Subgroups — #21438871

Order 7552.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838237	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#16838214	C₂	1	1	yes	maximal, characteristic, complemented
4	#16838213	C₂	1	1	yes	maximal, characteristic, complemented
5	#16838212	C₂	1	3	yes	maximal, complemented
6	#16838209	C₂	1	3	yes	maximal, complemented
7	#16838206	C₂	1	3	yes	maximal, complemented
8	#16838205	C₂	1	1	yes	maximal, characteristic, complemented
9	#16838203	C₂	1	3	yes	maximal, complemented
10	#16838199	C₂	1	3	yes	maximal, complemented
11	#16838198	C₂	1	3	yes	maximal, complemented
12	C₂×#14273751	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₅₉	C₂	1	3	yes	maximal, complemented
14	#16838167	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#576	C₂	1	1	yes	maximal, characteristic, complemented
16	#14273774	—	2	1	no	—
17	#14273774	C₂²	1	3	yes	complemented
18	#14273774	C₂²	1	1	yes	characteristic, complemented
19	#14273773	—	2	1	no	—
20	#14273773	C₂²	1	3	yes	complemented
21	#14273773	C₂²	1	1	yes	characteristic, complemented
22	#14273772	—	2	3	no	—
23	#14273772	—	2	3	no	—
24	#14273772	C₂²	1	3	yes	complemented
25	#14273772	C₂²	1	3	yes	complemented
26	C₂×#11745687	—	2	3	no	—
27	C₂×#11745687	C₂²	1	3	yes	complemented
28	#41×D₅₉	—	2	1	no	—
29	#41×D₅₉	—	2	1	no	—
30	#41×D₅₉	C₂²	1	1	yes	characteristic
31	#41×D₅₉	C₂²	1	3	yes	complemented
32	#41×D₅₉	C₂²	1	3	yes	complemented
33	C₂×D₄×D₅₉	—	2	3	no	—
34	C₂×D₄×D₅₉	C₂²	1	3	yes	complemented
35	#14273760	C₂²	1	3	yes	complemented
36	#14273759	C₂²	1	1	yes	characteristic, complemented
37	#14273759	C₂²	1	3	yes	complemented
38	#14273757	C₂²	1	3	yes	complemented
39	#14273756	C₂²	1	3	yes	complemented
40	#14273756	C₂²	1	3	yes	complemented
41	#14273755	C₂²	1	3	yes	complemented
42	#14273754	C₂²	1	3	yes	complemented
43	#14273754	C₂²	1	3	yes	complemented
44	#14273753	C₂²	1	3	yes	complemented
45	#14273753	C₂²	1	3	yes	complemented
46	#14273752	C₂²	1	3	yes	complemented
47	#14273751	C₂²	1	6	yes	complemented
48	#14273751	C₂²	1	3	yes	complemented
49	#14273751	C₂²	1	6	yes	complemented
50	#14273751	C₂²	1	6	yes	complemented
51	#14273751	C₂²	1	3	yes	complemented
52	#14273749	C₂²	1	3	yes	complemented
53	#14273748	C₂²	1	6	yes	complemented
54	#14273747	C₂²	1	3	yes	complemented
