Subgroups — C₅₉×#25672 #28437781

Order 15104.

1094 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2857	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2035	C₂	1	4	yes	maximal
6	C₅₉×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1865	C₂	1	4	yes	maximal, complemented
9	C₄×C₂²⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#533	—	2	4	no	—
11	C₅₉×#533	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#125×C₅₉	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₅₉	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₅₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
21	C₂×#117×C₅₉	—	2	1	no	—
22	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#498	—	2	4	no	—
24	C₅₉×#487	—	2	4	no	—
25	C₂×#106×C₅₉	C₂²	1	4	yes	—
26	C₂×#103×C₅₉	C₂²	1	4	yes	—
27	C₂×#103×C₅₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₅₉	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#391	—	2	1	no	—
32	C₅₉×#389	—	2	1	no	—
33	C₅₉×#389	C₂²	1	2	yes	—
34	C₅₉×#384	C₂²	1	1	yes	characteristic
35	C₅₉×#380	—	2	1	no	—
36	C₅₉×#380	C₂²	1	2	yes	—
37	C₅₉×#340	C₂²	1	4	yes	—
38	C₅₉×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₅₉	—	2	1	no	—
40	C₂²×Q₈×C₅₉	—	2	1	no	—
41	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₅₉	—	2	2	no	—
48	C₄⋊Q₈×C₅₉	—	2	2	no	—
49	C₄⋊Q₈×C₅₉	—	2	2	no	—
50	C₄⋊Q₈×C₅₉	—	2	2	no	—
51	C₄⋊Q₈×C₅₉	D₄	1	4	yes	—
52	C₄⋊Q₈×C₅₉	D₄	1	4	yes	—
53	#125×C₅₉	—	2	8	no	—
54	C₂²⋊Q₈×C₅₉	—	2	8	no	—
55	C₂²⋊Q₈×C₅₉	—	2	4	no	—
56	C₂²⋊Q₈×C₅₉	—	2	4	no	—
57	C₂²⋊Q₈×C₅₉	—	4	4	no	—
58	C₄×Q₈×C₅₉	—	2	8	no	—
59	C₄×Q₈×C₅₉	—	2	4	no	—
60	C₄×Q₈×C₅₉	—	2	4	no	—
61	#117×C₅₉	—	2	8	no	—
62	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₄²×C₅₉	—	2	2	no	—
77	C₂×C₄²×C₅₉	—	2	2	no	—
78	C₂×C₄²×C₅₉	—	2	2	no	—
79	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
83	#106×C₅₉	—	2	8	no	—
84	#103×C₅₉	—	2	8	no	—
85	#103×C₅₉	—	2	8	no	—
86	C₂²⋊C₈×C₅₉	—	2	4	no	—
87	C₄×C₈×C₅₉	—	2	2	no	—
88	C₄×C₈×C₅₉	—	2	2	no	—
89	#95×C₅₉	—	2	2	no	—
90	#95×C₅₉	—	2	2	no	—
91	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₅₉	—	2	4	no	—
93	C₂×Q₈×C₅₉	—	2	2	no	—
94	C₂×Q₈×C₅₉	—	2	4	no	—
95	C₂×Q₈×C₅₉	—	2	4	no	—
96	C₂×Q₈×C₅₉	—	4	2	no	—
97	C₂×Q₈×C₅₉	—	4	2	no	—
98	C₂×Q₈×C₅₉	—	4	2	no	—
99	C₂×Q₈×C₅₉	—	4	2	no	—
100	C₂×Q₈×C₅₉	—	4	2	no	—
101	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
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	1	no	—
110	C₂²×C₄×C₅₉	—	2	1	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	SD₁₆	1	4	yes	—
116	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
122	C₂×C₈×C₅₉	—	2	2	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	—	2	2	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₂×C₈×C₅₉	—	2	2	no	—
127	C₂×C₈×C₅₉	#41	1	4	yes	—
128	C₄⋊C₄×C₅₉	—	2	8	no	—
129	C₄⋊C₄×C₅₉	—	2	8	no	—
130	C₄⋊C₄×C₅₉	—	2	4	no	—
131	C₄⋊C₄×C₅₉	—	2	4	no	—
132	C₄⋊C₄×C₅₉	—	2	4	no	—
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	2	2	no	—
135	C₄⋊C₄×C₅₉	—	2	2	no	—
136	C₄⋊C₄×C₅₉	—	2	4	no	—
137	C₄⋊C₄×C₅₉	—	4	2	no	—
138	C₄⋊C₄×C₅₉	—	4	2	no	—
139	C₄⋊C₄×C₅₉	—	4	4	no	—
140	C₄⋊C₄×C₅₉	—	4	2	no	—
141	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₅₉	—	2	8	no	—
143	C₂²⋊C₄×C₅₉	—	4	4	no	—
144	C₄²×C₅₉	—	2	8	no	—
145	C₄²×C₅₉	—	2	2	no	—
146	C₄²×C₅₉	—	2	2	no	—
147	C₄²×C₅₉	—	2	1	no	—
148	C₄²×C₅₉	—	2	1	no	—
149	C₄²×C₅₉	C₂×D₄	1	2	yes	—
150	C₄²×C₅₉	C₂×D₄	1	2	yes	—
151	C₂³×C₅₉	—	2	1	no	—
152	C₂³×C₅₉	—	2	1	no	—
153	C₂³×C₅₉	—	2	1	no	—
