Subgroups — #28559828

Order 15104.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434168	C₂	1	1	yes	maximal, characteristic
2	#21433113	C₂	1	1	yes	maximal, characteristic
3	#21433039	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422997	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422985	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422973	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422966	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422938	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422914	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422902	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422568	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422481	C₂	1	1	yes	maximal, characteristic
14	#21422391	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1573	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837959	C₂²	1	1	yes	characteristic
17	C₄×#11745685	C₂²	1	1	yes	characteristic
18	#16837744	C₄	1	1	yes	characteristic
19	#16837744	C₄	1	1	yes	characteristic
20	#16837688	C₄	1	1	yes	characteristic
21	#16837683	C₄	1	1	yes	characteristic
22	#16837613	C₄	1	1	yes	characteristic
23	#16837608	C₄	1	1	yes	characteristic
24	#16837566	C₄	1	1	yes	characteristic
25	#16837566	C₄	1	1	yes	characteristic
26	#16837531	—	2	1	no	—
27	#16837531	—	2	1	no	—
28	#16837529	C₂²	1	1	yes	characteristic
29	#16837529	C₂²	1	1	yes	characteristic
30	#16837526	C₂²	1	1	yes	characteristic
31	#16837526	C₂²	1	1	yes	characteristic
32	#16837526	C₂²	1	1	yes	characteristic
33	#16837526	C₂²	1	1	yes	characteristic
34	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
35	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
36	C₄×#11745660	C₂²	1	1	yes	characteristic
37	C₄×#11745660	C₂²	1	1	yes	characteristic
38	#16837479	C₂²	1	1	yes	characteristic
39	#16837479	C₂²	1	1	yes	characteristic
40	#16837477	—	2	1	no	—
41	#16837477	—	2	1	no	—
42	#16837457	—	2	1	no	—
43	#16837455	C₂²	1	1	yes	characteristic
44	#16837428	—	2	1	no	—
45	#16837357	—	2	1	no	—
46	C₄×#11745664	C₂²	1	1	yes	characteristic
47	#16837354	—	2	1	no	—
48	#16837132	C₂²	1	1	yes	characteristic
49	#16837132	C₂²	1	1	yes	characteristic
50	#16837132	C₂²	1	1	yes	characteristic
51	#16837132	C₂²	1	1	yes	characteristic
52	#16837132	C₂²	1	1	yes	characteristic
53	#16837132	C₂²	1	1	yes	characteristic
54	#16837129	C₂²	1	1	yes	characteristic
55	#16837129	C₂²	1	1	yes	characteristic
56	#16837124	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic
58	#16837123	C₂²	1	1	yes	characteristic
59	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
60	C₅₉×#432	C₂²	1	1	yes	characteristic
61	C₅₉×#431	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×#335	C₂²	1	1	yes	characteristic
65	C₅₉×#334	C₂²	1	1	yes	characteristic
66	C₅₉×#334	C₂²	1	1	yes	characteristic
67	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745660	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745664	D₄	1	1	yes	characteristic
73	C₂×#11745664	D₄	1	1	yes	characteristic
74	C₂×#11745659	—	2	1	no	—
75	C₂×#11745659	—	2	1	no	—
76	#14273727	C₂×C₄	1	1	yes	characteristic
77	#14273727	C₂×C₄	1	1	yes	characteristic
78	#14273719	—	2	1	no	—
79	#14273706	—	2	1	no	—
80	#14273706	C₂×C₄	1	1	yes	characteristic
81	#14273706	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₁₈	—	2	1	no	—
83	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
86	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
87	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
89	C₄×C₂²⋊D₅₉	—	2	1	no	—
90	C₄×C₂²⋊D₅₉	—	2	1	no	—
91	#14273686	—	2	1	no	—
92	#14273686	C₂×C₄	1	1	yes	characteristic
93	#14273684	—	2	1	no	—
94	C₄²×D₅₉	—	2	1	no	—
