Subgroups — #28481591

Order 15104.

524 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	#21424125	C₂	1	1	yes	maximal, characteristic, complemented
2	#21424121	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424084	C₂	1	2	yes	maximal
4	#21421964	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₉×#435	C₂	1	1	yes	maximal, characteristic
6	C₂×#14273661	—	2	1	no	—
7	C₂×#14273659	—	2	1	no	—
8	C₂×#14273642	—	2	2	no	—
9	#16837262	C₂²	1	2	yes	—
10	#16837262	C₂²	1	2	yes	—
11	#16837169	—	2	2	no	—
12	#16837165	—	2	1	no	—
13	#16837165	—	2	1	no	—
14	C₂²×M₁₆×C₅₉	C₄	1	1	yes	characteristic, complemented
15	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₅₉	C₂²	1	1	yes	characteristic
17	C₅₉×#435	—	2	1	no	—
18	C₅₉×#435	—	2	1	no	—
19	C₅₉×#435	—	2	1	no	—
20	C₅₉×#435	—	2	1	no	—
21	C₂×C₄⋊C₈×C₅₉	C₄	1	1	yes	characteristic, complemented
22	C₂×C₂²⋊C₈×C₅₉	C₄	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
24	C₂×#97×C₅₉	C₄	1	1	yes	characteristic, complemented
25	C₂×C₄⋊Dic₅₉	—	2	2	no	—
26	C₂×C₄⋊Dic₅₉	—	2	2	no	—
27	C₂×C₂²⋊Dic₅₉	—	2	2	no	—
28	C₂×C₂²⋊Dic₅₉	—	2	2	no	—
29	#14273661	—	4	2	no	—
30	#14273659	—	4	2	no	—
31	#14273642	—	4	4	no	—
32	C₅₉⋊#95	—	2	2	no	—
33	C₅₉⋊#95	—	2	2	no	—
34	C₂²×D₄×C₅₉	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₅₉	—	2	1	no	—
38	C₂×M₁₆×C₅₉	—	2	1	no	—
39	C₂×M₁₆×C₅₉	—	4	2	no	—
40	C₂²×C₈×C₅₉	—	4	2	no	—
41	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
49	C₄×D₄×C₅₉	—	2	1	no	—
50	C₄×D₄×C₅₉	—	2	1	no	—
51	C₄×D₄×C₅₉	—	2	1	no	—
52	C₄×D₄×C₅₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₉	Q₈	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₅₉	D₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₅₉	Q₈	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
57	C₄⋊C₈×C₅₉	—	2	1	no	—
58	C₄⋊C₈×C₅₉	—	2	1	no	—
59	C₂²⋊C₈×C₅₉	—	2	1	no	—
60	C₂²⋊C₈×C₅₉	—	2	1	no	—
61	C₂²⋊C₈×C₅₉	—	2	1	no	—
62	C₂²⋊C₈×C₅₉	—	2	1	no	—
63	#97×C₅₉	—	2	1	no	—
64	#97×C₅₉	—	2	1	no	—
65	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
66	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
67	C₂×D₄×C₅₉	—	2	1	no	—
68	C₂×D₄×C₅₉	—	2	1	no	—
69	C₂×D₄×C₅₉	—	2	2	no	—
70	C₂×D₄×C₅₉	—	2	2	no	—
71	C₂²×C₄×C₅₉	—	2	1	no	—
72	C₂²×C₄×C₅₉	—	2	1	no	—
73	C₂²×C₄×C₅₉	—	4	1	no	—
74	C₂²×C₄×C₅₉	—	4	1	no	—
75	C₂²×C₄×C₅₉	—	4	1	no	—
76	C₂²×C₄×C₅₉	—	4	1	no	—
77	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
86	C₂²×Dic₅₉	—	4	2	no	—
87	C₂²×Dic₅₉	—	4	2	no	—
88	M₁₆×C₅₉	—	4	2	no	—
89	M₁₆×C₅₉	—	4	2	no	—
90	C₂×C₈×C₅₉	—	2	2	no	—
91	C₂×C₈×C₅₉	—	2	2	no	—
92	C₂×C₈×C₅₉	—	2	2	no	—
93	C₂×C₈×C₅₉	—	2	1	no	—
94	C₂×C₈×C₅₉	—	2	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	—	4	1	no	—
100	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
104	C₄⋊C₄×C₅₉	—	2	1	no	—
105	C₄⋊C₄×C₅₉	—	2	1	no	—
