Subgroups — #28559432

Order 15104.

590 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434679	C₂	1	1	yes	maximal, characteristic
2	#21433027	C₂	1	1	yes	maximal, characteristic
3	#21433025	C₂	1	1	yes	maximal, characteristic
4	#21422970	C₂	1	1	yes	maximal, characteristic, complemented
5	#21422969	C₂	1	1	yes	maximal, characteristic, complemented
6	#21422968	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422967	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422966	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422965	C₂	1	1	yes	maximal, characteristic, complemented
10	#21422964	C₂	1	1	yes	maximal, characteristic, complemented
11	#21422850	C₂	1	1	yes	maximal, characteristic
12	#21422549	C₂	1	1	yes	maximal, characteristic
13	#21422549	C₂	1	1	yes	maximal, characteristic
14	#322×D₅₉	C₂	1	1	yes	maximal, characteristic
15	C₅₉×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#16837956	C₂²	1	1	yes	characteristic
17	#16837956	C₂²	1	1	yes	characteristic
18	#16837806	C₄	1	1	yes	characteristic
19	#16837780	C₄	1	1	yes	characteristic
20	#16837751	C₄	1	1	yes	characteristic
21	#16837751	C₄	1	1	yes	characteristic
22	#16837644	C₄	1	1	yes	characteristic
23	#16837642	C₄	1	1	yes	characteristic
24	#16837642	C₄	1	1	yes	characteristic
25	#16837640	C₄	1	1	yes	characteristic
26	#16837533	C₂²	1	1	yes	characteristic
27	#16837532	C₂²	1	1	yes	characteristic
28	#16837531	—	2	1	no	—
29	#16837530	—	2	1	no	—
30	#16837529	C₂²	1	1	yes	characteristic
31	Q₈×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₈×Dic₁₁₈	—	2	1	no	—
33	C₈×Dic₁₁₈	C₂²	1	1	yes	characteristic
34	#16837526	—	2	1	no	—
35	#16837526	C₂²	1	1	yes	characteristic
36	C₄×Dic₂₃₆	C₂²	1	1	yes	characteristic
37	C₄×#11745672	C₂²	1	1	yes	characteristic
38	C₄×#11745672	C₂²	1	1	yes	characteristic
39	#16837427	—	2	1	no	—
40	#16837427	—	2	1	no	—
41	#16837424	C₂²	1	1	yes	characteristic
42	#16837424	C₂²	1	1	yes	characteristic
43	#16837359	—	2	1	no	—
44	#16837356	—	2	1	no	—
45	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
48	#16837153	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×#334	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×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745659	—	2	1	no	—
71	C₂×#11745659	—	2	1	no	—
72	C₂×C₈×D₅₉	—	2	1	no	—
73	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
76	C₂×C₈×D₅₉	D₄	1	1	yes	characteristic
77	#14273726	C₂×C₄	1	1	yes	characteristic
78	#14273726	C₂×C₄	1	1	yes	characteristic
79	#14273725	C₂×C₄	1	1	yes	characteristic
80	#14273725	C₂×C₄	1	1	yes	characteristic
81	#14273717	—	2	1	no	—
82	#14273717	—	2	1	no	—
83	#14273707	C₂×C₄	1	1	yes	characteristic
84	#14273707	C₂×C₄	1	1	yes	characteristic
85	#14273705	—	2	1	no	—
86	#14273705	—	2	1	no	—
87	#14273703	C₂×C₄	1	1	yes	characteristic
88	#14273703	C₂×C₄	1	1	yes	characteristic
89	C₄×Dic₁₁₈	—	2	1	no	—
90	C₄×Dic₁₁₈	—	2	1	no	—
