Subgroups — #28607207

Order 15104.

812 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433011	C₂	1	1	yes	maximal, characteristic
2	#21433009	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837516	C₂	1	1	yes	maximal, characteristic
4	#21432706	C₂	1	1	yes	maximal, characteristic, complemented
5	#21432705	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424885	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424883	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424338	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424337	C₂	1	1	yes	maximal, characteristic, complemented
10	#21424335	C₂	1	1	yes	maximal, characteristic, complemented
11	#21424267	C₂	1	1	yes	maximal, characteristic, complemented
12	#21424149	C₂	1	1	yes	maximal, characteristic, complemented
13	#21424148	C₂	1	1	yes	maximal, characteristic, complemented
14	#21423974	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1861	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273747	C₂²	1	1	yes	characteristic
17	#16838169	C₂²	1	1	yes	characteristic
18	#16838168	C₂²	1	1	yes	characteristic
19	#16838168	C₂²	1	1	yes	characteristic
20	C₂×#14273735	C₂²	1	1	yes	characteristic
21	C₂×#14273734	C₂²	1	1	yes	characteristic
22	#16837522	—	2	2	no	—
23	#16837521	—	2	2	no	—
24	#16837517	—	2	2	no	—
25	#16837516	—	2	2	no	—
26	#16837516	C₄	1	2	yes	complemented
27	#16837516	C₄	1	2	yes	complemented
28	#16837516	C₄	1	2	yes	complemented
29	#16837516	C₄	1	2	yes	complemented
30	#16837451	C₂²	1	1	yes	characteristic
31	#16837450	—	2	2	no	—
32	#16837450	C₂²	1	1	yes	characteristic
33	#16837450	C₂²	1	1	yes	characteristic
34	#16837449	—	2	2	no	—
35	C₂×#14273662	—	2	2	no	—
36	C₂×#14273662	C₂²	1	1	yes	characteristic
37	C₂×#14273662	C₂²	1	1	yes	characteristic
38	C₂×#14273662	C₂²	1	1	yes	characteristic
39	C₂×#14273662	C₂²	1	1	yes	characteristic
40	C₂×#14273662	C₂²	1	1	yes	characteristic
41	C₂×#14273662	C₂²	1	1	yes	characteristic
42	#108×D₅₉	—	2	2	no	—
43	#16837438	C₂²	1	1	yes	characteristic
44	#16837426	C₂²	1	1	yes	characteristic
45	#16837420	C₂²	1	1	yes	characteristic
46	#16837419	C₂²	1	1	yes	characteristic
47	#16837418	C₂²	1	1	yes	characteristic
48	C₂×#14273655	C₂²	1	1	yes	characteristic
49	#16837360	C₂²	1	1	yes	characteristic
50	#16837358	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
52	#16837174	C₂²	1	1	yes	characteristic
53	#16837173	C₂²	1	1	yes	characteristic
54	#16837172	C₂²	1	1	yes	characteristic
55	#16837162	C₂²	1	1	yes	characteristic
56	C₅₉×#568	C₂²	1	1	yes	characteristic
57	C₅₉×#430	C₂²	1	1	yes	characteristic
58	C₅₉×#423	C₂²	1	1	yes	characteristic
59	C₅₉×#421	C₂²	1	1	yes	characteristic
