Subgroups — #28560100

Order 15104.

598 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433256	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433228	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422999	C₂	1	1	yes	maximal, characteristic, complemented
4	#21422981	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422975	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422975	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422947	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422926	C₂	1	1	yes	maximal, characteristic, complemented
9	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	Q₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422871	C₂	1	1	yes	maximal, characteristic, complemented
12	#21422561	C₂	1	1	yes	maximal, characteristic, complemented
13	#21422483	C₂	1	1	yes	maximal, characteristic, complemented
14	#21422396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3102	C₂	1	1	yes	maximal, characteristic
16	#16837533	C₂²	1	1	yes	characteristic
17	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
18	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
20	#16837480	—	2	1	no	—
21	#16837480	—	2	1	no	—
22	#16837480	C₂²	1	1	yes	characteristic
23	#16837480	C₂²	1	1	yes	characteristic
24	#16837480	C₂²	1	1	yes	characteristic
25	#16837474	—	2	1	no	—
26	D₄×C₅₉⋊C₈	—	2	1	no	—
27	D₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
28	#16837463	—	2	1	no	—
29	#16837455	—	2	1	no	—
30	#16837455	C₂²	1	1	yes	characteristic
31	#16837455	C₂²	1	1	yes	characteristic
32	#16837429	—	2	1	no	—
33	#16837426	—	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	#16837155	C₂²	1	1	yes	characteristic
39	#16837155	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	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
45	D₄⋊(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×#529	C₂²	1	1	yes	characteristic
53	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
54	C₅₉×#485	C₄	1	1	yes	characteristic
55	C₅₉×#482	C₄	1	1	yes	characteristic
56	C₅₉×#479	C₄	1	1	yes	characteristic
57	C₅₉×#478	C₄	1	1	yes	characteristic
58	C₅₉×#464	C₄	1	1	yes	characteristic
59	C₅₉×#463	C₄	1	1	yes	characteristic
60	C₅₉×#452	C₄	1	1	yes	characteristic
61	C₅₉×#449	C₄	1	1	yes	characteristic
62	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
64	C₄×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
66	C₅₉×#431	C₂²	1	1	yes	characteristic
67	C₂×#11745664	—	2	1	no	—
68	C₂×#11745664	—	2	1	no	—
69	C₂×#11745664	—	2	1	no	—
70	C₂×#11745664	—	2	1	no	—
71	C₂²×C₅₉⋊C₈	—	2	1	no	—
72	C₂²×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)	—	2	1	no	—
79	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
80	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
81	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
82	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
83	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
84	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
85	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
86	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
87	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
88	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
89	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
92	C₂²⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
93	#14273638	—	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×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
105	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
106	#126×C₅₉	—	2	1	no	—
