Subgroups — #28558302

Order 15104.

662 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11745687	C₂	1	1	yes	maximal, characteristic
2	#446×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14273756	C₂	1	1	yes	maximal, characteristic
4	#21422969	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422965	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422953	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422949	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422933	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422929	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422847	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422489	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422480	C₂	1	1	yes	maximal, characteristic
14	#21422384	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1585	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273756	C₄	1	1	yes	characteristic
17	C₄×#11745687	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
19	#16837533	C₂²	1	1	yes	characteristic
20	#16837532	C₂²	1	1	yes	characteristic
21	#16837531	—	2	1	no	—
22	#16837530	—	2	1	no	—
23	#16837529	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
25	#16837526	C₂²	1	1	yes	characteristic
26	#16837508	C₄	1	1	yes	characteristic
27	#16837506	C₄	1	1	yes	characteristic
28	#16837503	C₄	1	1	yes	characteristic
29	#16837499	C₄	1	1	yes	characteristic
30	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
31	C₄×#11745672	C₂²	1	1	yes	characteristic
32	C₄×#11745670	C₂²	1	1	yes	characteristic
33	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₅₉	—	2	1	no	—
35	(C₂²⋊D₅₉)⋊C₈	—	2	1	no	—
36	#16837454	C₂²	1	1	yes	characteristic
37	#16837453	C₂²	1	1	yes	characteristic
38	#16837452	—	2	1	no	—
39	#16837441	C₄	1	1	yes	characteristic
40	C₄⋊C₈×D₅₉	—	2	1	no	—
41	C₄⋊C₈×D₅₉	C₂²	1	1	yes	characteristic
42	#16837409	C₄	1	1	yes	characteristic
43	#16837400	C₄	1	1	yes	characteristic
44	C₄×#11745659	C₂²	1	1	yes	characteristic
45	#97×D₅₉	—	2	1	no	—
46	C₂×C₈×Dic₅₉	—	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	#16837124	C₂²	1	1	yes	characteristic
59	#16837124	C₂²	1	1	yes	characteristic
60	C₅₉×#446	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×#11745687	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
69	#14273756	—	2	4	no	—
70	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
73	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
74	C₂×#11745659	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₅₉⋊C₈	—	2	1	no	—
76	C₂×C₈×D₅₉	—	2	1	no	—
77	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
78	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
79	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₁₁₈	—	2	1	no	—
81	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
82	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
83	#14273692	—	2	1	no	—
84	#14273692	C₂×C₄	1	1	yes	characteristic
85	#14273692	C₂×C₄	1	1	yes	characteristic
86	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₅₉	—	2	1	no	—
88	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
89	#14273685	C₂×C₄	1	1	yes	characteristic
90	#14273683	—	2	1	no	—
