₂²×Q₈×C₅₉	—	2	4	no	—
51	C₂²×Q₈×C₅₉	—	4	2	no	—
52	C₂²×Q₈×C₅₉	—	4	2	no	—
53	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
54	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₅₉	—	2	2	no	—
56	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₅₉	—	2	2	no	—
59	C₂³×C₄×C₅₉	—	2	1	no	—
60	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
61	C₂×SD₁₆×C₅₉	—	2	2	no	—
62	C₂×SD₁₆×C₅₉	—	2	2	no	—
63	C₂×SD₁₆×C₅₉	—	2	4	no	—
64	C₂×SD₁₆×C₅₉	—	2	4	no	—
65	C₂×SD₁₆×C₅₉	—	4	2	no	—
66	C₂×SD₁₆×C₅₉	D₄	1	4	yes	complemented
67	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₄⋊Q₈×C₅₉	—	2	8	no	—
71	C₄⋊Q₈×C₅₉	—	2	2	no	—
72	C₄⋊Q₈×C₅₉	D₄	1	4	yes	complemented
73	C₂²⋊Q₈×C₅₉	—	2	16	no	—
74	C₂²⋊Q₈×C₅₉	—	2	4	no	—
75	C₂²⋊Q₈×C₅₉	—	2	4	no	—
76	#121×C₅₉	—	2	4	no	—
77	#121×C₅₉	—	4	2	no	—
78	#121×C₅₉	—	4	4	no	—
79	C₄×Q₈×C₅₉	—	2	2	no	—
80	C₄×Q₈×C₅₉	D₄	1	4	yes	complemented
81	C₄×D₄×C₅₉	—	2	8	no	—
82	C₄×D₄×C₅₉	—	2	2	no	—
83	C₄×D₄×C₅₉	—	2	2	no	—
84	C₄×D₄×C₅₉	—	2	2	no	—
85	C₄×D₄×C₅₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₅₉	D₄	1	2	yes	—
101	C₂×C₄²×C₅₉	—	2	1	no	—
102	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
103	#106×C₅₉	—	2	2	no	—
104	C₄⋊C₈×C₅₉	—	2	2	no	—
105	#103×C₅₉	—	2	2	no	—
106	#103×C₅₉	—	2	4	no	—
107	#103×C₅₉	—	2	4	no	—
108	#103×C₅₉	—	2	4	no	—
109	#103×C₅₉	—	4	2	no	—
110	#102×C₅₉	—	2	2	no	—
111	C₂²⋊C₈×C₅₉	—	2	4	no	—
112	C₂²⋊C₈×C₅₉	—	4	2	no	—
113	C₄×C₈×C₅₉	—	2	2	no	—
114	#95×C₅₉	—	2	2	no	—
115	C₂⁴×C₅₉	—	2	1	no	—
116	C₂⁴×C₅₉	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₅₉	—	2	8	no	—
118	C₂×Q₈×C₅₉	—	2	1	no	—
119	C₂×Q₈×C₅₉	—	2	2	no	—
120	C₂×Q₈×C₅₉	—	2	1	no	—
121	C₂×Q₈×C₅₉	—	2	1	no	—
122	C₂×Q₈×C₅₉	—	2	2	no	—
123	C₂×Q₈×C₅₉	—	2	2	no	—
124	C₂×Q₈×C₅₉	—	2	2	no	—
125	C₂×Q₈×C₅₉	—	2	2	no	—
126	C₂×Q₈×C₅₉	—	4	4	no	—
127	C₂×Q₈×C₅₉	—	4	4	no	—
128	C₂×Q₈×C₅₉	—	4	8	no	—
129	C₂×Q₈×C₅₉	—	4	8	no	—
130	C₂×Q₈×C₅₉	—	4	8	no	—
131	C₂×Q₈×C₅₉	—	4	8	no	—
132	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
133	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₅₉	#41	1	2	yes	—
136	C₂×D₄×C₅₉	—	2	2	no	—
137	C₂×D₄×C₅₉	—	2	2	no	—
138	C₂×D₄×C₅₉	—	2	1	no	—
139	C₂×D₄×C₅₉	—	2	1	no	—
140	C₂×D₄×C₅₉	—	2	1	no	—
141	C₂×D₄×C₅₉	—	2	1	no	—
142	C₂×D₄×C₅₉	—	2	1	no	—
143	C₂×D₄×C₅₉	—	4	4	no	—
144	C₂×D₄×C₅₉	—	4	4	no	—
145	C₂×D₄×C₅₉	—	8	2	no	—
146	C₂×D₄×C₅₉	SD₁₆	1	4	yes	complemented
147	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₅₉	—	2	1	no	—
149	C₂²×C₄×C₅₉	—	2	8	no	—
150	C₂²×C₄×C₅₉	—	2	1	no	—
151	C₂²×C₄×C₅₉	—	2	2	no	—
152	C₂²×C₄×C₅₉	—	2	2	no	—
153	C₂²×C₄×C₅₉	—	2	2	no	—
154	C₂²×C₄×C₅₉	—	2	2	no	—
155	C₂²×C₄×C₅₉	—	2	2	no	—
156	C₂²×C₄×C₅₉	—	2	2	no	—
157	C₂²×C₄×C₅₉	—	2	2	no	—
158	C₂²×C₄×C₅₉	—	2	1	no	—
159	C₂²×C₄×C₅₉	—	2	2	no	—
160	C₂²×C₄×C₅₉	—	4	4	no	—
161	C₂²×C₄×C₅₉	—	4	4	no	—
162	C₂²×C₄×C₅₉	—	4	2	no	—
163	C₂²×C₄×C₅₉	—	4	2	no	—
164	C₂²×C₄×C₅₉	—	4	2	no	—
165	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
169	SD₁₆×C₅₉	—	2	8	no	—
170	SD₁₆×C₅₉	—	4	8	no	—
171	C₂×C₈×C₅₉	—	2	1	no	—
