Subgroups — #28560646

Order 15104.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434702	C₂	1	1	yes	maximal, characteristic
2	#21433252	C₂	1	1	yes	maximal, characteristic
3	#21433197	C₂	1	1	yes	maximal, characteristic, complemented
4	#21423004	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422985	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422973	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422966	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422931	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422907	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422902	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422502	C₂	1	1	yes	maximal, characteristic
13	#21422498	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422393	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837959	C₂²	1	1	yes	characteristic
17	#16837936	C₂²	1	1	yes	characteristic
18	#16837811	C₄	1	1	yes	characteristic
19	#16837796	C₄	1	1	yes	characteristic
20	#16837771	C₄	1	1	yes	characteristic
21	#16837762	C₄	1	1	yes	characteristic
22	#16837660	C₄	1	1	yes	characteristic
23	#16837660	C₄	1	1	yes	characteristic
24	#16837648	C₄	1	1	yes	characteristic
25	#16837648	C₄	1	1	yes	characteristic
26	#16837532	—	2	1	no	—
27	#16837529	C₂²	1	1	yes	characteristic
28	#16837529	C₂²	1	1	yes	characteristic
29	#16837529	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₁₈	—	2	1	no	—
31	#16837526	C₂²	1	1	yes	characteristic
32	#16837526	C₂²	1	1	yes	characteristic
33	#16837526	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
35	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
36	C₄×#11745660	C₂²	1	1	yes	characteristic
37	C₄×#11745660	C₂²	1	1	yes	characteristic
38	#16837479	C₂²	1	1	yes	characteristic
39	#16837473	—	2	1	no	—
40	#16837467	C₂²	1	1	yes	characteristic
41	C₈×C₂²⋊D₅₉	—	2	1	no	—
42	#16837462	—	2	1	no	—
43	#16837460	—	2	1	no	—
44	#16837460	—	2	1	no	—
45	#16837455	C₂²	1	1	yes	characteristic
46	#16837455	C₂²	1	1	yes	characteristic
47	#16837427	—	2	1	no	—
48	#16837132	C₂²	1	1	yes	characteristic
49	#16837132	C₂²	1	1	yes	characteristic
50	#16837132	C₂²	1	1	yes	characteristic
51	#16837132	C₂²	1	1	yes	characteristic
52	#16837132	C₂²	1	1	yes	characteristic
53	#16837132	C₂²	1	1	yes	characteristic
54	#16837129	C₂²	1	1	yes	characteristic
55	#16837129	C₂²	1	1	yes	characteristic
56	#16837124	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic
58	#16837123	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₅₉×#431	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×#335	C₂²	1	1	yes	characteristic
65	C₅₉×#334	C₂²	1	1	yes	characteristic
66	C₅₉×#334	C₂²	1	1	yes	characteristic
67	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745659	—	2	1	no	—
72	C₂×C₈×D₅₉	—	2	1	no	—
73	#14273727	C₂×C₄	1	1	yes	characteristic
74	#14273727	C₂×C₄	1	1	yes	characteristic
75	#14273721	—	2	1	no	—
76	#14273719	—	2	1	no	—
77	#14273719	C₂×C₄	1	1	yes	characteristic
78	#14273715	C₂×C₄	1	1	yes	characteristic
79	#14273710	—	2	1	no	—
80	#14273706	—	2	1	no	—
81	#14273706	C₂×C₄	1	1	yes	characteristic
82	#14273706	C₂×C₄	1	1	yes	characteristic
83	#14273706	C₂×C₄	1	1	yes	characteristic
