Subgroups — #28560710

Order 15104.

604 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	#21433198	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433163	C₂	1	1	yes	maximal, characteristic
3	#21422999	C₂	1	2	yes	maximal, complemented
4	#21422940	C₂	1	2	yes	maximal, complemented
5	#21422933	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊(C₅₉⋊C₈)	C₂	1	2	yes	maximal, complemented
7	#21422844	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422517	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422513	C₂	1	1	yes	maximal, characteristic
10	#21422385	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3167	C₂	1	1	yes	maximal, characteristic
12	#16837533	—	2	1	no	—
13	#16837533	C₂²	1	2	yes	—
14	Q₈×C₅₉⋊C₈	—	2	1	no	—
15	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
16	#16837480	—	2	1	no	—
17	#16837480	C₂²	1	2	yes	—
18	D₄×C₅₉⋊C₈	—	2	1	no	—
19	D₄×C₅₉⋊C₈	C₂²	1	2	yes	—
20	#16837463	—	2	2	no	—
21	#16837455	C₂²	1	1	yes	characteristic
22	#16837455	C₂²	1	1	yes	characteristic
23	#16837455	C₂²	1	1	yes	characteristic
24	#16837369	—	2	2	no	—
25	C₄×#11745664	C₂²	1	1	yes	characteristic
26	#16837155	C₂²	1	1	yes	characteristic
27	#16837155	C₂²	1	1	yes	characteristic
28	#16837153	C₂²	1	1	yes	characteristic
29	#16837153	C₂²	1	1	yes	characteristic
30	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
31	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
32	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
34	#16837124	C₂²	1	2	yes	—
35	#16837123	C₂²	1	2	yes	—
36	C₅₉×#533	C₂²	1	1	yes	characteristic
37	C₅₉×#532	C₂²	1	1	yes	characteristic
38	C₅₉×#498	C₄	1	1	yes	characteristic
39	C₅₉×#492	C₄	1	1	yes	characteristic
40	C₅₉×#487	C₄	1	1	yes	characteristic
41	C₅₉×#486	C₄	1	1	yes	characteristic
42	C₅₉×#465	C₄	1	2	yes	—
43	C₅₉×#465	C₄	1	2	yes	—
44	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₅₉	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₂×#11745664	—	2	1	no	—
48	C₂×#11745664	—	2	2	no	—
49	C₂²×C₅₉⋊C₈	—	2	2	no	—
50	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
53	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
54	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
55	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
56	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
57	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
58	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
59	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
63	#14273638	—	2	1	no	—
64	#14273638	—	2	2	no	—
65	C₄×C₅₉⋊C₈	—	2	1	no	—
66	C₄×C₅₉⋊C₈	—	2	1	no	—
67	C₄×C₅₉⋊C₈	—	2	2	no	—
68	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
69	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₅₉	—	2	1	no	—
71	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
72	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
76	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
78	#127×C₅₉	C₂×C₄	1	1	yes	characteristic
79	#125×C₅₉	—	2	1	no	—
80	#124×C₅₉	—	2	1	no	—
81	C₂²⋊Q₈×C₅₉	—	2	1	no	—
82	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
83	#121×C₅₉	—	2	1	no	—
84	#121×C₅₉	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₅₉	—	2	1	no	—
86	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
87	C₄×D₄×C₅₉	—	2	1	no	—
88	C₄×D₄×C₅₉	C₂³	1	2	yes	—
89	#117×C₅₉	—	2	1	no	—
90	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
91	#106×C₅₉	C₂×C₄	1	2	yes	—
92	#106×C₅₉	C₂×C₄	1	2	yes	—
93	#103×C₅₉	C₂×C₄	1	2	yes	—
94	#103×C₅₉	C₂×C₄	1	2	yes	—
95	#102×C₅₉	C₂×C₄	1	2	yes	—
96	#102×C₅₉	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
101	#41×C₅₉	—	8	1	no	—
102	#41×C₅₉	—	8	1	no	—
103	C₂×Q₈×C₅₉	—	2	1	no	—
104	C₂×Q₈×C₅₉	—	2	1	no	—
105	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₅₉	—	2	2	no	—
107	C₂×D₄×C₅₉	—	2	1	no	—
108	C₂×D₄×C₅₉	—	2	1	no	—
109	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅₉	—	2	2	no	—
111	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
