Subgroups — #28607205

Order 15104.

812 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433009	C₂	1	2	yes	maximal
2	C₂×#16837517	C₂	1	1	yes	maximal, characteristic
3	#21432707	C₂	1	1	yes	maximal, characteristic, complemented
4	#21432704	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424885	C₂	1	2	yes	maximal, complemented
6	#21424339	C₂	1	2	yes	maximal, complemented
7	#21424334	C₂	1	2	yes	maximal, complemented
8	#21424266	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424147	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₂²	1	1	yes	characteristic
13	#16838169	C₂²	1	2	yes	—
14	#16838168	C₂²	1	2	yes	—
15	C₂×#14273733	C₂²	1	1	yes	characteristic
16	#16837521	—	2	4	no	—
17	#16837517	C₄	1	2	yes	complemented
18	#16837517	C₄	1	2	yes	complemented
19	#16837517	C₄	1	2	yes	complemented
20	#16837517	C₄	1	2	yes	complemented
21	#16837516	—	2	4	no	—
22	#16837451	—	2	2	no	—
23	#16837451	C₂²	1	2	yes	—
24	#16837450	C₂²	1	2	yes	—
25	#16837449	—	2	2	no	—
26	C₂×#14273663	—	2	2	no	—
27	C₂×#14273663	C₂²	1	1	yes	characteristic
28	C₂×#14273663	C₂²	1	1	yes	characteristic
29	C₂×#14273662	C₂²	1	2	yes	—
30	C₂×#14273662	C₂²	1	1	yes	characteristic
31	#108×D₅₉	—	2	2	no	—
32	#16837425	C₂²	1	2	yes	—
33	#16837420	C₂²	1	2	yes	—
34	C₂×#14273654	C₂²	1	1	yes	characteristic
35	C₂×#14273653	C₂²	1	1	yes	characteristic
36	#16837358	C₂²	1	2	yes	—
37	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
38	#16837172	C₂²	1	2	yes	—
39	#16837161	C₂²	1	2	yes	—
40	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#427	C₂²	1	1	yes	characteristic
43	C₅₉×#421	C₂²	1	2	yes	—
44	C₅₉×#344	C₂²	1	2	yes	—
45	C₂×#11745685	C₂³	1	1	yes	characteristic
46	#14273747	C₂×C₄	1	2	yes	—
47	#14273747	C₂×C₄	1	2	yes	—
48	#14273747	D₄	1	2	yes	—
49	#14273747	D₄	1	2	yes	—
50	C₂×#11745672	Q₈	1	1	yes	characteristic
51	C₂×#11745670	Q₈	1	1	yes	characteristic
52	C₂×#11745671	Q₈	1	1	yes	characteristic
53	C₂×#11745669	Q₈	1	1	yes	characteristic
54	#14273735	—	2	4	no	—
55	#14273734	—	2	4	no	—
56	#14273734	—	4	2	no	—
57	#14273733	—	2	1	no	—
58	#14273733	—	2	1	no	—
59	#14273733	—	4	2	no	—
60	#14273733	C₂×C₄	1	2	yes	—
61	#14273733	C₂×C₄	1	2	yes	—
62	C₂×#11745664	—	2	4	no	—
63	C₂×#11745664	C₂³	1	2	yes	—
64	C₂×#11745664	C₂³	1	1	yes	characteristic
65	C₂×#11745664	C₂³	1	2	yes	—
66	C₂×#11745659	—	2	1	no	—
67	M₁₆×D₅₉	—	2	4	no	—
68	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₈×D₅₉	—	2	1	no	—
70	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
71	#14273663	—	2	1	no	—
72	#14273663	—	2	1	no	—
73	#14273663	—	2	4	no	—
74	#14273663	D₄	1	2	yes	—
75	#14273663	D₄	1	2	yes	—
76	#14273662	—	2	4	no	—
77	#14273662	—	2	2	no	—
78	#14273662	—	2	2	no	—
79	#14273662	C₂×C₄	1	2	yes	—
80	#14273662	C₂×C₄	1	2	yes	—
81	Dic₅₉⋊C₈	—	4	2	no	—
82	#14273655	—	2	4	no	—
83	#14273654	C₂×C₄	1	2	yes	—
84	#14273654	C₂×C₄	1	2	yes	—
85	#14273653	C₂×C₄	1	2	yes	—
86	#14273653	C₂×C₄	1	2	yes	—
87	#14273638	—	2	2	no	—