84	#14273701	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₁₁₈	—	2	1	no	—
86	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
87	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
88	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
89	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
90	C₄×C₂²⋊D₅₉	—	2	1	no	—
91	#14273686	—	2	1	no	—
92	#14273684	—	2	1	no	—
93	#14273661	C₂×C₄	1	1	yes	characteristic
94	#14273661	C₂×C₄	1	1	yes	characteristic
95	#14273659	C₂×C₄	1	1	yes	characteristic
96	#14273659	C₂×C₄	1	1	yes	characteristic
97	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
98	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
100	Dic₅₉⋊C₈	—	2	1	no	—
101	Dic₅₉⋊C₈	—	2	1	no	—
102	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	#14273652	C₂×C₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273652	C₂×C₄	1	1	yes	characteristic
110	#14273652	C₂×C₄	1	1	yes	characteristic
111	#14273652	C₂×C₄	1	1	yes	characteristic
112	#14273649	C₂×C₄	1	1	yes	characteristic
113	#14273649	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
116	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
117	(C₂×D₅₉)⋊C₈	—	2	1	no	—
118	(C₂×D₅₉)⋊C₈	—	2	1	no	—
119	#14273637	—	2	1	no	—
120	#14273637	—	2	1	no	—
121	#14273637	—	2	1	no	—
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	—	2	1	no	—
129	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₂²×C₈×C₅₉	—	2	1	no	—
132	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	—	2	1	no	—
134	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₅₉	—	2	1	no	—
139	#97×C₅₉	C₂×C₄	1	1	yes	characteristic
140	#97×C₅₉	C₂×C₄	1	1	yes	characteristic
141	C₄×C₈×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
147	C₂×C₂²⋊D₅₉	—	2	1	no	—
148	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₅₉	—	2	1	no	—
150	C₂×Dic₁₁₈	—	2	1	no	—
151	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
154	M₁₆×C₅₉	—	2	2	no	—
155	M₁₆×C₅₉	—	4	1	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	—	2	1	no	—
158	C₂×C₈×C₅₉	—	2	1	no	—
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	8	1	no	—
161	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₅₉	#41	1	1	yes	characteristic
168	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
169	C₂²⋊Dic₅₉	—	2	1	no	—
170	C₂²⋊Dic₅₉	—	2	1	no	—
171	C₂²⋊Dic₅₉	—	2	1	no	—
172	(C₂×D₅₉)⋊C₄	—	2	1	no	—
173	(C₂×D₅₉)⋊C₄	—	2	1	no	—
174	(C₂×D₅₉)⋊C₄	—	2	1	no	—
175	(C₂×D₅₉)⋊C₄	—	2	1	no	—
176	C₄⋊Dic₅₉	—	2	1	no	—
177	C₄⋊Dic₅₉	—	2	1	no	—
178	C₄⋊Dic₅₉	—	2	1	no	—
179	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
183	Dic₅₉⋊C₄	—	2	1	no	—
184	Dic₅₉⋊C₄	—	2	1	no	—
185	Dic₅₉⋊C₄	—	2	1	no	—
186	Dic₅₉⋊C₄	—	2	1	no	—
187	Dic₅₉⋊C₄	—	2	1	no	—
188	Dic₅₉⋊C₄	—	2	1	no	—
189	Dic₅₉⋊C₄	—	2	1	no	—
190	Dic₅₉⋊C₄	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	C₂×C₅₉⋊C₈	—	2	1	no	—
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
200	Dic₂₃₆	—	2	2	no	—
201	Dic₂₃₆	—	4	1	no	—
202	#11745660	—	2	2	no	—
203	#11745660	—	4	1	no	—
204	#11745659	—	8	1	no	—
205	C₈×D₅₉	—	8	1	no	—
206	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
207	C₂²×D₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	2	1	no	—
