Subgroups — #28557739

Order 15104.

666 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433214	C₂	1	1	yes	maximal, characteristic
2	#21433209	C₂	1	1	yes	maximal, characteristic
3	C₄×#14273735	C₂	1	1	yes	maximal, characteristic
4	#21422862	C₂	1	2	yes	maximal, complemented
5	#21422860	C₂	1	2	yes	maximal, complemented
6	#21422856	C₂	1	2	yes	maximal, complemented
7	#21422853	C₂	1	2	yes	maximal, complemented
8	#21422848	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16837154	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273735	C₄	1	1	yes	characteristic
13	C₂×#14273735	C₄	1	1	yes	characteristic
14	C₄×#11745685	C₂²	1	1	yes	characteristic
15	#16837532	—	2	1	no	—
16	#16837529	—	2	1	no	—
17	#16837481	—	2	1	no	—
18	#16837479	—	2	1	no	—
19	#16837473	—	2	2	no	—
20	#16837470	—	2	2	no	—
21	#16837458	C₂²	1	2	yes	—
22	#16837458	C₂²	1	2	yes	—
23	#16837455	C₂²	1	1	yes	characteristic
24	#16837424	C₂²	1	2	yes	—
25	#16837424	C₂²	1	2	yes	—
26	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#16837360	C₄	1	1	yes	characteristic
28	#16837360	C₄	1	1	yes	characteristic
29	#16837359	C₄	1	2	yes	—
30	#16837359	C₄	1	2	yes	—
31	C₄×#11745659	C₂²	1	2	yes	—
32	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₅₉	C₂²	1	2	yes	—
34	#16837155	C₂²	1	2	yes	—
35	#16837154	C₂²	1	1	yes	characteristic
36	#16837154	C₂²	1	2	yes	—
37	#16837154	C₂²	1	1	yes	characteristic
38	#16837154	C₂²	1	2	yes	—
39	#16837153	C₂²	1	2	yes	—
40	#16837152	C₂²	1	1	yes	characteristic
41	#16837152	C₂²	1	1	yes	characteristic
42	C₅₉×#431	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#335	C₂²	1	2	yes	—
46	C₅₉×#334	C₂²	1	2	yes	—
47	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
48	#14273735	—	2	4	no	—
49	#14273735	—	2	4	no	—
50	C₂×#11745659	—	2	2	no	—
51	C₂×#11745659	—	2	2	no	—
52	C₂×#11745659	C₂×C₄	1	2	yes	—
53	C₂×#11745659	C₂×C₄	1	2	yes	—
54	C₂²×C₅₉⋊C₈	—	2	1	no	—
55	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₅₉	C₂×C₄	1	2	yes	—
59	C₄×Dic₁₁₈	D₄	1	1	yes	characteristic
60	C₄×Dic₁₁₈	Q₈	1	1	yes	characteristic
61	C₄×D₂₃₆	D₄	1	1	yes	characteristic
62	C₄×D₂₃₆	Q₈	1	1	yes	characteristic
63	C₄×C₂²⋊D₅₉	D₄	1	2	yes	—
64	C₄×C₂²⋊D₅₉	Q₈	1	2	yes	—
65	#14273686	C₂×C₄	1	1	yes	characteristic
66	#14273684	C₂×C₄	1	2	yes	—
67	C₄²×D₅₉	C₂³	1	2	yes	—
68	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
72	Dic₅₉⋊C₈	—	2	2	no	—
73	Dic₅₉⋊C₈	—	2	2	no	—
74	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
75	(C₂×D₅₉)⋊C₈	—	2	2	no	—
76	(C₂×D₅₉)⋊C₈	—	2	2	no	—
77	#14273637	—	2	2	no	—
78	#14273637	—	2	2	no	—
79	#14273637	C₂×C₄	1	2	yes	—
80	#14273637	C₂×C₄	1	2	yes	—
81	C₄×C₅₉⋊C₈	—	2	1	no	—
82	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
84	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
87	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
88	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂×M₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₅₉	—	2	1	no	—
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₉	—	2	1	no	—
93	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