106	C₂²⋊C₄×C₅₉	—	2	1	no	—
107	C₂²⋊C₄×C₅₉	—	2	1	no	—
108	C₂²⋊C₄×C₅₉	—	2	1	no	—
109	C₂²⋊C₄×C₅₉	—	2	1	no	—
110	C₄²×C₅₉	—	2	1	no	—
111	C₄²×C₅₉	—	2	1	no	—
112	C₂²⋊Dic₅₉	—	4	2	no	—
113	C₂²⋊Dic₅₉	—	4	2	no	—
114	C₂²⋊Dic₅₉	—	4	2	no	—
115	C₂²⋊Dic₅₉	—	4	2	no	—
116	C₄⋊Dic₅₉	—	4	2	no	—
117	C₄⋊Dic₅₉	—	4	2	no	—
118	C₄⋊Dic₅₉	—	4	2	no	—
119	C₄⋊Dic₅₉	—	4	2	no	—
120	C₂³×C₅₉	—	2	1	no	—
121	C₂³×C₅₉	—	2	2	no	—
122	C₂³×C₅₉	—	4	1	no	—
123	C₂³×C₅₉	—	4	1	no	—
124	C₂³×C₅₉	—	4	1	no	—
125	C₂³×C₅₉	—	4	1	no	—
126	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₅₉	#121	1	1	yes	characteristic
128	C₂³×C₅₉	#121	1	1	yes	characteristic
129	C₂³×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
130	C₂³×C₅₉	#137	1	2	yes	—
131	D₄×C₅₉	—	4	2	no	—
132	D₄×C₅₉	—	4	1	no	—
133	D₄×C₅₉	—	4	1	no	—
134	C₂×C₄×C₅₉	—	2	1	no	—
135	C₂×C₄×C₅₉	—	2	1	no	—
136	C₂×C₄×C₅₉	—	2	1	no	—
137	C₂×C₄×C₅₉	—	2	1	no	—
138	C₂×C₄×C₅₉	—	2	1	no	—
139	C₂×C₄×C₅₉	—	2	1	no	—
140	C₂×C₄×C₅₉	—	2	1	no	—
141	C₂×C₄×C₅₉	—	2	1	no	—
142	C₂×C₄×C₅₉	—	2	1	no	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	4	1	no	—
145	C₂×C₄×C₅₉	—	4	1	no	—
146	C₂×C₄×C₅₉	—	4	1	no	—
147	C₂×C₄×C₅₉	—	4	2	no	—
148	C₂×C₄×C₅₉	—	4	1	no	—
149	C₂×C₄×C₅₉	—	4	1	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	—	4	1	no	—
152	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
154	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×Dic₅₉	—	8	2	no	—
157	C₂×Dic₅₉	—	8	2	no	—
158	C₂×Dic₅₉	—	8	2	no	—
159	C₂×Dic₅₉	—	8	2	no	—
160	C₂×Dic₅₉	—	8	2	no	—
161	C₂×Dic₅₉	—	8	2	no	—
162	C₈×C₅₉	—	2	1	no	—
163	C₈×C₅₉	—	2	1	no	—
164	C₈×C₅₉	—	2	1	no	—
165	C₈×C₅₉	—	4	1	no	—
166	C₈×C₅₉	—	4	1	no	—
167	C₈×C₅₉	#99	1	2	yes	complemented
168	#8610	—	59	1	no	maximal, Sylow
169	C₂²×C₅₉	—	2	1	no	—
170	C₂²×C₅₉	—	2	1	no	—
171	C₂²×C₅₉	—	2	1	no	—
172	C₂²×C₅₉	—	2	1	no	—
173	C₂²×C₅₉	—	2	1	no	—
174	C₂²×C₅₉	—	2	1	no	—
175	C₂²×C₅₉	—	4	2	no	—
176	C₂²×C₅₉	—	4	2	no	—
177	C₂²×C₅₉	—	4	1	no	—
178	C₂²×C₅₉	—	4	1	no	—
179	C₂²×C₅₉	—	4	1	no	—
180	C₂²×C₅₉	—	8	2	no	—
181	C₂²×C₅₉	#380	1	1	yes	characteristic
182	C₂²×C₅₉	#428	1	2	yes	—
183	C₂²×C₅₉	#468	1	2	yes	—
184	C₂²×C₅₉	#469	1	1	yes	characteristic
185	C₂²×C₅₉	#470	1	1	yes	characteristic
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	2	1	no	—
189	C₄×C₅₉	—	4	1	no	—
190	C₄×C₅₉	—	4	1	no	—
191	C₄×C₅₉	—	4	1	no	—
192	C₄×C₅₉	C₂×#99	1	1	yes	characteristic
193	C₄×C₅₉	#410	1	1	yes	characteristic
194	Dic₅₉	—	16	2	no	—
195	Dic₅₉	—	16	2	no	—
196	C₂×#435	D₅₉	1	1	yes	characteristic
197	#1808	—	59	1	no	—
198	#1807	—	59	1	no	—
199	#1799	—	59	2	no	—
200	#1289	—	59	2	no	—
201	C₂×C₅₉	—	2	1	no	—
202	C₂×C₅₉	—	2	2	no	—
203	C₂×C₅₉	—	2	2	no	—
204	C₂×C₅₉	—	2	1	no	—
205	C₂×C₅₉	—	8	1	no	—
206	C₂×C₅₉	#1799	1	1	yes	characteristic
207	C₂×C₅₉	#1809	1	1	yes	characteristic