95	#14273661	C₂×C₄	1	1	yes	characteristic
96	#14273661	C₂×C₄	1	1	yes	characteristic
97	#14273659	C₂×C₄	1	1	yes	characteristic
98	#14273659	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
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	—	2	1	no	—
106	#14273652	C₂×C₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273652	C₂×C₄	1	1	yes	characteristic
109	#14273652	C₂×C₄	1	1	yes	characteristic
110	#14273652	C₂×C₄	1	1	yes	characteristic
111	#14273652	C₂×C₄	1	1	yes	characteristic
112	#14273649	C₂×C₄	1	1	yes	characteristic
113	#14273649	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	D₄	1	1	yes	characteristic
118	#14273638	D₄	1	1	yes	characteristic
119	#14273637	—	2	1	no	—
120	#14273637	—	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	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	—	2	1	no	—
129	C₂²×C₈×C₅₉	—	2	1	no	—
130	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₅₉	—	2	1	no	—
132	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₅₉	—	2	1	no	—
139	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
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	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
147	C₂×C₂²⋊D₅₉	—	2	1	no	—
148	#11745685	—	2	2	no	—
149	#11745685	—	4	1	no	—
150	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₅₉	—	2	1	no	—
152	C₂×C₄×D₅₉	—	2	1	no	—
153	C₂×C₄×D₅₉	—	2	1	no	—
154	C₂×Dic₁₁₈	—	2	1	no	—
155	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	—	2	1	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	—	4	2	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	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₅₉	#41	1	1	yes	characteristic
170	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊Dic₅₉	—	2	1	no	—
172	C₂²⋊Dic₅₉	—	2	1	no	—
173	C₂²⋊Dic₅₉	—	2	1	no	—
174	(C₂×D₅₉)⋊C₄	—	2	1	no	—
175	(C₂×D₅₉)⋊C₄	—	2	1	no	—
176	C₄⋊Dic₅₉	—	2	1	no	—
177	C₄⋊Dic₅₉	—	2	1	no	—
178	C₄⋊Dic₅₉	—	2	1	no	—
179	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	#11745664	—	2	2	no	—
195	#11745664	—	4	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂×D₄	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	Dic₂₃₆	—	2	2	no	—
204	#11745660	—	4	1	no	—
205	#11745660	—	4	1	no	—
206	#11745659	—	4	2	no	—
207	#11745659	—	4	2	no	—
208	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
209	C₂²×D₅₉	—	2	1	no	—
210	C₂×C₄×C₅₉	—	2	1	no	—
211	C₂×C₄×C₅₉	—	2	1	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	4	1	no	—
215	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₅₉	—	4	2	no	—
222	C₂×Dic₅₉	—	2	1	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	—	2	1	no	—
228	C₂×Dic₅₉	—	2	1	no	—
229	D₂₃₆	—	2	1	no	—
230	D₂₃₆	—	2	1	no	—
231	C₄×D₅₉	—	4	2	no	—
232	C₄×D₅₉	—	4	1	no	—
233	C₄×D₅₉	—	4	1	no	—
234	C₄×D₅₉	—	8	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	2	1	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	—	2	1	no	—
240	Dic₁₁₈	—	8	1	no	—
241	Dic₁₁₈	#131	1	2	yes	—
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	C₈×C₅₉	—	4	1	no	—
249	C₈×C₅₉	—	4	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	C₅₉⋊C₈	#137	1	2	yes	—
256	#18013	—	59	1	no	maximal, Sylow
257	C₂²×C₅₉	—	2	1	no	—
258	C₂²×C₅₉	—	2	1	no	—
259	C₂²×C₅₉	—	2	1	no	—
260	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
261	C₂×D₅₉	—	4	1	no	—
262	C₂×D₅₉	—	4	1	no	—
263	C₂×D₅₉	—	4	1	no	—
264	C₄×C₅₉	—	2	1	no	—
265	C₄×C₅₉	—	2	1	no	—
266	C₄×C₅₉	—	2	1	no	—
267	C₄×C₅₉	—	2	1	no	—
268	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
269	C₄×C₅₉	#568	1	1	yes	characteristic
270	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
271	C₄×C₅₉	#575	1	1	yes	characteristic
272	Dic₅₉	—	2	2	no	—
273	Dic₅₉	—	4	1	no	—
274	Dic₅₉	—	4	1	no	—
