Subgroups — #28595133

Order 15104.

922 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433551	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837517	C₂	1	2	yes	maximal, complemented
3	#21432809	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425015	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424871	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424744	C₂	1	2	yes	maximal, complemented
7	#21424423	C₂	1	2	yes	maximal, complemented
8	#21424116	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423935	C₂	1	2	yes	maximal, complemented
11	C₄×#131×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₂²	1	2	yes	—
13	C₂×#14273733	C₂²	1	2	yes	—
14	#16837952	C₂²	1	1	yes	characteristic
15	#16837624	C₄	1	2	yes	complemented
16	#16837617	C₄	1	2	yes	complemented
17	#16837612	C₄	1	1	yes	characteristic, complemented
18	#16837607	C₄	1	1	yes	characteristic, complemented
19	#16837602	C₄	1	1	yes	characteristic, complemented
20	#16837597	C₄	1	1	yes	characteristic, complemented
21	#16837517	—	2	8	no	—
22	#16837481	—	2	1	no	—
23	#16837481	—	2	1	no	—
24	C₈×D₂₃₆	—	2	1	no	—
25	C₈×D₂₃₆	—	2	1	no	—
26	C₂×#14273662	C₂²	1	2	yes	—
27	#16837426	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×#14273654	C₂²	1	2	yes	—
30	C₂×#14273653	C₂²	1	2	yes	—
31	C₂×#14273653	C₂²	1	2	yes	—
32	#16837396	C₂²	1	2	yes	—
33	#16837368	C₂²	1	2	yes	—
34	C₂×C₈×Dic₅₉	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
36	#16837166	C₂²	1	2	yes	—
37	#16837161	C₂²	1	2	yes	—
38	#16837156	C₂²	1	2	yes	—
39	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
41	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#405	—	2	1	no	—
43	C₅₉×#405	—	2	1	no	—
44	C₅₉×#405	C₂²	1	1	yes	characteristic
45	C₅₉×#405	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₅₉	—	2	1	no	—
47	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₅₉	—	2	1	no	—
49	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#11745685	C₂³	1	2	yes	—
51	#14273747	—	2	4	no	—
52	#14273747	—	2	4	no	—
53	C₂×#11745672	C₂×C₄	1	2	yes	—
54	C₂×#11745670	C₂×C₄	1	2	yes	—
55	C₂×#11745671	C₂×C₄	1	2	yes	—
56	C₂×#11745669	C₂×C₄	1	2	yes	—
57	#14273733	—	2	4	no	—
58	#14273733	—	2	4	no	—
59	C₂×#11745664	C₂³	1	2	yes	—
60	C₂×#11745659	—	2	2	no	—
61	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
62	C₂×C₈×D₅₉	—	2	2	no	—
63	#14273727	C₂×C₄	1	1	yes	characteristic
64	#14273724	C₂×C₄	1	1	yes	characteristic
65	#14273715	C₂×C₄	1	2	yes	—
66	#14273701	—	2	1	no	—
67	#14273701	—	2	1	no	—
68	C₄×D₂₃₆	—	2	1	no	—
69	C₄×D₂₃₆	—	2	1	no	—
70	C₂×C₄⋊Dic₅₉	—	2	1	no	—
71	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
72	#14273662	—	2	4	no	—
73	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
76	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
78	#14273654	—	2	4	no	—
79	#14273653	—	2	4	no	—
80	#14273653	—	2	4	no	—
81	#14273650	C₂×C₄	1	2	yes	—
82	#14273650	C₂×C₄	1	2	yes	—
83	#14273647	C₂×C₄	1	2	yes	—
84	#14273647	C₂×C₄	1	2	yes	—
85	(C₂×D₅₉)⋊C₈	—	2	2	no	—
86	(C₂×D₅₉)⋊C₈	—	2	2	no	—
87	C₈×Dic₅₉	—	2	4	no	—
88	C₅₉⋊#95	—	2	1	no	—
89	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
90	#131×C₅₉	—	2	2	no	—
91	#131×C₅₉	—	2	2	no	—
92	#131×C₅₉	—	2	2	no	—
93	#131×C₅₉	D₄	1	4	yes	complemented
94	C₂×M₁₆×C₅₉	—	2	1	no	—
95	C₂×M₁₆×C₅₉	—	2	1	no	—