60	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
61	C₅₉×#344	C₂²	1	1	yes	characteristic
62	C₅₉×#339	C₂²	1	1	yes	characteristic
63	C₂×#11745685	C₂³	1	1	yes	characteristic
64	#14273747	C₂×C₄	1	2	yes	—
65	#14273747	C₂×C₄	1	2	yes	—
66	#14273747	D₄	1	2	yes	—
67	#14273747	D₄	1	2	yes	—
68	C₂×#11745672	Q₈	1	1	yes	characteristic
69	C₂×#11745670	Q₈	1	1	yes	characteristic
70	C₂×#11745671	Q₈	1	1	yes	characteristic
71	C₂×#11745669	Q₈	1	1	yes	characteristic
72	#14273735	—	2	1	no	—
73	#14273735	—	2	1	no	—
74	#14273735	—	2	2	no	—
75	#14273735	—	4	1	no	—
76	#14273735	C₂×C₄	1	2	yes	—
77	#14273735	C₂×C₄	1	2	yes	—
78	#14273734	—	2	1	no	—
79	#14273734	—	2	1	no	—
80	#14273734	—	2	2	no	—
81	#14273734	—	4	1	no	—
82	#14273734	C₂×C₄	1	2	yes	—
83	#14273734	C₂×C₄	1	2	yes	—
84	#14273733	—	2	2	no	—
85	#14273733	—	4	1	no	—
86	C₂×#11745664	—	2	1	no	—
87	C₂×#11745664	—	2	2	no	—
88	C₂×#11745664	C₂³	1	1	yes	characteristic
89	C₂×#11745664	C₂³	1	1	yes	characteristic
90	C₂×#11745664	C₂³	1	1	yes	characteristic
91	C₂×#11745664	C₂³	1	1	yes	characteristic
92	C₂×#11745659	—	2	1	no	—
93	M₁₆×D₅₉	—	2	2	no	—
94	M₁₆×D₅₉	—	2	2	no	—
95	C₂²×C₅₉⋊C₈	—	2	1	no	—
96	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
97	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₅₉	—	2	1	no	—
99	#14273686	C₂³	1	1	yes	characteristic
100	#14273663	—	2	2	no	—
101	#14273662	—	2	2	no	—
102	#14273662	—	2	2	no	—
103	#14273662	—	2	1	no	—
104	#14273662	—	2	1	no	—
105	#14273662	—	2	1	no	—
106	#14273662	—	2	1	no	—
107	#14273662	—	2	1	no	—
108	#14273662	—	2	1	no	—
109	#14273662	—	2	1	no	—
110	#14273662	—	2	1	no	—
111	#14273662	C₂×C₄	1	2	yes	—
112	#14273662	C₂×C₄	1	2	yes	—
113	#14273662	D₄	1	2	yes	—
114	#14273662	D₄	1	2	yes	—
115	#14273660	—	2	1	no	—
116	#14273658	—	2	1	no	—
117	C₄⋊(C₅₉⋊C₈)	—	4	1	no	—
118	#14273655	—	2	2	no	—
119	#14273655	C₂×C₄	1	2	yes	—
120	#14273655	C₂×C₄	1	2	yes	—
121	#14273654	—	2	2	no	—
122	#14273653	—	2	2	no	—
123	#14273638	—	2	1	no	—
124	#14273637	—	2	1	no	—
125	C₄×C₅₉⋊C₈	—	2	1	no	—
126	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
127	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
128	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₅₉	—	2	1	no	—
131	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
132	#131×C₅₉	—	2	2	no	—
133	#131×C₅₉	—	4	1	no	—
134	C₂×M₁₆×C₅₉	—	2	2	no	—
135	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
139	#117×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
141	#108×C₅₉	—	2	2	no	—
142	C₄⋊C₈×C₅₉	—	4	1	no	—
143	#104×C₅₉	—	2	2	no	—
144	#104×C₅₉	C₂×C₄	1	2	yes	—
145	#104×C₅₉	C₂×C₄	1	2	yes	—
146	#41×C₅₉	—	2	1	no	—
147	#41×C₅₉	—	2	1	no	—
