Subgroups — #28559307

Order 15104.

594 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434698	C₂	1	1	yes	maximal, characteristic
2	#21433068	C₂	1	1	yes	maximal, characteristic
3	#21433025	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422992	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422990	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422989	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422987	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422916	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422913	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422908	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422862	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422567	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422558	C₂	1	1	yes	maximal, characteristic
14	#21422375	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837956	C₂²	1	1	yes	characteristic
17	#16837934	C₂²	1	1	yes	characteristic
18	#16837809	C₄	1	1	yes	characteristic
19	#16837793	C₄	1	1	yes	characteristic
20	#16837769	C₄	1	1	yes	characteristic
21	#16837760	C₄	1	1	yes	characteristic
22	#16837661	C₄	1	1	yes	characteristic
23	#16837659	C₄	1	1	yes	characteristic
24	#16837647	C₄	1	1	yes	characteristic
25	#16837645	C₄	1	1	yes	characteristic
26	#16837533	C₂²	1	1	yes	characteristic
27	#16837531	—	2	1	no	—
28	#16837529	C₂²	1	1	yes	characteristic
29	#16837529	C₂²	1	1	yes	characteristic
30	C₈×Dic₁₁₈	—	2	1	no	—
31	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₁₈	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	#16837480	C₂²	1	1	yes	characteristic
37	#16837476	—	2	1	no	—
38	C₈×C₂²⋊D₅₉	—	2	1	no	—
39	#16837460	—	2	1	no	—
40	#16837458	C₂²	1	1	yes	characteristic
41	#16837453	C₂²	1	1	yes	characteristic
42	#16837427	—	2	1	no	—
43	#16837424	C₂²	1	1	yes	characteristic
44	#16837357	—	2	1	no	—
45	#16837356	—	2	1	no	—
46	C₄×#11745659	C₂²	1	1	yes	characteristic
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	C₈×D₄×C₅₉	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×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745664	—	2	1	no	—
71	C₂×#11745659	—	2	1	no	—
72	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
73	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
75	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
76	#14273726	C₂×C₄	1	1	yes	characteristic
77	#14273725	C₂×C₄	1	1	yes	characteristic
78	#14273720	—	2	1	no	—
79	#14273718	C₂×C₄	1	1	yes	characteristic
80	#14273717	—	2	1	no	—
81	#14273714	C₂×C₄	1	1	yes	characteristic
82	#14273709	—	2	1	no	—
83	#14273707	C₂×C₄	1	1	yes	characteristic
84	#14273707	C₂×C₄	1	1	yes	characteristic
85	#14273705	—	2	1	no	—
86	#14273703	C₂×C₄	1	1	yes	characteristic
87	#14273698	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₁₁₈	—	2	1	no	—
89	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
90	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
91	C₄×C₂²⋊D₅₉	—	2	1	no	—
92	#14273686	—	2	1	no	—
93	#14273684	—	2	1	no	—
94	C₄²×D₅₉	C₂³	1	1	yes	characteristic
95	#14273661	C₂×C₄	1	1	yes	characteristic
96	#14273660	C₂×C₄	1	1	yes	characteristic
97	#14273658	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
99	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
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	Dic₅₉⋊C₈	—	2	1	no	—
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	—	2	1	no	—
116	#14273638	—	2	1	no	—
117	#14273637	—	2	1	no	—
