Subgroups — #28560463

Order 15104.

586 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434679	C₂	1	1	yes	maximal, characteristic
2	#21433044	C₂	1	1	yes	maximal, characteristic
3	#21433038	C₂	1	1	yes	maximal, characteristic
4	#21422991	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422990	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422948	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422947	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#11745672	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422900	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₅₉	C₂	1	1	yes	maximal, characteristic
12	#21422497	C₂	1	1	yes	maximal, characteristic
13	#21422497	C₂	1	1	yes	maximal, characteristic
14	#21422375	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837956	C₂²	1	1	yes	characteristic
17	#16837956	C₂²	1	1	yes	characteristic
18	#16837806	C₄	1	1	yes	characteristic
19	#16837780	C₄	1	1	yes	characteristic
20	#16837751	C₄	1	1	yes	characteristic
21	#16837751	C₄	1	1	yes	characteristic
22	#16837644	C₄	1	1	yes	characteristic
23	#16837642	C₄	1	1	yes	characteristic
24	#16837642	C₄	1	1	yes	characteristic
25	#16837640	C₄	1	1	yes	characteristic
26	#16837533	C₂²	1	1	yes	characteristic
27	#16837532	—	2	1	no	—
28	#16837532	C₂²	1	1	yes	characteristic
29	#16837531	—	2	1	no	—
30	#16837530	—	2	1	no	—
31	#16837529	—	2	1	no	—
32	#16837529	C₂²	1	1	yes	characteristic
33	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
35	#16837526	C₂²	1	1	yes	characteristic
36	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
37	C₄×#11745672	C₂²	1	1	yes	characteristic
38	C₄×#11745672	C₂²	1	1	yes	characteristic
39	#16837453	C₂²	1	1	yes	characteristic
40	#16837427	—	2	1	no	—
41	#16837427	—	2	1	no	—
42	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
44	#16837359	—	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	#16837155	C₂²	1	1	yes	characteristic
49	#16837154	C₂²	1	1	yes	characteristic
50	#16837154	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	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
55	#16837132	C₂²	1	1	yes	characteristic
56	#16837132	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	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×#335	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×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745659	D₄	1	1	yes	characteristic
71	C₂×#11745659	D₄	1	1	yes	characteristic
72	C₂×C₈×D₅₉	—	2	1	no	—
73	C₂×C₈×D₅₉	—	2	1	no	—
74	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
76	#14273726	C₂×C₄	1	1	yes	characteristic
77	#14273726	C₂×C₄	1	1	yes	characteristic
78	#14273725	C₂×C₄	1	1	yes	characteristic
79	#14273725	C₂×C₄	1	1	yes	characteristic
80	#14273717	—	2	1	no	—
81	#14273717	—	2	1	no	—
82	#14273707	C₂×C₄	1	1	yes	characteristic
