Subgroups — C₅₉×#21083 #28433192

Order 15104.

1178 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#416	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#416	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2297	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1934	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1933	C₂	1	4	yes	maximal, complemented
8	C₅₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#416	—	2	4	no	—
18	C₅₉×#416	C₄	1	8	yes	complemented
19	C₂×#103×C₅₉	C₂²	1	2	yes	—
20	C₂×#103×C₅₉	C₂²	1	2	yes	—
21	C₂×#102×C₅₉	C₂²	1	2	yes	—
22	C₂×#102×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₅₉	—	2	4	no	—
24	C₂×C₄×C₈×C₅₉	C₂²	1	4	yes	—
25	C₅₉×#391	C₂²	1	2	yes	—
26	C₅₉×#390	C₂²	1	2	yes	—
27	C₅₉×#389	C₂²	1	4	yes	—
28	C₅₉×#386	—	2	2	no	—
29	C₅₉×#385	—	2	2	no	—
30	C₄×C₄⋊C₄×C₅₉	—	2	2	no	—
31	C₄×C₂²⋊C₄×C₅₉	—	2	2	no	—
32	C₅₉×#340	C₂²	1	4	yes	—
33	C₅₉×#340	C₂²	1	4	yes	—
34	C₂×#41×C₅₉	—	2	2	no	—
35	C₂×#41×C₅₉	—	2	2	no	—
36	C₂×#41×C₅₉	—	2	2	no	—
37	C₂×#41×C₅₉	—	2	2	no	—
38	C₂×#41×C₅₉	—	2	2	no	—
39	C₂×#41×C₅₉	C₂×C₄	1	4	yes	—
40	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₅₉	—	2	1	no	—
42	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₅₉	—	2	1	no	—
44	C₂³×C₄×C₅₉	D₄	1	2	yes	—
45	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₅₉	—	2	2	no	—
47	C₂²×C₈×C₅₉	—	2	2	no	—
48	C₂²×C₈×C₅₉	—	2	2	no	—
49	C₂²×C₈×C₅₉	—	2	2	no	—
50	C₂²×C₈×C₅₉	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₅₉	D₄	1	4	yes	—
52	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
54	#117×C₅₉	—	2	2	no	—
55	#117×C₅₉	—	2	2	no	—
56	#117×C₅₉	—	2	2	no	—
57	#117×C₅₉	—	2	2	no	—
58	#117×C₅₉	—	2	2	no	—
59	#117×C₅₉	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
68	C₂×C₄²×C₅₉	—	2	2	no	—
69	C₂×C₄²×C₅₉	—	2	1	no	—
70	C₂×C₄²×C₅₉	—	2	2	no	—
71	C₂×C₄²×C₅₉	—	2	1	no	—
72	C₂×C₄²×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	D₄	1	2	yes	—
74	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
75	#103×C₅₉	—	2	4	no	—
76	#103×C₅₉	C₂×C₄	1	8	yes	complemented
77	#102×C₅₉	—	2	4	no	—
78	#102×C₅₉	C₂×C₄	1	8	yes	complemented
79	C₄×C₈×C₅₉	—	2	8	no	—
80	#95×C₅₉	—	2	4	no	—
81	#95×C₅₉	—	2	4	no	—
82	C₂⁴×C₅₉	—	2	1	no	—
83	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
84	#41×C₅₉	—	2	8	no	—
85	#41×C₅₉	—	2	8	no	—
86	#41×C₅₉	—	4	4	no	—
87	#41×C₅₉	—	4	4	no	—
88	C₂×Q₈×C₅₉	—	2	1	no	—
89	C₂×Q₈×C₅₉	—	2	1	no	—
90	C₂×Q₈×C₅₉	—	2	1	no	—
91	C₂×Q₈×C₅₉	—	2	1	no	—
92	C₂×Q₈×C₅₉	—	2	1	no	—
93	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₅₉	—	2	4	no	—
95	C₂×D₄×C₅₉	—	2	1	no	—
96	C₂×D₄×C₅₉	—	2	1	no	—
97	C₂×D₄×C₅₉	—	2	1	no	—
98	C₂×D₄×C₅₉	—	2	1	no	—
99	C₂×D₄×C₅₉	—	2	1	no	—
100	C₂×D₄×C₅₉	—	4	2	no	—
101	C₂×D₄×C₅₉	—	4	2	no	—
102	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅₉	—	2	4	no	—
