Subgroups — #28554355

Order 15104.

750 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433058	C₂	1	1	yes	maximal, characteristic
2	C₈×#11745685	C₂	1	1	yes	maximal, characteristic
3	#21432735	C₂	1	1	yes	maximal, characteristic
4	#21422397	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422396	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422394	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422393	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422387	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422382	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422379	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422378	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×#11745659	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#11745659	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11745685	C₂²	1	1	yes	characteristic
17	#16837530	C₄	1	2	yes	—
18	C₈×Dic₁₁₈	C₄	1	2	yes	—
19	#16837478	C₄	1	2	yes	—
20	#16837475	C₄	1	2	yes	—
21	#16837471	C₄	1	2	yes	—
22	C₈×D₂₃₆	C₄	1	2	yes	—
23	C₈×C₂²⋊D₅₉	C₄	1	2	yes	—
24	C₈×C₂²⋊D₅₉	C₄	1	2	yes	—
25	#16837462	C₄	1	2	yes	—
26	#16837460	C₄	1	2	yes	—
27	#16837455	C₂²	1	1	yes	characteristic
28	#16837455	C₂²	1	1	yes	characteristic
29	#16837455	C₂²	1	1	yes	characteristic
30	#16837453	C₂²	1	1	yes	characteristic
31	#16837453	C₂²	1	1	yes	characteristic
32	#16837453	C₂²	1	1	yes	characteristic
33	#16837453	C₂²	1	1	yes	characteristic
34	#16837453	C₂²	1	1	yes	characteristic
35	#16837453	C₂²	1	1	yes	characteristic
36	#16837427	C₄	1	2	yes	—
37	#16837367	C₄	1	2	yes	—
38	C₄×#11745659	C₂²	1	1	yes	characteristic
39	C₄×#11745659	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
44	#16837124	C₂²	1	1	yes	characteristic
45	#16837124	C₂²	1	1	yes	characteristic
46	#16837124	C₂²	1	1	yes	characteristic
47	#16837124	C₂²	1	1	yes	characteristic
48	#16837123	C₂²	1	1	yes	characteristic
49	#16837123	C₂²	1	1	yes	characteristic
50	#16837123	C₂²	1	1	yes	characteristic
51	#16837123	C₂²	1	1	yes	characteristic
52	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
53	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
54	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
55	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
56	C₅₉×#431	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
59	C₅₉×#322	C₂²	1	1	yes	characteristic
60	C₅₉×#322	C₂²	1	1	yes	characteristic
61	C₈²×C₅₉	C₂²	1	1	yes	characteristic
62	C₈²×C₅₉	C₂²	1	1	yes	characteristic
63	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
64	C₂×#11745659	C₂×C₄	1	2	yes	—
65	C₂×#11745659	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
68	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
70	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
72	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
73	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
74	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
75	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
76	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