55	#14273747	C₂²	1	3	yes	complemented
56	#14273746	C₂²	1	6	yes	complemented
57	C₂×#11745660	C₂²	1	3	yes	complemented
58	C₂×#11745670	C₂²	1	3	yes	complemented
59	SD₁₆×D₅₉	C₂²	1	6	yes	complemented
60	C₂×#11745669	C₂²	1	3	yes	complemented
61	D₈×D₅₉	C₂²	1	6	yes	complemented
62	#14273735	C₂²	1	3	yes	complemented
63	#14273734	C₂²	1	1	yes	characteristic, complemented
64	#14273733	C₂²	1	3	yes	complemented
65	C₂×#11745659	C₂²	1	3	yes	complemented
66	M₁₆×D₅₉	C₂²	1	3	yes	complemented
67	H(5,𝔽₂)×C₅₉	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₅₉	C₂²	1	1	yes	characteristic, complemented
69	AGL(1,ℤ/8)×C₅₉	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₅₉	C₂²	1	3	yes	complemented
71	#135×C₅₉	C₂²	1	3	yes	complemented
72	C₂×D₈×C₅₉	C₂²	1	3	yes	complemented
73	#131×C₅₉	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₅₉	—	2	3	no	—
75	#41×C₅₉	—	2	1	no	—
76	#41×C₅₉	—	2	1	no	—
77	#41×C₅₉	C₂³	1	3	yes	—
78	#41×C₅₉	C₂³	1	1	yes	characteristic
79	#41×C₅₉	C₂³	1	3	yes	complemented
80	C₂×D₄×C₅₉	—	2	3	no	—
81	C₂×D₄×C₅₉	—	2	3	no	—
82	C₂×D₄×C₅₉	C₂³	1	3	yes	—
83	C₂×D₄×C₅₉	C₂³	1	3	yes	complemented
84	C₂×C₂²⋊D₅₉	—	2	3	no	—
85	C₂×C₂²⋊D₅₉	—	2	6	no	—
86	C₂×C₂²⋊D₅₉	—	2	6	no	—
87	C₂×C₂²⋊D₅₉	—	2	3	no	—
88	C₂²×Dic₅₉	—	2	3	no	—
89	#11745689	—	2	1	no	—
90	#11745689	D₄	1	1	yes	characteristic
91	#11745689	C₂³	1	3	yes	—
92	#11745689	C₂³	1	1	yes	characteristic
93	Q₈×D₅₉	—	2	1	no	—
94	Q₈×D₅₉	D₄	1	1	yes	characteristic
95	Q₈×D₅₉	C₂³	1	1	yes	characteristic
96	Q₈×D₅₉	C₂³	1	3	yes	complemented
97	#11745687	—	2	3	no	—
98	#11745687	—	2	6	no	—
99	#11745687	—	2	3	no	—
100	#11745687	—	2	3	no	—
101	#11745687	—	2	3	no	—
102	#11745687	—	2	3	no	—
103	#11745687	—	2	3	no	—
104	#11745687	—	2	3	no	—
105	#11745687	D₄	1	3	yes	—
106	#11745687	C₂³	1	3	yes	—
107	#11745687	C₂³	1	3	yes	—
108	#11745687	C₂³	1	6	yes	complemented
109	D₄×D₅₉	—	2	3	no	—
110	D₄×D₅₉	—	2	3	no	—
111	D₄×D₅₉	—	2	3	no	—
112	D₄×D₅₉	—	2	6	no	—
113	D₄×D₅₉	—	2	3	no	—
114	D₄×D₅₉	—	2	3	no	—
115	D₄×D₅₉	—	2	3	no	—
116	D₄×D₅₉	—	2	3	no	—
117	D₄×D₅₉	D₄	1	3	yes	—
118	D₄×D₅₉	C₂³	1	6	yes	—
119	D₄×D₅₉	C₂³	1	3	yes	—
120	D₄×D₅₉	C₂³	1	3	yes	complemented
121	#11745685	—	2	3	no	—
122	#11745685	—	2	3	no	—
123	#11745685	—	2	3	no	—
124	#11745685	—	2	3	no	—
125	#11745685	C₂³	1	3	yes	—
