Subgroups — #28558673

Order 15104.

632 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434174	C₂	1	1	yes	maximal, characteristic
2	#21433074	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422972	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422969	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422967	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422902	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422900	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422899	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422880	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422541	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422506	C₂	1	1	yes	maximal, characteristic
14	#21422375	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1588	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837934	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
18	#16837734	C₄	1	1	yes	characteristic
19	#16837714	C₄	1	1	yes	characteristic
20	#16837712	C₄	1	1	yes	characteristic
21	#16837711	C₄	1	1	yes	characteristic
22	#16837623	C₄	1	1	yes	characteristic
23	#16837622	C₄	1	1	yes	characteristic
24	#16837559	C₄	1	1	yes	characteristic
25	#16837539	C₄	1	1	yes	characteristic
26	#16837532	C₂²	1	1	yes	characteristic
27	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₁₈	—	2	1	no	—
29	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
30	#16837526	—	2	1	no	—
31	#16837526	C₂²	1	1	yes	characteristic
32	#16837526	C₂²	1	1	yes	characteristic
33	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
34	C₄×#11745672	C₂²	1	1	yes	characteristic
35	C₄×#11745670	C₂²	1	1	yes	characteristic
36	#16837471	—	2	1	no	—
37	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
38	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
39	#16837460	—	2	1	no	—
40	#16837458	C₂²	1	1	yes	characteristic
41	#16837453	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×D₅₉	—	2	1	no	—
43	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
44	#16837360	—	2	1	no	—
45	C₄×#11745659	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅₉	—	2	1	no	—
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837154	C₂²	1	1	yes	characteristic
49	#16837153	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837134	C₂²	1	1	yes	characteristic
52	#16837134	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
54	#16837132	C₂²	1	1	yes	characteristic
55	#16837132	C₂²	1	1	yes	characteristic
56	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic
58	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
62	C₅₉×#436	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₉×D₄⋊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×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745659	—	2	1	no	—
72	C₂²×C₅₉⋊C₈	—	2	1	no	—
73	C₂×C₈×D₅₉	—	2	1	no	—
74	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
75	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
76	#14273720	—	2	1	no	—
77	#14273718	C₂×C₄	1	1	yes	characteristic
78	#14273714	C₂×C₄	1	1	yes	characteristic
79	#14273709	—	2	1	no	—
80	#14273707	C₂×C₄	1	1	yes	characteristic
