Subgroups — C₅₉×#11063 #28423172

Order 15104.

1174 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×#418	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#418	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#390	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₅₉	—	2	2	no	—
15	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#418	—	2	2	no	—
17	C₅₉×#418	—	2	2	no	—
18	C₅₉×#418	—	2	2	no	—
19	C₅₉×#418	C₄	1	4	yes	complemented
20	C₂×#102×C₅₉	—	2	1	no	—
21	C₂×#102×C₅₉	—	2	1	no	—
22	C₂×#102×C₅₉	—	2	2	no	—
23	C₅₉×#390	—	2	2	no	—
24	C₅₉×#390	—	2	2	no	—
25	C₅₉×#389	—	2	2	no	—
26	C₅₉×#385	—	2	2	no	—
27	C₅₉×#384	—	2	1	no	—
28	C₅₉×#382	—	2	1	no	—
29	C₅₉×#343	—	2	2	no	—
30	C₅₉×#339	—	2	2	no	—
31	C₅₉×#339	—	2	2	no	—
32	C₂⁵×C₅₉	—	2	1	no	—
33	C₂²×D₄×C₅₉	—	2	1	no	—
34	C₂²×D₄×C₅₉	—	2	1	no	—
35	C₂²×D₄×C₅₉	—	2	1	no	—
36	C₂²×D₄×C₅₉	—	2	1	no	—
37	C₂²×D₄×C₅₉	—	2	1	no	—
38	C₂²×D₄×C₅₉	—	2	1	no	—
39	C₂²×D₄×C₅₉	—	2	1	no	—
40	C₂²×D₄×C₅₉	—	2	1	no	—
41	C₂²×D₄×C₅₉	—	2	1	no	—
42	C₂²×D₄×C₅₉	—	2	1	no	—
43	C₂²×D₄×C₅₉	—	2	1	no	—
44	C₂²×D₄×C₅₉	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₅₉	D₄	1	2	yes	—
46	C₂²×D₄×C₅₉	Q₈	1	2	yes	—
47	C₂³×C₄×C₅₉	—	2	1	no	—
48	C₂³×C₄×C₅₉	D₄	1	2	yes	—
49	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₅₉	—	2	1	no	—
51	C₂×M₁₆×C₅₉	—	2	1	no	—
52	C₂×M₁₆×C₅₉	—	2	1	no	—
53	C₂×M₁₆×C₅₉	—	2	1	no	—
54	C₂×M₁₆×C₅₉	—	2	1	no	—
55	C₂×M₁₆×C₅₉	—	2	1	no	—
56	C₂×M₁₆×C₅₉	—	2	1	no	—
57	C₂×M₁₆×C₅₉	—	2	1	no	—
58	C₂×M₁₆×C₅₉	—	2	1	no	—
59	C₂×M₁₆×C₅₉	—	2	1	no	—
60	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
62	C₂²×C₈×C₅₉	—	2	1	no	—
63	C₂²×C₈×C₅₉	—	2	1	no	—
64	#117×C₅₉	—	2	1	no	—
65	#117×C₅₉	—	2	1	no	—
66	#117×C₅₉	—	2	1	no	—
67	#117×C₅₉	—	2	1	no	—
68	#117×C₅₉	—	2	1	no	—
69	#117×C₅₉	—	2	1	no	—
70	#117×C₅₉	C₂×C₄	1	2	yes	—
71	#117×C₅₉	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	1	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	4	no	—
79	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
84	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₅₉	—	4	8	no	—
86	C₂×C₄²×C₅₉	—	2	1	no	—
87	C₂×C₄²×C₅₉	—	2	1	no	—
88	C₂×C₄²×C₅₉	—	2	1	no	—
89	C₂×C₄²×C₅₉	—	2	1	no	—
90	C₂×C₄²×C₅₉	—	2	1	no	—
91	C₂×C₄²×C₅₉	—	2	1	no	—
92	C₂×C₄²×C₅₉	—	2	1	no	—
93	C₂×C₄²×C₅₉	D₄	1	2	yes	—
94	#102×C₅₉	—	2	4	no	—
95	#102×C₅₉	—	2	4	no	—
96	#102×C₅₉	—	2	8	no	—
97	#95×C₅₉	—	2	4	no	—
98	C₂⁴×C₅₉	—	2	2	no	—
99	C₂⁴×C₅₉	—	2	2	no	—
100	C₂⁴×C₅₉	—	2	2	no	—
101	C₂⁴×C₅₉	—	4	4	no	—
102	C₂⁴×C₅₉	—	4	4	no	—
103	C₂⁴×C₅₉	—	4	1	no	—
104	C₂⁴×C₅₉	—	4	1	no	—
105	C₂⁴×C₅₉	—	4	1	no	—
106	C₂⁴×C₅₉	—	4	1	no	—
107	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₅₉	—	2	2	no	—
109	C₂×D₄×C₅₉	—	2	2	no	—
110	C₂×D₄×C₅₉	—	2	2	no	—
111	C₂×D₄×C₅₉	—	2	2	no	—
112	C₂×D₄×C₅₉	—	2	2	no	—
113	C₂×D₄×C₅₉	—	2	2	no	—
114	C₂×D₄×C₅₉	—	2	2	no	—
115	C₂×D₄×C₅₉	—	2	2	no	—
116	C₂×D₄×C₅₉	—	2	2	no	—
117	C₂×D₄×C₅₉	—	2	2	no	—
118	C₂×D₄×C₅₉	—	2	2	no	—
