Subgroups — C₅₉×#8068 #28420177

Order 15104.

740 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1300	C₂	1	4	yes	maximal, complemented
5	C₂²×M₁₆×C₅₉	—	2	1	no	—
6	C₂×#117×C₅₉	—	2	1	no	—
7	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
8	C₅₉×#432	—	2	1	no	—
9	C₅₉×#432	C₂²	1	2	yes	—
10	C₅₉×#431	—	2	1	no	—
11	C₅₉×#431	C₄	1	2	yes	complemented
12	C₅₉×#423	C₄	1	2	yes	complemented
13	C₅₉×#407	—	2	1	no	—
14	C₄×M₁₆×C₅₉	—	2	1	no	—
15	C₄×M₁₆×C₅₉	—	2	1	no	—
16	C₄×M₁₆×C₅₉	—	2	1	no	—
17	C₄×M₁₆×C₅₉	C₄	1	2	yes	complemented
18	C₄×M₁₆×C₅₉	C₂²	1	2	yes	—
19	C₂×#97×C₅₉	C₄	1	2	yes	complemented
20	C₂×C₄×C₈×C₅₉	—	2	1	no	—
21	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
22	C₄×C₄⋊C₄×C₅₉	C₄	1	2	yes	—
23	C₄×C₂²⋊C₄×C₅₉	—	2	1	no	—
24	C₄×C₂²⋊C₄×C₅₉	C₄	1	2	yes	—
25	C₅₉×#376	C₂²	1	2	yes	—
26	C₄³×C₅₉	—	2	1	no	—
27	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₅₉	—	2	8	no	—
31	C₂×M₁₆×C₅₉	—	2	2	no	—
32	C₂×M₁₆×C₅₉	—	2	2	no	—
33	C₂×M₁₆×C₅₉	—	2	2	no	—
34	C₂²×C₈×C₅₉	—	2	2	no	—
35	#117×C₅₉	—	2	8	no	—
36	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
38	C₂×C₄²×C₅₉	—	2	2	no	—
39	C₂×C₄²×C₅₉	—	2	2	no	—
40	C₂×C₄²×C₅₉	—	2	2	no	—
41	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
52	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
53	C₄⋊C₈×C₅₉	—	2	2	no	—
54	C₄⋊C₈×C₅₉	C₂×C₄	1	4	yes	—
55	C₂²⋊C₈×C₅₉	—	2	2	no	—
56	C₂²⋊C₈×C₅₉	—	2	2	no	—
57	#97×C₅₉	—	2	2	no	—
58	#97×C₅₉	—	2	2	no	—
59	#97×C₅₉	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₅₉	—	2	2	no	—
61	C₄×C₈×C₅₉	—	2	2	no	—
62	C₄×C₈×C₅₉	—	2	2	no	—
63	#95×C₅₉	—	2	2	no	—
64	#95×C₅₉	C₂×C₄	1	4	yes	—
65	C₂⁴×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₉	—	2	4	no	—
67	C₂²×C₄×C₅₉	—	2	4	no	—
68	C₂²×C₄×C₅₉	—	2	4	no	—
69	C₂²×C₄×C₅₉	—	4	2	no	—
70	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₅₉	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
88	M₁₆×C₅₉	—	2	8	no	—
89	M₁₆×C₅₉	—	2	8	no	—
90	M₁₆×C₅₉	—	4	4	no	—
91	C₂×C₈×C₅₉	—	2	8	no	—
92	C₂×C₈×C₅₉	—	2	4	no	—
93	C₂×C₈×C₅₉	—	2	4	no	—
94	C₄⋊C₄×C₅₉	—	2	8	no	—
95	C₂²⋊C₄×C₅₉	—	2	8	no	—
96	C₄²×C₅₉	—	2	8	no	—
97	C₄²×C₅₉	—	4	4	no	—
98	C₄²×C₅₉	—	4	4	no	—
99	C₄²×C₅₉	C₄²	1	1	yes	characteristic
100	C₄²×C₅₉	C₄²	1	1	yes	characteristic
101	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
115	C₂³×C₅₉	—	2	2	no	—
116	C₂³×C₅₉	—	2	2	no	—
117	C₂³×C₅₉	—	4	1	no	—
118	C₂³×C₅₉	#95	1	1	yes	characteristic
119	C₂³×C₅₉	#95	1	1	yes	characteristic
120	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₅₉	—	2	2	no	—
122	C₂×C₄×C₅₉	—	2	2	no	—
123	C₂×C₄×C₅₉	—	2	2	no	—
124	C₂×C₄×C₅₉	—	2	2	no	—
125	C₂×C₄×C₅₉	—	2	2	no	—
126	C₂×C₄×C₅₉	—	2	2	no	—
127	C₂×C₄×C₅₉	—	2	2	no	—
128	C₂×C₄×C₅₉	—	2	2	no	—
129	C₂×C₄×C₅₉	—	2	2	no	—
130	C₂×C₄×C₅₉	—	2	2	no	—
131	C₂×C₄×C₅₉	—	2	2	no	—
132	C₂×C₄×C₅₉	—	2	2	no	—
133	C₂×C₄×C₅₉	—	2	2	no	—
134	C₂×C₄×C₅₉	—	2	8	no	—
135	C₂×C₄×C₅₉	—	4	1	no	—
136	C₂×C₄×C₅₉	—	4	1	no	—
137	C₂×C₄×C₅₉	—	4	1	no	—
138	C₂×C₄×C₅₉	—	4	4	no	—
139	C₂×C₄×C₅₉	—	4	4	no	—
140	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
142	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
