Subgroups — #21432822

Order 7552.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273735	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11745659	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837911	C₂	1	1	yes	maximal, characteristic
4	#16837479	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837478	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837475	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837470	C₂	1	1	yes	maximal, characteristic, complemented
8	#16837470	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#16837427	C₂	1	1	yes	maximal, characteristic, complemented
12	#16837367	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#16837359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11745685	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₅₉	C₂²	1	1	yes	characteristic
18	#14273735	—	2	4	no	—
19	C₂×#11745659	—	2	4	no	—
20	C₂×#11745659	C₂²	1	1	yes	characteristic
21	C₂×#11745659	C₂²	1	1	yes	characteristic
22	C₂×#11745659	C₂²	1	1	yes	characteristic
23	C₂×#11745659	C₂²	1	1	yes	characteristic
24	C₂×#11745659	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₈×D₅₉	C₂²	1	1	yes	characteristic, complemented
30	#14273712	C₄	1	1	yes	characteristic
31	#14273709	C₄	1	1	yes	characteristic
32	#14273705	C₄	1	1	yes	characteristic
33	#14273704	C₄	1	1	yes	characteristic
34	#14273700	C₄	1	1	yes	characteristic
35	#14273699	C₄	1	1	yes	characteristic
36	#14273697	C₄	1	1	yes	characteristic
37	#14273695	C₄	1	1	yes	characteristic
38	C₄×D₂₃₆	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₅₉	C₂²	1	1	yes	characteristic
41	#14273684	C₂²	1	1	yes	characteristic
42	C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
43	Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	Dic₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
46	C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
48	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic
49	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₅₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	#14273637	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
56	C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
57	C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
58	C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
59	C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
60	#97×C₅₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₅₉	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₅₉	C₂×C₄	1	1	yes	characteristic
70	#11745685	—	2	2	no	—
71	#11745685	—	2	2	no	—
72	C₂×D₂₃₆	C₂×C₄	1	1	yes	characteristic
73	C₂×D₂₃₆	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₅₉	—	2	2	no	—
75	C₂×C₄×D₅₉	—	2	2	no	—
76	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₅₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₅₉	C₂³	1	1	yes	characteristic
81	C₂×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
