Subgroups — #28560712

Order 15104.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434655	C₂	1	1	yes	maximal, characteristic
2	#21433197	C₂	1	1	yes	maximal, characteristic, complemented
3	#21433162	C₂	1	1	yes	maximal, characteristic
4	#21423000	C₂	1	2	yes	maximal, complemented
5	#21422941	C₂	1	2	yes	maximal, complemented
6	#21422934	C₂	1	2	yes	maximal, complemented
7	#21422910	C₂	1	2	yes	maximal, complemented
8	#21422844	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422518	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422514	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837952	C₂²	1	1	yes	characteristic
14	#16837800	C₄	1	1	yes	characteristic
15	#16837775	C₄	1	1	yes	characteristic
16	#16837753	C₄	1	1	yes	characteristic
17	#16837749	C₄	1	1	yes	characteristic
18	#16837631	C₄	1	2	yes	—
19	#16837631	C₄	1	2	yes	—
20	#16837532	C₂²	1	2	yes	—
21	#16837529	—	2	1	no	—
22	C₈×Dic₁₁₈	C₂²	1	2	yes	—
23	#16837526	—	2	1	no	—
24	C₄×#11745660	C₂²	1	2	yes	—
25	C₄×#11745660	C₂²	1	2	yes	—
26	#16837481	C₂²	1	2	yes	—
27	#16837479	—	2	1	no	—
28	C₈×D₂₃₆	C₂²	1	2	yes	—
29	#16837467	—	2	1	no	—
30	#16837460	—	2	2	no	—
31	#16837455	C₂²	1	1	yes	characteristic
32	#16837455	C₂²	1	1	yes	characteristic
33	#16837367	—	2	2	no	—
34	#16837155	C₂²	1	1	yes	characteristic
35	#16837155	C₂²	1	1	yes	characteristic
36	#16837153	C₂²	1	1	yes	characteristic
37	#16837153	C₂²	1	1	yes	characteristic
38	#16837134	C₂²	1	2	yes	—
39	#16837134	C₂²	1	2	yes	—
40	#16837131	C₂²	1	2	yes	—
41	#16837131	C₂²	1	2	yes	—
42	C₅₉×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#322	C₂²	1	2	yes	—
46	C₅₉×#322	C₂²	1	2	yes	—
47	C₂×#11745685	—	2	1	no	—
48	C₂×#11745660	C₂×C₄	1	2	yes	—
49	C₂×#11745660	C₂×C₄	1	2	yes	—
50	C₂×#11745659	—	2	2	no	—
51	C₂×C₈×D₅₉	—	2	2	no	—
52	#14273727	C₂×C₄	1	1	yes	characteristic
53	#14273727	C₂×C₄	1	1	yes	characteristic
54	#14273727	C₂×C₄	1	1	yes	characteristic
55	#14273724	C₂×C₄	1	1	yes	characteristic
56	#14273719	—	2	1	no	—
57	#14273715	—	2	1	no	—
58	#14273706	—	2	1	no	—
59	#14273706	C₂×C₄	1	2	yes	—
60	#14273701	—	2	1	no	—
61	#14273701	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₁₈	—	2	1	no	—
63	C₄×Dic₁₁₈	C₂³	1	2	yes	—
64	C₄×D₂₃₆	—	2	1	no	—
65	C₄×D₂₃₆	C₂³	1	2	yes	—
66	#14273686	—	2	1	no	—
67	#14273659	C₂×C₄	1	2	yes	—
68	#14273659	C₂×C₄	1	2	yes	—
69	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
72	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
73	Dic₅₉⋊C₈	—	2	2	no	—
74	Dic₅₉⋊C₈	—	2	2	no	—
75	#14273652	C₂×C₄	1	2	yes	—
76	#14273652	C₂×C₄	1	2	yes	—
77	#14273649	C₂×C₄	1	2	yes	—
78	#14273649	C₂×C₄	1	2	yes	—
79	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
81	(C₂×D₅₉)⋊C₈	—	2	2	no	—
82	(C₂×D₅₉)⋊C₈	—	2	2	no	—
83	#14273637	—	2	2	no	—
84	C₄×C₅₉⋊C₈	—	2	1	no	—
85	C₄×C₅₉⋊C₈	—	2	1	no	—
86	C₈×Dic₅₉	—	2	2	no	—
87	C₂×M₁₆×C₅₉	—	2	1	no	—
88	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
93	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
