Subgroups — #28595145

Order 15104.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837524	C₂	1	2	yes	maximal, complemented
2	#21432808	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14273734	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425016	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424872	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424746	C₂	1	2	yes	maximal, complemented
7	#21424425	C₂	1	2	yes	maximal, complemented
8	#21424116	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423966	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423943	C₂	1	2	yes	maximal, complemented
11	C₅₉×#3035	C₂	1	1	yes	maximal, characteristic
12	C₂×#14273734	C₂²	1	1	yes	characteristic
13	C₂×#14273734	C₂²	1	2	yes	—
14	C₂×#14273734	C₂²	1	1	yes	characteristic
15	#16837524	—	2	8	no	—
16	#16837480	—	2	1	no	—
17	#16837480	—	2	1	no	—
18	D₄×C₅₉⋊C₈	—	2	1	no	—
19	D₄×C₅₉⋊C₈	—	2	1	no	—
20	C₂×#14273663	C₂²	1	2	yes	—
21	#16837426	C₂²	1	1	yes	characteristic
22	C₂×#14273654	C₂²	1	2	yes	—
23	C₂×#14273654	C₂²	1	2	yes	—
24	C₂×#14273654	C₂²	1	2	yes	—
25	#16837369	C₂²	1	2	yes	—
26	#16837358	—	2	1	no	—
27	#16837358	—	2	1	no	—
28	#16837358	C₂²	1	1	yes	characteristic
29	#16837358	C₂²	1	1	yes	characteristic
30	C₄×#11745664	—	2	1	no	—
31	C₄×#11745664	C₂²	1	1	yes	characteristic
32	C₂×#14273637	C₂²	1	2	yes	—
33	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
34	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
36	#16837167	C₂²	1	2	yes	—
37	#16837161	C₂²	1	2	yes	—
38	#16837156	C₂²	1	2	yes	—
39	C₂×#135×C₅₉	C₂²	1	2	yes	—
40	C₅₉×#532	C₂²	1	1	yes	characteristic
41	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#464	C₄	1	2	yes	complemented
43	C₅₉×#463	C₄	1	2	yes	complemented
44	C₅₉×#462	C₄	1	1	yes	characteristic, complemented
45	C₅₉×#461	C₄	1	1	yes	characteristic, complemented
46	C₅₉×#460	C₄	1	1	yes	characteristic, complemented
47	C₅₉×#459	C₄	1	1	yes	characteristic, complemented
48	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
49	C₅₉×#416	C₂²	1	2	yes	—
50	#14273734	—	2	2	no	—
51	#14273734	—	2	2	no	—
52	#14273734	—	2	2	no	—
53	#14273734	—	2	4	no	—
54	#14273734	—	2	4	no	—
55	#14273734	D₄	1	4	yes	complemented
56	C₂×#11745664	—	2	1	no	—
57	C₂×#11745664	—	2	1	no	—
58	C₂×#11745664	—	2	2	no	—
59	C₂×#11745664	C₂³	1	2	yes	—
60	C₂×#11745664	C₂³	1	1	yes	characteristic
61	C₂×#11745664	C₂³	1	1	yes	characteristic
62	C₂²×C₅₉⋊C₈	—	2	1	no	—
63	C₂²×C₅₉⋊C₈	—	2	1	no	—
64	C₂²×C₅₉⋊C₈	—	2	2	no	—
65	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₅₉	—	2	1	no	—
68	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
69	#14273663	—	2	4	no	—
70	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
72	#14273654	—	2	4	no	—
73	#14273654	—	2	4	no	—
74	#14273654	—	2	4	no	—
75	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
77	#14273638	—	2	1	no	—
78	#14273638	—	2	1	no	—
79	#14273638	—	2	1	no	—
80	#14273637	—	2	4	no	—
81	C₄×C₅₉⋊C₈	—	2	1	no	—
82	C₄×C₅₉⋊C₈	—	2	1	no	—
83	C₄×C₅₉⋊C₈	—	2	1	no	—
84	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
85	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
86	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₅₉⋊C₈	D₄	1	1	yes	characteristic
88	C₅₉⋊#95	—	2	1	no	—
89	C₂×#41×C₅₉	C₂³	1	2	yes	—