91	C₄⋊C₄×D₅₉	—	2	1	no	—
92	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₅₉	—	2	1	no	—
94	C₄²×D₅₉	—	2	1	no	—
95	C₄²×D₅₉	C₂³	1	1	yes	characteristic
96	#14273661	C₂×C₄	1	1	yes	characteristic
97	#14273660	C₂×C₄	1	1	yes	characteristic
98	#14273658	C₂×C₄	1	1	yes	characteristic
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	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273652	C₂×C₄	1	1	yes	characteristic
110	#14273651	C₂×C₄	1	1	yes	characteristic
111	#14273650	C₂×C₄	1	1	yes	characteristic
112	#14273650	C₂×C₄	1	1	yes	characteristic
113	#14273648	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	—	2	1	no	—
116	(C₂×D₅₉)⋊C₈	—	2	1	no	—
117	#14273638	—	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	—	2	1	no	—
128	C₈×Dic₅₉	D₄	1	1	yes	characteristic
129	C₈×Dic₅₉	D₄	1	1	yes	characteristic
130	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₂²×C₈×C₅₉	—	2	1	no	—
132	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
134	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	—	2	1	no	—
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₉	—	2	1	no	—
141	#97×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅₉	—	2	1	no	—
148	C₂×C₂²⋊D₅₉	—	2	1	no	—
149	C₂²×Dic₅₉	—	2	1	no	—
150	C₂²×Dic₅₉	—	2	1	no	—
151	Q₈×D₅₉	—	2	2	no	—
152	Q₈×D₅₉	—	2	2	no	—
153	#11745687	—	2	2	no	—
154	#11745687	M₁₆	1	4	yes	—
155	C₂×C₄×D₅₉	—	2	1	no	—
156	C₂×C₄×D₅₉	—	2	1	no	—
157	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
160	C₂×Dic₁₁₈	—	2	1	no	—
161	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
163	SD₁₆×C₅₉	—	2	2	no	—
164	C₂×C₈×C₅₉	—	2	1	no	—
165	C₂×C₈×C₅₉	—	2	1	no	—
166	C₂×C₈×C₅₉	—	2	1	no	—
167	C₂×C₈×C₅₉	—	4	2	no	—
168	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₅₉	—	2	1	no	—
173	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²⋊C₄×C₅₉	—	2	1	no	—
176	C₄²×C₅₉	—	2	1	no	—
177	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
178	C₂²⋊Dic₅₉	—	2	1	no	—
179	#11745672	—	2	2	no	—
180	#11745670	—	2	2	no	—
181	(C₂×D₅₉)⋊C₄	—	2	1	no	—
182	C₄⋊Dic₅₉	—	2	1	no	—
183	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
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	Dic₅₉⋊C₄	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	C₄×Dic₅₉	—	2	1	no	—
195	C₄×Dic₅₉	—	2	1	no	—
196	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
198	C₄×Dic₅₉	#41	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	—	2	1	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	4	2	no	—
203	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
207	Dic₂₃₆	—	2	2	no	—
208	#11745659	—	2	2	no	—
209	#11745659	—	2	2	no	—
210	C₈×D₅₉	—	2	2	no	—
211	C₈×D₅₉	—	4	1	no	—
212	C₈×D₅₉	—	4	2	no	—
213	C₂³×C₅₉	—	2	1	no	—
214	C₂²×D₅₉	C₄×D₄	1	1	yes	characteristic
215	Q₈×C₅₉	—	2	1	no	—
216	Q₈×C₅₉	—	2	1	no	—
217	D₄×C₅₉	—	2	1	no	—
218	D₄×C₅₉	C₂×M₁₆	1	2	yes	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	1	no	—
224	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
227	C₂²⋊D₅₉	—	2	4	no	—
228	C₂×Dic₅₉	—	2	1	no	—
229	C₂×Dic₅₉	—	2	4	no	—
230	C₂×Dic₅₉	—	2	1	no	—
231	C₂×Dic₅₉	—	2	1	no	—
232	C₂×Dic₅₉	—	2	1	no	—
233	C₂×Dic₅₉	—	4	2	no	—
