Subgroups — C₅₉×#23709 #28435818

Order 15104.

874 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#432	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₄×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2077	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2036	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#2035	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2001	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#1776	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1763	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#441	—	2	4	no	—
23	C₅₉×#432	—	2	4	no	—
24	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#391	C₂²	1	1	yes	characteristic
40	C₅₉×#391	C₂²	1	1	yes	characteristic
41	C₅₉×#389	C₂²	1	1	yes	characteristic
42	C₅₉×#389	C₂²	1	1	yes	characteristic
43	C₅₉×#387	—	2	1	no	—
44	C₅₉×#387	—	2	1	no	—
45	C₅₉×#385	—	2	1	no	—
46	C₅₉×#385	—	2	1	no	—
47	C₅₉×#380	C₂²	1	1	yes	characteristic
48	C₅₉×#380	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
50	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
51	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
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	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
66	C₂×Q₁₆×C₅₉	—	2	2	no	—
67	C₂×Q₁₆×C₅₉	—	2	2	no	—
68	C₂×Q₁₆×C₅₉	—	2	2	no	—
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	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
73	C₂²⋊Q₈×C₅₉	—	2	2	no	—
74	C₂²⋊Q₈×C₅₉	—	2	2	no	—
75	C₂²⋊Q₈×C₅₉	—	2	2	no	—
76	C₂²⋊Q₈×C₅₉	—	2	2	no	—
77	C₄×Q₈×C₅₉	—	2	2	no	—
78	C₄×Q₈×C₅₉	—	2	2	no	—
79	C₄×Q₈×C₅₉	—	2	2	no	—
80	C₄×Q₈×C₅₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
97	C₂×C₄²×C₅₉	—	2	2	no	—
98	C₂×C₄²×C₅₉	—	2	2	no	—
99	C₂×C₄²×C₅₉	—	2	1	no	—
100	C₂×C₄²×C₅₉	—	2	1	no	—
101	C₂×C₄²×C₅₉	—	2	1	no	—
102	C₂×C₄²×C₅₉	—	2	1	no	—
103	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
107	#107×C₅₉	—	2	2	no	—
108	#106×C₅₉	—	2	2	no	—
109	#106×C₅₉	—	2	2	no	—
110	C₄⋊C₈×C₅₉	—	2	2	no	—
111	C₄⋊C₈×C₅₉	—	2	2	no	—
112	#103×C₅₉	—	2	2	no	—
113	#103×C₅₉	—	2	2	no	—
114	#103×C₅₉	—	2	2	no	—
115	#103×C₅₉	—	2	2	no	—
116	#103×C₅₉	—	2	2	no	—
117	#103×C₅₉	—	2	2	no	—
118	C₂²⋊C₈×C₅₉	—	2	2	no	—
119	C₂²⋊C₈×C₅₉	—	2	2	no	—
120	#97×C₅₉	—	2	2	no	—
121	#97×C₅₉	D₄	1	4	yes	—
122	#95×C₅₉	—	2	1	no	—
123	#95×C₅₉	—	2	1	no	—
124	#95×C₅₉	—	2	1	no	—
125	#95×C₅₉	—	2	1	no	—
126	#95×C₅₉	—	2	1	no	—
127	#95×C₅₉	—	2	1	no	—
128	#95×C₅₉	—	2	1	no	—
129	#95×C₅₉	—	2	1	no	—
130	#95×C₅₉	—	2	1	no	—
131	#95×C₅₉	—	2	1	no	—
132	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₅₉	—	2	1	no	—
134	C₂×Q₈×C₅₉	—	2	1	no	—
135	C₂×Q₈×C₅₉	—	2	1	no	—
136	C₂×Q₈×C₅₉	—	2	1	no	—
137	C₂×Q₈×C₅₉	—	2	1	no	—
138	C₂×Q₈×C₅₉	—	2	1	no	—
139	C₂×Q₈×C₅₉	—	2	1	no	—
140	C₂×Q₈×C₅₉	—	2	1	no	—
141	C₂×Q₈×C₅₉	—	2	1	no	—
142	C₂×Q₈×C₅₉	—	2	1	no	—
143	C₂×Q₈×C₅₉	#41	1	2	yes	—
