Subgroups — #28557895

Order 15104.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433213	C₂	1	1	yes	maximal, characteristic
2	#21432740	C₂	1	1	yes	maximal, characteristic
3	#21422887	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422884	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422882	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422879	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422877	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422874	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422868	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422866	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422864	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422861	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422857	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422851	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2989	C₂	1	1	yes	maximal, characteristic
16	#16837533	—	2	1	no	—
17	#16837480	—	2	1	no	—
18	#16837474	—	2	1	no	—
19	#16837474	—	2	1	no	—
20	#16837463	C₄	1	2	yes	—
21	#16837463	C₄	1	2	yes	—
22	#16837459	C₂²	1	1	yes	characteristic
23	#16837459	C₂²	1	1	yes	characteristic
24	#16837455	C₂²	1	1	yes	characteristic
25	#16837455	C₂²	1	1	yes	characteristic
26	#16837455	C₂²	1	1	yes	characteristic
27	#16837455	C₂²	1	1	yes	characteristic
28	#16837455	C₂²	1	1	yes	characteristic
29	#16837429	C₄	1	2	yes	—
30	#16837426	C₂²	1	1	yes	characteristic
31	#16837426	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
33	#16837369	C₄	1	2	yes	—
34	C₄×#11745664	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
36	#16837154	C₂²	1	1	yes	characteristic
37	#16837154	C₂²	1	1	yes	characteristic
38	#16837154	C₂²	1	1	yes	characteristic
39	#16837154	C₂²	1	1	yes	characteristic
40	#16837154	C₂²	1	1	yes	characteristic
41	#16837154	C₂²	1	1	yes	characteristic
42	#16837152	C₂²	1	1	yes	characteristic
43	#16837152	C₂²	1	1	yes	characteristic
44	#16837152	C₂²	1	1	yes	characteristic
45	#16837152	C₂²	1	1	yes	characteristic
46	#16837152	C₂²	1	1	yes	characteristic
47	#16837152	C₂²	1	1	yes	characteristic
48	#16837152	C₂²	1	1	yes	characteristic
49	#16837152	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837152	C₂²	1	1	yes	characteristic
52	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
53	C₅₉×#446	—	2	1	no	—
54	C₅₉×#436	—	2	1	no	—
55	C₅₉×#435	—	2	1	no	—
56	C₅₉×#435	—	2	1	no	—
57	C₅₉×#432	C₂²	1	1	yes	characteristic
58	C₅₉×#432	C₂²	1	1	yes	characteristic
59	C₅₉×#431	C₂²	1	1	yes	characteristic
60	C₅₉×#423	C₂²	1	1	yes	characteristic
61	C₅₉×#423	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
63	C₂×#11745664	—	2	1	no	—
64	C₂×#11745664	—	2	1	no	—
65	C₂×#11745664	C₂×C₄	1	2	yes	—
66	C₂²×C₅₉⋊C₈	—	2	1	no	—
67	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
68	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
72	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
73	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
74	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
75	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
78	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
79	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
81	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
82	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
83	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
84	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
86	#14273638	—	2	1	no	—
87	#14273638	—	2	1	no	—
88	#14273638	C₂×C₄	1	2	yes	—
89	C₄×C₅₉⋊C₈	—	2	1	no	—
90	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
91	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₂×M₁₆×C₅₉	—	2	1	no	—
97	C₂×M₁₆×C₅₉	—	2	1	no	—
98	C₂²×C₈×C₅₉	—	2	1	no	—
