Subgroups — #28558796

Order 15104.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433207	C₂	1	1	yes	maximal, characteristic
2	#21433191	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422968	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422954	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422947	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422933	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422915	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422881	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422530	C₂	1	1	yes	maximal, characteristic
13	#21422499	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3107	C₂	1	1	yes	maximal, characteristic
16	#16837533	—	2	1	no	—
17	#16837533	—	2	1	no	—
18	#16837533	C₂²	1	1	yes	characteristic
19	#16837533	C₂²	1	1	yes	characteristic
20	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
21	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
22	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
23	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
24	D₄×C₅₉⋊C₈	—	2	1	no	—
25	D₄×C₅₉⋊C₈	—	2	1	no	—
26	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
27	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	#16837463	—	2	1	no	—
29	#16837463	—	2	1	no	—
30	#16837459	C₂²	1	1	yes	characteristic
31	#16837455	—	2	1	no	—
32	#16837455	C₂²	1	1	yes	characteristic
33	#16837455	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
35	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
36	#16837155	C₂²	1	1	yes	characteristic
37	#16837155	C₂²	1	1	yes	characteristic
38	#16837153	C₂²	1	1	yes	characteristic
39	#16837153	C₂²	1	1	yes	characteristic
40	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
42	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
43	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
44	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
45	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
46	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
47	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
48	#16837124	C₂²	1	1	yes	characteristic
49	#16837124	C₂²	1	1	yes	characteristic
50	#16837123	C₂²	1	1	yes	characteristic
51	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
52	C₅₉×#533	C₂²	1	1	yes	characteristic
53	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#485	C₄	1	1	yes	characteristic
55	C₅₉×#485	C₄	1	1	yes	characteristic
56	C₅₉×#475	C₄	1	1	yes	characteristic
57	C₅₉×#474	C₄	1	1	yes	characteristic
58	C₅₉×#462	C₄	1	1	yes	characteristic
59	C₅₉×#461	C₄	1	1	yes	characteristic
60	C₅₉×#452	C₄	1	1	yes	characteristic
61	C₅₉×#452	C₄	1	1	yes	characteristic
62	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
64	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
65	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
66	C₅₉×#431	C₂²	1	1	yes	characteristic
67	C₂²×C₅₉⋊C₈	—	2	1	no	—
68	C₂²×C₅₉⋊C₈	—	2	1	no	—
69	C₂²×C₅₉⋊C₈	—	2	1	no	—
70	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
81	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
82	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
84	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
86	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
89	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
90	#14273638	—	2	1	no	—
91	#14273638	—	2	1	no	—
92	#14273638	—	2	1	no	—
93	C₄×C₅₉⋊C₈	—	2	1	no	—
94	C₄×C₅₉⋊C₈	—	2	1	no	—
95	C₄×C₅₉⋊C₈	—	2	1	no	—
96	C₄×C₅₉⋊C₈	—	2	1	no	—
97	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
101	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
108	#125×C₅₉	—	2	1	no	—
109	C₂²⋊Q₈×C₅₉	—	2	1	no	—
110	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₅₉	—	2	1	no	—
113	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
114	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₅₉	—	2	1	no	—