209	C₂×C₄×C₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	4	1	no	—
213	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
219	C₂²⋊D₅₉	—	4	2	no	—
220	C₂×Dic₅₉	—	2	1	no	—
221	C₂×Dic₅₉	—	2	1	no	—
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	—	2	1	no	—
224	C₂×Dic₅₉	—	2	1	no	—
225	C₂×Dic₅₉	—	2	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	D₂₃₆	—	2	1	no	—
228	D₂₃₆	—	2	1	no	—
229	C₄×D₅₉	—	4	1	no	—
230	C₄×D₅₉	—	4	1	no	—
231	Dic₁₁₈	—	2	1	no	—
232	Dic₁₁₈	—	2	1	no	—
233	Dic₁₁₈	—	2	1	no	—
234	Dic₁₁₈	—	2	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	4	2	no	—
238	C₈×C₅₉	—	2	1	no	—
239	C₈×C₅₉	—	2	1	no	—
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	—	4	1	no	—
242	C₈×C₅₉	—	4	1	no	—
243	C₈×C₅₉	—	4	1	no	—
244	C₈×C₅₉	—	4	1	no	—
245	C₈×C₅₉	#131	1	2	yes	—
246	C₅₉⋊C₈	—	2	1	no	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	2	1	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	4	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	#18083	—	59	1	no	maximal, Sylow
253	C₂²×C₅₉	—	2	1	no	—
254	C₂²×C₅₉	—	2	1	no	—
255	C₂²×C₅₉	—	2	1	no	—
256	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₅₉	—	4	1	no	—
258	C₂×D₅₉	—	4	1	no	—
259	C₂×D₅₉	—	4	1	no	—
260	C₄×C₅₉	—	2	1	no	—
261	C₄×C₅₉	—	2	1	no	—
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	2	1	no	—
264	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
265	C₄×C₅₉	#568	1	1	yes	characteristic
266	C₄×C₅₉	#577	1	1	yes	characteristic
267	C₄×C₅₉	#578	1	1	yes	characteristic
268	Dic₅₉	—	4	1	no	—
269	Dic₅₉	—	4	1	no	—
270	Dic₅₉	—	4	1	no	—
271	Dic₅₉	—	4	1	no	—
272	Dic₅₉	—	4	1	no	—
273	Dic₅₉	—	4	1	no	—
274	Dic₅₉	—	4	1	no	—
275	#3172	—	59	1	no	—
276	#2994	—	59	1	no	—
277	#2986	—	59	1	no	—
278	#1593	—	59	1	no	—
279	#1590	—	59	1	no	—
280	#1588	—	59	1	no	—
281	#1587	—	59	1	no	—
282	#1584	—	59	1	no	—
283	#1582	—	59	1	no	—
284	SD₁₆⋊C₈	—	59	1	no	—
285	C₈×Q₁₆	—	59	1	no	—
286	#1565	D₅₉	1	1	yes	characteristic, complemented
287	#1482	—	59	1	no	—
288	#1481	—	59	1	no	—
289	#1453	—	59	1	no	—
290	C₂×C₅₉	—	4	1	no	—
291	C₂×C₅₉	#2935	1	1	yes	characteristic
292	C₂×C₅₉	#2947	1	1	yes	characteristic
293	C₂×C₅₉	#2955	1	1	yes	characteristic
294	D₅₉	—	8	1	no	—
295	#533	—	59	1	no	—
296	#529	—	59	1	no	—
297	#501	—	59	1	no	—
298	#497	—	59	1	no	—
299	#491	—	59	1	no	—
300	#489	—	59	1	no	—
301	#470	—	59	1	no	—
302	#470	—	59	1	no	—
303	#468	—	59	1	no	—
304	#468	—	59	1	no	—
305	#446	—	59	1	no	—
306	#446	—	59	1	no	—
307	#446	—	59	1	no	—
308	#446	—	118	1	no	—
309	C₈×Q₈	—	59	1	no	—
310	C₈×Q₈	—	59	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	118	1	no	—
313	C₄×Q₁₆	—	59	1	no	—
314	C₄×Q₁₆	—	59	1	no	—
315	C₄×SD₁₆	—	59	1	no	—
316	C₄×SD₁₆	—	59	1	no	—
317	#436	—	59	1	no	—
318	#435	—	118	1	no	—
319	C₈×D₄	—	59	1	no	—
320	C₈×D₄	—	118	1	no	—
321	#433	—	118	1	no	—
322	#433	—	118	1	no	—
323	#433	—	118	1	no	—
324	#431	—	59	1	no	—
325	#431	—	59	1	no	—
326	#431	C₂×D₅₉	1	1	yes	characteristic
327	#424	—	118	1	no	—
328	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
329	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
330	#335	C₂×D₅₉	1	1	yes	characteristic
331	#335	C₂×D₅₉	1	1	yes	characteristic
