Subgroups — #28558382

Order 15104.

626 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	#21433178	C₂	1	1	yes	maximal, characteristic
2	#21433175	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic
4	#21422970	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422967	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422965	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422964	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422948	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422947	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422945	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422843	C₂	1	1	yes	maximal, characteristic
12	#21422489	C₂	1	1	yes	maximal, characteristic
13	#21422489	C₂	1	1	yes	maximal, characteristic
14	#21422387	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₅₉	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₅₉	C₂²	1	1	yes	characteristic
19	#16837533	C₂²	1	1	yes	characteristic
20	#16837532	C₂²	1	1	yes	characteristic
21	#16837531	—	2	1	no	—
22	#16837530	—	2	1	no	—
23	#16837529	C₂²	1	1	yes	characteristic
24	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₁₈	—	2	1	no	—
26	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
27	#16837526	—	2	1	no	—
28	#16837526	C₂²	1	1	yes	characteristic
29	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₅₉	C₄	1	1	yes	characteristic
31	#16837496	C₄	1	1	yes	characteristic
32	C₄×#11745672	C₂²	1	1	yes	characteristic
33	C₄×#11745672	C₂²	1	1	yes	characteristic
34	#16837494	C₄	1	1	yes	characteristic
35	#16837494	C₄	1	1	yes	characteristic
36	#16837458	—	2	1	no	—
37	#16837457	—	2	1	no	—
38	#16837454	—	2	1	no	—
39	#16837454	C₂²	1	1	yes	characteristic
40	#16837454	C₂²	1	1	yes	characteristic
41	#16837453	—	2	1	no	—
42	#16837453	C₂²	1	1	yes	characteristic
43	#16837453	C₂²	1	1	yes	characteristic
44	#107×D₅₉	C₄	1	1	yes	characteristic
45	#103×D₅₉	C₄	1	1	yes	characteristic
46	#103×D₅₉	C₄	1	1	yes	characteristic
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837155	C₂²	1	1	yes	characteristic
49	#16837152	C₂²	1	1	yes	characteristic
50	#16837152	C₂²	1	1	yes	characteristic
51	#16837134	C₂²	1	1	yes	characteristic
52	#16837134	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
54	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
55	#16837132	C₂²	1	1	yes	characteristic
56	#16837132	C₂²	1	1	yes	characteristic
57	#16837124	C₂²	1	1	yes	characteristic
58	#16837124	C₂²	1	1	yes	characteristic
59	#16837123	C₂²	1	1	yes	characteristic
60	C₅₉×#446	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₅₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#335	C₂²	1	1	yes	characteristic
64	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅₉×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₅₉×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₅₉	—	2	4	no	—
73	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
75	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
76	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₁₁₈	—	2	1	no	—