144	C₂×Q₈×C₅₉	#41	1	2	yes	—
145	C₂²×C₄×C₅₉	—	2	2	no	—
146	C₂²×C₄×C₅₉	—	2	1	no	—
147	C₂²×C₄×C₅₉	—	2	1	no	—
148	C₂²×C₄×C₅₉	—	2	1	no	—
149	C₂²×C₄×C₅₉	—	2	1	no	—
150	C₂²×C₄×C₅₉	—	2	2	no	—
151	C₂²×C₄×C₅₉	—	2	2	no	—
152	C₂²×C₄×C₅₉	—	2	2	no	—
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	—	4	1	no	—
164	C₂²×C₄×C₅₉	—	4	1	no	—
165	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
171	Q₁₆×C₅₉	—	2	8	no	—
172	C₂×C₈×C₅₉	—	2	1	no	—
173	C₂×C₈×C₅₉	—	2	1	no	—
174	C₂×C₈×C₅₉	—	2	1	no	—
175	C₂×C₈×C₅₉	—	2	1	no	—
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	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
184	C₄⋊C₄×C₅₉	—	2	4	no	—
185	C₄⋊C₄×C₅₉	—	2	4	no	—
186	C₄⋊C₄×C₅₉	—	2	1	no	—
187	C₄⋊C₄×C₅₉	—	2	1	no	—
188	C₄⋊C₄×C₅₉	—	2	1	no	—
189	C₄⋊C₄×C₅₉	—	2	1	no	—
190	C₄⋊C₄×C₅₉	—	2	1	no	—
191	C₄⋊C₄×C₅₉	—	2	1	no	—
192	C₄⋊C₄×C₅₉	—	2	1	no	—
193	C₄⋊C₄×C₅₉	—	2	1	no	—
194	C₄⋊C₄×C₅₉	—	2	1	no	—
195	C₄⋊C₄×C₅₉	—	2	1	no	—
196	C₄⋊C₄×C₅₉	—	4	2	no	—
197	C₄⋊C₄×C₅₉	—	4	2	no	—
198	C₄⋊C₄×C₅₉	—	4	2	no	—
199	C₄⋊C₄×C₅₉	—	4	2	no	—
200	C₄⋊C₄×C₅₉	#41	1	2	yes	—
201	C₄⋊C₄×C₅₉	#41	1	2	yes	—
202	C₂²⋊C₄×C₅₉	—	2	4	no	—
203	C₂²⋊C₄×C₅₉	—	2	4	no	—
204	C₂²⋊C₄×C₅₉	—	4	2	no	—
205	C₂²⋊C₄×C₅₉	—	4	2	no	—
206	C₄²×C₅₉	—	2	2	no	—
207	C₄²×C₅₉	—	2	2	no	—
208	C₄²×C₅₉	—	2	1	no	—
209	C₄²×C₅₉	—	2	1	no	—
210	C₄²×C₅₉	—	4	2	no	—
211	C₄²×C₅₉	—	4	2	no	—
212	C₄²×C₅₉	—	4	2	no	—
213	C₄²×C₅₉	—	4	2	no	—
214	C₄²×C₅₉	C₂×D₄	1	2	yes	—
215	C₄²×C₅₉	#41	1	2	yes	—
216	C₂³×C₅₉	—	2	1	no	—
217	C₂³×C₅₉	—	2	1	no	—
218	C₂³×C₅₉	—	2	1	no	—
219	C₂³×C₅₉	—	2	1	no	—
220	C₂³×C₅₉	—	2	1	no	—
221	C₂³×C₅₉	—	2	1	no	—
222	C₂³×C₅₉	#137	1	2	yes	—
223	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₅₉	—	2	2	no	—
225	Q₈×C₅₉	—	2	2	no	—
226	Q₈×C₅₉	—	2	2	no	—
227	Q₈×C₅₉	—	2	2	no	—
228	Q₈×C₅₉	—	4	1	no	—
229	Q₈×C₅₉	—	4	1	no	—
230	Q₈×C₅₉	—	4	1	no	—
231	Q₈×C₅₉	—	4	1	no	—
232	C₂×C₄×C₅₉	—	2	1	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	1	no	—
235	C₂×C₄×C₅₉	—	2	1	no	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	1	no	—
239	C₂×C₄×C₅₉	—	2	1	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	2	2	no	—
242	C₂×C₄×C₅₉	—	2	2	no	—
243	C₂×C₄×C₅₉	—	2	2	no	—
244	C₂×C₄×C₅₉	—	2	1	no	—
245	C₂×C₄×C₅₉	—	2	1	no	—
246	C₂×C₄×C₅₉	—	2	1	no	—
247	C₂×C₄×C₅₉	—	2	1	no	—
248	C₂×C₄×C₅₉	—	4	4	no	—
249	C₂×C₄×C₅₉	—	4	4	no	—
250	C₂×C₄×C₅₉	—	4	1	no	—
251	C₂×C₄×C₅₉	—	4	1	no	—
252	C₂×C₄×C₅₉	—	4	1	no	—
253	C₂×C₄×C₅₉	—	4	1	no	—
254	C₂×C₄×C₅₉	—	4	1	no	—
255	C₂×C₄×C₅₉	—	4	1	no	—
256	C₂×C₄×C₅₉	—	4	1	no	—
257	C₂×C₄×C₅₉	—	4	1	no	—
258	C₂×C₄×C₅₉	—	4	1	no	—
259	C₂×C₄×C₅₉	—	4	1	no	—
260	C₂×C₄×C₅₉	—	4	1	no	—
261	C₂×C₄×C₅₉	—	4	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	#121	1	2	yes	—
275	C₂×C₄×C₅₉	#121	1	2	yes	—
276	C₂×C₄×C₅₉	#137	1	2	yes	—
277	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
279	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