96	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₅₉	—	2	1	no	—
99	C₂²×C₈×C₅₉	—	2	1	no	—
100	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₅₉	—	2	1	no	—
105	C₄×D₄×C₅₉	—	2	1	no	—
106	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
107	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
108	#117×C₅₉	—	2	1	no	—
109	#117×C₅₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅₉	—	2	1	no	—
111	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
112	#97×C₅₉	—	2	1	no	—
113	#97×C₅₉	—	2	1	no	—
114	#97×C₅₉	—	2	1	no	—
115	C₄×C₈×C₅₉	—	2	1	no	—
116	C₄×C₈×C₅₉	—	2	1	no	—
117	C₄×C₈×C₅₉	—	2	1	no	—
118	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
119	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
120	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
121	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
122	#41×C₅₉	—	2	1	no	—
123	#41×C₅₉	—	2	1	no	—
124	#41×C₅₉	C₂×D₄	1	2	yes	—
125	#41×C₅₉	#41	1	2	yes	—
126	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₅₉	—	2	1	no	—
128	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	1	no	—
131	C₂²×C₄×C₅₉	—	2	1	no	—
132	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
135	C₂×C₂²⋊D₅₉	—	2	2	no	—
136	C₂²×Dic₅₉	—	2	2	no	—
137	#11745685	—	2	2	no	—
138	#11745685	—	2	2	no	—
139	#11745685	—	2	2	no	—
140	#11745685	—	2	2	no	—
141	C₂×D₂₃₆	—	2	1	no	—
142	C₂×D₂₃₆	—	2	1	no	—
143	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
144	C₂×C₄×D₅₉	—	2	2	no	—
145	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
146	M₁₆×C₅₉	—	2	4	no	—
147	M₁₆×C₅₉	—	2	1	no	—
148	M₁₆×C₅₉	—	2	1	no	—
149	M₁₆×C₅₉	—	2	4	no	—
150	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
151	M₁₆×C₅₉	#41	1	2	yes	—
152	C₂×C₈×C₅₉	—	2	4	no	—
153	C₂×C₈×C₅₉	—	2	1	no	—
154	C₂×C₈×C₅₉	—	2	1	no	—
155	C₂×C₈×C₅₉	—	2	1	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	—	2	4	no	—
158	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	#41	1	2	yes	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²⋊C₄×C₅₉	—	2	1	no	—
169	C₂²⋊C₄×C₅₉	—	2	1	no	—
170	C₂²⋊C₄×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	—	2	1	no	—
173	C₄²×C₅₉	—	2	1	no	—
174	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
178	#11745672	—	2	4	no	—
179	#11745671	—	2	4	no	—
180	#11745670	—	2	4	no	—
181	#11745669	—	2	4	no	—
182	(C₂×D₅₉)⋊C₄	—	2	2	no	—
183	(C₂×D₅₉)⋊C₄	—	2	2	no	—
184	C₄⋊Dic₅₉	—	2	4	no	—
185	C₄⋊Dic₅₉	—	2	1	no	—
186	C₄⋊Dic₅₉	—	2	1	no	—
187	C₄×Dic₅₉	—	2	2	no	—
188	C₄×Dic₅₉	—	2	2	no	—
189	#11745664	—	2	2	no	—
190	#11745664	—	2	2	no	—
191	C₂×C₅₉⋊C₈	—	2	2	no	—
192	C₂×C₅₉⋊C₈	—	2	2	no	—
193	C₂×C₅₉⋊C₈	—	2	2	no	—
194	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
196	#11745659	—	4	4	no	—
197	C₈×D₅₉	—	4	4	no	—
198	C₂³×C₅₉	—	2	1	no	—
199	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
200	C₂²×D₅₉	—	2	2	no	—
201	Q₈×C₅₉	—	2	1	no	—
202	Q₈×C₅₉	C₄×D₄	1	2	yes	—
203	D₄×C₅₉	—	2	2	no	—
204	D₄×C₅₉	—	2	2	no	—
205	D₄×C₅₉	—	2	1	no	—
206	D₄×C₅₉	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	2	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	2	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	4	1	no	—
214	C₂×C₄×C₅₉	—	4	2	no	—
215	C₂×C₄×C₅₉	—	4	2	no	—
216	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
226	C₂²⋊D₅₉	—	4	2	no	—