126	#11745685	C₂³	1	3	yes	—
127	#11745685	C₂³	1	3	yes	complemented
128	C₂×D₂₃₆	—	2	3	no	—
129	C₂×D₂₃₆	C₂³	1	3	yes	—
130	C₂×C₄×D₅₉	—	2	3	no	—
131	C₂×C₄×D₅₉	—	2	3	no	—
132	C₂×C₄×D₅₉	C₂³	1	3	yes	—
133	C₂×Dic₁₁₈	—	2	3	no	—
134	C₂×Dic₁₁₈	C₂³	1	3	yes	complemented
135	Q₁₆×C₅₉	C₂³	1	1	yes	characteristic, complemented
136	SD₁₆×C₅₉	C₂³	1	3	yes	complemented
137	SD₁₆×C₅₉	C₂³	1	3	yes	complemented
138	D₈×C₅₉	C₂³	1	3	yes	complemented
139	D₈×C₅₉	C₂³	1	6	yes	complemented
140	M₁₆×C₅₉	C₂³	1	3	yes	complemented
141	C₂×C₈×C₅₉	C₂³	1	3	yes	complemented
142	#11745672	C₂³	1	1	yes	characteristic, complemented
143	#11745672	C₂³	1	3	yes	complemented
144	#11745671	C₂³	1	3	yes	complemented
145	#11745671	C₂³	1	1	yes	characteristic, complemented
146	#11745670	C₂³	1	6	yes	complemented
147	#11745670	C₂³	1	3	yes	complemented
148	#11745670	C₂³	1	3	yes	complemented
149	#11745669	C₂³	1	3	yes	complemented
150	#11745669	C₂³	1	6	yes	complemented
151	#11745669	C₂³	1	3	yes	complemented
152	#11745664	C₂³	1	3	yes	complemented
153	C₂×C₅₉⋊C₈	C₂³	1	3	yes	complemented
154	Dic₂₃₆	C₂³	1	3	yes	complemented
155	D₄₇₂	C₂³	1	3	yes	complemented
156	#11745660	C₂³	1	6	yes	complemented
157	#11745660	C₂³	1	3	yes	complemented
158	#11745660	C₂³	1	1	yes	characteristic, complemented
159	#11745659	C₂³	1	3	yes	—
160	#11745659	C₂³	1	1	yes	characteristic
161	#11745659	C₂³	1	3	yes	complemented
162	#11745659	C₂³	1	3	yes	complemented
163	C₈×D₅₉	C₂³	1	6	yes	complemented
164	C₂³×C₅₉	—	2	3	no	—
165	C₂³×C₅₉	—	2	3	no	—
166	C₂²×D₅₉	—	2	3	no	—
167	C₂²×D₅₉	—	2	3	no	—
168	C₂²×D₅₉	—	2	3	no	—
169	C₂²×D₅₉	—	2	6	no	—
170	C₂²×D₅₉	—	8	6	no	—
171	C₂²×D₅₉	C₂×D₄	1	3	yes	—
172	Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
173	Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
174	Q₈×C₅₉	C₂⁴	1	1	yes	characteristic
175	D₄×C₅₉	—	2	3	no	—
176	D₄×C₅₉	—	2	3	no	—
177	D₄×C₅₉	—	2	3	no	—
178	D₄×C₅₉	—	2	3	no	—
179	D₄×C₅₉	C₂×D₄	1	3	yes	—
180	D₄×C₅₉	C₂⁴	1	3	yes	—
181	D₄×C₅₉	C₂⁴	1	3	yes	—
182	C₂×C₄×C₅₉	—	2	3	no	—
183	C₂×C₄×C₅₉	—	2	3	no	—
184	C₂×C₄×C₅₉	C₂⁴	1	3	yes	—
185	C₂²⋊D₅₉	—	2	3	no	—
186	C₂²⋊D₅₉	—	2	3	no	—
187	C₂²⋊D₅₉	—	2	3	no	—
188	C₂²⋊D₅₉	—	2	3	no	—
189	C₂²⋊D₅₉	—	2	6	no	—
190	C₂²⋊D₅₉	—	2	6	no	—
191	C₂²⋊D₅₉	—	2	3	no	—
192	C₂²⋊D₅₉	—	2	3	no	—
193	C₂²⋊D₅₉	C₂×D₄	1	6	yes	—
194	C₂×Dic₅₉	—	2	3	no	—