83	#14273707	C₂×C₄	1	1	yes	characteristic
84	#14273705	—	2	1	no	—
85	#14273705	—	2	1	no	—
86	#14273703	C₂×C₄	1	1	yes	characteristic
87	#14273703	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₁₁₈	—	2	1	no	—
89	C₄×Dic₁₁₈	—	2	1	no	—
90	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
91	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
92	#14273684	—	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	#14273660	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
99	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
100	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
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	Dic₅₉⋊C₈	—	2	1	no	—
108	Dic₅₉⋊C₈	—	2	1	no	—
109	#14273652	C₂×C₄	1	1	yes	characteristic
110	#14273652	C₂×C₄	1	1	yes	characteristic
111	#14273651	C₂×C₄	1	1	yes	characteristic
112	#14273651	C₂×C₄	1	1	yes	characteristic
113	#14273650	C₂×C₄	1	1	yes	characteristic
114	#14273650	C₂×C₄	1	1	yes	characteristic
115	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	#14273638	—	2	1	no	—
117	#14273637	—	2	1	no	—
118	#14273637	—	2	1	no	—
119	#14273637	D₄	1	1	yes	characteristic
120	#14273637	D₄	1	1	yes	characteristic
121	C₄×C₅₉⋊C₈	—	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	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
149	C₂×Dic₁₁₈	—	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	Q₁₆×C₅₉	—	4	1	no	—
154	C₂×C₈×C₅₉	—	2	1	no	—
155	C₂×C₈×C₅₉	—	2	1	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
161	C₄⋊C₄×C₅₉	—	2	1	no	—
162	C₄⋊C₄×C₅₉	—	2	1	no	—
163	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₅₉	—	2	1	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
168	#11745672	—	2	2	no	—
169	#11745672	—	2	2	no	—
170	(C₂×D₅₉)⋊C₄	—	2	1	no	—
171	(C₂×D₅₉)⋊C₄	—	2	1	no	—
172	(C₂×D₅₉)⋊C₄	—	2	1	no	—
173	(C₂×D₅₉)⋊C₄	—	2	1	no	—
174	C₄⋊Dic₅₉	—	2	1	no	—
175	C₄⋊Dic₅₉	—	2	1	no	—
176	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
178	Dic₅₉⋊C₄	—	2	1	no	—
179	Dic₅₉⋊C₄	—	2	1	no	—
180	Dic₅₉⋊C₄	—	2	1	no	—
181	Dic₅₉⋊C₄	—	2	1	no	—
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	C₄×Dic₅₉	—	2	1	no	—
189	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
191	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
192	C₄×Dic₅₉	#41	1	1	yes	characteristic
193	C₂×C₅₉⋊C₈	—	2	1	no	—
194	C₂×C₅₉⋊C₈	—	2	1	no	—
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅₉⋊C₈	C₂²×C₄	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	—	4	1	no	—
201	#11745659	—	2	2	no	—
202	#11745659	Q₁₆	1	4	yes	complemented
203	C₈×D₅₉	—	2	2	no	—
204	C₈×D₅₉	—	4	1	no	—
205	C₈×D₅₉	—	4	2	no	—
206	C₈×D₅₉	—	4	2	no	—
207	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₅₉	—	2	1	no	—
209	Q₈×C₅₉	—	2	1	no	—
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
