Subgroups — #28559336

Order 15104.

582 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	#21433245	C₂	1	1	yes	maximal, characteristic
2	#21433191	C₂	1	1	yes	maximal, characteristic, complemented
3	#21423005	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422999	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422993	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422987	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	#21422863	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422556	C₂	1	1	yes	maximal, characteristic
13	#21422551	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3172	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	#16837533	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	#16837480	—	2	1	no	—
25	#16837480	C₂²	1	1	yes	characteristic
26	#16837474	—	2	1	no	—
27	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	#16837463	—	2	1	no	—
29	#16837463	—	2	1	no	—
30	#16837463	—	2	1	no	—
31	#16837459	C₂²	1	1	yes	characteristic
32	#16837455	C₂²	1	1	yes	characteristic
33	#16837429	—	2	1	no	—
34	#16837426	C₂²	1	1	yes	characteristic
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	#16837123	C₂²	1	1	yes	characteristic
49	#16837123	C₂²	1	1	yes	characteristic
50	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
51	C₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
52	C₅₉×#533	C₂²	1	1	yes	characteristic
53	C₅₉×#529	C₂²	1	1	yes	characteristic
54	C₅₉×#501	C₄	1	1	yes	characteristic
55	C₅₉×#497	C₄	1	1	yes	characteristic
56	C₅₉×#491	C₄	1	1	yes	characteristic
57	C₅₉×#489	C₄	1	1	yes	characteristic
58	C₅₉×#470	C₄	1	1	yes	characteristic
59	C₅₉×#470	C₄	1	1	yes	characteristic
60	C₅₉×#468	C₄	1	1	yes	characteristic
61	C₅₉×#468	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	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
67	C₂×#11745664	—	2	1	no	—
68	C₂×#11745664	—	2	1	no	—
69	C₂²×C₅₉⋊C₈	—	2	1	no	—
70	C₂²×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)	D₄	1	1	yes	characteristic
88	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
89	#14273638	—	2	1	no	—
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×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
107	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
108	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
109	#126×C₅₉	—	2	1	no	—
110	#125×C₅₉	—	2	1	no	—
111	#125×C₅₉	C₂×C₄	1	1	yes	characteristic
112	#124×C₅₉	C₂×C₄	1	1	yes	characteristic
113	#123×C₅₉	—	2	1	no	—
114	C₂²⋊Q₈×C₅₉	—	2	1	no	—
115	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
116	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
118	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
119	C₄×Q₈×C₅₉	—	2	1	no	—
120	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
121	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
122	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₅₉	—	2	1	no	—
124	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
125	#117×C₅₉	—	2	1	no	—
126	#117×C₅₉	—	2	1	no	—
127	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
128	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
129	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
130	#106×C₅₉	C₂×C₄	1	1	yes	characteristic
131	#106×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	#97×C₅₉	C₂×C₄	1	1	yes	characteristic
141	#97×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	C₂×Q₈×C₅₉	—	2	1	no	—
145	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₅₉	—	2	1	no	—
149	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅₉	—	2	1	no	—
151	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
154	Q₁₆×C₅₉	—	2	2	no	—
155	Q₁₆×C₅₉	—	2	2	no	—
156	SD₁₆×C₅₉	—	2	2	no	—
157	SD₁₆×C₅₉	—	2	2	no	—
158	M₁₆×C₅₉	—	2	2	no	—
159	M₁₆×C₅₉	—	2	2	no	—
160	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
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	C₂²⋊C₄×C₅₉	—	2	1	no	—
185	C₂²⋊C₄×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	#11745664	—	8	1	no	—
194	#11745664	—	8	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	—	2	1	no	—
200	C₂×C₅₉⋊C₈	—	2	1	no	—