234	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
235	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
237	C₄×D₅₉	—	2	1	no	—
238	C₄×D₅₉	—	2	1	no	—
239	C₄×D₅₉	—	4	1	no	—
240	C₄×D₅₉	—	4	2	no	—
241	C₄×D₅₉	—	4	2	no	—
242	C₄×D₅₉	C₂×M₁₆	1	2	yes	—
243	C₄×D₅₉	#131	1	2	yes	—
244	Dic₁₁₈	—	2	1	no	—
245	Dic₁₁₈	—	2	1	no	—
246	Dic₁₁₈	—	2	1	no	—
247	Dic₁₁₈	—	4	2	no	—
248	Dic₁₁₈	C₂×M₁₆	1	2	yes	—
249	C₈×C₅₉	—	2	1	no	—
250	C₈×C₅₉	—	2	1	no	—
251	C₈×C₅₉	—	2	1	no	—
252	C₈×C₅₉	—	2	1	no	—
253	C₈×C₅₉	—	4	1	no	—
254	C₈×C₅₉	—	4	1	no	—
255	C₈×C₅₉	—	4	1	no	—
256	C₅₉⋊C₈	—	2	1	no	—
257	C₅₉⋊C₈	—	2	1	no	—
258	C₅₉⋊C₈	—	2	1	no	—
259	C₅₉⋊C₈	—	4	1	no	—
260	C₅₉⋊C₈	—	4	1	no	—
261	C₅₉⋊C₈	—	4	1	no	—
262	C₅₉⋊C₈	#137	1	2	yes	complemented
263	#17872	—	59	1	no	maximal, Sylow
264	C₂²×C₅₉	—	2	2	no	—
265	C₂²×C₅₉	—	4	1	no	—
266	C₂²×C₅₉	—	4	1	no	—
267	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
268	C₂×D₅₉	—	2	1	no	—
269	C₂×D₅₉	—	2	1	no	—
270	C₂×D₅₉	#435	1	2	yes	—
271	C₄×C₅₉	—	2	1	no	—
272	C₄×C₅₉	—	4	1	no	—
273	C₄×C₅₉	—	4	1	no	—
274	C₄×C₅₉	—	4	1	no	—
275	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
276	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
277	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
278	C₄×C₅₉	#575	1	1	yes	characteristic
279	Dic₅₉	—	2	2	no	—
280	Dic₅₉	—	2	1	no	—
281	Dic₅₉	—	2	1	no	—
282	Dic₅₉	—	4	1	no	—
283	Dic₅₉	—	4	1	no	—
284	Dic₅₉	—	4	1	no	—
285	Dic₅₉	#435	1	2	yes	—
286	C₈×#41	—	59	1	no	—
287	C₂×#446	—	59	1	no	—
288	C₄×#137	—	59	1	no	—
289	#1587	—	59	1	no	—
290	#1587	—	59	1	no	—
291	#1585	—	59	1	no	—
292	#1585	D₅₉	1	1	yes	characteristic, complemented
293	#1584	—	59	1	no	—
294	#1584	—	59	1	no	—
295	#1582	—	59	1	no	—
296	#1582	—	59	1	no	—
297	#1565	—	59	1	no	—
298	#1479	—	59	1	no	—
299	#1477	—	59	1	no	—
300	#1451	—	59	1	no	—
301	C₂×C₅₉	—	4	2	no	—
302	C₂×C₅₉	C₂×#435	1	1	yes	characteristic
303	C₂×C₅₉	C₄×#137	1	1	yes	characteristic
304	C₂×C₅₉	#2955	1	1	yes	characteristic
305	D₅₉	—	2	2	no	—
306	C₂×#137	—	59	1	no	—
307	C₄×#41	—	59	1	no	—
308	C₂×C₄×Q₈	—	59	1	no	—
309	#446	—	59	1	no	—
310	#446	—	59	1	no	—
311	#446	—	59	1	no	—
312	#446	—	118	1	no	—
313	#446	—	118	1	no	—
314	#446	C₂×D₅₉	1	1	yes	characteristic
315	C₈×Q₈	—	59	1	no	—
316	C₈×Q₈	—	59	1	no	—
317	#441	—	59	1	no	—
318	#441	—	59	1	no	—
319	#440	—	59	1	no	—
320	#440	—	59	1	no	—
321	C₄×Q₁₆	—	59	1	no	—
322	C₄×Q₁₆	—	59	1	no	—
323	C₄×SD₁₆	—	59	1	no	—
324	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
325	C₈×D₄	—	59	1	no	—
326	C₈×D₄	—	118	1	no	—
327	C₈×D₄	—	118	1	no	—
328	C₈×D₄	C₂×D₅₉	1	1	yes	characteristic
329	#431	—	59	1	no	—
330	#431	—	59	1	no	—
331	#431	—	118	1	no	—
332	#428	—	59	1	no	—
333	C₂×C₄⋊C₈	—	59	1	no	—
334	C₂×C₄⋊C₈	—	118	1	no	—
335	#419	—	59	1	no	—
336	#417	—	59	1	no	—
337	C₄×M₁₆	—	59	1	no	—
338	C₂×#97	—	118	1	no	—
339	C₂×C₄×C₈	—	59	1	no	—
340	C₂×C₄×C₈	—	118	1	no	—
341	#335	—	59	1	no	—
342	#335	C₂×D₅₉	1	1	yes	characteristic
343	#334	—	59	1	no	—
344	#334	—	59	1	no	—
345	Q₈⋊C₈	—	59	1	no	—
346	Q₈⋊C₈	—	59	1	no	—
347	Q₈⋊C₈	—	59	1	no	—
348	Q₈⋊C₈	—	59	1	no	—
349	Q₈⋊C₈	—	59	1	no	—
350	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
351	D₄⋊C₈	—	59	1	no	—
352	D₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