81	#14273698	C₂×C₄	1	1	yes	characteristic
82	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₁₁₈	—	2	1	no	—
84	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
86	#14273692	—	2	1	no	—
87	#14273692	C₂×C₄	1	1	yes	characteristic
88	C₄×C₂²⋊D₅₉	—	2	1	no	—
89	#14273686	—	2	1	no	—
90	C₄⋊C₄×D₅₉	—	2	1	no	—
91	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
92	C₄²×D₅₉	—	2	1	no	—
93	C₄²×D₅₉	C₂³	1	1	yes	characteristic
94	#14273661	C₂×C₄	1	1	yes	characteristic
95	#14273660	C₂×C₄	1	1	yes	characteristic
96	#14273658	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
106	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273651	C₂×C₄	1	1	yes	characteristic
110	#14273650	C₂×C₄	1	1	yes	characteristic
111	#14273650	C₂×C₄	1	1	yes	characteristic
112	#14273648	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
114	(C₂×D₅₉)⋊C₈	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	#14273637	—	2	1	no	—
118	#14273637	—	2	1	no	—
119	#14273637	—	2	1	no	—
120	C₄×C₅₉⋊C₈	—	2	1	no	—
121	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₅₉	—	2	1	no	—
125	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	D₄	1	1	yes	characteristic
128	C₈×Dic₅₉	D₄	1	1	yes	characteristic
129	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₂×M₁₆×C₅₉	—	2	1	no	—
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
133	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
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	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×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×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	—	2	1	no	—
147	C₂×C₂²⋊D₅₉	—	2	1	no	—
148	Q₈×D₅₉	—	2	2	no	—
149	Q₈×D₅₉	—	2	2	no	—
150	C₂×C₄×D₅₉	—	2	1	no	—
151	C₂×C₄×D₅₉	—	2	1	no	—
152	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
155	C₂×Dic₁₁₈	—	2	1	no	—
156	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
158	SD₁₆×C₅₉	—	2	2	no	—
159	M₁₆×C₅₉	—	4	2	no	—
160	C₂×C₈×C₅₉	—	2	1	no	—
161	C₂×C₈×C₅₉	—	2	1	no	—
162	C₂×C₈×C₅₉	—	2	1	no	—
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₅₉	—	2	1	no	—
171	C₄²×C₅₉	—	2	1	no	—
172	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₂²⋊Dic₅₉	—	2	1	no	—
174	C₂²⋊Dic₅₉	—	2	1	no	—
175	C₂²⋊Dic₅₉	—	2	1	no	—
176	#11745672	—	2	2	no	—
177	#11745670	—	2	2	no	—
178	(C₂×D₅₉)⋊C₄	—	2	1	no	—
179	C₄⋊Dic₅₉	—	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	—	2	1	no	—
193	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₅₉	#41	1	1	yes	characteristic
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	4	2	no	—
200	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
204	Dic₂₃₆	—	2	2	no	—
205	#11745659	—	2	4	no	—
206	C₈×D₅₉	—	2	2	no	—
207	C₈×D₅₉	—	4	1	no	—
208	C₈×D₅₉	—	4	2	no	—
209	C₂³×C₅₉	—	2	1	no	—
210	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
211	Q₈×C₅₉	—	2	1	no	—
212	Q₈×C₅₉	#131	1	2	yes	—
213	D₄×C₅₉	—	2	1	no	—
214	D₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	—	2	1	no	—
218	C₂×C₄×C₅₉	—	4	1	no	—
219	C₂×C₄×C₅₉	—	4	1	no	—
220	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
223	C₂²⋊D₅₉	—	4	2	no	—