227	C₂²⋊D₅₉	—	4	2	no	—
228	C₂×Dic₅₉	—	2	4	no	—
229	C₂×Dic₅₉	—	2	2	no	—
230	C₂×Dic₅₉	—	4	2	no	—
231	C₂×Dic₅₉	—	4	2	no	—
232	D₂₃₆	—	2	2	no	—
233	D₂₃₆	—	2	2	no	—
234	D₂₃₆	—	4	2	no	—
235	D₂₃₆	—	4	2	no	—
236	C₄×D₅₉	—	4	2	no	—
237	C₄×D₅₉	—	4	2	no	—
238	Dic₁₁₈	—	2	2	no	—
239	Dic₁₁₈	—	2	2	no	—
240	C₈×C₅₉	—	2	2	no	—
241	C₈×C₅₉	—	2	1	no	—
242	C₈×C₅₉	—	2	2	no	—
243	C₈×C₅₉	—	2	1	no	—
244	C₈×C₅₉	#121	1	2	yes	—
245	C₈×C₅₉	#121	1	2	yes	—
246	C₅₉⋊C₈	—	2	2	no	—
247	C₅₉⋊C₈	—	2	2	no	—
248	C₅₉⋊C₈	—	4	2	no	—
249	#21517	—	59	1	no	maximal, Sylow
250	C₂²×C₅₉	—	2	1	no	—
251	C₂²×C₅₉	—	2	1	no	—
252	C₂²×C₅₉	—	2	2	no	—
253	C₂²×C₅₉	—	4	1	no	—
254	C₂²×C₅₉	—	4	1	no	—
255	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂²×C₅₉	#529	1	1	yes	characteristic
257	C₂²×C₅₉	#532	1	1	yes	characteristic
258	C₂×D₅₉	—	4	2	no	—
259	C₂×D₅₉	—	4	2	no	—
260	C₂×D₅₉	—	4	2	no	—
261	C₄×C₅₉	—	2	1	no	—
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	2	1	no	—
264	C₄×C₅₉	—	2	2	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	—	4	1	no	—
267	C₄×C₅₉	#443	1	2	yes	complemented
268	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
269	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
270	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
271	C₄×C₅₉	#525	1	1	yes	characteristic
272	Dic₅₉	—	4	4	no	—
273	Dic₅₉	—	4	2	no	—
274	#3035	—	59	1	no	—
275	C₂×#443	—	59	2	no	—
276	#2931	—	59	1	no	—
277	C₄×#131	D₅₉	1	1	yes	characteristic, complemented
278	#1980	—	59	1	no	—
279	#1950	—	59	1	no	—
280	#1929	—	59	2	no	—
281	#1876	—	59	2	no	—
282	#1806	—	59	1	no	—
283	C₈×C₄⋊C₄	—	59	1	no	—
284	#1764	—	59	2	no	—
285	C₂×C₅₉	—	2	1	no	—
286	C₂×C₅₉	—	2	1	no	—
287	C₂×C₅₉	—	4	2	no	—
288	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
289	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
290	C₂×C₅₉	#2955	1	1	yes	characteristic
291	D₅₉	—	8	2	no	—
292	C₂×#135	—	59	2	no	—
293	C₂×#131	—	59	2	no	—
294	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
295	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
296	#532	—	59	1	no	—
297	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
298	#464	—	59	2	no	—
299	#463	—	59	2	no	—
300	#462	—	59	1	no	—
301	#461	—	59	1	no	—
302	#460	—	59	1	no	—
303	#459	—	59	1	no	—
304	#443	—	118	8	no	—
305	#436	—	118	1	no	—
306	#436	—	118	1	no	—
307	C₈×D₄	—	118	1	no	—
308	C₈×D₄	—	118	1	no	—
309	C₂×#108	—	59	2	no	—
310	#423	—	59	1	no	—
311	C₂×C₄⋊C₈	—	59	1	no	—
312	C₂×#104	—	59	2	no	—
313	C₂×#104	—	59	2	no	—
314	C₂×#104	—	59	2	no	—
315	#416	—	59	2	no	—
316	#408	—	59	2	no	—
317	#405	—	2	1	no	—
318	#405	—	2	1	no	—
319	#405	C₂×D₅₉	1	1	yes	characteristic
320	#405	C₂×D₅₉	1	1	yes	characteristic
321	C₄×M₁₆	—	2	1	no	—
322	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
323	C₂×C₄×C₈	—	2	1	no	—
324	C₂×C₄×C₈	—	59	2	no	—
325	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
326	C₄×C₄⋊C₄	—	59	1	no	—
327	#341	—	59	2	no	—
328	#339	—	59	2	no	—
329	#336	—	59	2	no	—
330	C₅₉	#21517	1	1	yes	characteristic, complemented, Sylow
331	C₂×#41	—	59	2	no	—
332	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
333	#135	—	118	4	no	—
334	#135	—	118	4	no	—
335	C₂×Q₁₆	—	59	2	no	—
336	C₂×SD₁₆	—	59	2	no	—
337	C₂×SD₁₆	—	59	2	no	—
338	C₂×D₈	—	59	2	no	—
339	#131	—	2	2	no	—
340	#131	—	2	2	no	—