91	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
92	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
93	#14273684	—	2	1	no	—
94	#14273684	—	2	1	no	—
95	C₄²×D₅₉	C₂³	1	1	yes	characteristic
96	#14273661	C₂×C₄	1	1	yes	characteristic
97	#14273660	C₂×C₄	1	1	yes	characteristic
98	#14273660	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
100	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
101	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₅₉⋊C₈	—	2	1	no	—
104	Dic₅₉⋊C₈	—	2	1	no	—
105	Dic₅₉⋊C₈	—	2	1	no	—
106	Dic₅₉⋊C₈	—	2	1	no	—
107	Dic₅₉⋊C₈	—	2	1	no	—
108	Dic₅₉⋊C₈	—	2	1	no	—
109	#14273652	C₂×C₄	1	1	yes	characteristic
110	#14273652	C₂×C₄	1	1	yes	characteristic
111	#14273651	C₂×C₄	1	1	yes	characteristic
112	#14273651	C₂×C₄	1	1	yes	characteristic
113	#14273650	C₂×C₄	1	1	yes	characteristic
114	#14273650	C₂×C₄	1	1	yes	characteristic
115	#14273638	—	2	1	no	—
116	#14273637	—	2	1	no	—
117	#14273637	—	2	1	no	—
118	C₄×C₅₉⋊C₈	—	2	1	no	—
119	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
120	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
122	C₈×Dic₅₉	—	2	1	no	—
123	C₈×Dic₅₉	—	2	1	no	—
124	C₈×Dic₅₉	—	2	1	no	—
125	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₅₉	D₄	1	1	yes	characteristic
128	C₈×Dic₅₉	D₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
132	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₅₉	—	2	1	no	—
134	C₄⋊C₈×C₅₉	—	2	1	no	—
135	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
137	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₅₉	—	2	1	no	—
140	C₄×C₈×C₅₉	—	2	1	no	—
141	C₄×C₈×C₅₉	C₂³	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	C₂²×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×D₅₉	#41	1	1	yes	characteristic
149	C₂×Dic₁₁₈	—	2	1	no	—
150	C₂×Dic₁₁₈	—	2	1	no	—
151	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
153	Q₁₆×C₅₉	—	4	1	no	—
154	C₂×C₈×C₅₉	—	2	1	no	—
155	C₂×C₈×C₅₉	—	2	1	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
161	C₄⋊C₄×C₅₉	—	2	1	no	—
162	C₄⋊C₄×C₅₉	—	2	1	no	—
163	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₅₉	—	2	1	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
168	#11745672	—	4	1	no	—
169	#11745672	—	4	1	no	—
170	(C₂×D₅₉)⋊C₄	—	2	1	no	—
171	(C₂×D₅₉)⋊C₄	—	2	1	no	—
172	(C₂×D₅₉)⋊C₄	—	2	1	no	—
173	(C₂×D₅₉)⋊C₄	—	2	1	no	—
174	C₄⋊Dic₅₉	—	2	1	no	—
175	C₄⋊Dic₅₉	—	2	1	no	—
176	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
178	Dic₅₉⋊C₄	—	2	1	no	—
179	Dic₅₉⋊C₄	—	2	1	no	—
180	Dic₅₉⋊C₄	—	2	1	no	—
181	Dic₅₉⋊C₄	—	2	1	no	—
182	Dic₅₉⋊C₄	—	2	1	no	—
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	C₄×Dic₅₉	—	2	1	no	—
189	C₄×Dic₅₉	—	2	1	no	—
190	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
191	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
192	C₄×Dic₅₉	#41	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	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
