Subgroups — #28482537

Order 15104.

520 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837424	C₂	1	1	yes	maximal, characteristic
2	#21424073	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₅₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#16837152	C₂	1	1	yes	maximal, characteristic, complemented
5	#21421931	C₂	1	1	yes	maximal, characteristic, complemented
6	#21421930	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₉×#334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11745659	—	2	1	no	—
9	C₂×C₄²×D₅₉	C₂²	1	1	yes	characteristic
10	#16837424	—	2	2	no	—
11	#16837424	—	2	2	no	—
12	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×Dic₅₉⋊C₈	—	2	1	no	—
15	C₂×(C₂×D₅₉)⋊C₈	—	2	1	no	—
16	C₂×(C₂×D₅₉)⋊C₈	C₄	1	1	yes	characteristic
17	C₂×(C₂×D₅₉)⋊C₈	C₄	1	1	yes	characteristic
18	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
19	#16837156	—	2	1	no	—
20	#16837156	C₄	1	1	yes	characteristic
21	#16837156	C₄	1	1	yes	characteristic
22	#16837152	—	2	2	no	—
23	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₅₉×#334	—	2	2	no	—
27	C₂²×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₅₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₅₉	Q₈	1	1	yes	characteristic
30	C₂×#11745659	—	2	4	no	—
31	C₂×#11745659	—	4	2	no	—
32	C₂×#11745659	—	4	2	no	—
33	C₂²×C₅₉⋊C₈	—	2	1	no	—
34	C₂²×C₅₉⋊C₈	—	2	1	no	—
35	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₅₉	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₅₉	Q₈	1	1	yes	characteristic
40	C₄²×D₅₉	—	2	1	no	—
41	C₄²×D₅₉	—	2	1	no	—
42	C₄²×D₅₉	—	2	1	no	—
43	C₄²×D₅₉	—	2	1	no	—
44	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
45	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
46	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
47	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
48	Dic₅₉⋊C₈	—	2	4	no	—
49	(C₂×D₅₉)⋊C₈	—	2	2	no	—
50	(C₂×D₅₉)⋊C₈	—	2	2	no	—
51	(C₂×D₅₉)⋊C₈	—	4	2	no	—
52	C₄×C₅₉⋊C₈	—	2	1	no	—
53	C₄×C₅₉⋊C₈	—	2	1	no	—
54	C₂²×C₈×C₅₉	—	2	1	no	—
55	C₂²×C₈×C₅₉	—	2	1	no	—
56	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₅₉	—	2	1	no	—
60	C₄⋊C₈×C₅₉	—	2	1	no	—
61	C₄⋊C₈×C₅₉	—	2	1	no	—
62	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
63	C₄×C₈×C₅₉	—	2	1	no	—
64	C₄×C₈×C₅₉	—	2	1	no	—
65	C₂³×D₅₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
69	C₂²×Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×D₅₉	—	2	1	no	—
73	C₂×C₄×D₅₉	—	2	1	no	—
74	C₂×C₄×D₅₉	—	2	1	no	—
75	C₂×C₄×D₅₉	—	2	1	no	—
76	C₂×C₄×D₅₉	—	2	1	no	—
77	C₂×C₄×D₅₉	—	2	1	no	—