275	Dic₅₉	—	4	1	no	—
276	Dic₅₉	—	4	1	no	—
277	Dic₅₉	—	4	1	no	—
278	Dic₅₉	—	4	1	no	—
279	#3107	—	59	1	no	—
280	#2971	—	59	1	no	—
281	#2962	—	59	1	no	—
282	#1592	—	59	1	no	—
283	#1590	—	59	1	no	—
284	#1588	—	59	1	no	—
285	#1587	—	59	1	no	—
286	#1584	—	59	1	no	—
287	#1583	—	59	1	no	—
288	#1579	—	59	1	no	—
289	C₈×Q₁₆	—	59	1	no	—
290	#1573	D₅₉	1	1	yes	characteristic, complemented
291	#1497	—	59	1	no	—
292	#1477	—	59	1	no	—
293	#1453	—	59	1	no	—
294	C₂×C₅₉	—	4	1	no	—
295	C₂×C₅₉	#2933	1	1	yes	characteristic
296	C₂×C₅₉	C₄×#137	1	1	yes	characteristic
297	C₂×C₅₉	#2957	1	1	yes	characteristic
298	D₅₉	—	8	1	no	—
299	#533	—	59	1	no	—
300	C₄×#41	—	59	1	no	—
301	#485	—	59	1	no	—
302	#485	—	59	1	no	—
303	#475	—	59	1	no	—
304	#474	—	59	1	no	—
305	#462	—	59	1	no	—
306	#461	—	59	1	no	—
307	#452	—	59	1	no	—
308	#452	—	59	1	no	—
309	#446	—	59	1	no	—
310	#446	—	59	1	no	—
311	#446	—	118	1	no	—
312	#446	—	118	1	no	—
313	C₈×Q₈	—	59	1	no	—
314	C₈×Q₈	—	59	1	no	—
315	C₈×Q₈	—	59	1	no	—
316	C₈×Q₈	—	59	1	no	—
317	C₄×Q₁₆	—	59	1	no	—
318	C₄×Q₁₆	—	59	1	no	—
319	C₄×SD₁₆	—	59	1	no	—
320	C₄×SD₁₆	—	59	1	no	—
321	#436	—	59	1	no	—
322	#436	—	59	1	no	—
323	#436	—	118	1	no	—
324	#436	—	118	1	no	—
325	#432	—	118	1	no	—
326	#432	C₂×D₅₉	1	1	yes	characteristic
327	#431	—	59	1	no	—
328	#431	C₂×D₅₉	1	1	yes	characteristic
329	#424	—	118	1	no	—
330	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
331	#405	—	118	1	no	—
332	C₄×M₁₆	—	59	1	no	—
333	C₄×M₁₆	—	118	1	no	—
334	#335	C₂×D₅₉	1	1	yes	characteristic
335	#335	C₂×D₅₉	1	1	yes	characteristic
336	#334	C₂×D₅₉	1	1	yes	characteristic
337	#334	C₂×D₅₉	1	1	yes	characteristic
338	Q₈⋊C₈	—	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	D₄⋊C₈	—	59	1	no	—
345	D₄⋊C₈	—	59	1	no	—
346	#322	—	59	1	no	—
347	#322	—	59	1	no	—
348	#322	—	59	1	no	—
349	C₈²	—	59	1	no	—
350	C₅₉	#18013	1	1	yes	characteristic, complemented, Sylow
351	C₂×#41	—	59	1	no	—
352	C₂×Q₁₆	—	59	1	no	—
353	C₂×Q₁₆	—	59	1	no	—
354	C₂×SD₁₆	—	59	1	no	—
355	C₂×SD₁₆	—	59	1	no	—
356	C₂×M₁₆	—	59	1	no	—
357	C₂×M₁₆	—	59	1	no	—
358	C₂×M₁₆	—	118	1	no	—
359	C₂×M₁₆	—	118	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₄⋊Q₈	—	59	1	no	—
362	C₄⋊Q₈	—	59	1	no	—
363	#125	—	118	1	no	—
364	C₂²⋊Q₈	—	59	1	no	—
365	C₂²⋊Q₈	—	59	1	no	—
366	C₂²⋊Q₈	—	118	1	no	—
367	C₄×Q₈	—	59	1	no	—
368	C₄×Q₈	—	59	1	no	—
369	C₄×Q₈	—	59	1	no	—
370	C₄×Q₈	—	59	1	no	—
371	C₄×Q₈	—	118	1	no	—
372	C₄×D₄	—	59	1	no	—
373	C₄×D₄	—	59	1	no	—
374	C₄×D₄	—	118	1	no	—
375	C₄×D₄	—	118	1	no	—
376	#117	—	59	1	no	—
377	#117	—	118	1	no	—
378	#117	—	118	1	no	—
379	C₂×C₄²	—	118	1	no	—
380	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
381	#107	—	59	1	no	—
382	#107	—	59	1	no	—
383	#106	—	59	1	no	—
384	#106	—	59	1	no	—
385	C₄⋊C₈	—	2	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	—	118	1	no	—
392	C₄⋊C₈	—	118	1	no	—
393	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
394	C₄⋊C₈	C₄×D₅₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
397	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
399	#103	—	59	1	no	—
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	#102	—	59	1	no	—
406	#102	—	59	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	118	1	no	—
409	C₂²⋊C₈	—	118	1	no	—
410	C₂²⋊C₈	—	118	1	no	—
411	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
412	C₂²⋊C₈	C₄×D₅₉	1	1	yes	characteristic
413	#97	—	2	1	no	—
414	#97	—	59	1	no	—
415	#97	—	59	1	no	—
416	#97	—	118	1	no	—
417	#97	—	118	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	#41	—	118	2	no	—
429	#41	—	236	1	no	—
430	C₂×Q₈	—	59	1	no	—
431	C₂×Q₈	—	59	1	no	—
432	C₂×Q₈	—	59	1	no	—
433	C₂×Q₈	—	118	1	no	—
434	C₂×D₄	—	59	1	no	—
435	C₂×D₄	—	118	1	no	—
436	C₂²×C₄	—	118	1	no	—
