Subgroups — #28559883

Order 15104.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434180	C₂	1	1	yes	maximal, characteristic
2	#21433259	C₂	1	1	yes	maximal, characteristic
3	#21433184	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422991	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422985	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422971	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422964	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422955	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11745671	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422878	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422555	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422381	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837939	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
18	#16837731	C₄	1	1	yes	characteristic
19	#16837717	C₄	1	1	yes	characteristic
20	#16837708	C₄	1	1	yes	characteristic
21	#16837707	C₄	1	1	yes	characteristic
22	#16837627	C₄	1	1	yes	characteristic
23	#16837626	C₄	1	1	yes	characteristic
24	#16837556	C₄	1	1	yes	characteristic
25	#16837542	C₄	1	1	yes	characteristic
26	#16837532	—	2	1	no	—
27	#16837532	C₂²	1	1	yes	characteristic
28	#16837529	—	2	1	no	—
29	#16837529	C₂²	1	1	yes	characteristic
30	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
31	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₄×#11745672	C₂²	1	1	yes	characteristic
33	C₄×#11745660	C₂²	1	1	yes	characteristic
34	C₄×#11745671	C₂²	1	1	yes	characteristic
35	#16837479	C₂²	1	1	yes	characteristic
36	#16837475	—	2	1	no	—
37	C₈×D₂₃₆	C₂²	1	1	yes	characteristic
38	#16837467	—	2	1	no	—
39	#16837464	—	2	1	no	—
40	#16837458	—	2	1	no	—
41	#16837458	C₂²	1	1	yes	characteristic
42	#16837453	—	2	1	no	—
43	#16837453	C₂²	1	1	yes	characteristic
44	#16837453	C₂²	1	1	yes	characteristic
45	#16837427	—	2	1	no	—
46	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837155	C₂²	1	1	yes	characteristic
49	#16837154	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837134	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
54	#16837132	C₂²	1	1	yes	characteristic
55	#16837131	C₂²	1	1	yes	characteristic
56	#16837129	C₂²	1	1	yes	characteristic
57	#16837123	C₂²	1	1	yes	characteristic
58	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₅₉×#446	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#334	C₂²	1	1	yes	characteristic
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₅₉×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745659	—	2	1	no	—
72	C₂×C₈×D₅₉	—	2	1	no	—
73	C₂×C₈×D₅₉	—	2	1	no	—
74	C₂×C₈×D₅₉	—	2	1	no	—
75	#14273722	—	2	1	no	—
76	#14273718	C₂×C₄	1	1	yes	characteristic
77	#14273716	C₂×C₄	1	1	yes	characteristic
78	#14273712	—	2	1	no	—
79	#14273703	C₂×C₄	1	1	yes	characteristic
80	#14273702	C₂×C₄	1	1	yes	characteristic
81	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₁₈	—	2	1	no	—
83	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
84	#14273692	—	2	1	no	—
85	#14273692	C₂×C₄	1	1	yes	characteristic
86	C₄×D₂₃₆	—	2	1	no	—
87	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