78	C₄×Dic₁₁₈	—	2	1	no	—
79	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
80	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
81	#14273692	—	2	1	no	—
82	#14273692	—	2	1	no	—
83	#14273692	C₂×C₄	1	1	yes	characteristic
84	#14273692	C₂×C₄	1	1	yes	characteristic
85	C₄⋊C₄×D₅₉	—	2	1	no	—
86	C₄⋊C₄×D₅₉	—	2	1	no	—
87	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
89	C₄²×D₅₉	—	2	1	no	—
90	C₄²×D₅₉	—	2	1	no	—
91	C₄²×D₅₉	C₂³	1	1	yes	characteristic
92	#14273661	C₂×C₄	1	1	yes	characteristic
93	#14273660	C₂×C₄	1	1	yes	characteristic
94	#14273660	C₂×C₄	1	1	yes	characteristic
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	Dic₅₉⋊C₈	—	2	1	no	—
100	Dic₅₉⋊C₈	—	2	1	no	—
101	Dic₅₉⋊C₈	—	2	1	no	—
102	Dic₅₉⋊C₈	—	2	1	no	—
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
105	Dic₅₉⋊C₈	D₄	1	1	yes	characteristic
106	#14273652	C₂×C₄	1	1	yes	characteristic
107	#14273652	C₂×C₄	1	1	yes	characteristic
108	#14273651	C₂×C₄	1	1	yes	characteristic
109	#14273651	C₂×C₄	1	1	yes	characteristic
110	#14273650	C₂×C₄	1	1	yes	characteristic
111	#14273650	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₅₉)⋊C₈	—	2	1	no	—
113	(C₂×D₅₉)⋊C₈	—	2	1	no	—
114	(C₂×D₅₉)⋊C₈	—	2	1	no	—
115	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
116	(C₂×D₅₉)⋊C₈	D₄	1	1	yes	characteristic
117	#14273638	—	2	1	no	—
118	#14273637	—	2	1	no	—
119	#14273637	—	2	1	no	—
120	C₄×C₅₉⋊C₈	—	2	1	no	—
121	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₅₉	—	2	1	no	—
125	C₈×Dic₅₉	—	2	1	no	—
126	C₈×Dic₅₉	—	2	1	no	—
127	C₈×Dic₅₉	—	2	1	no	—
128	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
133	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₅₉	—	2	1	no	—
135	C₄⋊C₈×C₅₉	—	2	1	no	—
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
138	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
140	#97×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	—	2	1	no	—
142	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	Q₈×D₅₉	—	2	2	no	—
148	Q₈×D₅₉	—	2	2	no	—
149	Q₈×D₅₉	—	2	2	no	—
150	Q₈×D₅₉	M₁₆	1	4	yes	—
151	C₂×C₄×D₅₉	—	2	1	no	—
152	C₂×C₄×D₅₉	—	2	1	no	—
153	C₂×C₄×D₅₉	—	2	1	no	—
154	C₂×C₄×D₅₉	—	2	1	no	—
155	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
158	C₂×Dic₁₁₈	—	2	1	no	—
159	C₂×Dic₁₁₈	—	2	1	no	—
160	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
162	Q₁₆×C₅₉	—	2	2	no	—
163	C₂×C₈×C₅₉	—	2	1	no	—
164	C₂×C₈×C₅₉	—	2	1	no	—
165	C₂×C₈×C₅₉	—	2	1	no	—
166	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₅₉	—	2	1	no	—
171	C₄⋊C₄×C₅₉	—	2	1	no	—
172	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₅₉	—	2	1	no	—
175	C₄²×C₅₉	—	2	1	no	—
176	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
177	#11745672	—	2	2	no	—
178	#11745672	—	2	2	no	—
179	C₄⋊Dic₅₉	—	2	1	no	—
180	C₄⋊Dic₅₉	—	2	1	no	—
181	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
183	Dic₅₉⋊C₄	—	2	1	no	—
184	Dic₅₉⋊C₄	—	2	1	no	—
185	Dic₅₉⋊C₄	—	2	1	no	—
186	Dic₅₉⋊C₄	—	2	1	no	—
187	Dic₅₉⋊C₄	—	2	1	no	—
188	Dic₅₉⋊C₄	—	2	1	no	—
189	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	—	2	1	no	—
191	C₄×Dic₅₉	—	2	1	no	—