90	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
91	#135×C₅₉	—	2	4	no	—
92	#135×C₅₉	—	2	4	no	—
93	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	—
94	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
95	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
96	C₂×D₈×C₅₉	C₂×C₄	1	2	yes	—
97	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
99	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
100	#124×C₅₉	C₂×C₄	1	2	yes	—
101	#121×C₅₉	—	2	1	no	—
102	#121×C₅₉	—	2	1	no	—
103	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₅₉	—	2	1	no	—
106	C₄×D₄×C₅₉	—	2	1	no	—
107	C₄×D₄×C₅₉	—	2	1	no	—
108	C₄×D₄×C₅₉	—	2	1	no	—
109	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
110	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
111	#117×C₅₉	—	2	1	no	—
112	#117×C₅₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅₉	—	2	1	no	—
114	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
116	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
117	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
118	#103×C₅₉	C₂×C₄	1	2	yes	—
119	#103×C₅₉	C₂×C₄	1	2	yes	—
120	#102×C₅₉	C₂×C₄	1	2	yes	—
121	#102×C₅₉	C₂×C₄	1	2	yes	—
122	#41×C₅₉	—	2	1	no	—
123	#41×C₅₉	—	2	1	no	—
124	#41×C₅₉	—	2	2	no	—
125	#41×C₅₉	—	2	2	no	—
126	#41×C₅₉	—	2	2	no	—
127	#41×C₅₉	—	2	2	no	—
128	#41×C₅₉	C₂×D₄	1	2	yes	—
129	#41×C₅₉	#41	1	2	yes	—
130	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
131	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₄×C₅₉	—	2	1	no	—
133	C₂×D₄×C₅₉	—	2	2	no	—
134	C₂×D₄×C₅₉	—	2	1	no	—
135	C₂×D₄×C₅₉	—	2	1	no	—
136	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
137	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	—	2	1	no	—
139	C₂²×C₄×C₅₉	—	2	1	no	—
140	C₂²×C₄×C₅₉	—	2	1	no	—
141	C₂²×C₄×C₅₉	—	2	2	no	—
142	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
143	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
144	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₅₉	—	2	2	no	—
146	Q₁₆×C₅₉	—	2	4	no	—
147	SD₁₆×C₅₉	—	2	4	no	—
148	SD₁₆×C₅₉	—	2	4	no	—
149	D₈×C₅₉	—	2	4	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₅₉	—	2	1	no	—
155	C₄⋊C₄×C₅₉	—	2	1	no	—
156	C₄⋊C₄×C₅₉	—	2	1	no	—
157	C₄⋊C₄×C₅₉	—	2	1	no	—
158	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₅₉	—	2	1	no	—
161	C₂²⋊C₄×C₅₉	—	2	1	no	—
162	C₂²⋊C₄×C₅₉	—	2	1	no	—
163	C₂²⋊C₄×C₅₉	—	2	2	no	—
164	C₂²⋊C₄×C₅₉	—	2	2	no	—
165	C₄²×C₅₉	—	2	1	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	—	2	1	no	—
168	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₄⋊Dic₅₉	—	4	2	no	—
173	C₄×Dic₅₉	—	2	2	no	—
174	C₄×Dic₅₉	—	2	2	no	—
175	#11745664	—	2	4	no	—
176	#11745664	—	2	1	no	—
177	#11745664	—	2	1	no	—
178	#11745664	—	2	4	no	—
179	#11745664	—	2	2	no	—
180	#11745664	—	2	2	no	—
181	#11745664	—	4	4	no	—
182	#11745664	C₂×D₄	1	2	yes	—
183	#11745664	#41	1	2	yes	—
184	C₂×C₅₉⋊C₈	—	2	4	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	4	no	—
190	C₂×C₅₉⋊C₈	—	2	2	no	—
191	C₂×C₅₉⋊C₈	—	4	4	no	—
192	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
193	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
194	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
195	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
