Subgroups — C₂×#21422975 #28558253

Order 15104.

750 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16837480	C₂	1	1	yes	maximal, characteristic
3	#21422975	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16837155	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
7	C₂×#16837124	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×SD₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11745664	—	2	1	no	—
10	Q₈×C₅₉⋊C₈	—	2	2	no	—
11	Q₈×C₅₉⋊C₈	C₂²	1	4	yes	complemented
12	#16837480	—	2	2	no	—
13	#16837480	C₂²	1	4	yes	—
14	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
18	C₂×C₄×C₅₉⋊C₈	—	2	1	no	—
19	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
21	#16837155	C₂²	1	4	yes	complemented
22	Q₈⋊(C₅₉⋊C₈)	C₂²	1	4	yes	complemented
23	D₄⋊(C₅₉⋊C₈)	C₂²	1	4	yes	—
24	#16837124	C₂²	1	4	yes	complemented
25	C₂²×SD₁₆×C₅₉	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
28	C₄×SD₁₆×C₅₉	C₄	1	4	yes	—
29	C₄×SD₁₆×C₅₉	C₂²	1	4	yes	—
30	C₂×#106×C₅₉	C₄	1	1	yes	characteristic
31	C₂×#103×C₅₉	C₄	1	1	yes	characteristic
32	C₂×#102×C₅₉	C₄	1	1	yes	characteristic
33	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#11745664	—	2	4	no	—
35	C₂×#11745664	—	4	4	no	—
36	C₂²×C₅₉⋊C₈	—	2	1	no	—
37	C₂²×C₅₉⋊C₈	—	2	1	no	—
38	C₂²×C₅₉⋊C₈	—	2	1	no	—
39	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
40	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
41	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
44	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
45	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
46	C₂²⋊(C₅₉⋊C₈)	—	2	4	no	—
47	C₄×C₅₉⋊C₈	—	2	1	no	—
48	C₄×C₅₉⋊C₈	—	2	4	no	—
49	C₄×C₅₉⋊C₈	D₄	1	2	yes	—
50	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
51	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
52	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₅₉	—	2	1	no	—
55	C₂×SD₁₆×C₅₉	—	2	4	no	—
56	C₂×SD₁₆×C₅₉	C₂×C₄	1	4	yes	—
57	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₅₉	—	2	1	no	—
60	C₄×Q₈×C₅₉	—	2	1	no	—
61	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
63	C₄×D₄×C₅₉	—	2	1	no	—
64	C₄×D₄×C₅₉	—	2	1	no	—
65	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₅₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₄²×C₅₉	—	2	1	no	—
72	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
73	#106×C₅₉	C₂×C₄	1	4	yes	—
74	#103×C₅₉	C₂×C₄	1	4	yes	—
75	#102×C₅₉	C₂×C₄	1	4	yes	—
76	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₅₉	C₂³	1	2	yes	—
78	C₂⁴×C₅₉	—	2	1	no	—
79	C₂×Q₈×C₅₉	—	2	1	no	—
80	C₂×Q₈×C₅₉	—	2	2	no	—
81	C₂×Q₈×C₅₉	M₁₆	1	4	yes	complemented
82	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₅₉	—	2	1	no	—
84	C₂×D₄×C₅₉	—	2	2	no	—
85	C₂×D₄×C₅₉	—	2	2	no	—