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	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	C₂×Dic₅₉	—	2	1	no	—
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	C₄×D₅₉	—	2	1	no	—
227	C₄×D₅₉	—	2	1	no	—
228	C₄×D₅₉	—	4	1	no	—
229	C₄×D₅₉	C₂×Q₁₆	1	2	yes	—
230	C₄×D₅₉	#135	1	2	yes	—
231	Dic₁₁₈	—	2	1	no	—
232	Dic₁₁₈	—	2	1	no	—
233	Dic₁₁₈	—	2	1	no	—
234	Dic₁₁₈	—	2	1	no	—
235	Dic₁₁₈	—	8	1	no	—
236	Dic₁₁₈	—	8	1	no	—
237	C₈×C₅₉	—	2	1	no	—
238	C₈×C₅₉	—	2	1	no	—
239	C₈×C₅₉	—	2	1	no	—
240	C₈×C₅₉	—	4	1	no	—
241	C₈×C₅₉	—	4	1	no	—
242	C₈×C₅₉	—	4	1	no	—
243	C₈×C₅₉	C₂×Q₁₆	1	2	yes	—
244	C₅₉⋊C₈	—	2	1	no	—
245	C₅₉⋊C₈	—	2	1	no	—
246	C₅₉⋊C₈	—	4	1	no	—
247	C₅₉⋊C₈	—	4	1	no	—
248	C₅₉⋊C₈	—	4	1	no	—
249	C₅₉⋊C₈	#131	1	2	yes	—
250	C₅₉⋊C₈	C₂×Q₁₆	1	2	yes	—
251	#18068	—	59	1	no	maximal, Sylow
252	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂×D₅₉	—	2	1	no	—
254	C₂×D₅₉	—	2	1	no	—
255	C₂×D₅₉	C₄×Q₁₆	1	2	yes	—
256	C₄×C₅₉	—	2	1	no	—
257	C₄×C₅₉	—	4	1	no	—
258	C₄×C₅₉	—	4	1	no	—
259	C₄×C₅₉	—	4	1	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
262	C₄×C₅₉	#568	1	1	yes	characteristic
263	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
264	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
265	Dic₅₉	—	2	1	no	—
266	Dic₅₉	—	2	1	no	—
267	Dic₅₉	—	4	1	no	—
268	Dic₅₉	—	4	1	no	—
269	Dic₅₉	—	4	1	no	—
270	Dic₅₉	—	4	1	no	—
271	Dic₅₉	C₄×Q₁₆	1	2	yes	—
272	#3170	—	59	1	no	—
273	#2962	—	59	1	no	—
274	#2962	—	59	1	no	—
275	#1591	—	59	1	no	—
276	#1591	—	59	1	no	—
277	#1584	—	59	1	no	—
278	#1584	—	59	1	no	—
279	#1584	—	59	1	no	—
280	#1584	D₅₉	1	1	yes	characteristic, complemented
281	C₈×Q₁₆	—	59	1	no	—
282	C₈×Q₁₆	—	59	1	no	—
283	C₂×#335	—	59	1	no	—
284	#1481	—	59	1	no	—
285	#1481	—	59	1	no	—
286	C₈×M₁₆	—	59	1	no	—
287	C₂×C₅₉	#2935	1	1	yes	characteristic
288	C₂×C₅₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
289	C₂×C₅₉	#2957	1	1	yes	characteristic
290	D₅₉	—	2	2	no	—
291	#533	—	59	1	no	—
292	#533	—	59	1	no	—
293	#500	—	59	1	no	—
294	#494	—	59	1	no	—
295	#487	—	59	1	no	—
296	#487	—	59	1	no	—
297	#467	—	59	1	no	—
298	#467	—	59	1	no	—
299	#467	—	59	1	no	—
300	#467	—	59	1	no	—
301	#446	—	59	1	no	—
302	#446	—	59	1	no	—
303	#446	—	59	1	no	—
304	#446	—	118	1	no	—
305	#446	—	118	1	no	—
306	#446	—	118	1	no	—
307	#446	—	118	1	no	—
308	#446	C₂×D₅₉	1	1	yes	characteristic
309	C₈×Q₈	—	59	1	no	—
310	C₈×Q₈	—	59	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
313	C₄×Q₁₆	—	59	1	no	—
314	C₄×Q₁₆	—	59	1	no	—
315	C₄×Q₁₆	—	59	1	no	—
316	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
317	#431	—	59	1	no	—
318	#424	—	118	1	no	—
319	#424	—	118	1	no	—
320	C₂×C₄⋊C₈	—	59	1	no	—
321	C₂×C₄⋊C₈	—	59	1	no	—
322	#405	—	118	1	no	—
323	#405	—	118	1	no	—
324	C₄×M₁₆	—	59	1	no	—
325	C₂×C₄×C₈	—	59	1	no	—
326	#335	—	59	1	no	—
327	#335	—	59	1	no	—
328	#335	—	59	1	no	—
329	#335	C₂×D₅₉	1	1	yes	characteristic