224	C₂×Dic₅₉	—	2	1	no	—
225	C₂×Dic₅₉	—	2	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	C₂×Dic₅₉	—	2	1	no	—
228	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
229	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
231	C₄×D₅₉	—	2	4	no	—
232	C₄×D₅₉	—	2	2	no	—
233	C₄×D₅₉	—	2	1	no	—
234	C₄×D₅₉	—	2	1	no	—
235	C₄×D₅₉	—	2	1	no	—
236	C₄×D₅₉	—	2	1	no	—
237	C₄×D₅₉	—	4	2	no	—
238	Dic₁₁₈	—	2	4	no	—
239	Dic₁₁₈	—	2	1	no	—
240	Dic₁₁₈	—	2	1	no	—
241	Dic₁₁₈	—	2	1	no	—
242	Dic₁₁₈	#131	1	2	yes	—
243	C₈×C₅₉	—	2	2	no	—
244	C₈×C₅₉	—	2	1	no	—
245	C₈×C₅₉	—	2	1	no	—
246	C₈×C₅₉	—	2	1	no	—
247	C₈×C₅₉	—	2	1	no	—
248	C₈×C₅₉	—	4	1	no	—
249	C₈×C₅₉	—	4	1	no	—
250	C₅₉⋊C₈	—	2	2	no	—
251	C₅₉⋊C₈	—	2	1	no	—
252	C₅₉⋊C₈	—	2	1	no	—
253	C₅₉⋊C₈	—	2	1	no	—
254	C₅₉⋊C₈	—	4	1	no	—
255	C₅₉⋊C₈	—	4	1	no	—
256	C₅₉⋊C₈	#137	1	2	yes	—
257	#17911	—	59	1	no	maximal, Sylow
258	C₂²×C₅₉	—	4	1	no	—
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂×D₅₉	—	2	1	no	—
263	C₂×D₅₉	—	2	1	no	—
264	C₂×D₅₉	#443	1	2	yes	—
265	C₄×C₅₉	—	2	2	no	—
266	C₄×C₅₉	—	2	1	no	—
267	C₄×C₅₉	—	4	1	no	—
268	C₄×C₅₉	—	4	1	no	—
269	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
270	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
271	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
272	C₄×C₅₉	#575	1	1	yes	characteristic
273	Dic₅₉	—	2	1	no	—
274	Dic₅₉	—	2	2	no	—
275	Dic₅₉	—	2	1	no	—
276	Dic₅₉	—	2	1	no	—
277	Dic₅₉	—	4	1	no	—
278	Dic₅₉	—	4	1	no	—
279	Dic₅₉	—	4	1	no	—
280	#3108	—	59	1	no	—
281	#2966	—	59	1	no	—
282	C₂×C₈×Q₈	—	59	1	no	—
283	#1588	—	59	1	no	—
284	#1588	D₅₉	1	1	yes	characteristic, complemented
285	#1587	—	59	1	no	—
286	#1587	—	59	1	no	—
287	C₈×Q₁₆	—	59	1	no	—
288	C₈×Q₁₆	—	59	1	no	—
289	C₈×SD₁₆	—	59	1	no	—
290	C₈×SD₁₆	—	59	1	no	—
291	#1573	—	59	1	no	—
292	#1491	—	59	1	no	—
293	#1483	—	59	1	no	—
294	C₈×M₁₆	—	59	1	no	—
295	C₂×C₅₉	—	8	1	no	—
296	C₂×C₅₉	#2929	1	1	yes	characteristic
297	C₂×C₅₉	C₄×#137	1	1	yes	characteristic
298	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
299	D₅₉	—	2	2	no	—
300	#529	—	59	1	no	—
301	C₂×C₄×Q₈	—	59	1	no	—
302	#483	—	59	1	no	—
303	#480	—	59	1	no	—
304	#479	—	59	1	no	—
305	#479	—	59	1	no	—
306	#464	—	59	1	no	—
307	#464	—	59	1	no	—
308	#451	—	59	1	no	—
309	#448	—	59	1	no	—
310	#446	—	59	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	59	1	no	—
313	C₈×Q₈	—	59	1	no	—
314	C₈×Q₈	—	59	1	no	—
315	C₈×Q₈	—	118	1	no	—
316	C₈×Q₈	—	118	1	no	—
317	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
318	C₄×Q₁₆	—	59	1	no	—
319	C₄×Q₁₆	—	59	1	no	—
320	C₄×SD₁₆	—	59	1	no	—
321	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
322	#436	C₂×D₅₉	1	1	yes	characteristic
323	#435	—	118	1	no	—
324	C₈×D₄	—	59	1	no	—
325	C₈×D₄	—	118	1	no	—
326	#433	—	118	1	no	—
327	#432	—	59	1	no	—
328	#431	—	59	1	no	—
329	C₂×C₄⋊C₈	—	59	1	no	—
330	C₂×C₄⋊C₈	—	118	1	no	—
331	#405	—	118	1	no	—
332	C₄×M₁₆	—	59	1	no	—
333	C₂×C₄×C₈	—	59	1	no	—
334	C₂×C₄×C₈	—	118	1	no	—
335	#335	—	59	1	no	—
336	#335	C₂×D₅₉	1	1	yes	characteristic
337	#334	—	59	1	no	—
338	#334	—	59	1	no	—
339	Q₈⋊C₈	—	59	1	no	—
340	Q₈⋊C₈	—	59	1	no	—
341	Q₈⋊C₈	—	59	1	no	—
342	Q₈⋊C₈	—	59	1	no	—