88	C₄×C₅₉⋊C₈	—	2	2	no	—
89	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
90	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
91	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
94	#131×C₅₉	—	2	1	no	—
95	#131×C₅₉	—	2	1	no	—
96	#131×C₅₉	C₂×C₄	1	2	yes	—
97	#131×C₅₉	C₂×C₄	1	2	yes	—
98	C₂×M₁₆×C₅₉	—	2	1	no	—
99	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
100	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₅₉	—	2	1	no	—
102	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
103	#117×C₅₉	C₂³	1	2	yes	—
104	#108×C₅₉	—	2	1	no	—
105	#108×C₅₉	—	2	1	no	—
106	#107×C₅₉	—	2	1	no	—
107	#106×C₅₉	—	2	1	no	—
108	#104×C₅₉	—	2	4	no	—
109	#41×C₅₉	—	2	1	no	—
110	#41×C₅₉	—	2	1	no	—
111	#41×C₅₉	C₂²×C₄	1	2	yes	—
112	#41×C₅₉	C₂×D₄	1	2	yes	—
113	C₂×Q₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
114	C₂×D₄×C₅₉	—	2	1	no	—
115	C₂×D₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₂²⋊D₅₉	—	2	1	no	—
119	C₂²×Dic₅₉	—	2	1	no	—
120	#11745685	—	2	1	no	—
121	#11745685	—	2	1	no	—
122	#11745685	C₂²×C₄	1	2	yes	—
123	#11745685	C₂×D₄	1	2	yes	—
124	C₂×D₂₃₆	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₄×D₅₉	—	2	1	no	—
126	C₂×Dic₁₁₈	C₂×Q₈	1	1	yes	characteristic
127	M₁₆×C₅₉	—	2	1	no	—
128	M₁₆×C₅₉	—	2	2	no	—
129	M₁₆×C₅₉	—	2	2	no	—
130	M₁₆×C₅₉	—	2	2	no	—
131	M₁₆×C₅₉	—	2	2	no	—
132	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₅₉	—	2	1	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₂×C₈×C₅₉	—	2	2	no	—
137	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
142	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
143	C₄⋊C₄×C₅₉	—	2	2	no	—
144	C₂²⋊C₄×C₅₉	—	2	2	no	—
145	C₄²×C₅₉	—	2	2	no	—
146	#11745672	C₄⋊C₄	1	2	yes	—
147	#11745672	C₄⋊C₄	1	2	yes	—
148	#11745671	C₄⋊C₄	1	2	yes	—
149	#11745671	C₄⋊C₄	1	2	yes	—
150	#11745670	C₄⋊C₄	1	2	yes	—
151	#11745670	C₄⋊C₄	1	2	yes	—
152	#11745669	C₄⋊C₄	1	2	yes	—
153	#11745669	C₄⋊C₄	1	2	yes	—
154	C₄×Dic₅₉	—	2	1	no	—
155	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
156	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
157	#11745664	—	2	1	no	—
158	#11745664	—	2	2	no	—
159	#11745664	—	2	2	no	—
160	#11745664	—	2	2	no	—
161	#11745664	—	4	4	no	—
162	#11745664	C₂²×C₄	1	2	yes	—
163	#11745664	C₂×D₄	1	4	yes	—
164	C₂×C₅₉⋊C₈	—	2	2	no	—
165	C₂×C₅₉⋊C₈	—	2	1	no	—
166	C₂×C₅₉⋊C₈	—	2	2	no	—
167	C₂×C₅₉⋊C₈	—	4	4	no	—
168	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₅₉⋊C₈	C₂×Q₈	1	1	yes	characteristic
173	C₂×C₅₉⋊C₈	C₂×Q₈	1	1	yes	characteristic
174	#11745659	—	2	2	no	—
175	#11745659	—	2	2	no	—
176	#11745659	—	4	4	no	—
177	C₈×D₅₉	—	2	2	no	—
178	C₈×D₅₉	—	2	2	no	—
179	C₈×D₅₉	—	4	4	no	—
180	C₂³×C₅₉	—	2	1	no	—
181	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂²×D₅₉	—	2	1	no	—
183	Q₈×C₅₉	—	2	1	no	—
184	Q₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
185	D₄×C₅₉	—	2	2	no	—
186	D₄×C₅₉	—	2	2	no	—
187	D₄×C₅₉	—	2	1	no	—
188	D₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₅₉	—	2	1	no	—