200	Dic₂₃₆	—	4	1	no	—
201	#11745659	—	4	2	no	—
202	#11745659	—	4	2	no	—
203	C₈×D₅₉	—	2	4	no	—
204	C₈×D₅₉	—	2	2	no	—
205	C₈×D₅₉	—	2	2	no	—
206	C₈×D₅₉	—	4	1	no	—
207	C₈×D₅₉	—	4	1	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	—	2	1	no	—
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	1	no	—
228	C₄×D₅₉	—	2	1	no	—
229	C₄×D₅₉	—	2	2	no	—
230	C₄×D₅₉	#137	1	2	yes	—
231	C₄×D₅₉	#137	1	2	yes	—
232	Dic₁₁₈	—	2	1	no	—
233	Dic₁₁₈	—	2	1	no	—
234	Dic₁₁₈	—	2	1	no	—
235	Dic₁₁₈	—	2	1	no	—
236	Dic₁₁₈	—	4	2	no	—
237	Dic₁₁₈	—	4	2	no	—
238	C₈×C₅₉	—	2	2	no	—
239	C₈×C₅₉	—	2	1	no	—
240	C₈×C₅₉	—	2	1	no	—
241	C₈×C₅₉	—	2	1	no	—
242	C₈×C₅₉	—	2	1	no	—
243	C₈×C₅₉	—	4	1	no	—
244	C₈×C₅₉	—	4	1	no	—
245	C₅₉⋊C₈	—	2	2	no	—
246	C₅₉⋊C₈	—	2	1	no	—
247	C₅₉⋊C₈	—	2	1	no	—
248	C₅₉⋊C₈	—	2	1	no	—
249	C₅₉⋊C₈	—	2	1	no	—
250	C₅₉⋊C₈	—	4	1	no	—
251	C₅₉⋊C₈	—	4	1	no	—
252	#17980	—	59	1	no	maximal, Sylow
253	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂×D₅₉	—	2	1	no	—
255	C₂×D₅₉	—	2	1	no	—
256	C₂×D₅₉	#441	1	2	yes	—
257	C₄×C₅₉	—	2	1	no	—
258	C₄×C₅₉	—	4	1	no	—
259	C₄×C₅₉	—	4	1	no	—
260	C₄×C₅₉	—	4	1	no	—
261	C₄×C₅₉	—	4	1	no	—
262	C₄×C₅₉	#568	1	1	yes	characteristic
263	C₄×C₅₉	#568	1	1	yes	characteristic
264	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
265	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
266	Dic₅₉	—	2	1	no	—
267	Dic₅₉	—	4	1	no	—
268	Dic₅₉	—	4	1	no	—
269	Dic₅₉	—	4	1	no	—
270	Dic₅₉	—	4	1	no	—
271	Dic₅₉	#441	1	2	yes	—
272	Dic₅₉	#443	1	2	yes	—
273	#3170	—	59	1	no	—
274	#2960	—	59	1	no	—
275	#2960	—	59	1	no	—
276	#1587	—	59	1	no	—
277	#1587	—	59	1	no	—
278	#1587	—	59	1	no	—
279	#1587	—	59	1	no	—
280	#1587	—	59	1	no	—
281	#1587	—	59	1	no	—
282	#1587	—	59	1	no	—
283	#1587	D₅₉	1	1	yes	characteristic, complemented
284	#1566	—	59	1	no	—
285	#1493	—	59	1	no	—
286	#1493	—	59	1	no	—
287	C₂×#322	—	59	1	no	—
288	C₂×C₅₉	#2932	1	1	yes	characteristic
289	C₂×C₅₉	C₂×#441	1	1	yes	characteristic
290	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
291	D₅₉	—	2	2	no	—
292	#533	—	59	1	no	—
293	#533	—	59	1	no	—
294	#500	—	59	1	no	—
295	#494	—	59	1	no	—
296	#487	—	59	1	no	—
297	#487	—	59	1	no	—
298	#467	—	59	1	no	—
299	#467	—	59	1	no	—
300	#467	—	59	1	no	—
301	#467	—	59	1	no	—
302	#446	—	59	1	no	—
303	#446	—	59	1	no	—
304	#446	—	59	1	no	—
305	#446	—	118	1	no	—
306	#446	—	118	1	no	—
307	#446	C₂×D₅₉	1	1	yes	characteristic
308	C₈×Q₈	—	59	1	no	—
309	C₈×Q₈	—	59	1	no	—
310	C₈×Q₈	—	59	1	no	—
311	C₈×Q₈	—	118	1	no	—
312	C₈×Q₈	—	118	1	no	—
313	C₈×Q₈	C₂×D₅₉	1	1	yes	characteristic
314	C₄×Q₁₆	—	59	1	no	—
315	C₄×Q₁₆	—	59	1	no	—
316	C₄×Q₁₆	—	59	1	no	—
317	C₄×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
318	#424	—	118	1	no	—
319	#424	—	118	1	no	—
320	#423	—	59	1	no	—
321	#423	—	59	1	no	—
322	#405	—	118	1	no	—
323	#405	—	118	1	no	—
324	C₂×C₄×C₈	—	59	1	no	—
325	C₂×C₄×C₈	—	59	1	no	—
326	C₂×C₄×C₈	—	59	1	no	—
