Subgroups — C₅₉×#23578 #28435687

Order 15104.

1176 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2036	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2034	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#2026	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#2000	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
18	C₅₉×#529	—	2	4	no	—
19	C₅₉×#529	—	2	4	no	—
20	C₂×#126×C₅₉	—	2	1	no	—
21	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#123×C₅₉	—	2	1	no	—
24	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₅₉	—	2	1	no	—
30	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₅₉	—	2	1	no	—
32	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#441	—	2	4	no	—
34	C₅₉×#440	—	2	4	no	—
35	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#103×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×#102×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₅₉	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
49	C₅₉×#391	C₂²	1	1	yes	characteristic
50	C₅₉×#389	C₂²	1	1	yes	characteristic
51	C₅₉×#387	—	2	1	no	—
52	C₅₉×#385	—	2	1	no	—
53	C₅₉×#380	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
55	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₅₉	—	2	1	no	—
66	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₅₉	—	2	1	no	—
68	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
70	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
71	C₂×Q₁₆×C₅₉	—	2	2	no	—
72	C₂×Q₁₆×C₅₉	—	2	2	no	—
73	C₂×Q₁₆×C₅₉	—	2	2	no	—
74	C₂×SD₁₆×C₅₉	—	2	2	no	—
75	C₂×SD₁₆×C₅₉	—	2	2	no	—
76	C₂×SD₁₆×C₅₉	—	2	2	no	—
77	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
81	#126×C₅₉	—	2	8	no	—
82	#125×C₅₉	—	2	2	no	—
83	#125×C₅₉	—	2	2	no	—
84	#124×C₅₉	—	2	2	no	—
85	#124×C₅₉	—	2	2	no	—
86	#123×C₅₉	—	2	8	no	—
87	C₂²⋊Q₈×C₅₉	—	2	2	no	—
88	C₂²⋊Q₈×C₅₉	—	2	2	no	—
89	C₂²⋊Q₈×C₅₉	—	2	2	no	—
90	C₂²⋊Q₈×C₅₉	—	2	2	no	—
91	#121×C₅₉	—	2	2	no	—
92	#121×C₅₉	—	2	2	no	—
93	C₄×Q₈×C₅₉	—	2	2	no	—
94	C₄×Q₈×C₅₉	—	2	2	no	—
95	C₄×Q₈×C₅₉	—	2	2	no	—
96	C₄×Q₈×C₅₉	D₄	1	4	yes	—
97	C₄×D₄×C₅₉	—	2	8	no	—
98	C₄×D₄×C₅₉	—	2	2	no	—
99	C₄×D₄×C₅₉	D₄	1	4	yes	—
100	#117×C₅₉	—	2	8	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	—	2	1	no	—
105	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
106	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
107	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
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	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
120	C₂×C₄²×C₅₉	—	2	1	no	—
121	C₂×C₄²×C₅₉	—	2	2	no	—
122	C₂×C₄²×C₅₉	—	2	2	no	—
123	C₂×C₄²×C₅₉	—	2	1	no	—
124	C₂×C₄²×C₅₉	—	2	1	no	—
125	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
