Subgroups — #28486869

Order 15104.

460 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21424890	C₂	1	1	yes	maximal, characteristic
2	C₄×#14273647	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16837129	C₂	1	1	yes	maximal, characteristic
5	#21421937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₃₆	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#14273647	C₄	1	1	yes	characteristic
11	C₂×#14273647	C₄	1	1	yes	characteristic
12	C₂×(C₂×D₅₉)⋊C₈	—	2	1	no	—
13	C₂×(C₂×D₅₉)⋊C₈	—	2	1	no	—
14	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
16	#16837164	C₄	1	1	yes	characteristic
17	#16837164	C₄	1	1	yes	characteristic
18	#16837152	—	2	2	no	—
19	#16837129	—	2	2	no	—
20	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₅₉	—	2	1	no	—
22	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#336	—	2	1	no	—
25	C₂²×D₂₃₆	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₅₉	—	2	1	no	—
27	C₂²×C₅₉⋊C₈	—	2	1	no	—
28	C₂²×C₅₉⋊C₈	—	2	1	no	—
29	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
31	C₄×D₂₃₆	—	2	1	no	—
32	C₄×D₂₃₆	—	2	1	no	—
33	C₄×D₂₃₆	—	2	1	no	—
34	C₄×D₂₃₆	—	2	1	no	—
35	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
36	C₂×(C₂×D₅₉)⋊C₄	—	2	1	no	—
37	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
38	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
39	#14273647	—	2	2	no	—
40	#14273647	C₈	1	4	yes	complemented
41	(C₂×D₅₉)⋊C₈	—	4	2	no	—
42	(C₂×D₅₉)⋊C₈	—	4	2	no	—
43	C₄×C₅₉⋊C₈	—	2	1	no	—
44	C₄×C₅₉⋊C₈	—	2	1	no	—
45	C₄×C₅₉⋊C₈	—	2	1	no	—
46	C₄×C₅₉⋊C₈	—	2	1	no	—
47	C₂²×C₈×C₅₉	—	2	1	no	—
48	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅₉	—	2	1	no	—
53	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₅₉	—	2	1	no	—
55	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
56	C₄×C₈×C₅₉	—	2	1	no	—
57	C₄×C₈×C₅₉	—	2	1	no	—
58	C₄×C₈×C₅₉	—	4	2	no	—
59	#95×C₅₉	—	2	1	no	—
60	C₂³×D₅₉	—	2	1	no	—
61	C₂²×C₄×C₅₉	—	2	1	no	—
62	C₂²×C₄×C₅₉	—	2	1	no	—
63	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
66	C₂²×Dic₅₉	—	2	1	no	—
67	C₂×D₂₃₆	—	2	1	no	—
68	C₂×D₂₃₆	—	2	1	no	—
69	C₂×D₂₃₆	—	2	1	no	—
70	C₂×D₂₃₆	—	2	1	no	—
71	C₂×D₂₃₆	—	2	1	no	—
72	C₂×D₂₃₆	C₂×C₈	1	2	yes	—
73	C₂×C₄×D₅₉	—	4	1	no	—
74	C₂×C₄×D₅₉	—	4	1	no	—
75	C₂×C₄×D₅₉	—	4	1	no	—
76	C₂×C₄×D₅₉	—	4	1	no	—
77	C₂×C₄×D₅₉	—	4	1	no	—
78	C₂×C₄×D₅₉	—	4	1	no	—
79	C₂×C₈×C₅₉	—	2	1	no	—
80	C₂×C₈×C₅₉	—	2	1	no	—
81	C₂×C₈×C₅₉	—	2	2	no	—
82	C₂×C₈×C₅₉	—	2	1	no	—
83	C₂×C₈×C₅₉	—	2	1	no	—
84	C₂×C₈×C₅₉	—	2	1	no	—
85	C₂×C₈×C₅₉	—	4	1	no	—
86	C₂×C₈×C₅₉	—	4	1	no	—
87	C₂×C₈×C₅₉	SD₁₆	1	2	yes	—
88	C₄⋊C₄×C₅₉	—	2	1	no	—
89	C₄⋊C₄×C₅₉	—	2	1	no	—
90	C₄⋊C₄×C₅₉	C₂×C₈	1	2	yes	—
91	C₄⋊C₄×C₅₉	M₁₆	1	2	yes	—
92	C₄²×C₅₉	—	4	1	no	—
93	C₄²×C₅₉	—	4	1	no	—
94	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
95	C₄²×C₅₉	#41	1	1	yes	characteristic
96	C₄²×C₅₉	#41	1	1	yes	characteristic
97	C₄²×C₅₉	#41	1	1	yes	characteristic
98	(C₂×D₅₉)⋊C₄	—	4	1	no	—
99	(C₂×D₅₉)⋊C₄	—	4	1	no	—