201	C₂×C₅₉⋊C₈	—	4	2	no	—
202	C₂×C₅₉⋊C₈	—	8	1	no	—
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	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
207	C₂³×C₅₉	—	2	1	no	—
208	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
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	—	2	1	no	—
214	Q₈×C₅₉	—	2	1	no	—
215	Q₈×C₅₉	—	8	1	no	—
216	D₄×C₅₉	—	2	1	no	—
217	D₄×C₅₉	—	2	1	no	—
218	D₄×C₅₉	—	8	1	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	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
239	C₈×C₅₉	—	2	1	no	—
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	#131	1	2	yes	—
242	C₈×C₅₉	#131	1	2	yes	—
243	C₅₉⋊C₈	—	2	2	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	#17969	—	59	1	no	maximal, Sylow
254	C₂²×C₅₉	—	2	1	no	—
255	C₂²×C₅₉	—	2	1	no	—
256	C₂²×C₅₉	—	2	1	no	—
257	C₂²×C₅₉	—	4	1	no	—
258	C₂²×C₅₉	—	4	1	no	—
259	C₂²×C₅₉	—	4	1	no	—
260	C₂²×C₅₉	C₂×C₄×D₄	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	1	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	—	4	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	C₂×#131	1	1	yes	characteristic
273	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
274	C₄×C₅₉	#577	1	1	yes	characteristic
275	C₄×C₅₉	#578	1	1	yes	characteristic
276	#3172	D₅₉	1	1	yes	characteristic
277	#2993	—	59	1	no	—
278	#2985	—	59	1	no	—
279	#1593	—	59	1	no	—
280	#1592	—	59	1	no	—
281	#1591	—	59	1	no	—
282	#1590	—	59	1	no	—
283	#1579	—	59	1	no	—
284	SD₁₆⋊C₈	—	59	1	no	—
285	C₈×Q₁₆	—	59	1	no	—
286	C₈×SD₁₆	—	59	1	no	—
287	#1569	—	59	1	no	—
288	#1494	—	59	1	no	—
289	#1493	—	59	1	no	—
290	C₈×M₁₆	—	59	1	no	—
291	C₂×C₅₉	—	4	1	no	—
292	C₂×C₅₉	—	8	1	no	—
293	C₂×C₅₉	#2931	1	1	yes	characteristic
294	C₂×C₅₉	#2947	1	1	yes	characteristic
295	C₂×C₅₉	#2956	1	1	yes	characteristic
296	#533	C₂×D₅₉	1	1	yes	characteristic
297	#529	C₂×D₅₉	1	1	yes	characteristic
298	#501	Dic₅₉	1	1	yes	characteristic
299	#497	Dic₅₉	1	1	yes	characteristic
300	#491	Dic₅₉	1	1	yes	characteristic
301	#489	Dic₅₉	1	1	yes	characteristic
302	#470	Dic₅₉	1	1	yes	characteristic
303	#470	Dic₅₉	1	1	yes	characteristic
304	#468	Dic₅₉	1	1	yes	characteristic
305	#468	Dic₅₉	1	1	yes	characteristic
306	#446	—	59	1	no	—
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	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
315	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
316	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
317	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
318	#436	—	59	1	no	—
319	#436	—	118	1	no	—
320	#435	—	118	1	no	—
321	C₈×D₄	—	59	1	no	—
322	#433	—	118	1	no	—
323	#433	—	118	1	no	—
324	#433	—	118	1	no	—
325	#432	—	59	1	no	—
326	#431	—	59	1	no	—
327	#424	—	118	1	no	—
328	#423	—	59	1	no	—
329	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
330	C₂×C₄×C₈	—	59	1	no	—
331	#335	—	59	1	no	—
332	#335	—	59	1	no	—
333	#334	—	59	1	no	—
334	#334	—	59	1	no	—
335	Q₈⋊C₈	—	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	D₄⋊C₈	—	59	1	no	—
342	D₄⋊C₈	—	59	1	no	—
343	#322	—	59	1	no	—
344	#322	—	59	1	no	—
345	C₈²	—	59	1	no	—
346	C₈²	—	59	1	no	—
347	C₅₉	#17969	1	1	yes	characteristic, complemented, Sylow
348	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
349	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
350	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
351	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
352	C₂×M₁₆	—	118	1	no	—
353	C₂×M₁₆	—	118	1	no	—
354	C₂×M₁₆	C₂×Dic₅₉	1	1	yes	characteristic
355	C₂×M₁₆	C₂×Dic₅₉	1	1	yes	characteristic
356	C₂²×C₈	—	118	1	no	—
357	C₂²×C₈	—	118	1	no	—
358	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
359	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
360	#126	—	2	1	no	—
361	#125	—	2	1	no	—
362	#125	C₂×Dic₅₉	1	1	yes	characteristic
363	#124	C₂×Dic₅₉	1	1	yes	characteristic
364	#123	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
367	C₂²⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
368	C₂²⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
369	#121	C₂×Dic₅₉	1	1	yes	characteristic
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