118	#14273637	—	2	1	no	—
119	#14273637	—	2	1	no	—
120	#14273637	C₂×C₄	1	1	yes	characteristic
121	#14273637	C₂×C₄	1	1	yes	characteristic
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	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	C₂²×C₈×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	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
151	C₂×Dic₁₁₈	—	2	1	no	—
152	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
154	SD₁₆×C₅₉	—	2	2	no	—
155	C₂×C₈×C₅₉	—	2	1	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	—	2	1	no	—
158	C₂×C₈×C₅₉	—	4	2	no	—
159	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₄⋊C₄×C₅₉	—	2	1	no	—
164	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊C₄×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	—	2	1	no	—
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	#11745672	—	2	2	no	—
173	#11745670	—	2	2	no	—
174	(C₂×D₅₉)⋊C₄	—	2	1	no	—
175	(C₂×D₅₉)⋊C₄	—	2	1	no	—
176	(C₂×D₅₉)⋊C₄	—	2	1	no	—
177	C₄⋊Dic₅₉	—	2	1	no	—
178	C₄⋊Dic₅₉	—	2	1	no	—
179	C₄⋊Dic₅₉	—	2	1	no	—
180	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
182	Dic₅₉⋊C₄	—	2	1	no	—
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	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
193	C₄×Dic₅₉	#41	1	1	yes	characteristic
194	#11745664	—	4	2	no	—
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	Dic₂₃₆	—	2	2	no	—
203	#11745659	—	2	2	no	—
204	#11745659	—	2	2	no	—
205	#11745659	—	4	2	no	—
206	C₈×D₅₉	—	2	2	no	—
207	C₈×D₅₉	—	4	1	no	—
208	C₂³×C₅₉	—	2	1	no	—
209	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	2	1	no	—
212	D₄×C₅₉	—	2	1	no	—
213	D₄×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	—	4	1	no	—
218	C₂×C₄×C₅₉	—	4	1	no	—
219	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
222	C₂²⋊D₅₉	—	4	2	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	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
228	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
229	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
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	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	2	1	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	—	4	2	no	—
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	—	2	1	no	—
242	C₈×C₅₉	—	2	1	no	—
243	C₈×C₅₉	—	4	1	no	—
244	C₈×C₅₉	—	4	1	no	—
245	C₈×C₅₉	—	4	1	no	—
246	C₈×C₅₉	#131	1	2	yes	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	2	1	no	—
249	C₅₉⋊C₈	—	4	1	no	—
250	C₅₉⋊C₈	—	4	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	C₅₉⋊C₈	#131	1	2	yes	—
253	C₅₉⋊C₈	#137	1	2	yes	—
254	#17967	—	59	1	no	maximal, Sylow
255	C₂²×C₅₉	—	4	1	no	—
256	C₂²×C₅₉	—	4	1	no	—
257	C₂²×C₅₉	—	4	1	no	—
258	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₅₉	—	2	1	no	—
260	C₂×D₅₉	—	2	1	no	—
261	C₂×D₅₉	—	2	1	no	—
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	4	1	no	—
264	C₄×C₅₉	—	4	1	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
267	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
268	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
269	C₄×C₅₉	#575	1	1	yes	characteristic
270	Dic₅₉	—	2	1	no	—
271	Dic₅₉	—	2	1	no	—
272	Dic₅₉	—	2	1	no	—
273	Dic₅₉	—	4	1	no	—
274	Dic₅₉	—	4	1	no	—
275	Dic₅₉	—	4	1	no	—
276	Dic₅₉	—	4	1	no	—
277	#3172	—	59	1	no	—
278	#2966	—	59	1	no	—
279	#2960	—	59	1	no	—
280	#1591	—	59	1	no	—
281	#1591	—	59	1	no	—
282	#1590	—	59	1	no	—
283	#1590	—	59	1	no	—
284	#1579	—	59	1	no	—