114	SD₁₆×C₅₉	—	2	4	no	—
115	SD₁₆×C₅₉	—	4	2	no	—
116	C₂×C₈×C₅₉	—	2	2	no	—
117	C₂×C₈×C₅₉	—	4	1	no	—
118	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₅₉	—	2	1	no	—
123	C₄⋊C₄×C₅₉	—	2	1	no	—
124	C₄⋊C₄×C₅₉	—	2	1	no	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	—	2	2	no	—
127	C₄⋊C₄×C₅₉	—	2	2	no	—
128	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
129	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
130	C₂²⋊C₄×C₅₉	—	2	2	no	—
131	C₂²⋊C₄×C₅₉	—	2	2	no	—
132	C₂²⋊C₄×C₅₉	—	2	2	no	—
133	C₄²×C₅₉	—	2	2	no	—
134	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₅₉	#41	1	1	yes	characteristic
137	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
138	#11745664	—	4	2	no	—
139	#11745664	—	8	2	no	—
140	C₂×C₅₉⋊C₈	—	2	1	no	—
141	C₂×C₅₉⋊C₈	—	2	1	no	—
142	C₂×C₅₉⋊C₈	—	2	1	no	—
143	C₂×C₅₉⋊C₈	—	2	1	no	—
144	C₂×C₅₉⋊C₈	—	2	2	no	—
145	C₂×C₅₉⋊C₈	—	8	2	no	—
146	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
147	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
148	C₂³×C₅₉	—	2	2	no	—
149	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
150	Q₈×C₅₉	—	2	2	no	—
151	Q₈×C₅₉	—	2	2	no	—
152	Q₈×C₅₉	—	4	2	no	—
153	Q₈×C₅₉	—	8	1	no	—
154	D₄×C₅₉	—	2	2	no	—
155	D₄×C₅₉	—	2	2	no	—
156	D₄×C₅₉	—	4	2	no	—
157	D₄×C₅₉	—	8	1	no	—
158	D₄×C₅₉	—	8	2	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	—	2	2	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	2	2	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	—	4	2	no	—
169	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
175	C₈×C₅₉	—	2	1	no	—
176	C₈×C₅₉	—	2	1	no	—
177	C₈×C₅₉	—	2	1	no	—
178	C₈×C₅₉	#131	1	2	yes	—
179	C₅₉⋊C₈	—	2	2	no	—
180	C₅₉⋊C₈	—	2	2	no	—
181	C₅₉⋊C₈	—	4	2	no	—
182	C₅₉⋊C₈	—	4	1	no	—
183	C₅₉⋊C₈	—	4	1	no	—
184	C₅₉⋊C₈	—	4	1	no	—
185	C₅₉⋊C₈	—	4	1	no	—
186	#18089	—	59	1	no	maximal, Sylow
187	C₂²×C₅₉	—	2	1	no	—
188	C₂²×C₅₉	—	2	1	no	—
189	C₂²×C₅₉	—	2	1	no	—
190	C₂²×C₅₉	—	4	2	no	—
191	C₂²×C₅₉	—	4	2	no	—
192	C₂²×C₅₉	—	4	2	no	—
193	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	—	2	1	no	—
196	C₄×C₅₉	—	2	1	no	—
197	C₄×C₅₉	—	4	2	no	—
198	C₄×C₅₉	—	4	2	no	—
199	C₄×C₅₉	—	4	2	no	—
200	C₄×C₅₉	#444	1	2	yes	—
201	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
202	C₄×C₅₉	#568	1	1	yes	characteristic
203	C₄×C₅₉	#577	1	1	yes	characteristic
204	C₄×C₅₉	#577	1	1	yes	characteristic
205	#3167	D₅₉	1	1	yes	characteristic
206	#2986	—	59	1	no	—
207	#2979	—	59	1	no	—
208	#1592	—	59	2	no	—
209	#1583	—	59	2	no	—
210	#1582	—	59	2	no	—
211	SD₁₆⋊C₈	—	59	2	no	—
212	#1564	—	59	1	no	—
213	#1485	—	59	1	no	—
214	#1484	—	59	1	no	—
215	#1451	—	59	1	no	—
216	C₂×C₅₉	—	4	1	no	—
217	C₂×C₅₉	—	8	2	no	—
218	C₂×C₅₉	#2935	1	1	yes	characteristic
219	C₂×C₅₉	#2949	1	1	yes	characteristic
220	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
221	#533	C₂×D₅₉	1	1	yes	characteristic
222	#532	C₂×D₅₉	1	1	yes	characteristic
223	#498	Dic₅₉	1	1	yes	characteristic
224	#492	Dic₅₉	1	1	yes	characteristic
225	#487	Dic₅₉	1	1	yes	characteristic
226	#486	Dic₅₉	1	1	yes	characteristic
227	#465	Dic₅₉	1	2	yes	—
228	#465	Dic₅₉	1	2	yes	—
229	#446	—	59	2	no	—
230	#446	—	118	1	no	—
231	C₈×Q₈	—	59	2	no	—
232	C₈×Q₈	—	118	1	no	—
233	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
234	C₄×SD₁₆	C₂×D₅₉	1	2	yes	—
235	#436	—	59	2	no	—
236	#436	—	118	1	no	—
237	C₈×D₄	—	59	2	no	—
238	C₈×D₄	—	118	1	no	—
239	#433	—	118	2	no	—
240	#431	—	59	1	no	—
241	#431	—	59	1	no	—
242	#431	—	59	1	no	—
243	#408	—	118	2	no	—
244	C₄×M₁₆	—	59	1	no	—
245	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
246	#335	—	59	1	no	—
247	#335	—	59	1	no	—
248	#334	—	59	1	no	—
249	#334	—	59	1	no	—
250	Q₈⋊C₈	—	59	2	no	—
251	Q₈⋊C₈	—	59	2	no	—
252	D₄⋊C₈	—	59	2	no	—
253	D₄⋊C₈	—	59	2	no	—
254	#322	—	59	2	no	—
255	#322	—	59	2	no	—
256	C₅₉	#18089	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	2	1	no	—
258	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
259	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