107	#125×C₅₉	C₂×C₄	1	1	yes	characteristic
108	#124×C₅₉	C₂×C₄	1	1	yes	characteristic
109	#123×C₅₉	—	2	1	no	—
110	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
111	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
112	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
113	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₅₉	—	2	1	no	—
116	C₄×D₄×C₅₉	—	2	1	no	—
117	C₄×D₄×C₅₉	—	2	1	no	—
118	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₅₉	C₂³	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	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
137	#102×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	—	4	1	no	—
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	—	2	1	no	—
150	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
156	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
159	Q₁₆×C₅₉	—	2	2	no	—
160	SD₁₆×C₅₉	—	2	2	no	—
161	SD₁₆×C₅₉	—	4	1	no	—
162	D₈×C₅₉	—	4	1	no	—
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	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
176	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₂²⋊C₄×C₅₉	—	2	1	no	—
178	C₂²⋊C₄×C₅₉	—	2	1	no	—
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	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	#11745664	—	8	1	no	—
194	#11745664	—	8	1	no	—
195	#11745664	—	8	1	no	—
196	#11745664	—	8	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	—	2	1	no	—
202	C₂×C₅₉⋊C₈	—	2	1	no	—
203	C₂×C₅₉⋊C₈	—	8	1	no	—
204	C₂×C₅₉⋊C₈	—	8	1	no	—
205	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
209	C₂³×C₅₉	—	2	1	no	—
210	C₂³×C₅₉	—	2	1	no	—
211	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
212	Q₈×C₅₉	—	2	1	no	—
213	Q₈×C₅₉	—	2	1	no	—
214	Q₈×C₅₉	—	2	1	no	—
215	Q₈×C₅₉	#131	1	2	yes	—
216	D₄×C₅₉	—	2	1	no	—
217	D₄×C₅₉	—	2	1	no	—
218	D₄×C₅₉	—	2	1	no	—
219	D₄×C₅₉	—	2	1	no	—
220	D₄×C₅₉	—	4	2	no	—
221	D₄×C₅₉	—	4	2	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	—	2	1	no	—
231	C₂×C₄×C₅₉	—	2	1	no	—
232	C₂×C₄×C₅₉	—	4	1	no	—
233	C₂×C₄×C₅₉	—	4	2	no	—
234	C₂×C₄×C₅₉	—	4	2	no	—
235	C₂×C₄×C₅₉	—	4	1	no	—
236	C₂×C₄×C₅₉	—	4	1	no	—
237	C₂×C₄×C₅₉	—	4	1	no	—
238	C₂×C₄×C₅₉	—	4	1	no	—
239	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
245	C₈×C₅₉	—	2	1	no	—
246	C₈×C₅₉	—	2	1	no	—
247	C₈×C₅₉	—	2	1	no	—
248	C₈×C₅₉	—	2	1	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	2	1	no	—
251	C₅₉⋊C₈	—	2	1	no	—
252	C₅₉⋊C₈	—	2	1	no	—
253	C₅₉⋊C₈	—	4	1	no	—
254	C₅₉⋊C₈	—	4	1	no	—
255	C₅₉⋊C₈	—	4	1	no	—
256	C₅₉⋊C₈	—	4	1	no	—
257	C₅₉⋊C₈	—	4	1	no	—
258	C₅₉⋊C₈	—	4	1	no	—
259	#18033	—	59	1	no	maximal, Sylow
260	C₂²×C₅₉	—	2	1	no	—
261	C₂²×C₅₉	—	2	1	no	—
262	C₂²×C₅₉	—	2	1	no	—
263	C₂²×C₅₉	—	4	1	no	—
264	C₂²×C₅₉	—	4	1	no	—
265	C₂²×C₅₉	—	4	1	no	—
266	C₂²×C₅₉	—	4	1	no	—
267	C₂²×C₅₉	—	4	1	no	—
268	C₂²×C₅₉	—	4	1	no	—
269	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₅₉	—	2	1	no	—
271	C₄×C₅₉	—	2	2	no	—
272	C₄×C₅₉	—	2	1	no	—
273	C₄×C₅₉	—	2	1	no	—
274	C₄×C₅₉	—	2	1	no	—
275	C₄×C₅₉	—	4	1	no	—
276	C₄×C₅₉	—	4	1	no	—
277	C₄×C₅₉	—	4	1	no	—
278	C₄×C₅₉	—	4	1	no	—
279	C₄×C₅₉	—	4	1	no	—
280	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
281	C₄×C₅₉	#568	1	1	yes	characteristic
282	C₄×C₅₉	#576	1	1	yes	characteristic
283	C₄×C₅₉	#578	1	1	yes	characteristic
284	#3102	D₅₉	1	1	yes	characteristic
285	#2994	—	59	1	no	—
286	#2991	—	59	1	no	—
287	#1592	—	59	1	no	—
288	#1589	—	59	1	no	—
289	#1588	—	59	1	no	—
290	#1588	—	59	1	no	—
291	#1584	—	59	1	no	—
292	#1581	—	59	1	no	—
293	SD₁₆⋊C₈	—	59	1	no	—
294	C₈×Q₁₆	—	59	1	no	—
295	#1571	—	59	1	no	—