78	#14273686	C₂×C₄	1	1	yes	characteristic
79	#14273684	C₂×C₄	1	1	yes	characteristic
80	#14273684	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₅₉	C₂³	1	1	yes	characteristic
82	C₄²×D₅₉	C₂³	1	1	yes	characteristic
83	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
84	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
85	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
86	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
87	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
88	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
89	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
90	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
91	Dic₅₉⋊C₈	C₂×C₄	1	2	yes	—
92	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
93	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
94	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
95	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
96	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
97	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
98	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
99	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
100	(C₂×D₅₉)⋊C₈	C₂×C₄	1	2	yes	—
101	#14273637	C₂×C₄	1	2	yes	—
102	#14273637	C₂×C₄	1	2	yes	—
103	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
104	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
105	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
106	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
107	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
109	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
110	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
111	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
112	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
113	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
114	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
115	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
117	C₂²⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
118	#97×C₅₉	C₂×C₄	1	2	yes	—
119	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
120	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
122	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
123	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
124	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₅₉	C₄²	1	1	yes	characteristic
130	C₂×C₂²⋊D₅₉	C₄²	1	1	yes	characteristic
131	#11745685	—	2	4	no	—
132	C₂×D₂₃₆	C₄²	1	1	yes	characteristic
133	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×Dic₁₁₈	C₄²	1	1	yes	characteristic
140	M₁₆×C₅₉	—	2	4	no	—
141	C₂×C₈×C₅₉	—	2	4	no	—
142	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
148	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
152	C₂²⋊Dic₅₉	C₄²	1	1	yes	characteristic
153	C₂²⋊Dic₅₉	C₄²	1	1	yes	characteristic
154	(C₂×D₅₉)⋊C₄	C₄²	1	1	yes	characteristic
155	(C₂×D₅₉)⋊C₄	C₄²	1	1	yes	characteristic
156	(C₂×D₅₉)⋊C₄	C₄²	1	1	yes	characteristic
157	(C₂×D₅₉)⋊C₄	C₄²	1	1	yes	characteristic