197	C₂×C₅₉⋊C₈	#41	1	2	yes	—
198	C₂³×C₅₉	—	2	1	no	—
199	C₂³×C₅₉	—	2	2	no	—
200	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
201	Q₈×C₅₉	—	2	1	no	—
202	Q₈×C₅₉	—	2	2	no	—
203	Q₈×C₅₉	—	2	2	no	—
204	Q₈×C₅₉	C₄×D₄	1	2	yes	—
205	D₄×C₅₉	—	2	2	no	—
206	D₄×C₅₉	—	2	2	no	—
207	D₄×C₅₉	—	2	2	no	—
208	D₄×C₅₉	—	2	1	no	—
209	D₄×C₅₉	—	2	2	no	—
210	D₄×C₅₉	—	4	2	no	—
211	D₄×C₅₉	—	4	2	no	—
212	D₄×C₅₉	—	4	2	no	—
213	D₄×C₅₉	—	4	2	no	—
214	D₄×C₅₉	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	2	no	—
217	C₂×C₄×C₅₉	—	2	2	no	—
218	C₂×C₄×C₅₉	—	2	2	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	2	no	—
222	C₂×C₄×C₅₉	—	4	1	no	—
223	C₂×C₄×C₅₉	—	4	2	no	—
224	C₂×C₄×C₅₉	—	4	2	no	—
225	C₂×C₄×C₅₉	—	4	2	no	—
226	C₂×C₄×C₅₉	—	4	2	no	—
227	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
237	C₂×Dic₅₉	—	4	2	no	—
238	C₂×Dic₅₉	—	4	2	no	—
239	C₂×Dic₅₉	—	4	2	no	—
240	C₈×C₅₉	—	2	2	no	—
241	C₈×C₅₉	—	2	2	no	—
242	C₅₉⋊C₈	—	2	2	no	—
243	C₅₉⋊C₈	—	2	1	no	—
244	C₅₉⋊C₈	—	2	2	no	—
245	C₅₉⋊C₈	—	2	1	no	—
246	C₅₉⋊C₈	—	4	2	no	—
247	C₅₉⋊C₈	#121	1	2	yes	—
248	C₅₉⋊C₈	#121	1	2	yes	—
249	#21518	—	59	1	no	maximal, Sylow
250	C₂²×C₅₉	—	2	1	no	—
251	C₂²×C₅₉	—	2	1	no	—
252	C₂²×C₅₉	—	2	2	no	—
253	C₂²×C₅₉	—	4	1	no	—
254	C₂²×C₅₉	—	4	1	no	—
255	C₂²×C₅₉	—	4	2	no	—
256	C₂²×C₅₉	—	4	2	no	—
257	C₂²×C₅₉	—	4	2	no	—
258	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂²×C₅₉	#529	1	1	yes	characteristic
260	C₂²×C₅₉	#532	1	1	yes	characteristic
261	C₄×C₅₉	—	2	1	no	—
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	2	1	no	—
264	C₄×C₅₉	—	2	2	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	—	4	1	no	—
267	C₄×C₅₉	—	4	2	no	—
268	C₄×C₅₉	#444	1	2	yes	complemented
269	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
271	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
272	C₄×C₅₉	#525	1	1	yes	characteristic
273	Dic₅₉	—	8	2	no	—
274	#3035	D₅₉	1	1	yes	characteristic
275	C₂×#444	—	59	2	no	—
276	#2931	—	59	1	no	—
277	C₄×#131	—	59	1	no	—
278	#1980	—	59	1	no	—
279	#1950	—	59	1	no	—
280	#1929	—	59	2	no	—
281	#1876	—	59	2	no	—
282	#1806	—	59	1	no	—
283	#1770	—	59	1	no	—
284	#1765	—	59	2	no	—
285	C₂×C₅₉	—	2	1	no	—
286	C₂×C₅₉	—	2	1	no	—
287	C₂×C₅₉	—	4	2	no	—
288	C₂×C₅₉	—	8	2	no	—
289	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
290	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
291	C₂×C₅₉	#2955	1	1	yes	characteristic
292	C₂×#135	C₂×D₅₉	1	2	yes	—
293	C₂×#131	—	59	1	no	—
294	C₂×#131	—	59	1	no	—
295	C₂×#131	—	59	2	no	—
296	#532	C₂×D₅₉	1	1	yes	characteristic
297	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
298	#464	Dic₅₉	1	2	yes	complemented
299	#463	Dic₅₉	1	2	yes	complemented
300	#462	Dic₅₉	1	1	yes	characteristic, complemented
301	#461	Dic₅₉	1	1	yes	characteristic, complemented
302	#460	Dic₅₉	1	1	yes	characteristic, complemented
303	#459	Dic₅₉	1	1	yes	characteristic, complemented
304	#444	—	118	8	no	—
305	#436	—	118	1	no	—
306	#436	—	118	1	no	—
307	C₈×D₄	—	118	1	no	—
308	C₈×D₄	—	118	1	no	—
309	C₂×#108	—	59	2	no	—
310	#423	—	59	1	no	—
311	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
312	C₂×#104	—	59	2	no	—
313	C₂×#104	—	59	2	no	—
314	C₂×#104	—	59	2	no	—
315	#416	C₂×D₅₉	1	2	yes	—
316	#408	—	59	2	no	—
317	#405	—	59	1	no	—
318	#405	—	59	1	no	—