86	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₅₉	—	2	1	no	—
88	C₂²×C₄×C₅₉	—	2	1	no	—
89	C₂²×C₄×C₅₉	—	2	1	no	—
90	C₂²×C₄×C₅₉	—	2	2	no	—
91	C₂²×C₄×C₅₉	—	2	2	no	—
92	C₂²×C₄×C₅₉	—	4	2	no	—
93	C₂²×C₄×C₅₉	—	4	2	no	—
94	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
97	SD₁₆×C₅₉	—	2	8	no	—
98	C₂×C₈×C₅₉	—	2	2	no	—
99	C₂×C₈×C₅₉	—	2	2	no	—
100	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
102	C₄⋊C₄×C₅₉	—	2	2	no	—
103	C₄⋊C₄×C₅₉	—	2	1	no	—
104	C₄⋊C₄×C₅₉	—	2	1	no	—
105	C₄⋊C₄×C₅₉	—	2	2	no	—
106	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
108	C₂²⋊C₄×C₅₉	—	2	2	no	—
109	C₂²⋊C₄×C₅₉	—	2	2	no	—
110	C₄²×C₅₉	—	2	2	no	—
111	C₄²×C₅₉	—	2	2	no	—
112	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₅₉	#41	1	1	yes	characteristic
115	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
116	#11745664	—	4	8	no	—
117	C₂×C₅₉⋊C₈	—	2	4	no	—
118	C₂×C₅₉⋊C₈	—	2	2	no	—
119	C₂×C₅₉⋊C₈	—	2	2	no	—
120	C₂×C₅₉⋊C₈	—	2	2	no	—
121	C₂×C₅₉⋊C₈	—	2	2	no	—
122	C₂×C₅₉⋊C₈	—	2	2	no	—
123	C₂×C₅₉⋊C₈	—	4	2	no	—
124	C₂×C₅₉⋊C₈	—	4	2	no	—
125	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
126	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
127	C₂³×C₅₉	—	2	2	no	—
128	C₂³×C₅₉	—	4	2	no	—
129	C₂³×C₅₉	—	4	2	no	—
130	C₂³×C₅₉	—	4	2	no	—
131	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
132	Q₈×C₅₉	—	2	2	no	—
133	Q₈×C₅₉	—	2	4	no	—
134	Q₈×C₅₉	C₂×M₁₆	1	4	yes	complemented
135	D₄×C₅₉	—	2	2	no	—
136	D₄×C₅₉	—	2	2	no	—
137	D₄×C₅₉	—	4	2	no	—
138	C₂×C₄×C₅₉	—	2	2	no	—
139	C₂×C₄×C₅₉	—	2	4	no	—
140	C₂×C₄×C₅₉	—	2	2	no	—
141	C₂×C₄×C₅₉	—	2	2	no	—
142	C₂×C₄×C₅₉	—	2	2	no	—
143	C₂×C₄×C₅₉	—	4	2	no	—
144	C₂×C₄×C₅₉	—	4	2	no	—
145	C₂×C₄×C₅₉	—	4	2	no	—
146	C₂×C₄×C₅₉	—	4	2	no	—
147	C₂×C₄×C₅₉	—	4	4	no	—
148	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₅₉	#131	1	2	yes	—
153	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
154	C₂×C₄×C₅₉	#137	1	2	yes	—
155	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
158	C₈×C₅₉	—	2	2	no	—
159	C₈×C₅₉	—	2	2	no	—
160	C₅₉⋊C₈	—	2	4	no	—
161	C₅₉⋊C₈	—	2	2	no	—
162	C₅₉⋊C₈	—	2	2	no	—
163	C₅₉⋊C₈	—	4	2	no	—
164	C₅₉⋊C₈	—	4	2	no	—
165	C₂×#1588	—	59	1	no	maximal, Sylow
166	C₂²×C₅₉	—	4	2	no	—
167	C₂²×C₅₉	—	4	2	no	—
168	C₂²×C₅₉	—	4	2	no	—
169	C₂²×C₅₉	—	8	4	no	—
170	C₂²×C₅₉	#435	1	2	yes	—
171	C₂²×C₅₉	#440	1	2	yes	—
172	C₂²×C₅₉	#443	1	2	yes	—
173	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
174	C₄×C₅₉	—	2	4	no	—
175	C₄×C₅₉	—	2	1	no	—
176	C₄×C₅₉	—	2	1	no	—
177	C₄×C₅₉	—	4	2	no	—
178	C₄×C₅₉	—	4	2	no	—
179	C₄×C₅₉	#435	1	2	yes	—
180	C₄×C₅₉	#440	1	2	yes	—
181	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
182	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
183	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