330	Q₈⋊C₈	—	59	1	no	—
331	Q₈⋊C₈	—	59	1	no	—
332	Q₈⋊C₈	—	59	1	no	—
333	Q₈⋊C₈	—	59	1	no	—
334	Q₈⋊C₈	—	59	1	no	—
335	Q₈⋊C₈	—	59	1	no	—
336	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
337	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
338	#322	—	59	1	no	—
339	#322	C₂×D₅₉	1	1	yes	characteristic
340	C₈²	—	59	1	no	—
341	C₈²	—	59	1	no	—
342	C₅₉	#18068	1	1	yes	characteristic, complemented, Sylow
343	C₂×Q₁₆	—	59	1	no	—
344	C₂×Q₁₆	—	59	1	no	—
345	C₂×Q₁₆	—	59	1	no	—
346	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
347	C₂×M₁₆	—	59	1	no	—
348	C₂×M₁₆	—	59	1	no	—
349	C₂²×C₈	—	59	1	no	—
350	C₂²×C₈	—	59	1	no	—
351	C₂²×C₈	—	118	1	no	—
352	C₂²×C₈	—	118	1	no	—
353	C₄⋊Q₈	—	59	1	no	—
354	C₄⋊Q₈	—	59	1	no	—
355	C₄⋊Q₈	—	59	1	no	—
356	C₄⋊Q₈	—	59	1	no	—
357	#125	—	118	1	no	—
358	#125	—	118	1	no	—
359	C₂²⋊Q₈	—	59	1	no	—
360	C₂²⋊Q₈	—	59	1	no	—
361	C₂²⋊Q₈	—	59	1	no	—
362	C₂²⋊Q₈	—	59	1	no	—
363	C₂²⋊Q₈	—	118	1	no	—
364	C₂²⋊Q₈	—	118	1	no	—
365	C₄×Q₈	—	59	1	no	—
366	C₄×Q₈	—	59	1	no	—
367	C₄×Q₈	—	118	1	no	—
368	C₄×Q₈	—	118	1	no	—
369	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
370	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
371	#117	—	118	1	no	—
372	#117	—	118	1	no	—
373	C₂×C₄²	—	59	1	no	—
374	#107	—	59	1	no	—
375	#107	—	59	1	no	—
376	#107	—	59	1	no	—
377	#107	C₄×D₅₉	1	1	yes	characteristic
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	59	1	no	—
381	C₄⋊C₈	—	59	1	no	—
382	C₄⋊C₈	—	118	1	no	—
383	C₄⋊C₈	—	118	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	#103	—	59	1	no	—
394	#103	—	59	1	no	—
395	#103	—	59	1	no	—
396	#103	—	59	1	no	—
397	#103	—	59	1	no	—
398	#103	—	59	1	no	—
399	#103	C₄×D₅₉	1	1	yes	characteristic
400	#103	C₄×D₅₉	1	1	yes	characteristic
401	C₂²⋊C₈	—	118	1	no	—
402	#97	—	2	1	no	—
403	#97	—	59	1	no	—
404	#97	—	59	1	no	—
405	#97	—	118	1	no	—
406	#97	—	118	1	no	—
407	#97	—	118	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	59	1	no	—
410	C₄×C₈	—	59	1	no	—
411	C₄×C₈	—	59	1	no	—
412	C₄×C₈	—	59	1	no	—
413	C₄×C₈	—	59	1	no	—
414	C₄×C₈	—	118	1	no	—
415	C₄×C₈	—	118	1	no	—
416	C₄×C₈	—	118	1	no	—
417	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
418	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
420	C₂×Q₈	—	59	1	no	—
421	C₂×Q₈	—	59	1	no	—
422	C₂×Q₈	—	118	1	no	—
423	C₂×Q₈	—	118	1	no	—
424	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
425	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
426	C₂²×C₄	—	59	1	no	—
427	C₂²×C₄	—	59	1	no	—
428	C₂²×C₄	—	59	1	no	—
429	Q₁₆	—	4	1	no	—
430	Q₁₆	—	118	2	no	—
431	Q₁₆	—	118	2	no	—
432	Q₁₆	—	236	1	no	—
433	M₁₆	—	59	4	no	—
434	M₁₆	—	118	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	59	1	no	—
439	C₂×C₈	—	59	1	no	—
440	C₂×C₈	—	59	1	no	—
441	C₂×C₈	—	59	1	no	—
442	C₂×C₈	—	118	2	no	—
443	C₂×C₈	—	118	1	no	—
444	C₂×C₈	—	118	1	no	—
445	C₂×C₈	—	118	1	no	—