190	C₂×C₄×C₅₉	—	2	2	no	—
191	C₂×C₄×C₅₉	—	2	2	no	—
192	C₂×C₄×C₅₉	—	4	2	no	—
193	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂²⋊D₅₉	—	2	2	no	—
200	C₂²⋊D₅₉	—	2	2	no	—
201	C₂×Dic₅₉	—	2	1	no	—
202	C₂×Dic₅₉	—	2	1	no	—
203	C₂×Dic₅₉	—	2	1	no	—
204	C₂×Dic₅₉	—	4	2	no	—
205	D₂₃₆	—	2	1	no	—
206	D₂₃₆	C₂×C₄⋊C₄	1	2	yes	—
207	C₄×D₅₉	—	2	2	no	—
208	C₄×D₅₉	—	2	2	no	—
209	Dic₁₁₈	—	2	1	no	—
210	Dic₁₁₈	C₂×C₄⋊C₄	1	2	yes	—
211	C₈×C₅₉	—	2	2	no	—
212	C₈×C₅₉	—	4	2	no	—
213	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
214	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
215	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
216	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
217	C₅₉⋊C₈	—	2	2	no	—
218	C₅₉⋊C₈	—	2	4	no	—
219	C₅₉⋊C₈	—	4	2	no	—
220	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
222	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
224	#22694	—	59	1	no	maximal, Sylow
225	C₂²×C₅₉	—	2	2	no	—
226	C₂²×C₅₉	—	4	1	no	—
227	C₂²×C₅₉	—	8	1	no	—
228	C₂²×C₅₉	#520	1	1	yes	characteristic
229	C₂²×C₅₉	#547	1	1	yes	characteristic
230	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
231	C₂×D₅₉	—	2	2	no	—
232	C₂×D₅₉	—	8	1	no	—
233	C₄×C₅₉	—	2	2	no	—
234	C₄×C₅₉	—	8	2	no	—
235	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
237	C₄×C₅₉	D₄²	1	1	yes	characteristic
238	C₄×C₅₉	#554	1	1	yes	characteristic
239	Dic₅₉	—	2	2	no	—
240	Dic₅₉	—	2	2	no	—
241	Dic₅₉	—	4	1	no	—
242	#2957	—	59	2	no	—
243	C₂×#443	—	59	1	no	—
244	#2916	—	59	1	no	—
245	#2916	—	59	1	no	—
246	#1953	—	59	2	no	—
247	#1861	—	59	2	no	—
248	#1861	—	59	2	no	—
249	#1848	—	59	1	no	—
250	#1814	—	59	1	no	—
251	#1814	D₅₉	1	1	yes	characteristic, complemented
252	#1772	—	59	1	no	—
253	C₂×C₅₉	—	2	1	no	—
254	C₂×C₅₉	—	2	1	no	—
255	C₂×C₅₉	—	2	1	no	—
256	C₂×C₅₉	—	4	2	no	—
257	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
258	D₅₉	—	4	2	no	—
259	C₂×#135	—	59	1	no	—
260	#568	—	59	2	no	—
261	#568	—	59	2	no	—
262	C₂×#131	—	59	1	no	—
263	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
264	#444	—	118	4	no	—
265	#443	—	59	2	no	—
266	#443	—	59	2	no	—
267	#443	—	59	2	no	—
268	#443	—	59	2	no	—
269	#443	—	118	4	no	—
270	#430	—	59	2	no	—
271	#430	—	59	2	no	—
272	#430	—	118	2	no	—
273	#430	—	118	2	no	—
274	C₂×#108	—	59	1	no	—
275	C₂×#108	—	59	1	no	—
276	C₂×#108	—	59	2	no	—
277	C₂×#108	—	59	1	no	—
278	C₂×#108	—	118	2	no	—
279	C₂×#108	—	118	2	no	—
280	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
281	#427	C₂×D₅₉	1	1	yes	characteristic
282	#423	—	59	2	no	—
283	#421	—	59	2	no	—
284	#421	C₂×D₅₉	1	2	yes	—
285	C₂×#104	—	59	1	no	—
286	C₂×#104	—	59	1	no	—
287	#405	—	59	2	no	—
288	C₂×C₄×C₈	—	59	1	no	—
289	#344	—	59	2	no	—
290	#344	C₂×D₅₉	1	2	yes	—
291	#339	—	59	2	no	—
292	C₅₉	#22694	1	1	yes	characteristic, complemented, Sylow
293	C₂×#41	—	59	1	no	—
294	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
295	#135	—	59	2	no	—
296	#135	—	59	2	no	—