195	C₂×Dic₅₉	—	2	6	no	—
196	C₂×Dic₅₉	—	2	3	no	—
197	C₂×Dic₅₉	—	2	3	no	—
198	C₂×Dic₅₉	C₂×D₄	1	3	yes	—
199	D₂₃₆	—	2	3	no	—
200	D₂₃₆	—	2	1	no	—
201	D₂₃₆	—	2	3	no	—
202	D₂₃₆	C₂×D₄	1	3	yes	—
203	D₂₃₆	C₂⁴	1	3	yes	—
204	D₂₃₆	C₂⁴	1	1	yes	characteristic
205	C₄×D₅₉	—	2	1	no	—
206	C₄×D₅₉	—	2	3	no	—
207	C₄×D₅₉	—	2	3	no	—
208	C₄×D₅₉	—	2	3	no	—
209	C₄×D₅₉	—	2	1	no	—
210	C₄×D₅₉	—	2	3	no	—
211	C₄×D₅₉	C₂×D₄	1	3	yes	—
212	C₄×D₅₉	C₂×D₄	1	3	yes	—
213	C₄×D₅₉	C₂⁴	1	3	yes	—
214	C₄×D₅₉	C₂⁴	1	1	yes	characteristic
215	Dic₁₁₈	—	2	3	no	—
216	Dic₁₁₈	—	2	3	no	—
217	Dic₁₁₈	—	2	1	no	—
218	Dic₁₁₈	C₂×D₄	1	3	yes	—
219	Dic₁₁₈	C₂⁴	1	3	yes	—
220	Dic₁₁₈	C₂⁴	1	1	yes	characteristic
221	C₈×C₅₉	C₂⁴	1	3	yes	—
222	C₈×C₅₉	C₂⁴	1	1	yes	characteristic
223	C₅₉⋊C₈	C₂⁴	1	3	yes	—
224	C₅₉⋊C₈	C₂⁴	1	1	yes	characteristic
225	C₂²×C₅₉	—	2	3	no	—
226	C₂²×C₅₉	—	2	3	no	—
227	C₂²×C₅₉	—	8	3	no	—
228	C₂²×C₅₉	—	8	3	no	—
229	C₂²×C₅₉	C₂²×D₄	1	3	yes	—
230	C₂×D₅₉	—	2	1	no	—
231	C₂×D₅₉	—	2	3	no	—
232	C₂×D₅₉	—	4	3	no	—
233	C₂×D₅₉	—	4	6	no	—
234	C₂×D₅₉	—	8	3	no	—
235	C₂×D₅₉	—	8	6	no	—
236	C₂×D₅₉	—	8	3	no	—
237	C₂×D₅₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₅₉	C₂²×D₄	1	3	yes	—
239	C₄×C₅₉	—	2	1	no	—
240	C₄×C₅₉	—	2	1	no	—
241	C₄×C₅₉	C₂²×D₄	1	3	yes	—
242	C₄×C₅₉	C₂⁵	1	1	yes	characteristic
243	Dic₅₉	—	2	3	no	—
244	Dic₅₉	—	2	1	no	—
245	Dic₅₉	C₂²×D₄	1	3	yes	—
246	Dic₅₉	C₂²×D₄	1	1	yes	characteristic
247	#3585	—	59	1	no	maximal, Sylow
248	C₂×C₅₉	—	2	3	no	—
249	C₂×C₅₉	—	4	3	no	—
250	C₂×C₅₉	—	4	3	no	—
251	C₂×C₅₉	C₂³×D₄	1	1	yes	characteristic
252	D₅₉	—	2	1	no	—
253	D₅₉	—	2	3	no	—
254	D₅₉	—	4	3	no	—
255	D₅₉	—	4	1	no	—
256	#585	—	59	1	no	—
257	C₂×H(5,𝔽₂)	—	59	1	no	—
258	#577	—	59	1	no	—
259	#577	—	59	3	no	—
260	#577	—	59	3	no	—
261	#577	—	59	1	no	—
262	#576	—	59	1	no	—
263	#576	—	59	3	no	—
264	#576	—	59	3	no	—
265	#576	D₅₉	1	1	yes	characteristic, complemented
266	#575	—	59	3	no	—
267	#575	—	59	3	no	—
268	C₂×AGL(1,ℤ/8)	—	59	3	no	—
269	C₂×AGL(1,ℤ/8)	—	59	3	no	—
270	#568	—	59	1	no	—
271	C₅₉	#3585	1	1	yes	characteristic, complemented, Sylow
272	2₋¹⁺⁴	—	59	1	no	—
273	2₋¹⁺⁴	—	59	3	no	—
274	2₋¹⁺⁴	—	118	1	no	—
275	H(5,𝔽₂)	—	59	3	no	—
276	H(5,𝔽₂)	—	59	1	no	—
277	H(5,𝔽₂)	—	59	3	no	—
278	H(5,𝔽₂)	—	59	3	no	—
279	H(5,𝔽₂)	—	118	3	no	—
280	H(5,𝔽₂)	—	118	3	no	—