129	#107×C₅₉	—	2	2	no	—
130	#106×C₅₉	—	2	2	no	—
131	#103×C₅₉	—	2	2	no	—
132	#103×C₅₉	—	2	2	no	—
133	#103×C₅₉	—	2	2	no	—
134	#103×C₅₉	—	2	2	no	—
135	#103×C₅₉	—	2	2	no	—
136	#102×C₅₉	—	2	2	no	—
137	#102×C₅₉	—	2	2	no	—
138	#102×C₅₉	—	2	2	no	—
139	C₂²⋊C₈×C₅₉	—	2	2	no	—
140	C₂²⋊C₈×C₅₉	—	2	2	no	—
141	#97×C₅₉	—	2	2	no	—
142	#97×C₅₉	—	2	2	no	—
143	#95×C₅₉	—	2	1	no	—
144	#95×C₅₉	—	2	1	no	—
145	#95×C₅₉	—	2	1	no	—
146	#95×C₅₉	—	2	1	no	—
147	#95×C₅₉	—	2	1	no	—
148	C₂⁴×C₅₉	—	2	1	no	—
149	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₅₉	—	2	1	no	—
151	C₂×Q₈×C₅₉	—	2	1	no	—
152	C₂×Q₈×C₅₉	—	2	1	no	—
153	C₂×Q₈×C₅₉	—	2	1	no	—
154	C₂×Q₈×C₅₉	—	2	1	no	—
155	C₂×Q₈×C₅₉	—	2	1	no	—
156	C₂×Q₈×C₅₉	—	2	1	no	—
157	C₂×Q₈×C₅₉	—	2	1	no	—
158	C₂×Q₈×C₅₉	—	2	1	no	—
159	C₂×Q₈×C₅₉	—	2	1	no	—
160	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
161	C₂×Q₈×C₅₉	#41	1	2	yes	—
162	C₂×D₄×C₅₉	—	2	4	no	—
163	C₂×D₄×C₅₉	—	2	1	no	—
164	C₂×D₄×C₅₉	—	2	1	no	—
165	C₂×D₄×C₅₉	—	2	1	no	—
166	C₂×D₄×C₅₉	—	2	1	no	—
167	C₂×D₄×C₅₉	—	2	1	no	—
168	C₂×D₄×C₅₉	—	4	2	no	—
169	C₂×D₄×C₅₉	—	4	2	no	—
170	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₅₉	—	2	2	no	—
172	C₂²×C₄×C₅₉	—	2	1	no	—
173	C₂²×C₄×C₅₉	—	2	1	no	—
174	C₂²×C₄×C₅₉	—	2	1	no	—
175	C₂²×C₄×C₅₉	—	2	1	no	—
176	C₂²×C₄×C₅₉	—	2	1	no	—
177	C₂²×C₄×C₅₉	—	2	2	no	—
178	C₂²×C₄×C₅₉	—	2	2	no	—
179	C₂²×C₄×C₅₉	—	2	4	no	—
180	C₂²×C₄×C₅₉	—	2	1	no	—
181	C₂²×C₄×C₅₉	—	2	1	no	—
182	C₂²×C₄×C₅₉	—	2	1	no	—
183	C₂²×C₄×C₅₉	—	2	1	no	—
184	C₂²×C₄×C₅₉	—	2	1	no	—
185	C₂²×C₄×C₅₉	—	2	1	no	—
186	C₂²×C₄×C₅₉	—	2	1	no	—
187	C₂²×C₄×C₅₉	—	2	1	no	—
188	C₂²×C₄×C₅₉	—	4	1	no	—
189	C₂²×C₄×C₅₉	—	4	1	no	—
190	C₂²×C₄×C₅₉	—	4	1	no	—
191	C₂²×C₄×C₅₉	—	4	2	no	—
192	C₂²×C₄×C₅₉	—	4	2	no	—
193	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
199	Q₁₆×C₅₉	—	2	8	no	—
200	SD₁₆×C₅₉	—	2	8	no	—
201	C₂×C₈×C₅₉	—	2	1	no	—
202	C₂×C₈×C₅₉	—	2	1	no	—
203	C₂×C₈×C₅₉	—	2	1	no	—
204	C₂×C₈×C₅₉	—	2	1	no	—
205	C₂×C₈×C₅₉	—	2	1	no	—
206	C₂×C₈×C₅₉	—	2	1	no	—
207	C₂×C₈×C₅₉	—	2	1	no	—
208	C₂×C₈×C₅₉	—	2	1	no	—
209	C₂×C₈×C₅₉	—	2	1	no	—
210	C₂×C₈×C₅₉	—	2	1	no	—
211	C₂×C₈×C₅₉	#41	1	2	yes	—
212	C₂×C₈×C₅₉	#41	1	2	yes	—
213	C₄⋊C₄×C₅₉	—	2	4	no	—
214	C₄⋊C₄×C₅₉	—	2	4	no	—
215	C₄⋊C₄×C₅₉	—	2	4	no	—
216	C₄⋊C₄×C₅₉	—	2	4	no	—
217	C₄⋊C₄×C₅₉	—	2	4	no	—
218	C₄⋊C₄×C₅₉	—	2	1	no	—
219	C₄⋊C₄×C₅₉	—	2	1	no	—
220	C₄⋊C₄×C₅₉	—	2	1	no	—
221	C₄⋊C₄×C₅₉	—	2	1	no	—
222	C₄⋊C₄×C₅₉	—	2	1	no	—
223	C₄⋊C₄×C₅₉	—	2	1	no	—
224	C₄⋊C₄×C₅₉	—	2	1	no	—
225	C₄⋊C₄×C₅₉	—	4	2	no	—
226	C₄⋊C₄×C₅₉	—	4	2	no	—
227	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
229	C₄⋊C₄×C₅₉	#41	1	2	yes	—
230	C₂²⋊C₄×C₅₉	—	2	4	no	—
231	C₂²⋊C₄×C₅₉	—	2	4	no	—
232	C₂²⋊C₄×C₅₉	—	2	4	no	—
