Subgroups — #28596882

Order 15104.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434439	C₂	1	1	yes	maximal, characteristic
2	#21433034	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432812	C₂	1	1	yes	maximal, characteristic
4	#21425071	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424922	C₂	1	1	yes	maximal, characteristic
6	#21424809	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424805	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424801	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424797	C₂	1	1	yes	maximal, characteristic, complemented
10	#21424235	C₂	1	1	yes	maximal, characteristic, complemented
11	#21423942	C₂	1	1	yes	maximal, characteristic, complemented
12	#21423938	C₂	1	1	yes	maximal, characteristic, complemented
13	#21423933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14273637	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273733	C₂²	1	1	yes	characteristic
17	#16837955	C₂²	1	1	yes	characteristic
18	#16837948	C₂²	1	1	yes	characteristic
19	#16837769	C₄	1	2	yes	complemented
20	#16837765	C₄	1	2	yes	complemented
21	#16837763	C₄	1	2	yes	complemented
22	#16837760	C₄	1	2	yes	complemented
23	#16837532	—	2	2	no	—
24	#16837530	—	2	2	no	—
25	#16837473	—	2	2	no	—
26	#16837471	—	2	2	no	—
27	#16837430	C₂²	1	1	yes	characteristic
28	#16837429	C₂²	1	1	yes	characteristic
29	#16837425	C₂²	1	1	yes	characteristic
30	#16837425	C₂²	1	1	yes	characteristic
31	C₂×#14273655	C₂²	1	1	yes	characteristic
32	C₂×#14273654	C₂²	1	1	yes	characteristic
33	C₂×#14273653	C₂²	1	1	yes	characteristic
34	#16837399	C₂²	1	1	yes	characteristic
35	#16837398	C₂²	1	1	yes	characteristic
36	#16837396	C₂²	1	1	yes	characteristic
37	#16837370	C₂²	1	1	yes	characteristic
38	#16837369	C₂²	1	1	yes	characteristic
39	#16837357	C₂²	1	1	yes	characteristic
40	C₂×#14273637	C₂²	1	1	yes	characteristic
41	C₂×#14273637	C₂²	1	1	yes	characteristic
42	C₂×#14273637	C₂²	1	1	yes	characteristic
43	C₂×#14273637	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
45	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
46	#16837167	C₂²	1	1	yes	characteristic
47	#16837166	C₂²	1	1	yes	characteristic
48	#16837166	C₂²	1	1	yes	characteristic
49	#16837163	C₂²	1	1	yes	characteristic
50	#16837162	C₂²	1	1	yes	characteristic
51	#16837161	C₂²	1	1	yes	characteristic
52	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
53	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#416	C₂²	1	1	yes	characteristic
55	C₅₉×#405	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
57	C₅₉×#341	C₂²	1	1	yes	characteristic
58	C₅₉×#339	C₂²	1	1	yes	characteristic
59	C₂×#11745685	C₂³	1	1	yes	characteristic
60	#14273733	—	2	2	no	—
61	#14273733	—	2	2	no	—
62	C₂×#11745664	C₂³	1	1	yes	characteristic
63	C₂×#11745664	C₂³	1	1	yes	characteristic
64	C₂×#11745659	—	2	1	no	—
65	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₅₉	—	2	1	no	—
68	#14273726	C₂×C₄	1	2	yes	—
69	#14273725	C₂×C₄	1	1	yes	characteristic
70	#14273723	C₂×C₄	1	1	yes	characteristic
71	#14273718	C₂×C₄	1	2	yes	—
72	#14273716	C₂×C₄	1	1	yes	characteristic
73	#14273714	C₂×C₄	1	1	yes	characteristic
74	#14273704	—	2	2	no	—
75	#14273699	—	2	2	no	—