118	C₄×D₄×C₅₉	—	2	1	no	—
119	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
121	#117×C₅₉	—	2	1	no	—
122	#117×C₅₉	—	2	1	no	—
123	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₅₉	—	2	1	no	—
125	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
126	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
127	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
128	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
129	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
132	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
133	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
134	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
135	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
136	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
137	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
138	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	#41×C₅₉	—	2	2	no	—
145	#41×C₅₉	—	2	2	no	—
146	C₂×Q₈×C₅₉	—	2	1	no	—
147	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₄×C₅₉	—	2	1	no	—
151	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₉	—	2	1	no	—
153	C₂²×C₄×C₅₉	—	2	1	no	—
154	C₂²×C₄×C₅₉	—	2	1	no	—
155	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
158	Q₁₆×C₅₉	—	2	2	no	—
159	Q₁₆×C₅₉	—	2	2	no	—
160	SD₁₆×C₅₉	—	2	2	no	—
161	SD₁₆×C₅₉	—	2	2	no	—
162	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	—	2	1	no	—
168	C₄⋊C₄×C₅₉	—	2	1	no	—
169	C₄⋊C₄×C₅₉	—	2	1	no	—
170	C₄⋊C₄×C₅₉	—	2	1	no	—
171	C₄⋊C₄×C₅₉	—	2	1	no	—
172	C₄⋊C₄×C₅₉	—	2	1	no	—
173	C₄⋊C₄×C₅₉	—	2	1	no	—
174	C₄⋊C₄×C₅₉	—	2	1	no	—
175	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
178	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²⋊C₄×C₅₉	—	2	1	no	—
180	C₂²⋊C₄×C₅₉	—	2	1	no	—
181	C₂²⋊C₄×C₅₉	—	2	1	no	—
182	C₂²⋊C₄×C₅₉	—	2	1	no	—
183	C₂²⋊C₄×C₅₉	—	2	1	no	—
184	C₄²×C₅₉	—	2	1	no	—
185	C₄²×C₅₉	—	2	1	no	—
186	C₄²×C₅₉	—	2	1	no	—
187	C₄²×C₅₉	—	2	1	no	—
188	C₄²×C₅₉	—	2	1	no	—
189	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₅₉	#41	1	1	yes	characteristic
192	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₅₉⋊C₈	—	2	1	no	—
194	C₂×C₅₉⋊C₈	—	2	1	no	—
195	C₂×C₅₉⋊C₈	—	2	1	no	—
196	C₂×C₅₉⋊C₈	—	2	1	no	—
197	C₂×C₅₉⋊C₈	—	2	1	no	—
198	C₂×C₅₉⋊C₈	—	2	1	no	—
199	C₂×C₅₉⋊C₈	—	8	1	no	—
200	C₂×C₅₉⋊C₈	—	8	1	no	—
201	C₂×C₅₉⋊C₈	—	8	1	no	—
202	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
206	C₂³×C₅₉	—	2	1	no	—
207	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₅₉	—	2	1	no	—
209	Q₈×C₅₉	—	2	1	no	—
210	Q₈×C₅₉	—	2	1	no	—
211	Q₈×C₅₉	—	2	1	no	—
212	Q₈×C₅₉	—	2	1	no	—
213	Q₈×C₅₉	—	8	1	no	—
214	Q₈×C₅₉	#131	1	2	yes	—
215	D₄×C₅₉	—	2	4	no	—
216	D₄×C₅₉	—	2	1	no	—
217	D₄×C₅₉	#131	1	2	yes	—
218	C₂×C₄×C₅₉	—	2	4	no	—
219	C₂×C₄×C₅₉	—	2	1	no	—
220	C₂×C₄×C₅₉	—	2	1	no	—
221	C₂×C₄×C₅₉	—	2	1	no	—
222	C₂×C₄×C₅₉	—	2	1	no	—
223	C₂×C₄×C₅₉	—	2	1	no	—
224	C₂×C₄×C₅₉	—	2	1	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	1	no	—
227	C₂×C₄×C₅₉	—	2	1	no	—
228	C₂×C₄×C₅₉	—	2	1	no	—
229	C₂×C₄×C₅₉	—	2	1	no	—
230	C₂×C₄×C₅₉	—	4	1	no	—
231	C₂×C₄×C₅₉	—	4	1	no	—
232	C₂×C₄×C₅₉	—	4	1	no	—
233	C₂×C₄×C₅₉	—	8	1	no	—
234	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	—	2	1	no	—
242	C₈×C₅₉	—	2	1	no	—
243	C₈×C₅₉	—	2	1	no	—
244	C₅₉⋊C₈	—	2	1	no	—
245	C₅₉⋊C₈	—	2	1	no	—
246	C₅₉⋊C₈	—	2	1	no	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	4	1	no	—
249	C₅₉⋊C₈	—	4	1	no	—
250	C₅₉⋊C₈	—	4	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	C₅₉⋊C₈	—	4	1	no	—
253	C₅₉⋊C₈	—	4	1	no	—
254	#17921	—	59	1	no	maximal, Sylow
255	C₂²×C₅₉	—	2	1	no	—
256	C₂²×C₅₉	—	2	2	no	—
257	C₂²×C₅₉	—	2	1	no	—
258	C₂²×C₅₉	—	2	1	no	—
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	2	2	no	—
264	C₄×C₅₉	—	2	1	no	—
265	C₄×C₅₉	—	2	1	no	—
266	C₄×C₅₉	—	2	1	no	—
267	C₄×C₅₉	—	4	1	no	—
268	C₄×C₅₉	—	4	1	no	—
269	C₄×C₅₉	—	4	1	no	—
270	C₄×C₅₉	—	4	1	no	—