437	C₂²×C₄	—	118	1	no	—
438	C₂²×C₄	—	118	1	no	—
439	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
440	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
441	C₂²×C₄	#11745689	1	1	yes	characteristic
442	Q₁₆	—	118	2	no	—
443	Q₁₆	—	118	2	no	—
444	SD₁₆	—	236	1	no	—
445	SD₁₆	—	236	1	no	—
446	M₁₆	—	118	2	no	—
447	M₁₆	—	236	2	no	—
448	M₁₆	—	236	2	no	—
449	M₁₆	—	236	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	4	2	no	—
455	C₂×C₈	—	59	1	no	—
456	C₂×C₈	—	59	1	no	—
457	C₂×C₈	—	59	1	no	—
458	C₂×C₈	—	59	1	no	—
459	C₂×C₈	—	118	1	no	—
460	C₂×C₈	—	118	1	no	—
461	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
462	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
463	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
465	C₄⋊C₄	—	59	1	no	—
466	C₄⋊C₄	—	59	1	no	—
467	C₄⋊C₄	—	59	1	no	—
468	C₄⋊C₄	—	59	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	—	118	1	no	—
475	C₄⋊C₄	—	118	1	no	—
476	C₄⋊C₄	—	118	1	no	—
477	C₄⋊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	—	118	1	no	—
484	C₄²	—	118	1	no	—
485	C₄²	—	118	1	no	—
486	C₄²	—	118	1	no	—
487	C₄²	—	118	1	no	—
488	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
489	C₄²	D₄×D₅₉	1	1	yes	characteristic
490	C₄²	#11745689	1	1	yes	characteristic
491	C₄²	C₂³×D₅₉	1	1	yes	characteristic
492	C₂³	—	118	1	no	—
493	C₂³	#14273689	1	1	yes	characteristic
494	Q₈	—	59	2	no	—
495	Q₈	—	118	1	no	—
496	Q₈	—	118	1	no	—
497	Q₈	—	118	1	no	—
498	Q₈	—	118	1	no	—
499	Q₈	—	118	1	no	—
500	Q₈	—	472	1	no	—
501	D₄	—	118	1	no	—
502	D₄	—	118	1	no	—
503	D₄	—	236	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	118	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	—	472	1	no	—
517	C₂×C₄	—	236	2	no	—
518	C₂×C₄	—	236	1	no	—
519	C₂×C₄	—	236	1	no	—
520	C₂×C₄	#14273689	1	1	yes	characteristic
521	C₂×C₄	#14273689	1	1	yes	characteristic
522	C₂×C₄	#14273689	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
524	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
525	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	59	2	no	—
535	C₈	—	118	1	no	—
536	C₈	—	118	1	no	—
537	C₈	—	118	1	no	—
538	C₈	—	236	1	no	—
539	C₈	—	236	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	236	1	no	—
544	C₂²	—	236	1	no	—
545	C₂²	—	236	1	no	—
546	C₂²	C₂×#14273689	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	118	2	no	—
552	C₄	—	236	1	no	—
553	C₄	—	236	1	no	—
554	C₄	—	236	1	no	—
555	C₄	—	236	1	no	—
556	C₄	—	236	1	no	—
557	C₄	—	236	1	no	—
558	C₄	#131×D₅₉	1	1	yes	characteristic
559	C₄	#16838167	1	1	yes	characteristic
560	C₄	#137×D₅₉	1	1	yes	characteristic
561	C₄	#16838198	1	1	yes	characteristic
562	C₂	—	4	1	no	—
563	C₂	—	472	1	no	—
564	C₂	#21432820	1	1	yes	characteristic
565	C₂	#21432914	1	1	yes	characteristic
566	C₂	#21433012	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×#1573	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#11745685	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1573	D₅₉
hypocenter	C₅₉	#18013
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
3. #21433039	C₂	semidirect
4. #21422997	C₂	semidirect
5. #21422985	C₂	semidirect
6. #21422973	C₂	semidirect
7. #21422966	C₂	semidirect
8. #21422945	C₂	semidirect
9. #21422938	C₂	semidirect
10. #21422914	C₂	semidirect
11. #21422902	C₂	semidirect
12. #21422568	C₂	semidirect
14. #21422391	C₂	semidirect
15. C₅₉×#1573	C₂	semidirect
290. #1573	D₅₉	semidirect
350. C₅₉	#18013	semidirect

Maximal subgroups

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

subgroup	index
#21434168	2
#21433113	2
#21433039	2
#21422997	2
#21422985	2
#21422973	2
#21422966	2
#21422945	2
#21422938	2
#21422914	2
#21422902	2
#21422568	2
#21422481	2
#21422391	2
C₅₉×#1573	2
#18013	59