296	#1495	—	59	1	no	—
297	#1477	—	59	1	no	—
298	#1454	—	59	1	no	—
299	C₂×C₅₉	—	4	1	no	—
300	C₂×C₅₉	—	8	1	no	—
301	C₂×C₅₉	—	8	1	no	—
302	C₂×C₅₉	#2933	1	1	yes	characteristic
303	C₂×C₅₉	#2951	1	1	yes	characteristic
304	C₂×C₅₉	#2955	1	1	yes	characteristic
305	#529	C₂×D₅₉	1	1	yes	characteristic
306	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
307	#485	Dic₅₉	1	1	yes	characteristic
308	#482	Dic₅₉	1	1	yes	characteristic
309	#479	Dic₅₉	1	1	yes	characteristic
310	#478	Dic₅₉	1	1	yes	characteristic
311	#464	Dic₅₉	1	1	yes	characteristic
312	#463	Dic₅₉	1	1	yes	characteristic
313	#452	Dic₅₉	1	1	yes	characteristic
314	#449	Dic₅₉	1	1	yes	characteristic
315	#446	—	59	1	no	—
316	C₈×Q₈	—	59	1	no	—
317	C₈×Q₈	—	59	1	no	—
318	C₈×Q₈	—	59	1	no	—
319	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
320	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
321	C₄×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
322	C₄×D₈	C₂×D₅₉	1	1	yes	characteristic
323	#436	—	59	1	no	—
324	#436	—	59	1	no	—
325	#436	—	59	1	no	—
326	#436	—	118	1	no	—
327	#436	—	118	1	no	—
328	#435	—	118	1	no	—
329	C₈×D₄	—	59	1	no	—
330	C₈×D₄	—	118	1	no	—
331	#433	—	118	1	no	—
332	#431	—	59	1	no	—
333	#431	—	59	1	no	—
334	#431	—	118	1	no	—
335	#431	C₂×D₅₉	1	1	yes	characteristic
336	#424	—	118	1	no	—
337	#423	—	59	1	no	—
338	#423	—	118	1	no	—
339	C₂×C₄⋊C₈	—	59	1	no	—
340	#335	—	59	1	no	—
341	#335	—	59	1	no	—
342	#335	—	59	1	no	—
343	#335	—	59	1	no	—
344	Q₈⋊C₈	—	59	1	no	—
345	Q₈⋊C₈	—	59	1	no	—
346	Q₈⋊C₈	—	59	1	no	—
347	Q₈⋊C₈	—	59	1	no	—
348	D₄⋊C₈	—	59	1	no	—
349	D₄⋊C₈	—	59	1	no	—
350	D₄⋊C₈	—	59	1	no	—
351	D₄⋊C₈	—	59	1	no	—
352	#322	—	59	1	no	—
353	#322	—	59	1	no	—
354	#322	—	59	1	no	—
355	C₈²	—	59	1	no	—
356	C₅₉	#18033	1	1	yes	characteristic, complemented, Sylow
357	C₂×#41	C₂×Dic₅₉	1	1	yes	characteristic
358	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
359	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic
361	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
362	C₂×M₁₆	—	118	1	no	—
363	C₂×M₁₆	—	118	1	no	—
364	C₂×M₁₆	—	118	1	no	—
365	C₂×M₁₆	—	118	1	no	—
366	C₂²×C₈	—	118	1	no	—
367	C₂²×C₈	—	118	1	no	—
368	#126	—	2	1	no	—
369	#125	C₂×Dic₅₉	1	1	yes	characteristic
370	#124	C₂×Dic₅₉	1	1	yes	characteristic
371	#123	—	2	1	no	—
372	C₂²⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
373	#121	C₂×Dic₅₉	1	1	yes	characteristic
374	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
375	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
381	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	C₂×Dic₅₉	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
388	#107	C₂×Dic₅₉	1	1	yes	characteristic
389	#107	C₂×Dic₅₉	1	1	yes	characteristic
390	#106	C₂×Dic₅₉	1	1	yes	characteristic
391	#106	C₂×Dic₅₉	1	1	yes	characteristic
392	C₄⋊C₈	—	59	1	no	—
393	C₄⋊C₈	—	59	1	no	—
394	C₄⋊C₈	—	59	1	no	—
395	C₄⋊C₈	—	59	1	no	—
396	C₄⋊C₈	—	59	1	no	—
397	C₄⋊C₈	—	59	1	no	—
398	C₄⋊C₈	—	118	1	no	—
399	C₄⋊C₈	—	118	1	no	—
400	C₄⋊C₈	—	118	1	no	—
401	C₄⋊C₈	—	118	1	no	—
402	C₄⋊C₈	—	118	1	no	—
403	C₄⋊C₈	—	118	1	no	—
404	C₄⋊C₈	—	118	1	no	—
405	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
406	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
407	#103	C₂×Dic₅₉	1	1	yes	characteristic
408	#103	C₂×Dic₅₉	1	1	yes	characteristic
409	#103	C₂×Dic₅₉	1	1	yes	characteristic
410	#103	C₂×Dic₅₉	1	1	yes	characteristic
411	#102	C₂×Dic₅₉	1	1	yes	characteristic
412	#102	C₂×Dic₅₉	1	1	yes	characteristic
413	#102	C₂×Dic₅₉	1	1	yes	characteristic
414	#102	C₂×Dic₅₉	1	1	yes	characteristic
415	C₂²⋊C₈	—	59	1	no	—