94	#97×C₅₉	—	2	1	no	—
95	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₅₉	C₂³	1	2	yes	—
98	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₅₉	C₂³	1	2	yes	—
101	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₅₉	—	2	2	no	—
105	#11745685	—	8	1	no	—
106	#11745685	—	8	1	no	—
107	C₂×D₂₃₆	—	2	1	no	—
108	C₂×D₂₃₆	—	2	1	no	—
109	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₅₉	—	2	2	no	—
111	C₂×Dic₁₁₈	—	2	1	no	—
112	C₂×Dic₁₁₈	—	2	1	no	—
113	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
114	M₁₆×C₅₉	—	4	2	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	—	2	2	no	—
117	C₂×C₈×C₅₉	—	4	1	no	—
118	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
124	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₅₉	#41	1	1	yes	characteristic
127	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₂²⋊Dic₅₉	—	2	2	no	—
129	(C₂×D₅₉)⋊C₄	—	2	2	no	—
130	(C₂×D₅₉)⋊C₄	—	2	2	no	—
131	C₄⋊Dic₅₉	—	2	1	no	—
132	C₄⋊Dic₅₉	—	2	1	no	—
133	C₄⋊Dic₅₉	—	2	1	no	—
134	C₄⋊Dic₅₉	—	2	1	no	—
135	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
136	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
137	Dic₅₉⋊C₄	—	2	2	no	—
138	Dic₅₉⋊C₄	—	2	2	no	—
139	C₄×Dic₅₉	—	2	2	no	—
140	C₂×C₅₉⋊C₈	—	2	1	no	—
141	C₂×C₅₉⋊C₈	—	2	1	no	—
142	C₂×C₅₉⋊C₈	—	2	1	no	—
143	C₂×C₅₉⋊C₈	—	2	1	no	—
144	#11745660	—	2	4	no	—
145	#11745660	—	4	2	no	—
146	#11745659	—	8	2	no	—
147	C₈×D₅₉	—	8	2	no	—
148	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	2	1	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	1	no	—
153	C₂×C₄×C₅₉	—	2	1	no	—
154	C₂×C₄×C₅₉	—	2	2	no	—
155	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
161	C₂²⋊D₅₉	—	8	2	no	—
162	C₂×Dic₅₉	—	2	2	no	—
163	C₂×Dic₅₉	—	2	2	no	—
164	C₂×Dic₅₉	—	2	2	no	—
165	D₂₃₆	—	2	2	no	—
166	D₂₃₆	—	2	2	no	—
167	D₂₃₆	—	4	2	no	—
168	D₂₃₆	—	8	1	no	—
169	C₄×D₅₉	—	4	2	no	—
170	C₄×D₅₉	—	4	2	no	—
171	Dic₁₁₈	—	2	2	no	—
172	Dic₁₁₈	—	2	2	no	—
173	Dic₁₁₈	—	4	2	no	—
174	Dic₁₁₈	—	8	1	no	—
175	C₈×C₅₉	—	2	1	no	—
176	C₈×C₅₉	—	2	1	no	—
177	C₈×C₅₉	—	2	1	no	—
178	C₈×C₅₉	—	2	2	no	—
179	C₈×C₅₉	—	2	2	no	—
180	C₈×C₅₉	—	4	2	no	—
181	C₈×C₅₉	#131	1	2	yes	—
182	C₅₉⋊C₈	—	4	1	no	—
183	C₅₉⋊C₈	—	4	1	no	—
184	C₅₉⋊C₈	—	4	1	no	—
185	C₅₉⋊C₈	—	4	1	no	—
186	#18089	—	59	1	no	maximal, Sylow
187	C₂²×C₅₉	—	2	1	no	—
188	C₂²×C₅₉	—	2	1	no	—
189	C₂²×C₅₉	—	2	1	no	—
190	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂×D₅₉	—	4	2	no	—
192	C₂×D₅₉	—	4	2	no	—
193	C₂×D₅₉	—	4	2	no	—
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	—	2	1	no	—
196	C₄×C₅₉	—	2	1	no	—
197	C₄×C₅₉	#444	1	2	yes	—
198	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
199	C₄×C₅₉	#568	1	1	yes	characteristic
200	C₄×C₅₉	#577	1	1	yes	characteristic
201	C₄×C₅₉	#577	1	1	yes	characteristic
202	Dic₅₉	—	4	2	no	—
203	Dic₅₉	—	4	2	no	—
204	Dic₅₉	—	4	2	no	—
205	#3167	—	59	1	no	—
206	#2986	—	59	1	no	—
207	#2979	—	59	1	no	—
208	#1592	—	59	2	no	—
209	#1583	—	59	2	no	—
210	#1582	—	59	2	no	—