88	#14273684	—	2	1	no	—
89	C₄⋊C₄×D₅₉	—	2	1	no	—
90	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₅₉	—	2	1	no	—
92	C₄²×D₅₉	C₂³	1	1	yes	characteristic
93	#14273660	C₂×C₄	1	1	yes	characteristic
94	#14273659	C₂×C₄	1	1	yes	characteristic
95	#14273658	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
97	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
98	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	C₂³	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	C₂×C₄	1	1	yes	characteristic
104	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
106	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273651	C₂×C₄	1	1	yes	characteristic
109	#14273651	C₂×C₄	1	1	yes	characteristic
110	#14273650	C₂×C₄	1	1	yes	characteristic
111	#14273649	C₂×C₄	1	1	yes	characteristic
112	#14273647	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₅₉)⋊C₈	—	2	1	no	—
114	(C₂×D₅₉)⋊C₈	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
118	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
119	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
120	#14273637	—	2	1	no	—
121	#14273637	—	2	1	no	—
122	#14273637	—	2	1	no	—
123	C₄×C₅₉⋊C₈	—	2	1	no	—
124	C₄×C₅₉⋊C₈	—	2	1	no	—
125	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
126	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
127	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
128	C₈×Dic₅₉	—	2	1	no	—
129	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	—	2	1	no	—
134	C₄⋊C₈×C₅₉	—	2	1	no	—
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₅₉	—	2	1	no	—
140	C₄×C₈×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	Q₈×D₅₉	—	2	2	no	—
147	Q₈×D₅₉	—	4	1	no	—
148	C₂×D₂₃₆	—	2	1	no	—
149	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₅₉	—	2	1	no	—
151	C₂×C₄×D₅₉	—	2	1	no	—
152	C₂×C₄×D₅₉	—	2	1	no	—
153	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
156	C₂×Dic₁₁₈	—	2	1	no	—
157	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
158	Q₁₆×C₅₉	—	2	2	no	—
159	C₂×C₈×C₅₉	—	2	1	no	—
160	C₂×C₈×C₅₉	—	2	1	no	—
161	C₂×C₈×C₅₉	—	2	1	no	—
162	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	1	no	—
168	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
173	#11745672	—	4	1	no	—
174	#11745671	—	2	2	no	—
175	(C₂×D₅₉)⋊C₄	—	2	1	no	—
176	(C₂×D₅₉)⋊C₄	—	2	1	no	—
177	(C₂×D₅₉)⋊C₄	—	2	1	no	—
178	(C₂×D₅₉)⋊C₄	—	2	1	no	—
179	(C₂×D₅₉)⋊C₄	—	2	1	no	—
180	C₄⋊Dic₅₉	—	2	1	no	—
181	C₄⋊Dic₅₉	—	2	1	no	—
182	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
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	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₅₉	#41	1	1	yes	characteristic
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
202	#11745660	—	4	1	no	—
203	#11745659	—	8	1	no	—
204	C₈×D₅₉	—	2	4	no	—
205	C₈×D₅₉	—	8	1	no	—
206	C₈×D₅₉	—	8	1	no	—
207	C₂²×D₅₉	—	2	1	no	—
208	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₅₉	—	2	1	no	—
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	2	1	no	—
212	Q₈×C₅₉	#131	1	2	yes	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₅₉	—	2	1	no	—
221	C₂×Dic₅₉	—	2	1	no	—