144	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₅₉	#95	1	1	yes	characteristic
146	C₂×C₄×C₅₉	#104	1	4	yes	—
147	C₂×C₄×C₅₉	#104	1	4	yes	—
148	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₈×C₅₉	—	2	8	no	—
155	C₈×C₅₉	—	4	4	no	—
156	#8068	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₅₉	—	2	1	no	—
158	C₂²×C₅₉	—	2	1	no	—
159	C₂²×C₅₉	—	2	1	no	—
160	C₂²×C₅₉	—	2	1	no	—
161	C₂²×C₅₉	—	2	1	no	—
162	C₂²×C₅₉	—	2	1	no	—
163	C₂²×C₅₉	—	2	1	no	—
164	C₂²×C₅₉	—	4	4	no	—
165	C₂²×C₅₉	#339	1	2	yes	—
166	C₂²×C₅₉	C₂×#95	1	1	yes	characteristic
167	C₂²×C₅₉	C₂×#104	1	2	yes	—
168	C₄×C₅₉	—	2	1	no	—
169	C₄×C₅₉	—	2	1	no	—
170	C₄×C₅₉	—	2	1	no	—
171	C₄×C₅₉	—	2	1	no	—
172	C₄×C₅₉	—	2	1	no	—
173	C₄×C₅₉	—	2	1	no	—
174	C₄×C₅₉	—	2	1	no	—
175	C₄×C₅₉	—	4	8	no	—
176	C₄×C₅₉	#339	1	2	yes	—
177	C₄×C₅₉	#339	1	2	yes	—
178	C₄×C₅₉	#339	1	2	yes	—
179	C₄×C₅₉	#344	1	2	yes	—
180	C₄×C₅₉	C₂×#104	1	2	yes	—
181	#2920	C₂×C₅₉	1	1	yes	characteristic
182	C₂×C₄×M₁₆	C₂×C₅₉	1	1	yes	characteristic
183	C₄×#117	C₂×C₅₉	1	1	yes	characteristic
184	#1300	C₂×C₅₉	1	4	yes	complemented
185	C₂×C₅₉	—	2	2	no	—
186	C₂×C₅₉	—	2	2	no	—
187	C₂×C₅₉	—	4	1	no	—
188	C₂×C₅₉	C₂×#339	1	1	yes	characteristic
189	C₂×C₅₉	C₂×#339	1	1	yes	characteristic
190	C₂×C₅₉	C₂×#344	1	1	yes	characteristic
191	C₂²×M₁₆	—	2	1	no	—
192	C₂×#117	—	2	1	no	—
193	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
194	#432	—	2	1	no	—
195	#432	C₂²×C₅₉	1	2	yes	—
196	#431	—	2	1	no	—
197	#431	C₄×C₅₉	1	2	yes	complemented
198	#423	C₄×C₅₉	1	2	yes	complemented
199	#407	—	2	1	no	—
200	C₄×M₁₆	—	2	1	no	—
201	C₄×M₁₆	—	2	1	no	—
202	C₄×M₁₆	—	2	1	no	—
203	C₄×M₁₆	C₄×C₅₉	1	2	yes	complemented
204	C₄×M₁₆	C₂²×C₅₉	1	2	yes	—
205	C₂×#97	C₄×C₅₉	1	2	yes	complemented
206	C₂×C₄×C₈	—	2	1	no	—
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₄⋊C₄	C₄×C₅₉	1	2	yes	—
209	C₄×C₂²⋊C₄	—	2	1	no	—
210	C₄×C₂²⋊C₄	C₄×C₅₉	1	2	yes	—
211	#376	C₂²×C₅₉	1	2	yes	—
212	C₄³	—	2	1	no	—
213	C₅₉	#8068	1	1	yes	characteristic, direct product factor, Sylow
214	C₂³×C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
215	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
216	C₂³×C₄	D₄×C₅₉	1	1	yes	characteristic
217	C₂×M₁₆	—	2	8	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	#117	—	2	8	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₅₉	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₅₉	1	1	yes	characteristic
237	C₂×C₄²	Q₈×C₅₉	1	1	yes	characteristic
238	C₂×C₄²	Q₈×C₅₉	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	C₂×C₄×C₅₉	1	4	yes	—
242	C₂²⋊C₈	—	2	2	no	—
243	C₂²⋊C₈	—	2	2	no	—
244	#97	—	2	2	no	—
245	#97	—	2	2	no	—
246	#97	C₂×C₄×C₅₉	1	4	yes	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	C₄×C₈	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	C₂×C₄×C₅₉	1	4	yes	—
252	C₂⁴	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
258	C₂²×C₄	C₄²×C₅₉	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
262	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