100	C₄⋊Dic₅₉	—	2	1	no	—
101	C₄⋊Dic₅₉	—	2	1	no	—
102	C₂×C₅₉⋊C₈	—	2	1	no	—
103	C₂×C₅₉⋊C₈	—	2	1	no	—
104	C₂×C₅₉⋊C₈	—	2	2	no	—
105	C₂×C₅₉⋊C₈	—	2	1	no	—
106	C₂×C₅₉⋊C₈	—	2	1	no	—
107	C₂×C₅₉⋊C₈	—	2	1	no	—
108	C₂×C₅₉⋊C₈	—	4	1	no	—
109	C₂×C₅₉⋊C₈	—	4	1	no	—
110	C₂×C₅₉⋊C₈	—	4	1	no	—
111	C₂×C₅₉⋊C₈	—	4	1	no	—
112	C₂×C₅₉⋊C₈	—	4	1	no	—
113	C₂×C₅₉⋊C₈	C₂×C₈	1	2	yes	—
114	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
115	C₂²×D₅₉	—	2	2	no	—
116	C₂²×D₅₉	—	4	1	no	—
117	C₂²×D₅₉	—	4	1	no	—
118	C₂²×D₅₉	—	4	1	no	—
119	C₂²×D₅₉	—	4	1	no	—
120	C₂²×D₅₉	—	4	1	no	—
121	C₂²×D₅₉	—	4	1	no	—
122	C₂×C₄×C₅₉	—	2	1	no	—
123	C₂×C₄×C₅₉	—	2	1	no	—
124	C₂×C₄×C₅₉	—	2	2	no	—
125	C₂×C₄×C₅₉	—	2	2	no	—
126	C₂×C₄×C₅₉	—	4	1	no	—
127	C₂×C₄×C₅₉	—	4	1	no	—
128	C₂×C₄×C₅₉	—	4	1	no	—
129	C₂×C₄×C₅₉	—	4	1	no	—
130	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
131	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
133	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
134	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
135	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
136	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
138	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
139	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×Dic₅₉	—	4	1	no	—
145	C₂×Dic₅₉	—	4	1	no	—
146	C₂×Dic₅₉	—	4	1	no	—
147	D₂₃₆	—	2	2	no	—
148	D₂₃₆	—	2	2	no	—
149	D₂₃₆	—	4	1	no	—
150	D₂₃₆	—	4	1	no	—
151	C₄×D₅₉	—	8	1	no	—
152	C₄×D₅₉	—	8	1	no	—
153	C₄×D₅₉	—	8	1	no	—
154	C₄×D₅₉	—	8	1	no	—
155	C₈×C₅₉	—	2	2	no	—
156	C₈×C₅₉	—	4	2	no	—
157	C₈×C₅₉	—	4	1	no	—
158	C₅₉⋊C₈	—	2	2	no	—
159	C₅₉⋊C₈	—	4	2	no	—
160	C₅₉⋊C₈	—	4	1	no	—
161	C₅₉⋊C₈	—	8	1	no	—
162	#9542	—	59	1	no	maximal, Sylow
163	C₂²×C₅₉	#388	1	1	yes	characteristic
164	C₂²×C₅₉	C₈×D₄	1	1	yes	characteristic
165	C₂²×C₅₉	#435	1	1	yes	characteristic
166	C₂²×C₅₉	C₄×SD₁₆	1	1	yes	characteristic
167	C₂²×C₅₉	#442	1	1	yes	characteristic
168	C₂²×C₅₉	#443	1	1	yes	characteristic
169	C₂²×C₅₉	#444	1	1	yes	characteristic
170	C₂×D₅₉	—	4	2	no	—
171	C₂×D₅₉	—	4	2	no	—
172	C₂×D₅₉	—	4	2	no	—
173	C₂×D₅₉	—	8	1	no	—
174	C₂×D₅₉	—	8	1	no	—
175	C₂×D₅₉	—	8	1	no	—
176	C₂×D₅₉	—	8	1	no	—
177	C₄×C₅₉	—	2	1	no	—
178	C₄×C₅₉	—	2	1	no	—
179	C₄×C₅₉	—	4	2	no	—
180	C₄×C₅₉	—	4	2	no	—
181	C₄×C₅₉	#431	1	1	yes	characteristic
182	C₄×C₅₉	#433	1	1	yes	characteristic
183	C₄×C₅₉	C₈×D₄	1	1	yes	characteristic
184	C₄×C₅₉	#436	1	1	yes	characteristic
185	C₄×C₅₉	#460	1	1	yes	characteristic
186	C₄×C₅₉	#463	1	1	yes	characteristic
187	C₄×C₅₉	#481	1	1	yes	characteristic
188	C₄×C₅₉	#482	1	1	yes	characteristic
189	Dic₅₉	—	8	1	no	—
190	#1954	—	59	1	no	—
191	C₈×C₄⋊C₄	D₅₉	1	1	yes	characteristic, complemented
192	C₄×#102	—	59	1	no	—
193	C₂×#334	—	59	1	no	—
194	C₂×D₄⋊C₈	—	59	1	no	—
195	#1279	—	59	1	no	—
196	#1273	—	59	1	no	—
197	C₂×C₅₉	C₈×SD₁₆	1	1	yes	characteristic
198	C₂×C₅₉	#1580	1	1	yes	characteristic
199	C₂×C₅₉	#1583	1	1	yes	characteristic