158	C₄⋊Dic₅₉	C₄²	1	1	yes	characteristic
159	C₄⋊Dic₅₉	C₄²	1	1	yes	characteristic
160	Dic₅₉⋊C₄	C₄²	1	1	yes	characteristic
161	Dic₅₉⋊C₄	C₄²	1	1	yes	characteristic
162	Dic₅₉⋊C₄	C₄²	1	1	yes	characteristic
163	Dic₅₉⋊C₄	C₄²	1	1	yes	characteristic
164	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
176	#11745659	—	2	4	no	—
177	#11745659	—	2	4	no	—
178	C₈×D₅₉	—	2	4	no	—
179	C₈×D₅₉	—	2	4	no	—
180	C₈×D₅₉	—	2	4	no	—
181	C₈×D₅₉	—	2	4	no	—
182	C₂³×C₅₉	C₂×C₄²	1	1	yes	characteristic
183	C₂²×D₅₉	C₂×C₄²	1	1	yes	characteristic
184	C₂²×D₅₉	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	2	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
191	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
194	C₂²⋊D₅₉	—	2	2	no	—
195	C₂²⋊D₅₉	—	2	2	no	—
196	C₂×Dic₅₉	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₅₉	C₂×C₄²	1	1	yes	characteristic
198	C₂×Dic₅₉	C₂×C₄²	1	1	yes	characteristic
199	C₂×Dic₅₉	C₂×C₄²	1	1	yes	characteristic
200	C₂×Dic₅₉	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₅₉	C₂×C₄²	1	1	yes	characteristic
202	D₂₃₆	—	2	2	no	—
203	C₄×D₅₉	—	2	2	no	—
204	C₄×D₅₉	—	2	2	no	—
205	C₄×D₅₉	—	2	2	no	—
206	C₄×D₅₉	—	2	2	no	—
207	C₄×D₅₉	—	2	2	no	—
208	C₄×D₅₉	#131	1	4	yes	—
209	Dic₁₁₈	—	2	2	no	—
210	C₈×C₅₉	—	2	2	no	—
211	C₈×C₅₉	—	2	2	no	—
212	C₈×C₅₉	—	2	2	no	—
213	C₈×C₅₉	—	2	2	no	—
214	C₈×C₅₉	#131	1	4	yes	—
215	C₈×C₅₉	#131	1	4	yes	—
216	C₅₉⋊C₈	—	2	2	no	—
217	C₅₉⋊C₈	—	2	2	no	—
218	C₅₉⋊C₈	—	2	2	no	—
219	C₅₉⋊C₈	—	2	2	no	—
220	C₅₉⋊C₈	—	2	2	no	—
221	C₅₉⋊C₈	—	2	2	no	—
222	#17328	—	59	1	no	maximal, Sylow
223	C₂²×C₅₉	—	2	1	no	—
224	C₂²×C₅₉	—	2	1	no	—
225	C₂²×C₅₉	—	2	1	no	—
226	C₂²×C₅₉	C₂²×C₄²	1	1	yes	characteristic
227	C₂×D₅₉	—	2	1	no	—
228	C₂×D₅₉	—	2	1	no	—
229	C₂×D₅₉	—	2	1	no	—
230	C₂×D₅₉	—	2	1	no	—
231	C₂×D₅₉	—	2	1	no	—
232	C₂×D₅₉	#405	1	2	yes	—
233	C₄×C₅₉	—	2	1	no	—
234	C₄×C₅₉	—	2	1	no	—
235	C₄×C₅₉	—	2	1	no	—
236	C₄×C₅₉	C₂×#131	1	2	yes	—
237	C₄×C₅₉	C₂×#131	1	2	yes	—
238	C₄×C₅₉	C₂×#131	1	2	yes	—
239	Dic₅₉	—	2	1	no	—
240	Dic₅₉	—	2	1	no	—
241	Dic₅₉	—	2	1	no	—
242	Dic₅₉	—	2	1	no	—
243	Dic₅₉	—	2	1	no	—
244	Dic₅₉	#405	1	2	yes	—
245	#2965	—	59	1	no	—
246	C₈×#41	—	59	1	no	—
247	#2922	—	59	1	no	—
248	#1454	—	59	1	no	—
249	#1454	—	59	1	no	—
250	#1453	—	59	1	no	—
251	#1453	—	59	1	no	—
252	#1452	—	59	1	no	—
253	#1451	—	59	1	no	—
254	#1450	—	59	1	no	—
255	#1450	—	59	1	no	—
256	C₈×M₁₆	—	59	1	no	—
257	C₈×M₁₆	—	59	1	no	—
258	C₈×M₁₆	D₅₉	1	1	yes	characteristic, complemented
259	C₂×C₈²	—	59	1	no	—
260	C₂×C₅₉	—	4	1	no	—
261	C₂×C₅₉	C₂×#405	1	1	yes	characteristic
262	C₂×C₅₉	C₄×#131	1	1	yes	characteristic
263	C₂×C₅₉	C₄×#131	1	1	yes	characteristic
264	D₅₉	—	2	2	no	—
265	D₅₉	—	4	1	no	—
266	C₄×#41	—	59	1	no	—
267	#446	—	59	2	no	—
268	C₈×Q₈	—	59	2	no	—
269	#436	—	59	2	no	—
270	#435	—	59	2	no	—
271	#435	—	59	2	no	—
272	C₈×D₄	—	59	2	no	—
273	C₈×D₄	—	59	2	no	—
274	C₈×D₄	—	59	2	no	—
275	#433	—	59	2	no	—
276	#433	—	59	2	no	—
277	#431	—	59	1	no	—
278	#431	—	59	1	no	—
279	#431	—	59	1	no	—
280	#431	—	59	1	no	—
281	#431	—	59	1	no	—
282	#431	—	59	1	no	—