281	H(5,𝔽₂)	—	118	1	no	—
282	H(5,𝔽₂)	C₂×D₅₉	1	1	yes	characteristic, complemented
283	H(5,𝔽₂)	C₂×D₅₉	1	1	yes	characteristic, complemented
284	C₂×#41	—	59	1	no	—
285	C₂×#41	—	59	3	no	—
286	C₂×#41	—	59	3	no	—
287	C₂×#41	—	59	3	no	—
288	C₂×#41	—	118	3	no	—
289	C₂×#41	—	118	1	no	—
290	C₂×#41	—	118	1	no	—
291	C₂²×D₄	—	59	3	no	—
292	C₂²×D₄	—	118	3	no	—
293	#137	—	59	3	no	—
294	#137	—	59	1	no	—
295	#137	—	59	3	no	—
296	#137	—	59	3	no	—
297	#137	—	59	3	no	—
298	#137	—	59	3	no	—
299	AGL(1,ℤ/8)	—	59	3	no	—
300	AGL(1,ℤ/8)	—	59	3	no	—
301	AGL(1,ℤ/8)	—	59	3	no	—
302	AGL(1,ℤ/8)	—	59	3	no	—
303	AGL(1,ℤ/8)	—	59	3	no	—
304	AGL(1,ℤ/8)	—	59	6	no	—
305	AGL(1,ℤ/8)	—	59	3	no	—
306	AGL(1,ℤ/8)	—	59	6	no	—
307	AGL(1,ℤ/8)	—	59	6	no	—
308	AGL(1,ℤ/8)	—	59	3	no	—
309	AGL(1,ℤ/8)	—	59	3	no	—
310	AGL(1,ℤ/8)	C₂×D₅₉	1	3	yes	complemented
311	AGL(1,ℤ/8)	C₂×D₅₉	1	3	yes	complemented
312	#135	—	59	3	no	—
313	#135	—	59	3	no	—
314	#135	—	59	6	no	—
315	#135	—	59	6	no	—
316	#135	—	59	3	no	—
317	#135	C₂×D₅₉	1	3	yes	complemented
318	C₂×SD₁₆	—	59	3	no	—
319	C₂×SD₁₆	—	59	6	no	—
320	C₂×SD₁₆	—	59	3	no	—
321	C₂×D₈	—	59	3	no	—
322	C₂×D₈	—	59	6	no	—
323	C₂×D₈	C₂×D₅₉	1	3	yes	complemented
324	#131	—	59	1	no	—
325	#131	—	59	3	no	—
326	#131	—	59	3	no	—
327	#131	C₂×D₅₉	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	59	3	no	—
329	C₂×M₁₆	—	59	3	no	—
330	C₂⁴	—	118	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	59	1	no	—
334	#41	—	59	3	no	—
335	#41	—	59	3	no	—
336	#41	—	59	3	no	—
337	#41	—	59	1	no	—
338	#41	—	59	6	no	—
339	#41	—	59	3	no	—
340	#41	—	59	3	no	—
341	#41	—	59	3	no	—
342	#41	—	59	3	no	—
343	#41	—	118	3	no	—
344	#41	—	118	3	no	—
345	#41	—	118	3	no	—
346	#41	—	118	3	no	—
347	#41	—	118	3	no	—
348	#41	—	118	3	no	—
349	#41	—	118	3	no	—
350	#41	—	118	3	no	—
351	#41	—	118	6	no	—
352	#41	—	118	3	no	—
353	#41	—	118	3	no	—
354	#41	—	118	1	no	—
355	#41	—	118	3	no	—
356	#41	C₂²×D₅₉	1	3	yes	—
357	#41	C₂²×D₅₉	1	1	yes	characteristic
358	#41	C₂²×D₅₉	1	3	yes	complemented
359	C₂×Q₈	—	59	1	no	—
360	C₂×Q₈	—	59	3	no	—
361	C₂×Q₈	—	59	1	no	—
362	C₂×Q₈	—	59	3	no	—
363	C₂×Q₈	—	118	3	no	—
364	C₂×Q₈	—	118	1	no	—
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	—	59	3	no	—
368	C₂×D₄	—	59	3	no	—
369	C₂×D₄	—	59	6	no	—
370	C₂×D₄	—	59	3	no	—
371	C₂×D₄	—	59	3	no	—