82	M₁₆×C₅₉	—	2	2	no	—
83	C₂×C₈×C₅₉	—	2	2	no	—
84	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
91	C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₅₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
101	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₅₉⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
106	C₂×C₅₉⋊C₈	—	2	2	no	—
107	C₂×C₅₉⋊C₈	—	2	2	no	—
108	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
112	#11745659	—	2	2	no	—
113	#11745659	—	2	2	no	—
114	#11745659	—	2	2	no	—
115	#11745659	—	2	2	no	—
116	#11745659	D₄	1	4	yes	complemented
117	C₈×D₅₉	—	2	2	no	—
118	C₈×D₅₉	—	2	2	no	—
119	C₈×D₅₉	—	2	2	no	—
120	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₅₉	—	2	2	no	—
123	C₂²×D₅₉	—	2	2	no	—
124	C₂²×D₅₉	—	4	1	no	—
125	C₂²×D₅₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₅₉	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₅₉	—	2	2	no	—
129	C₂×C₄×C₅₉	—	2	1	no	—
130	C₂×C₄×C₅₉	—	2	1	no	—
131	C₂×C₄×C₅₉	—	2	1	no	—
132	C₂×C₄×C₅₉	—	2	1	no	—
133	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₅₉	—	2	2	no	—
139	C₂²⋊D₅₉	—	2	2	no	—
140	C₂²⋊D₅₉	—	2	2	no	—
141	C₂²⋊D₅₉	—	4	1	no	—
142	C₂×Dic₅₉	—	2	2	no	—
143	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
148	D₂₃₆	—	2	2	no	—
149	D₂₃₆	—	4	1	no	—
150	C₄×D₅₉	—	2	2	no	—
151	C₄×D₅₉	—	2	1	no	—
152	C₄×D₅₉	—	2	1	no	—
153	C₄×D₅₉	—	2	1	no	—
154	C₄×D₅₉	—	2	1	no	—
155	C₄×D₅₉	—	2	2	no	—
156	C₄×D₅₉	C₂×D₄	1	2	yes	—
157	C₄×D₅₉	#41	1	2	yes	—
158	Dic₁₁₈	—	2	2	no	—
159	C₈×C₅₉	—	2	1	no	—
160	C₈×C₅₉	—	2	1	no	—
161	C₈×C₅₉	—	2	1	no	—
162	C₈×C₅₉	C₂×D₄	1	2	yes	—
163	C₅₉⋊C₈	—	2	1	no	—
164	C₅₉⋊C₈	—	2	1	no	—
165	C₅₉⋊C₈	—	2	1	no	—
166	C₅₉⋊C₈	C₂×D₄	1	2	yes	—
167	C₂²×C₅₉	—	2	1	no	—
168	C₂²×C₅₉	—	2	1	no	—
169	C₂²×C₅₉	—	2	1	no	—
170	C₂²×C₅₉	—	2	1	no	—
171	C₂²×C₅₉	—	2	1	no	—
172	C₂²×C₅₉	#131	1	2	yes	complemented
173	C₂²×C₅₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×D₅₉	—	2	1	no	—
175	C₂×D₅₉	—	2	1	no	—
176	C₂×D₅₉	—	2	1	no	—
177	C₂×D₅₉	—	2	1	no	—
178	C₂×D₅₉	—	2	1	no	—
179	C₂×D₅₉	—	2	1	no	—
180	C₂×D₅₉	—	2	1	no	—
181	C₂×D₅₉	—	2	1	no	—
182	C₂×D₅₉	—	4	4	no	—
183	C₂×D₅₉	C₄×D₄	1	2	yes	—
184	C₄×C₅₉	—	2	1	no	—
185	C₄×C₅₉	—	2	1	no	—
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
190	Dic₅₉	—	2	1	no	—
191	Dic₅₉	—	2	1	no	—
192	Dic₅₉	—	2	1	no	—
193	Dic₅₉	—	2	1	no	—
194	Dic₅₉	C₄×D₄	1	2	yes	—
195	#2933	—	59	1	no	maximal, Sylow
196	C₂×C₅₉	—	2	2	no	—
197	C₂×C₅₉	—	4	1	no	—
198	C₂×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂×C₅₉	C₂×#131	1	1	yes	characteristic
200	C₂×C₅₉	#568	1	1	yes	characteristic
201	D₅₉	—	2	2	no	—
202	D₅₉	—	4	1	no	—
203	D₅₉	—	4	1	no	—
204	C₂×#131	—	59	1	no	—
205	C₂²×M₁₆	—	59	1	no	—
206	#525	—	59	1	no	—
207	#436	—	59	1	no	—
208	#436	—	59	1	no	—
209	#435	—	59	1	no	—
210	#435	—	59	1	no	—
211	#435	—	59	1	no	—
212	#435	D₅₉	1	1	yes	characteristic, complemented
213	C₈×D₄	—	59	1	no	—
214	C₈×D₄	—	59	1	no	—