192	C₄×Dic₅₉	—	2	1	no	—
193	C₄×Dic₅₉	—	2	1	no	—
194	C₄×Dic₅₉	—	2	1	no	—
195	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
197	C₄×Dic₅₉	#41	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₅₉⋊C₈	C₂²×C₄	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	Dic₂₃₆	—	2	2	no	—
206	C₈×D₅₉	—	2	2	no	—
207	C₈×D₅₉	—	2	2	no	—
208	C₂²×D₅₉	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	C₂×M₁₆	1	2	yes	—
213	C₂×C₄×C₅₉	—	2	1	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	1	no	—
216	C₂×C₄×C₅₉	—	2	1	no	—
217	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₅₉	—	2	1	no	—
221	C₂×Dic₅₉	—	2	1	no	—
222	C₂×Dic₅₉	—	2	1	no	—
223	C₂×Dic₅₉	—	2	1	no	—
224	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
227	C₄×D₅₉	—	2	4	no	—
228	C₄×D₅₉	—	2	1	no	—
229	C₄×D₅₉	—	2	1	no	—
230	C₄×D₅₉	—	4	1	no	—
231	C₄×D₅₉	—	4	2	no	—
232	C₄×D₅₉	—	8	1	no	—
233	C₄×D₅₉	—	8	1	no	—
234	C₄×D₅₉	C₂×M₁₆	1	2	yes	—
235	C₄×D₅₉	#131	1	2	yes	—
236	Dic₁₁₈	—	2	1	no	—
237	Dic₁₁₈	—	2	4	no	—
238	Dic₁₁₈	—	2	1	no	—
239	Dic₁₁₈	—	2	1	no	—
240	Dic₁₁₈	—	4	2	no	—
241	Dic₁₁₈	C₂×M₁₆	1	2	yes	—
242	C₈×C₅₉	—	2	1	no	—
243	C₈×C₅₉	—	2	1	no	—
244	C₈×C₅₉	—	2	1	no	—
245	C₈×C₅₉	—	2	1	no	—
246	C₈×C₅₉	—	4	1	no	—
247	C₈×C₅₉	—	4	1	no	—
248	C₈×C₅₉	—	4	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	#17880	—	59	1	no	maximal, Sylow
257	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂×D₅₉	—	2	1	no	—
259	C₂×D₅₉	—	2	1	no	—
260	C₂×D₅₉	#435	1	2	yes	—
261	C₄×C₅₉	—	2	2	no	—
262	C₄×C₅₉	—	2	1	no	—
263	C₄×C₅₉	—	4	1	no	—
264	C₄×C₅₉	—	4	1	no	—
265	C₄×C₅₉	—	4	1	no	—
266	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
267	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
268	C₄×C₅₉	#578	1	1	yes	characteristic
269	C₄×C₅₉	#578	1	1	yes	characteristic
270	Dic₅₉	—	2	2	no	—
271	Dic₅₉	—	2	1	no	—
272	Dic₅₉	—	2	1	no	—
273	Dic₅₉	—	4	1	no	—
274	Dic₅₉	—	4	1	no	—
275	Dic₅₉	—	4	1	no	—
276	Dic₅₉	#435	1	2	yes	—
277	#2983	—	59	1	no	—
278	#2982	—	59	1	no	—
279	C₂×C₄×Q₁₆	—	59	1	no	—
280	#1587	—	59	1	no	—
281	#1587	—	59	1	no	—
282	#1587	—	59	1	no	—
283	#1587	—	59	1	no	—
284	#1584	—	59	1	no	—
285	#1584	—	59	1	no	—
286	#1584	—	59	1	no	—
287	#1584	D₅₉	1	1	yes	characteristic, complemented
288	#1564	—	59	1	no	—
289	#1479	—	59	1	no	—
290	#1479	—	59	1	no	—
291	#1452	—	59	1	no	—
292	C₂×C₅₉	C₂×#435	1	1	yes	characteristic
293	C₂×C₅₉	#2950	1	1	yes	characteristic
294	C₂×C₅₉	#2957	1	1	yes	characteristic
295	D₅₉	—	2	2	no	—
296	C₂²×Q₁₆	—	59	1	no	—
297	C₂×C₄×Q₈	—	59	1	no	—
298	C₂×C₄×Q₈	—	59	1	no	—
299	#446	—	59	1	no	—
300	#446	—	59	1	no	—
301	#446	—	59	1	no	—
302	#446	—	118	1	no	—
303	#446	—	118	1	no	—
304	#446	C₂×D₅₉	1	1	yes	characteristic
305	C₈×Q₈	—	59	1	no	—
306	C₈×Q₈	—	59	1	no	—
307	C₈×Q₈	—	59	1	no	—
308	C₈×Q₈	—	118	1	no	—
309	C₈×Q₈	—	118	1	no	—
310	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
311	C₄×Q₁₆	—	59	1	no	—
312	C₄×Q₁₆	—	59	1	no	—
313	C₄×Q₁₆	—	59	1	no	—
314	C₄×Q₁₆	—	59	1	no	—
315	C₄×Q₁₆	—	59	1	no	—
316	C₄×Q₁₆	—	59	1	no	—
317	C₄×Q₁₆	—	59	1	no	—
318	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