76	C₄×Dic₁₁₈	—	2	2	no	—
77	C₄×C₂²⋊D₅₉	—	2	2	no	—
78	#14273686	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₅₉	—	2	2	no	—
80	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
82	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
83	Dic₅₉⋊C₈	—	2	2	no	—
84	Dic₅₉⋊C₈	—	2	2	no	—
85	Dic₅₉⋊C₈	—	2	2	no	—
86	#14273655	—	2	2	no	—
87	#14273654	—	2	2	no	—
88	#14273653	—	2	2	no	—
89	#14273652	C₂×C₄	1	2	yes	—
90	#14273651	C₂×C₄	1	2	yes	—
91	#14273650	C₂×C₄	1	2	yes	—
92	#14273649	C₂×C₄	1	2	yes	—
93	#14273648	C₂×C₄	1	2	yes	—
94	#14273647	C₂×C₄	1	2	yes	—
95	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
96	(C₂×D₅₉)⋊C₈	—	2	2	no	—
97	#14273637	—	2	1	no	—
98	#14273637	—	2	2	no	—
99	#14273637	—	2	2	no	—
100	#14273637	C₂×C₄	1	2	yes	—
101	#14273637	C₂×C₄	1	2	yes	—
102	#14273637	D₄	1	2	yes	—
103	#14273637	D₄	1	2	yes	—
104	C₄×C₅₉⋊C₈	—	2	2	no	—
105	C₈×Dic₅₉	—	2	1	no	—
106	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
107	#131×C₅₉	—	2	2	no	—
108	#131×C₅₉	—	2	2	no	—
109	C₂×M₁₆×C₅₉	—	2	1	no	—
110	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₅₉	—	2	1	no	—
113	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
115	#117×C₅₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
117	#104×C₅₉	—	2	2	no	—
118	#103×C₅₉	C₂×C₄	1	2	yes	—
119	#102×C₅₉	C₂×C₄	1	2	yes	—
120	#97×C₅₉	—	2	1	no	—
121	C₄×C₈×C₅₉	—	2	1	no	—
122	C₄×C₈×C₅₉	—	2	2	no	—
123	#41×C₅₉	—	2	1	no	—
124	#41×C₅₉	—	2	1	no	—
125	#41×C₅₉	—	2	1	no	—
126	#41×C₅₉	—	2	1	no	—
127	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₅₉	—	2	1	no	—
129	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	—	2	1	no	—
131	C₂²×C₄×C₅₉	—	2	1	no	—
132	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₅₉	—	2	1	no	—
134	C₂×C₂²⋊D₅₉	—	2	2	no	—
135	C₂²×Dic₅₉	—	2	1	no	—
136	C₂²×Dic₅₉	#41	1	2	yes	—
137	#11745685	—	2	1	no	—
138	#11745685	—	2	1	no	—
139	#11745685	—	2	1	no	—
140	#11745685	—	2	1	no	—
141	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₅₉	—	2	1	no	—
143	C₂×Dic₁₁₈	—	2	2	no	—
144	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
145	M₁₆×C₅₉	—	2	1	no	—
146	M₁₆×C₅₉	—	2	1	no	—
147	M₁₆×C₅₉	—	2	1	no	—
148	M₁₆×C₅₉	—	2	1	no	—
149	M₁₆×C₅₉	—	4	2	no	—
150	C₂×C₈×C₅₉	—	2	1	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	1	no	—
154	C₂×C₈×C₅₉	—	4	2	no	—
155	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	#41	1	2	yes	—
159	C₂×C₈×C₅₉	#41	1	2	yes	—
160	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
161	C₂²⋊C₄×C₅₉	—	2	1	no	—
162	C₄²×C₅₉	—	2	1	no	—
163	C₄²×C₅₉	—	2	1	no	—
164	C₄²×C₅₉	#41	1	2	yes	—
165	C₂²⋊Dic₅₉	—	2	1	no	—
166	C₂²⋊Dic₅₉	—	2	2	no	—
167	(C₂×D₅₉)⋊C₄	—	2	2	no	—
168	C₄⋊Dic₅₉	—	2	2	no	—
169	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
170	Dic₅₉⋊C₄	—	2	2	no	—
171	Dic₅₉⋊C₄	—	2	2	no	—
172	Dic₅₉⋊C₄	—	2	2	no	—
173	C₄×Dic₅₉	—	2	1	no	—
174	C₄×Dic₅₉	—	2	1	no	—
175	C₄×Dic₅₉	—	4	4	no	—
176	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
178	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
179	C₄×Dic₅₉	#41	1	2	yes	—
180	#11745664	—	2	1	no	—
181	#11745664	—	2	1	no	—
182	#11745664	—	2	1	no	—
183	#11745664	—	2	1	no	—
184	C₂×C₅₉⋊C₈	—	2	1	no	—
185	C₂×C₅₉⋊C₈	—	2	1	no	—
186	C₂×C₅₉⋊C₈	—	2	1	no	—