119	C₂×D₄×C₅₉	—	2	2	no	—
120	C₂×D₄×C₅₉	—	2	2	no	—
121	C₂×D₄×C₅₉	—	2	2	no	—
122	C₂×D₄×C₅₉	—	2	2	no	—
123	C₂×D₄×C₅₉	—	4	1	no	—
124	C₂×D₄×C₅₉	—	4	1	no	—
125	C₂×D₄×C₅₉	—	4	1	no	—
126	C₂×D₄×C₅₉	—	4	1	no	—
127	C₂×D₄×C₅₉	—	4	1	no	—
128	C₂×D₄×C₅₉	—	4	1	no	—
129	C₂×D₄×C₅₉	—	4	1	no	—
130	C₂×D₄×C₅₉	—	4	1	no	—
131	C₂×D₄×C₅₉	—	4	1	no	—
132	C₂×D₄×C₅₉	—	4	1	no	—
133	C₂×D₄×C₅₉	—	4	1	no	—
134	C₂×D₄×C₅₉	—	4	1	no	—
135	C₂×D₄×C₅₉	C₄⋊C₄	1	4	yes	complemented
136	C₂²×C₄×C₅₉	—	2	4	no	—
137	C₂²×C₄×C₅₉	—	2	2	no	—
138	C₂²×C₄×C₅₉	—	2	2	no	—
139	C₂²×C₄×C₅₉	—	2	2	no	—
140	C₂²×C₄×C₅₉	—	2	1	no	—
141	C₂²×C₄×C₅₉	—	2	2	no	—
142	C₂²×C₄×C₅₉	—	2	1	no	—
143	C₂²×C₄×C₅₉	—	2	2	no	—
144	C₂²×C₄×C₅₉	—	4	2	no	—
145	C₂²×C₄×C₅₉	—	4	1	no	—
146	C₂²×C₄×C₅₉	—	4	1	no	—
147	C₂²×C₄×C₅₉	—	4	4	no	—
148	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
156	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
159	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
160	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
161	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
162	M₁₆×C₅₉	—	2	2	no	—
163	M₁₆×C₅₉	—	2	2	no	—
164	M₁₆×C₅₉	—	2	2	no	—
165	M₁₆×C₅₉	—	2	2	no	—
166	M₁₆×C₅₉	—	4	1	no	—
167	M₁₆×C₅₉	—	4	1	no	—
168	M₁₆×C₅₉	—	4	1	no	—
169	M₁₆×C₅₉	—	4	1	no	—
170	C₂×C₈×C₅₉	—	2	2	no	—
171	C₂×C₈×C₅₉	—	2	2	no	—
172	C₂×C₈×C₅₉	—	4	1	no	—
173	C₂×C₈×C₅₉	—	4	1	no	—
174	C₂×C₈×C₅₉	—	4	1	no	—
175	C₂×C₈×C₅₉	—	4	1	no	—
176	C₄⋊C₄×C₅₉	—	2	2	no	—
177	C₄⋊C₄×C₅₉	—	2	1	no	—
178	C₄⋊C₄×C₅₉	—	2	1	no	—
179	C₄⋊C₄×C₅₉	—	2	1	no	—
180	C₄⋊C₄×C₅₉	—	2	1	no	—
181	C₄⋊C₄×C₅₉	—	4	1	no	—
182	C₄⋊C₄×C₅₉	—	4	1	no	—
183	C₄⋊C₄×C₅₉	—	4	1	no	—
184	C₄⋊C₄×C₅₉	—	4	1	no	—
185	C₄⋊C₄×C₅₉	—	8	4	no	—
186	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	4	yes	complemented
187	C₂²⋊C₄×C₅₉	—	2	2	no	—
188	C₂²⋊C₄×C₅₉	—	2	2	no	—
189	C₂²⋊C₄×C₅₉	—	4	16	no	—
190	C₂²⋊C₄×C₅₉	—	4	1	no	—
191	C₂²⋊C₄×C₅₉	—	4	1	no	—
192	C₄²×C₅₉	—	2	2	no	—
193	C₄²×C₅₉	—	2	2	no	—
194	C₄²×C₅₉	—	2	2	no	—
195	C₄²×C₅₉	—	2	2	no	—
196	C₄²×C₅₉	—	4	1	no	—
197	C₄²×C₅₉	—	4	1	no	—
198	C₄²×C₅₉	—	4	1	no	—
199	C₄²×C₅₉	—	4	1	no	—
200	C₂³×C₅₉	—	2	2	no	—
201	C₂³×C₅₉	—	2	2	no	—
202	C₂³×C₅₉	—	2	4	no	—
203	C₂³×C₅₉	—	4	4	no	—
204	C₂³×C₅₉	—	4	8	no	—
205	C₂³×C₅₉	—	4	4	no	—
206	C₂³×C₅₉	—	4	8	no	—
207	C₂³×C₅₉	—	4	2	no	—
208	C₂³×C₅₉	—	4	2	no	—
209	C₂³×C₅₉	—	4	2	no	—
210	C₂³×C₅₉	—	4	2	no	—
211	C₂³×C₅₉	—	4	2	no	—
212	C₂³×C₅₉	—	4	2	no	—
213	C₂³×C₅₉	—	8	4	no	—
214	C₂³×C₅₉	—	8	2	no	—
215	C₂³×C₅₉	—	8	2	no	—
216	C₂³×C₅₉	—	8	4	no	—
217	C₂³×C₅₉	—	8	2	no	—
218	C₂³×C₅₉	—	8	2	no	—
219	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₅₉	#120	1	1	yes	characteristic
221	C₂³×C₅₉	#120	1	1	yes	characteristic
222	C₂³×C₅₉	#121	1	1	yes	characteristic
223	C₂³×C₅₉	#121	1	1	yes	characteristic
224	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₅₉	#124	1	1	yes	characteristic
226	D₄×C₅₉	—	2	4	no	—
227	D₄×C₅₉	—	2	4	no	—
228	D₄×C₅₉	—	4	2	no	—
