Subgroups — C₅₉×#22601 #28434710

Order 15104.

932 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1940	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1917	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1916	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1817	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1817	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#1797	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#1771	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1749	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#432	—	2	4	no	—
18	C₅₉×#431	—	2	4	no	—
19	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#97×C₅₉	C₂²	1	2	yes	—
27	C₂×#97×C₅₉	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₅₉	C₄	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#95×C₅₉	C₄	1	1	yes	characteristic
38	C₂×#95×C₅₉	C₄	1	1	yes	characteristic
39	C₅₉×#336	C₂²	1	2	yes	—
40	C₅₉×#336	C₂²	1	2	yes	—
41	C₅₉×#336	C₂²	1	2	yes	—
42	C₅₉×#336	C₂²	1	2	yes	—
43	C₅₉×#336	C₂²	1	2	yes	—
44	C₅₉×#336	C₂²	1	2	yes	—
45	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅₉	—	2	2	no	—
67	C₂×C₄²×C₅₉	—	2	2	no	—
68	C₂×C₄²×C₅₉	—	2	2	no	—
69	C₂×C₄²×C₅₉	—	2	2	no	—
70	C₂×C₄²×C₅₉	—	2	4	no	—
71	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₅₉	—	2	4	no	—
84	C₄⋊C₈×C₅₉	—	2	4	no	—
85	C₄⋊C₈×C₅₉	—	2	4	no	—
86	C₂²⋊C₈×C₅₉	—	2	2	no	—
87	C₂²⋊C₈×C₅₉	—	2	2	no	—
88	C₂²⋊C₈×C₅₉	—	2	2	no	—
89	C₂²⋊C₈×C₅₉	D₄	1	4	yes	—
90	#97×C₅₉	—	2	4	no	—
91	#97×C₅₉	—	2	4	no	—
92	C₄×C₈×C₅₉	—	2	4	no	—
93	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
94	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
95	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
96	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
97	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
98	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
99	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
100	#95×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₂⁴×C₅₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	—	2	2	no	—
103	C₂²×C₄×C₅₉	—	2	2	no	—
104	C₂²×C₄×C₅₉	—	2	2	no	—
105	C₂²×C₄×C₅₉	—	2	2	no	—
106	C₂²×C₄×C₅₉	—	2	2	no	—
107	C₂²×C₄×C₅₉	—	2	2	no	—
108	C₂²×C₄×C₅₉	—	2	2	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	2	2	no	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	—	2	2	no	—
113	C₂²×C₄×C₅₉	—	2	2	no	—
114	C₂²×C₄×C₅₉	—	2	2	no	—
115	C₂²×C₄×C₅₉	—	2	2	no	—
116	C₂²×C₄×C₅₉	—	2	2	no	—
117	C₂²×C₄×C₅₉	—	2	2	no	—
118	C₂²×C₄×C₅₉	—	4	1	no	—
119	C₂²×C₄×C₅₉	—	4	1	no	—
120	C₂²×C₄×C₅₉	—	4	1	no	—
121	C₂²×C₄×C₅₉	M₁₆	1	4	yes	—
122	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₅₉	#41	1	2	yes	—
137	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₅₉	—	2	2	no	—
139	C₂×C₈×C₅₉	—	2	2	no	—
140	C₂×C₈×C₅₉	—	2	2	no	—
141	C₂×C₈×C₅₉	—	2	2	no	—
142	C₂×C₈×C₅₉	—	2	2	no	—
143	C₂×C₈×C₅₉	—	2	2	no	—
144	C₂×C₈×C₅₉	—	2	2	no	—
145	C₂×C₈×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₅₉	—	2	2	no	—
151	C₄⋊C₄×C₅₉	—	2	2	no	—
152	C₄⋊C₄×C₅₉	—	2	2	no	—
153	C₄⋊C₄×C₅₉	—	2	2	no	—
154	C₄⋊C₄×C₅₉	—	2	2	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	2	2	no	—
157	C₄⋊C₄×C₅₉	M₁₆	1	4	yes	—
158	C₄²×C₅₉	—	2	2	no	—
159	C₄²×C₅₉	—	2	2	no	—
160	C₄²×C₅₉	—	2	2	no	—
161	C₄²×C₅₉	—	2	2	no	—
162	C₄²×C₅₉	—	2	2	no	—
163	C₄²×C₅₉	—	2	2	no	—
164	C₄²×C₅₉	—	2	1	no	—
165	C₄²×C₅₉	—	2	1	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	—	2	1	no	—
168	C₄²×C₅₉	—	2	2	no	—
169	C₄²×C₅₉	—	2	1	no	—
170	C₄²×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	—	2	1	no	—
173	C₄²×C₅₉	#41	1	4	yes	—
174	C₂³×C₅₉	—	2	1	no	—
175	C₂³×C₅₉	—	2	1	no	—
176	C₂³×C₅₉	—	2	1	no	—
177	C₂³×C₅₉	—	2	1	no	—
178	C₂³×C₅₉	C₄×D₄	1	2	yes	—
179	C₂³×C₅₉	C₂×M₁₆	1	2	yes	—
180	C₂³×C₅₉	#131	1	2	yes	—
181	C₂³×C₅₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₉	—	2	8	no	—
183	C₂×C₄×C₅₉	—	2	1	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	1	no	—
186	C₂×C₄×C₅₉	—	2	1	no	—
187	C₂×C₄×C₅₉	—	2	1	no	—
188	C₂×C₄×C₅₉	—	2	1	no	—
189	C₂×C₄×C₅₉	—	2	1	no	—
190	C₂×C₄×C₅₉	—	2	1	no	—
191	C₂×C₄×C₅₉	—	2	1	no	—
192	C₂×C₄×C₅₉	—	2	1	no	—
193	C₂×C₄×C₅₉	—	2	1	no	—
194	C₂×C₄×C₅₉	—	2	1	no	—
195	C₂×C₄×C₅₉	—	2	1	no	—
196	C₂×C₄×C₅₉	—	2	1	no	—
197	C₂×C₄×C₅₉	—	2	1	no	—
198	C₂×C₄×C₅₉	—	2	1	no	—
199	C₂×C₄×C₅₉	—	2	8	no	—
200	C₂×C₄×C₅₉	—	2	4	no	—