372	C₂×D₄	—	118	3	no	—
373	C₂×D₄	—	118	3	no	—
374	C₂×D₄	—	118	3	no	—
375	C₂×D₄	—	118	3	no	—
376	C₂×D₄	—	118	6	no	—
377	C₂×D₄	—	118	3	no	—
378	C₂×D₄	—	118	3	no	—
379	C₂×D₄	—	118	3	no	—
380	C₂×D₄	—	118	3	no	—
381	C₂×D₄	—	118	6	no	—
382	C₂×D₄	—	118	6	no	—
383	C₂×D₄	—	118	3	no	—
384	C₂×D₄	—	118	3	no	—
385	C₂×D₄	C₂²×D₅₉	1	3	yes	—
386	C₂×D₄	C₂²×D₅₉	1	3	yes	complemented
387	C₂²×C₄	—	59	3	no	—
388	C₂²×C₄	—	118	3	no	—
389	C₂²×C₄	—	118	3	no	—
390	C₂²×C₄	—	118	3	no	—
391	Q₁₆	—	59	3	no	—
392	Q₁₆	—	59	1	no	—
393	Q₁₆	—	59	3	no	—
394	Q₁₆	C₂²×D₅₉	1	1	yes	characteristic, complemented
395	SD₁₆	—	59	3	no	—
396	SD₁₆	—	59	1	no	—
397	SD₁₆	—	59	3	no	—
398	SD₁₆	—	59	6	no	—
399	SD₁₆	—	59	3	no	—
400	SD₁₆	—	59	6	no	—
401	SD₁₆	—	59	3	no	—
402	SD₁₆	—	59	1	no	—
403	SD₁₆	C₂²×D₅₉	1	3	yes	complemented
404	SD₁₆	C₂²×D₅₉	1	3	yes	complemented
405	D₈	—	59	3	no	—
406	D₈	—	59	3	no	—
407	D₈	—	59	6	no	—
408	D₈	—	59	3	no	—
409	D₈	C₂²×D₅₉	1	6	yes	complemented
410	D₈	C₂²×D₅₉	1	3	yes	complemented
411	M₁₆	—	59	3	no	—
412	M₁₆	—	59	3	no	—
413	M₁₆	—	59	1	no	—
414	M₁₆	—	59	3	no	—
415	M₁₆	—	59	3	no	—
416	M₁₆	C₂²×D₅₉	1	3	yes	complemented
417	C₂×C₈	—	59	3	no	—
418	C₂×C₈	—	59	6	no	—
419	C₂×C₈	C₂²×D₅₉	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	2	3	no	—
422	C₂³	—	59	3	no	—
423	C₂³	—	118	3	no	—
424	C₂³	—	118	6	no	—
425	C₂³	—	118	3	no	—
426	C₂³	—	118	3	no	—
427	C₂³	—	472	6	no	—
428	Q₈	—	59	3	no	—
429	Q₈	—	59	3	no	—
430	Q₈	—	59	1	no	—
431	Q₈	—	118	3	no	—
432	Q₈	—	118	1	no	—
433	Q₈	—	118	3	no	—
434	Q₈	D₄×D₅₉	1	1	yes	characteristic
435	Q₈	C₂³×D₅₉	1	1	yes	characteristic
436	Q₈	C₂³×D₅₉	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	2	3	no	—
441	D₄	—	59	6	no	—
442	D₄	—	59	3	no	—
443	D₄	—	59	1	no	—
444	D₄	—	59	3	no	—
445	D₄	—	118	3	no	—
446	D₄	—	118	1	no	—
447	D₄	—	118	3	no	—
448	D₄	—	118	6	no	—
449	D₄	—	118	3	no	—
450	D₄	—	118	3	no	—
451	D₄	—	118	3	no	—
452	D₄	—	118	6	no	—
453	D₄	—	118	3	no	—
454	D₄	—	118	3	no	—
455	D₄	—	118	3	no	—
456	D₄	D₄×D₅₉	1	3	yes	—
457	D₄	C₂³×D₅₉	1	3	yes	—
458	D₄	C₂³×D₅₉	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	59	3	no	—
462	C₂×C₄	—	59	3	no	—
463	C₂×C₄	—	59	3	no	—
464	C₂×C₄	—	59	3	no	—
465	C₂×C₄	—	59	1	no	—
466	C₂×C₄	—	118	1	no	—
467	C₂×C₄	—	118	3	no	—
468	C₂×C₄	—	118	1	no	—
469	C₂×C₄	—	118	3	no	—