185	C₂×C₈×Q₈	—	59	1	no	—
186	C₂×C₄×SD₁₆	D₅₉	1	1	yes	characteristic
187	C₂×#436	—	59	1	no	—
188	#1588	—	59	8	no	—
189	C₂×#335	—	59	1	no	—
190	C₂×Q₈⋊C₈	—	59	1	no	—
191	C₂×D₄⋊C₈	—	59	1	no	—
192	C₂×#322	—	59	1	no	—
193	C₂×C₅₉	—	8	2	no	—
194	C₂×C₅₉	#1588	1	4	yes	complemented
195	C₂×C₅₉	C₂×#435	1	1	yes	characteristic
196	C₂×C₅₉	C₂×#440	1	1	yes	characteristic
197	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
198	C₂²×SD₁₆	Dic₅₉	1	1	yes	characteristic
199	C₂²×M₁₆	—	118	1	no	—
200	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
202	C₈×Q₈	—	59	4	no	—
203	C₈×Q₈	—	118	2	no	—
204	C₄×SD₁₆	Dic₅₉	1	4	yes	—
205	C₄×SD₁₆	C₂×D₅₉	1	4	yes	—
206	#436	—	59	4	no	—
207	#436	—	118	2	no	—
208	C₂×#106	Dic₅₉	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	59	1	no	—
210	C₂×C₄⋊C₈	—	59	1	no	—
211	C₂×C₄⋊C₈	—	118	1	no	—
212	C₂×#103	Dic₅₉	1	1	yes	characteristic
213	C₂×#102	Dic₅₉	1	1	yes	characteristic
214	C₂×C₂²⋊C₈	—	118	1	no	—
215	C₂×C₄×C₈	—	59	1	no	—
216	C₂×C₄×C₈	—	59	1	no	—
217	C₂×C₄×C₈	—	118	1	no	—
218	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
219	#335	—	59	4	no	—
220	Q₈⋊C₈	—	59	4	no	—
221	D₄⋊C₈	—	59	4	no	—
222	#322	—	59	4	no	—
223	C₅₉	C₂×#1588	1	1	yes	characteristic, complemented, Sylow
224	C₂²×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
225	C₂²×D₄	C₂×Dic₅₉	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×SD₁₆	C₂×Dic₅₉	1	4	yes	—
229	C₂×M₁₆	—	118	4	no	—
230	C₂×M₁₆	—	236	4	no	—
231	C₂²×C₈	—	59	1	no	—
232	C₂²×C₈	—	59	1	no	—
233	C₂²×C₈	—	118	1	no	—
234	C₂²×C₈	—	118	1	no	—
235	C₂²×C₈	—	118	1	no	—
236	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
237	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
241	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
245	C₄×D₄	C₂²×D₅₉	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₅₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
252	#106	C₂×Dic₅₉	1	4	yes	—
253	C₄⋊C₈	—	59	2	no	—
254	C₄⋊C₈	—	59	2	no	—
255	C₄⋊C₈	—	118	4	no	—
256	C₄⋊C₈	—	118	1	no	—
257	C₄⋊C₈	—	118	1	no	—
258	#103	C₂×Dic₅₉	1	4	yes	—
259	#102	C₂×Dic₅₉	1	4	yes	—
260	C₂²⋊C₈	—	118	4	no	—
261	C₄×C₈	—	59	2	no	—
262	C₄×C₈	—	59	2	no	—
263	C₄×C₈	—	59	2	no	—
264	C₄×C₈	—	118	4	no	—
265	C₄×C₈	—	118	1	no	—
266	C₄×C₈	C₂×Dic₅₉	1	2	yes	—
267	C₄×C₈	C₂²×D₅₉	1	2	yes	—
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	#11745664	1	4	yes	complemented
272	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
285	C₂²×C₄	#11745687	1	1	yes	characteristic
286	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
287	SD₁₆	—	2	8	no	—
288	M₁₆	—	236	8	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	59	2	no	—
292	C₂×C₈	—	59	2	no	—
293	C₂×C₈	—	118	4	no	—
294	C₂×C₈	—	118	2	no	—