208	C₂×C₅₉	#1812	1	1	yes	characteristic
209	C₂²×M₁₆	Dic₅₉	1	1	yes	characteristic, complemented
210	C₂³×C₈	C₂×D₅₉	1	1	yes	characteristic
211	C₂×C₄×D₄	C₂×D₅₉	1	1	yes	characteristic
212	#435	—	2	1	no	—
213	#435	—	2	1	no	—
214	#435	—	2	1	no	—
215	#435	—	2	1	no	—
216	C₂×#107	—	118	1	no	—
217	C₂×#106	—	118	1	no	—
218	C₂×C₄⋊C₈	Dic₅₉	1	1	yes	characteristic, complemented
219	C₂×#99	—	118	2	no	—
220	C₂×C₂²⋊C₈	Dic₅₉	1	1	yes	characteristic, complemented
221	C₂×C₂²⋊C₈	C₂×D₅₉	1	1	yes	characteristic
222	C₂×#97	Dic₅₉	1	1	yes	characteristic, complemented
223	#380	—	59	2	no	—
224	#380	—	59	2	no	—
225	#342	—	118	2	no	—
226	#340	—	118	1	no	—
227	#340	—	118	1	no	—
228	C₅₉	#8610	1	1	yes	characteristic, complemented, Sylow
229	C₂²×D₄	D₂₃₆	1	1	yes	characteristic
230	C₂³×C₄	C₂×Dic₅₉	1	1	yes	characteristic
231	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
232	C₂×M₁₆	—	2	1	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂×M₁₆	—	4	2	no	—
235	C₂²×C₈	—	4	2	no	—
236	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
237	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
238	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
239	C₂²×C₈	C₂×Dic₅₉	1	1	yes	characteristic
240	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
241	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
242	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
243	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
244	C₄×D₄	—	2	1	no	—
245	C₄×D₄	—	2	1	no	—
246	C₄×D₄	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	118	2	no	—
249	C₂×C₄⋊C₄	—	118	2	no	—
250	C₂×C₄⋊C₄	Dic₁₁₈	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	—	118	2	no	—
252	C₂×C₂²⋊C₄	—	118	2	no	—
253	C₂×C₂²⋊C₄	Dic₁₁₈	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	D₂₃₆	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₅₉	1	1	yes	characteristic
256	#107	—	236	2	no	—
257	#106	—	236	2	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	2	1	no	—
260	#99	—	236	4	no	—
261	C₂²⋊C₈	—	2	1	no	—
262	C₂²⋊C₈	—	2	1	no	—
263	C₂²⋊C₈	—	2	1	no	—
264	C₂²⋊C₈	—	2	1	no	—
265	#97	—	2	1	no	—
266	#97	—	2	1	no	—
267	#95	—	118	2	no	—
268	#95	—	118	2	no	—
269	C₂⁴	C₄⋊Dic₅₉	1	1	yes	characteristic
270	C₂⁴	C₂×D₂₃₆	1	1	yes	characteristic
271	C₂×D₄	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	1	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	236	2	no	—
282	C₂²×C₄	—	236	2	no	—
283	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
284	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
285	C₂²×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
287	C₂²×C₄	#11745685	1	1	yes	characteristic
288	C₂²×C₄	#11745685	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
292	M₁₆	—	4	2	no	—
293	M₁₆	—	4	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