341	#131	—	2	2	no	—
342	#131	—	118	4	no	—
343	#131	—	118	4	no	—
344	#131	D₂₃₆	1	4	yes	complemented
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	59	2	no	—
348	C₂×M₁₆	—	118	2	no	—
349	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
350	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	59	2	no	—
354	C₂²×C₈	—	118	2	no	—
355	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
356	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
357	C₄⋊Q₈	—	59	1	no	—
358	#127	—	59	1	no	—
359	#124	—	59	2	no	—
360	#121	—	118	1	no	—
361	#121	—	118	1	no	—
362	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
363	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	118	1	no	—
367	C₄×D₄	—	118	1	no	—
368	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
369	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	C₂²×D₅₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	—	118	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	59	2	no	—
375	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
376	#108	—	118	4	no	—
377	C₄⋊C₈	—	59	1	no	—
378	C₄⋊C₈	—	59	1	no	—
379	C₄⋊C₈	—	59	2	no	—
380	C₄⋊C₈	—	118	1	no	—
381	C₄⋊C₈	—	118	1	no	—
382	#104	—	118	4	no	—
383	#104	—	118	4	no	—
384	#104	—	118	4	no	—
385	#103	—	59	2	no	—
386	#103	—	59	2	no	—
387	#102	—	59	2	no	—
388	#102	—	59	2	no	—
389	C₂²⋊C₈	—	118	2	no	—
390	C₂²⋊C₈	—	118	2	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	#97	—	2	1	no	—
394	C₄×C₈	—	2	1	no	—
395	C₄×C₈	—	2	1	no	—
396	C₄×C₈	—	2	1	no	—
397	C₄×C₈	—	118	4	no	—
398	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
399	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
400	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
401	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
402	#95	—	118	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	118	2	no	—
406	#41	—	118	2	no	—
407	#41	—	118	2	no	—
408	#41	—	118	2	no	—
409	#41	C₂×D₂₃₆	1	2	yes	—
410	#41	#11745685	1	2	yes	—
411	C₂×Q₈	—	59	2	no	—
412	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	59	2	no	—
415	C₂×D₄	—	118	2	no	—
416	C₂×D₄	—	118	1	no	—
417	C₂×D₄	—	118	1	no	—
418	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	118	2	no	—
423	C₂²×C₄	—	118	2	no	—
424	C₂²×C₄	#11745685	1	1	yes	characteristic
425	C₂²×C₄	#11745685	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
427	Q₁₆	—	118	4	no	—
428	SD₁₆	—	118	4	no	—
429	SD₁₆	—	118	4	no	—
430	D₈	—	118	4	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	1	no	—
433	M₁₆	—	2	1	no	—
434	M₁₆	—	2	4	no	—
435	M₁₆	—	118	2	no	—
436	M₁₆	—	118	2	no	—
437	M₁₆	—	236	4	no	—
438	M₁₆	C₂×D₂₃₆	1	2	yes	—
439	M₁₆	#11745685	1	2	yes	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	4	no	—
446	C₂×C₈	—	59	2	no	—
447	C₂×C₈	—	59	2	no	—
448	C₂×C₈	—	118	2	no	—
449	C₂×C₈	—	118	2	no	—
450	C₂×C₈	—	118	2	no	—
451	C₂×C₈	—	236	4	no	—
452	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
453	C₂×C₈	#11745685	1	2	yes	—
454	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
455	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
456	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
457	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	118	4	no	—
461	C₄⋊C₄	—	118	1	no	—
462	C₄⋊C₄	—	118	1	no	—
463	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