295	C₂×C₈	—	118	2	no	—
296	C₂×C₈	—	118	2	no	—
297	C₂×C₈	—	118	2	no	—
298	C₂×C₈	—	118	2	no	—
299	C₂×C₈	—	236	2	no	—
300	C₂×C₈	—	236	2	no	—
301	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
302	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
308	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	D₄×D₅₉	1	1	yes	characteristic
314	C₄²	#11745687	1	1	yes	characteristic
315	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
316	C₄²	C₂³×D₅₉	1	1	yes	characteristic
317	C₂³	—	2	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
322	Q₈	—	2	2	no	—
323	Q₈	—	2	4	no	—
324	Q₈	C₂×#11745664	1	4	yes	complemented
325	D₄	—	2	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
339	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
341	C₂×C₄	C₂×#11745664	1	2	yes	—
342	C₂×C₄	#14273734	1	2	yes	—
343	C₂×C₄	#14273754	1	2	yes	—
344	C₂×C₄	#14273756	1	2	yes	—
345	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
347	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	2	2	no	—
350	C₈	—	118	4	no	—
351	C₈	—	118	2	no	—
352	C₈	—	118	2	no	—
353	C₈	—	236	2	no	—
354	C₈	—	236	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	#16837474	1	2	yes	—
360	C₂²	#16837503	1	2	yes	—
361	C₂²	#16837519	1	2	yes	—
362	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	#16837474	1	2	yes	—
369	C₄	#16837503	1	2	yes	—
370	C₄	C₂²×#11745664	1	1	yes	characteristic
371	C₄	C₂×#14273734	1	1	yes	characteristic
372	C₄	C₂×#14273754	1	1	yes	characteristic
373	C₄	C₂×#14273756	1	1	yes	characteristic
374	C₂	—	8	2	no	—
375	C₂	#21422975	1	4	yes	direct product factor
376	C₂	C₂×#16837474	1	1	yes	characteristic
377	C₂	C₂×#16837503	1	1	yes	characteristic
378	C₂	C₂×#16837519	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₄×SD₁₆×C₅₉	C₂
socle	C₂³×C₅₉	C₄×D₄
prime radical	C₂²×D₄×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₅₉
hypocenter	C₅₉	C₂×#1588
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₅₉⋊C₈	C₂	semidirect
3. #21422975	C₂	direct (N × H)
4. C₂×#16837155	C₂	semidirect
5. C₂×Q₈⋊(C₅₉⋊C₈)	C₂	semidirect
7. C₂×#16837124	C₂	semidirect
11. Q₈×C₅₉⋊C₈	C₂²	semidirect
21. #16837155	C₂²	semidirect
22. Q₈⋊(C₅₉⋊C₈)	C₂²	semidirect
24. #16837124	C₂²	semidirect
81. C₂×Q₈×C₅₉	M₁₆	semidirect
134. Q₈×C₅₉	C₂×M₁₆	semidirect
194. C₂×C₅₉	#1588	semidirect
223. C₅₉	C₂×#1588	semidirect
271. C₂×Q₈	#11745664	semidirect
324. Q₈	C₂×#11745664	semidirect
375. C₂	#21422975	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₅₉⋊C₈	2
C₂×#16837480	2
#21422975	2
C₂×#16837155	2
C₂×Q₈⋊(C₅₉⋊C₈)	2
C₂×D₄⋊(C₅₉⋊C₈)	2
C₂×#16837124	2
C₂×C₄×SD₁₆×C₅₉	2
C₂×#1588	59

Subgroups — C2×#21422975 #28558253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21422975 #28558253