201	C₂×C₄×C₅₉	—	2	4	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	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	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	—	4	4	no	—
218	C₂×C₄×C₅₉	—	4	4	no	—
219	C₂×C₄×C₅₉	—	4	4	no	—
220	C₂×C₄×C₅₉	—	4	4	no	—
221	C₂×C₄×C₅₉	#117	1	2	yes	—
222	C₂×C₄×C₅₉	#117	1	2	yes	—
223	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
225	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
226	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
227	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
228	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
231	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
233	C₈×C₅₉	—	2	4	no	—
234	C₈×C₅₉	—	4	2	no	—
235	C₈×C₅₉	—	4	2	no	—
236	C₈×C₅₉	—	4	2	no	—
237	#22601	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₅₉	—	2	2	no	—
239	C₂²×C₅₉	—	2	2	no	—
240	C₂²×C₅₉	—	2	2	no	—
241	C₂²×C₅₉	—	2	2	no	—
242	C₂²×C₅₉	—	2	2	no	—
243	C₂²×C₅₉	—	2	2	no	—
244	C₂²×C₅₉	#435	1	4	yes	—
245	C₂²×C₅₉	C₂×#117	1	1	yes	characteristic
246	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₅₉	#519	1	1	yes	characteristic
248	C₂²×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
249	C₂²×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
250	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
251	C₂²×C₅₉	#568	1	1	yes	characteristic
252	C₄×C₅₉	—	2	2	no	—
253	C₄×C₅₉	—	2	2	no	—
254	C₄×C₅₉	—	2	2	no	—
255	C₄×C₅₉	—	2	2	no	—
256	C₄×C₅₉	—	2	2	no	—
257	C₄×C₅₉	—	2	2	no	—
258	C₄×C₅₉	—	2	2	no	—
259	C₄×C₅₉	—	2	2	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	—	4	1	no	—
262	C₄×C₅₉	—	4	1	no	—
263	C₄×C₅₉	—	4	1	no	—
264	C₄×C₅₉	—	4	1	no	—
265	C₄×C₅₉	#547	1	2	yes	—
266	C₄×C₅₉	#552	1	2	yes	—
267	C₂×#432	C₂×C₅₉	1	1	yes	characteristic
268	C₂×#431	C₂×C₅₉	1	1	yes	characteristic
269	C₂×C₄×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic
270	#1940	C₂×C₅₉	1	2	yes	complemented
271	#1917	C₂×C₅₉	1	2	yes	complemented
272	#1916	C₂×C₅₉	1	2	yes	complemented
273	#1817	C₂×C₅₉	1	1	yes	characteristic
274	#1817	C₂×C₅₉	1	1	yes	characteristic
275	#1797	C₂×C₅₉	1	1	yes	characteristic
276	#1771	C₂×C₅₉	1	2	yes	complemented
277	#1749	C₂×C₅₉	1	1	yes	characteristic
278	C₂×C₅₉	—	2	4	no	—
279	C₂×C₅₉	#2344	1	1	yes	characteristic
280	C₂×C₅₉	#2920	1	1	yes	characteristic
281	C₂×C₅₉	#2924	1	1	yes	characteristic
282	C₂×C₅₉	C₂×#435	1	1	yes	characteristic
283	C₂×C₅₉	D₄×M₁₆	1	1	yes	characteristic
284	C₂×C₅₉	#2983	1	1	yes	characteristic
285	C₂×C₅₉	#2984	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₄×C₅₉	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₄×C₅₉	1	1	yes	characteristic
288	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
289	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
290	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
291	#432	—	2	4	no	—
292	#431	—	2	4	no	—
293	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
294	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
295	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
296	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
297	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
298	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
299	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
300	C₂×#97	C₂²×C₅₉	1	2	yes	—
301	C₂×#97	C₂²×C₅₉	1	2	yes	—
302	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
303	C₄×C₄⋊C₄	C₄×C₅₉	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₄×C₅₉	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₄×C₅₉	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₄×C₅₉	1	1	yes	characteristic
307	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
310	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
311	C₂×#95	C₄×C₅₉	1	1	yes	characteristic
312	C₂×#95	C₄×C₅₉	1	1	yes	characteristic
313	#336	C₂²×C₅₉	1	2	yes	—
314	#336	C₂²×C₅₉	1	2	yes	—
315	#336	C₂²×C₅₉	1	2	yes	—
316	#336	C₂²×C₅₉	1	2	yes	—
317	#336	C₂²×C₅₉	1	2	yes	—
318	#336	C₂²×C₅₉	1	2	yes	—
319	C₅₉	#22601	1	1	yes	characteristic, direct product factor, Sylow
320	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
321	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
322	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
323	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
324	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