187	C₂×C₅₉⋊C₈	—	2	1	no	—
188	C₂×C₅₉⋊C₈	—	2	1	no	—
189	C₂×C₅₉⋊C₈	—	2	1	no	—
190	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
191	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
192	#11745659	—	4	2	no	—
193	C₈×D₅₉	—	4	2	no	—
194	C₂³×C₅₉	—	2	1	no	—
195	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
196	C₂²×D₅₉	—	2	1	no	—
197	Q₈×C₅₉	—	2	1	no	—
198	Q₈×C₅₉	—	2	1	no	—
199	D₄×C₅₉	—	2	1	no	—
200	D₄×C₅₉	—	2	1	no	—
201	D₄×C₅₉	—	4	1	no	—
202	D₄×C₅₉	—	4	1	no	—
203	C₂×C₄×C₅₉	—	2	4	no	—
204	C₂×C₄×C₅₉	—	2	2	no	—
205	C₂×C₄×C₅₉	—	2	2	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	4	1	no	—
208	C₂×C₄×C₅₉	—	4	1	no	—
209	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₅₉	—	4	1	no	—
216	C₂²⋊D₅₉	—	4	1	no	—
217	C₂²⋊D₅₉	—	8	2	no	—
218	C₂×Dic₅₉	—	2	2	no	—
219	C₂×Dic₅₉	—	2	1	no	—
220	C₂×Dic₅₉	—	2	2	no	—
221	C₂×Dic₅₉	—	4	2	no	—
222	C₂×Dic₅₉	—	4	2	no	—
223	C₂×Dic₅₉	C₄×D₄	1	2	yes	—
224	C₂×Dic₅₉	C₄×D₄	1	2	yes	—
225	D₂₃₆	—	2	1	no	—
226	D₂₃₆	—	2	1	no	—
227	C₄×D₅₉	—	4	1	no	—
228	C₄×D₅₉	—	4	1	no	—
229	Dic₁₁₈	—	2	1	no	—
230	Dic₁₁₈	—	2	1	no	—
231	Dic₁₁₈	—	8	2	no	—
232	C₈×C₅₉	—	2	2	no	—
233	C₈×C₅₉	—	4	1	no	—
234	C₈×C₅₉	—	4	1	no	—
235	C₈×C₅₉	#124	1	2	yes	—
236	C₈×C₅₉	#124	1	2	yes	—
237	C₅₉⋊C₈	—	2	2	no	—
238	C₅₉⋊C₈	—	2	2	no	—
239	C₅₉⋊C₈	—	4	1	no	—
240	C₅₉⋊C₈	—	4	1	no	—
241	#21662	—	59	1	no	maximal, Sylow
242	C₂²×C₅₉	—	2	2	no	—
243	C₂²×C₅₉	—	4	2	no	—
244	C₂²×C₅₉	—	4	1	no	—
245	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₅₉	#529	1	1	yes	characteristic
247	C₂²×C₅₉	#529	1	1	yes	characteristic
248	C₂×D₅₉	—	4	2	no	—
249	C₂×D₅₉	—	4	1	no	—
250	C₄×C₅₉	—	2	4	no	—
251	C₄×C₅₉	—	4	2	no	—
252	C₄×C₅₉	—	4	1	no	—
253	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
254	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
255	C₄×C₅₉	C₂×#124	1	1	yes	characteristic
256	C₄×C₅₉	#532	1	1	yes	characteristic
257	Dic₅₉	—	2	2	no	—
258	Dic₅₉	—	2	2	no	—
259	Dic₅₉	—	4	2	no	—
260	Dic₅₉	—	4	2	no	—
261	Dic₅₉	—	4	1	no	—
262	#3135	—	59	1	no	—
263	#2961	—	59	1	no	—
264	#2932	—	59	1	no	—
265	#1994	—	59	1	no	—
266	#1962	—	59	1	no	—
267	#1938	—	59	1	no	—
268	#1938	—	59	1	no	—
269	#1937	—	59	1	no	—
270	#1937	—	59	1	no	—
271	#1838	—	59	1	no	—
272	#1765	—	59	1	no	—
273	#1765	—	59	1	no	—
274	#1764	—	59	1	no	—
275	#1764	D₅₉	1	1	yes	characteristic, complemented
276	C₄×#97	—	59	1	no	—
277	C₂×C₅₉	—	2	1	no	—
278	C₂×C₅₉	—	2	1	no	—
279	C₂×C₅₉	—	8	1	no	—
280	C₂×C₅₉	C₄×#124	1	1	yes	characteristic
281	C₂×C₅₉	#2956	1	2	yes	—
282	D₅₉	—	8	1	no	—
283	C₂×#131	—	59	1	no	—
284	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
285	#533	—	59	1	no	—
286	#532	—	59	1	no	—
287	#491	—	59	2	no	—
288	#490	—	59	2	no	—
289	#489	—	59	2	no	—
290	#489	—	59	2	no	—
291	#446	—	118	2	no	—
292	#446	—	118	2	no	—
293	#435	—	118	2	no	—
294	#435	—	118	2	no	—
295	#424	—	59	1	no	—
296	#424	—	59	1	no	—
297	#423	—	59	1	no	—
298	#423	—	59	1	no	—
299	C₂×#104	—	59	1	no	—
300	C₂×#104	—	59	1	no	—
301	C₂×#104	—	59	1	no	—
302	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
303	#416	—	59	1	no	—
304	#416	—	59	1	no	—
305	#416	—	59	1	no	—
306	#416	C₂×D₅₉	1	1	yes	characteristic
307	#408	—	59	1	no	—
308	#408	—	59	1	no	—
309	#405	—	59	1	no	—