104	C₂²×C₄×C₅₉	—	2	8	no	—
105	C₂²×C₄×C₅₉	—	2	1	no	—
106	C₂²×C₄×C₅₉	—	2	2	no	—
107	C₂²×C₄×C₅₉	—	2	4	no	—
108	C₂²×C₄×C₅₉	—	2	2	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	4	2	no	—
111	C₂²×C₄×C₅₉	—	4	2	no	—
112	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	#41	1	2	yes	—
117	C₂²×C₄×C₅₉	#41	1	2	yes	—
118	C₂²×C₄×C₅₉	#41	1	2	yes	—
119	C₂²×C₄×C₅₉	#41	1	2	yes	—
120	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₅₉	—	2	8	no	—
122	C₂×C₈×C₅₉	—	2	8	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	C₂²×C₄	1	4	yes	—
128	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₅₉	—	2	2	no	—
130	C₄⋊C₄×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	2	2	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	4	8	no	—
135	C₄⋊C₄×C₅₉	C₂²×C₄	1	4	yes	—
136	C₂²⋊C₄×C₅₉	—	2	4	no	—
137	C₂²⋊C₄×C₅₉	—	4	2	no	—
138	C₂²⋊C₄×C₅₉	—	4	2	no	—
139	C₂²⋊C₄×C₅₉	—	4	8	no	—
140	C₄²×C₅₉	—	2	4	no	—
141	C₄²×C₅₉	—	2	4	no	—
142	C₄²×C₅₉	—	2	2	no	—
143	C₄²×C₅₉	—	2	2	no	—
144	C₄²×C₅₉	—	4	2	no	—
145	C₄²×C₅₉	—	4	2	no	—
146	C₂³×C₅₉	—	2	4	no	—
147	C₂³×C₅₉	—	2	2	no	—
148	C₂³×C₅₉	—	4	1	no	—
149	C₂³×C₅₉	—	4	1	no	—
150	C₂³×C₅₉	—	4	4	no	—
151	C₂³×C₅₉	C₄×D₄	1	2	yes	—
152	C₂³×C₅₉	#121	1	2	yes	—
153	C₂³×C₅₉	#124	1	2	yes	—
154	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₅₉	—	2	2	no	—
156	Q₈×C₅₉	—	2	2	no	—
157	Q₈×C₅₉	—	4	1	no	—
158	Q₈×C₅₉	—	4	1	no	—
159	D₄×C₅₉	—	2	2	no	—
160	D₄×C₅₉	—	2	2	no	—
161	D₄×C₅₉	—	4	8	no	—
162	D₄×C₅₉	—	4	1	no	—
163	D₄×C₅₉	—	4	1	no	—
164	C₂×C₄×C₅₉	—	2	16	no	—
165	C₂×C₄×C₅₉	—	2	4	no	—
166	C₂×C₄×C₅₉	—	2	4	no	—
167	C₂×C₄×C₅₉	—	2	4	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	4	1	no	—
170	C₂×C₄×C₅₉	—	4	1	no	—
171	C₂×C₄×C₅₉	—	4	4	no	—
172	C₂×C₄×C₅₉	—	4	8	no	—
173	C₂×C₄×C₅₉	—	4	2	no	—
174	C₂×C₄×C₅₉	—	4	2	no	—
175	C₂×C₄×C₅₉	—	4	4	no	—
176	C₂×C₄×C₅₉	—	4	4	no	—
177	C₂×C₄×C₅₉	#117	1	4	yes	—
178	C₂×C₄×C₅₉	C₄×D₄	1	4	yes	—
179	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₅₉	#121	1	2	yes	—
181	C₂×C₄×C₅₉	#123	1	4	yes	—
182	C₂×C₄×C₅₉	#124	1	2	yes	—
183	C₂×C₄×C₅₉	#126	1	4	yes	—
184	C₂×C₄×C₅₉	#135	1	8	yes	—
185	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
191	C₈×C₅₉	—	2	4	no	—
192	C₈×C₅₉	—	2	4	no	—
193	#21083	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₅₉	—	2	4	no	—
195	C₂²×C₅₉	—	2	4	no	—
196	C₂²×C₅₉	—	2	4	no	—
197	C₂²×C₅₉	—	4	4	no	—
198	C₂²×C₅₉	—	4	2	no	—
199	C₂²×C₅₉	—	8	2	no	—
200	C₂²×C₅₉	—	8	2	no	—
201	C₂²×C₅₉	#388	1	4	yes	—
202	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
204	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
205	C₂²×C₅₉	C₂×#135	1	4	yes	—
206	C₄×C₅₉	—	2	8	no	—
207	C₄×C₅₉	—	4	4	no	—
208	C₄×C₅₉	—	4	2	no	—
209	C₄×C₅₉	—	8	2	no	—
210	C₄×C₅₉	—	8	2	no	—
211	C₄×C₅₉	#388	1	4	yes	—