271	C₄×C₅₉	—	4	1	no	—
272	C₄×C₅₉	—	4	1	no	—
273	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
274	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
275	C₄×C₅₉	#577	1	1	yes	characteristic
276	C₄×C₅₉	#578	1	1	yes	characteristic
277	#3107	D₅₉	1	1	yes	characteristic
278	#2988	—	59	1	no	—
279	#2985	—	59	1	no	—
280	#1587	—	59	1	no	—
281	#1585	—	59	1	no	—
282	#1584	—	59	1	no	—
283	#1582	—	59	1	no	—
284	#1579	—	59	1	no	—
285	SD₁₆⋊C₈	—	59	1	no	—
286	C₈×Q₁₆	—	59	1	no	—
287	C₈×SD₁₆	—	59	1	no	—
288	#1573	—	59	1	no	—
289	#1488	—	59	1	no	—
290	#1481	—	59	1	no	—
291	#1454	—	59	1	no	—
292	C₂×C₅₉	—	4	1	no	—
293	C₂×C₅₉	—	4	2	no	—
294	C₂×C₅₉	#2929	1	1	yes	characteristic
295	C₂×C₅₉	#2947	1	1	yes	characteristic
296	C₂×C₅₉	#2957	1	1	yes	characteristic
297	#533	C₂×D₅₉	1	1	yes	characteristic
298	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
299	#485	Dic₅₉	1	1	yes	characteristic
300	#485	Dic₅₉	1	1	yes	characteristic
301	#475	Dic₅₉	1	1	yes	characteristic
302	#474	Dic₅₉	1	1	yes	characteristic
303	#462	Dic₅₉	1	1	yes	characteristic
304	#461	Dic₅₉	1	1	yes	characteristic
305	#452	Dic₅₉	1	1	yes	characteristic
306	#452	Dic₅₉	1	1	yes	characteristic
307	#446	—	59	1	no	—
308	#446	—	59	1	no	—
309	#446	—	118	1	no	—
310	#446	—	118	1	no	—
311	C₈×Q₈	—	59	1	no	—
312	C₈×Q₈	—	59	1	no	—
313	C₈×Q₈	—	59	1	no	—
314	C₈×Q₈	—	59	1	no	—
315	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
316	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
317	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
318	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
319	C₈×D₄	—	59	1	no	—
320	C₈×D₄	—	59	1	no	—
321	C₈×D₄	—	118	1	no	—
322	C₈×D₄	—	118	1	no	—
323	#433	—	118	1	no	—
324	#433	—	118	1	no	—
325	#432	—	59	1	no	—
326	#431	—	59	1	no	—
327	#431	—	59	1	no	—
328	#431	—	118	1	no	—
329	#431	C₂×D₅₉	1	1	yes	characteristic
330	C₂×C₄⋊C₈	—	59	1	no	—
331	C₂×C₄⋊C₈	—	118	1	no	—
332	#335	—	59	1	no	—
333	#335	—	59	1	no	—
334	#334	—	59	1	no	—
335	#334	—	59	1	no	—
336	Q₈⋊C₈	—	59	1	no	—
337	Q₈⋊C₈	—	59	1	no	—
338	Q₈⋊C₈	—	59	1	no	—
339	Q₈⋊C₈	—	59	1	no	—
340	Q₈⋊C₈	—	59	1	no	—
341	Q₈⋊C₈	—	59	1	no	—
342	D₄⋊C₈	—	59	1	no	—
343	D₄⋊C₈	—	59	1	no	—
344	#322	—	59	1	no	—
345	#322	—	59	1	no	—
346	#322	—	59	1	no	—
347	C₈²	—	59	1	no	—
348	C₅₉	#17921	1	1	yes	characteristic, complemented, Sylow
349	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
350	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
351	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
352	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
353	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
354	C₂²×C₈	—	118	1	no	—
355	C₂²×C₈	—	118	1	no	—
356	C₂²×C₈	—	118	1	no	—
357	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
358	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
359	#125	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
362	C₂²⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
365	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
366	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
367	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
371	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	C₂×Dic₅₉	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
377	#107	C₂×Dic₅₉	1	1	yes	characteristic
378	#107	C₂×Dic₅₉	1	1	yes	characteristic
379	#106	C₂×Dic₅₉	1	1	yes	characteristic
380	#106	C₂×Dic₅₉	1	1	yes	characteristic
381	C₄⋊C₈	—	59	1	no	—
382	C₄⋊C₈	—	59	1	no	—
383	C₄⋊C₈	—	59	1	no	—
384	C₄⋊C₈	—	59	1	no	—
385	C₄⋊C₈	—	59	1	no	—
386	C₄⋊C₈	—	59	1	no	—
387	C₄⋊C₈	—	118	1	no	—
388	C₄⋊C₈	—	118	1	no	—
389	C₄⋊C₈	—	118	1	no	—
390	C₄⋊C₈	—	118	1	no	—
391	C₄⋊C₈	—	118	1	no	—
392	C₄⋊C₈	—	118	1	no	—
393	C₄⋊C₈	—	118	1	no	—
394	C₄⋊C₈	—	118	1	no	—
395	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
396	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