332	#334	C₂×D₅₉	1	1	yes	characteristic
333	#334	C₂×D₅₉	1	1	yes	characteristic
334	Q₈⋊C₈	—	59	1	no	—
335	Q₈⋊C₈	—	59	1	no	—
336	Q₈⋊C₈	—	59	1	no	—
337	Q₈⋊C₈	—	59	1	no	—
338	Q₈⋊C₈	—	59	1	no	—
339	Q₈⋊C₈	—	59	1	no	—
340	D₄⋊C₈	—	59	1	no	—
341	D₄⋊C₈	—	59	1	no	—
342	#322	—	59	1	no	—
343	#322	—	59	1	no	—
344	#322	—	59	1	no	—
345	C₈²	—	59	1	no	—
346	C₅₉	#18083	1	1	yes	characteristic, complemented, Sylow
347	C₂×Q₁₆	—	59	1	no	—
348	C₂×Q₁₆	—	59	1	no	—
349	C₂×SD₁₆	—	59	1	no	—
350	C₂×SD₁₆	—	59	1	no	—
351	C₂×M₁₆	—	118	1	no	—
352	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
353	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	118	1	no	—
356	C₄⋊Q₈	—	59	1	no	—
357	C₄⋊Q₈	—	59	1	no	—
358	#126	—	118	1	no	—
359	#125	—	59	1	no	—
360	#125	—	118	1	no	—
361	#124	—	59	1	no	—
362	#123	—	118	1	no	—
363	C₂²⋊Q₈	—	59	1	no	—
364	C₂²⋊Q₈	—	59	1	no	—
365	C₂²⋊Q₈	—	59	1	no	—
366	C₂²⋊Q₈	—	118	1	no	—
367	#121	—	59	1	no	—
368	C₄×Q₈	—	59	1	no	—
369	C₄×Q₈	—	59	1	no	—
370	C₄×Q₈	—	59	1	no	—
371	C₄×Q₈	—	118	1	no	—
372	C₄×D₄	—	59	1	no	—
373	C₄×D₄	—	118	1	no	—
374	#117	—	118	1	no	—
375	#117	—	118	1	no	—
376	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
377	#107	—	59	1	no	—
378	#107	—	59	1	no	—
379	#106	—	59	1	no	—
380	#106	—	59	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	59	1	no	—
383	C₄⋊C₈	—	59	1	no	—
384	C₄⋊C₈	—	118	1	no	—
385	C₄⋊C₈	—	118	1	no	—
386	C₄⋊C₈	—	118	1	no	—
387	C₄⋊C₈	—	118	1	no	—
388	C₄⋊C₈	—	118	1	no	—
389	C₄⋊C₈	—	118	1	no	—
390	C₄⋊C₈	—	118	1	no	—
391	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
395	#103	—	59	1	no	—
396	#103	—	59	1	no	—
397	#103	—	59	1	no	—
398	#103	—	59	1	no	—
399	#103	—	59	1	no	—
400	#103	—	59	1	no	—
401	#102	—	59	1	no	—
402	#102	—	59	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	59	1	no	—
405	C₂²⋊C₈	—	59	1	no	—
406	C₂²⋊C₈	—	118	1	no	—
407	C₂²⋊C₈	—	118	1	no	—
408	C₂²⋊C₈	—	118	1	no	—
409	#97	—	118	1	no	—
410	#97	—	118	1	no	—
411	#97	—	118	1	no	—
412	#97	C₄×D₅₉	1	1	yes	characteristic
413	#97	C₄×D₅₉	1	1	yes	characteristic
414	C₄×C₈	—	2	1	no	—
415	C₄×C₈	—	59	1	no	—
416	C₄×C₈	—	59	1	no	—
417	C₄×C₈	—	59	1	no	—
418	C₄×C₈	—	59	1	no	—
419	C₄×C₈	—	118	1	no	—
420	C₄×C₈	—	118	1	no	—
421	C₄×C₈	—	118	1	no	—
422	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
423	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
424	C₂×Q₈	—	59	1	no	—
425	C₂×Q₈	—	59	1	no	—
426	C₂×Q₈	—	59	1	no	—
427	C₂×Q₈	—	118	1	no	—
428	C₂×D₄	—	59	1	no	—
429	C₂×D₄	—	118	1	no	—
430	C₂²×C₄	—	118	1	no	—
431	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
433	C₂²×C₄	#11745689	1	1	yes	characteristic
434	Q₁₆	—	118	2	no	—
435	Q₁₆	—	236	1	no	—
436	SD₁₆	—	118	2	no	—
437	SD₁₆	—	236	1	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	4	1	no	—
440	M₁₆	—	472	1	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	—	8	1	no	—
446	C₂×C₈	—	59	1	no	—
447	C₂×C₈	—	59	1	no	—
448	C₂×C₈	—	59	1	no	—
449	C₂×C₈	—	59	1	no	—
450	C₂×C₈	—	118	1	no	—
451	C₂×C₈	—	118	1	no	—
452	C₂×C₈	—	472	1	no	—
453	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
454	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
455	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