285	#1579	—	59	1	no	—
286	SD₁₆⋊C₈	—	59	1	no	—
287	SD₁₆⋊C₈	D₅₉	1	1	yes	characteristic, complemented
288	#1569	—	59	1	no	—
289	#1497	—	59	1	no	—
290	#1495	—	59	1	no	—
291	C₈×M₁₆	—	59	1	no	—
292	C₂×C₅₉	—	8	1	no	—
293	C₂×C₅₉	#2931	1	1	yes	characteristic
294	C₂×C₅₉	C₄×#137	1	1	yes	characteristic
295	C₂×C₅₉	#2955	1	1	yes	characteristic
296	D₅₉	—	4	1	no	—
297	#533	—	59	1	no	—
298	#529	—	59	1	no	—
299	#501	—	59	1	no	—
300	#497	—	59	1	no	—
301	#491	—	59	1	no	—
302	#489	—	59	1	no	—
303	#470	—	59	1	no	—
304	#470	—	59	1	no	—
305	#468	—	59	1	no	—
306	#468	—	59	1	no	—
307	#446	—	59	1	no	—
308	#446	—	59	1	no	—
309	#446	—	59	1	no	—
310	#446	—	118	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	59	1	no	—
313	C₈×Q₈	—	118	1	no	—
314	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
315	C₄×Q₁₆	—	59	1	no	—
316	C₄×Q₁₆	—	59	1	no	—
317	C₄×SD₁₆	—	59	1	no	—
318	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
319	#436	—	59	1	no	—
320	#435	—	118	1	no	—
321	C₈×D₄	—	118	1	no	—
322	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
323	#433	—	118	1	no	—
324	#432	—	59	1	no	—
325	#431	—	59	1	no	—
326	#424	—	118	1	no	—
327	#423	—	59	1	no	—
328	#405	—	118	1	no	—
329	#405	—	118	1	no	—
330	C₄×M₁₆	—	59	1	no	—
331	C₂×C₄×C₈	—	59	1	no	—
332	#335	—	59	1	no	—
333	#335	C₂×D₅₉	1	1	yes	characteristic
334	#334	—	59	1	no	—
335	#334	—	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	Q₈⋊C₈	—	59	1	no	—
341	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
342	D₄⋊C₈	—	59	1	no	—
343	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
344	#322	—	59	1	no	—
345	#322	C₂×D₅₉	1	1	yes	characteristic
346	C₈²	—	59	1	no	—
347	C₈²	—	59	1	no	—
348	C₅₉	#17967	1	1	yes	characteristic, complemented, Sylow
349	C₂×Q₁₆	—	59	1	no	—
350	C₂×Q₁₆	—	59	1	no	—
351	C₂×SD₁₆	—	59	1	no	—
352	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
353	C₂×M₁₆	—	59	1	no	—
354	C₂×M₁₆	—	59	1	no	—
355	C₂×M₁₆	—	118	1	no	—
356	C₂×M₁₆	—	118	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	—	59	1	no	—
359	C₂²×C₈	—	59	1	no	—
360	C₄⋊Q₈	—	59	1	no	—
361	C₄⋊Q₈	—	59	1	no	—
362	#126	—	118	1	no	—
363	#125	—	59	1	no	—
364	#125	—	118	1	no	—
365	#124	—	59	1	no	—
366	#123	—	118	1	no	—
367	C₂²⋊Q₈	—	59	1	no	—
368	C₂²⋊Q₈	—	59	1	no	—
369	C₂²⋊Q₈	—	59	1	no	—
370	C₂²⋊Q₈	—	118	1	no	—
371	#121	—	59	1	no	—
372	C₄×Q₈	—	59	1	no	—
373	C₄×Q₈	—	59	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	#117	—	118	1	no	—
380	C₂×C₄²	—	59	1	no	—
381	#107	—	59	1	no	—
382	#107	—	59	1	no	—
383	#106	—	59	1	no	—
384	#106	C₄×D₅₉	1	1	yes	characteristic
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	59	1	no	—
387	C₄⋊C₈	—	59	1	no	—
388	C₄⋊C₈	—	118	1	no	—
389	C₄⋊C₈	—	118	1	no	—
390	C₄⋊C₈	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
397	#103	—	59	1	no	—
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	#102	—	59	1	no	—
404	#102	C₄×D₅₉	1	1	yes	characteristic
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	118	1	no	—
407	C₂²⋊C₈	—	118	1	no	—
408	C₂²⋊C₈	—	118	1	no	—
409	#97	—	59	1	no	—
410	#97	—	59	1	no	—
411	#97	—	118	1	no	—
412	#97	—	118	1	no	—
413	#97	—	118	1	no	—
414	#97	—	118	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	59	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	—	118	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
426	C₂×Q₈	—	59	1	no	—
427	C₂×Q₈	—	59	1	no	—
428	C₂×Q₈	—	118	1	no	—
429	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₂×D₄	—	118	1	no	—