283	C₈×C₅₉	—	2	2	no	—
284	C₈×C₅₉	—	2	2	no	—
285	C₈×C₅₉	—	4	1	no	—
286	C₈×C₅₉	—	4	1	no	—
287	#23709	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂²×C₅₉	—	2	2	no	—
289	C₂²×C₅₉	—	2	2	no	—
290	C₂²×C₅₉	—	2	2	no	—
291	C₂²×C₅₉	—	4	1	no	—
292	C₂²×C₅₉	—	4	1	no	—
293	C₂²×C₅₉	—	4	1	no	—
294	C₂²×C₅₉	—	4	1	no	—
295	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
296	C₂²×C₅₉	#525	1	1	yes	characteristic
297	C₂²×C₅₉	#525	1	1	yes	characteristic
298	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
299	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
300	C₂²×C₅₉	#575	1	1	yes	characteristic
301	C₂²×C₅₉	#575	1	1	yes	characteristic
302	C₄×C₅₉	—	2	2	no	—
303	C₄×C₅₉	—	2	2	no	—
304	C₄×C₅₉	—	2	2	no	—
305	C₄×C₅₉	—	4	2	no	—
306	C₄×C₅₉	—	4	2	no	—
307	C₄×C₅₉	—	4	1	no	—
308	C₄×C₅₉	—	4	2	no	—
309	C₄×C₅₉	—	4	2	no	—
310	C₄×C₅₉	—	4	1	no	—
311	C₄×C₅₉	—	8	1	no	—
312	C₄×C₅₉	—	8	1	no	—
313	C₄×C₅₉	—	8	1	no	—
314	C₄×C₅₉	—	8	1	no	—
315	C₄×C₅₉	#525	1	1	yes	characteristic
316	C₄×C₅₉	#529	1	1	yes	characteristic
317	C₄×C₅₉	#529	1	1	yes	characteristic
318	C₄×C₅₉	#532	1	1	yes	characteristic
319	C₂×#441	C₂×C₅₉	1	1	yes	characteristic, complemented
320	C₂×#432	C₂×C₅₉	1	1	yes	characteristic
321	C₄×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
322	C₄×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
323	#2088	C₂×C₅₉	1	1	yes	characteristic, complemented
324	#2077	C₂×C₅₉	1	1	yes	characteristic
325	#2068	C₂×C₅₉	1	1	yes	characteristic, complemented
326	#2066	C₂×C₅₉	1	1	yes	characteristic, complemented
327	#2056	C₂×C₅₉	1	1	yes	characteristic, complemented
328	#2036	C₂×C₅₉	1	1	yes	characteristic
329	#2035	C₂×C₅₉	1	1	yes	characteristic
330	#2001	C₂×C₅₉	1	1	yes	characteristic
331	#1776	C₂×C₅₉	1	1	yes	characteristic, complemented
332	#1763	C₂×C₅₉	1	1	yes	characteristic, complemented
333	#1763	C₂×C₅₉	1	1	yes	characteristic, complemented
334	C₂×C₅₉	—	4	2	no	—
335	C₂×C₅₉	#2392	1	1	yes	characteristic
336	C₂×C₅₉	#3056	1	1	yes	characteristic
337	C₂×C₅₉	#3056	1	1	yes	characteristic
338	C₂×C₅₉	#3111	1	1	yes	characteristic
339	C₂×C₅₉	#3113	1	1	yes	characteristic
340	C₂×C₅₉	#3116	1	1	yes	characteristic
341	C₂×C₅₉	#3117	1	1	yes	characteristic
342	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
343	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
344	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
345	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
346	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
348	#441	—	2	4	no	—
349	#432	—	2	4	no	—
350	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
351	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
352	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
353	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
354	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