200	C₂×C₅₉	#1586	1	1	yes	characteristic
201	C₂×C₅₉	#1923	1	1	yes	characteristic
202	C₂×C₅₉	#1926	1	1	yes	characteristic
203	C₂×C₅₉	#1929	1	1	yes	characteristic
204	D₅₉	—	8	2	no	—
205	C₂×C₄×D₄	—	59	1	no	—
206	C₂×C₄⋊C₈	—	59	1	no	—
207	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
208	C₂×#102	—	59	1	no	—
209	C₂×#102	—	59	1	no	—
210	C₂×C₂²⋊C₈	—	118	1	no	—
211	C₂×C₂²⋊C₈	—	118	1	no	—
212	C₂×C₄×C₈	—	2	1	no	—
213	C₂×C₄×C₈	—	59	1	no	—
214	C₂×C₄×C₈	—	59	1	no	—
215	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
216	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
217	#340	—	59	1	no	—
218	#340	—	59	1	no	—
219	#336	—	2	1	no	—
220	#334	—	118	2	no	—
221	D₄⋊C₈	—	118	2	no	—
222	C₅₉	#9542	1	1	yes	characteristic, complemented, Sylow
223	C₂²×D₄	—	59	1	no	—
224	C₂³×C₄	—	118	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	59	1	no	—
227	C₂²×C₈	—	59	1	no	—
228	C₂²×C₈	—	118	1	no	—
229	C₂²×C₈	—	118	1	no	—
230	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
231	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
232	C₄×D₄	—	118	1	no	—
233	C₄×D₄	—	118	1	no	—
234	C₄×D₄	—	118	1	no	—
235	C₄×D₄	—	118	1	no	—
236	C₂×C₄⋊C₄	—	59	1	no	—
237	C₂×C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	118	1	no	—
240	C₂×C₄²	—	2	1	no	—
241	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	118	1	no	—
244	C₄⋊C₈	—	118	1	no	—
245	C₄⋊C₈	D₂₃₆	1	2	yes	—
246	#102	—	59	4	no	—
247	#102	—	118	2	no	—
248	C₂²⋊C₈	—	236	2	no	—
249	C₂²⋊C₈	—	236	2	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	4	2	no	—
253	C₄×C₈	—	118	1	no	—
254	C₄×C₈	—	118	1	no	—
255	C₄×C₈	—	118	1	no	—
256	C₄×C₈	—	118	1	no	—
257	#95	—	2	1	no	—
258	C₂⁴	—	118	1	no	—
259	C₂×D₄	—	59	2	no	—
260	C₂×D₄	—	118	1	no	—
261	C₂×D₄	—	118	1	no	—
262	C₂×D₄	—	118	1	no	—
263	C₂×D₄	—	118	1	no	—
264	C₂×D₄	—	118	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	118	1	no	—
268	C₂²×C₄	—	236	1	no	—
269	C₂²×C₄	—	236	1	no	—
270	C₂²×C₄	—	236	1	no	—
271	C₂²×C₄	—	236	1	no	—
272	C₂²×C₄	—	236	1	no	—
273	C₂²×C₄	—	236	1	no	—
274	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
275	C₂²×C₄	#11745685	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	59	2	no	—
286	C₂×C₈	—	118	1	no	—
287	C₂×C₈	—	118	1	no	—
288	C₂×C₈	—	118	2	no	—
289	C₂×C₈	—	118	1	no	—
290	C₂×C₈	—	118	1	no	—
291	C₂×C₈	—	118	1	no	—
292	C₂×C₈	—	236	1	no	—
293	C₂×C₈	—	236	1	no	—
294	C₂×C₈	—	236	1	no	—
295	C₂×C₈	—	236	1	no	—
296	C₂×C₈	—	236	1	no	—
297	C₂×C₈	#11745671	1	2	yes	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	118	1	no	—
301	C₄⋊C₄	—	118	1	no	—
302	C₄⋊C₄	C₈×D₅₉	1	2	yes	—
303	C₄⋊C₄	#11745659	1	2	yes	—
304	C₂²⋊C₄	—	236	1	no	—
305	C₂²⋊C₄	—	236	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
309	C₄²	#11745685	1	1	yes	characteristic
310	C₄²	#11745685	1	1	yes	characteristic
311	C₄²	#11745685	1	1	yes	characteristic
312	C₂³	—	118	2	no	—
313	C₂³	—	236	1	no	—
314	C₂³	—	236	1	no	—
315	C₂³	—	236	1	no	—