319	#432	—	118	1	no	—
320	#432	—	118	1	no	—
321	#431	—	59	1	no	—
322	#431	—	59	1	no	—
323	#431	—	59	1	no	—
324	#431	—	59	1	no	—
325	#431	—	118	1	no	—
326	#431	—	118	1	no	—
327	C₂×#107	—	59	1	no	—
328	C₂×#103	—	59	1	no	—
329	C₂×#103	—	59	1	no	—
330	C₂×C₄×C₈	—	59	1	no	—
331	#335	—	59	1	no	—
332	#335	C₂×D₅₉	1	1	yes	characteristic
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	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
342	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
343	#322	—	59	1	no	—
344	#322	—	59	1	no	—
345	#322	—	59	1	no	—
346	#322	C₂×D₅₉	1	1	yes	characteristic
347	C₅₉	#17880	1	1	yes	characteristic, complemented, Sylow
348	C₂²×Q₈	—	59	1	no	—
349	C₂²×Q₈	—	59	1	no	—
350	C₂×Q₁₆	—	59	1	no	—
351	C₂×Q₁₆	—	59	1	no	—
352	C₂×Q₁₆	—	59	1	no	—
353	C₂×Q₁₆	—	118	4	no	—
354	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
355	C₂²×C₈	—	59	1	no	—
356	C₂²×C₈	—	59	1	no	—
357	C₄×Q₈	—	59	1	no	—
358	C₄×Q₈	—	59	1	no	—
359	C₄×Q₈	—	59	1	no	—
360	C₄×Q₈	—	59	1	no	—
361	C₄×Q₈	—	59	1	no	—
362	C₄×Q₈	—	59	1	no	—
363	C₄×Q₈	—	118	1	no	—
364	C₄×Q₈	—	118	1	no	—
365	C₄×Q₈	—	118	1	no	—
366	C₄×Q₈	—	118	1	no	—
367	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
368	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
369	C₂×C₄⋊C₄	—	59	1	no	—
370	C₂×C₄⋊C₄	—	59	1	no	—
371	C₂×C₄⋊C₄	—	118	1	no	—
372	C₂×C₄⋊C₄	—	118	1	no	—
373	C₂×C₄²	—	59	1	no	—
374	C₂×C₄²	—	118	1	no	—
375	C₂×C₄²	—	118	1	no	—
376	#107	—	59	1	no	—
377	#107	—	59	1	no	—
378	#107	—	59	1	no	—
379	#107	C₄×D₅₉	1	1	yes	characteristic
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	2	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	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
395	#103	—	59	1	no	—
396	#103	—	59	1	no	—
397	#103	—	59	1	no	—
398	#103	—	59	1	no	—
399	#103	—	59	1	no	—
400	#103	—	59	1	no	—
401	#103	C₄×D₅₉	1	1	yes	characteristic
402	#103	C₄×D₅₉	1	1	yes	characteristic
403	C₂²⋊C₈	—	59	1	no	—
404	C₂²⋊C₈	—	59	1	no	—
405	C₂²⋊C₈	—	118	1	no	—
406	C₂²⋊C₈	—	118	1	no	—
407	C₂²⋊C₈	—	118	1	no	—
408	#97	—	2	1	no	—
409	#97	—	118	1	no	—
410	#97	—	118	1	no	—
411	#97	—	118	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	—	59	1	no	—
414	C₄×C₈	—	59	1	no	—
415	C₄×C₈	—	59	1	no	—
416	C₄×C₈	—	59	1	no	—
417	C₄×C₈	—	59	1	no	—
418	C₄×C₈	—	118	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	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
426	C₂×Q₈	—	59	4	no	—
427	C₂×Q₈	—	59	1	no	—
428	C₂×Q₈	—	59	1	no	—
429	C₂×Q₈	—	118	1	no	—
430	C₂×Q₈	—	118	1	no	—
431	C₂×Q₈	—	118	2	no	—
432	C₂×Q₈	—	118	2	no	—
433	C₂×Q₈	—	118	2	no	—
434	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
435	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
436	C₂²×C₄	—	59	1	no	—
437	C₂²×C₄	—	59	1	no	—
438	C₂²×C₄	—	59	1	no	—
439	C₂²×C₄	—	118	1	no	—
440	C₂²×C₄	—	118	1	no	—
441	C₂²×C₄	—	118	1	no	—
442	C₂²×C₄	—	118	1	no	—
443	Q₁₆	—	2	2	no	—
444	Q₁₆	—	118	2	no	—
445	Q₁₆	—	118	2	no	—
446	Q₁₆	—	118	2	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	59	1	no	—
451	C₂×C₈	—	59	1	no	—
452	C₂×C₈	—	59	1	no	—