148	#41×C₅₉	C₂²×C₄	1	2	yes	—
149	#41×C₅₉	C₂×D₄	1	2	yes	—
150	C₂×Q₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
151	C₂×D₄×C₅₉	—	2	1	no	—
152	C₂×D₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	—	2	1	no	—
154	C₂²×C₄×C₅₉	—	2	1	no	—
155	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
156	C₂×C₂²⋊D₅₉	—	2	1	no	—
157	#11745685	—	2	1	no	—
158	#11745685	—	2	1	no	—
159	#11745685	C₂²×C₄	1	2	yes	—
160	#11745685	C₂×D₄	1	2	yes	—
161	C₂×D₂₃₆	C₂×Q₈	1	1	yes	characteristic
162	C₂×C₄×D₅₉	—	2	1	no	—
163	C₂×Dic₁₁₈	C₂×Q₈	1	1	yes	characteristic
164	M₁₆×C₅₉	—	2	1	no	—
165	M₁₆×C₅₉	—	2	1	no	—
166	M₁₆×C₅₉	—	2	1	no	—
167	M₁₆×C₅₉	—	2	1	no	—
168	M₁₆×C₅₉	—	2	1	no	—
169	M₁₆×C₅₉	—	2	1	no	—
170	M₁₆×C₅₉	—	4	2	no	—
171	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
172	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₅₉	—	2	1	no	—
174	C₂×C₈×C₅₉	—	2	1	no	—
175	C₂×C₈×C₅₉	—	2	1	no	—
176	C₂×C₈×C₅₉	—	2	1	no	—
177	C₂×C₈×C₅₉	—	4	2	no	—
178	C₄⋊C₄×C₅₉	—	2	1	no	—
179	C₂²⋊C₄×C₅₉	—	2	1	no	—
180	C₄²×C₅₉	—	2	1	no	—
181	C₄²×C₅₉	—	2	1	no	—
182	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
184	C₂²⋊Dic₅₉	—	2	1	no	—
185	#11745672	C₄⋊C₄	1	2	yes	—
186	#11745672	C₄⋊C₄	1	2	yes	—
187	#11745671	C₄⋊C₄	1	2	yes	—
188	#11745671	C₄⋊C₄	1	2	yes	—
189	#11745670	C₄⋊C₄	1	2	yes	—
190	#11745670	C₄⋊C₄	1	2	yes	—
191	#11745669	C₄⋊C₄	1	2	yes	—
192	#11745669	C₄⋊C₄	1	2	yes	—
193	C₄⋊Dic₅₉	—	2	1	no	—
194	C₄×Dic₅₉	—	2	1	no	—
195	#11745664	—	2	1	no	—
196	#11745664	—	2	1	no	—
197	#11745664	—	2	2	no	—
198	#11745664	—	2	2	no	—
199	#11745664	—	2	1	no	—
200	#11745664	—	2	1	no	—
201	#11745664	—	2	1	no	—
202	#11745664	—	2	1	no	—
203	#11745664	—	4	2	no	—
204	#11745664	C₂²×C₄	1	2	yes	—
205	#11745664	C₂×D₄	1	2	yes	—
206	C₂×C₅₉⋊C₈	—	2	1	no	—
207	C₂×C₅₉⋊C₈	—	2	1	no	—
208	C₂×C₅₉⋊C₈	—	2	2	no	—
209	C₂×C₅₉⋊C₈	—	2	2	no	—
210	C₂×C₅₉⋊C₈	—	2	1	no	—
211	C₂×C₅₉⋊C₈	—	2	1	no	—
212	C₂×C₅₉⋊C₈	—	4	2	no	—
213	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
219	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
221	C₂×C₅₉⋊C₈	C₂×Q₈	1	1	yes	characteristic
222	C₂×C₅₉⋊C₈	C₂×Q₈	1	1	yes	characteristic
223	C₂×C₅₉⋊C₈	#41	1	1	yes	characteristic
224	C₂×C₅₉⋊C₈	#41	1	1	yes	characteristic
225	#11745659	—	2	2	no	—
226	#11745659	—	2	2	no	—
227	#11745659	—	4	2	no	—
228	#11745659	—	4	2	no	—
229	C₈×D₅₉	—	2	2	no	—
230	C₈×D₅₉	—	2	2	no	—
231	C₈×D₅₉	—	4	2	no	—
232	C₈×D₅₉	—	4	2	no	—
233	C₂³×C₅₉	—	2	1	no	—
234	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂²×D₅₉	—	2	1	no	—
236	Q₈×C₅₉	—	2	1	no	—
237	Q₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
238	D₄×C₅₉	—	2	2	no	—
239	D₄×C₅₉	—	2	2	no	—
240	D₄×C₅₉	—	2	1	no	—
