Subgroups — #28560453

Order 15104.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434651	C₂	1	1	yes	maximal, characteristic
2	#21433043	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422984	C₂	1	2	yes	maximal, complemented
4	#21422937	C₂	1	2	yes	maximal, complemented
5	#21422932	C₂	1	2	yes	maximal, complemented
6	C₈×#11745670	C₂	1	2	yes	maximal, complemented
7	C₂×#16837152	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422498	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422495	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2935	C₂	1	1	yes	maximal, characteristic
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837798	C₄	1	1	yes	characteristic
14	#16837774	C₄	1	1	yes	characteristic
15	#16837754	C₄	1	1	yes	characteristic
16	#16837748	C₄	1	1	yes	characteristic
17	#16837629	C₄	1	2	yes	—
18	#16837629	C₄	1	2	yes	—
19	#16837532	C₂²	1	2	yes	—
20	#16837530	—	2	2	no	—
21	C₈×Dic₁₁₈	C₂²	1	2	yes	—
22	C₄×#11745670	C₂²	1	2	yes	—
23	C₄×#11745670	C₂²	1	2	yes	—
24	#16837455	C₂²	1	1	yes	characteristic
25	#16837430	—	2	1	no	—
26	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#16837360	—	2	1	no	—
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	#16837152	C₂²	1	1	yes	characteristic
30	#16837152	C₂²	1	1	yes	characteristic
31	#16837152	C₂²	1	1	yes	characteristic
32	#16837152	C₂²	1	1	yes	characteristic
33	#16837132	C₂²	1	2	yes	—
34	#16837132	C₂²	1	2	yes	—
35	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
37	#16837123	C₂²	1	2	yes	—
38	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
39	C₂×#131×C₅₉	—	2	1	no	—
40	C₅₉×#532	C₂²	1	1	yes	characteristic
41	C₅₉×#436	C₂²	1	2	yes	—
42	C₅₉×#435	—	2	2	no	—
43	C₈×D₄×C₅₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#408	—	2	1	no	—
46	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#11745670	C₂×C₄	1	2	yes	—
48	C₂×#11745670	C₂×C₄	1	2	yes	—
49	C₂²×C₅₉⋊C₈	—	2	1	no	—
50	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	#14273727	C₂×C₄	1	1	yes	characteristic
53	#14273727	C₂×C₄	1	1	yes	characteristic
54	#14273719	—	2	1	no	—
55	#14273706	—	2	1	no	—
56	#14273706	C₂×C₄	1	2	yes	—
57	C₄×Dic₁₁₈	—	2	1	no	—
58	C₄×Dic₁₁₈	C₂³	1	2	yes	—
59	#14273686	—	2	1	no	—
60	#14273658	C₂×C₄	1	2	yes	—
61	#14273658	C₂×C₄	1	2	yes	—
62	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
66	Dic₅₉⋊C₈	—	2	2	no	—
67	Dic₅₉⋊C₈	—	2	2	no	—
68	#14273650	C₂×C₄	1	2	yes	—
69	#14273650	C₂×C₄	1	2	yes	—
70	#14273648	C₂×C₄	1	2	yes	—
71	#14273648	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
73	#14273637	—	2	2	no	—
74	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
77	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×Dic₅₉	—	2	2	no	—
80	C₂×#41×C₅₉	—	2	1	no	—
81	#131×C₅₉	—	4	4	no	—
82	C₂×M₁₆×C₅₉	—	2	2	no	—
83	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
84	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₅₉	—	2	1	no	—
86	C₂²×C₈×C₅₉	—	2	2	no	—
87	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