310	#405	C₂×D₅₉	1	1	yes	characteristic
311	C₂×#97	—	59	1	no	—
312	C₂×#97	—	59	1	no	—
313	C₂×#97	—	59	1	no	—
314	C₂×#97	—	59	1	no	—
315	C₂×C₄×C₈	—	59	1	no	—
316	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
317	C₄³	—	59	1	no	—
318	#341	—	59	1	no	—
319	#341	—	59	1	no	—
320	#341	—	59	1	no	—
321	#341	C₂×D₅₉	1	1	yes	characteristic
322	#339	—	59	1	no	—
323	#339	—	59	1	no	—
324	#339	—	59	1	no	—
325	#339	C₂×D₅₉	1	1	yes	characteristic
326	C₅₉	#21662	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	59	1	no	—
328	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
329	#131	—	2	2	no	—
330	#131	—	2	2	no	—
331	#131	—	118	2	no	—
332	#131	—	118	2	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	59	1	no	—
335	C₂×M₁₆	—	59	1	no	—
336	C₂×M₁₆	—	118	1	no	—
337	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	59	1	no	—
341	C₂²×C₈	—	59	1	no	—
342	C₂²×C₈	—	118	1	no	—
343	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
345	C₄⋊Q₈	—	59	2	no	—
346	C₄⋊Q₈	—	59	1	no	—
347	#127	—	59	1	no	—
348	#125	—	59	2	no	—
349	#124	—	59	1	no	—
350	#124	—	59	1	no	—
351	C₂²⋊Q₈	—	118	2	no	—
352	#121	—	118	2	no	—
353	C₄×Q₈	—	118	2	no	—
354	C₄×D₄	—	118	2	no	—
355	#117	—	59	1	no	—
356	#117	C₂²×D₅₉	1	1	yes	characteristic
357	C₂×C₄²	—	59	1	no	—
358	C₂×C₄²	—	59	1	no	—
359	C₂×C₄²	—	118	2	no	—
360	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
361	C₄⋊C₈	—	118	2	no	—
362	C₄⋊C₈	—	118	2	no	—
363	C₄⋊C₈	—	118	2	no	—
364	C₄⋊C₈	—	118	2	no	—
365	#104	—	2	2	no	—
366	#104	—	118	2	no	—
367	#104	—	118	2	no	—
368	#104	—	118	2	no	—
369	#103	—	59	2	no	—
370	#103	—	59	2	no	—
371	#103	—	59	2	no	—
372	#103	C₄×D₅₉	1	2	yes	—
373	#102	—	59	2	no	—
374	#102	—	59	2	no	—
375	#102	—	59	2	no	—
376	#102	C₄×D₅₉	1	2	yes	—
377	C₂²⋊C₈	—	118	2	no	—
378	C₂²⋊C₈	—	118	2	no	—
379	#97	—	2	1	no	—
380	#97	—	59	2	no	—
381	#97	—	59	2	no	—
382	#97	—	59	2	no	—
383	#97	—	59	2	no	—
384	#97	—	118	2	no	—
385	#97	—	118	2	no	—
386	#97	—	118	1	no	—
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	—	2	2	no	—
389	C₄×C₈	—	118	1	no	—
390	C₄×C₈	—	118	2	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	118	1	no	—
396	#41	—	118	1	no	—
397	#41	—	118	1	no	—
398	#41	—	118	1	no	—
399	C₂×Q₈	—	59	1	no	—
400	C₂×Q₈	—	118	2	no	—
401	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	59	1	no	—
404	C₂×D₄	—	118	2	no	—
405	C₂×D₄	—	118	1	no	—
406	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	59	2	no	—
410	C₂²×C₄	—	118	1	no	—
411	C₂²×C₄	—	118	1	no	—
412	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
413	M₁₆	—	2	1	no	—
414	M₁₆	—	2	1	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	4	2	no	—
418	M₁₆	—	118	1	no	—
419	M₁₆	—	118	1	no	—
420	M₁₆	—	118	1	no	—
421	M₁₆	—	118	1	no	—
422	M₁₆	—	236	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	4	2	no	—
428	C₂×C₈	—	59	2	no	—
429	C₂×C₈	—	59	2	no	—
430	C₂×C₈	—	118	1	no	—
431	C₂×C₈	—	118	1	no	—
432	C₂×C₈	—	118	1	no	—
433	C₂×C₈	—	118	1	no	—
434	C₂×C₈	—	118	1	no	—
435	C₂×C₈	—	118	1	no	—
436	C₂×C₈	—	236	2	no	—
437	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
438	C₂×C₈	#11745685	1	2	yes	—
439	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