327	#334	—	59	1	no	—
328	#334	—	59	1	no	—
329	#334	—	59	1	no	—
330	#334	C₂×D₅₉	1	1	yes	characteristic
331	Q₈⋊C₈	—	59	1	no	—
332	Q₈⋊C₈	—	59	1	no	—
333	Q₈⋊C₈	—	59	1	no	—
334	Q₈⋊C₈	—	59	1	no	—
335	Q₈⋊C₈	—	59	1	no	—
336	Q₈⋊C₈	—	59	1	no	—
337	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
338	Q₈⋊C₈	C₂×D₅₉	1	1	yes	characteristic
339	#322	—	59	1	no	—
340	#322	—	59	1	no	—
341	#322	—	59	1	no	—
342	#322	C₂×D₅₉	1	1	yes	characteristic
343	C₅₉	#17980	1	1	yes	characteristic, complemented, Sylow
344	C₂×Q₁₆	—	59	1	no	—
345	C₂×Q₁₆	—	59	1	no	—
346	C₂×Q₁₆	—	59	1	no	—
347	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
348	C₂×M₁₆	—	118	1	no	—
349	C₂×M₁₆	—	118	1	no	—
350	C₂²×C₈	—	59	1	no	—
351	C₂²×C₈	—	59	1	no	—
352	C₂²×C₈	—	59	1	no	—
353	C₂²×C₈	—	59	1	no	—
354	C₂²×C₈	—	118	1	no	—
355	C₄⋊Q₈	—	59	1	no	—
356	C₄⋊Q₈	—	59	1	no	—
357	C₄⋊Q₈	—	59	1	no	—
358	C₄⋊Q₈	—	59	1	no	—
359	#125	—	118	1	no	—
360	#125	—	118	1	no	—
361	C₂²⋊Q₈	—	59	1	no	—
362	C₂²⋊Q₈	—	59	1	no	—
363	C₂²⋊Q₈	—	59	1	no	—
364	C₂²⋊Q₈	—	59	1	no	—
365	C₂²⋊Q₈	—	118	1	no	—
366	C₂²⋊Q₈	—	118	1	no	—
367	C₄×Q₈	—	59	1	no	—
368	C₄×Q₈	—	59	1	no	—
369	C₄×Q₈	—	118	1	no	—
370	C₄×Q₈	—	118	1	no	—
371	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
372	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
373	#117	—	118	1	no	—
374	#117	—	118	1	no	—
375	C₂×C₄²	—	59	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	—	118	1	no	—
385	C₄⋊C₈	—	118	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	C₂²×D₅₉	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
394	#103	—	59	1	no	—
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	C₄×D₅₉	1	1	yes	characteristic
401	#103	C₄×D₅₉	1	1	yes	characteristic
402	#97	—	2	1	no	—
403	#97	—	118	1	no	—
404	#97	—	118	1	no	—
405	#97	—	118	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	—	59	1	no	—
408	C₄×C₈	—	59	1	no	—
409	C₄×C₈	—	59	1	no	—
410	C₄×C₈	—	59	1	no	—
411	C₄×C₈	—	59	1	no	—
412	C₄×C₈	—	59	1	no	—
413	C₄×C₈	—	59	1	no	—
414	C₄×C₈	—	118	1	no	—
415	C₄×C₈	—	118	1	no	—
416	C₄×C₈	—	118	1	no	—
417	C₄×C₈	—	118	1	no	—
418	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
421	C₂×Q₈	—	59	1	no	—
422	C₂×Q₈	—	59	1	no	—
423	C₂×Q₈	—	118	1	no	—
424	C₂×Q₈	—	118	1	no	—
425	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
426	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
427	C₂²×C₄	—	59	1	no	—
428	C₂²×C₄	—	59	1	no	—
429	C₂²×C₄	—	59	1	no	—
430	Q₁₆	—	4	1	no	—
431	Q₁₆	—	236	1	no	—
432	Q₁₆	—	236	1	no	—
433	Q₁₆	—	236	1	no	—
434	M₁₆	—	236	2	no	—
435	M₁₆	—	236	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	59	1	no	—
440	C₂×C₈	—	59	1	no	—
441	C₂×C₈	—	59	1	no	—
442	C₂×C₈	—	59	1	no	—
443	C₂×C₈	—	118	2	no	—
444	C₂×C₈	—	118	2	no	—
445	C₂×C₈	—	118	4	no	—
446	C₂×C₈	—	118	1	no	—
447	C₂×C₈	—	118	1	no	—
448	C₂×C₈	—	118	1	no	—
449	C₂×C₈	—	236	1	no	—
450	C₂×C₈	—	236	1	no	—
451	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