241	D₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
242	C₂×C₄×C₅₉	—	2	1	no	—
243	C₂×C₄×C₅₉	—	2	1	no	—
244	C₂×C₄×C₅₉	—	2	2	no	—
245	C₂×C₄×C₅₉	—	2	2	no	—
246	C₂×C₄×C₅₉	—	2	1	no	—
247	C₂×C₄×C₅₉	—	4	2	no	—
248	C₂×C₄×C₅₉	—	4	1	no	—
249	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
253	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²⋊D₅₉	—	2	2	no	—
256	C₂²⋊D₅₉	—	2	2	no	—
257	C₂×Dic₅₉	—	2	1	no	—
258	C₂×Dic₅₉	—	4	1	no	—
259	D₂₃₆	—	2	1	no	—
260	D₂₃₆	C₂×C₄⋊C₄	1	2	yes	—
261	C₄×D₅₉	—	2	2	no	—
262	C₄×D₅₉	—	2	2	no	—
263	Dic₁₁₈	—	2	1	no	—
264	Dic₁₁₈	C₂×C₄⋊C₄	1	2	yes	—
265	C₈×C₅₉	—	2	2	no	—
266	C₈×C₅₉	—	2	2	no	—
267	C₈×C₅₉	—	4	1	no	—
268	C₈×C₅₉	—	4	1	no	—
269	C₅₉⋊C₈	—	2	2	no	—
270	C₅₉⋊C₈	—	2	2	no	—
271	C₅₉⋊C₈	—	4	1	no	—
272	C₅₉⋊C₈	—	4	1	no	—
273	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
275	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₅₉⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
278	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
279	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
280	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
281	#22694	—	59	1	no	maximal, Sylow
282	C₂²×C₅₉	—	2	2	no	—
283	C₂²×C₅₉	—	4	1	no	—
284	C₂²×C₅₉	—	8	1	no	—
285	C₂²×C₅₉	#520	1	1	yes	characteristic
286	C₂²×C₅₉	#547	1	1	yes	characteristic
287	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
288	C₂×D₅₉	—	2	2	no	—
289	C₂×D₅₉	—	8	1	no	—
290	C₄×C₅₉	—	2	2	no	—
291	C₄×C₅₉	—	2	2	no	—
292	C₄×C₅₉	—	4	1	no	—
293	C₄×C₅₉	—	8	1	no	—
294	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
295	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
296	C₄×C₅₉	D₄²	1	1	yes	characteristic
297	C₄×C₅₉	#554	1	1	yes	characteristic
298	Dic₅₉	—	2	2	no	—
299	Dic₅₉	—	8	1	no	—
300	#2957	—	59	1	no	—
301	#2957	—	59	1	no	—
302	C₂×#443	—	59	1	no	—
303	#2916	—	59	1	no	—
304	#2916	—	59	1	no	—
305	#1953	—	59	1	no	—
306	#1953	—	59	1	no	—
307	#1861	—	59	1	no	—
308	#1861	—	59	1	no	—
309	#1861	—	59	1	no	—
310	#1861	D₅₉	1	1	yes	characteristic, complemented
311	#1848	—	59	1	no	—
312	#1814	—	59	1	no	—
313	#1814	—	59	1	no	—
314	#1772	—	59	1	no	—
315	C₂×C₅₉	—	2	1	no	—
316	C₂×C₅₉	—	2	1	no	—
317	C₂×C₅₉	—	2	1	no	—
318	C₂×C₅₉	—	4	2	no	—
319	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
320	D₅₉	—	4	2	no	—
321	C₂×#135	—	59	1	no	—
322	#568	—	59	1	no	—
323	#568	—	59	1	no	—
324	#568	—	59	1	no	—
325	#568	C₂×D₅₉	1	1	yes	characteristic
326	C₂×#131	—	59	1	no	—
327	C₂×#131	—	59	1	no	—
328	#444	—	118	2	no	—
329	#444	—	118	2	no	—
330	#443	—	59	2	no	—
331	#443	—	59	2	no	—
332	#443	—	59	2	no	—
333	#443	—	59	2	no	—
334	#443	—	118	2	no	—
335	#443	—	118	2	no	—
336	#430	—	59	1	no	—