431	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	59	1	no	—
434	C₂²×C₄	—	59	1	no	—
435	C₂²×C₄	—	59	1	no	—
436	Q₁₆	—	118	2	no	—
437	Q₁₆	—	118	2	no	—
438	SD₁₆	—	2	2	no	—
439	SD₁₆	—	118	2	no	—
440	M₁₆	—	118	2	no	—
441	M₁₆	—	118	2	no	—
442	M₁₆	—	236	2	no	—
443	M₁₆	—	236	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	4	2	no	—
448	C₂×C₈	—	59	1	no	—
449	C₂×C₈	—	59	1	no	—
450	C₂×C₈	—	59	1	no	—
451	C₂×C₈	—	59	1	no	—
452	C₂×C₈	—	118	2	no	—
453	C₂×C₈	—	118	1	no	—
454	C₂×C₈	—	118	1	no	—
455	C₂×C₈	—	118	1	no	—
456	C₂×C₈	—	236	1	no	—
457	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
459	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
460	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	59	1	no	—
463	C₄⋊C₄	—	59	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	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	—	2	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	C₂²⋊C₄	—	118	1	no	—
482	C₂²⋊C₄	—	118	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	59	1	no	—
485	C₄²	—	59	1	no	—
486	C₄²	—	59	1	no	—
487	C₄²	—	118	1	no	—
488	C₄²	—	118	1	no	—
489	C₄²	C₂³×D₅₉	1	1	yes	characteristic
490	C₂³	—	2	1	no	—
491	C₂³	—	59	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	118	1	no	—
495	Q₈	—	118	1	no	—
496	Q₈	—	118	1	no	—
497	Q₈	—	118	1	no	—
498	Q₈	—	236	2	no	—
499	D₄	—	2	1	no	—
500	D₄	—	2	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	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	59	1	no	—
508	C₂×C₄	—	59	1	no	—
509	C₂×C₄	—	59	1	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	—	118	1	no	—
518	C₂×C₄	—	236	1	no	—
519	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
521	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	59	2	no	—
529	C₈	—	59	2	no	—
530	C₈	—	118	1	no	—
531	C₈	—	118	1	no	—
532	C₈	—	236	1	no	—
533	C₈	—	236	1	no	—
534	C₈	—	236	1	no	—
535	C₈	#14273733	1	2	yes	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	118	1	no	—
540	C₂²	—	118	1	no	—
541	C₂²	—	118	1	no	—
542	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	118	1	no	—
548	C₄	—	118	1	no	—
549	C₄	—	118	1	no	—
550	C₄	—	236	1	no	—
551	C₄	—	236	1	no	—
552	C₄	—	236	1	no	—
553	C₄	—	236	1	no	—
554	C₄	#131×D₅₉	1	1	yes	characteristic
555	C₄	C₂×#14273733	1	1	yes	characteristic
556	C₄	#137×D₅₉	1	1	yes	characteristic
557	C₄	#16838198	1	1	yes	characteristic
558	C₂	—	8	1	no	—
559	C₂	—	236	1	no	—
560	C₂	#21432803	1	1	yes	characteristic
561	C₂	#21432918	1	1	yes	characteristic
562	C₂	#21432996	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×SD₁₆⋊C₈	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#14273698	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	SD₁₆⋊C₈	D₅₉
hypocenter	C₅₉	#17967
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
3. #21433025	C₂	semidirect
4. #21422992	C₂	semidirect
5. #21422990	C₂	semidirect
6. #21422989	C₂	semidirect
7. #21422987	C₂	semidirect
8. #21422916	C₂	semidirect
9. #21422913	C₂	semidirect
10. #21422908	C₂	semidirect
11. #21422862	C₂	semidirect
12. #21422567	C₂	semidirect
14. #21422375	C₂	semidirect
15. C₅₉×SD₁₆⋊C₈	C₂	semidirect
287. SD₁₆⋊C₈	D₅₉	semidirect
348. C₅₉	#17967	semidirect

Maximal subgroups

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

subgroup	index
#21434698	2
#21433068	2
#21433025	2
#21422992	2
#21422990	2
#21422989	2
#21422987	2
#21422916	2
#21422913	2
#21422908	2
#21422862	2
#21422567	2
#21422558	2
#21422375	2
C₅₉×SD₁₆⋊C₈	2
#17967	59