215	#424	—	59	1	no	—
216	#408	—	59	1	no	—
217	C₂×C₂²⋊C₈	—	59	1	no	—
218	#405	—	59	1	no	—
219	C₅₉	#2933	1	1	yes	characteristic, complemented, Sylow
220	C₂×#41	—	59	1	no	—
221	C₂³×C₄	—	59	1	no	—
222	#131	—	118	4	no	—
223	C₂×M₁₆	—	59	1	no	—
224	C₂×M₁₆	—	59	1	no	—
225	C₂×M₁₆	—	59	1	no	—
226	C₂×M₁₆	—	59	1	no	—
227	C₂×M₁₆	—	59	1	no	—
228	C₂×M₁₆	—	118	4	no	—
229	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
230	C₂²×C₈	—	59	1	no	—
231	C₂²×C₈	—	59	1	no	—
232	C₂²×C₈	—	59	1	no	—
233	C₂²×C₈	—	59	1	no	—
234	C₂²×C₈	—	59	1	no	—
235	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
236	#123	—	59	1	no	—
237	#123	—	59	1	no	—
238	C₂²⋊Q₈	—	59	1	no	—
239	C₂²⋊Q₈	—	59	1	no	—
240	#121	—	59	1	no	—
241	#121	—	59	1	no	—
242	#120	—	59	1	no	—
243	#120	—	59	1	no	—
244	C₄×D₄	—	59	1	no	—
245	C₄×D₄	—	59	1	no	—
246	C₄×D₄	—	59	1	no	—
247	C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
248	#117	—	59	1	no	—
249	C₄⋊C₈	—	59	1	no	—
250	C₄⋊C₈	—	59	1	no	—
251	C₄⋊C₈	—	59	1	no	—
252	C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
253	C₂²⋊C₈	—	59	1	no	—
254	C₂²⋊C₈	—	59	1	no	—
255	C₂²⋊C₈	—	59	1	no	—
256	C₂²⋊C₈	—	59	1	no	—
257	C₂²⋊C₈	—	59	1	no	—
258	C₂²⋊C₈	—	59	1	no	—
259	C₂²⋊C₈	C₂×D₅₉	1	1	yes	characteristic
260	C₂²⋊C₈	C₂×D₅₉	1	1	yes	characteristic, complemented
261	#97	—	59	1	no	—
262	#97	C₂×D₅₉	1	1	yes	characteristic, complemented
263	C₄×C₈	—	59	1	no	—
264	C₄×C₈	—	59	1	no	—
265	C₂⁴	—	59	1	no	—
266	#41	—	118	2	no	—
267	#41	—	118	2	no	—
268	C₂×Q₈	—	59	1	no	—
269	C₂×D₄	—	59	1	no	—
270	C₂×D₄	—	59	1	no	—
271	C₂×D₄	—	59	1	no	—
272	C₂×D₄	—	59	1	no	—
273	C₂×D₄	—	59	1	no	—
274	C₂×D₄	—	59	1	no	—
275	C₂×D₄	C₄×D₅₉	1	1	yes	characteristic
276	C₂²×C₄	—	59	1	no	—
277	C₂²×C₄	—	59	1	no	—
278	C₂²×C₄	—	59	1	no	—
279	C₂²×C₄	—	59	1	no	—
280	C₂²×C₄	—	59	1	no	—
281	C₂²×C₄	—	59	1	no	—
282	C₂²×C₄	—	118	2	no	—
283	C₂²×C₄	—	118	2	no	—
284	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	59	4	no	—
288	M₁₆	—	118	2	no	—
289	M₁₆	—	118	2	no	—
290	M₁₆	—	118	2	no	—
291	M₁₆	—	118	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	59	1	no	—
294	C₂×C₈	—	59	1	no	—
295	C₂×C₈	—	59	1	no	—
296	C₂×C₈	—	59	1	no	—
297	C₂×C₈	—	118	2	no	—
298	C₂×C₈	—	118	2	no	—
299	C₂×C₈	—	118	2	no	—
300	C₂×C₈	—	118	2	no	—
301	C₂×C₈	—	118	2	no	—
302	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
306	C₄⋊C₄	—	59	1	no	—
307	C₄⋊C₄	—	59	1	no	—
308	C₄⋊C₄	—	59	1	no	—
309	C₄⋊C₄	—	59	1	no	—
310	C₄⋊C₄	—	59	1	no	—
311	C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
312	C₂²⋊C₄	—	59	1	no	—
313	C₂²⋊C₄	—	59	1	no	—
314	C₂²⋊C₄	—	59	1	no	—
315	C₂²⋊C₄	—	59	1	no	—
316	C₂²⋊C₄	—	59	1	no	—
317	C₂²⋊C₄	—	59	1	no	—
318	C₂²⋊C₄	—	59	1	no	—
319	C₂²⋊C₄	—	59	1	no	—
320	C₂²⋊C₄	C₄×D₅₉	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₅₉	1	1	yes	characteristic
322	C₄²	—	59	1	no	—
323	C₄²	C₂²×D₅₉	1	1	yes	characteristic
324	C₂³	—	59	1	no	—
325	C₂³	—	59	1	no	—
326	C₂³	—	59	1	no	—
327	C₂³	—	118	2	no	—