337	#430	—	59	1	no	—
338	#430	—	59	1	no	—
339	#430	—	118	2	no	—
340	#430	—	118	2	no	—
341	#430	C₂×D₅₉	1	1	yes	characteristic
342	C₂×#108	—	59	1	no	—
343	C₂×#108	—	59	1	no	—
344	C₂×#108	—	59	1	no	—
345	C₂×#108	—	59	1	no	—
346	C₂×#108	—	59	1	no	—
347	C₂×#108	—	59	1	no	—
348	C₂×#108	—	118	2	no	—
349	C₂×#108	—	118	2	no	—
350	#427	—	59	1	no	—
351	#423	—	59	1	no	—
352	#423	C₂×D₅₉	1	1	yes	characteristic
353	#421	—	59	1	no	—
354	#421	—	59	1	no	—
355	#421	—	59	1	no	—
356	#421	C₂×D₅₉	1	1	yes	characteristic
357	C₂×#104	—	59	1	no	—
358	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
359	#405	—	59	1	no	—
360	#405	—	59	1	no	—
361	C₂×C₄×C₈	—	59	1	no	—
362	#344	—	59	1	no	—
363	#344	—	59	1	no	—
364	#344	—	59	1	no	—
365	#344	C₂×D₅₉	1	1	yes	characteristic
366	#339	—	59	1	no	—
367	#339	C₂×D₅₉	1	1	yes	characteristic
368	C₅₉	#22694	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	59	1	no	—
370	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
371	#135	—	59	2	no	—
372	#135	—	59	2	no	—
373	#135	—	59	2	no	—
374	#135	—	59	2	no	—
375	C₂×Q₁₆	—	59	1	no	—
376	C₂×SD₁₆	—	59	1	no	—
377	C₂×SD₁₆	—	59	1	no	—
378	C₂×D₈	—	59	1	no	—
379	#131	—	2	2	no	—
380	#131	—	4	1	no	—
381	#131	—	59	2	no	—
382	#131	—	59	2	no	—
383	#131	—	59	2	no	—
384	#131	—	59	2	no	—
385	#131	—	118	2	no	—
386	#131	—	118	1	no	—
387	#131	—	118	1	no	—
388	#131	—	118	1	no	—
389	#131	—	118	1	no	—
390	#131	—	118	2	no	—
391	#131	—	118	2	no	—
392	#131	—	236	1	no	—
393	#131	—	236	1	no	—
394	#131	—	236	1	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	59	1	no	—
397	C₂×M₁₆	—	59	1	no	—
398	C₂×M₁₆	—	59	1	no	—
399	C₂×M₁₆	—	59	1	no	—
400	C₂×M₁₆	—	118	1	no	—
401	C₂×M₁₆	—	118	1	no	—
402	C₂×M₁₆	—	118	2	no	—
403	C₂×M₁₆	—	118	2	no	—
404	C₂×M₁₆	—	118	2	no	—
405	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
406	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
407	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
408	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
409	C₂²×C₈	—	59	1	no	—
410	C₂²×C₈	—	59	1	no	—
411	C₂²×C₈	—	118	1	no	—
412	C₂²×C₈	—	118	1	no	—
413	#117	—	59	1	no	—
414	#117	C₂²×D₅₉	1	1	yes	characteristic
415	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
416	#108	—	2	2	no	—
417	#108	—	59	2	no	—
418	#108	—	59	2	no	—
419	#108	—	59	2	no	—
420	#108	—	59	2	no	—
421	#108	—	118	2	no	—
422	#108	—	118	1	no	—
423	#108	—	118	1	no	—
424	#108	—	118	1	no	—
425	#108	—	118	1	no	—
426	#108	—	118	1	no	—
427	#108	—	118	1	no	—
428	#108	—	118	1	no	—
429	#108	—	118	1	no	—
430	#108	—	118	2	no	—
431	#108	—	118	2	no	—
432	#107	—	118	1	no	—
433	#106	—	118	1	no	—
434	C₄⋊C₈	—	4	1	no	—