260	C₂×M₁₆	—	118	2	no	—
261	C₂×M₁₆	—	118	1	no	—
262	C₂²×C₈	—	118	2	no	—
263	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
264	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
265	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
266	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
267	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
268	#127	C₂×Dic₅₉	1	1	yes	characteristic
269	#125	—	2	1	no	—
270	#124	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₂×Dic₅₉	1	2	yes	—
273	#121	—	2	1	no	—
274	#121	C₂×Dic₅₉	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	C₂²×D₅₉	1	2	yes	—
279	#117	—	2	1	no	—
280	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
281	#106	C₂×Dic₅₉	1	2	yes	—
282	#106	C₂×Dic₅₉	1	2	yes	—
283	C₄⋊C₈	—	59	1	no	—
284	C₄⋊C₈	—	59	1	no	—
285	C₄⋊C₈	—	59	1	no	—
286	C₄⋊C₈	—	59	1	no	—
287	C₄⋊C₈	—	59	1	no	—
288	C₄⋊C₈	—	59	1	no	—
289	C₄⋊C₈	—	118	2	no	—
290	C₄⋊C₈	—	118	2	no	—
291	#103	C₂×Dic₅₉	1	2	yes	—
292	#103	C₂×Dic₅₉	1	2	yes	—
293	#102	C₂×Dic₅₉	1	2	yes	—
294	#102	C₂×Dic₅₉	1	2	yes	—
295	C₂²⋊C₈	—	59	2	no	—
296	C₂²⋊C₈	—	118	2	no	—
297	C₂²⋊C₈	—	118	2	no	—
298	C₂²⋊C₈	—	118	1	no	—
299	C₂²⋊C₈	—	118	1	no	—
300	#97	—	118	2	no	—
301	#97	—	118	1	no	—
302	C₄×C₈	—	59	2	no	—
303	C₄×C₈	—	59	2	no	—
304	C₄×C₈	—	118	2	no	—
305	C₄×C₈	—	118	1	no	—
306	C₄×C₈	—	118	1	no	—
307	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
308	C₄×C₈	C₂×Dic₅₉	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
311	#41	—	8	1	no	—
312	#41	—	8	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
322	C₂²×C₄	#11745687	1	1	yes	characteristic
323	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	4	2	no	—
326	M₁₆	—	472	2	no	—
327	M₁₆	—	236	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	59	2	no	—
331	C₂×C₈	—	59	2	no	—
332	C₂×C₈	—	118	1	no	—
333	C₂×C₈	—	118	1	no	—
334	C₂×C₈	—	118	1	no	—
335	C₂×C₈	—	118	1	no	—
336	C₂×C₈	—	118	2	no	—
337	C₂×C₈	—	472	2	no	—
338	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
339	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
340	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
341	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
349	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	D₄×D₅₉	1	1	yes	characteristic
355	C₄²	#11745687	1	1	yes	characteristic
356	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
357	C₄²	C₂³×D₅₉	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	D₄×Dic₅₉	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	8	1	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
381	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	118	2	no	—
389	C₈	—	118	2	no	—
390	C₈	—	236	2	no	—
391	C₈	—	236	1	no	—
392	C₈	—	236	1	no	—
393	C₈	—	236	1	no	—
394	C₈	—	236	1	no	—
395	C₈	#14273734	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	#16837524	1	2	yes	—
410	C₄	C₂×#14273734	1	1	yes	characteristic
411	C₄	#16838169	1	1	yes	characteristic
412	C₄	#16838208	1	1	yes	characteristic
413	C₄	#16838208	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	8	2	no	—
416	C₂	#21432840	1	1	yes	characteristic
417	C₂	#21432956	1	1	yes	characteristic
418	C₂	C₂×#16837524	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×#3167	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#532	C₂²
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#3167	D₅₉
hypocenter	C₅₉	#18089
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #21433198	C₂	semidirect
3. #21422999	C₂	semidirect
4. #21422940	C₂	semidirect
5. #21422933	C₂	semidirect
6. SD₁₆⋊(C₅₉⋊C₈)	C₂	semidirect
7. #21422844	C₂	semidirect
8. #21422517	C₂	semidirect
10. #21422385	C₂	semidirect
256. C₅₉	#18089	semidirect

Maximal subgroups

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

subgroup	index
#21433198	2
#21433163	2
#21422999	2
#21422940	2
#21422933	2
SD₁₆⋊(C₅₉⋊C₈)	2
#21422844	2
#21422517	2
#21422513	2
#21422385	2
C₅₉×#3167	2
#18089	59