78	C₂×C₄×D₅₉	—	2	1	no	—
79	C₂×C₄×D₅₉	—	2	1	no	—
80	C₂×C₄×D₅₉	—	2	1	no	—
81	C₂×C₄×D₅₉	—	2	1	no	—
82	C₂×C₄×D₅₉	—	2	1	no	—
83	C₂×C₄×D₅₉	—	2	1	no	—
84	C₂×C₄×D₅₉	—	2	2	no	—
85	C₂×C₄×D₅₉	—	4	1	no	—
86	C₂×C₄×D₅₉	SD₁₆	1	2	yes	—
87	C₂×C₄×D₅₉	SD₁₆	1	2	yes	—
88	C₂×C₈×C₅₉	—	2	1	no	—
89	C₂×C₈×C₅₉	—	2	1	no	—
90	C₂×C₈×C₅₉	—	2	1	no	—
91	C₂×C₈×C₅₉	—	2	2	no	—
92	C₂×C₈×C₅₉	—	2	1	no	—
93	C₂×C₈×C₅₉	—	2	1	no	—
94	C₂×C₈×C₅₉	—	4	1	no	—
95	C₂×C₈×C₅₉	—	4	1	no	—
96	C₂×C₈×C₅₉	—	4	1	no	—
97	C₂×C₈×C₅₉	—	4	1	no	—
98	C₂×C₈×C₅₉	—	4	1	no	—
99	C₂×C₈×C₅₉	M₁₆	1	2	yes	complemented
100	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₅₉	#41	1	1	yes	characteristic
103	C₄²×C₅₉	#41	1	1	yes	characteristic
104	C₄×Dic₅₉	—	2	1	no	—
105	C₄×Dic₅₉	—	2	1	no	—
106	C₄×Dic₅₉	—	2	1	no	—
107	C₄×Dic₅₉	—	2	1	no	—
108	C₄×Dic₅₉	—	2	1	no	—
109	C₄×Dic₅₉	—	2	1	no	—
110	C₂×C₅₉⋊C₈	—	2	1	no	—
111	C₂×C₅₉⋊C₈	—	2	1	no	—
112	C₂×C₅₉⋊C₈	—	2	1	no	—
113	C₂×C₅₉⋊C₈	—	2	2	no	—
114	C₂×C₅₉⋊C₈	—	2	1	no	—
115	C₂×C₅₉⋊C₈	—	2	1	no	—
116	C₂×C₅₉⋊C₈	—	4	1	no	—
117	C₂×C₅₉⋊C₈	—	4	1	no	—
118	C₂×C₅₉⋊C₈	—	4	1	no	—
119	C₂×C₅₉⋊C₈	—	4	1	no	—
120	C₂×C₅₉⋊C₈	—	4	1	no	—
121	C₂×C₅₉⋊C₈	M₁₆	1	2	yes	complemented
122	#11745659	—	4	8	no	—
123	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₅₉	—	2	1	no	—
125	C₂²×D₅₉	—	2	1	no	—
126	C₂²×D₅₉	—	2	1	no	—
127	C₂²×D₅₉	—	2	1	no	—
128	C₂²×D₅₉	—	2	1	no	—
129	C₂²×D₅₉	—	2	1	no	—
130	C₂²×D₅₉	#106	1	2	yes	—
131	C₂×C₄×C₅₉	—	2	1	no	—
132	C₂×C₄×C₅₉	—	2	1	no	—
133	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
136	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
139	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
140	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
141	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
142	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
143	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
144	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
147	C₂×Dic₅₉	—	2	1	no	—
148	C₂×Dic₅₉	—	2	1	no	—
149	C₂×Dic₅₉	—	2	1	no	—
150	C₂×Dic₅₉	—	2	1	no	—
151	C₂×Dic₅₉	—	2	1	no	—
152	C₂×Dic₅₉	—	2	1	no	—
153	C₂×Dic₅₉	—	2	1	no	—
154	C₂×Dic₅₉	#106	1	2	yes	—
155	C₂×Dic₅₉	#108	1	2	yes	—
156	C₄×D₅₉	—	2	2	no	—
157	C₄×D₅₉	—	2	2	no	—
158	C₄×D₅₉	—	2	2	no	—
159	C₄×D₅₉	—	2	2	no	—
160	C₄×D₅₉	—	4	2	no	—
161	C₄×D₅₉	—	4	2	no	—
162	C₄×D₅₉	—	4	1	no	—
163	C₄×D₅₉	—	4	1	no	—
164	C₄×D₅₉	—	4	1	no	—
165	C₄×D₅₉	—	4	1	no	—
166	C₈×C₅₉	—	2	2	no	—
167	C₈×C₅₉	—	4	1	no	—
168	C₈×C₅₉	—	4	2	no	—
169	C₈×C₅₉	—	8	1	no	—
170	C₅₉⋊C₈	—	2	2	no	—
171	C₅₉⋊C₈	—	4	1	no	—