211	SD₁₆⋊C₈	—	59	2	no	—
212	#1564	—	59	1	no	—
213	#1485	—	59	1	no	—
214	#1484	—	59	1	no	—
215	#1451	D₅₉	1	1	yes	characteristic, complemented
216	C₂×C₅₉	—	4	1	no	—
217	C₂×C₅₉	#2935	1	1	yes	characteristic
218	C₂×C₅₉	#2949	1	1	yes	characteristic
219	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
220	D₅₉	—	8	2	no	—
221	#533	—	59	1	no	—
222	#532	—	59	1	no	—
223	#498	—	59	1	no	—
224	#492	—	59	1	no	—
225	#487	—	59	1	no	—
226	#486	—	59	1	no	—
227	#465	—	59	2	no	—
228	#465	—	59	2	no	—
229	#446	—	59	2	no	—
230	#446	—	118	1	no	—
231	C₈×Q₈	—	59	2	no	—
232	C₈×Q₈	—	118	1	no	—
233	C₄×SD₁₆	—	59	2	no	—
234	C₄×SD₁₆	—	59	2	no	—
235	#436	—	59	2	no	—
236	#436	—	118	1	no	—
237	C₈×D₄	—	59	2	no	—
238	C₈×D₄	—	118	1	no	—
239	#433	—	118	2	no	—
240	#431	—	59	1	no	—
241	#431	—	59	1	no	—
242	#431	C₂×D₅₉	1	1	yes	characteristic
243	#408	—	118	2	no	—
244	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
246	#335	—	59	1	no	—
247	#335	—	59	1	no	—
248	#334	—	59	1	no	—
249	#334	—	59	1	no	—
250	Q₈⋊C₈	—	59	2	no	—
251	Q₈⋊C₈	—	59	2	no	—
252	D₄⋊C₈	—	59	2	no	—
253	D₄⋊C₈	—	59	2	no	—
254	#322	C₂×D₅₉	1	2	yes	—
255	#322	C₂×D₅₉	1	2	yes	—
256	C₅₉	#18089	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	118	1	no	—
258	C₂×SD₁₆	—	59	2	no	—
259	C₂×SD₁₆	—	59	2	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	118	2	no	—
262	C₂²×C₈	—	118	2	no	—
263	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
265	C₄⋊Q₈	—	59	1	no	—
266	C₄⋊Q₈	—	59	1	no	—
267	C₄⋊Q₈	—	59	1	no	—
268	#127	—	59	1	no	—
269	#125	—	118	1	no	—
270	#124	—	118	1	no	—
271	C₂²⋊Q₈	—	59	2	no	—
272	C₂²⋊Q₈	—	118	1	no	—
273	#121	—	59	2	no	—
274	#121	—	118	1	no	—
275	C₄×Q₈	—	59	2	no	—
276	C₄×Q₈	—	118	1	no	—
277	C₄×D₄	—	59	2	no	—
278	C₄×D₄	—	118	1	no	—
279	#117	—	118	1	no	—
280	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
281	#106	—	59	2	no	—
282	#106	—	59	2	no	—
283	C₄⋊C₈	—	59	1	no	—
284	C₄⋊C₈	—	59	1	no	—
285	C₄⋊C₈	—	59	1	no	—
286	C₄⋊C₈	—	59	1	no	—
287	C₄⋊C₈	—	118	2	no	—
288	C₄⋊C₈	—	118	2	no	—
289	C₄⋊C₈	D₂₃₆	1	1	yes	characteristic
290	C₄⋊C₈	D₂₃₆	1	1	yes	characteristic
291	#103	—	59	2	no	—
292	#103	—	59	2	no	—
293	#102	—	59	2	no	—
294	#102	—	59	2	no	—
295	C₂²⋊C₈	—	118	1	no	—
296	C₂²⋊C₈	—	118	1	no	—
297	C₂²⋊C₈	—	118	2	no	—
298	C₂²⋊C₈	—	118	2	no	—
299	C₂²⋊C₈	D₂₃₆	1	2	yes	—
300	#97	—	2	1	no	—
301	#97	—	118	2	no	—
302	C₄×C₈	—	118	2	no	—
303	C₄×C₈	—	118	1	no	—
304	C₄×C₈	—	118	1	no	—
305	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
306	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₅₉	1	2	yes	—
308	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₅₉	1	2	yes	—
311	#41	—	472	1	no	—
312	#41	—	472	1	no	—
313	C₂×Q₈	—	59	2	no	—
314	C₂×Q₈	—	118	1	no	—
315	C₂×Q₈	—	118	1	no	—
316	C₂×D₄	—	59	2	no	—
317	C₂×D₄	—	118	2	no	—
318	C₂×D₄	—	118	1	no	—
319	C₂×D₄	—	118	1	no	—
320	C₂²×C₄	—	118	2	no	—
321	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
323	C₂²×C₄	#11745685	1	1	yes	characteristic
324	SD₁₆	—	118	4	no	—