233	C₂²⋊C₄×C₅₉	—	2	4	no	—
234	C₂²⋊C₄×C₅₉	—	2	4	no	—
235	C₂²⋊C₄×C₅₉	—	2	4	no	—
236	C₂²⋊C₄×C₅₉	—	4	2	no	—
237	C₄²×C₅₉	—	2	2	no	—
238	C₄²×C₅₉	—	2	2	no	—
239	C₄²×C₅₉	—	2	4	no	—
240	C₄²×C₅₉	—	2	1	no	—
241	C₄²×C₅₉	—	2	1	no	—
242	C₄²×C₅₉	—	4	2	no	—
243	C₄²×C₅₉	—	4	2	no	—
244	C₄²×C₅₉	C₂×D₄	1	2	yes	—
245	C₄²×C₅₉	C₂×D₄	1	2	yes	—
246	C₂³×C₅₉	—	2	1	no	—
247	C₂³×C₅₉	—	2	1	no	—
248	C₂³×C₅₉	—	2	1	no	—
249	C₂³×C₅₉	—	2	1	no	—
250	C₂³×C₅₉	—	2	1	no	—
251	C₂³×C₅₉	—	2	1	no	—
252	C₂³×C₅₉	—	2	2	no	—
253	C₂³×C₅₉	—	4	1	no	—
254	C₂³×C₅₉	—	4	1	no	—
255	C₂³×C₅₉	—	4	1	no	—
256	C₂³×C₅₉	—	4	1	no	—
257	C₂³×C₅₉	—	4	1	no	—
258	C₂³×C₅₉	—	4	1	no	—
259	C₂³×C₅₉	#137	1	2	yes	—
260	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
261	Q₈×C₅₉	—	2	2	no	—
262	Q₈×C₅₉	—	2	2	no	—
263	Q₈×C₅₉	—	2	2	no	—
264	Q₈×C₅₉	—	2	2	no	—
265	Q₈×C₅₉	—	4	1	no	—
266	Q₈×C₅₉	—	4	1	no	—
267	Q₈×C₅₉	—	4	1	no	—
268	Q₈×C₅₉	—	4	1	no	—
269	D₄×C₅₉	—	2	2	no	—
270	D₄×C₅₉	—	2	2	no	—
271	D₄×C₅₉	—	4	8	no	—
272	D₄×C₅₉	—	4	1	no	—
273	D₄×C₅₉	—	4	1	no	—
274	C₂×C₄×C₅₉	—	2	1	no	—
275	C₂×C₄×C₅₉	—	2	1	no	—
276	C₂×C₄×C₅₉	—	2	1	no	—
277	C₂×C₄×C₅₉	—	2	1	no	—
278	C₂×C₄×C₅₉	—	2	1	no	—
279	C₂×C₄×C₅₉	—	2	1	no	—
280	C₂×C₄×C₅₉	—	2	1	no	—
281	C₂×C₄×C₅₉	—	2	2	no	—
282	C₂×C₄×C₅₉	—	2	2	no	—
283	C₂×C₄×C₅₉	—	2	2	no	—
284	C₂×C₄×C₅₉	—	2	2	no	—
285	C₂×C₄×C₅₉	—	2	2	no	—
286	C₂×C₄×C₅₉	—	2	1	no	—
287	C₂×C₄×C₅₉	—	2	1	no	—
288	C₂×C₄×C₅₉	—	2	1	no	—
289	C₂×C₄×C₅₉	—	2	1	no	—
290	C₂×C₄×C₅₉	—	2	1	no	—
291	C₂×C₄×C₅₉	—	2	1	no	—
292	C₂×C₄×C₅₉	—	4	4	no	—
293	C₂×C₄×C₅₉	—	4	4	no	—
294	C₂×C₄×C₅₉	—	4	8	no	—
295	C₂×C₄×C₅₉	—	4	1	no	—
296	C₂×C₄×C₅₉	—	4	1	no	—
297	C₂×C₄×C₅₉	—	4	1	no	—
298	C₂×C₄×C₅₉	—	4	1	no	—
299	C₂×C₄×C₅₉	—	4	1	no	—
300	C₂×C₄×C₅₉	—	4	1	no	—
301	C₂×C₄×C₅₉	—	4	1	no	—
302	C₂×C₄×C₅₉	—	4	1	no	—
303	C₂×C₄×C₅₉	—	4	1	no	—
304	C₂×C₄×C₅₉	—	4	1	no	—
305	C₂×C₄×C₅₉	—	4	1	no	—
306	C₂×C₄×C₅₉	—	4	1	no	—
307	C₂×C₄×C₅₉	—	4	1	no	—
308	C₂×C₄×C₅₉	—	4	1	no	—
309	C₂×C₄×C₅₉	—	4	1	no	—
310	C₂×C₄×C₅₉	—	4	1	no	—
311	C₂×C₄×C₅₉	—	4	1	no	—
312	C₂×C₄×C₅₉	—	4	1	no	—
313	C₂×C₄×C₅₉	—	4	1	no	—
314	C₂×C₄×C₅₉	—	4	1	no	—
315	C₂×C₄×C₅₉	#120	1	2	yes	—
316	C₂×C₄×C₅₉	#120	1	2	yes	—
317	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
320	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
321	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
322	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
323	C₈×C₅₉	—	2	2	no	—
324	C₈×C₅₉	—	2	2	no	—
325	C₈×C₅₉	—	4	1	no	—
326	C₈×C₅₉	—	4	1	no	—
327	#23578	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
328	C₂²×C₅₉	—	2	2	no	—
329	C₂²×C₅₉	—	2	2	no	—
330	C₂²×C₅₉	—	2	2	no	—
331	C₂²×C₅₉	—	4	1	no	—
332	C₂²×C₅₉	—	4	1	no	—
333	C₂²×C₅₉	—	4	1	no	—