172	C₅₉⋊C₈	—	4	2	no	—
173	C₅₉⋊C₈	—	8	1	no	—
174	#8833	—	59	1	no	maximal, Sylow
175	C₂²×C₅₉	#385	1	1	yes	characteristic
176	C₂²×C₅₉	#423	1	1	yes	characteristic
177	C₂²×C₅₉	#424	1	1	yes	characteristic
178	C₂²×C₅₉	C₂×#106	1	1	yes	characteristic
179	C₂²×C₅₉	#428	1	1	yes	characteristic
180	C₂²×C₅₉	C₂×#108	1	1	yes	characteristic
181	C₂²×C₅₉	#430	1	1	yes	characteristic
182	C₂×D₅₉	—	2	2	no	—
183	C₂×D₅₉	—	2	2	no	—
184	C₂×D₅₉	—	2	2	no	—
185	C₂×D₅₉	—	4	1	no	—
186	C₂×D₅₉	—	4	1	no	—
187	C₂×D₅₉	—	4	1	no	—
188	C₂×D₅₉	—	4	1	no	—
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	#435	1	1	yes	characteristic
192	C₄×C₅₉	#435	1	1	yes	characteristic
193	C₄×C₅₉	#436	1	1	yes	characteristic
194	C₄×C₅₉	#436	1	1	yes	characteristic
195	C₄×C₅₉	#448	1	1	yes	characteristic
196	C₄×C₅₉	#450	1	1	yes	characteristic
197	C₄×C₅₉	#481	1	1	yes	characteristic
198	C₄×C₅₉	#483	1	1	yes	characteristic
199	Dic₅₉	—	2	2	no	—
200	Dic₅₉	—	2	2	no	—
201	Dic₅₉	—	4	1	no	—
202	C₂×#423	—	59	1	no	—
203	#1797	—	59	1	no	—
204	C₄×C₂²⋊C₈	—	59	1	no	—
205	C₂×#334	—	59	1	no	—
206	C₂×#334	D₅₉	1	1	yes	characteristic, complemented
207	#1277	—	59	1	no	—
208	#1277	—	59	1	no	—
209	C₂×C₅₉	#1566	1	1	yes	characteristic
210	C₂×C₅₉	#1569	1	1	yes	characteristic
211	C₂×C₅₉	#1570	1	1	yes	characteristic
212	C₂×C₅₉	#1574	1	1	yes	characteristic
213	C₂×C₅₉	#1851	1	1	yes	characteristic
214	C₂×C₅₉	#1853	1	1	yes	characteristic
215	C₂×C₅₉	#1855	1	1	yes	characteristic
216	D₅₉	—	4	2	no	—
217	C₂²×M₁₆	—	118	1	no	—
218	C₂²×C₄²	—	59	1	no	—
219	#423	—	118	2	no	—
220	#423	—	118	2	no	—
221	C₂×C₄⋊C₈	—	59	1	no	—
222	C₂×C₄⋊C₈	—	59	1	no	—
223	C₂×C₄⋊C₈	—	118	1	no	—
224	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	—	59	1	no	—
227	C₂×C₂²⋊C₈	—	59	1	no	—
228	C₂×C₂²⋊C₈	—	118	1	no	—
229	C₂×C₄×C₈	—	59	1	no	—
230	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
231	#336	—	59	1	no	—
232	#336	—	59	1	no	—
233	#336	—	118	1	no	—
234	#334	—	2	2	no	—
235	#334	—	118	2	no	—
236	C₅₉	#8833	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	—	59	1	no	—
238	C₂³×C₄	—	59	1	no	—
239	C₂³×C₄	—	59	1	no	—
240	C₂×M₁₆	—	118	4	no	—
241	C₂×M₁₆	—	236	2	no	—
242	C₂×M₁₆	—	236	2	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	59	1	no	—
246	C₂²×C₈	—	59	1	no	—
247	C₂²×C₈	—	118	1	no	—
248	C₂²×C₈	—	118	1	no	—
249	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
250	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
251	C₂×C₄²	—	59	1	no	—
252	C₂×C₄²	—	59	1	no	—
253	C₂×C₄²	—	59	1	no	—
254	C₂×C₄²	—	118	1	no	—
255	C₂×C₄²	—	118	1	no	—