435	C₄⋊C₈	—	236	1	no	—
436	#104	—	2	2	no	—
437	#104	—	59	2	no	—
438	#104	—	59	2	no	—
439	#104	—	118	2	no	—
440	#104	—	118	2	no	—
441	#104	—	118	2	no	—
442	#104	C₄×D₅₉	1	2	yes	—
443	#104	C₄×D₅₉	1	2	yes	—
444	#97	—	118	1	no	—
445	#97	—	118	1	no	—
446	C₄×C₈	—	59	1	no	—
447	C₄×C₈	—	59	1	no	—
448	C₄×C₈	—	59	1	no	—
449	C₄×C₈	—	59	1	no	—
450	C₄×C₈	—	118	1	no	—
451	C₄×C₈	—	118	1	no	—
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	59	2	no	—
455	#41	—	59	2	no	—
456	#41	—	118	1	no	—
457	#41	—	118	1	no	—
458	#41	C₂×C₄×D₅₉	1	2	yes	—
459	#41	D₄×D₅₉	1	2	yes	—
460	C₂×Q₈	—	59	1	no	—
461	C₂×Q₈	Q₈×D₅₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	59	1	no	—
464	C₂×D₄	—	118	1	no	—
465	C₂×D₄	Q₈×D₅₉	1	1	yes	characteristic
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	118	1	no	—
469	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
470	Q₁₆	—	59	2	no	—
471	Q₁₆	—	59	2	no	—
472	SD₁₆	—	59	2	no	—
473	SD₁₆	—	59	2	no	—
474	SD₁₆	—	59	2	no	—
475	SD₁₆	—	59	2	no	—
476	D₈	—	59	2	no	—
477	D₈	—	59	2	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	1	no	—
480	M₁₆	—	2	1	no	—
481	M₁₆	—	2	1	no	—
482	M₁₆	—	2	1	no	—
483	M₁₆	—	2	1	no	—
484	M₁₆	—	4	2	no	—
485	M₁₆	—	59	2	no	—
486	M₁₆	—	59	2	no	—
487	M₁₆	—	118	2	no	—
488	M₁₆	—	118	2	no	—
489	M₁₆	—	118	2	no	—
490	M₁₆	—	118	2	no	—
491	M₁₆	—	118	1	no	—
492	M₁₆	—	118	1	no	—
493	M₁₆	—	118	1	no	—
494	M₁₆	—	118	1	no	—
495	M₁₆	—	118	1	no	—
496	M₁₆	—	118	1	no	—
497	M₁₆	—	236	2	no	—
498	M₁₆	—	236	2	no	—
499	M₁₆	—	236	2	no	—
500	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
501	M₁₆	D₄×D₅₉	1	2	yes	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	4	2	no	—
507	C₂×C₈	—	59	1	no	—
508	C₂×C₈	—	59	1	no	—
509	C₂×C₈	—	59	1	no	—
510	C₂×C₈	—	59	1	no	—
511	C₂×C₈	—	59	1	no	—
512	C₂×C₈	—	59	1	no	—
513	C₂×C₈	—	59	1	no	—
514	C₂×C₈	—	59	1	no	—
515	C₂×C₈	—	59	1	no	—
516	C₂×C₈	—	59	1	no	—
517	C₂×C₈	—	59	1	no	—
518	C₂×C₈	—	59	1	no	—
519	C₂×C₈	—	118	2	no	—
520	C₂×C₈	—	118	2	no	—
521	C₂×C₈	—	118	2	no	—
522	C₂×C₈	—	118	2	no	—
523	C₂×C₈	—	118	1	no	—
524	C₂×C₈	—	118	1	no	—
525	C₂×C₈	—	118	1	no	—
526	C₂×C₈	—	118	1	no	—
527	C₂×C₈	—	236	2	no	—
528	C₂×C₈	—	236	2	no	—
529	C₂×C₈	—	236	2	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	118	1	no	—
532	C₂²⋊C₄	—	2	1	no	—
533	C₂²⋊C₄	—	118	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	118	1	no	—
537	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
538	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
539	C₂³	—	2	1	no	—
540	C₂³	—	118	1	no	—
541	C₂³	#14273774	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	—	59	2	no	—
544	Q₈	—	118	1	no	—
545	Q₈	C₄⋊C₄×D₅₉	1	2	yes	—