328	C₂³	—	118	2	no	—
329	C₂³	—	236	1	no	—
330	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₅₉	1	1	yes	characteristic
332	Q₈	—	118	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	118	2	no	—
335	D₄	—	118	2	no	—
336	D₄	—	118	2	no	—
337	D₄	—	118	2	no	—
338	D₄	—	236	1	no	—
339	D₄	—	236	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	59	1	no	—
345	C₂×C₄	—	59	2	no	—
346	C₂×C₄	—	59	2	no	—
347	C₂×C₄	—	59	1	no	—
348	C₂×C₄	—	59	1	no	—
349	C₂×C₄	—	59	1	no	—
350	C₂×C₄	—	59	1	no	—
351	C₂×C₄	—	118	2	no	—
352	C₂×C₄	—	118	2	no	—
353	C₂×C₄	—	118	2	no	—
354	C₂×C₄	—	118	1	no	—
355	C₂×C₄	—	118	1	no	—
356	C₂×C₄	—	118	1	no	—
357	C₂×C₄	—	118	1	no	—
358	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	59	2	no	—
367	C₈	—	118	1	no	—
368	C₈	—	118	1	no	—
369	C₈	—	118	1	no	—
370	C₈	D₄×D₅₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	59	2	no	—
377	C₂²	—	118	1	no	—
378	C₂²	—	118	1	no	—
379	C₂²	—	118	1	no	—
380	C₂²	—	118	1	no	—
381	C₂²	—	118	1	no	—
382	C₂²	—	118	1	no	—
383	C₂²	—	118	1	no	—
384	C₂²	—	118	1	no	—
385	C₂²	—	236	4	no	—
386	C₂²	#14273735	1	2	yes	complemented
387	C₂²	C₂²×C₄×D₅₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	59	2	no	—
393	C₄	—	118	1	no	—
394	C₄	—	118	1	no	—
395	C₄	—	118	1	no	—
396	C₄	—	118	1	no	—
397	C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
398	C₄	#41×D₅₉	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	118	2	no	—
402	C₂	—	236	1	no	—
403	C₂	—	236	1	no	—
404	C₂	C₄×D₄×D₅₉	1	1	yes	characteristic
405	C₂	C₂×#14273735	1	1	yes	characteristic
406	C₂	#16838167	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₅₉
commutator, socle	C₂²×C₅₉	C₂³×C₄
Fitting	C₅₉×#435	C₂
hypercenter	#435	D₅₉
hypocenter	C₅₉	#2933
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#14273735	C₂	semidirect
2. C₂²×#11745659	C₂	semidirect
4. #16837479	C₂	semidirect
5. #16837478	C₂	semidirect
6. #16837475	C₂	semidirect
7. #16837470	C₂	semidirect
8. #16837470	C₂	semidirect
9. D₄×C₅₉⋊C₈	C₂	semidirect
10. C₈×C₂²⋊D₅₉	C₂	semidirect
11. #16837427	C₂	semidirect
12. #16837367	C₂	semidirect
13. C₂²⋊C₈×D₅₉	C₂	semidirect
14. #16837359	C₂	semidirect
15. C₅₉×#435	C₂	semidirect
24. C₂×#11745659	C₂²	semidirect
26. C₂²×C₅₉⋊C₈	C₂²	semidirect
29. C₂×C₈×D₅₉	C₂²	semidirect
42. C₄⋊(C₅₉⋊C₈)	C₂²	semidirect
43. Dic₅₉⋊C₈	C₂²	semidirect
44. Dic₅₉⋊C₈	C₂²	semidirect
46. C₂²⋊(C₅₉⋊C₈)	C₂²	semidirect
49. (C₂×D₅₉)⋊C₈	C₂²	semidirect
50. (C₂×D₅₉)⋊C₈	C₂²	semidirect
51. #14273637	C₂²	semidirect
52. C₄×C₅₉⋊C₈	C₂²	semidirect
53. C₈×Dic₅₉	C₂²	semidirect
54. C₂×M₁₆×C₅₉	C₂²	semidirect
57. C₄⋊C₈×C₅₉	C₂²	semidirect
59. C₂²⋊C₈×C₅₉	C₂²	semidirect
60. #97×C₅₉	C₂²	semidirect
116. #11745659	D₄	semidirect
172. C₂²×C₅₉	#131	semidirect
212. #435	D₅₉	semidirect
219. C₅₉	#2933	semidirect
229. C₂×M₁₆	C₂×D₅₉	semidirect
252. C₄⋊C₈	C₂×D₅₉	semidirect
260. C₂²⋊C₈	C₂×D₅₉	semidirect
262. #97	C₂×D₅₉	semidirect
386. C₂²	#14273735	semidirect