453	C₂×C₈	—	59	1	no	—
454	C₂×C₈	—	118	2	no	—
455	C₂×C₈	—	118	2	no	—
456	C₂×C₈	—	118	1	no	—
457	C₂×C₈	—	118	1	no	—
458	C₂×C₈	—	118	1	no	—
459	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
461	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
462	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	59	1	no	—
466	C₄⋊C₄	—	59	1	no	—
467	C₄⋊C₄	—	118	1	no	—
468	C₄⋊C₄	—	118	1	no	—
469	C₄⋊C₄	—	118	1	no	—
470	C₄⋊C₄	—	118	1	no	—
471	C₄⋊C₄	—	118	1	no	—
472	C₄⋊C₄	—	118	1	no	—
473	C₄⋊C₄	—	118	1	no	—
474	C₄⋊C₄	—	118	1	no	—
475	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	59	1	no	—
480	C₄²	—	59	1	no	—
481	C₄²	—	59	1	no	—
482	C₄²	—	118	1	no	—
483	C₄²	—	118	1	no	—
484	C₄²	—	118	1	no	—
485	C₄²	—	118	1	no	—
486	C₄²	—	118	1	no	—
487	C₄²	—	118	1	no	—
488	C₄²	C₂³×D₅₉	1	1	yes	characteristic
489	C₂³	—	59	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	59	2	no	—
494	Q₈	—	118	4	no	—
495	Q₈	—	118	1	no	—
496	Q₈	—	118	1	no	—
497	Q₈	—	118	1	no	—
498	Q₈	—	236	2	no	—
499	Q₈	M₁₆×D₅₉	1	2	yes	—
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	—	59	1	no	—
505	C₂×C₄	—	59	2	no	—
506	C₂×C₄	—	59	2	no	—
507	C₂×C₄	—	59	1	no	—
508	C₂×C₄	—	59	1	no	—
509	C₂×C₄	—	118	4	no	—
510	C₂×C₄	—	118	1	no	—
511	C₂×C₄	—	118	1	no	—
512	C₂×C₄	—	118	1	no	—
513	C₂×C₄	—	118	1	no	—
514	C₂×C₄	—	118	1	no	—
515	C₂×C₄	—	118	1	no	—
516	C₂×C₄	—	472	1	no	—
517	C₂×C₄	—	472	1	no	—
518	C₂×C₄	—	236	1	no	—
519	C₂×C₄	—	236	2	no	—
520	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
521	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
522	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	118	1	no	—
531	C₈	—	118	1	no	—
532	C₈	—	118	1	no	—
533	C₈	—	118	1	no	—
534	C₈	—	236	1	no	—
535	C₈	—	236	1	no	—
536	C₈	—	236	1	no	—
537	C₂²	—	59	2	no	—
538	C₂²	—	118	1	no	—
539	C₂²	—	118	1	no	—
540	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	59	2	no	—
547	C₄	—	118	1	no	—
548	C₄	—	118	1	no	—
549	C₄	—	118	2	no	—
550	C₄	—	236	1	no	—
551	C₄	—	236	1	no	—
552	C₄	—	236	1	no	—
553	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
554	C₄	#131×D₅₉	1	1	yes	characteristic
555	C₄	#16838215	1	1	yes	characteristic
556	C₄	#16838216	1	1	yes	characteristic
557	C₂	—	118	2	no	—
558	C₂	#435×D₅₉	1	1	yes	characteristic
559	C₂	#21432959	1	1	yes	characteristic
560	C₂	#21433010	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×#1584	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1584	D₅₉
hypocenter	C₅₉	#17880
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #21422970	C₂	semidirect
5. #21422967	C₂	semidirect
6. #21422965	C₂	semidirect
7. #21422964	C₂	semidirect
8. #21422948	C₂	semidirect
9. #21422947	C₂	semidirect
10. #21422945	C₂	semidirect
15. C₅₉×#1584	C₂	semidirect
287. #1584	D₅₉	semidirect
347. C₅₉	#17880	semidirect

Maximal subgroups

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

subgroup	index
#21433178	2
#21433175	2
C₄×Q₁₆×D₅₉	2
#21422970	2
#21422967	2
#21422965	2
#21422964	2
#21422948	2
#21422947	2
#21422945	2
#21422843	2
#21422489	2
#21422387	2
C₅₉×#1584	2
#17880	59