343	Q₈⋊C₈	—	59	1	no	—
344	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
345	D₄⋊C₈	—	59	1	no	—
346	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
347	#322	—	59	1	no	—
348	#322	C₂×D₅₉	1	1	yes	characteristic
349	C₈²	—	59	1	no	—
350	C₈²	—	59	1	no	—
351	C₅₉	#17911	1	1	yes	characteristic, complemented, Sylow
352	C₂²×Q₈	—	59	1	no	—
353	C₂×Q₁₆	—	59	1	no	—
354	C₂×Q₁₆	—	59	1	no	—
355	C₂×SD₁₆	—	59	1	no	—
356	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	118	1	no	—
359	C₂²×C₈	—	59	1	no	—
360	C₂²×C₈	—	59	1	no	—
361	C₂²×C₈	—	118	1	no	—
362	C₂²×C₈	—	118	1	no	—
363	#126	—	118	1	no	—
364	#125	—	59	1	no	—
365	#124	—	59	1	no	—
366	#123	—	118	1	no	—
367	C₂²⋊Q₈	—	59	1	no	—
368	#121	—	59	1	no	—
369	C₄×Q₈	—	59	1	no	—
370	C₄×Q₈	—	59	1	no	—
371	C₄×Q₈	—	59	1	no	—
372	C₄×Q₈	—	59	1	no	—
373	C₄×Q₈	—	118	1	no	—
374	C₄×Q₈	—	118	1	no	—
375	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
376	C₄×D₄	—	118	1	no	—
377	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
378	#117	—	118	1	no	—
379	C₂×C₄⋊C₄	—	59	1	no	—
380	C₂×C₄⋊C₄	—	118	1	no	—
381	C₂×C₄²	—	59	1	no	—
382	C₂×C₄²	—	118	1	no	—
383	#107	—	59	1	no	—
384	#107	—	59	1	no	—
385	#106	—	59	1	no	—
386	#106	C₄×D₅₉	1	1	yes	characteristic
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	59	1	no	—
389	C₄⋊C₈	—	59	1	no	—
390	C₄⋊C₈	—	59	1	no	—
391	C₄⋊C₈	—	59	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	—	118	1	no	—
397	C₄⋊C₈	—	118	1	no	—
398	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
400	#103	—	59	1	no	—
401	#103	—	59	1	no	—
402	#103	—	59	1	no	—
403	#103	—	59	1	no	—
404	#103	—	59	1	no	—
405	#103	C₄×D₅₉	1	1	yes	characteristic
406	#102	—	59	1	no	—
407	#102	C₄×D₅₉	1	1	yes	characteristic
408	C₂²⋊C₈	—	2	1	no	—
409	C₂²⋊C₈	—	59	1	no	—
410	C₂²⋊C₈	—	59	1	no	—
411	C₂²⋊C₈	—	118	1	no	—
412	C₂²⋊C₈	—	118	1	no	—
413	#97	—	118	1	no	—
414	#97	—	118	1	no	—
415	#97	—	118	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	59	1	no	—
418	C₄×C₈	—	59	1	no	—
419	C₄×C₈	—	59	1	no	—
420	C₄×C₈	—	59	1	no	—
421	C₄×C₈	—	59	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	—	118	1	no	—
424	C₄×C₈	—	118	1	no	—
425	C₄×C₈	—	118	1	no	—
426	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
429	C₂×Q₈	—	59	1	no	—
430	C₂×Q₈	—	59	1	no	—
431	C₂×Q₈	—	118	1	no	—
432	C₂×Q₈	—	118	2	no	—
433	C₂×Q₈	—	118	2	no	—
434	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
435	C₂×D₄	—	118	1	no	—
436	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	59	1	no	—
439	C₂²×C₄	—	59	1	no	—
440	C₂²×C₄	—	59	1	no	—
441	C₂²×C₄	—	118	1	no	—
442	C₂²×C₄	—	118	1	no	—
443	Q₁₆	—	118	2	no	—
444	Q₁₆	—	118	2	no	—
445	SD₁₆	—	2	2	no	—
446	SD₁₆	—	118	2	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	—	118	4	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	59	1	no	—
453	C₂×C₈	—	59	1	no	—
454	C₂×C₈	—	59	1	no	—
455	C₂×C₈	—	59	1	no	—
456	C₂×C₈	—	118	2	no	—
457	C₂×C₈	—	118	1	no	—
458	C₂×C₈	—	118	1	no	—
459	C₂×C₈	—	118	1	no	—
460	C₂×C₈	—	236	1	no	—
461	C₂×C₈	—	236	2	no	—
462	C₂×C₈	—	236	2	no	—
463	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
465	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