334	C₂²×C₅₉	—	4	1	no	—
335	C₂²×C₅₉	—	4	2	no	—
336	C₂²×C₅₉	—	4	2	no	—
337	C₂²×C₅₉	—	4	2	no	—
338	C₂²×C₅₉	—	8	1	no	—
339	C₂²×C₅₉	—	8	1	no	—
340	C₂²×C₅₉	—	8	1	no	—
341	C₂²×C₅₉	—	8	1	no	—
342	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
343	C₂²×C₅₉	#525	1	1	yes	characteristic
344	C₂²×C₅₉	#532	1	1	yes	characteristic
345	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
346	C₂²×C₅₉	#575	1	1	yes	characteristic
347	C₂²×C₅₉	#575	1	1	yes	characteristic
348	C₂²×C₅₉	#575	1	1	yes	characteristic
349	C₄×C₅₉	—	2	2	no	—
350	C₄×C₅₉	—	2	2	no	—
351	C₄×C₅₉	—	4	2	no	—
352	C₄×C₅₉	—	4	1	no	—
353	C₄×C₅₉	—	4	2	no	—
354	C₄×C₅₉	—	4	2	no	—
355	C₄×C₅₉	—	4	1	no	—
356	C₄×C₅₉	—	4	2	no	—
357	C₄×C₅₉	—	4	1	no	—
358	C₄×C₅₉	—	4	2	no	—
359	C₄×C₅₉	—	8	1	no	—
360	C₄×C₅₉	—	8	1	no	—
361	C₄×C₅₉	#525	1	1	yes	characteristic
362	C₄×C₅₉	#525	1	1	yes	characteristic
363	C₄×C₅₉	#532	1	1	yes	characteristic
364	C₄×C₅₉	#532	1	1	yes	characteristic
365	C₂×#529	C₂×C₅₉	1	1	yes	characteristic
366	C₂×#441	C₂×C₅₉	1	1	yes	characteristic, complemented
367	C₂×#440	C₂×C₅₉	1	1	yes	characteristic, complemented
368	C₄×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
369	#2059	C₂×C₅₉	1	1	yes	characteristic, complemented
370	#2042	C₂×C₅₉	1	1	yes	characteristic, complemented
371	#2036	C₂×C₅₉	1	1	yes	characteristic, complemented
372	#2034	C₂×C₅₉	1	1	yes	characteristic
373	#2026	C₂×C₅₉	1	1	yes	characteristic, complemented
374	#2015	C₂×C₅₉	1	1	yes	characteristic, complemented
375	#2001	C₂×C₅₉	1	1	yes	characteristic, complemented
376	#2000	C₂×C₅₉	1	1	yes	characteristic
377	#1763	C₂×C₅₉	1	1	yes	characteristic, complemented
378	#1762	C₂×C₅₉	1	1	yes	characteristic, complemented
379	#1749	C₂×C₅₉	1	1	yes	characteristic, complemented
380	C₂×C₅₉	—	4	2	no	—
381	C₂×C₅₉	—	8	2	no	—
382	C₂×C₅₉	#2388	1	1	yes	characteristic
383	C₂×C₅₉	#3005	1	1	yes	characteristic
384	C₂×C₅₉	#3007	1	1	yes	characteristic
385	C₂×C₅₉	#3111	1	1	yes	characteristic
386	C₂×C₅₉	#3117	1	1	yes	characteristic
387	C₂×C₅₉	#3181	1	1	yes	characteristic
388	C₂×C₅₉	#3183	1	1	yes	characteristic
389	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
390	C₂²×SD₁₆	C₂²×C₅₉	1	1	yes	characteristic
391	#529	—	2	4	no	—
392	#529	—	2	4	no	—
393	C₂×#126	—	2	1	no	—
394	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
395	C₂×#124	C₂²×C₅₉	1	1	yes	characteristic
396	C₂×#123	—	2	1	no	—
397	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
398	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
399	C₂×#121	C₂²×C₅₉	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
402	C₂×C₄×D₄	—	2	1	no	—
403	C₂×C₄×D₄	C₂²×C₅₉	1	1	yes	characteristic
404	C₂×#117	—	2	1	no	—