95	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₅₉	—	2	1	no	—
97	#97×C₅₉	C₂×C₄	1	2	yes	—
98	C₄×C₈×C₅₉	—	2	1	no	—
99	C₄×C₈×C₅₉	C₂³	1	2	yes	—
100	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	2	yes	—
104	#11745685	—	2	2	no	—
105	#11745685	—	2	2	no	—
106	C₂×D₂₃₆	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₉	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₅₉	C₂×D₄	1	2	yes	—
109	C₂×C₄×D₅₉	C₂×Q₈	1	2	yes	—
110	C₂×Dic₁₁₈	C₄⋊C₄	1	1	yes	characteristic
111	M₁₆×C₅₉	—	2	2	no	—
112	M₁₆×C₅₉	M₁₆	1	4	yes	complemented
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	1	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	—	8	1	no	—
117	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
119	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
124	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	2	yes	—
125	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	2	yes	—
126	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
128	Dic₅₉⋊C₄	C₄⋊C₄	1	2	yes	—
129	Dic₅₉⋊C₄	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
131	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
132	C₄×Dic₅₉	C₂×Q₈	1	2	yes	—
133	C₂×C₅₉⋊C₈	—	2	2	no	—
134	C₂×C₅₉⋊C₈	—	2	1	no	—
135	C₂×C₅₉⋊C₈	—	2	1	no	—
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	8	1	no	—
138	C₂×C₅₉⋊C₈	M₁₆	1	4	yes	complemented
139	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	#11745659	—	2	4	no	—
144	#11745659	—	2	4	no	—
145	#11745659	—	8	2	no	—
146	#11745659	—	8	2	no	—
147	C₈×D₅₉	—	2	4	no	—
148	C₈×D₅₉	—	2	4	no	—
149	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×D₅₉	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	1	no	—
153	C₂×C₄×C₅₉	—	4	1	no	—
154	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
158	C₂×C₄×C₅₉	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
162	C₂²⋊D₅₉	—	2	4	no	—
163	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×Dic₅₉	C₂×C₄⋊C₄	1	2	yes	—
166	D₂₃₆	—	2	2	no	—
167	C₄×D₅₉	—	2	2	no	—
168	C₄×D₅₉	—	2	2	no	—
169	C₄×D₅₉	—	2	2	no	—
170	C₄×D₅₉	—	2	2	no	—
171	C₄×D₅₉	—	4	2	no	—
172	Dic₁₁₈	—	2	2	no	—
173	C₈×C₅₉	—	2	2	no	—
174	C₈×C₅₉	—	4	1	no	—
175	C₈×C₅₉	—	4	2	no	—
176	C₈×C₅₉	—	4	1	no	—
177	C₈×C₅₉	C₂×M₁₆	1	4	yes	—
178	C₅₉⋊C₈	—	2	1	no	—
179	C₅₉⋊C₈	—	2	1	no	—
180	C₅₉⋊C₈	—	4	1	no	—
181	C₅₉⋊C₈	—	4	2	no	—
182	C₅₉⋊C₈	—	4	1	no	—
183	C₅₉⋊C₈	C₂×M₁₆	1	2	yes	—
184	C₅₉⋊C₈	C₂×M₁₆	1	2	yes	—
185	#17799	—	59	1	no	maximal, Sylow
186	C₂²×C₅₉	—	2	1	no	—
187	C₂²×C₅₉	—	2	1	no	—
188	C₂²×C₅₉	#423	1	2	yes	—
189	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂×D₅₉	—	2	2	no	—
191	C₂×D₅₉	—	2	2	no	—
192	C₂×D₅₉	—	2	2	no	—
193	C₄×C₅₉	—	2	1	no	—
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	—	2	1	no	—
196	C₄×C₅₉	#423	1	2	yes	—
197	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
198	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
199	C₄×C₅₉	#576	1	1	yes	characteristic
200	C₄×C₅₉	#578	1	1	yes	characteristic
201	Dic₅₉	—	2	2	no	—
202	Dic₅₉	—	2	2	no	—
203	Dic₅₉	—	2	2	no	—
204	#2989	—	59	1	no	—
205	#2989	—	59	1	no	—
206	C₄×#131	—	59	1	no	—
207	#1569	—	59	2	no	—