229	D₄×C₅₉	—	4	2	no	—
230	D₄×C₅₉	—	4	2	no	—
231	D₄×C₅₉	—	4	2	no	—
232	D₄×C₅₉	—	4	2	no	—
233	D₄×C₅₉	—	4	2	no	—
234	C₂×C₄×C₅₉	—	2	4	no	—
235	C₂×C₄×C₅₉	—	2	4	no	—
236	C₂×C₄×C₅₉	—	4	4	no	—
237	C₂×C₄×C₅₉	—	4	2	no	—
238	C₂×C₄×C₅₉	—	4	4	no	—
239	C₂×C₄×C₅₉	—	4	2	no	—
240	C₂×C₄×C₅₉	—	4	2	no	—
241	C₂×C₄×C₅₉	—	4	2	no	—
242	C₂×C₄×C₅₉	—	4	4	no	—
243	C₂×C₄×C₅₉	—	4	1	no	—
244	C₂×C₄×C₅₉	—	4	1	no	—
245	C₂×C₄×C₅₉	—	4	2	no	—
246	C₂×C₄×C₅₉	—	4	2	no	—
247	C₂×C₄×C₅₉	—	4	4	no	—
248	C₂×C₄×C₅₉	—	4	2	no	—
249	C₂×C₄×C₅₉	—	8	2	no	—
250	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
253	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
257	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
258	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
259	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
260	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
261	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
262	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
263	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
269	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
270	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
271	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
272	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
273	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
274	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
275	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
276	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
277	C₂×C₄×C₅₉	#127	1	1	yes	characteristic
278	C₈×C₅₉	—	4	2	no	—
279	C₈×C₅₉	—	4	2	no	—
280	#11063	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂²×C₅₉	—	2	2	no	—
282	C₂²×C₅₉	—	2	2	no	—
283	C₂²×C₅₉	—	2	1	no	—
284	C₂²×C₅₉	—	2	1	no	—
285	C₂²×C₅₉	—	2	1	no	—
286	C₂²×C₅₉	—	2	1	no	—
287	C₂²×C₅₉	—	2	2	no	—
288	C₂²×C₅₉	—	2	2	no	—
289	C₂²×C₅₉	—	4	8	no	—
290	C₂²×C₅₉	—	4	4	no	—
291	C₂²×C₅₉	—	8	4	no	—
292	C₂²×C₅₉	—	8	4	no	—
293	C₂²×C₅₉	—	8	4	no	—
294	C₂²×C₅₉	—	8	4	no	—
295	C₂²×C₅₉	—	8	2	no	—
296	C₂²×C₅₉	—	8	2	no	—
297	C₂²×C₅₉	—	8	4	no	—
298	C₂²×C₅₉	#385	1	1	yes	characteristic
299	C₂²×C₅₉	#386	1	1	yes	characteristic
300	C₂²×C₅₉	#388	1	1	yes	characteristic
301	C₂²×C₅₉	#392	1	1	yes	characteristic
302	C₂²×C₅₉	#393	1	1	yes	characteristic
303	C₂²×C₅₉	#394	1	1	yes	characteristic
304	C₂²×C₅₉	#396	1	1	yes	characteristic
305	C₂²×C₅₉	#453	1	2	yes	—
306	C₂²×C₅₉	#454	1	2	yes	—
307	C₄×C₅₉	—	4	4	no	—
308	C₄×C₅₉	—	4	4	no	—
309	C₄×C₅₉	—	8	1	no	—
310	C₄×C₅₉	—	8	2	no	—
311	C₄×C₅₉	—	8	1	no	—
312	C₄×C₅₉	#380	1	1	yes	characteristic
313	C₄×C₅₉	#385	1	1	yes	characteristic
314	C₄×C₅₉	#388	1	1	yes	characteristic
315	C₄×C₅₉	#390	1	1	yes	characteristic
316	C₄×C₅₉	#394	1	1	yes	characteristic
317	C₄×C₅₉	#396	1	1	yes	characteristic
318	C₄×C₅₉	#397	1	1	yes	characteristic
319	C₄×C₅₉	#399	1	1	yes	characteristic
320	C₂×#418	C₂×C₅₉	1	1	yes	characteristic