154	C₂³×C₅₉	—	2	1	no	—
155	C₂³×C₅₉	—	2	1	no	—
156	C₂³×C₅₉	—	2	1	no	—
157	C₂³×C₅₉	C₂×SD₁₆	1	2	yes	—
158	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₅₉	—	2	8	no	—
160	Q₈×C₅₉	—	4	4	no	—
161	Q₈×C₅₉	—	4	8	no	—
162	Q₈×C₅₉	—	8	4	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	2	8	no	—
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	4	no	—
169	C₂×C₄×C₅₉	—	2	4	no	—
170	C₂×C₄×C₅₉	—	2	1	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	2	1	no	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	4	2	no	—
175	C₂×C₄×C₅₉	—	4	2	no	—
176	C₂×C₄×C₅₉	—	4	2	no	—
177	C₂×C₄×C₅₉	—	4	2	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	4	2	no	—
180	C₂×C₄×C₅₉	—	4	4	no	—
181	C₂×C₄×C₅₉	—	4	2	no	—
182	C₂×C₄×C₅₉	—	4	2	no	—
183	C₂×C₄×C₅₉	—	4	2	no	—
184	C₂×C₄×C₅₉	—	4	2	no	—
185	C₂×C₄×C₅₉	—	4	2	no	—
186	C₂×C₄×C₅₉	—	4	2	no	—
187	C₂×C₄×C₅₉	#120	1	2	yes	—
188	C₂×C₄×C₅₉	#120	1	2	yes	—
189	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
190	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₅₉	#135	1	2	yes	—
192	C₂×C₄×C₅₉	#137	1	2	yes	—
193	C₂×C₄×C₅₉	#137	1	2	yes	—
194	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
197	C₂×C₄×C₅₉	2₋¹⁺⁴	1	2	yes	—
198	C₈×C₅₉	—	2	4	no	—
199	C₈×C₅₉	—	4	2	no	—
200	#25672	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₅₉	—	2	2	no	—
202	C₂²×C₅₉	—	2	2	no	—
203	C₂²×C₅₉	—	2	2	no	—
204	C₂²×C₅₉	—	4	1	no	—
205	C₂²×C₅₉	—	4	1	no	—
206	C₂²×C₅₉	—	4	1	no	—
207	C₂²×C₅₉	—	4	1	no	—
208	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
209	C₂²×C₅₉	#532	1	1	yes	characteristic
210	C₂²×C₅₉	#536	1	1	yes	characteristic
211	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
212	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
213	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
214	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
215	C₄×C₅₉	—	2	2	no	—
216	C₄×C₅₉	—	4	1	no	—
217	C₄×C₅₉	—	4	4	no	—
218	C₄×C₅₉	—	4	1	no	—
219	C₄×C₅₉	—	4	4	no	—
220	C₄×C₅₉	—	8	2	no	—
221	C₄×C₅₉	—	8	2	no	—
222	C₄×C₅₉	#448	1	4	yes	—
223	C₄×C₅₉	#452	1	4	yes	—
224	C₄×C₅₉	#547	1	2	yes	—
225	C₄×C₅₉	#548	1	2	yes	—
226	C₂×#533	C₂×C₅₉	1	1	yes	characteristic
227	C₂×#498	C₂×C₅₉	1	1	yes	characteristic, complemented
228	C₂×#487	C₂×C₅₉	1	1	yes	characteristic, complemented
229	#2857	C₂×C₅₉	1	1	yes	characteristic
230	#2035	C₂×C₅₉	1	4	yes	—
231	#1990	C₂×C₅₉	1	1	yes	characteristic, complemented
232	#1956	C₂×C₅₉	1	1	yes	characteristic, complemented
233	#1865	C₂×C₅₉	1	4	yes	complemented
234	C₄×C₂²⋊C₈	C₂×C₅₉	1	1	yes	characteristic
235	C₂×C₅₉	—	4	2	no	—
236	C₂×C₅₉	#2432	1	1	yes	characteristic
237	C₂×C₅₉	C₂×#448	1	1	yes	characteristic
238	C₂×C₅₉	C₂×#452	1	1	yes	characteristic
239	C₂×C₅₉	#3167	1	1	yes	characteristic
240	C₂×C₅₉	#3185	1	1	yes	characteristic
241	C₂×C₅₉	#3229	1	1	yes	characteristic
242	C₂×C₅₉	#3231	1	1	yes	characteristic
243	#533	—	2	4	no	—
244	#533	—	2	4	no	—
245	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
248	C₂×#125	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
252	C₂×C₄×Q₈	—	2	1	no	—
253	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
254	C₂×#117	—	2	1	no	—
255	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
256	#498	—	2	4	no	—
257	#487	—	2	4	no	—
258	C₂×#106	C₂²×C₅₉	1	4	yes	—
259	C₂×#103	C₂²×C₅₉	1	4	yes	—
260	C₂×#103	C₂²×C₅₉	1	4	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₅₉	1	2	yes	—
262	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