325	SD₁₆	—	236	2	no	—
326	M₁₆	—	4	2	no	—
327	M₁₆	—	472	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	118	1	no	—
332	C₂×C₈	—	118	1	no	—
333	C₂×C₈	—	118	1	no	—
334	C₂×C₈	—	118	1	no	—
335	C₂×C₈	—	472	2	no	—
336	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
340	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
341	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
342	C₄⋊C₄	—	59	2	no	—
343	C₄⋊C₄	—	59	2	no	—
344	C₄⋊C₄	—	118	1	no	—
345	C₄⋊C₄	—	118	1	no	—
346	C₄⋊C₄	—	118	1	no	—
347	C₄⋊C₄	—	118	2	no	—
348	C₄⋊C₄	—	118	1	no	—
349	C₄⋊C₄	—	118	2	no	—
350	C₂²⋊C₄	—	118	2	no	—
351	C₂²⋊C₄	—	118	2	no	—
352	C₂²⋊C₄	—	118	2	no	—
353	C₄²	—	118	2	no	—
354	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
355	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
356	C₄²	#11745685	1	1	yes	characteristic
357	C₄²	C₂³×D₅₉	1	1	yes	characteristic
358	C₂³	—	118	2	no	—
359	C₂³	C₄×D₂₃₆	1	1	yes	characteristic
360	Q₈	—	118	2	no	—
361	Q₈	—	118	2	no	—
362	Q₈	—	472	1	no	—
363	Q₈	—	236	2	no	—
364	D₄	—	118	2	no	—
365	D₄	—	118	2	no	—
366	D₄	—	472	1	no	—
367	D₄	—	472	2	no	—
368	D₄	—	236	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	118	2	no	—
375	C₂×C₄	—	118	2	no	—
376	C₂×C₄	—	118	2	no	—
377	C₂×C₄	—	236	2	no	—
378	C₂×C₄	—	236	2	no	—
379	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
380	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
381	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
384	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	236	1	no	—
392	C₈	—	236	1	no	—
393	C₈	—	236	1	no	—
394	C₈	—	236	1	no	—
395	C₈	#14273735	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	236	2	no	—
400	C₂²	—	236	2	no	—
401	C₂²	—	236	2	no	—
402	C₂²	C₂×C₄×D₂₃₆	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	236	2	no	—
407	C₄	—	236	2	no	—
408	C₄	—	236	2	no	—
409	C₄	#16837525	1	2	yes	—
410	C₄	C₂×#14273735	1	1	yes	characteristic
411	C₄	#16838168	1	1	yes	characteristic
412	C₄	#16838214	1	1	yes	characteristic
413	C₄	#16838214	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	472	2	no	—
416	C₂	#21432842	1	1	yes	characteristic
417	C₂	#21432957	1	1	yes	characteristic
418	C₂	C₂×#16837525	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1451	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#16837952	C₂²
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1451	D₅₉
hypocenter	C₅₉	#18089
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #21433197	C₂	semidirect
4. #21423000	C₂	semidirect
5. #21422941	C₂	semidirect
6. #21422934	C₂	semidirect
7. #21422910	C₂	semidirect
8. #21422844	C₂	semidirect
9. #21422518	C₂	semidirect
11. C₅₉×#1451	C₂	semidirect
215. #1451	D₅₉	semidirect
256. C₅₉	#18089	semidirect

Maximal subgroups

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

subgroup	index
#21434655	2
#21433197	2
#21433162	2
#21423000	2
#21422941	2
#21422934	2
#21422910	2
#21422844	2
#21422518	2
#21422514	2
C₅₉×#1451	2
#18089	59