256	C₂×C₄²	—	118	1	no	—
257	C₂×C₄²	—	118	1	no	—
258	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
259	C₄⋊C₈	—	2	1	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	59	2	no	—
263	C₄⋊C₈	—	118	4	no	—
264	C₄⋊C₈	—	118	1	no	—
265	C₄⋊C₈	—	118	1	no	—
266	C₄⋊C₈	—	118	1	no	—
267	C₄⋊C₈	C₂²⋊D₅₉	1	2	yes	—
268	C₂²⋊C₈	—	118	2	no	—
269	C₂²⋊C₈	—	118	2	no	—
270	C₂²⋊C₈	—	236	2	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	118	1	no	—
274	C₄×C₈	—	118	1	no	—
275	C₂⁴	—	59	1	no	—
276	C₂²×C₄	—	59	1	no	—
277	C₂²×C₄	—	59	1	no	—
278	C₂²×C₄	—	59	2	no	—
279	C₂²×C₄	—	59	2	no	—
280	C₂²×C₄	—	59	1	no	—
281	C₂²×C₄	—	118	2	no	—
282	C₂²×C₄	—	118	1	no	—
283	C₂²×C₄	—	118	1	no	—
284	C₂²×C₄	—	118	1	no	—
285	C₂²×C₄	—	118	1	no	—
286	C₂²×C₄	—	118	1	no	—
287	C₂²×C₄	—	118	1	no	—
288	C₂²×C₄	—	118	1	no	—
289	C₂²×C₄	—	118	1	no	—
290	C₂²×C₄	—	118	1	no	—
291	C₂²×C₄	—	118	1	no	—
292	C₂²×C₄	—	118	1	no	—
293	C₂²×C₄	—	118	1	no	—
294	C₂²×C₄	—	236	1	no	—
295	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
297	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
298	M₁₆	—	236	8	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	59	2	no	—
311	C₂×C₈	—	118	1	no	—
312	C₂×C₈	—	118	1	no	—
313	C₂×C₈	—	118	1	no	—
314	C₂×C₈	—	118	2	no	—
315	C₂×C₈	—	118	1	no	—
316	C₂×C₈	—	118	1	no	—
317	C₂×C₈	—	236	1	no	—
318	C₂×C₈	—	236	1	no	—
319	C₂×C₈	—	236	1	no	—
320	C₂×C₈	—	236	1	no	—
321	C₂×C₈	—	236	1	no	—
322	C₂×C₈	#11745659	1	2	yes	complemented
323	C₄²	—	118	1	no	—
324	C₄²	—	118	1	no	—
325	C₄²	—	118	1	no	—
326	C₄²	—	118	1	no	—
327	C₄²	—	118	1	no	—
328	C₄²	—	118	1	no	—
329	C₄²	#11745685	1	1	yes	characteristic
330	C₄²	D₄×D₅₉	1	1	yes	characteristic
331	C₄²	#11745689	1	1	yes	characteristic
332	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
333	C₂³	—	59	2	no	—
334	C₂³	—	118	1	no	—
335	C₂³	—	118	1	no	—
336	C₂³	—	118	1	no	—
337	C₂³	—	118	1	no	—
338	C₂³	—	118	1	no	—
339	C₂³	—	118	1	no	—
340	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	59	2	no	—
344	C₂×C₄	—	59	2	no	—
345	C₂×C₄	—	118	1	no	—
346	C₂×C₄	—	118	1	no	—
347	C₂×C₄	—	118	1	no	—
348	C₂×C₄	—	118	1	no	—
349	C₂×C₄	—	118	2	no	—
350	C₂×C₄	—	118	2	no	—
351	C₂×C₄	—	118	2	no	—
352	C₂×C₄	—	118	2	no	—
353	C₂×C₄	—	118	1	no	—
354	C₂×C₄	—	118	1	no	—
355	C₂×C₄	—	118	1	no	—
356	C₂×C₄	—	236	2	no	—
357	C₂×C₄	—	236	2	no	—
358	C₂×C₄	—	236	1	no	—
359	C₂×C₄	—	236	1	no	—
360	C₂×C₄	—	236	1	no	—
361	C₂×C₄	—	236	1	no	—
362	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
363	C₂×C₄	#14273689	1	1	yes	characteristic
364	C₂×C₄	#14273695	1	1	yes	characteristic