264	#391	—	2	1	no	—
265	#389	—	2	1	no	—
266	#389	C₂²×C₅₉	1	2	yes	—
267	#384	C₂²×C₅₉	1	1	yes	characteristic
268	#380	—	2	1	no	—
269	#380	C₂²×C₅₉	1	2	yes	—
270	#340	C₂²×C₅₉	1	4	yes	—
271	#336	C₂²×C₅₉	1	2	yes	—
272	C₅₉	#25672	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	—	2	1	no	—
275	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
276	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
277	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
280	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	D₄×C₅₉	1	4	yes	—
286	C₄⋊Q₈	D₄×C₅₉	1	4	yes	—
287	#125	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	4	4	no	—
292	C₄×Q₈	—	2	8	no	—
293	C₄×Q₈	—	2	4	no	—
294	C₄×Q₈	—	2	4	no	—
295	#117	—	2	8	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
314	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
317	#106	—	2	8	no	—
318	#103	—	2	8	no	—
319	#103	—	2	8	no	—
320	C₂²⋊C₈	—	2	4	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	SD₁₆×C₅₉	1	4	yes	—
350	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
355	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	#41×C₅₉	1	4	yes	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	8	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	C₂×D₄×C₅₉	1	2	yes	—
384	C₄²	C₂×D₄×C₅₉	1	2	yes	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	C₂×SD₁₆×C₅₉	1	2	yes	—
392	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
393	Q₈	—	2	8	no	—
394	Q₈	—	4	8	no	—
395	Q₈	—	4	4	no	—
396	Q₈	—	8	4	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	#120×C₅₉	1	2	yes	—
422	C₂×C₄	#120×C₅₉	1	2	yes	—
423	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
424	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
425	C₂×C₄	#135×C₅₉	1	2	yes	—
426	C₂×C₄	#137×C₅₉	1	2	yes	—
427	C₂×C₄	#137×C₅₉	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
431	C₂×C₄	2₋¹⁺⁴×C₅₉	1	2	yes	—
432	C₈	—	2	4	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
442	C₂²	C₅₉×#532	1	1	yes	characteristic
443	C₂²	C₅₉×#536	1	1	yes	characteristic
444	C₂²	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
445	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
446	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
447	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	4	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₅₉×#448	1	4	yes	—
456	C₄	C₅₉×#452	1	4	yes	—
457	C₄	C₅₉×#547	1	2	yes	—
458	C₄	C₅₉×#548	1	2	yes	—
459	C₂	—	4	2	no	—
460	C₂	C₅₉×#2432	1	1	yes	characteristic
461	C₂	C₂×C₅₉×#448	1	1	yes	characteristic
462	C₂	C₂×C₅₉×#452	1	1	yes	characteristic
463	C₂	C₅₉×#3167	1	1	yes	characteristic
464	C₂	C₅₉×#3185	1	1	yes	characteristic
465	C₂	C₅₉×#3229	1	1	yes	characteristic
466	C₂	C₅₉×#3231	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
2. C₂×C₅₉×#498	C₂	semidirect
3. C₂×C₅₉×#487	C₂	semidirect
6. C₅₉×#1990	C₂	semidirect
7. C₅₉×#1956	C₂	semidirect
8. C₅₉×#1865	C₂	semidirect
200. #25672	C₅₉	direct (N × H)
227. C₂×#498	C₂×C₅₉	semidirect
228. C₂×#487	C₂×C₅₉	semidirect
231. #1990	C₂×C₅₉	semidirect
232. #1956	C₂×C₅₉	semidirect
233. #1865	C₂×C₅₉	semidirect
272. C₅₉	#25672	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×#533	2
C₂×C₅₉×#498	2
C₂×C₅₉×#487	2
C₅₉×#2857	2
C₅₉×#2035	2
C₅₉×#1990	2
C₅₉×#1956	2
C₅₉×#1865	2
C₄×C₂²⋊C₈×C₅₉	2
#25672	59

Subgroups — C59×#25672 #28437781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#25672 #28437781