172	C₂×C₈×C₅₉	—	2	1	no	—
173	C₂×C₈×C₅₉	—	2	1	no	—
174	C₂×C₈×C₅₉	—	2	2	no	—
175	C₂×C₈×C₅₉	—	2	2	no	—
176	C₂×C₈×C₅₉	—	2	1	no	—
177	C₂×C₈×C₅₉	—	2	2	no	—
178	C₂×C₈×C₅₉	—	2	1	no	—
179	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₅₉	—	2	8	no	—
181	C₄⋊C₄×C₅₉	—	2	4	no	—
182	C₄⋊C₄×C₅₉	—	2	4	no	—
183	C₄⋊C₄×C₅₉	—	2	4	no	—
184	C₄⋊C₄×C₅₉	—	2	2	no	—
185	C₄⋊C₄×C₅₉	—	2	1	no	—
186	C₄⋊C₄×C₅₉	—	2	1	no	—
187	C₄⋊C₄×C₅₉	—	2	2	no	—
188	C₄⋊C₄×C₅₉	—	2	1	no	—
189	C₄⋊C₄×C₅₉	—	2	2	no	—
190	C₄⋊C₄×C₅₉	—	4	2	no	—
191	C₄⋊C₄×C₅₉	—	8	1	no	—
192	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
193	C₂²⋊C₄×C₅₉	—	2	8	no	—
194	C₂²⋊C₄×C₅₉	—	2	4	no	—
195	C₂²⋊C₄×C₅₉	—	4	4	no	—
196	C₂²⋊C₄×C₅₉	—	4	4	no	—
197	C₂²⋊C₄×C₅₉	—	4	2	no	—
198	C₄²×C₅₉	—	2	4	no	—
199	C₄²×C₅₉	C₂×D₄	1	2	yes	—
200	C₄²×C₅₉	C₂×D₄	1	2	yes	—
201	C₂³×C₅₉	—	2	2	no	—
202	C₂³×C₅₉	—	2	2	no	—
203	C₂³×C₅₉	—	2	2	no	—
204	C₂³×C₅₉	—	2	2	no	—
205	C₂³×C₅₉	—	2	2	no	—
206	C₂³×C₅₉	—	2	2	no	—
207	C₂³×C₅₉	—	2	2	no	—
208	C₂³×C₅₉	—	4	1	no	—
209	C₂³×C₅₉	—	4	1	no	—
210	C₂³×C₅₉	—	4	1	no	—
211	C₂³×C₅₉	—	4	1	no	—
212	C₂³×C₅₉	—	4	1	no	—
213	C₂³×C₅₉	—	4	1	no	—
214	C₂³×C₅₉	C₂×SD₁₆	1	4	yes	—
215	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₅₉	—	2	2	no	—
217	Q₈×C₅₉	—	2	2	no	—
218	Q₈×C₅₉	—	2	2	no	—
219	Q₈×C₅₉	—	2	4	no	—
220	Q₈×C₅₉	—	2	4	no	—
221	Q₈×C₅₉	—	4	16	no	—
222	Q₈×C₅₉	—	4	2	no	—
223	Q₈×C₅₉	—	4	2	no	—
224	Q₈×C₅₉	#121	1	4	yes	complemented
225	D₄×C₅₉	—	2	2	no	—
226	D₄×C₅₉	—	2	2	no	—
227	D₄×C₅₉	—	2	8	no	—
228	D₄×C₅₉	—	4	1	no	—
229	D₄×C₅₉	—	4	1	no	—
230	D₄×C₅₉	—	8	8	no	—
231	C₂×C₄×C₅₉	—	2	2	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	2	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	2	no	—
237	C₂×C₄×C₅₉	—	2	4	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	2	2	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	4	16	no	—
242	C₂×C₄×C₅₉	—	4	2	no	—
243	C₂×C₄×C₅₉	—	4	2	no	—
244	C₂×C₄×C₅₉	—	4	1	no	—
245	C₂×C₄×C₅₉	—	4	1	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	1	no	—
251	C₂×C₄×C₅₉	—	4	2	no	—
252	C₂×C₄×C₅₉	—	4	1	no	—
253	C₂×C₄×C₅₉	—	4	2	no	—
254	C₂×C₄×C₅₉	—	4	1	no	—
255	C₂×C₄×C₅₉	—	4	2	no	—
256	C₂×C₄×C₅₉	—	8	4	no	—
257	C₂×C₄×C₅₉	#120	1	2	yes	—
258	C₂×C₄×C₅₉	#120	1	2	yes	—
259	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
260	C₂×C₄×C₅₉	#137	1	2	yes	—
261	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
267	C₈×C₅₉	—	2	2	no	—
268	C₈×C₅₉	—	4	1	no	—
269	C₈×C₅₉	—	4	2	no	—
270	#24239	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₅₉	—	2	4	no	—
272	C₂²×C₅₉	—	2	4	no	—
273	C₂²×C₅₉	—	2	4	no	—
274	C₂²×C₅₉	—	4	2	no	—
275	C₂²×C₅₉	—	4	2	no	—
276	C₂²×C₅₉	—	4	2	no	—
277	C₂²×C₅₉	—	4	2	no	—
278	C₂²×C₅₉	—	4	2	no	—
279	C₂²×C₅₉	—	4	2	no	—
280	C₂²×C₅₉	—	4	2	no	—
281	C₂²×C₅₉	—	8	1	no	—
282	C₂²×C₅₉	—	8	1	no	—
283	C₂²×C₅₉	—	8	1	no	—
284	C₂²×C₅₉	—	8	1	no	—
285	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
286	C₂²×C₅₉	D₄²	1	1	yes	characteristic
287	C₂²×C₅₉	#546	1	1	yes	characteristic