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
224	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
226	D₂₃₆	—	2	1	no	—
227	D₂₃₆	—	2	1	no	—
228	D₂₃₆	—	4	2	no	—
229	C₄×D₅₉	—	2	2	no	—
230	C₄×D₅₉	—	2	1	no	—
231	C₄×D₅₉	—	2	1	no	—
232	C₄×D₅₉	—	2	1	no	—
233	C₄×D₅₉	—	2	1	no	—
234	C₄×D₅₉	—	4	2	no	—
235	C₄×D₅₉	—	4	2	no	—
236	C₄×D₅₉	—	4	1	no	—
237	C₄×D₅₉	—	4	1	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	—	2	1	no	—
240	Dic₁₁₈	—	4	2	no	—
241	C₈×C₅₉	—	2	2	no	—
242	C₈×C₅₉	—	2	1	no	—
243	C₈×C₅₉	—	2	1	no	—
244	C₈×C₅₉	—	2	1	no	—
245	C₈×C₅₉	—	2	1	no	—
246	C₈×C₅₉	—	4	1	no	—
247	C₈×C₅₉	—	4	1	no	—
248	C₅₉⋊C₈	—	2	2	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	2	1	no	—
251	C₅₉⋊C₈	—	2	1	no	—
252	C₅₉⋊C₈	—	2	1	no	—
253	C₅₉⋊C₈	—	4	1	no	—
254	C₅₉⋊C₈	—	4	1	no	—
255	#18017	—	59	1	no	maximal, Sylow
256	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₅₉	—	2	1	no	—
258	C₂×D₅₉	—	2	1	no	—
259	C₂×D₅₉	—	4	1	no	—
260	C₂×D₅₉	—	4	1	no	—
261	C₂×D₅₉	—	4	1	no	—
262	C₂×D₅₉	#443	1	2	yes	—
263	C₄×C₅₉	—	2	2	no	—
264	C₄×C₅₉	—	2	1	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	—	4	1	no	—
267	C₄×C₅₉	—	4	1	no	—
268	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
269	C₄×C₅₉	#568	1	1	yes	characteristic
270	C₄×C₅₉	#577	1	1	yes	characteristic
271	C₄×C₅₉	#578	1	1	yes	characteristic
272	Dic₅₉	—	2	1	no	—
273	Dic₅₉	—	2	1	no	—
274	Dic₅₉	—	2	1	no	—
275	Dic₅₉	—	4	1	no	—
276	Dic₅₉	—	4	1	no	—
277	Dic₅₉	—	4	1	no	—
278	#3108	—	59	1	no	—
279	#2994	—	59	1	no	—
280	#2984	—	59	1	no	—
281	#1591	—	59	1	no	—
282	#1590	—	59	1	no	—
283	#1588	—	59	1	no	—
284	#1587	—	59	1	no	—
285	#1587	D₅₉	1	1	yes	characteristic, complemented
286	#1585	—	59	1	no	—
287	C₈×Q₁₆	—	59	1	no	—
288	C₈×SD₁₆	—	59	1	no	—
289	#1573	—	59	1	no	—
290	#1494	—	59	1	no	—
291	C₂×Q₈⋊C₈	—	59	1	no	—
292	#1450	—	59	1	no	—
293	C₂×C₅₉	#2933	1	1	yes	characteristic
294	C₂×C₅₉	#2947	1	1	yes	characteristic
295	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
296	D₅₉	—	2	2	no	—
297	D₅₉	—	8	1	no	—
298	#529	—	59	1	no	—
299	C₂×C₄×Q₈	—	59	1	no	—
300	#483	—	59	1	no	—
301	#480	—	59	1	no	—
302	#479	—	59	1	no	—
303	#479	—	59	1	no	—
304	#464	—	59	1	no	—
305	#464	—	59	1	no	—
306	#451	—	59	1	no	—
307	#448	—	59	1	no	—
308	#446	—	59	1	no	—
309	#446	—	59	1	no	—
310	#446	—	118	1	no	—
311	#446	—	118	1	no	—
312	#446	C₂×D₅₉	1	1	yes	characteristic
313	C₈×Q₈	—	59	1	no	—
314	C₈×Q₈	—	59	1	no	—
315	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
316	C₄×Q₁₆	—	59	1	no	—
317	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
318	C₄×SD₁₆	—	59	1	no	—
319	C₄×SD₁₆	—	59	1	no	—
320	#436	—	59	1	no	—
321	#435	—	118	1	no	—
322	C₈×D₄	—	59	1	no	—
323	C₈×D₄	—	118	1	no	—
324	#433	—	118	1	no	—
325	#432	—	59	1	no	—
326	#432	—	118	1	no	—
327	#431	—	59	1	no	—
328	#431	—	59	1	no	—
329	#431	—	118	1	no	—
330	#424	—	118	1	no	—
331	C₂×C₄⋊C₈	—	59	1	no	—
332	C₂×C₄×C₈	—	59	1	no	—
333	#335	—	59	1	no	—
334	#335	—	59	1	no	—
335	#334	—	59	1	no	—
336	#334	C₂×D₅₉	1	1	yes	characteristic
337	Q₈⋊C₈	—	59	1	no	—
338	Q₈⋊C₈	—	59	1	no	—
339	Q₈⋊C₈	—	59	1	no	—
340	Q₈⋊C₈	—	59	1	no	—
341	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