365	C₂×C₄	#14273703	1	1	yes	characteristic
366	C₂×C₄	#14273705	1	1	yes	characteristic
367	C₂×C₄	#14273712	1	1	yes	characteristic
368	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
369	C₂×C₄	C₂×#11745659	1	1	yes	characteristic
370	C₂×C₄	#14273733	1	1	yes	characteristic
371	C₂×C₄	#14273735	1	1	yes	characteristic
372	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
373	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
374	C₂×C₄	#14273754	1	1	yes	characteristic
375	C₂×C₄	#14273756	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	8	1	no	—
380	C₈	—	118	2	no	—
381	C₈	—	472	1	no	—
382	C₈	—	236	1	no	—
383	C₈	—	236	2	no	—
384	C₂²	—	118	2	no	—
385	C₂²	—	118	2	no	—
386	C₂²	—	118	2	no	—
387	C₂²	—	236	1	no	—
388	C₂²	—	236	1	no	—
389	C₂²	—	236	1	no	—
390	C₂²	—	236	1	no	—
391	C₂²	#16837273	1	1	yes	characteristic
392	C₂²	#16837424	1	1	yes	characteristic
393	C₂²	#16837427	1	1	yes	characteristic
394	C₂²	#106×D₅₉	1	1	yes	characteristic
395	C₂²	#16837441	1	1	yes	characteristic
396	C₂²	#108×D₅₉	1	1	yes	characteristic
397	C₂²	#16837449	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	118	2	no	—
401	C₄	—	118	2	no	—
402	C₄	—	236	1	no	—
403	C₄	#16837472	1	1	yes	characteristic
404	C₄	#16837473	1	1	yes	characteristic
405	C₄	#16837478	1	1	yes	characteristic
406	C₄	#16837479	1	1	yes	characteristic
407	C₄	#16837539	1	1	yes	characteristic
408	C₄	#16837551	1	1	yes	characteristic
409	C₄	#16837722	1	1	yes	characteristic
410	C₄	#16837734	1	1	yes	characteristic
411	C₂	—	236	2	no	—
412	C₂	#21422850	1	1	yes	characteristic
413	C₂	#21422860	1	1	yes	characteristic
414	C₂	#21422865	1	1	yes	characteristic
415	C₂	#21422883	1	1	yes	characteristic
416	C₂	#21424277	1	1	yes	characteristic
417	C₂	#21424287	1	1	yes	characteristic
418	C₂	#21424299	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₉
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₂×C₅₉×#334	C₂
socle	C₂³×C₅₉	C₂×C₄⋊C₄
prime radical	C₂³×D₅₉	C₄⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₂×#334	D₅₉
hypocenter	C₅₉	#8833
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. C₂×#16837152	C₂	semidirect
5. #21421931	C₂	semidirect
6. #21421930	C₂	semidirect
7. C₂×C₅₉×#334	C₂	semidirect
99. C₂×C₈×C₅₉	M₁₆	semidirect
121. C₂×C₅₉⋊C₈	M₁₆	semidirect
206. C₂×#334	D₅₉	semidirect
236. C₅₉	#8833	semidirect
322. C₂×C₈	#11745659	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837424	2
#21424073	2
C₄×(C₂×D₅₉)⋊C₈	2
C₂×#16837152	2
#21421931	2
#21421930	2
C₂×C₅₉×#334	2
#8833	59