288	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
289	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
290	C₂²×C₅₉	#577	1	1	yes	characteristic
291	C₂²×C₅₉	#578	1	1	yes	characteristic
292	C₄×C₅₉	—	2	4	no	—
293	C₄×C₅₉	—	2	2	no	—
294	C₄×C₅₉	—	4	2	no	—
295	C₄×C₅₉	—	4	4	no	—
296	C₄×C₅₉	—	4	2	no	—
297	C₄×C₅₉	—	8	1	no	—
298	C₄×C₅₉	—	8	2	no	—
299	C₄×C₅₉	#448	1	4	yes	complemented
300	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
301	C₄×C₅₉	#535	1	1	yes	characteristic
302	C₄×C₅₉	D₄²	1	1	yes	characteristic
303	C₄×C₅₉	#546	1	1	yes	characteristic
304	C₂×D₄×Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
305	C₂×#461	C₂×C₅₉	1	1	yes	characteristic, complemented
306	C₂×#448	C₂×C₅₉	1	2	yes	complemented
307	C₂×C₄×SD₁₆	C₂×C₅₉	1	1	yes	characteristic, complemented
308	#2537	C₂×C₅₉	1	1	yes	characteristic
309	#2035	C₂×C₅₉	1	2	yes	complemented
310	#2000	C₂×C₅₉	1	2	yes	complemented
311	#1956	C₂×C₅₉	1	1	yes	characteristic, complemented
312	#1954	C₂×C₅₉	1	1	yes	characteristic, complemented
313	#1803	C₂×C₅₉	1	1	yes	characteristic, complemented
314	#1787	C₂×C₅₉	1	2	yes	complemented
315	C₂×C₅₉	—	4	4	no	—
316	C₂×C₅₉	—	8	2	no	—
317	C₂×C₅₉	#2408	1	1	yes	characteristic
318	C₂×C₅₉	C₂×#448	1	1	yes	characteristic
319	C₂×C₅₉	#3013	1	1	yes	characteristic
320	C₂×C₅₉	#3276	1	1	yes	characteristic
321	C₂×C₅₉	D₄×SD₁₆	1	1	yes	characteristic
322	C₂×C₅₉	#3298	1	1	yes	characteristic
323	C₂×C₅₉	#3329	1	1	yes	characteristic
324	C₂³×Q₈	C₂²×C₅₉	1	2	yes	—
325	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
326	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
327	D₄×Q₈	—	2	4	no	—
328	D₄×Q₈	—	2	4	no	—
329	C₂×C₄⋊Q₈	—	2	1	no	—
330	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
331	C₂×C₂²⋊Q₈	—	2	2	no	—
332	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
333	C₂×#121	—	2	1	no	—
334	C₂×#121	C₂²×C₅₉	1	2	yes	—
335	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
336	C₂×C₄×D₄	—	2	1	no	—
337	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
339	#461	—	2	4	no	—
340	#448	—	2	8	no	—
341	C₄×SD₁₆	—	2	4	no	—
342	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
343	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
344	C₂×#103	C₂²×C₅₉	1	2	yes	—
345	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
346	C₂×#103	C₂²×C₅₉	1	2	yes	—
347	C₂×#103	C₂²×C₅₉	1	2	yes	—
348	C₂×#103	C₂²×C₅₉	1	2	yes	—
349	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
351	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
352	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
353	#394	—	2	2	no	—
354	#384	C₂²×C₅₉	1	1	yes	characteristic
355	#380	—	2	1	no	—
356	#380	C₂²×C₅₉	1	2	yes	—
357	#340	C₂²×C₅₉	1	2	yes	—
358	C₅₉	#24239	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²×Q₈	—	2	4	no	—
360	C₂²×Q₈	—	2	4	no	—
361	C₂²×Q₈	—	2	2	no	—
362	C₂²×Q₈	—	2	4	no	—
363	C₂²×Q₈	—	2	4	no	—
364	C₂²×Q₈	—	4	2	no	—
365	C₂²×Q₈	—	4	2	no	—
366	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