466	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	59	1	no	—
469	C₄⋊C₄	—	59	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	—	118	1	no	—
475	C₄⋊C₄	—	118	1	no	—
476	C₄⋊C₄	—	118	1	no	—
477	C₄⋊C₄	—	118	1	no	—
478	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	118	1	no	—
482	C₂²⋊C₄	—	118	1	no	—
483	C₂²⋊C₄	—	118	1	no	—
484	C₂²⋊C₄	—	118	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	59	1	no	—
487	C₄²	—	59	1	no	—
488	C₄²	—	59	1	no	—
489	C₄²	—	118	1	no	—
490	C₄²	—	118	1	no	—
491	C₄²	—	118	1	no	—
492	C₄²	—	118	1	no	—
493	C₄²	C₂³×D₅₉	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	59	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	59	2	no	—
498	Q₈	—	118	4	no	—
499	Q₈	—	118	1	no	—
500	Q₈	—	118	1	no	—
501	Q₈	—	118	1	no	—
502	Q₈	#14273735	1	2	yes	—
503	D₄	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	236	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	59	1	no	—
512	C₂×C₄	—	59	1	no	—
513	C₂×C₄	—	59	1	no	—
514	C₂×C₄	—	118	2	no	—
515	C₂×C₄	—	118	4	no	—
516	C₂×C₄	—	118	1	no	—
517	C₂×C₄	—	118	1	no	—
518	C₂×C₄	—	118	1	no	—
519	C₂×C₄	—	118	1	no	—
520	C₂×C₄	—	118	1	no	—
521	C₂×C₄	—	118	1	no	—
522	C₂×C₄	—	118	1	no	—
523	C₂×C₄	—	118	1	no	—
524	C₂×C₄	—	236	2	no	—
525	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
527	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	59	2	no	—
536	C₈	—	118	2	no	—
537	C₈	—	118	1	no	—
538	C₈	—	118	1	no	—
539	C₈	—	118	1	no	—
540	C₈	—	236	1	no	—
541	C₈	—	236	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	59	2	no	—
546	C₂²	—	118	1	no	—
547	C₂²	—	118	1	no	—
548	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	118	1	no	—
554	C₄	—	118	1	no	—
555	C₄	—	118	1	no	—
556	C₄	—	118	2	no	—
557	C₄	—	236	1	no	—
558	C₄	—	236	1	no	—
559	C₄	—	236	1	no	—
560	C₄	#131×D₅₉	1	1	yes	characteristic
561	C₄	C₂×#14273735	1	1	yes	characteristic
562	C₄	#137×D₅₉	1	1	yes	characteristic
563	C₄	#16838198	1	1	yes	characteristic
564	C₂	—	8	1	no	—
565	C₂	—	118	2	no	—
566	C₂	#21432787	1	1	yes	characteristic
567	C₂	#21432918	1	1	yes	characteristic
568	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×#1588	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#14273698	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1588	D₅₉
hypocenter	C₅₉	#17911
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1588

Complements

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

N	H ≅ G/N	type
3. C₈×Q₈×D₅₉	C₂	semidirect
4. #21422972	C₂	semidirect
5. #21422969	C₂	semidirect
6. #21422967	C₂	semidirect
7. #21422902	C₂	semidirect
8. #21422900	C₂	semidirect
9. #21422899	C₂	semidirect
10. SD₁₆×C₅₉⋊C₈	C₂	semidirect
11. #21422880	C₂	semidirect
12. #21422541	C₂	semidirect
14. #21422375	C₂	semidirect
15. C₅₉×#1588	C₂	semidirect
284. #1588	D₅₉	semidirect
351. C₅₉	#17911	semidirect

Maximal subgroups

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

subgroup	index
#21434174	2
#21433074	2
C₈×Q₈×D₅₉	2
#21422972	2
#21422969	2
#21422967	2
#21422902	2
#21422900	2
#21422899	2
SD₁₆×C₅₉⋊C₈	2
#21422880	2
#21422541	2
#21422506	2
#21422375	2
C₅₉×#1588	2
#17911	59