470	C₂×C₄	—	118	3	no	—
471	C₂×C₄	—	118	3	no	—
472	C₂×C₄	—	118	6	no	—
473	C₂×C₄	—	118	3	no	—
474	C₂×C₄	—	118	3	no	—
475	C₂×C₄	—	118	3	no	—
476	C₂×C₄	C₂³×D₅₉	1	3	yes	—
477	C₈	—	59	3	no	—
478	C₈	—	59	1	no	—
479	C₈	C₂³×D₅₉	1	3	yes	—
480	C₈	C₂³×D₅₉	1	1	yes	characteristic
481	C₂²	—	2	3	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	8	3	no	—
485	C₂²	—	59	1	no	—
486	C₂²	—	59	3	no	—
487	C₂²	—	118	1	no	—
488	C₂²	—	118	3	no	—
489	C₂²	—	472	3	no	—
490	C₂²	—	472	6	no	—
491	C₂²	—	472	3	no	—
492	C₂²	—	236	3	no	—
493	C₂²	—	236	6	no	—
494	C₂²	C₂×D₄×D₅₉	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	59	1	no	—
498	C₄	—	59	3	no	—
499	C₄	—	118	1	no	—
500	C₄	—	118	3	no	—
501	C₄	C₂×D₄×D₅₉	1	3	yes	—
502	C₄	C₂⁴×D₅₉	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	3	no	—
506	C₂	—	118	3	no	—
507	C₂	—	118	1	no	—
508	C₂	—	236	3	no	—
509	C₂	—	236	1	no	—
510	C₂	C₂²×D₄×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₅₉
commutator	C₄×C₅₉	C₂⁵
Frattini	C₄	C₂⁴×D₅₉
Fitting	C₅₉×#576	C₂
socle	C₂×C₅₉	C₂³×D₄
hypercenter	#576	D₅₉
hypocenter	C₅₉	#3585
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. #16838237	C₂	semidirect
2. H(5,𝔽₂)×D₅₉	C₂	semidirect
3. #16838214	C₂	semidirect
4. #16838213	C₂	semidirect
5. #16838212	C₂	semidirect
6. #16838209	C₂	semidirect
7. #16838206	C₂	semidirect
8. #16838205	C₂	semidirect
9. #16838203	C₂	semidirect
10. #16838199	C₂	semidirect
11. #16838198	C₂	semidirect
12. C₂×#14273751	C₂	semidirect
13. AGL(1,ℤ/8)×D₅₉	C₂	semidirect
14. #16838167	C₂	semidirect
15. C₅₉×#576	C₂	semidirect
17. #14273774	C₂²	semidirect
18. #14273774	C₂²	semidirect
20. #14273773	C₂²	semidirect
21. #14273773	C₂²	semidirect
24. #14273772	C₂²	semidirect
25. #14273772	C₂²	semidirect
27. C₂×#11745687	C₂²	semidirect
31. #41×D₅₉	C₂²	semidirect
32. #41×D₅₉	C₂²	semidirect
34. C₂×D₄×D₅₉	C₂²	semidirect
35. #14273760	C₂²	semidirect
36. #14273759	C₂²	semidirect
37. #14273759	C₂²	semidirect
38. #14273757	C₂²	semidirect
39. #14273756	C₂²	semidirect
40. #14273756	C₂²	semidirect
41. #14273755	C₂²	semidirect
42. #14273754	C₂²	semidirect
43. #14273754	C₂²	semidirect
44. #14273753	C₂²	semidirect
45. #14273753	C₂²	semidirect
46. #14273752	C₂²	semidirect
47. #14273751	C₂²	semidirect
48. #14273751	C₂²	semidirect
49. #14273751	C₂²	semidirect