446	C₂×C₈	—	236	1	no	—
447	C₂×C₈	—	236	2	no	—
448	C₂×C₈	—	236	2	no	—
449	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
450	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
451	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
452	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	59	1	no	—
456	C₄⋊C₄	—	59	1	no	—
457	C₄⋊C₄	—	118	1	no	—
458	C₄⋊C₄	—	118	1	no	—
459	C₄⋊C₄	—	118	1	no	—
460	C₄⋊C₄	—	118	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	C₂×C₄×D₅₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
471	C₂²⋊C₄	—	118	1	no	—
472	C₂²⋊C₄	—	118	1	no	—
473	C₂²⋊C₄	—	118	1	no	—
474	C₂²⋊C₄	—	118	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	59	1	no	—
478	C₄²	—	59	1	no	—
479	C₄²	—	59	1	no	—
480	C₄²	—	118	1	no	—
481	C₄²	—	118	1	no	—
482	C₄²	C₂³×D₅₉	1	1	yes	characteristic
483	C₂³	—	59	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	118	1	no	—
489	Q₈	—	118	1	no	—
490	Q₈	—	118	1	no	—
491	Q₈	—	118	1	no	—
492	Q₈	—	472	1	no	—
493	Q₈	—	472	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	59	1	no	—
499	C₂×C₄	—	59	2	no	—
500	C₂×C₄	—	59	2	no	—
501	C₂×C₄	—	59	1	no	—
502	C₂×C₄	—	59	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	—	236	1	no	—
510	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
512	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	59	2	no	—
520	C₈	—	59	2	no	—
521	C₈	—	118	1	no	—
522	C₈	—	118	1	no	—
523	C₈	—	236	1	no	—
524	C₈	—	236	1	no	—
525	C₈	—	236	1	no	—
526	C₈	Q₁₆×D₅₉	1	2	yes	—
527	C₂²	—	59	2	no	—
528	C₂²	—	118	1	no	—
529	C₂²	—	118	1	no	—
530	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	59	2	no	—
537	C₄	—	118	1	no	—
538	C₄	—	118	1	no	—
539	C₄	—	236	1	no	—
540	C₄	—	236	1	no	—
541	C₄	—	236	1	no	—
542	C₄	—	236	1	no	—
543	C₄	#131×D₅₉	1	1	yes	characteristic
544	C₄	#16838168	1	1	yes	characteristic
545	C₄	C₂×Q₁₆×D₅₉	1	1	yes	characteristic
546	C₄	#135×D₅₉	1	1	yes	characteristic
547	C₂	—	118	2	no	—
548	C₂	#21432837	1	1	yes	characteristic
549	C₂	C₄×Q₁₆×D₅₉	1	1	yes	characteristic
550	C₂	#21433010	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×#1584	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1584	D₅₉
hypocenter	C₅₉	#18068
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #21422991	C₂	semidirect
5. #21422990	C₂	semidirect
6. #21422948	C₂	semidirect
7. #21422947	C₂	semidirect
8. #21422945	C₂	semidirect
9. C₈×#11745672	C₂	semidirect
10. #21422900	C₂	semidirect
15. C₅₉×#1584	C₂	semidirect
202. #11745659	Q₁₆	semidirect
280. #1584	D₅₉	semidirect
342. C₅₉	#18068	semidirect

Maximal subgroups

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

subgroup	index
#21434679	2
#21433044	2
#21433038	2
#21422991	2
#21422990	2
#21422948	2
#21422947	2
#21422945	2
C₈×#11745672	2
#21422900	2
#335×D₅₉	2
#21422497	2
#21422375	2
C₅₉×#1584	2
#18068	59