316	C₂³	—	236	1	no	—
317	C₂³	—	236	1	no	—
318	C₂³	—	236	1	no	—
319	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
320	D₄	—	118	2	no	—
321	D₄	—	118	2	no	—
322	D₄	—	236	1	no	—
323	D₄	—	236	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	472	1	no	—
333	C₂×C₄	—	472	1	no	—
334	C₂×C₄	—	472	1	no	—
335	C₂×C₄	—	472	1	no	—
336	C₂×C₄	—	236	1	no	—
337	C₂×C₄	—	236	1	no	—
338	C₂×C₄	—	236	1	no	—
339	C₂×C₄	#14273684	1	1	yes	characteristic
340	C₂×C₄	C₄×D₂₃₆	1	1	yes	characteristic
341	C₂×C₄	#14273701	1	1	yes	characteristic
342	C₂×C₄	#14273710	1	1	yes	characteristic
343	C₂×C₄	#14273715	1	1	yes	characteristic
344	C₂×C₄	#14273721	1	1	yes	characteristic
345	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
346	C₂×C₄	C₂×#11745659	1	1	yes	characteristic
347	C₂×C₄	#14273733	1	1	yes	characteristic
348	C₂×C₄	#14273733	1	1	yes	characteristic
349	C₂×C₄	C₂×#11745671	1	1	yes	characteristic
350	C₂×C₄	#14273747	1	1	yes	characteristic
351	C₂×C₄	#14273752	1	1	yes	characteristic
352	C₂×C₄	#14273753	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	2	no	—
356	C₈	—	118	2	no	—
357	C₈	—	472	1	no	—
358	C₈	—	236	2	no	—
359	C₈	—	236	1	no	—
360	C₂²	—	472	1	no	—
361	C₂²	—	472	1	no	—
362	C₂²	—	472	1	no	—
363	C₂²	—	472	1	no	—
364	C₂²	—	236	2	no	—
365	C₂²	—	236	2	no	—
366	C₂²	—	236	2	no	—
367	C₂²	#16837293	1	1	yes	characteristic
368	C₂²	C₈×C₂²⋊D₅₉	1	1	yes	characteristic
369	C₂²	#16837473	1	1	yes	characteristic
370	C₂²	C₄×#11745671	1	1	yes	characteristic
371	C₂²	#16837512	1	1	yes	characteristic
372	C₂²	#16837517	1	1	yes	characteristic
373	C₂²	#16837522	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	472	1	no	—
379	C₄	#16837453	1	1	yes	characteristic
380	C₄	#16837461	1	1	yes	characteristic
381	C₄	C₈×D₂₃₆	1	1	yes	characteristic
382	C₄	#16837481	1	1	yes	characteristic
383	C₄	#16837602	1	1	yes	characteristic
384	C₄	#16837617	1	1	yes	characteristic
385	C₄	#16837720	1	1	yes	characteristic
386	C₄	#16837726	1	1	yes	characteristic
387	C₂	—	472	2	no	—
388	C₂	C₈×#11745671	1	1	yes	characteristic
389	C₂	#21422918	1	1	yes	characteristic
390	C₂	#21422939	1	1	yes	characteristic
391	C₂	#21422960	1	1	yes	characteristic
392	C₂	#21424702	1	1	yes	characteristic
393	C₂	#21424723	1	1	yes	characteristic
394	C₂	#21424744	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₈×C₄⋊C₄×C₅₉	C₂
socle	C₂³×C₅₉	C₄×D₄
prime radical	C₂²×D₂₃₆	C₂×C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₈×C₄⋊C₄	D₅₉
hypocenter	C₅₉	#9542
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×#16837152	C₂	semidirect
5. #21421937	C₂	semidirect
6. C₅₉⋊#1273	C₂	semidirect
7. C₈×C₄⋊C₄×C₅₉	C₂	semidirect
40. #14273647	C₈	semidirect
191. C₈×C₄⋊C₄	D₅₉	semidirect
222. C₅₉	#9542	semidirect

Maximal subgroups

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

subgroup	index
#21424890	2
C₄×#14273647	2
C₂×#16837152	2
C₂×#16837129	2
#21421937	2
C₅₉⋊#1273	2
C₈×C₄⋊C₄×C₅₉	2
#9542	59