268	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₅₉	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
275	M₁₆	—	2	8	no	—
276	M₁₆	—	2	8	no	—
277	M₁₆	—	4	4	no	—
278	C₂×C₈	—	2	8	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₂²⋊C₄	—	2	8	no	—
283	C₄²	—	2	8	no	—
284	C₄²	—	4	4	no	—
285	C₄²	—	4	4	no	—
286	C₄²	C₄²×C₅₉	1	1	yes	characteristic
287	C₄²	C₄²×C₅₉	1	1	yes	characteristic
288	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
289	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
290	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
292	C₄²	C₄⋊C₄×C₅₉	1	1	yes	characteristic
293	C₄²	C₄⋊C₄×C₅₉	1	1	yes	characteristic
294	C₄²	C₄⋊C₄×C₅₉	1	1	yes	characteristic
295	C₄²	C₄⋊C₄×C₅₉	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₅₉	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₅₉	1	1	yes	characteristic
298	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
299	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
300	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
301	C₄²	C₂×Q₈×C₅₉	1	1	yes	characteristic
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	4	1	no	—
305	C₂³	#95×C₅₉	1	1	yes	characteristic
306	C₂³	#95×C₅₉	1	1	yes	characteristic
307	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
328	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
329	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
330	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
331	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
332	C₂×C₄	#95×C₅₉	1	1	yes	characteristic
333	C₂×C₄	#104×C₅₉	1	4	yes	—
334	C₂×C₄	#104×C₅₉	1	4	yes	—
335	C₂×C₄	C₂×C₄²×C₅₉	1	1	yes	characteristic
336	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊C₄×C₅₉	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₈	—	4	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	4	4	no	—
351	C₂²	C₅₉×#339	1	2	yes	—
352	C₂²	C₂×#95×C₅₉	1	1	yes	characteristic
353	C₂²	C₂×#104×C₅₉	1	2	yes	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	4	8	no	—
362	C₄	C₅₉×#339	1	2	yes	—
363	C₄	C₅₉×#339	1	2	yes	—
364	C₄	C₅₉×#339	1	2	yes	—
365	C₄	C₅₉×#344	1	2	yes	—
366	C₄	C₂×#104×C₅₉	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₂×C₅₉×#339	1	1	yes	characteristic
371	C₂	C₂×C₅₉×#339	1	1	yes	characteristic
372	C₂	C₂×C₅₉×#344	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅₉
Frattini, cosocle	C₂×C₄²	C₂³×C₅₉
socle	C₂²×C₅₉	C₂×#95
prime radical	C₂⁴×C₅₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₅₉ ◁ C₂²×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₉×#1300	C₂	semidirect
11. C₅₉×#431	C₄	semidirect
12. C₅₉×#423	C₄	semidirect
17. C₄×M₁₆×C₅₉	C₄	semidirect
19. C₂×#97×C₅₉	C₄	semidirect
156. #8068	C₅₉	direct (N × H)
184. #1300	C₂×C₅₉	semidirect
197. #431	C₄×C₅₉	semidirect
198. #423	C₄×C₅₉	semidirect
203. C₄×M₁₆	C₄×C₅₉	semidirect
205. C₂×#97	C₄×C₅₉	semidirect
213. C₅₉	#8068	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2920	2
C₂×C₄×M₁₆×C₅₉	2
C₄×#117×C₅₉	2
C₅₉×#1300	2
#8068	59

Subgroups — C59×#8068 #28420177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#8068 #28420177