367	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	D₄×C₅₉	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
371	C₂³×C₄	—	2	2	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	—	2	4	no	—
378	C₂×SD₁₆	—	4	2	no	—
379	C₂×SD₁₆	D₄×C₅₉	1	4	yes	complemented
380	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
381	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
382	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
383	C₄⋊Q₈	—	2	8	no	—
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	D₄×C₅₉	1	4	yes	complemented
386	C₂²⋊Q₈	—	2	16	no	—
387	C₂²⋊Q₈	—	2	4	no	—
388	C₂²⋊Q₈	—	2	4	no	—
389	#121	—	2	4	no	—
390	#121	—	4	2	no	—
391	#121	—	4	4	no	—
392	C₄×Q₈	—	2	2	no	—
393	C₄×Q₈	D₄×C₅₉	1	4	yes	complemented
394	C₄×D₄	—	2	8	no	—
395	C₄×D₄	—	2	2	no	—
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	2	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	2	no	—
410	C₂×C₂²⋊C₄	—	2	2	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₂²⋊C₄	D₄×C₅₉	1	2	yes	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
416	#106	—	2	2	no	—
417	C₄⋊C₈	—	2	2	no	—
418	#103	—	2	2	no	—
419	#103	—	2	4	no	—
420	#103	—	2	4	no	—
421	#103	—	2	4	no	—
422	#103	—	4	2	no	—
423	#102	—	2	2	no	—
424	C₂²⋊C₈	—	2	4	no	—
425	C₂²⋊C₈	—	4	2	no	—
426	C₄×C₈	—	2	2	no	—
427	#95	—	2	2	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	C₂×D₄×C₅₉	1	2	yes	—
430	C₂×Q₈	—	2	8	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	4	4	no	—
440	C₂×Q₈	—	4	4	no	—
441	C₂×Q₈	—	4	8	no	—
442	C₂×Q₈	—	4	8	no	—
443	C₂×Q₈	—	4	8	no	—
444	C₂×Q₈	—	4	8	no	—
445	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
446	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
447	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
448	C₂×Q₈	#41×C₅₉	1	2	yes	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	8	2	no	—
459	C₂×D₄	SD₁₆×C₅₉	1	4	yes	complemented
460	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
479	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
481	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
482	SD₁₆	—	2	8	no	—
483	SD₁₆	—	4	8	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	2	no	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
493	C₄⋊C₄	—	2	8	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	8	1	no	—
505	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	4	no	—
508	C₂²⋊C₄	—	4	4	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₄²	—	2	4	no	—
512	C₄²	C₂×D₄×C₅₉	1	2	yes	—
513	C₄²	C₂×D₄×C₅₉	1	2	yes	—
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	C₂×SD₁₆×C₅₉	1	4	yes	—
528	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	4	no	—
533	Q₈	—	2	4	no	—
534	Q₈	—	4	16	no	—
535	Q₈	—	4	2	no	—
536	Q₈	—	4	2	no	—
537	Q₈	#121×C₅₉	1	4	yes	complemented
538	D₄	—	2	8	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	8	8	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	16	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	8	4	no	—
570	C₂×C₄	#120×C₅₉	1	2	yes	—