212	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
213	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
215	C₄×C₅₉	C₂×#126	1	1	yes	characteristic
216	C₂×#416	C₂×C₅₉	1	1	yes	characteristic
217	C₂×#416	C₂×C₅₉	1	1	yes	characteristic
218	C₂²×C₄×C₈	C₂×C₅₉	1	1	yes	characteristic, complemented
219	#2297	C₂×C₅₉	1	1	yes	characteristic
220	#2296	C₂×C₅₉	1	1	yes	characteristic, complemented
221	#1934	C₂×C₅₉	1	4	yes	complemented
222	#1933	C₂×C₅₉	1	4	yes	complemented
223	#1735	C₂×C₅₉	1	1	yes	characteristic, complemented
224	#1735	C₂×C₅₉	1	1	yes	characteristic, complemented
225	C₂×C₅₉	—	2	4	no	—
226	C₂×C₅₉	—	8	2	no	—
227	C₂×C₅₉	C₂×#388	1	1	yes	characteristic
228	C₂×C₅₉	C₄×#135	1	2	yes	—
229	C₂×C₅₉	#3050	1	2	yes	—
230	C₂×C₅₉	#3131	1	2	yes	—
231	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
234	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
235	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
236	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
238	#416	—	2	4	no	—
239	#416	C₄×C₅₉	1	8	yes	complemented
240	C₂×#103	C₂²×C₅₉	1	2	yes	—
241	C₂×#103	C₂²×C₅₉	1	2	yes	—
242	C₂×#102	C₂²×C₅₉	1	2	yes	—
243	C₂×#102	C₂²×C₅₉	1	2	yes	—
244	C₂×C₄×C₈	—	2	4	no	—
245	C₂×C₄×C₈	C₂²×C₅₉	1	4	yes	—
246	#391	C₂²×C₅₉	1	2	yes	—
247	#390	C₂²×C₅₉	1	2	yes	—
248	#389	C₂²×C₅₉	1	4	yes	—
249	#386	—	2	2	no	—
250	#385	—	2	2	no	—
251	C₄×C₄⋊C₄	—	2	2	no	—
252	C₄×C₂²⋊C₄	—	2	2	no	—
253	#340	C₂²×C₅₉	1	4	yes	—
254	#340	C₂²×C₅₉	1	4	yes	—
255	C₅₉	#21083	1	1	yes	characteristic, direct product factor, Sylow
256	C₂×#41	—	2	2	no	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	C₂×C₄×C₅₉	1	4	yes	—
262	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	D₄×C₅₉	1	2	yes	—
267	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
268	C₂²×C₈	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂×C₄×C₅₉	1	4	yes	—
273	C₂²×C₈	D₄×C₅₉	1	4	yes	—
274	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
275	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
276	#117	—	2	2	no	—
277	#117	—	2	2	no	—
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	C₂×C₄×C₅₉	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	D₄×C₅₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
297	#103	—	2	4	no	—
298	#103	C₂×C₄×C₅₉	1	8	yes	complemented
299	#102	—	2	4	no	—
300	#102	C₂×C₄×C₅₉	1	8	yes	complemented
301	C₄×C₈	—	2	8	no	—
302	#95	—	2	4	no	—
303	#95	—	2	4	no	—
304	C₂⁴	—	2	1	no	—
305	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
306	#41	—	2	8	no	—
307	#41	—	2	8	no	—
308	#41	—	4	4	no	—
309	#41	—	4	4	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
338	C₂²×C₄	#41×C₅₉	1	2	yes	—
339	C₂²×C₄	#41×C₅₉	1	2	yes	—
340	C₂²×C₄	#41×C₅₉	1	2	yes	—
341	C₂²×C₄	#41×C₅₉	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