416	C₂²⋊C₈	—	59	1	no	—
417	C₂²⋊C₈	—	118	1	no	—
418	C₂²⋊C₈	—	118	1	no	—
419	C₂²⋊C₈	—	118	1	no	—
420	C₂²⋊C₈	—	118	1	no	—
421	C₂²⋊C₈	—	118	1	no	—
422	C₂²⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
423	C₂²⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
424	#97	—	118	1	no	—
425	C₄×C₈	—	59	1	no	—
426	C₄×C₈	—	59	1	no	—
427	C₄×C₈	—	59	1	no	—
428	C₄×C₈	—	59	1	no	—
429	C₄×C₈	—	118	1	no	—
430	C₄×C₈	—	118	1	no	—
431	C₄×C₈	—	118	1	no	—
432	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	4	1	no	—
436	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
437	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
441	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
447	C₂²×C₄	#11745687	1	1	yes	characteristic
448	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
449	Q₁₆	—	2	2	no	—
450	SD₁₆	—	2	2	no	—
451	SD₁₆	—	4	1	no	—
452	D₈	—	4	1	no	—
453	M₁₆	—	472	1	no	—
454	M₁₆	—	472	1	no	—
455	M₁₆	—	472	1	no	—
456	M₁₆	—	472	1	no	—
457	C₂×C₈	—	59	1	no	—
458	C₂×C₈	—	59	1	no	—
459	C₂×C₈	—	59	1	no	—
460	C₂×C₈	—	59	1	no	—
461	C₂×C₈	—	118	1	no	—
462	C₂×C₈	—	118	1	no	—
463	C₂×C₈	—	118	1	no	—
464	C₂×C₈	—	118	1	no	—
465	C₂×C₈	—	118	1	no	—
466	C₂×C₈	—	118	1	no	—
467	C₂×C₈	—	472	1	no	—
468	C₂×C₈	—	472	1	no	—
469	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
470	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
471	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
472	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	D₄×D₅₉	1	1	yes	characteristic
496	C₄²	#11745687	1	1	yes	characteristic
497	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
498	C₄²	C₂³×D₅₉	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	#14273734	1	2	yes	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
530	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
531	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
532	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
534	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	118	1	no	—
540	C₈	—	118	1	no	—
541	C₈	—	118	1	no	—
542	C₈	—	118	1	no	—
543	C₈	—	236	1	no	—
544	C₈	—	236	1	no	—
545	C₈	—	236	1	no	—
546	C₈	—	236	1	no	—
547	C₈	—	236	1	no	—
548	C₈	—	236	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	C₂×#14273734	1	1	yes	characteristic
570	C₄	#16838169	1	1	yes	characteristic
571	C₄	#16838204	1	1	yes	characteristic
572	C₄	#16838216	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	8	1	no	—
575	C₂	—	8	1	no	—
576	C₂	#21432823	1	1	yes	characteristic
577	C₂	#21432972	1	1	yes	characteristic
578	C₂	#21432999	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×#3102	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#449	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3102	D₅₉
hypocenter	C₅₉	#18033
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #21433256	C₂	semidirect
2. #21433228	C₂	semidirect
3. #21422999	C₂	semidirect
4. #21422981	C₂	semidirect
5. #21422975	C₂	semidirect
6. #21422975	C₂	semidirect
7. #21422947	C₂	semidirect
8. #21422926	C₂	semidirect
9. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
10. Q₁₆×C₅₉⋊C₈	C₂	semidirect
11. #21422871	C₂	semidirect
12. #21422561	C₂	semidirect
13. #21422483	C₂	semidirect
14. #21422396	C₂	semidirect
356. C₅₉	#18033	semidirect

Maximal subgroups

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

subgroup	index
#21433256	2
#21433228	2
#21422999	2
#21422981	2
#21422975	2
#21422947	2
#21422926	2
SD₁₆⋊(C₅₉⋊C₈)	2
Q₁₆×C₅₉⋊C₈	2
#21422871	2
#21422561	2
#21422483	2
#21422396	2
C₅₉×#3102	2
#18033	59