321	C₂×#418	C₂×C₅₉	1	1	yes	characteristic
322	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
323	C₂×#390	C₂×C₅₉	1	1	yes	characteristic
324	C₂×#343	C₂×C₅₉	1	1	yes	characteristic, complemented
325	C₂×#339	C₂×C₅₉	1	1	yes	characteristic, complemented
326	C₂×#339	C₂×C₅₉	1	1	yes	characteristic, complemented
327	C₂×C₅₉	—	2	1	no	—
328	C₂×C₅₉	—	2	1	no	—
329	C₂×C₅₉	—	2	1	no	—
330	C₂×C₅₉	—	2	1	no	—
331	C₂×C₅₉	—	8	4	no	—
332	C₂×C₅₉	#1439	1	1	yes	characteristic
333	C₂×C₅₉	#1883	1	2	yes	—
334	C₂×C₅₉	#2002	1	1	yes	characteristic
335	C₂×C₅₉	#2003	1	1	yes	characteristic
336	C₂×C₅₉	#2027	1	2	yes	—
337	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
338	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
339	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
340	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
341	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	—	2	2	no	—
344	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
345	#418	—	2	2	no	—
346	#418	—	2	2	no	—
347	#418	—	2	2	no	—
348	#418	C₄×C₅₉	1	4	yes	complemented
349	C₂×#102	—	2	1	no	—
350	C₂×#102	—	2	1	no	—
351	C₂×#102	—	2	2	no	—
352	#390	—	2	2	no	—
353	#390	—	2	2	no	—
354	#389	—	2	2	no	—
355	#385	—	2	2	no	—
356	#384	—	2	1	no	—
357	#382	—	2	1	no	—
358	#343	—	2	2	no	—
359	#339	—	2	2	no	—
360	#339	—	2	2	no	—
361	C₅₉	#11063	1	1	yes	characteristic, direct product factor, Sylow
362	C₂⁵	—	2	1	no	—
363	C₂²×D₄	—	2	1	no	—
364	C₂²×D₄	—	2	1	no	—
365	C₂²×D₄	—	2	1	no	—
366	C₂²×D₄	—	2	1	no	—
367	C₂²×D₄	—	2	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	2	1	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	—	2	1	no	—
374	C₂²×D₄	C₂×C₄×C₅₉	1	2	yes	—
375	C₂²×D₄	D₄×C₅₉	1	2	yes	—
376	C₂²×D₄	Q₈×C₅₉	1	2	yes	—
377	C₂³×C₄	—	2	1	no	—
378	C₂³×C₄	D₄×C₅₉	1	2	yes	—
379	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	—	2	1	no	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	2	1	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	C₂×C₄×C₅₉	1	2	yes	—
391	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	C₂×C₄×C₅₉	1	2	yes	—
401	#117	D₄×C₅₉	1	2	yes	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
410	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
411	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
412	C₂×C₂²⋊C₄	—	2	1	no	—
413	C₂×C₂²⋊C₄	—	2	8	no	—
414	C₂×C₂²⋊C₄	—	2	1	no	—
415	C₂×C₂²⋊C₄	—	4	8	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	2	1	no	—
419	C₂×C₄²	—	2	1	no	—
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	D₄×C₅₉	1	2	yes	—
424	#102	—	2	4	no	—
425	#102	—	2	4	no	—
426	#102	—	2	8	no	—
427	#95	—	2	4	no	—
428	C₂⁴	—	2	2	no	—
429	C₂⁴	—	2	2	no	—
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	4	4	no	—
432	C₂⁴	—	4	4	no	—
433	C₂⁴	—	4	1	no	—
434	C₂⁴	—	4	1	no	—
435	C₂⁴	—	4	1	no	—
436	C₂⁴	—	4	1	no	—