372	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
373	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
379	#107	C₂×Dic₅₉	1	1	yes	characteristic
380	#107	C₂×Dic₅₉	1	1	yes	characteristic
381	#106	C₂×Dic₅₉	1	1	yes	characteristic
382	#106	C₂×Dic₅₉	1	1	yes	characteristic
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	—	59	1	no	—
388	C₄⋊C₈	—	59	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	—	118	1	no	—
396	#103	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	#102	C₂×Dic₅₉	1	1	yes	characteristic
403	#102	C₂×Dic₅₉	1	1	yes	characteristic
404	C₂²⋊C₈	—	59	1	no	—
405	C₂²⋊C₈	—	59	1	no	—
406	C₂²⋊C₈	—	118	1	no	—
407	C₂²⋊C₈	—	118	1	no	—
408	C₂²⋊C₈	—	118	1	no	—
409	#97	—	118	1	no	—
410	#97	—	118	1	no	—
411	#97	—	118	1	no	—
412	#97	—	118	1	no	—
413	#97	C₂×Dic₅₉	1	1	yes	characteristic
414	#97	C₂×Dic₅₉	1	1	yes	characteristic
415	C₄×C₈	—	59	1	no	—
416	C₄×C₈	—	59	1	no	—
417	C₄×C₈	—	59	1	no	—
418	C₄×C₈	—	59	1	no	—
419	C₄×C₈	—	118	1	no	—
420	C₄×C₈	—	118	1	no	—
421	C₄×C₈	—	118	1	no	—
422	C₄×C₈	—	118	1	no	—
423	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
427	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
428	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
433	C₂²×C₄	#11745687	1	1	yes	characteristic
434	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
435	Q₁₆	—	2	2	no	—
436	Q₁₆	—	2	2	no	—
437	SD₁₆	—	2	2	no	—
438	SD₁₆	—	2	2	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	472	1	no	—
442	M₁₆	—	472	1	no	—
443	C₂×C₈	—	59	1	no	—
444	C₂×C₈	—	59	1	no	—
445	C₂×C₈	—	59	1	no	—
446	C₂×C₈	—	59	1	no	—
447	C₂×C₈	—	118	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	—	472	1	no	—
454	C₂×C₈	—	236	2	no	—
455	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
456	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
457	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
458	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	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	—	2	1	no	—
496	Q₈	—	8	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	2	1	no	—
499	D₄	—	8	1	no	—
500	C₂×C₄	—	2	1	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	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
515	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
516	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
517	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
518	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
519	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	118	2	no	—
523	C₈	—	118	1	no	—
524	C₈	—	118	1	no	—
525	C₈	—	118	1	no	—
526	C₈	—	118	1	no	—
527	C₈	—	236	1	no	—
528	C₈	—	236	1	no	—
529	C₈	—	236	1	no	—
530	C₈	—	236	1	no	—
531	C₈	—	236	1	no	—
532	C₈	#14273734	1	2	yes	—
533	C₈	#14273734	1	2	yes	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	4	1	no	—
540	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	C₂×#14273734	1	1	yes	characteristic
553	C₄	C₂×#14273734	1	1	yes	characteristic
554	C₄	#16838211	1	1	yes	characteristic
555	C₄	#16838218	1	1	yes	characteristic
556	C₂	—	4	1	no	—
557	C₂	—	8	1	no	—
558	C₂	#21432808	1	1	yes	characteristic
559	C₂	#21432940	1	1	yes	characteristic
560	C₂	#21433006	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×#3172	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	#121×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3172	D₅₉
hypocenter	C₅₉	#17969
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3172

Complements

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

N	H ≅ G/N	type
2. #21433191	C₂	semidirect
3. #21423005	C₂	semidirect
4. #21422999	C₂	semidirect
5. #21422993	C₂	semidirect
6. #21422987	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. #21422863	C₂	semidirect
13. #21422551	C₂	semidirect
14. M₁₆×C₅₉⋊C₈	C₂	semidirect
347. C₅₉	#17969	semidirect

Maximal subgroups

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

subgroup	index
#21433245	2
#21433191	2
#21423005	2
#21422999	2
#21422993	2
#21422987	2
#21422915	2
SD₁₆⋊(C₅₉⋊C₈)	2
Q₁₆×C₅₉⋊C₈	2
SD₁₆×C₅₉⋊C₈	2
#21422863	2
#21422556	2
#21422551	2
M₁₆×C₅₉⋊C₈	2
C₅₉×#3172	2
#17969	59