405	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
406	#441	—	2	4	no	—
407	#440	—	2	4	no	—
408	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
409	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
410	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
411	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
412	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
413	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
414	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
415	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
416	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
417	C₂×#102	C₂²×C₅₉	1	1	yes	characteristic
418	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
419	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
420	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
421	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
422	#391	C₂²×C₅₉	1	1	yes	characteristic
423	#389	C₂²×C₅₉	1	1	yes	characteristic
424	#387	—	2	1	no	—
425	#385	—	2	1	no	—
426	#380	C₂²×C₅₉	1	1	yes	characteristic
427	C₄×C₄⋊C₄	—	2	1	no	—
428	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
429	C₄×C₂²⋊C₄	—	2	1	no	—
430	#340	C₂²×C₅₉	1	1	yes	characteristic
431	#340	C₂²×C₅₉	1	1	yes	characteristic
432	#340	C₂²×C₅₉	1	1	yes	characteristic
433	#340	C₂²×C₅₉	1	1	yes	characteristic
434	#336	C₂²×C₅₉	1	1	yes	characteristic
435	#336	C₂²×C₅₉	1	1	yes	characteristic
436	C₅₉	#23578	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
438	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
443	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
444	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
445	C₂×Q₁₆	—	2	2	no	—
446	C₂×Q₁₆	—	2	2	no	—
447	C₂×Q₁₆	—	2	2	no	—
448	C₂×SD₁₆	—	2	2	no	—
449	C₂×SD₁₆	—	2	2	no	—
450	C₂×SD₁₆	—	2	2	no	—
451	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
455	#126	—	2	8	no	—
456	#125	—	2	2	no	—
457	#125	—	2	2	no	—
458	#124	—	2	2	no	—
459	#124	—	2	2	no	—
460	#123	—	2	8	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	2	2	no	—
463	C₂²⋊Q₈	—	2	2	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	—	2	2	no	—
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	D₄×C₅₉	1	4	yes	—
471	C₄×D₄	—	2	8	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	D₄×C₅₉	1	4	yes	—
474	#117	—	2	8	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₄⋊C₄	—	2	1	no	—
478	C₂×C₄⋊C₄	—	2	1	no	—
479	C₂×C₄⋊C₄	—	2	1	no	—
480	C₂×C₄⋊C₄	—	2	1	no	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
483	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
487	C₂×C₂²⋊C₄	—	2	1	no	—
488	C₂×C₂²⋊C₄	—	2	1	no	—
489	C₂×C₂²⋊C₄	—	2	1	no	—