88	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
89	#124×C₅₉	—	2	1	no	—
90	#121×C₅₉	—	2	1	no	—
91	#121×C₅₉	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₅₉	—	2	1	no	—
93	C₄×D₄×C₅₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₅₉	—	2	1	no	—
96	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₅₉	—	2	2	no	—
99	C₂²⋊C₈×C₅₉	—	2	2	no	—
100	#97×C₅₉	D₄	1	2	yes	—
101	C₄×C₈×C₅₉	C₂³	1	2	yes	—
102	#41×C₅₉	—	4	2	no	—
103	#41×C₅₉	—	4	2	no	—
104	C₂×Q₈×C₅₉	—	2	1	no	—
105	C₂×D₄×C₅₉	—	2	2	no	—
106	C₂×D₄×C₅₉	—	2	1	no	—
107	C₂×D₄×C₅₉	—	2	1	no	—
108	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
113	C₂×Dic₁₁₈	—	2	1	no	—
114	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
115	M₁₆×C₅₉	—	2	2	no	—
116	M₁₆×C₅₉	—	4	4	no	—
117	M₁₆×C₅₉	SD₁₆	1	4	yes	complemented
118	C₂×C₈×C₅₉	—	2	1	no	—
119	C₂×C₈×C₅₉	—	2	1	no	—
120	C₂×C₈×C₅₉	—	4	2	no	—
121	C₂×C₈×C₅₉	—	4	4	no	—
122	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₅₉	—	2	2	no	—
127	C₂²⋊C₄×C₅₉	—	2	2	no	—
128	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₅₉	#41	1	1	yes	characteristic
131	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₅₉	—	2	2	no	—
133	#11745670	—	2	4	no	—
134	#11745670	—	4	2	no	—
135	C₄⋊Dic₅₉	—	2	1	no	—
136	C₄⋊Dic₅₉	—	2	1	no	—
137	C₄⋊Dic₅₉	—	2	1	no	—
138	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
139	Dic₅₉⋊C₄	—	2	2	no	—
140	Dic₅₉⋊C₄	—	2	2	no	—
141	C₄×Dic₅₉	—	2	2	no	—
142	C₂×C₅₉⋊C₈	—	2	2	no	—
143	C₂×C₅₉⋊C₈	—	2	1	no	—
144	C₂×C₅₉⋊C₈	—	2	1	no	—
145	C₂×C₅₉⋊C₈	—	2	2	no	—
146	C₂×C₅₉⋊C₈	—	4	1	no	—
147	C₂×C₅₉⋊C₈	—	4	2	no	—
148	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂³×C₅₉	—	2	2	no	—
153	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
154	Q₈×C₅₉	—	4	2	no	—
155	D₄×C₅₉	—	2	2	no	—
156	D₄×C₅₉	—	2	2	no	—
157	D₄×C₅₉	—	4	4	no	—
158	D₄×C₅₉	—	4	2	no	—
159	D₄×C₅₉	—	8	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	2	no	—
163	C₂×C₄×C₅₉	—	4	1	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₅₉	#135	1	2	yes	—
171	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₅₉	—	2	2	no	—
175	C₂×Dic₅₉	—	2	2	no	—
176	Dic₁₁₈	—	2	2	no	—
177	Dic₁₁₈	—	2	2	no	—
178	Dic₁₁₈	—	8	1	no	—
179	C₈×C₅₉	—	2	2	no	—
180	C₈×C₅₉	—	4	1	no	—
181	C₈×C₅₉	—	4	1	no	—
182	C₈×C₅₉	C₂×SD₁₆	1	4	yes	—
183	C₅₉⋊C₈	—	2	1	no	—
184	C₅₉⋊C₈	—	2	1	no	—
185	C₅₉⋊C₈	—	2	1	no	—
186	C₅₉⋊C₈	—	4	2	no	—
187	C₅₉⋊C₈	—	4	1	no	—
188	C₅₉⋊C₈	—	4	1	no	—
189	C₅₉⋊C₈	#131	1	2	yes	complemented
190	#18067	—	59	1	no	maximal, Sylow
191	C₂²×C₅₉	—	2	1	no	—
192	C₂²×C₅₉	—	2	1	no	—
193	C₂²×C₅₉	—	4	2	no	—
194	C₂²×C₅₉	—	4	2	no	—
195	C₂²×C₅₉	—	4	2	no	—
196	C₂²×C₅₉	C₄×SD₁₆	1	2	yes	—
197	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₅₉	—	2	1	no	—
199	C₄×C₅₉	—	2	1	no	—
200	C₄×C₅₉	—	2	1	no	—
201	C₄×C₅₉	—	4	2	no	—
202	C₄×C₅₉	C₄×SD₁₆	1	2	yes	—
203	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
204	C₄×C₅₉	#568	1	1	yes	characteristic
205	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