355	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
356	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
357	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
358	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
359	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
360	C₂×#103	C₂²×C₅₉	1	1	yes	characteristic
361	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
363	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
364	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
365	#391	C₂²×C₅₉	1	1	yes	characteristic
366	#391	C₂²×C₅₉	1	1	yes	characteristic
367	#389	C₂²×C₅₉	1	1	yes	characteristic
368	#389	C₂²×C₅₉	1	1	yes	characteristic
369	#387	—	2	1	no	—
370	#387	—	2	1	no	—
371	#385	—	2	1	no	—
372	#385	—	2	1	no	—
373	#380	C₂²×C₅₉	1	1	yes	characteristic
374	#380	C₂²×C₅₉	1	1	yes	characteristic
375	C₄×C₄⋊C₄	—	2	1	no	—
376	C₄×C₄⋊C₄	—	2	1	no	—
377	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	—	2	1	no	—
380	C₄×C₂²⋊C₄	—	2	1	no	—
381	#340	C₂²×C₅₉	1	1	yes	characteristic
382	#340	C₂²×C₅₉	1	1	yes	characteristic
383	#340	C₂²×C₅₉	1	1	yes	characteristic
384	#340	C₂²×C₅₉	1	1	yes	characteristic
385	#340	C₂²×C₅₉	1	1	yes	characteristic
386	#340	C₂²×C₅₉	1	1	yes	characteristic
387	C₅₉	#23709	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
389	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
390	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
391	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
393	C₂×Q₁₆	—	2	2	no	—
394	C₂×Q₁₆	—	2	2	no	—
395	C₂×Q₁₆	—	2	2	no	—
396	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
400	C₂²⋊Q₈	—	2	2	no	—
401	C₂²⋊Q₈	—	2	2	no	—
402	C₂²⋊Q₈	—	2	2	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	—	2	2	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₄²	—	2	2	no	—
425	C₂×C₄²	—	2	2	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
431	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
434	#107	—	2	2	no	—
435	#106	—	2	2	no	—
436	#106	—	2	2	no	—
437	C₄⋊C₈	—	2	2	no	—
438	C₄⋊C₈	—	2	2	no	—
439	#103	—	2	2	no	—
440	#103	—	2	2	no	—
441	#103	—	2	2	no	—
442	#103	—	2	2	no	—
443	#103	—	2	2	no	—
444	#103	—	2	2	no	—
445	C₂²⋊C₈	—	2	2	no	—
446	C₂²⋊C₈	—	2	2	no	—
447	#97	—	2	2	no	—
448	#97	D₄×C₅₉	1	4	yes	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	#41×C₅₉	1	2	yes	—
471	C₂×Q₈	#41×C₅₉	1	2	yes	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	4	1	no	—
491	C₂²×C₄	—	4	1	no	—
492	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
496	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
498	Q₁₆	—	2	8	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
510	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	4	2	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₄⋊C₄	—	4	2	no	—
526	C₄⋊C₄	—	4	2	no	—
527	C₄⋊C₄	#41×C₅₉	1	2	yes	—