99	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₅₉	Q₈	1	1	yes	characteristic
101	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
102	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
103	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
104	C₄×D₄×C₅₉	Q₈	1	1	yes	characteristic
105	C₄×D₄×C₅₉	Q₈	1	1	yes	characteristic
106	C₄×D₄×C₅₉	Q₈	1	1	yes	characteristic
107	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
108	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
109	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₅₉	—	2	1	no	—
114	C₄⋊C₈×C₅₉	—	2	1	no	—
115	C₄⋊C₈×C₅₉	—	2	1	no	—
116	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
120	C₂²⋊C₈×C₅₉	—	2	1	no	—
121	C₂²⋊C₈×C₅₉	—	2	1	no	—
122	C₂²⋊C₈×C₅₉	—	2	1	no	—
123	#97×C₅₉	—	2	1	no	—
124	#97×C₅₉	—	2	1	no	—
125	C₄×C₈×C₅₉	—	2	1	no	—
126	#41×C₅₉	—	4	2	no	—
127	C₂×Q₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
128	C₂×D₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
129	C₂×D₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
130	C₂×D₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
140	M₁₆×C₅₉	—	8	1	no	—
141	M₁₆×C₅₉	—	8	1	no	—
142	C₂×C₈×C₅₉	—	2	1	no	—
143	C₂×C₈×C₅₉	—	2	1	no	—
144	C₂×C₈×C₅₉	—	2	1	no	—
145	C₂×C₈×C₅₉	—	2	1	no	—
146	C₂×C₈×C₅₉	—	8	1	no	—
147	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
149	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
150	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
153	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
157	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
158	C₂²⋊C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
159	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
166	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
167	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
168	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
169	#11745664	—	4	2	no	—
170	#11745664	—	8	1	no	—
171	#11745664	—	8	1	no	—
172	C₂×C₅₉⋊C₈	—	2	1	no	—
173	C₂×C₅₉⋊C₈	—	2	1	no	—
174	C₂×C₅₉⋊C₈	—	2	1	no	—
175	C₂×C₅₉⋊C₈	—	2	1	no	—
176	C₂×C₅₉⋊C₈	—	4	2	no	—
177	C₂×C₅₉⋊C₈	—	8	1	no	—
178	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
181	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
182	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	Q₈×C₅₉	—	4	1	no	—
186	D₄×C₅₉	—	4	1	no	—
187	D₄×C₅₉	—	4	1	no	—
188	D₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	2	2	no	—
190	C₂×C₄×C₅₉	—	2	2	no	—
191	C₂×C₄×C₅₉	—	2	2	no	—
192	C₂×C₄×C₅₉	—	2	1	no	—
193	C₂×C₄×C₅₉	—	2	1	no	—
194	C₂×C₄×C₅₉	—	2	1	no	—
195	C₂×C₄×C₅₉	—	2	1	no	—
196	C₂×C₄×C₅₉	—	2	1	no	—
197	C₂×C₄×C₅₉	—	2	1	no	—
198	C₂×C₄×C₅₉	—	4	1	no	—
199	C₂×C₄×C₅₉	—	4	1	no	—
200	C₂×C₄×C₅₉	—	4	1	no	—
201	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
213	C₈×C₅₉	—	4	1	no	—
214	C₈×C₅₉	—	4	1	no	—
215	C₈×C₅₉	—	4	1	no	—
216	C₈×C₅₉	—	4	1	no	—
217	C₅₉⋊C₈	—	2	2	no	—
218	C₅₉⋊C₈	—	2	2	no	—
219	C₅₉⋊C₈	—	2	2	no	—
220	C₅₉⋊C₈	—	2	2	no	—
221	C₅₉⋊C₈	—	4	1	no	—
222	C₅₉⋊C₈	—	4	1	no	—
223	C₅₉⋊C₈	—	4	1	no	—
224	C₅₉⋊C₈	—	4	1	no	—
225	#17824	—	59	1	no	maximal, Sylow
226	C₂²×C₅₉	—	2	1	no	—
227	C₂²×C₅₉	—	2	1	no	—
228	C₂²×C₅₉	—	2	1	no	—
229	C₂²×C₅₉	—	2	1	no	—
230	C₂²×C₅₉	—	2	1	no	—
231	C₂²×C₅₉	—	2	1	no	—
232	C₂²×C₅₉	—	2	1	no	—
233	C₂²×C₅₉	—	2	1	no	—
234	C₂²×C₅₉	—	2	1	no	—
235	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₄×C₅₉	—	2	1	no	—
237	C₄×C₅₉	—	2	1	no	—
238	C₄×C₅₉	—	2	1	no	—
239	C₄×C₅₉	—	2	1	no	—
240	C₄×C₅₉	—	2	1	no	—
241	C₄×C₅₉	—	2	1	no	—
242	C₄×C₅₉	—	2	1	no	—
243	C₄×C₅₉	—	2	1	no	—
244	C₄×C₅₉	—	2	1	no	—
245	C₄×C₅₉	—	2	1	no	—
246	C₄×C₅₉	#568	1	2	yes	—
247	C₄×C₅₉	#577	1	1	yes	characteristic
248	C₄×C₅₉	#577	1	1	yes	characteristic
249	#2989	—	59	1	no	—
250	#2989	D₅₉	1	1	yes	characteristic
251	#2922	—	59	1	no	—
252	#1574	—	59	1	no	—