343	C₂×C₈	—	2	8	no	—
344	C₂×C₈	—	2	8	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	C₂²×C₄×C₅₉	1	4	yes	—
350	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	8	no	—
357	C₄⋊C₄	C₂²×C₄×C₅₉	1	4	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	8	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	2	no	—
367	C₄²	—	4	2	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	4	no	—
373	C₂³	C₄×D₄×C₅₉	1	2	yes	—
374	C₂³	#121×C₅₉	1	2	yes	—
375	C₂³	#124×C₅₉	1	2	yes	—
376	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	4	8	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	C₂×C₄	—	2	16	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	#117×C₅₉	1	4	yes	—
400	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
401	C₂×C₄	C₄×D₄×C₅₉	1	4	yes	—
402	C₂×C₄	#121×C₅₉	1	2	yes	—
403	C₂×C₄	#123×C₅₉	1	4	yes	—
404	C₂×C₄	#124×C₅₉	1	2	yes	—
405	C₂×C₄	#126×C₅₉	1	4	yes	—
406	C₂×C₄	#135×C₅₉	1	8	yes	—
407	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
408	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
413	C₈	—	2	4	no	—
414	C₈	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	C₅₉×#388	1	4	yes	—
423	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
424	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
425	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
426	C₂²	C₂×#135×C₅₉	1	4	yes	—
427	C₄	—	2	8	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	C₅₉×#388	1	4	yes	—
433	C₄	C₂×#117×C₅₉	1	1	yes	characteristic
434	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
435	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
436	C₄	C₂×#126×C₅₉	1	1	yes	characteristic
437	C₂	—	2	4	no	—
438	C₂	—	8	2	no	—
439	C₂	C₂×C₅₉×#388	1	1	yes	characteristic
440	C₂	C₄×#135×C₅₉	1	2	yes	—
441	C₂	C₅₉×#3050	1	2	yes	—
442	C₂	C₅₉×#3131	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂³×C₅₉	C₂²×D₄
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₈×C₅₉	C₂	semidirect
5. C₅₉×#2296	C₂	semidirect
6. C₅₉×#1934	C₂	semidirect
7. C₅₉×#1933	C₂	semidirect
8. C₅₉×#1735	C₂	semidirect
9. C₅₉×#1735	C₂	semidirect
18. C₅₉×#416	C₄	semidirect
76. #103×C₅₉	C₂×C₄	semidirect
78. #102×C₅₉	C₂×C₄	semidirect
193. #21083	C₅₉	direct (N × H)
218. C₂²×C₄×C₈	C₂×C₅₉	semidirect
220. #2296	C₂×C₅₉	semidirect
221. #1934	C₂×C₅₉	semidirect
222. #1933	C₂×C₅₉	semidirect
223. #1735	C₂×C₅₉	semidirect
224. #1735	C₂×C₅₉	semidirect
239. #416	C₄×C₅₉	semidirect
255. C₅₉	#21083	direct (N × H)
298. #103	C₂×C₄×C₅₉	semidirect
300. #102	C₂×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×#416	2
C₂²×C₄×C₈×C₅₉	2
C₅₉×#2297	2
C₅₉×#2296	2
C₅₉×#1934	2
C₅₉×#1933	2
C₅₉×#1735	2
#21083	59

Subgroups — C59×#21083 #28433192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21083 #28433192