437	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	4	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	—	4	1	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	C₄⋊C₄×C₅₉	1	4	yes	complemented
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	—	4	4	no	—
478	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
484	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
485	C₂²×C₄	C₂×Q₈×C₅₉	1	1	yes	characteristic
486	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
487	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
488	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
489	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
490	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
491	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	M₁₆	—	4	1	no	—
499	M₁₆	—	4	1	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	—	4	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	8	4	no	—
516	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	4	yes	complemented
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	4	16	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	4	1	no	—
527	C₄²	—	4	1	no	—
528	C₄²	—	4	1	no	—
529	C₄²	—	4	1	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	8	no	—
536	C₂³	—	4	8	no	—
537	C₂³	—	4	2	no	—
538	C₂³	—	4	2	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	8	2	no	—
544	C₂³	—	8	2	no	—
545	C₂³	—	8	4	no	—
546	C₂³	—	8	4	no	—
547	C₂³	—	8	2	no	—
548	C₂³	—	8	2	no	—
549	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
550	C₂³	#120×C₅₉	1	1	yes	characteristic
551	C₂³	#120×C₅₉	1	1	yes	characteristic
552	C₂³	#121×C₅₉	1	1	yes	characteristic
553	C₂³	#121×C₅₉	1	1	yes	characteristic
554	C₂³	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
555	C₂³	#124×C₅₉	1	1	yes	characteristic
556	D₄	—	2	4	no	—
557	D₄	—	2	4	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	2	no	—
560	D₄	—	4	2	no	—
561	D₄	—	4	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	4	no	—
568	C₂×C₄	—	4	4	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	8	2	no	—
580	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
581	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
582	C₂×C₄	#117×C₅₉	1	1	yes	characteristic
583	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
584	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
585	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
586	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
587	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
588	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
589	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
590	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
591	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
592	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
593	C₂×C₄	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
594	C₂×C₄	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