50. #14273751	C₂²	semidirect
51. #14273751	C₂²	semidirect
52. #14273749	C₂²	semidirect
53. #14273748	C₂²	semidirect
54. #14273747	C₂²	semidirect
55. #14273747	C₂²	semidirect
56. #14273746	C₂²	semidirect
57. C₂×#11745660	C₂²	semidirect
58. C₂×#11745670	C₂²	semidirect
59. SD₁₆×D₅₉	C₂²	semidirect
60. C₂×#11745669	C₂²	semidirect
61. D₈×D₅₉	C₂²	semidirect
62. #14273735	C₂²	semidirect
63. #14273734	C₂²	semidirect
64. #14273733	C₂²	semidirect
65. C₂×#11745659	C₂²	semidirect
66. M₁₆×D₅₉	C₂²	semidirect
67. H(5,𝔽₂)×C₅₉	C₂²	semidirect
68. H(5,𝔽₂)×C₅₉	C₂²	semidirect
69. AGL(1,ℤ/8)×C₅₉	C₂²	semidirect
70. AGL(1,ℤ/8)×C₅₉	C₂²	semidirect
71. #135×C₅₉	C₂²	semidirect
72. C₂×D₈×C₅₉	C₂²	semidirect
73. #131×C₅₉	C₂²	semidirect
79. #41×C₅₉	C₂³	semidirect
83. C₂×D₄×C₅₉	C₂³	semidirect
96. Q₈×D₅₉	C₂³	semidirect
108. #11745687	C₂³	semidirect
120. D₄×D₅₉	C₂³	semidirect
127. #11745685	C₂³	semidirect
134. C₂×Dic₁₁₈	C₂³	semidirect
135. Q₁₆×C₅₉	C₂³	semidirect
136. SD₁₆×C₅₉	C₂³	semidirect
137. SD₁₆×C₅₉	C₂³	semidirect
138. D₈×C₅₉	C₂³	semidirect
139. D₈×C₅₉	C₂³	semidirect
140. M₁₆×C₅₉	C₂³	semidirect
141. C₂×C₈×C₅₉	C₂³	semidirect
142. #11745672	C₂³	semidirect
143. #11745672	C₂³	semidirect
144. #11745671	C₂³	semidirect
145. #11745671	C₂³	semidirect
146. #11745670	C₂³	semidirect
147. #11745670	C₂³	semidirect
148. #11745670	C₂³	semidirect
149. #11745669	C₂³	semidirect
150. #11745669	C₂³	semidirect
151. #11745669	C₂³	semidirect
152. #11745664	C₂³	semidirect
153. C₂×C₅₉⋊C₈	C₂³	semidirect
154. Dic₂₃₆	C₂³	semidirect
155. D₄₇₂	C₂³	semidirect
156. #11745660	C₂³	semidirect
157. #11745660	C₂³	semidirect
158. #11745660	C₂³	semidirect
161. #11745659	C₂³	semidirect
162. #11745659	C₂³	semidirect
163. C₈×D₅₉	C₂³	semidirect
265. #576	D₅₉	semidirect
271. C₅₉	#3585	semidirect
282. H(5,𝔽₂)	C₂×D₅₉	semidirect
283. H(5,𝔽₂)	C₂×D₅₉	semidirect
310. AGL(1,ℤ/8)	C₂×D₅₉	semidirect
311. AGL(1,ℤ/8)	C₂×D₅₉	semidirect
317. #135	C₂×D₅₉	semidirect
323. C₂×D₈	C₂×D₅₉	semidirect
327. #131	C₂×D₅₉	semidirect
358. #41	C₂²×D₅₉	semidirect
386. C₂×D₄	C₂²×D₅₉	semidirect
394. Q₁₆	C₂²×D₅₉	semidirect
403. SD₁₆	C₂²×D₅₉	semidirect
404. SD₁₆	C₂²×D₅₉	semidirect
409. D₈	C₂²×D₅₉	semidirect
410. D₈	C₂²×D₅₉	semidirect
416. M₁₆	C₂²×D₅₉	semidirect
419. C₂×C₈	C₂²×D₅₉	semidirect