297	#135	—	59	2	no	—
298	#135	—	59	2	no	—
299	C₂×Q₁₆	—	59	1	no	—
300	C₂×SD₁₆	—	59	1	no	—
301	C₂×SD₁₆	—	59	1	no	—
302	C₂×D₈	—	59	1	no	—
303	#131	—	2	1	no	—
304	#131	—	2	1	no	—
305	#131	—	59	2	no	—
306	#131	—	59	2	no	—
307	#131	—	118	1	no	—
308	#131	—	118	1	no	—
309	#131	—	118	4	no	—
310	#131	—	118	4	no	—
311	#131	—	236	2	no	—
312	#131	—	236	2	no	—
313	#131	C₄×D₅₉	1	2	yes	—
314	#131	C₄×D₅₉	1	2	yes	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	59	1	no	—
317	C₂×M₁₆	—	59	2	no	—
318	C₂×M₁₆	—	59	2	no	—
319	C₂×M₁₆	—	118	1	no	—
320	C₂×M₁₆	—	118	4	no	—
321	C₂×M₁₆	—	118	4	no	—
322	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
323	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	59	1	no	—
326	C₂²×C₈	—	118	1	no	—
327	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
328	#117	C₂²×D₅₉	1	2	yes	—
329	C₂×C₄²	—	59	1	no	—
330	#108	—	2	1	no	—
331	#108	—	2	1	no	—
332	#108	—	59	2	no	—
333	#108	—	59	2	no	—
334	#108	—	59	2	no	—
335	#108	—	59	2	no	—
336	#108	—	118	4	no	—
337	#108	—	118	2	no	—
338	#108	—	118	2	no	—
339	#108	—	118	4	no	—
340	#108	—	118	1	no	—
341	#108	—	118	1	no	—
342	#107	—	2	1	no	—
343	#106	—	2	1	no	—
344	C₄⋊C₈	—	236	2	no	—
345	#104	—	2	4	no	—
346	#104	—	59	2	no	—
347	#104	—	59	2	no	—
348	#104	—	59	2	no	—
349	#104	—	59	2	no	—
350	#104	—	118	4	no	—
351	#97	—	118	2	no	—
352	C₄×C₈	—	59	1	no	—
353	C₄×C₈	—	59	1	no	—
354	C₄×C₈	—	59	1	no	—
355	C₄×C₈	—	59	1	no	—
356	C₄×C₈	—	118	2	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	59	2	no	—
360	#41	—	59	2	no	—
361	#41	—	118	1	no	—
362	#41	—	118	1	no	—
363	#41	C₂×C₄×D₅₉	1	2	yes	—
364	#41	D₄×D₅₉	1	2	yes	—
365	C₂×Q₈	—	59	1	no	—
366	C₂×Q₈	Q₈×D₅₉	1	1	yes	characteristic
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	59	1	no	—
369	C₂×D₄	—	118	1	no	—
370	C₂×D₄	Q₈×D₅₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	118	1	no	—
373	C₂²×C₄	—	118	1	no	—
374	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
375	Q₁₆	—	59	2	no	—
376	Q₁₆	—	59	2	no	—
377	SD₁₆	—	59	2	no	—
378	SD₁₆	—	59	2	no	—
379	SD₁₆	—	59	2	no	—
380	SD₁₆	—	59	2	no	—
381	D₈	—	59	2	no	—
382	D₈	—	59	2	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	59	2	no	—
389	M₁₆	—	59	4	no	—
390	M₁₆	—	118	1	no	—
391	M₁₆	—	118	2	no	—
392	M₁₆	—	118	2	no	—
393	M₁₆	—	118	2	no	—
394	M₁₆	—	118	2	no	—
395	M₁₆	—	118	2	no	—
396	M₁₆	—	236	4	no	—
397	M₁₆	—	236	4	no	—
398	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	59	1	no	—
404	C₂×C₈	—	59	1	no	—
405	C₂×C₈	—	59	1	no	—
406	C₂×C₈	—	59	1	no	—
407	C₂×C₈	—	59	1	no	—
408	C₂×C₈	—	59	1	no	—
409	C₂×C₈	—	118	2	no	—
410	C₂×C₈	—	118	1	no	—
411	C₂×C₈	—	118	2	no	—
412	C₂×C₈	—	118	2	no	—
413	C₂×C₈	—	118	2	no	—
414	C₂×C₈	—	236	4	no	—
415	C₂×C₈	—	236	4	no	—
416	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
417	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
418	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
419	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