397	#103	C₂×Dic₅₉	1	1	yes	characteristic
398	#103	C₂×Dic₅₉	1	1	yes	characteristic
399	#103	C₂×Dic₅₉	1	1	yes	characteristic
400	#103	C₂×Dic₅₉	1	1	yes	characteristic
401	#103	C₂×Dic₅₉	1	1	yes	characteristic
402	#103	C₂×Dic₅₉	1	1	yes	characteristic
403	#102	C₂×Dic₅₉	1	1	yes	characteristic
404	#102	C₂×Dic₅₉	1	1	yes	characteristic
405	C₂²⋊C₈	—	59	1	no	—
406	C₂²⋊C₈	—	59	1	no	—
407	C₂²⋊C₈	—	118	1	no	—
408	C₂²⋊C₈	—	118	1	no	—
409	C₂²⋊C₈	—	118	1	no	—
410	C₂²⋊C₈	—	118	1	no	—
411	C₂²⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
412	C₂²⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
413	#97	—	118	1	no	—
414	#97	—	118	1	no	—
415	#97	—	118	1	no	—
416	C₄×C₈	—	59	1	no	—
417	C₄×C₈	—	59	1	no	—
418	C₄×C₈	—	59	1	no	—
419	C₄×C₈	—	59	1	no	—
420	C₄×C₈	—	118	1	no	—
421	C₄×C₈	—	118	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	—	118	1	no	—
424	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
430	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
431	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
438	C₂²×C₄	#11745687	1	1	yes	characteristic
439	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
440	Q₁₆	—	2	2	no	—
441	Q₁₆	—	2	2	no	—
442	SD₁₆	—	2	2	no	—
443	SD₁₆	—	2	2	no	—
444	C₂×C₈	—	59	1	no	—
445	C₂×C₈	—	59	1	no	—
446	C₂×C₈	—	59	1	no	—
447	C₂×C₈	—	59	1	no	—
448	C₂×C₈	—	118	1	no	—
449	C₂×C₈	—	118	1	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	—	472	1	no	—
455	C₂×C₈	—	472	1	no	—
456	C₂×C₈	—	472	1	no	—
457	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
458	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
459	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
460	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
471	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	D₄×D₅₉	1	1	yes	characteristic
485	C₄²	#11745687	1	1	yes	characteristic
486	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
487	C₄²	C₂³×D₅₉	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	8	1	no	—
496	Q₈	#14273734	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	#14273734	1	2	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	8	1	no	—
516	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
517	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
518	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
519	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
521	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	118	1	no	—
527	C₈	—	118	1	no	—
528	C₈	—	118	1	no	—
529	C₈	—	118	1	no	—
530	C₈	—	236	1	no	—
531	C₈	—	236	1	no	—
532	C₈	—	236	1	no	—
533	C₈	—	236	1	no	—
534	C₈	—	236	1	no	—
535	C₈	—	236	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	C₂×#14273734	1	1	yes	characteristic
555	C₄	C₂×#14273734	1	1	yes	characteristic
556	C₄	#16838211	1	1	yes	characteristic
557	C₄	#16838218	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	#21432791	1	1	yes	characteristic
561	C₂	#21432940	1	1	yes	characteristic
562	C₂	#21433013	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#3107	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3107	D₅₉
hypocenter	C₅₉	#17921
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
2. #21433191	C₂	semidirect
3. #21422968	C₂	semidirect
4. #21422954	C₂	semidirect
5. #21422947	C₂	semidirect
6. #21422933	C₂	semidirect
7. #21422915	C₂	semidirect
8. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
9. Q₁₆×C₅₉⋊C₈	C₂	semidirect
10. SD₁₆×C₅₉⋊C₈	C₂	semidirect
11. #21422881	C₂	semidirect
13. #21422499	C₂	semidirect
14. #21422396	C₂	semidirect
348. C₅₉	#17921	semidirect

Maximal subgroups

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

subgroup	index
#21433207	2
#21433191	2
#21422968	2
#21422954	2
#21422947	2
#21422933	2
#21422915	2
SD₁₆⋊(C₅₉⋊C₈)	2
Q₁₆×C₅₉⋊C₈	2
SD₁₆×C₅₉⋊C₈	2
#21422881	2
#21422530	2
#21422499	2
#21422396	2
C₅₉×#3107	2
#17921	59