319	#405	—	118	1	no	—
320	#405	—	118	1	no	—
321	C₄×M₁₆	—	59	1	no	—
322	C₄×M₁₆	—	118	1	no	—
323	C₂×#97	—	59	2	no	—
324	C₂×C₄×C₈	—	59	1	no	—
325	C₂×C₄×C₈	—	118	1	no	—
326	C₄×C₄⋊C₄	—	59	1	no	—
327	#341	—	59	2	no	—
328	#339	—	59	2	no	—
329	#336	—	59	2	no	—
330	C₅₉	#21518	1	1	yes	characteristic, complemented, Sylow
331	C₂×#41	C₂²×D₅₉	1	2	yes	—
332	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
333	#135	—	2	4	no	—
334	#135	—	2	4	no	—
335	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	—
336	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
337	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
338	C₂×D₈	C₂×Dic₅₉	1	2	yes	—
339	#131	—	59	4	no	—
340	#131	—	118	2	no	—
341	#131	—	118	4	no	—
342	#131	—	118	4	no	—
343	#131	—	118	2	no	—
344	#131	—	118	2	no	—
345	C₂×M₁₆	—	59	1	no	—
346	C₂×M₁₆	—	59	1	no	—
347	C₂×M₁₆	—	59	2	no	—
348	C₂×M₁₆	—	118	1	no	—
349	C₂×M₁₆	—	118	1	no	—
350	C₂×M₁₆	—	118	2	no	—
351	C₂²×C₈	—	59	1	no	—
352	C₂²×C₈	—	59	1	no	—
353	C₂²×C₈	—	118	1	no	—
354	C₂²×C₈	—	118	1	no	—
355	C₂²×C₈	—	118	2	no	—
356	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
357	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
358	#127	C₂×Dic₅₉	1	1	yes	characteristic
359	#124	C₂×Dic₅₉	1	2	yes	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
363	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
369	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
370	#117	—	2	1	no	—
371	#117	C₂²×D₅₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	—	118	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	59	2	no	—
375	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
376	#108	—	118	4	no	—
377	C₄⋊C₈	—	118	1	no	—
378	C₄⋊C₈	—	118	1	no	—
379	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
381	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
382	#104	—	118	4	no	—
383	#104	—	118	4	no	—
384	#104	—	118	4	no	—
385	#103	C₂×Dic₅₉	1	2	yes	—
386	#103	C₂×Dic₅₉	1	2	yes	—
387	#102	C₂×Dic₅₉	1	2	yes	—
388	#102	C₂×Dic₅₉	1	2	yes	—
389	C₂²⋊C₈	—	118	2	no	—
390	C₂²⋊C₈	—	118	2	no	—
391	#97	—	118	1	no	—
392	#97	—	118	1	no	—
393	#97	—	118	4	no	—
394	#97	—	118	1	no	—
395	C₄×C₈	—	59	1	no	—
396	C₄×C₈	—	59	1	no	—
397	C₄×C₈	—	59	1	no	—
398	C₄×C₈	—	59	1	no	—
399	C₄×C₈	—	118	1	no	—
400	C₄×C₈	—	118	1	no	—
401	C₄×C₈	—	118	1	no	—
402	#95	—	118	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	D₄×D₅₉	1	2	yes	—
410	#41	#11745687	1	2	yes	—
411	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
412	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
418	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	118	2	no	—
424	C₂²×C₄	#11745687	1	1	yes	characteristic
425	C₂²×C₄	#11745687	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
427	Q₁₆	—	2	4	no	—
428	SD₁₆	—	2	4	no	—
429	SD₁₆	—	2	4	no	—
430	D₈	—	2	4	no	—
431	M₁₆	—	59	2	no	—
432	M₁₆	—	59	2	no	—
433	M₁₆	—	118	4	no	—
434	M₁₆	—	118	4	no	—
435	M₁₆	—	118	1	no	—
436	M₁₆	—	118	1	no	—
437	M₁₆	—	118	2	no	—
438	M₁₆	—	118	2	no	—
439	M₁₆	—	236	4	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	59	2	no	—
443	C₂×C₈	—	59	1	no	—
444	C₂×C₈	—	59	1	no	—
445	C₂×C₈	—	59	2	no	—
446	C₂×C₈	—	59	1	no	—
447	C₂×C₈	—	59	1	no	—
448	C₂×C₈	—	118	4	no	—
449	C₂×C₈	—	118	4	no	—
450	C₂×C₈	—	118	1	no	—