253	#1574	—	59	1	no	—
254	#1573	—	59	1	no	—
255	#1573	—	59	1	no	—
256	#1572	—	59	1	no	—
257	#1572	—	59	1	no	—
258	#1570	—	59	1	no	—
259	#1570	—	59	1	no	—
260	#1569	—	59	1	no	—
261	#1569	—	59	1	no	—
262	#1568	—	59	1	no	—
263	#1566	—	59	1	no	—
264	C₂×C₅₉	—	4	1	no	—
265	C₂×C₅₉	—	4	1	no	—
266	C₂×C₅₉	—	4	1	no	—
267	C₂×C₅₉	#2905	1	1	yes	characteristic
268	C₂×C₅₉	#2912	1	1	yes	characteristic
269	C₂×C₅₉	#2916	1	1	yes	characteristic
270	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
271	#446	—	2	1	no	—
272	#446	—	118	1	no	—
273	#436	—	2	1	no	—
274	#436	—	118	1	no	—
275	#435	—	2	1	no	—
276	#435	—	2	1	no	—
277	#435	—	118	1	no	—
278	#435	—	118	1	no	—
279	#433	—	59	2	no	—
280	#433	—	59	2	no	—
281	#432	—	59	1	no	—
282	#432	—	59	1	no	—
283	#432	C₂×D₅₉	1	1	yes	characteristic
284	#432	C₂×D₅₉	1	1	yes	characteristic
285	#431	—	59	1	no	—
286	#431	—	59	1	no	—
287	#431	—	59	1	no	—
288	#431	—	59	1	no	—
289	#431	—	59	1	no	—
290	#431	C₂×D₅₉	1	1	yes	characteristic
291	#424	—	59	2	no	—
292	#423	—	59	1	no	—
293	#423	—	59	1	no	—
294	#423	C₂×D₅₉	1	1	yes	characteristic
295	#423	C₂×D₅₉	1	1	yes	characteristic
296	C₂×C₄⋊C₈	—	59	1	no	—
297	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
298	#408	—	59	2	no	—
299	C₄×M₁₆	—	59	1	no	—
300	C₂×C₄×C₈	—	59	1	no	—
301	#335	—	59	1	no	—
302	#335	—	59	1	no	—
303	#335	—	59	1	no	—
304	#335	—	59	1	no	—
305	#335	—	59	1	no	—
306	#335	—	59	1	no	—
307	#334	—	59	1	no	—
308	#334	—	59	1	no	—
309	#334	—	59	1	no	—
310	#334	—	59	1	no	—
311	#334	—	59	1	no	—
312	#334	—	59	1	no	—
313	#334	—	59	1	no	—
314	#334	—	59	1	no	—
315	#334	—	59	1	no	—
316	#334	—	59	1	no	—
317	C₅₉	#17824	1	1	yes	characteristic, complemented, Sylow
318	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	59	2	no	—
322	C₂×M₁₆	—	118	1	no	—
323	C₂×M₁₆	—	118	1	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	59	2	no	—
326	C₂²×C₈	—	118	1	no	—
327	C₄×Q₈	Dic₁₁₈	1	1	yes	characteristic
328	C₄×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
329	C₄×D₄	Dic₁₁₈	1	1	yes	characteristic
330	C₄×D₄	Dic₁₁₈	1	1	yes	characteristic
331	C₄×D₄	Dic₁₁₈	1	1	yes	characteristic
332	C₄×D₄	C₂²⋊D₅₉	1	1	yes	characteristic
333	C₄×D₄	C₂²⋊D₅₉	1	1	yes	characteristic
334	C₄×D₄	C₂²⋊D₅₉	1	1	yes	characteristic
335	#117	C₄×D₅₉	1	1	yes	characteristic
336	#117	C₄×D₅₉	1	1	yes	characteristic
337	#117	C₄×D₅₉	1	1	yes	characteristic
338	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
339	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	59	2	no	—
345	C₄⋊C₈	—	59	2	no	—
346	C₄⋊C₈	—	59	2	no	—
347	C₄⋊C₈	—	59	2	no	—
348	C₄⋊C₈	—	59	1	no	—
349	C₄⋊C₈	—	59	1	no	—
350	C₄⋊C₈	—	59	1	no	—
351	C₄⋊C₈	—	59	1	no	—
352	C₄⋊C₈	—	118	1	no	—
353	C₄⋊C₈	—	118	1	no	—
354	C₄⋊C₈	—	118	1	no	—
355	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
356	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
357	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	1	no	—
361	C₂²⋊C₈	—	2	1	no	—
362	C₂²⋊C₈	—	59	2	no	—
363	C₂²⋊C₈	—	59	2	no	—
364	C₂²⋊C₈	—	59	2	no	—
365	C₂²⋊C₈	—	59	2	no	—
366	C₂²⋊C₈	—	118	1	no	—
367	C₂²⋊C₈	—	118	1	no	—
368	C₂²⋊C₈	—	118	1	no	—
369	#97	—	2	1	no	—
370	#97	—	2	1	no	—
371	#97	—	59	2	no	—
372	#97	—	118	1	no	—
373	#97	—	118	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	—	59	2	no	—
376	C₄×C₈	—	59	1	no	—
377	C₄×C₈	—	59	1	no	—
378	C₄×C₈	—	59	1	no	—
379	C₄×C₈	—	59	1	no	—
380	C₄×C₈	—	118	1	no	—
381	#41	—	4	2	no	—
382	C₂×Q₈	Dic₅₉⋊C₄	1	1	yes	characteristic
383	C₂×D₄	Dic₅₉⋊C₄	1	1	yes	characteristic
384	C₂×D₄	Dic₅₉⋊C₄	1	1	yes	characteristic
385	C₂×D₄	Dic₅₉⋊C₄	1	1	yes	characteristic
386	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
387	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
388	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
395	M₁₆	—	8	1	no	—