325	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
328	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
329	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
330	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
335	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	4	no	—
346	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
347	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
348	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
349	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
350	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
351	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
358	C₄⋊C₈	—	2	4	no	—
359	C₄⋊C₈	—	2	4	no	—
360	C₄⋊C₈	—	2	4	no	—
361	C₂²⋊C₈	—	2	2	no	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	D₄×C₅₉	1	4	yes	—
365	#97	—	2	4	no	—
366	#97	—	2	4	no	—
367	C₄×C₈	—	2	4	no	—
368	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
369	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
370	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
371	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
372	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
373	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
374	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
375	#95	C₂×C₄×C₅₉	1	1	yes	characteristic
376	C₂⁴	C₂²×C₄×C₅₉	1	1	yes	characteristic
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	M₁₆×C₅₉	1	4	yes	—
397	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
402	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
403	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
404	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
405	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
407	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
408	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
409	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
411	C₂²×C₄	#41×C₅₉	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	M₁₆×C₅₉	1	4	yes	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	#41×C₅₉	1	4	yes	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	C₄×D₄×C₅₉	1	2	yes	—
454	C₂³	C₂×M₁₆×C₅₉	1	2	yes	—
455	C₂³	#131×C₅₉	1	2	yes	—
456	C₂³	C₂³×C₄×C₅₉	1	1	yes	characteristic
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	#117×C₅₉	1	2	yes	—
497	C₂×C₄	#117×C₅₉	1	2	yes	—
498	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
499	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
500	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
501	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
502	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
503	C₂×C₄	C₂×M₁₆×C₅₉	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
506	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
507	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
508	C₈	—	2	4	no	—
509	C₈	—	4	2	no	—
510	C₈	—	4	2	no	—
511	C₈	—	4	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	C₅₉×#435	1	4	yes	—
519	C₂²	C₂×#117×C₅₉	1	1	yes	characteristic
520	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
521	C₂²	C₅₉×#519	1	1	yes	characteristic
522	C₂²	C₂²×M₁₆×C₅₉	1	1	yes	characteristic
523	C₂²	C₂²×M₁₆×C₅₉	1	1	yes	characteristic
524	C₂²	C₂×#131×C₅₉	1	1	yes	characteristic
525	C₂²	C₅₉×#568	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	C₅₉×#547	1	2	yes	—
540	C₄	C₅₉×#552	1	2	yes	—
541	C₂	—	2	4	no	—
542	C₂	C₅₉×#2344	1	1	yes	characteristic
543	C₂	C₅₉×#2920	1	1	yes	characteristic
544	C₂	C₅₉×#2924	1	1	yes	characteristic
545	C₂	C₂×C₅₉×#435	1	1	yes	characteristic
546	C₂	D₄×M₁₆×C₅₉	1	1	yes	characteristic
547	C₂	C₅₉×#2983	1	1	yes	characteristic
548	C₂	C₅₉×#2984	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₅₉×#1940	C₂	semidirect
5. C₅₉×#1917	C₂	semidirect
6. C₅₉×#1916	C₂	semidirect
10. C₅₉×#1771	C₂	semidirect
237. #22601	C₅₉	direct (N × H)
270. #1940	C₂×C₅₉	semidirect
271. #1917	C₂×C₅₉	semidirect
272. #1916	C₂×C₅₉	semidirect
276. #1771	C₂×C₅₉	semidirect
319. C₅₉	#22601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#432	2
C₂×C₅₉×#431	2
C₂×C₄×C₄⋊C₄×C₅₉	2
C₅₉×#1940	2
C₅₉×#1917	2
C₅₉×#1916	2
C₅₉×#1817	2
C₅₉×#1797	2
C₅₉×#1771	2
C₅₉×#1749	2
#22601	59

Subgroups — C59×#22601 #28434710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#22601 #28434710