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₄²	—	2	1	no	—
495	C₂×C₄²	—	2	2	no	—
496	C₂×C₄²	—	2	2	no	—
497	C₂×C₄²	—	2	1	no	—
498	C₂×C₄²	—	2	1	no	—
499	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
500	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
501	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
502	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
503	#107	—	2	2	no	—
504	#106	—	2	2	no	—
505	#103	—	2	2	no	—
506	#103	—	2	2	no	—
507	#103	—	2	2	no	—
508	#103	—	2	2	no	—
509	#103	—	2	2	no	—
510	#102	—	2	2	no	—
511	#102	—	2	2	no	—
512	#102	—	2	2	no	—
513	C₂²⋊C₈	—	2	2	no	—
514	C₂²⋊C₈	—	2	2	no	—
515	#97	—	2	2	no	—
516	#97	—	2	2	no	—
517	#95	—	2	1	no	—
518	#95	—	2	1	no	—
519	#95	—	2	1	no	—
520	#95	—	2	1	no	—
521	#95	—	2	1	no	—
522	C₂⁴	—	2	1	no	—
523	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
524	C₂×Q₈	—	2	1	no	—
525	C₂×Q₈	—	2	1	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
535	C₂×Q₈	#41×C₅₉	1	2	yes	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	4	2	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	4	1	no	—
563	C₂²×C₄	—	4	1	no	—
564	C₂²×C₄	—	4	1	no	—
565	C₂²×C₄	—	4	2	no	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
573	Q₁₆	—	2	8	no	—
574	SD₁₆	—	2	8	no	—
575	C₂×C₈	—	2	1	no	—
576	C₂×C₈	—	2	1	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	#41×C₅₉	1	2	yes	—
586	C₂×C₈	#41×C₅₉	1	2	yes	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	4	2	no	—
600	C₄⋊C₄	—	4	2	no	—
601	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
602	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
603	C₄⋊C₄	#41×C₅₉	1	2	yes	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	4	no	—
607	C₂²⋊C₄	—	2	4	no	—
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	4	2	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	4	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	4	2	no	—
617	C₄²	—	4	2	no	—
618	C₄²	C₂×D₄×C₅₉	1	2	yes	—
619	C₄²	C₂×D₄×C₅₉	1	2	yes	—
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	4	1	no	—
628	C₂³	—	4	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	—	4	1	no	—
631	C₂³	—	4	1	no	—
632	C₂³	—	4	1	no	—
633	C₂³	#137×C₅₉	1	2	yes	—
634	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
635	Q₈	—	2	2	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	2	2	no	—
638	Q₈	—	2	2	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	D₄	—	2	2	no	—
644	D₄	—	2	2	no	—
645	D₄	—	4	8	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	4	no	—
668	C₂×C₄	—	4	8	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	4	1	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	1	no	—
683	C₂×C₄	—	4	1	no	—
684	C₂×C₄	—	4	1	no	—