206	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
207	Dic₅₉	—	4	2	no	—
208	Dic₅₉	—	4	2	no	—
209	#3167	—	59	1	no	—
210	#2962	—	59	1	no	—
211	#2935	D₅₉	1	1	yes	characteristic
212	#1590	—	59	2	no	—
213	#1583	—	59	2	no	—
214	#1582	—	59	2	no	—
215	C₈×SD₁₆	—	59	2	no	—
216	C₂×#334	—	59	1	no	—
217	#1481	—	59	1	no	—
218	#1480	—	59	1	no	—
219	C₈×M₁₆	—	59	1	no	—
220	C₂×C₅₉	—	2	2	no	—
221	C₂×C₅₉	—	8	2	no	—
222	C₂×C₅₉	#2935	1	1	yes	characteristic
223	C₂×C₅₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
224	C₂×C₅₉	#2957	1	1	yes	characteristic
225	C₂×#131	—	2	1	no	—
226	#533	—	59	1	no	—
227	#532	C₂×D₅₉	1	1	yes	characteristic
228	#498	—	59	1	no	—
229	#492	—	59	1	no	—
230	#487	—	59	1	no	—
231	#486	—	59	1	no	—
232	#465	—	59	2	no	—
233	#465	—	59	2	no	—
234	#446	—	59	2	no	—
235	#446	—	118	2	no	—
236	C₈×Q₈	—	59	2	no	—
237	C₄×SD₁₆	—	59	2	no	—
238	C₄×SD₁₆	—	59	2	no	—
239	#436	C₂×D₅₉	1	2	yes	—
240	#435	—	2	2	no	—
241	C₈×D₄	C₂×D₅₉	1	2	yes	—
242	#431	—	59	1	no	—
243	#424	—	118	1	no	—
244	C₂×C₄⋊C₈	—	59	1	no	—
245	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
246	#408	—	2	1	no	—
247	#405	—	118	1	no	—
248	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
249	C₂×C₄×C₈	—	59	1	no	—
250	#334	—	59	1	no	—
251	#334	—	59	1	no	—
252	#334	—	59	1	no	—
253	#334	—	59	1	no	—
254	Q₈⋊C₈	—	59	2	no	—
255	Q₈⋊C₈	—	59	2	no	—
256	D₄⋊C₈	—	59	2	no	—
257	D₄⋊C₈	—	59	2	no	—
258	#322	—	59	2	no	—
259	C₈²	—	59	2	no	—
260	C₅₉	#18067	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	2	1	no	—
262	C₂×SD₁₆	—	59	2	no	—
263	C₂×SD₁₆	—	59	2	no	—
264	#131	—	4	4	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
267	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	59	1	no	—
271	C₂²×C₈	—	59	1	no	—
272	C₂²×C₈	—	118	1	no	—
273	C₄⋊Q₈	—	59	1	no	—
274	C₄⋊Q₈	—	59	1	no	—
275	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
276	#127	C₄×D₅₉	1	1	yes	characteristic
277	#125	—	118	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	59	2	no	—
280	C₂²⋊Q₈	—	118	1	no	—
281	#121	—	2	1	no	—
282	#121	C₄×D₅₉	1	2	yes	—
283	C₄×Q₈	—	59	2	no	—
284	C₄×Q₈	—	118	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂²×D₅₉	1	2	yes	—
287	#117	—	118	1	no	—
288	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
289	#106	—	59	2	no	—
290	#106	—	59	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	59	1	no	—
293	C₄⋊C₈	—	59	1	no	—
294	C₄⋊C₈	—	118	2	no	—
295	C₄⋊C₈	—	118	2	no	—
296	C₄⋊C₈	—	118	1	no	—
297	C₄⋊C₈	—	118	1	no	—
298	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
300	#103	—	59	2	no	—
301	#103	—	59	2	no	—
302	#102	—	59	2	no	—
303	#102	—	59	2	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	118	1	no	—
307	#97	—	118	2	no	—
308	#97	C₂²⋊D₅₉	1	2	yes	—
309	C₄×C₈	—	59	1	no	—
310	C₄×C₈	—	59	1	no	—
311	C₄×C₈	—	59	1	no	—
312	C₄×C₈	—	59	1	no	—
313	C₄×C₈	—	59	2	no	—
314	C₄×C₈	—	118	2	no	—
315	C₄×C₈	C₂²×D₅₉	1	2	yes	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	59	2	no	—