353	#322	—	59	1	no	—
354	#322	—	59	1	no	—
355	#322	—	59	1	no	—
356	#322	C₂×D₅₉	1	1	yes	characteristic
357	C₅₉	#17872	1	1	yes	characteristic, complemented, Sylow
358	C₂×#41	—	59	1	no	—
359	C₂²×Q₈	—	59	1	no	—
360	#137	—	118	4	no	—
361	C₂×Q₁₆	—	59	1	no	—
362	C₂×Q₁₆	—	59	1	no	—
363	C₂×SD₁₆	—	59	1	no	—
364	C₂×SD₁₆	C₄×D₅₉	1	1	yes	characteristic
365	C₂×M₁₆	—	59	1	no	—
366	C₂×M₁₆	—	59	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	59	1	no	—
369	C₂²×C₈	—	59	1	no	—
370	C₂²×C₈	—	118	1	no	—
371	C₂²×C₈	—	118	1	no	—
372	C₄×Q₈	—	59	1	no	—
373	C₄×Q₈	—	59	1	no	—
374	C₄×Q₈	—	59	1	no	—
375	C₄×Q₈	—	59	1	no	—
376	C₄×Q₈	—	59	1	no	—
377	C₄×Q₈	—	118	1	no	—
378	C₄×Q₈	—	118	1	no	—
379	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
380	C₄×D₄	—	59	1	no	—
381	C₄×D₄	—	118	1	no	—
382	C₄×D₄	—	118	1	no	—
383	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
384	#117	—	59	1	no	—
385	#117	—	118	1	no	—
386	C₂×C₄⋊C₄	—	59	1	no	—
387	C₂×C₄⋊C₄	—	118	1	no	—
388	C₂×C₄²	—	59	1	no	—
389	C₂×C₄²	—	118	1	no	—
390	C₂×C₄²	—	118	1	no	—
391	#107	—	59	1	no	—
392	#107	—	59	1	no	—
393	#106	—	59	1	no	—
394	#106	C₄×D₅₉	1	1	yes	characteristic
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	59	1	no	—
397	C₄⋊C₈	—	59	1	no	—
398	C₄⋊C₈	—	118	1	no	—
399	C₄⋊C₈	—	118	1	no	—
400	C₄⋊C₈	—	118	1	no	—
401	C₄⋊C₈	—	118	1	no	—
402	C₄⋊C₈	—	118	1	no	—
403	C₄⋊C₈	—	118	1	no	—
404	C₄⋊C₈	—	118	1	no	—
405	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
407	#103	—	59	1	no	—
408	#103	—	59	1	no	—
409	#103	—	59	1	no	—
410	#103	—	59	1	no	—
411	#103	—	59	1	no	—
412	#103	C₄×D₅₉	1	1	yes	characteristic
413	#102	—	59	1	no	—
414	#102	C₄×D₅₉	1	1	yes	characteristic
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	118	1	no	—
417	C₂²⋊C₈	—	118	1	no	—
418	C₂²⋊C₈	—	118	1	no	—
419	#97	—	2	1	no	—
420	#97	—	59	1	no	—
421	#97	—	59	1	no	—
422	#97	—	118	1	no	—
423	#97	—	118	1	no	—
424	#97	—	118	1	no	—
425	C₄×C₈	—	59	1	no	—
426	C₄×C₈	—	59	1	no	—
427	C₄×C₈	—	59	1	no	—
428	C₄×C₈	—	59	1	no	—
429	C₄×C₈	—	59	1	no	—
430	C₄×C₈	—	118	1	no	—
431	C₄×C₈	—	118	1	no	—
432	C₄×C₈	—	118	1	no	—
433	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
436	#41	—	59	4	no	—
437	#41	—	118	2	no	—
438	C₂×Q₈	—	59	1	no	—
439	C₂×Q₈	—	59	1	no	—
440	C₂×Q₈	—	118	1	no	—
441	C₂×Q₈	—	118	2	no	—
442	C₂×Q₈	—	118	2	no	—
443	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
444	C₂×D₄	—	118	1	no	—
445	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	59	1	no	—
448	C₂²×C₄	—	59	1	no	—
449	C₂²×C₄	—	59	1	no	—
450	C₂²×C₄	—	118	1	no	—
451	C₂²×C₄	—	118	1	no	—
452	C₂²×C₄	—	118	1	no	—
453	C₂²×C₄	—	118	1	no	—
454	Q₁₆	—	118	2	no	—
455	Q₁₆	—	118	2	no	—
456	SD₁₆	—	2	2	no	—
457	SD₁₆	—	118	2	no	—
458	M₁₆	—	118	2	no	—
459	M₁₆	—	118	2	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	4	2	no	—
464	C₂×C₈	—	59	1	no	—
465	C₂×C₈	—	59	1	no	—
466	C₂×C₈	—	59	1	no	—
467	C₂×C₈	—	59	1	no	—
468	C₂×C₈	—	118	2	no	—
469	C₂×C₈	—	118	1	no	—
470	C₂×C₈	—	118	1	no	—
471	C₂×C₈	—	118	1	no	—
472	C₂×C₈	—	236	1	no	—
473	C₂×C₈	—	236	2	no	—
474	C₂×C₈	—	236	2	no	—
475	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