420	C₂×C₈	#11745687	1	1	yes	characteristic
421	C₂×C₈	#11745687	1	1	yes	characteristic
422	C₄⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	59	1	no	—
426	C₄²	—	59	1	no	—
427	C₄²	—	118	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	118	1	no	—
430	C₂³	#14273774	1	1	yes	characteristic
431	Q₈	—	2	1	no	—
432	Q₈	—	59	2	no	—
433	Q₈	—	118	1	no	—
434	Q₈	C₄⋊C₄×D₅₉	1	2	yes	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	1	no	—
438	D₄	—	59	2	no	—
439	D₄	—	118	2	no	—
440	D₄	—	118	2	no	—
441	D₄	—	118	1	no	—
442	D₄	C₄⋊C₄×D₅₉	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	118	1	no	—
448	C₂×C₄	—	118	1	no	—
449	C₂×C₄	—	118	2	no	—
450	C₂×C₄	—	118	2	no	—
451	C₂×C₄	—	118	1	no	—
452	C₂×C₄	—	236	2	no	—
453	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
454	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
455	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
456	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
458	C₂×C₄	#14273773	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	59	1	no	—
462	C₈	—	59	1	no	—
463	C₈	—	59	1	no	—
464	C₈	—	59	1	no	—
465	C₈	—	118	4	no	—
466	C₈	—	118	2	no	—
467	C₈	—	236	2	no	—
468	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
469	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
470	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
471	C₈	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	118	2	no	—
476	C₂²	—	472	1	no	—
477	C₂²	#16837882	1	1	yes	characteristic
478	C₂²	#16838052	1	1	yes	characteristic
479	C₂²	#16838065	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	8	2	no	—
482	C₄	—	118	2	no	—
483	C₄	—	118	2	no	—
484	C₄	—	236	1	no	—
485	C₄	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
486	C₄	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
487	C₄	#16838036	1	1	yes	characteristic
488	C₄	#16838110	1	1	yes	characteristic
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	236	2	no	—
494	C₂	#21426992	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16838036
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1814	C₂
socle	C₂×C₅₉	D₄×C₄⋊C₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1814	D₅₉
hypocenter	C₅₉	#22694
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
3. #21432707	C₂	semidirect
4. #21432704	C₂	semidirect
5. #21424885	C₂	semidirect
6. #21424339	C₂	semidirect
7. #21424334	C₂	semidirect
8. #21424266	C₂	semidirect
9. #21424147	C₂	semidirect
10. #21423977	C₂	semidirect
11. C₅₉×#1814	C₂	semidirect
17. #16837517	C₄	semidirect
18. #16837517	C₄	semidirect
19. #16837517	C₄	semidirect
20. #16837517	C₄	semidirect
251. #1814	D₅₉	semidirect
292. C₅₉	#22694	semidirect

Maximal subgroups

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

subgroup	index
#21433009	2
C₂×#16837517	2
#21432707	2
#21432704	2
#21424885	2
#21424339	2
#21424334	2
#21424266	2
#21424147	2
#21423977	2
C₅₉×#1814	2
#22694	59