283	#431	—	59	1	no	—
284	#431	—	59	1	no	—
285	#431	—	59	1	no	—
286	#431	C₂×D₅₉	1	1	yes	characteristic
287	#424	—	59	2	no	—
288	#408	—	59	2	no	—
289	C₄×M₁₆	—	59	1	no	—
290	C₄×M₁₆	—	59	1	no	—
291	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
292	C₂×C₄×C₈	—	59	1	no	—
293	C₂×C₄×C₈	—	59	1	no	—
294	C₂×C₄×C₈	—	59	1	no	—
295	C₂×C₄×C₈	—	59	1	no	—
296	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
297	#322	—	59	1	no	—
298	#322	—	59	1	no	—
299	#322	—	59	1	no	—
300	#322	—	59	1	no	—
301	#322	—	59	1	no	—
302	#322	—	59	1	no	—
303	#322	—	59	1	no	—
304	#322	—	59	1	no	—
305	#322	C₂×D₅₉	1	1	yes	characteristic
306	#322	C₂×D₅₉	1	1	yes	characteristic
307	C₈²	—	59	1	no	—
308	C₈²	—	59	1	no	—
309	C₈²	—	59	1	no	—
310	C₈²	—	59	1	no	—
311	C₈²	C₂×D₅₉	1	1	yes	characteristic
312	C₈²	C₂×D₅₉	1	1	yes	characteristic
313	C₅₉	#17328	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	59	1	no	—
315	C₂×M₁₆	—	59	2	no	—
316	C₂×M₁₆	—	59	2	no	—
317	C₂×M₁₆	C₄×D₅₉	1	2	yes	—
318	C₂²×C₈	—	59	2	no	—
319	C₂²×C₈	—	59	2	no	—
320	C₂²×C₈	—	59	2	no	—
321	C₂²×C₈	—	59	2	no	—
322	C₂²×C₈	C₄×D₅₉	1	2	yes	—
323	C₄×Q₈	—	59	1	no	—
324	C₄×Q₈	—	59	1	no	—
325	C₄×D₄	—	59	1	no	—
326	C₄×D₄	—	59	1	no	—
327	C₄×D₄	—	59	1	no	—
328	C₄×D₄	—	59	1	no	—
329	C₄×D₄	—	59	1	no	—
330	C₄×D₄	—	59	1	no	—
331	#117	—	59	1	no	—
332	#117	—	59	1	no	—
333	#117	—	59	1	no	—
334	C₂×C₄²	—	59	1	no	—
335	C₂×C₄²	—	59	1	no	—
336	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
337	C₄⋊C₈	—	59	2	no	—
338	C₄⋊C₈	—	59	2	no	—
339	C₄⋊C₈	—	59	2	no	—
340	C₄⋊C₈	—	59	2	no	—
341	C₄⋊C₈	—	59	2	no	—
342	C₄⋊C₈	—	59	2	no	—
343	C₄⋊C₈	—	59	2	no	—
344	C₄⋊C₈	—	59	2	no	—
345	C₄⋊C₈	—	59	2	no	—
346	C₄⋊C₈	C₄×D₅₉	1	2	yes	—
347	C₂²⋊C₈	—	59	2	no	—
348	C₂²⋊C₈	—	59	2	no	—
349	C₂²⋊C₈	—	59	2	no	—
350	C₂²⋊C₈	—	59	2	no	—
351	C₂²⋊C₈	—	59	2	no	—
352	C₂²⋊C₈	—	59	2	no	—
353	C₂²⋊C₈	—	59	2	no	—
354	C₂²⋊C₈	—	59	2	no	—
355	C₂²⋊C₈	—	59	2	no	—
356	C₂²⋊C₈	C₄×D₅₉	1	2	yes	—
357	#97	—	59	2	no	—
358	#97	—	59	2	no	—
359	#97	C₄×D₅₉	1	2	yes	—
360	C₄×C₈	—	59	2	no	—
361	C₄×C₈	—	59	2	no	—
362	C₄×C₈	—	59	2	no	—
363	C₄×C₈	—	59	2	no	—
364	C₄×C₈	—	59	1	no	—
365	C₄×C₈	—	59	1	no	—
366	C₄×C₈	—	59	1	no	—
367	C₄×C₈	—	59	1	no	—
368	C₄×C₈	—	59	1	no	—
369	C₄×C₈	—	59	1	no	—
370	C₄×C₈	C₄×D₅₉	1	2	yes	—
371	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
372	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
374	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
375	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
376	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
377	#41	—	118	4	no	—
378	C₂×Q₈	—	59	1	no	—
379	C₂×D₄	—	59	1	no	—
380	C₂×D₄	—	59	1	no	—
381	C₂×D₄	—	59	1	no	—
382	C₂²×C₄	—	59	1	no	—
383	C₂²×C₄	—	59	1	no	—
384	C₂²×C₄	—	59	1	no	—
385	C₂²×C₄	—	59	1	no	—
386	C₂²×C₄	—	59	1	no	—
387	C₂²×C₄	—	59	1	no	—
388	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
391	M₁₆	—	2	4	no	—
392	M₁₆	—	118	4	no	—
393	M₁₆	—	118	4	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	59	2	no	—
396	C₂×C₈	—	59	2	no	—
397	C₂×C₈	—	59	2	no	—
398	C₂×C₈	—	59	2	no	—