464	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	118	2	no	—
469	C₂²⋊C₄	—	118	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	118	2	no	—
474	C₄²	—	118	2	no	—
475	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
476	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
477	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
478	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	118	2	no	—
481	C₂³	C₂×#11745685	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	118	2	no	—
484	Q₈	—	118	2	no	—
485	Q₈	C₄×D₂₃₆	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	—	118	2	no	—
490	D₄	—	118	2	no	—
491	D₄	—	236	2	no	—
492	D₄	—	236	2	no	—
493	D₄	—	236	2	no	—
494	D₄	—	236	2	no	—
495	D₄	C₄×D₂₃₆	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	118	4	no	—
506	C₂×C₄	—	118	2	no	—
507	C₂×C₄	—	236	2	no	—
508	C₂×C₄	—	236	2	no	—
509	C₂×C₄	—	236	2	no	—
510	C₂×C₄	—	236	2	no	—
511	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
512	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
514	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
516	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
518	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
519	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
520	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	1	no	—
525	C₈	—	118	2	no	—
526	C₈	—	118	2	no	—
527	C₈	—	236	2	no	—
528	C₈	#14273701	1	2	yes	—
529	C₈	#14273701	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	236	2	no	—
536	C₂²	—	236	2	no	—
537	C₂²	—	236	2	no	—
538	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
539	C₂²	#16837936	1	1	yes	characteristic
540	C₂²	#16837952	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	236	4	no	—
548	C₄	—	236	2	no	—
549	C₄	#16837517	1	2	yes	complemented
550	C₄	C₂×C₄×D₂₃₆	1	1	yes	characteristic
551	C₄	C₄×#11745685	1	1	yes	characteristic
552	C₄	C₂×#14273701	1	1	yes	characteristic
553	C₄	#16837913	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	472	2	no	—
558	C₂	C₄×#14273701	1	1	yes	characteristic
559	C₂	C₂×#16837517	1	1	yes	characteristic
560	C₂	#21432997	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₄×#131×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#21433551	C₂
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₄×#131	D₅₉
hypocenter	C₅₉	#21517
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. C₂×#16837517	C₂	semidirect
3. #21432809	C₂	semidirect
4. #21425015	C₂	semidirect
5. #21424871	C₂	semidirect
6. #21424744	C₂	semidirect
7. #21424423	C₂	semidirect
8. #21424116	C₂	semidirect
9. C₈×C₄⋊Dic₅₉	C₂	semidirect
10. #21423935	C₂	semidirect
11. C₄×#131×C₅₉	C₂	semidirect
15. #16837624	C₄	semidirect
16. #16837617	C₄	semidirect
17. #16837612	C₄	semidirect
18. #16837607	C₄	semidirect
19. #16837602	C₄	semidirect
20. #16837597	C₄	semidirect
93. #131×C₅₉	D₄	semidirect
267. C₄×C₅₉	#443	semidirect
277. C₄×#131	D₅₉	semidirect
330. C₅₉	#21517	semidirect
344. #131	D₂₃₆	semidirect
549. C₄	#16837517	semidirect

Maximal subgroups

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

subgroup	index
#21433551	2
C₂×#16837517	2
#21432809	2
#21425015	2
#21424871	2
#21424744	2
#21424423	2
#21424116	2
C₈×C₄⋊Dic₅₉	2
#21423935	2
C₄×#131×C₅₉	2
#21517	59