208	#1569	—	59	2	no	—
209	#1568	—	59	2	no	—
210	#1567	—	59	2	no	—
211	#1565	—	59	1	no	—
212	#1565	D₅₉	1	1	yes	characteristic, complemented
213	#1564	—	59	1	no	—
214	C₂×#335	—	59	1	no	—
215	C₂×C₅₉	—	2	2	no	—
216	C₂×C₅₉	C₂×#423	1	1	yes	characteristic
217	C₂×C₅₉	#2913	1	1	yes	characteristic
218	C₂×C₅₉	#2916	1	1	yes	characteristic
219	D₅₉	—	4	2	no	—
220	C₂×#131	—	59	1	no	—
221	C₂×#131	—	59	1	no	—
222	C₄×#41	—	59	1	no	—
223	#446	—	118	1	no	—
224	#446	—	118	1	no	—
225	#436	—	118	1	no	—
226	#436	—	118	1	no	—
227	#435	—	118	2	no	—
228	#435	—	118	2	no	—
229	#432	—	59	2	no	—
230	#432	—	59	2	no	—
231	#431	—	59	1	no	—
232	#431	C₂×D₅₉	1	1	yes	characteristic
233	#423	—	59	2	no	—
234	#423	—	59	2	no	—
235	C₂×C₄⋊C₈	—	59	1	no	—
236	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
237	#405	—	59	1	no	—
238	#405	—	59	1	no	—
239	#405	—	59	2	no	—
240	#405	—	59	2	no	—
241	C₄×M₁₆	—	59	2	no	—
242	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
243	C₂×C₄×C₈	—	59	1	no	—
244	C₂×C₄×C₈	—	59	2	no	—
245	#335	—	59	2	no	—
246	#335	—	59	2	no	—
247	#335	—	59	1	no	—
248	#335	—	59	1	no	—
249	#335	—	59	2	no	—
250	#335	C₂×D₅₉	1	2	yes	—
251	#334	—	59	1	no	—
252	#334	—	59	1	no	—
253	#334	—	59	2	no	—
254	#334	C₂×D₅₉	1	2	yes	—
255	C₅₉	#17799	1	1	yes	characteristic, complemented, Sylow
256	C₂×#41	—	59	1	no	—
257	#131	—	118	4	no	—
258	#131	—	118	4	no	—
259	C₂×M₁₆	—	59	2	no	—
260	C₂×M₁₆	—	59	2	no	—
261	C₂×M₁₆	—	118	2	no	—
262	C₂×M₁₆	—	118	2	no	—
263	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
264	C₂×M₁₆	C₄×D₅₉	1	1	yes	characteristic
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	59	1	no	—
267	C₂²×C₈	—	59	1	no	—
268	C₂²×C₈	—	59	2	no	—
269	C₂²×C₈	—	59	2	no	—
270	C₂²×C₈	—	118	1	no	—
271	C₄×Q₈	—	59	1	no	—
272	C₄×Q₈	—	59	1	no	—
273	C₄×D₄	—	59	2	no	—
274	C₄×D₄	—	59	2	no	—
275	C₄×D₄	—	59	1	no	—
276	C₄×D₄	—	59	1	no	—
277	#117	—	59	1	no	—
278	#117	—	59	2	no	—
279	C₂×C₄²	—	59	2	no	—
280	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	59	1	no	—
283	C₄⋊C₈	—	59	2	no	—
284	C₄⋊C₈	—	59	1	no	—
285	C₄⋊C₈	—	118	2	no	—
286	C₄⋊C₈	—	118	2	no	—
287	C₄⋊C₈	—	118	1	no	—
288	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
291	C₂²⋊C₈	—	2	1	no	—
292	C₂²⋊C₈	—	118	2	no	—
293	C₂²⋊C₈	—	118	2	no	—
294	C₂²⋊C₈	—	118	1	no	—
295	#97	—	59	2	no	—
296	#97	—	59	2	no	—
297	#97	—	118	2	no	—
298	#97	—	118	2	no	—
299	#97	C₄×D₅₉	1	2	yes	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	59	2	no	—
302	C₄×C₈	—	59	2	no	—
303	C₄×C₈	—	59	1	no	—
304	C₄×C₈	—	59	1	no	—
305	C₄×C₈	—	59	1	no	—
306	C₄×C₈	—	59	1	no	—
307	C₄×C₈	—	118	1	no	—
308	C₄×C₈	C₂²×D₅₉	1	2	yes	—
309	#41	—	118	2	no	—
310	#41	—	118	2	no	—
311	C₂×Q₈	—	59	1	no	—
312	C₂×D₄	—	59	2	no	—
313	C₂×D₄	—	59	1	no	—
314	C₂²×C₄	—	59	2	no	—
315	C₂²×C₄	—	59	2	no	—
316	C₂²×C₄	—	59	2	no	—
317	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
319	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
320	M₁₆	—	2	2	no	—
321	M₁₆	—	118	4	no	—
322	M₁₆	—	118	4	no	—
323	M₁₆	—	472	2	no	—
324	M₁₆	—	472	2	no	—
325	M₁₆	#11745659	1	4	yes	complemented