528	C₄⋊C₄	#41×C₅₉	1	2	yes	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	4	2	no	—
538	C₄²	—	4	2	no	—
539	C₄²	—	4	2	no	—
540	C₄²	—	4	2	no	—
541	C₄²	C₂×D₄×C₅₉	1	2	yes	—
542	C₄²	#41×C₅₉	1	2	yes	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	#137×C₅₉	1	2	yes	—
550	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
551	Q₈	—	2	2	no	—
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	—	4	1	no	—
558	Q₈	—	4	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	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	#121×C₅₉	1	2	yes	—
602	C₂×C₄	#121×C₅₉	1	2	yes	—
603	C₂×C₄	#137×C₅₉	1	2	yes	—
604	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
605	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
606	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
607	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
608	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
609	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
610	C₈	—	2	2	no	—
611	C₈	—	2	2	no	—
612	C₈	—	4	1	no	—
613	C₈	—	4	1	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
622	C₂²	C₅₉×#525	1	1	yes	characteristic
623	C₂²	C₅₉×#525	1	1	yes	characteristic
624	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
625	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
626	C₂²	C₅₉×#575	1	1	yes	characteristic
627	C₂²	C₅₉×#575	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	2	2	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	—	8	1	no	—
640	C₄	—	8	1	no	—
641	C₄	C₅₉×#525	1	1	yes	characteristic
642	C₄	C₅₉×#529	1	1	yes	characteristic
643	C₄	C₅₉×#529	1	1	yes	characteristic
644	C₄	C₅₉×#532	1	1	yes	characteristic
645	C₂	—	4	2	no	—
646	C₂	C₅₉×#2392	1	1	yes	characteristic
647	C₂	C₅₉×#3056	1	1	yes	characteristic
648	C₂	C₅₉×#3056	1	1	yes	characteristic
649	C₂	C₅₉×#3111	1	1	yes	characteristic
650	C₂	C₅₉×#3113	1	1	yes	characteristic
651	C₂	C₅₉×#3116	1	1	yes	characteristic
652	C₂	C₅₉×#3117	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 ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#441	C₂	semidirect
5. C₅₉×#2088	C₂	semidirect
7. C₅₉×#2068	C₂	semidirect
8. C₅₉×#2066	C₂	semidirect
9. C₅₉×#2056	C₂	semidirect
13. C₅₉×#1776	C₂	semidirect
14. C₅₉×#1763	C₂	semidirect
15. C₅₉×#1763	C₂	semidirect
287. #23709	C₅₉	direct (N × H)
319. C₂×#441	C₂×C₅₉	semidirect
323. #2088	C₂×C₅₉	semidirect
325. #2068	C₂×C₅₉	semidirect
326. #2066	C₂×C₅₉	semidirect
327. #2056	C₂×C₅₉	semidirect
331. #1776	C₂×C₅₉	semidirect
332. #1763	C₂×C₅₉	semidirect
333. #1763	C₂×C₅₉	semidirect
387. C₅₉	#23709	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×#441	2
C₂×C₅₉×#432	2
C₄×C₂²⋊Q₈×C₅₉	2
C₅₉×#2088	2
C₅₉×#2077	2
C₅₉×#2068	2
C₅₉×#2066	2
C₅₉×#2056	2
C₅₉×#2036	2
C₅₉×#2035	2
C₅₉×#2001	2
C₅₉×#1776	2
C₅₉×#1763	2
#23709	59

Subgroups — C59×#23709 #28435818

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23709 #28435818