477	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
478	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	59	1	no	—
481	C₄⋊C₄	—	59	1	no	—
482	C₄⋊C₄	—	118	1	no	—
483	C₄⋊C₄	—	118	1	no	—
484	C₄⋊C₄	—	118	1	no	—
485	C₄⋊C₄	—	118	1	no	—
486	C₄⋊C₄	—	118	1	no	—
487	C₄⋊C₄	—	118	1	no	—
488	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	118	1	no	—
492	C₂²⋊C₄	—	118	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	59	1	no	—
495	C₄²	—	59	1	no	—
496	C₄²	—	59	1	no	—
497	C₄²	—	118	1	no	—
498	C₄²	—	118	1	no	—
499	C₄²	—	118	1	no	—
500	C₄²	—	118	1	no	—
501	C₄²	—	118	1	no	—
502	C₄²	—	118	1	no	—
503	C₄²	C₂³×D₅₉	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	59	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	59	2	no	—
509	Q₈	—	118	1	no	—
510	Q₈	—	118	1	no	—
511	Q₈	—	118	1	no	—
512	Q₈	—	236	2	no	—
513	D₄	—	2	1	no	—
514	D₄	—	118	4	no	—
515	D₄	M₁₆×D₅₉	1	2	yes	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	59	1	no	—
522	C₂×C₄	—	59	2	no	—
523	C₂×C₄	—	59	2	no	—
524	C₂×C₄	—	59	1	no	—
525	C₂×C₄	—	59	1	no	—
526	C₂×C₄	—	118	4	no	—
527	C₂×C₄	—	118	1	no	—
528	C₂×C₄	—	118	1	no	—
529	C₂×C₄	—	118	1	no	—
530	C₂×C₄	—	118	1	no	—
531	C₂×C₄	—	118	1	no	—
532	C₂×C₄	—	118	1	no	—
533	C₂×C₄	—	236	1	no	—
534	C₂×C₄	—	236	2	no	—
535	C₂×C₄	—	236	2	no	—
536	C₂×C₄	—	236	2	no	—
537	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
539	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	59	2	no	—
548	C₈	—	118	1	no	—
549	C₈	—	118	1	no	—
550	C₈	—	118	1	no	—
551	C₈	—	236	1	no	—
552	C₈	—	236	1	no	—
553	C₈	—	236	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	59	2	no	—
558	C₂²	—	118	1	no	—
559	C₂²	—	118	1	no	—
560	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	59	2	no	—
566	C₄	—	118	1	no	—
567	C₄	—	118	1	no	—
568	C₄	—	118	2	no	—
569	C₄	—	236	1	no	—
570	C₄	—	236	1	no	—
571	C₄	—	236	1	no	—
572	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
573	C₄	#131×D₅₉	1	1	yes	characteristic
574	C₄	#137×D₅₉	1	1	yes	characteristic
575	C₄	#16838198	1	1	yes	characteristic
576	C₂	—	4	2	no	—
577	C₂	—	118	2	no	—
578	C₂	#435×D₅₉	1	1	yes	characteristic
579	C₂	#21432918	1	1	yes	characteristic
580	C₂	#21432994	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×#1585	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#11745687	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1585	D₅₉
hypocenter	C₅₉	#17872
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1585

Complements

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

N	H ≅ G/N	type
2. #446×D₅₉	C₂	semidirect
4. #21422969	C₂	semidirect
5. #21422965	C₂	semidirect
6. #21422953	C₂	semidirect
7. #21422949	C₂	semidirect
8. #21422945	C₂	semidirect
9. #21422933	C₂	semidirect
10. #21422929	C₂	semidirect
11. #21422847	C₂	semidirect
12. #21422489	C₂	semidirect
14. #21422384	C₂	semidirect
15. C₅₉×#1585	C₂	semidirect
262. C₅₉⋊C₈	#137	semidirect
292. #1585	D₅₉	semidirect
357. C₅₉	#17872	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11745687	2
#446×D₅₉	2
C₄×#14273756	2
#21422969	2
#21422965	2
#21422953	2
#21422949	2
#21422945	2
#21422933	2
#21422929	2
#21422847	2
#21422489	2
#21422480	2
#21422384	2
C₅₉×#1585	2
#17872	59