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	8	1	no	—
330	C₂×C₈	—	59	4	no	—
331	C₂×C₈	—	59	1	no	—
332	C₂×C₈	—	59	1	no	—
333	C₂×C₈	—	59	1	no	—
334	C₂×C₈	—	59	1	no	—
335	C₂×C₈	—	118	4	no	—
336	C₂×C₈	—	118	2	no	—
337	C₂×C₈	—	118	4	no	—
338	C₂×C₈	—	118	1	no	—
339	C₂×C₈	—	118	1	no	—
340	C₂×C₈	—	118	2	no	—
341	C₂×C₈	—	472	1	no	—
342	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
343	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
344	C₄⋊C₄	—	59	2	no	—
345	C₄⋊C₄	—	59	2	no	—
346	C₄⋊C₄	—	59	1	no	—
347	C₄⋊C₄	—	59	1	no	—
348	C₂²⋊C₄	—	59	2	no	—
349	C₂²⋊C₄	—	59	2	no	—
350	C₂²⋊C₄	—	59	2	no	—
351	C₄²	—	59	2	no	—
352	C₄²	—	59	2	no	—
353	C₄²	—	59	2	no	—
354	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
355	C₄²	D₄×D₅₉	1	1	yes	characteristic
356	C₄²	Q₈×D₅₉	1	1	yes	characteristic
357	C₄²	C₂³×D₅₉	1	1	yes	characteristic
358	C₂³	—	59	2	no	—
359	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
360	Q₈	—	118	2	no	—
361	D₄	—	118	4	no	—
362	D₄	—	118	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	59	2	no	—
367	C₂×C₄	—	59	2	no	—
368	C₂×C₄	—	59	2	no	—
369	C₂×C₄	—	118	2	no	—
370	C₂×C₄	—	118	2	no	—
371	C₂×C₄	—	118	2	no	—
372	C₂×C₄	—	118	2	no	—
373	C₂×C₄	—	236	2	no	—
374	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
375	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
377	C₂×C₄	M₁₆×D₅₉	1	2	yes	—
378	C₂×C₄	C₂×#11745659	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	59	2	no	—
387	C₈	—	59	2	no	—
388	C₈	—	118	1	no	—
389	C₈	—	118	1	no	—
390	C₈	—	236	2	no	—
391	C₈	—	236	1	no	—
392	C₈	—	236	1	no	—
393	C₈	C₂×#11745659	1	4	yes	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	118	2	no	—
397	C₂²	—	118	2	no	—
398	C₂²	—	118	2	no	—
399	C₂²	#16837424	1	2	yes	—
400	C₂²	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	118	2	no	—
405	C₄	—	118	2	no	—
406	C₄	—	118	2	no	—
407	C₄	#16837424	1	2	yes	—
408	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
409	C₄	C₂²×#11745659	1	1	yes	characteristic
410	C₄	#16838206	1	1	yes	characteristic
411	C₄	#16838218	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	236	2	no	—
414	C₂	C₂×#16837424	1	1	yes	characteristic
415	C₂	#21432695	1	1	yes	characteristic
416	C₂	#21432706	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×#1565	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#11745685	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1565	D₅₉
hypocenter	C₅₉	#17799
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #21422862	C₂	semidirect
5. #21422860	C₂	semidirect
6. #21422856	C₂	semidirect
7. #21422853	C₂	semidirect
8. #21422848	C₂	semidirect
9. #21422842	C₂	semidirect
10. C₂×#16837154	C₂	semidirect
11. C₅₉×#1565	C₂	semidirect
112. M₁₆×C₅₉	M₁₆	semidirect
138. C₂×C₅₉⋊C₈	M₁₆	semidirect
212. #1565	D₅₉	semidirect
255. C₅₉	#17799	semidirect
325. M₁₆	#11745659	semidirect

Maximal subgroups

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

subgroup	index
#21433214	2
#21433209	2
C₄×#14273735	2
#21422862	2
#21422860	2
#21422856	2
#21422853	2
#21422848	2
#21422842	2
C₂×#16837154	2
C₅₉×#1565	2
#17799	59