399	C₂×C₈	—	59	2	no	—
400	C₂×C₈	—	59	2	no	—
401	C₂×C₈	—	118	4	no	—
402	C₂×C₈	—	118	4	no	—
403	C₂×C₈	—	118	4	no	—
404	C₂×C₈	—	118	4	no	—
405	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
411	C₄⋊C₄	—	59	1	no	—
412	C₄⋊C₄	—	59	1	no	—
413	C₄⋊C₄	—	59	1	no	—
414	C₄⋊C₄	—	59	1	no	—
415	C₄⋊C₄	—	59	1	no	—
416	C₄⋊C₄	—	59	1	no	—
417	C₂²⋊C₄	—	59	1	no	—
418	C₂²⋊C₄	—	59	1	no	—
419	C₂²⋊C₄	—	59	1	no	—
420	C₂²⋊C₄	—	59	1	no	—
421	C₂²⋊C₄	—	59	1	no	—
422	C₂²⋊C₄	—	59	1	no	—
423	C₄²	—	59	1	no	—
424	C₄²	—	59	1	no	—
425	C₄²	—	59	1	no	—
426	C₄²	—	59	1	no	—
427	C₄²	—	59	1	no	—
428	C₄²	—	59	1	no	—
429	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₄²	C₂³×D₅₉	1	1	yes	characteristic
433	C₂³	—	59	1	no	—
434	C₂³	—	59	1	no	—
435	C₂³	C₄²×D₅₉	1	1	yes	characteristic
436	Q₈	—	118	2	no	—
437	D₄	—	118	2	no	—
438	D₄	—	118	2	no	—
439	D₄	—	118	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	59	1	no	—
444	C₂×C₄	—	59	4	no	—
445	C₂×C₄	—	59	1	no	—
446	C₂×C₄	—	59	1	no	—
447	C₂×C₄	—	59	1	no	—
448	C₂×C₄	—	59	1	no	—
449	C₂×C₄	—	59	1	no	—
450	C₂×C₄	—	118	2	no	—
451	C₂×C₄	—	118	2	no	—
452	C₂×C₄	—	118	2	no	—
453	C₂×C₄	—	118	2	no	—
454	C₂×C₄	—	118	2	no	—
455	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
457	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	118	2	no	—
466	C₈	—	118	2	no	—
467	C₈	—	118	2	no	—
468	C₈	—	118	2	no	—
469	C₈	—	118	2	no	—
470	C₈	—	118	2	no	—
471	C₈	#14273733	1	4	yes	—
472	C₈	#14273735	1	4	yes	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	59	2	no	—
477	C₂²	—	118	1	no	—
478	C₂²	—	118	1	no	—
479	C₂²	—	118	1	no	—
480	C₂²	—	118	1	no	—
481	C₂²	—	118	1	no	—
482	C₂²	C₂×C₄²×D₅₉	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	59	2	no	—
487	C₄	—	118	1	no	—
488	C₄	—	118	1	no	—
489	C₄	—	118	1	no	—
490	C₄	—	118	1	no	—
491	C₄	—	118	1	no	—
492	C₄	#131×D₅₉	1	2	yes	—
493	C₄	C₂×#14273733	1	2	yes	—
494	C₄	C₂×#14273735	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	118	2	no	—
497	C₂	—	236	1	no	—
498	C₂	#405×D₅₉	1	1	yes	characteristic
499	C₂	C₄×#14273733	1	1	yes	characteristic
500	C₂	C₄×#14273735	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₅₉
commutator, socle	C₂²×C₅₉	C₂²×C₄²
Frattini	C₄²	C₂³×D₅₉
Fitting	C₈×M₁₆×C₅₉	C₂
prime radical	C₂×#11745685	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₈×M₁₆	D₅₉
hypocenter	C₅₉	#17328
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #21422397	C₂	semidirect
5. #21422396	C₂	semidirect
6. #21422394	C₂	semidirect
7. #21422393	C₂	semidirect
8. #21422387	C₂	semidirect
9. #21422382	C₂	semidirect
10. #21422379	C₂	semidirect
11. #21422378	C₂	semidirect
12. C₈×#11745659	C₂	semidirect
13. C₈×#11745659	C₂	semidirect
14. C₈²×D₅₉	C₂	semidirect
15. C₈×M₁₆×C₅₉	C₂	semidirect
258. C₈×M₁₆	D₅₉	semidirect
313. C₅₉	#17328	semidirect

Maximal subgroups

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

subgroup	index
#21433058	2
C₈×#11745685	2
#21432735	2
#21422397	2
#21422396	2
#21422394	2
#21422393	2
#21422387	2
#21422382	2
#21422379	2
#21422378	2
C₈×#11745659	2
C₈²×D₅₉	2
C₈×M₁₆×C₅₉	2
#17328	59