Subgroups — #28559869

Order 15104.

600 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434167	C₂	1	1	yes	maximal, characteristic
2	#21433197	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422991	C₂	1	2	yes	maximal, complemented
4	#21422965	C₂	1	2	yes	maximal, complemented
5	#21422953	C₂	1	2	yes	maximal, complemented
6	C₈×#11745670	C₂	1	2	yes	maximal, complemented
7	#21422887	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422550	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422478	C₂	1	1	yes	maximal, characteristic
10	#21422380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2990	C₂	1	1	yes	maximal, characteristic
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837743	C₄	1	2	yes	—
14	#16837687	C₄	1	1	yes	characteristic
15	#16837682	C₄	1	1	yes	characteristic
16	#16837612	C₄	1	1	yes	characteristic
17	#16837607	C₄	1	1	yes	characteristic
18	#16837564	C₄	1	2	yes	—
19	#16837532	C₂²	1	2	yes	—
20	#16837529	—	2	1	no	—
21	C₈×Dic₁₁₈	C₂²	1	2	yes	—
22	#16837526	—	2	1	no	—
23	C₄×#11745672	C₂²	1	2	yes	—
24	C₄×#11745670	C₂²	1	2	yes	—
25	#16837460	—	2	2	no	—
26	#16837455	C₂²	1	1	yes	characteristic
27	#16837455	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
29	#16837154	C₂²	1	2	yes	—
30	#16837152	C₂²	1	2	yes	—
31	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
32	Q₈⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
33	#16837132	C₂²	1	2	yes	—
34	#16837132	C₂²	1	2	yes	—
35	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
36	D₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
37	#16837124	C₂²	1	2	yes	—
38	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
39	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#446	C₂²	1	2	yes	—
41	C₅₉×#435	—	2	2	no	—
42	C₈×D₄×C₅₉	C₂²	1	2	yes	—
43	C₅₉×#432	—	2	1	no	—
44	C₅₉×#431	C₂²	1	1	yes	characteristic
45	C₅₉×#423	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
47	C₂×#11745672	C₂×C₄	1	2	yes	—
48	C₂×#11745670	C₂×C₄	1	2	yes	—
49	C₂²×C₅₉⋊C₈	—	2	1	no	—
50	#14273727	C₂×C₄	1	1	yes	characteristic
51	#14273727	C₂×C₄	1	1	yes	characteristic
52	#14273719	—	2	1	no	—
53	#14273706	—	2	1	no	—
54	#14273706	C₂×C₄	1	2	yes	—
55	C₄×Dic₁₁₈	—	2	1	no	—
56	C₄×Dic₁₁₈	C₂³	1	2	yes	—
57	#14273686	—	2	1	no	—
58	#14273660	C₂×C₄	1	2	yes	—
59	#14273658	C₂×C₄	1	2	yes	—
60	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
61	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
62	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
63	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
64	Dic₅₉⋊C₈	—	2	2	no	—
65	Dic₅₉⋊C₈	—	2	2	no	—
66	#14273651	C₂×C₄	1	2	yes	—
67	#14273650	C₂×C₄	1	2	yes	—
68	#14273650	C₂×C₄	1	2	yes	—
69	#14273648	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
71	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
72	#14273637	—	2	2	no	—
73	C₄×C₅₉⋊C₈	—	2	1	no	—
74	C₄×C₅₉⋊C₈	—	2	1	no	—
75	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
78	C₈×Dic₅₉	—	2	2	no	—
79	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₅₉	—	2	1	no	—
81	C₂²×C₈×C₅₉	—	2	2	no	—
82	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₅₉	—	2	1	no	—
85	C₄×D₄×C₅₉	—	2	1	no	—
86	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
88	#117×C₅₉	—	2	1	no	—
89	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₅₉	—	2	1	no	—
91	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₅₉	—	2	2	no	—
93	C₄⋊C₈×C₅₉	—	2	1	no	—
94	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
95	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
96	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
97	C₂²⋊C₈×C₅₉	—	2	2	no	—
98	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
99	#97×C₅₉	—	2	2	no	—