343	D₄⋊C₈	—	59	1	no	—
344	D₄⋊C₈	—	59	1	no	—
345	#322	—	59	1	no	—
346	#322	C₂×D₅₉	1	1	yes	characteristic
347	C₈²	—	59	1	no	—
348	C₈²	—	59	1	no	—
349	C₅₉	#18017	1	1	yes	characteristic, complemented, Sylow
350	C₂²×Q₈	—	59	1	no	—
351	C₂×Q₁₆	—	59	1	no	—
352	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
353	C₂×SD₁₆	—	59	1	no	—
354	C₂×SD₁₆	—	59	1	no	—
355	C₂×M₁₆	—	118	1	no	—
356	C₂²×C₈	—	118	1	no	—
357	C₂²×C₈	—	118	1	no	—
358	C₂²×C₈	—	118	1	no	—
359	#126	—	118	1	no	—
360	#125	—	59	1	no	—
361	#124	—	59	1	no	—
362	#123	—	118	1	no	—
363	C₂²⋊Q₈	—	59	1	no	—
364	#121	—	59	1	no	—
365	C₄×Q₈	—	59	1	no	—
366	C₄×Q₈	—	59	1	no	—
367	C₄×Q₈	—	59	1	no	—
368	C₄×Q₈	—	118	1	no	—
369	C₄×Q₈	—	118	1	no	—
370	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
371	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
372	C₄×D₄	—	59	1	no	—
373	C₄×D₄	—	118	1	no	—
374	#117	—	118	1	no	—
375	C₂×C₄⋊C₄	—	59	1	no	—
376	C₂×C₄⋊C₄	—	118	1	no	—
377	C₂×C₄²	—	59	1	no	—
378	C₂×C₄²	—	118	1	no	—
379	#107	—	59	1	no	—
380	#107	C₄×D₅₉	1	1	yes	characteristic
381	#106	—	59	1	no	—
382	#106	—	59	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	59	1	no	—
386	C₄⋊C₈	—	59	1	no	—
387	C₄⋊C₈	—	59	1	no	—
388	C₄⋊C₈	—	59	1	no	—
389	C₄⋊C₈	—	59	1	no	—
390	C₄⋊C₈	—	59	1	no	—
391	C₄⋊C₈	—	118	1	no	—
392	C₄⋊C₈	—	118	1	no	—
393	C₄⋊C₈	—	118	1	no	—
394	C₄⋊C₈	—	118	1	no	—
395	C₄⋊C₈	—	118	1	no	—
396	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
398	#103	—	59	1	no	—
399	#103	—	59	1	no	—
400	#103	—	59	1	no	—
401	#103	—	59	1	no	—
402	#103	C₄×D₅₉	1	1	yes	characteristic
403	#103	C₄×D₅₉	1	1	yes	characteristic
404	#102	—	59	1	no	—
405	#102	—	59	1	no	—
406	C₂²⋊C₈	—	59	1	no	—
407	C₂²⋊C₈	—	59	1	no	—
408	C₂²⋊C₈	—	59	1	no	—
409	C₂²⋊C₈	—	59	1	no	—
410	C₂²⋊C₈	—	118	1	no	—
411	C₂²⋊C₈	—	118	1	no	—
412	C₂²⋊C₈	—	118	1	no	—
413	#97	—	2	1	no	—
414	#97	—	118	1	no	—
415	#97	—	118	1	no	—
416	#97	—	118	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	59	1	no	—
419	C₄×C₈	—	59	1	no	—
420	C₄×C₈	—	59	1	no	—
421	C₄×C₈	—	118	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	—	118	1	no	—
424	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
427	C₂×Q₈	—	59	1	no	—
428	C₂×Q₈	—	118	1	no	—
429	C₂×Q₈	—	118	2	no	—
430	C₂×Q₈	—	236	1	no	—
431	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
433	C₂×D₄	—	59	1	no	—
434	C₂×D₄	—	118	1	no	—
435	C₂²×C₄	—	59	1	no	—
436	C₂²×C₄	—	59	1	no	—
437	C₂²×C₄	—	59	1	no	—
438	C₂²×C₄	—	118	1	no	—
439	C₂²×C₄	—	118	1	no	—
440	C₂²×C₄	—	118	1	no	—
441	Q₁₆	—	2	2	no	—
442	Q₁₆	—	236	1	no	—
443	SD₁₆	—	118	2	no	—
444	SD₁₆	—	236	1	no	—
445	M₁₆	—	472	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	59	1	no	—
450	C₂×C₈	—	59	1	no	—
451	C₂×C₈	—	59	1	no	—
452	C₂×C₈	—	59	1	no	—
453	C₂×C₈	—	118	4	no	—
454	C₂×C₈	—	118	1	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	—	472	1	no	—
458	C₂×C₈	—	472	1	no	—
459	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
461	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
462	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	59	1	no	—