320	C₂×Q₈	—	118	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×C₄×D₅₉	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
327	C₂²×C₄	#11745685	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
329	SD₁₆	—	118	4	no	—
330	SD₁₆	—	236	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	4	no	—
333	M₁₆	#11745670	1	4	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	—	59	1	no	—
339	C₂×C₈	—	59	1	no	—
340	C₂×C₈	—	59	1	no	—
341	C₂×C₈	—	59	1	no	—
342	C₂×C₈	—	118	2	no	—
343	C₂×C₈	—	118	1	no	—
344	C₂×C₈	—	118	1	no	—
345	C₂×C₈	—	118	2	no	—
346	C₂×C₈	—	236	1	no	—
347	C₂×C₈	—	236	2	no	—
348	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
349	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	59	2	no	—
352	C₄⋊C₄	—	118	1	no	—
353	C₄⋊C₄	—	118	1	no	—
354	C₄⋊C₄	—	118	2	no	—
355	C₄⋊C₄	—	118	1	no	—
356	C₄⋊C₄	—	118	2	no	—
357	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	118	2	no	—
361	C₄²	—	118	2	no	—
362	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
363	C₄²	#11745685	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
365	C₄²	C₂³×D₅₉	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	118	2	no	—
370	Q₈	—	118	2	no	—
371	Q₈	—	472	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	118	2	no	—
384	C₂×C₄	—	118	2	no	—
385	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
388	C₂×C₄	C₂×#11745670	1	2	yes	—
389	C₂×C₄	#14273747	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	59	2	no	—
397	C₈	—	118	1	no	—
398	C₈	—	118	1	no	—
399	C₈	—	118	1	no	—
400	C₈	—	236	2	no	—
401	C₈	—	236	1	no	—
402	C₈	—	236	1	no	—
403	C₈	C₂×#11745670	1	4	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₄×#11745670	1	2	yes	—
410	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	236	2	no	—
416	C₄	—	236	2	no	—
417	C₄	C₄×#11745670	1	2	yes	—
418	C₄	#131×D₅₉	1	1	yes	characteristic
419	C₄	#16838167	1	1	yes	characteristic
420	C₄	C₂²×#11745670	1	1	yes	characteristic
421	C₄	C₂×#14273747	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	#21432838	1	1	yes	characteristic
425	C₂	C₂×C₄×#11745670	1	1	yes	characteristic
426	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2935	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#532	C₂²
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2935	D₅₉
hypocenter	C₅₉	#18067
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #21433043	C₂	semidirect
3. #21422984	C₂	semidirect
4. #21422937	C₂	semidirect
5. #21422932	C₂	semidirect
6. C₈×#11745670	C₂	semidirect
7. C₂×#16837152	C₂	semidirect
8. #21422498	C₂	semidirect
10. M₁₆×C₅₉⋊C₈	C₂	semidirect
117. M₁₆×C₅₉	SD₁₆	semidirect
189. C₅₉⋊C₈	#131	semidirect
260. C₅₉	#18067	semidirect
333. M₁₆	#11745670	semidirect

Maximal subgroups

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

subgroup	index
#21434651	2
#21433043	2
#21422984	2
#21422937	2
#21422932	2
C₈×#11745670	2
C₂×#16837152	2
#21422498	2
#21422495	2
M₁₆×C₅₉⋊C₈	2
C₅₉×#2935	2
#18067	59