685	C₂×C₄	—	4	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	#120×C₅₉	1	2	yes	—
690	C₂×C₄	#120×C₅₉	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
693	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
694	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
695	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
696	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	4	1	no	—
700	C₈	—	4	1	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	4	1	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	2	no	—
711	C₂²	—	8	1	no	—
712	C₂²	—	8	1	no	—
713	C₂²	—	8	1	no	—
714	C₂²	—	8	1	no	—
715	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
716	C₂²	C₅₉×#525	1	1	yes	characteristic
717	C₂²	C₅₉×#532	1	1	yes	characteristic
718	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
719	C₂²	C₅₉×#575	1	1	yes	characteristic
720	C₂²	C₅₉×#575	1	1	yes	characteristic
721	C₂²	C₅₉×#575	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	8	1	no	—
733	C₄	—	8	1	no	—
734	C₄	C₅₉×#525	1	1	yes	characteristic
735	C₄	C₅₉×#525	1	1	yes	characteristic
736	C₄	C₅₉×#532	1	1	yes	characteristic
737	C₄	C₅₉×#532	1	1	yes	characteristic
738	C₂	—	4	2	no	—
739	C₂	—	8	2	no	—
740	C₂	C₅₉×#2388	1	1	yes	characteristic
741	C₂	C₅₉×#3005	1	1	yes	characteristic
742	C₂	C₅₉×#3007	1	1	yes	characteristic
743	C₂	C₅₉×#3111	1	1	yes	characteristic
744	C₂	C₅₉×#3117	1	1	yes	characteristic
745	C₂	C₅₉×#3181	1	1	yes	characteristic
746	C₂	C₅₉×#3183	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂×#121×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#441	C₂	semidirect
3. C₂×C₅₉×#440	C₂	semidirect
4. C₄×C₂²⋊Q₈×C₅₉	C₂	semidirect
5. C₅₉×#2059	C₂	semidirect
6. C₅₉×#2042	C₂	semidirect
7. C₅₉×#2036	C₂	semidirect
9. C₅₉×#2026	C₂	semidirect
10. C₅₉×#2015	C₂	semidirect
11. C₅₉×#2001	C₂	semidirect
13. C₅₉×#1763	C₂	semidirect
14. C₅₉×#1762	C₂	semidirect
15. C₅₉×#1749	C₂	semidirect
327. #23578	C₅₉	direct (N × H)
366. C₂×#441	C₂×C₅₉	semidirect
367. C₂×#440	C₂×C₅₉	semidirect
368. C₄×C₂²⋊Q₈	C₂×C₅₉	semidirect
369. #2059	C₂×C₅₉	semidirect
370. #2042	C₂×C₅₉	semidirect
371. #2036	C₂×C₅₉	semidirect
373. #2026	C₂×C₅₉	semidirect
374. #2015	C₂×C₅₉	semidirect
375. #2001	C₂×C₅₉	semidirect
377. #1763	C₂×C₅₉	semidirect
378. #1762	C₂×C₅₉	semidirect
379. #1749	C₂×C₅₉	semidirect
436. C₅₉	#23578	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×#529	2
C₂×C₅₉×#441	2
C₂×C₅₉×#440	2
C₄×C₂²⋊Q₈×C₅₉	2
C₅₉×#2059	2
C₅₉×#2042	2
C₅₉×#2036	2
C₅₉×#2034	2
C₅₉×#2026	2
C₅₉×#2015	2
C₅₉×#2001	2
C₅₉×#2000	2
C₅₉×#1763	2
C₅₉×#1762	2
C₅₉×#1749	2
#23578	59

Subgroups — C59×#23578 #28435687

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23578 #28435687