466	C₄⋊C₄	—	59	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	C₄⋊C₄	—	118	1	no	—
473	C₄⋊C₄	—	118	1	no	—
474	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
476	C₂²⋊C₄	—	118	1	no	—
477	C₂²⋊C₄	—	118	1	no	—
478	C₂²⋊C₄	—	118	1	no	—
479	C₂²⋊C₄	—	118	1	no	—
480	C₂²⋊C₄	—	118	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	59	1	no	—
484	C₄²	—	59	1	no	—
485	C₄²	—	59	1	no	—
486	C₄²	—	118	1	no	—
487	C₄²	—	118	1	no	—
488	C₄²	—	118	1	no	—
489	C₄²	C₂³×D₅₉	1	1	yes	characteristic
490	C₂³	—	59	1	no	—
491	C₂³	—	118	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	118	1	no	—
496	Q₈	—	118	1	no	—
497	Q₈	—	236	2	no	—
498	Q₈	#14273735	1	2	yes	—
499	D₄	—	118	1	no	—
500	D₄	—	118	1	no	—
501	D₄	—	236	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	59	1	no	—
507	C₂×C₄	—	59	1	no	—
508	C₂×C₄	—	59	1	no	—
509	C₂×C₄	—	118	2	no	—
510	C₂×C₄	—	118	1	no	—
511	C₂×C₄	—	118	1	no	—
512	C₂×C₄	—	118	1	no	—
513	C₂×C₄	—	118	1	no	—
514	C₂×C₄	—	118	1	no	—
515	C₂×C₄	—	118	1	no	—
516	C₂×C₄	—	118	1	no	—
517	C₂×C₄	—	236	2	no	—
518	C₂×C₄	—	236	2	no	—
519	C₂×C₄	—	236	1	no	—
520	C₂×C₄	—	236	1	no	—
521	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
522	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
523	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	118	2	no	—
532	C₈	—	118	1	no	—
533	C₈	—	118	1	no	—
534	C₈	—	118	1	no	—
535	C₈	—	118	1	no	—
536	C₈	—	236	1	no	—
537	C₈	—	236	1	no	—
538	C₂²	—	59	2	no	—
539	C₂²	—	118	1	no	—
540	C₂²	—	118	1	no	—
541	C₂²	—	236	1	no	—
542	C₂²	—	236	1	no	—
543	C₂²	—	236	1	no	—
544	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
545	C₄	—	2	1	no	—
546	C₄	—	2	2	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	118	1	no	—
551	C₄	—	118	1	no	—
552	C₄	—	118	1	no	—
553	C₄	—	236	1	no	—
554	C₄	—	236	1	no	—
555	C₄	—	236	1	no	—
556	C₄	C₂×#14273735	1	1	yes	characteristic
557	C₄	#16838167	1	1	yes	characteristic
558	C₄	#16838211	1	1	yes	characteristic
559	C₄	#16838218	1	1	yes	characteristic
560	C₂	—	118	2	no	—
561	C₂	—	472	1	no	—
562	C₂	#21432822	1	1	yes	characteristic
563	C₂	#21432938	1	1	yes	characteristic
564	C₂	#443×D₅₉	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×#1587	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#14273702	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1587	D₅₉
hypocenter	C₅₉	#18017
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1587

Complements

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

N	H ≅ G/N	type
3. #21433184	C₂	semidirect
4. #21422991	C₂	semidirect
5. #21422985	C₂	semidirect
6. #21422971	C₂	semidirect
7. #21422964	C₂	semidirect
8. #21422955	C₂	semidirect
9. Q₁₆×C₅₉⋊C₈	C₂	semidirect
10. C₈×#11745671	C₂	semidirect
11. #21422878	C₂	semidirect
13. Q₈⋊C₈×D₅₉	C₂	semidirect
14. #21422381	C₂	semidirect
15. C₅₉×#1587	C₂	semidirect
285. #1587	D₅₉	semidirect
349. C₅₉	#18017	semidirect

Maximal subgroups

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

subgroup	index
#21434180	2
#21433259	2
#21433184	2
#21422991	2
#21422985	2
#21422971	2
#21422964	2
#21422955	2
Q₁₆×C₅₉⋊C₈	2
C₈×#11745671	2
#21422878	2
#21422555	2
Q₈⋊C₈×D₅₉	2
#21422381	2
C₅₉×#1587	2
#18017	59