451	C₂×C₈	—	118	1	no	—
452	C₂×C₈	—	118	1	no	—
453	C₂×C₈	—	118	1	no	—
454	C₂×C₈	—	118	2	no	—
455	C₂×C₈	—	236	4	no	—
456	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
457	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	236	2	no	—
463	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
464	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	118	2	no	—
474	C₄²	—	118	2	no	—
475	C₄²	D₄×D₅₉	1	1	yes	characteristic
476	C₄²	D₄×D₅₉	1	1	yes	characteristic
477	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
478	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	C₂×#11745687	1	1	yes	characteristic
482	Q₈	—	2	1	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	D₄×Dic₅₉	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	2	no	—
495	D₄	D₄×Dic₅₉	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	236	2	no	—
509	C₂×C₄	—	236	2	no	—
510	C₂×C₄	—	236	2	no	—
511	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
512	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
513	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
514	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
515	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
518	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
519	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
521	C₈	—	2	2	no	—
522	C₈	—	2	2	no	—
523	C₈	—	59	2	no	—
524	C₈	—	59	2	no	—
525	C₈	—	118	2	no	—
526	C₈	—	118	1	no	—
527	C₈	—	118	1	no	—
528	C₈	—	118	2	no	—
529	C₈	—	236	2	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
539	C₂²	#16837933	1	1	yes	characteristic
540	C₂²	#16837947	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	2	no	—
548	C₄	—	472	2	no	—
549	C₄	#16837524	1	2	yes	complemented
550	C₄	C₂×D₄×Dic₅₉	1	1	yes	characteristic
551	C₄	#41×Dic₅₉	1	1	yes	characteristic
552	C₄	#121×D₅₉	1	1	yes	characteristic
553	C₄	#16837912	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	#121×Dic₅₉	1	1	yes	characteristic
559	C₂	C₂×#16837524	1	1	yes	characteristic
560	C₂	#21432999	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting, prime radical	C₅₉×#3035	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#3035	D₅₉
hypocenter	C₅₉	#21518
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3035

Complements

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

N	H ≅ G/N	type
1. C₂×#16837524	C₂	semidirect
2. #21432808	C₂	semidirect
3. C₄×#14273734	C₂	semidirect
4. #21425016	C₂	semidirect
5. #21424872	C₂	semidirect
6. #21424746	C₂	semidirect
7. #21424425	C₂	semidirect
8. #21424116	C₂	semidirect
9. #21423966	C₂	semidirect
10. #21423943	C₂	semidirect
42. C₅₉×#464	C₄	semidirect
43. C₅₉×#463	C₄	semidirect
44. C₅₉×#462	C₄	semidirect
45. C₅₉×#461	C₄	semidirect
46. C₅₉×#460	C₄	semidirect
47. C₅₉×#459	C₄	semidirect
55. #14273734	D₄	semidirect
268. C₄×C₅₉	#444	semidirect
298. #464	Dic₅₉	semidirect
299. #463	Dic₅₉	semidirect
300. #462	Dic₅₉	semidirect
301. #461	Dic₅₉	semidirect
302. #460	Dic₅₉	semidirect
303. #459	Dic₅₉	semidirect
330. C₅₉	#21518	semidirect
549. C₄	#16837524	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837524	2
#21432808	2
C₄×#14273734	2
#21425016	2
#21424872	2
#21424746	2
#21424425	2
#21424116	2
#21423966	2
#21423943	2
C₅₉×#3035	2
#21518	59