440	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
441	C₂×C₈	#11745687	1	2	yes	—
442	C₄⋊C₄	—	59	2	no	—
443	C₄⋊C₄	—	118	2	no	—
444	C₄⋊C₄	—	118	2	no	—
445	C₄⋊C₄	—	118	2	no	—
446	C₄⋊C₄	—	118	2	no	—
447	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	118	2	no	—
450	C₂²⋊C₄	—	118	2	no	—
451	C₂²⋊C₄	—	118	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	59	1	no	—
455	C₄²	—	59	1	no	—
456	C₄²	—	59	2	no	—
457	C₄²	—	59	2	no	—
458	C₄²	—	118	1	no	—
459	C₄²	—	118	1	no	—
460	C₄²	—	236	4	no	—
461	C₄²	#11745685	1	2	yes	—
462	C₂³	—	2	1	no	—
463	C₂³	—	118	1	no	—
464	C₂³	#41×D₅₉	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	118	1	no	—
468	Q₈	—	118	1	no	—
469	Q₈	—	472	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	118	1	no	—
475	D₄	—	118	1	no	—
476	D₄	—	472	2	no	—
477	D₄	—	236	1	no	—
478	D₄	—	236	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	59	2	no	—
486	C₂×C₄	—	59	2	no	—
487	C₂×C₄	—	118	2	no	—
488	C₂×C₄	—	118	2	no	—
489	C₂×C₄	—	118	1	no	—
490	C₂×C₄	—	236	2	no	—
491	C₂×C₄	—	236	2	no	—
492	C₂×C₄	—	236	1	no	—
493	C₂×C₄	—	236	1	no	—
494	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
496	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
497	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
498	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
499	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	—	118	2	no	—
504	C₈	—	118	2	no	—
505	C₈	—	236	1	no	—
506	C₈	—	236	1	no	—
507	C₈	#14273713	1	2	yes	—
508	C₈	#14273713	1	2	yes	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	236	2	no	—
513	C₂²	—	236	1	no	—
514	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
515	C₂²	#16837930	1	1	yes	characteristic
516	C₂²	#16837932	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	118	2	no	—
521	C₄	—	118	2	no	—
522	C₄	—	236	2	no	—
523	C₄	—	236	2	no	—
524	C₄	—	236	1	no	—
525	C₄	C₄×#11745687	1	1	yes	characteristic
526	C₄	C₄×#11745685	1	1	yes	characteristic
527	C₄	C₂×#14273713	1	1	yes	characteristic
528	C₄	#16837949	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	472	1	no	—
533	C₂	C₄×#14273713	1	1	yes	characteristic
534	C₂	#21433001	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1764	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#16837948	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1764	D₅₉
hypocenter	C₅₉	#21662
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #21433034	C₂	semidirect
4. #21425071	C₂	semidirect
6. #21424809	C₂	semidirect
7. #21424805	C₂	semidirect
8. #21424801	C₂	semidirect
9. #21424797	C₂	semidirect
10. #21424235	C₂	semidirect
11. #21423942	C₂	semidirect
12. #21423938	C₂	semidirect
13. #21423933	C₂	semidirect
14. C₄×#14273637	C₂	semidirect
15. C₅₉×#1764	C₂	semidirect
19. #16837769	C₄	semidirect
20. #16837765	C₄	semidirect
21. #16837763	C₄	semidirect
22. #16837760	C₄	semidirect
275. #1764	D₅₉	semidirect
326. C₅₉	#21662	semidirect

Maximal subgroups

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

subgroup	index
#21434439	2
#21433034	2
#21432812	2
#21425071	2
#21424922	2
#21424809	2
#21424805	2
#21424801	2
#21424797	2
#21424235	2
#21423942	2
#21423938	2
#21423933	2
C₄×#14273637	2
C₅₉×#1764	2
#21662	59