546	D₄	—	2	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	2	1	no	—
549	D₄	—	59	2	no	—
550	D₄	—	118	2	no	—
551	D₄	—	118	2	no	—
552	D₄	—	118	1	no	—
553	D₄	C₄⋊C₄×D₅₉	1	2	yes	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	118	1	no	—
562	C₂×C₄	—	118	2	no	—
563	C₂×C₄	—	118	2	no	—
564	C₂×C₄	—	236	1	no	—
565	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
566	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
568	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
569	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
570	C₂×C₄	#14273772	1	1	yes	characteristic
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	59	1	no	—
576	C₈	—	59	1	no	—
577	C₈	—	59	1	no	—
578	C₈	—	59	1	no	—
579	C₈	—	59	1	no	—
580	C₈	—	59	1	no	—
581	C₈	—	59	1	no	—
582	C₈	—	59	1	no	—
583	C₈	—	118	2	no	—
584	C₈	—	118	2	no	—
585	C₈	—	236	1	no	—
586	C₈	—	236	1	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	8	1	no	—
590	C₂²	—	118	2	no	—
591	C₂²	—	472	1	no	—
592	C₂²	#16837881	1	1	yes	characteristic
593	C₂²	#16838050	1	1	yes	characteristic
594	C₂²	#16838065	1	1	yes	characteristic
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	118	2	no	—
600	C₄	—	472	1	no	—
601	C₄	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
602	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
603	C₄	#16838034	1	1	yes	characteristic
604	C₄	#16838106	1	1	yes	characteristic
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	4	2	no	—
609	C₂	—	236	2	no	—
610	C₂	#21426994	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16838034
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1861	C₂
socle	C₂×C₅₉	D₄×C₄⋊C₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1861	D₅₉
hypocenter	C₅₉	#22694
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1861

Complements

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

N	H ≅ G/N	type
4. #21432706	C₂	semidirect
5. #21432705	C₂	semidirect
6. #21424885	C₂	semidirect
7. #21424883	C₂	semidirect
8. #21424338	C₂	semidirect
9. #21424337	C₂	semidirect
10. #21424335	C₂	semidirect
11. #21424267	C₂	semidirect
12. #21424149	C₂	semidirect
13. #21424148	C₂	semidirect
14. #21423974	C₂	semidirect
15. C₅₉×#1861	C₂	semidirect
26. #16837516	C₄	semidirect
27. #16837516	C₄	semidirect
28. #16837516	C₄	semidirect
29. #16837516	C₄	semidirect
310. #1861	D₅₉	semidirect
368. C₅₉	#22694	semidirect

Maximal subgroups

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

subgroup	index
#21433011	2
#21433009	2
C₂×#16837516	2
#21432706	2
#21432705	2
#21424885	2
#21424883	2
#21424338	2
#21424337	2
#21424335	2
#21424267	2
#21424149	2
#21424148	2
#21423974	2
C₅₉×#1861	2
#22694	59