452	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
453	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
454	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	59	1	no	—
458	C₄⋊C₄	—	59	1	no	—
459	C₄⋊C₄	—	118	1	no	—
460	C₄⋊C₄	—	118	1	no	—
461	C₄⋊C₄	—	118	1	no	—
462	C₄⋊C₄	—	118	1	no	—
463	C₄⋊C₄	—	118	1	no	—
464	C₄⋊C₄	—	118	1	no	—
465	C₄⋊C₄	—	118	1	no	—
466	C₄⋊C₄	—	118	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	C₂×C₄×D₅₉	1	1	yes	characteristic
472	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
473	C₂²⋊C₄	—	118	1	no	—
474	C₂²⋊C₄	—	118	1	no	—
475	C₂²⋊C₄	—	118	1	no	—
476	C₂²⋊C₄	—	118	1	no	—
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	C₂³×D₅₉	1	1	yes	characteristic
485	C₂³	—	59	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	118	1	no	—
491	Q₈	—	118	1	no	—
492	Q₈	—	118	1	no	—
493	Q₈	—	118	1	no	—
494	Q₈	—	236	2	no	—
495	Q₈	—	236	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	59	1	no	—
501	C₂×C₄	—	59	1	no	—
502	C₂×C₄	—	59	2	no	—
503	C₂×C₄	—	59	2	no	—
504	C₂×C₄	—	59	1	no	—
505	C₂×C₄	—	118	2	no	—
506	C₂×C₄	—	118	1	no	—
507	C₂×C₄	—	118	1	no	—
508	C₂×C₄	—	118	1	no	—
509	C₂×C₄	—	118	1	no	—
510	C₂×C₄	—	118	1	no	—
511	C₂×C₄	—	118	1	no	—
512	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
513	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
514	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	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	C₂²	—	59	2	no	—
530	C₂²	—	118	1	no	—
531	C₂²	—	118	1	no	—
532	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	59	2	no	—
539	C₄	—	59	2	no	—
540	C₄	—	118	1	no	—
541	C₄	—	236	1	no	—
542	C₄	—	236	1	no	—
543	C₄	—	236	1	no	—
544	C₄	—	236	1	no	—
545	C₄	#16838167	1	1	yes	characteristic
546	C₄	#16838168	1	1	yes	characteristic
547	C₄	#137×D₅₉	1	1	yes	characteristic
548	C₄	#137×D₅₉	1	1	yes	characteristic
549	C₂	—	118	2	no	—
550	C₂	#21432810	1	1	yes	characteristic
551	C₂	#441×D₅₉	1	1	yes	characteristic
552	C₂	#443×D₅₉	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×#1587	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂²×D₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1587	D₅₉
hypocenter	C₅₉	#17980
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1587

Complements

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

N	H ≅ G/N	type
4. #21422970	C₂	semidirect
5. #21422969	C₂	semidirect
6. #21422968	C₂	semidirect
7. #21422967	C₂	semidirect
8. #21422966	C₂	semidirect
9. #21422965	C₂	semidirect
10. #21422964	C₂	semidirect
15. C₅₉×#1587	C₂	semidirect
283. #1587	D₅₉	semidirect
343. C₅₉	#17980	semidirect

Maximal subgroups

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

subgroup	index
#21434679	2
#21433027	2
#21433025	2
#21422970	2
#21422969	2
#21422968	2
#21422967	2
#21422966	2
#21422965	2
#21422964	2
#21422850	2
#21422549	2
#322×D₅₉	2
C₅₉×#1587	2
#17980	59