457	C₄⋊C₄	—	59	1	no	—
458	C₄⋊C₄	—	59	1	no	—
459	C₄⋊C₄	—	59	1	no	—
460	C₄⋊C₄	—	59	1	no	—
461	C₄⋊C₄	—	118	1	no	—
462	C₄⋊C₄	—	118	1	no	—
463	C₄⋊C₄	—	118	1	no	—
464	C₄⋊C₄	—	118	1	no	—
465	C₄⋊C₄	—	118	1	no	—
466	C₄⋊C₄	—	118	1	no	—
467	C₄⋊C₄	—	118	1	no	—
468	C₄⋊C₄	—	118	1	no	—
469	C₄⋊C₄	—	118	1	no	—
470	C₄⋊C₄	—	118	1	no	—
471	C₄⋊C₄	—	118	1	no	—
472	C₂²⋊C₄	—	118	1	no	—
473	C₂²⋊C₄	—	118	1	no	—
474	C₂²⋊C₄	—	118	1	no	—
475	C₂²⋊C₄	—	118	1	no	—
476	C₂²⋊C₄	—	118	1	no	—
477	C₂²⋊C₄	—	118	1	no	—
478	C₂²⋊C₄	—	118	1	no	—
479	C₄²	—	118	1	no	—
480	C₄²	—	118	1	no	—
481	C₄²	—	118	1	no	—
482	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
483	C₄²	D₄×D₅₉	1	1	yes	characteristic
484	C₄²	#11745689	1	1	yes	characteristic
485	C₄²	C₂³×D₅₉	1	1	yes	characteristic
486	C₂³	—	118	1	no	—
487	C₂³	#14273689	1	1	yes	characteristic
488	Q₈	—	118	1	no	—
489	Q₈	—	118	1	no	—
490	Q₈	—	118	1	no	—
491	Q₈	—	118	1	no	—
492	Q₈	—	118	1	no	—
493	Q₈	—	118	1	no	—
494	Q₈	—	236	2	no	—
495	D₄	—	118	1	no	—
496	D₄	—	118	1	no	—
497	D₄	—	236	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	118	1	no	—
504	C₂×C₄	—	118	1	no	—
505	C₂×C₄	—	118	1	no	—
506	C₂×C₄	—	118	1	no	—
507	C₂×C₄	—	118	1	no	—
508	C₂×C₄	—	118	1	no	—
509	C₂×C₄	—	118	1	no	—
510	C₂×C₄	—	236	1	no	—
511	C₂×C₄	—	236	1	no	—
512	C₂×C₄	#14273689	1	1	yes	characteristic
513	C₂×C₄	#14273689	1	1	yes	characteristic
514	C₂×C₄	#14273689	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	118	1	no	—
526	C₈	—	118	1	no	—
527	C₈	—	118	1	no	—
528	C₈	—	118	1	no	—
529	C₈	—	236	1	no	—
530	C₈	—	236	1	no	—
531	C₈	#14273733	1	2	yes	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	236	1	no	—
536	C₂²	—	236	1	no	—
537	C₂²	—	236	1	no	—
538	C₂²	C₂×#14273689	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	236	1	no	—
544	C₄	—	236	1	no	—
545	C₄	—	236	1	no	—
546	C₄	—	236	1	no	—
547	C₄	—	236	1	no	—
548	C₄	—	236	1	no	—
549	C₄	—	236	1	no	—
550	C₄	C₂×#14273733	1	1	yes	characteristic
551	C₄	#16838168	1	1	yes	characteristic
552	C₄	#16838212	1	1	yes	characteristic
553	C₄	#16838218	1	1	yes	characteristic
554	C₂	—	4	1	no	—
555	C₂	—	472	1	no	—
556	C₂	#21432839	1	1	yes	characteristic
557	C₂	#21432937	1	1	yes	characteristic
558	C₂	#21432998	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1565	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#14273701	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1565	D₅₉
hypocenter	C₅₉	#18083
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
3. #21433197	C₂	semidirect
4. #21423004	C₂	semidirect
5. #21422985	C₂	semidirect
6. #21422973	C₂	semidirect
7. #21422966	C₂	semidirect
8. #21422945	C₂	semidirect
9. #21422931	C₂	semidirect
10. #21422907	C₂	semidirect
11. #21422902	C₂	semidirect
13. #21422498	C₂	semidirect
14. #21422393	C₂	semidirect
15. C₅₉×#1565	C₂	semidirect
286. #1565	D₅₉	semidirect
346. C₅₉	#18083	semidirect

Maximal subgroups

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

subgroup	index
#21434702	2
#21433252	2
#21433197	2
#21423004	2
#21422985	2
#21422973	2
#21422966	2
#21422945	2
#21422931	2
#21422907	2
#21422902	2
#21422502	2
#21422498	2
#21422393	2
C₅₉×#1565	2
#18083	59