396	M₁₆	—	8	1	no	—
397	M₁₆	—	472	1	no	—
398	M₁₆	—	472	1	no	—
399	M₁₆	—	236	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	8	1	no	—
405	C₂×C₈	—	59	2	no	—
406	C₂×C₈	—	59	2	no	—
407	C₂×C₈	—	59	2	no	—
408	C₂×C₈	—	59	2	no	—
409	C₂×C₈	—	118	1	no	—
410	C₂×C₈	—	118	1	no	—
411	C₂×C₈	—	118	1	no	—
412	C₂×C₈	—	118	1	no	—
413	C₂×C₈	—	472	1	no	—
414	C₂×C₈	—	236	2	no	—
415	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
416	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
417	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
418	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
419	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
420	C₄⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
421	C₂²⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
422	C₂²⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
423	C₂²⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
424	C₂²⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
425	C₂²⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
426	C₂²⋊C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
427	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
428	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
429	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
432	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
433	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
434	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
435	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
436	C₄²	C₂³×D₅₉	1	1	yes	characteristic
437	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
438	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
439	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
440	Q₈	—	4	1	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	4	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
457	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
458	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
459	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
460	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
461	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
463	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
467	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
468	C₈	—	4	1	no	—
469	C₈	—	4	1	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	118	2	no	—
473	C₈	—	118	2	no	—
474	C₈	—	118	2	no	—
475	C₈	—	118	2	no	—
476	C₈	—	236	1	no	—
477	C₈	—	236	1	no	—
478	C₈	—	236	1	no	—
479	C₈	—	236	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	#16838168	1	2	yes	—
501	C₄	#16838210	1	1	yes	characteristic
502	C₄	#16838213	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	4	1	no	—
505	C₂	—	4	1	no	—
506	C₂	#21432659	1	1	yes	characteristic
507	C₂	#21432689	1	1	yes	characteristic
508	C₂	#21432705	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2989	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2989	D₅₉
hypocenter	C₅₉	#17824
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2989

Complements

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

N	H ≅ G/N	type
3. #21422887	C₂	semidirect
4. #21422884	C₂	semidirect
5. #21422882	C₂	semidirect
6. #21422879	C₂	semidirect
7. #21422877	C₂	semidirect
8. #21422874	C₂	semidirect
9. #21422868	C₂	semidirect
10. #21422866	C₂	semidirect
11. #21422864	C₂	semidirect
12. #21422861	C₂	semidirect
13. #21422857	C₂	semidirect
14. #21422851	C₂	semidirect
317. C₅₉	#17824	semidirect

Maximal subgroups

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

subgroup	index
#21433213	2
#21432740	2
#21422887	2
#21422884	2
#21422882	2
#21422879	2
#21422877	2
#21422874	2
#21422868	2
#21422866	2
#21422864	2
#21422861	2
#21422857	2
#21422851	2
C₅₉×#2989	2
#17824	59