305	C₂×C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
306	C₂×C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
307	C₂×C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	236	2	no	—
311	C₄⋊C₄	—	236	2	no	—
312	C₄⋊C₄	—	236	2	no	—
313	C₄⋊C₄	—	236	2	no	—
314	C₂²⋊C₄	—	2	1	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	236	2	no	—
319	C₂²⋊C₄	—	236	2	no	—
320	C₂²⋊C₄	—	236	2	no	—
321	C₂²⋊C₄	—	236	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	1	no	—
330	C₂³	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
331	C₂³	#14273701	1	1	yes	characteristic
332	C₂³	#14273701	1	1	yes	characteristic
333	C₂³	#14273755	1	2	yes	—
334	C₂³	#14273760	1	2	yes	—
335	D₄	—	4	2	no	—
336	D₄	—	4	1	no	—
337	D₄	—	4	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	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	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	472	2	no	—
357	C₂×C₄	—	472	2	no	—
358	C₂×C₄	—	472	2	no	—
359	C₂×C₄	—	472	2	no	—
360	C₂×C₄	—	472	2	no	—
361	C₂×C₄	—	472	2	no	—
362	C₂×C₄	C₂×C₂²⋊Dic₅₉	1	1	yes	characteristic
363	C₂×C₄	#14273686	1	1	yes	characteristic
364	C₂×C₄	#14273706	1	1	yes	characteristic
365	C₂×C₄	#14273706	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₈	#14273642	1	2	yes	complemented
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	8	2	no	—
384	C₂²	#16837262	1	1	yes	characteristic
385	C₂²	#16837444	1	2	yes	—
386	C₂²	#16837648	1	2	yes	—
387	C₂²	#16837655	1	1	yes	characteristic
388	C₂²	#16837660	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	944	2	no	—
396	C₄	—	944	2	no	—
397	C₄	C₂×#14273642	1	1	yes	characteristic
398	C₄	#16837376	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	—	2	1	no	—
403	C₂	—	8	1	no	—
404	C₂	#21424084	1	1	yes	characteristic
405	C₂	#21424129	1	1	yes	characteristic
406	C₂	#21424142	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16837262
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₅₉
Fitting	C₂×C₅₉×#435	C₂
socle	C₂²×C₅₉	#380
prime radical	C₂²×D₄×C₅₉	D₄
cosocle	C₂³×C₄×C₅₉	C₂³
hypercenter	C₂×#435	D₅₉
hypocenter	C₅₉	#8610
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
1. #21424125	C₂	semidirect
2. #21424121	C₂	semidirect
4. #21421964	C₂	semidirect
14. C₂²×M₁₆×C₅₉	C₄	semidirect
21. C₂×C₄⋊C₈×C₅₉	C₄	semidirect
22. C₂×C₂²⋊C₈×C₅₉	C₄	semidirect
24. C₂×#97×C₅₉	C₄	semidirect
167. C₈×C₅₉	#99	semidirect
209. C₂²×M₁₆	Dic₅₉	semidirect
218. C₂×C₄⋊C₈	Dic₅₉	semidirect
220. C₂×C₂²⋊C₈	Dic₅₉	semidirect
222. C₂×#97	Dic₅₉	semidirect
228. C₅₉	#8610	semidirect
371. C₈	#14273642	semidirect

Maximal subgroups

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

subgroup	index
#21424125	2
#21424121	2
#21424084	2
#21421964	2
C₂×C₅₉×#435	2
#8610	59