595	C₂×C₄	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
596	C₂×C₄	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
597	C₂×C₄	C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
598	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
599	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
600	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
601	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
602	C₂×C₄	#123×C₅₉	1	1	yes	characteristic
603	C₂×C₄	#124×C₅₉	1	1	yes	characteristic
604	C₂×C₄	#124×C₅₉	1	1	yes	characteristic
605	C₂×C₄	#126×C₅₉	1	1	yes	characteristic
606	C₂×C₄	#126×C₅₉	1	1	yes	characteristic
607	C₂×C₄	#127×C₅₉	1	1	yes	characteristic
608	C₈	—	4	2	no	—
609	C₈	—	4	2	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	1	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	4	8	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	8	4	no	—
621	C₂²	—	8	4	no	—
622	C₂²	—	8	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	—	8	4	no	—
626	C₂²	—	8	4	no	—
627	C₂²	C₅₉×#385	1	1	yes	characteristic
628	C₂²	C₅₉×#386	1	1	yes	characteristic
629	C₂²	C₅₉×#388	1	1	yes	characteristic
630	C₂²	C₅₉×#392	1	1	yes	characteristic
631	C₂²	C₅₉×#393	1	1	yes	characteristic
632	C₂²	C₅₉×#394	1	1	yes	characteristic
633	C₂²	C₅₉×#396	1	1	yes	characteristic
634	C₂²	C₅₉×#453	1	2	yes	—
635	C₂²	C₅₉×#454	1	2	yes	—
636	C₄	—	4	4	no	—
637	C₄	—	4	4	no	—
638	C₄	—	8	2	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	C₅₉×#380	1	1	yes	characteristic
642	C₄	C₅₉×#385	1	1	yes	characteristic
643	C₄	C₅₉×#388	1	1	yes	characteristic
644	C₄	C₅₉×#390	1	1	yes	characteristic
645	C₄	C₅₉×#394	1	1	yes	characteristic
646	C₄	C₅₉×#396	1	1	yes	characteristic
647	C₄	C₅₉×#397	1	1	yes	characteristic
648	C₄	C₅₉×#399	1	1	yes	characteristic
649	C₂	—	2	1	no	—
650	C₂	—	2	1	no	—
651	C₂	—	2	1	no	—
652	C₂	—	2	1	no	—
653	C₂	—	8	4	no	—
654	C₂	C₅₉×#1439	1	1	yes	characteristic
655	C₂	C₅₉×#1883	1	2	yes	—
656	C₂	C₅₉×#2002	1	1	yes	characteristic
657	C₂	C₅₉×#2003	1	1	yes	characteristic
658	C₂	C₅₉×#2027	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₅₉
Frattini, cosocle	C₂³×C₄	C₂³×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₉×#2317	C₂	semidirect
5. C₂×C₅₉×#343	C₂	semidirect
6. C₂×C₅₉×#339	C₂	semidirect
7. C₂×C₅₉×#339	C₂	semidirect
19. C₅₉×#418	C₄	semidirect
135. C₂×D₄×C₅₉	C₄⋊C₄	semidirect
186. C₄⋊C₄×C₅₉	C₂²⋊C₄	semidirect
280. #11063	C₅₉	direct (N × H)
322. #2317	C₂×C₅₉	semidirect
324. C₂×#343	C₂×C₅₉	semidirect
325. C₂×#339	C₂×C₅₉	semidirect
326. C₂×#339	C₂×C₅₉	semidirect
348. #418	C₄×C₅₉	semidirect
361. C₅₉	#11063	direct (N × H)
465. C₂×D₄	C₄⋊C₄×C₅₉	semidirect
516. C₄⋊C₄	C₂²⋊C₄×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×#418	2
C₅₉×#2317	2
C₂×C₅₉×#390	2
C₂×C₅₉×#343	2
C₂×C₅₉×#339	2
#11063	59

Subgroups — C59×#11063 #28423172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#11063 #28423172