571	C₂×C₄	#120×C₅₉	1	2	yes	—
572	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
573	C₂×C₄	#137×C₅₉	1	2	yes	—
574	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
575	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
577	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
578	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
579	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
580	C₈	—	2	2	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	2	no	—
583	C₂²	—	2	4	no	—
584	C₂²	—	2	4	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
598	C₂²	D₄²×C₅₉	1	1	yes	characteristic
599	C₂²	C₅₉×#546	1	1	yes	characteristic
600	C₂²	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
601	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
602	C₂²	C₅₉×#577	1	1	yes	characteristic
603	C₂²	C₅₉×#578	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	4	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	4	no	—
609	C₄	—	8	1	no	—
610	C₄	—	8	2	no	—
611	C₄	C₅₉×#448	1	4	yes	complemented
612	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
613	C₄	C₅₉×#535	1	1	yes	characteristic
614	C₄	D₄²×C₅₉	1	1	yes	characteristic
615	C₄	C₅₉×#546	1	1	yes	characteristic
616	C₂	—	4	4	no	—
617	C₂	—	8	2	no	—
618	C₂	C₅₉×#2408	1	1	yes	characteristic
619	C₂	C₂×C₅₉×#448	1	1	yes	characteristic
620	C₂	C₅₉×#3013	1	1	yes	characteristic
621	C₂	C₅₉×#3276	1	1	yes	characteristic
622	C₂	D₄×SD₁₆×C₅₉	1	1	yes	characteristic
623	C₂	C₅₉×#3298	1	1	yes	characteristic
624	C₂	C₅₉×#3329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#2537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂×C₄×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₅₉	C₂	semidirect
2. C₂×C₅₉×#461	C₂	semidirect
3. C₂×C₅₉×#448	C₂	semidirect
4. C₂×C₄×SD₁₆×C₅₉	C₂	semidirect
6. C₅₉×#2035	C₂	semidirect
7. C₅₉×#2000	C₂	semidirect
8. C₅₉×#1956	C₂	semidirect
9. C₅₉×#1954	C₂	semidirect
10. C₅₉×#1803	C₂	semidirect
11. C₅₉×#1787	C₂	semidirect
66. C₂×SD₁₆×C₅₉	D₄	semidirect
72. C₄⋊Q₈×C₅₉	D₄	semidirect
80. C₄×Q₈×C₅₉	D₄	semidirect
146. C₂×D₄×C₅₉	SD₁₆	semidirect
224. Q₈×C₅₉	#121	semidirect
270. #24239	C₅₉	direct (N × H)
299. C₄×C₅₉	#448	semidirect
304. C₂×D₄×Q₈	C₂×C₅₉	semidirect
305. C₂×#461	C₂×C₅₉	semidirect
306. C₂×#448	C₂×C₅₉	semidirect
307. C₂×C₄×SD₁₆	C₂×C₅₉	semidirect
309. #2035	C₂×C₅₉	semidirect
310. #2000	C₂×C₅₉	semidirect
311. #1956	C₂×C₅₉	semidirect
312. #1954	C₂×C₅₉	semidirect
313. #1803	C₂×C₅₉	semidirect
314. #1787	C₂×C₅₉	semidirect
358. C₅₉	#24239	direct (N × H)
379. C₂×SD₁₆	D₄×C₅₉	semidirect
385. C₄⋊Q₈	D₄×C₅₉	semidirect
393. C₄×Q₈	D₄×C₅₉	semidirect
459. C₂×D₄	SD₁₆×C₅₉	semidirect
537. Q₈	#121×C₅₉	semidirect
611. C₄	C₅₉×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₅₉	2
C₂×C₅₉×#461	2
C₂×C₅₉×#448	2
C₂×C₄×SD₁₆×C₅₉	2
C₅₉×#2537	2
C₅₉×#2035	2
C₅₉×#2000	2
C₅₉×#1956	2
C₅₉×#1954	2
C₅₉×#1803	2
C₅₉×#1787	2
#24239	59

Subgroups — C59×#24239 #28436348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24239 #28436348