100	C₄×C₈×C₅₉	C₂³	1	2	yes	—
101	#41×C₅₉	—	2	2	no	—
102	#41×C₅₉	—	4	1	no	—
103	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₂×D₄×C₅₉	—	2	1	no	—
105	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
112	C₂×Dic₁₁₈	—	2	1	no	—
113	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
114	M₁₆×C₅₉	—	8	1	no	—
115	C₂×C₈×C₅₉	—	2	2	no	—
116	C₂×C₈×C₅₉	—	8	2	no	—
117	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₅₉	—	2	1	no	—
120	C₄⋊C₄×C₅₉	—	2	1	no	—
121	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²⋊C₄×C₅₉	—	2	1	no	—
124	C₂²⋊C₄×C₅₉	—	2	1	no	—
125	C₂²⋊C₄×C₅₉	—	2	1	no	—
126	C₄²×C₅₉	—	2	1	no	—
127	C₄²×C₅₉	—	2	1	no	—
128	C₄²×C₅₉	—	2	1	no	—
129	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅₉	#41	1	1	yes	characteristic
132	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₅₉	—	2	2	no	—
134	#11745672	—	4	2	no	—
135	#11745670	—	2	4	no	—
136	C₄⋊Dic₅₉	—	2	1	no	—
137	C₄⋊Dic₅₉	—	2	1	no	—
138	C₄⋊Dic₅₉	—	2	1	no	—
139	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
140	Dic₅₉⋊C₄	—	2	2	no	—
141	Dic₅₉⋊C₄	—	2	2	no	—
142	C₄×Dic₅₉	—	2	2	no	—
143	C₂×C₅₉⋊C₈	—	2	4	no	—
144	C₂×C₅₉⋊C₈	—	2	1	no	—
145	C₂×C₅₉⋊C₈	—	2	1	no	—
146	C₂×C₅₉⋊C₈	—	2	1	no	—
147	C₂×C₅₉⋊C₈	—	2	1	no	—
148	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂³×C₅₉	—	2	1	no	—
151	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
152	Q₈×C₅₉	—	2	1	no	—
153	Q₈×C₅₉	—	2	1	no	—
154	D₄×C₅₉	—	2	1	no	—
155	D₄×C₅₉	—	4	2	no	—
156	D₄×C₅₉	#131	1	2	yes	—
157	C₂×C₄×C₅₉	—	2	1	no	—
158	C₂×C₄×C₅₉	—	2	1	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	1	no	—
167	C₂×C₄×C₅₉	—	4	1	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	C₂×Dic₅₉	—	2	2	no	—
176	C₂×Dic₅₉	—	2	2	no	—
177	Dic₁₁₈	—	2	2	no	—
178	Dic₁₁₈	—	2	2	no	—
179	Dic₁₁₈	—	4	2	no	—
180	C₈×C₅₉	—	2	2	no	—
181	C₈×C₅₉	—	2	2	no	—
182	C₈×C₅₉	—	4	2	no	—
183	C₅₉⋊C₈	—	2	2	no	—
184	C₅₉⋊C₈	—	2	2	no	—
185	C₅₉⋊C₈	—	2	2	no	—
186	C₅₉⋊C₈	—	2	2	no	—
187	C₅₉⋊C₈	—	4	1	no	—
188	C₅₉⋊C₈	—	4	1	no	—
189	#18016	—	59	1	no	maximal, Sylow
190	C₂²×C₅₉	—	2	1	no	—
191	C₂²×C₅₉	—	2	2	no	—
192	C₂²×C₅₉	—	2	1	no	—
193	C₂²×C₅₉	—	2	1	no	—
194	C₂²×C₅₉	—	4	1	no	—
195	C₂²×C₅₉	—	4	1	no	—
196	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₅₉	—	2	1	no	—
198	C₄×C₅₉	—	2	1	no	—
199	C₄×C₅₉	—	2	1	no	—
200	C₄×C₅₉	—	4	1	no	—
201	C₄×C₅₉	—	4	1	no	—
202	C₄×C₅₉	—	4	1	no	—
203	C₄×C₅₉	#443	1	2	yes	—
204	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
205	C₄×C₅₉	#568	1	1	yes	characteristic
206	C₄×C₅₉	#577	1	1	yes	characteristic
207	C₄×C₅₉	#578	1	1	yes	characteristic
208	Dic₅₉	—	4	2	no	—
209	Dic₅₉	—	4	2	no	—
210	#3107	—	59	1	no	—
211	#2990	D₅₉	1	1	yes	characteristic
212	#2986	—	59	1	no	—
213	#1591	—	59	2	no	—
214	#1587	—	59	2	no	—
215	#1585	—	59	2	no	—
216	C₈×SD₁₆	—	59	2	no	—
217	#1574	—	59	1	no	—
218	#1493	—	59	1	no	—
219	#1476	—	59	1	no	—
220	#1450	—	59	1	no	—
221	C₂×C₅₉	—	4	1	no	—
222	C₂×C₅₉	—	4	2	no	—
223	C₂×C₅₉	#2933	1	1	yes	characteristic
224	C₂×C₅₉	#2947	1	1	yes	characteristic
225	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
226	#533	—	59	1	no	—
227	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
228	#485	—	59	2	no	—
229	#475	—	59	1	no	—
230	#474	—	59	1	no	—
231	#462	—	59	1	no	—
232	#461	—	59	1	no	—
233	#452	—	59	2	no	—
234	#446	—	59	2	no	—
235	#446	—	118	1	no	—
236	#446	C₂×D₅₉	1	2	yes	—
237	C₈×Q₈	—	59	2	no	—
238	C₈×Q₈	—	118	1	no	—
239	C₄×Q₁₆	—	59	2	no	—
240	C₄×SD₁₆	—	59	2	no	—
241	#435	—	2	2	no	—
242	C₈×D₄	C₂×D₅₉	1	2	yes	—
243	#433	—	118	2	no	—
244	#432	—	2	1	no	—
245	#431	—	59	1	no	—
246	#431	—	59	1	no	—
247	#431	C₂×D₅₉	1	1	yes	characteristic
248	#423	C₂×D₅₉	1	1	yes	characteristic
249	C₂×C₄⋊C₈	—	2	1	no	—
250	C₂×C₄×C₈	—	59	1	no	—
251	#335	—	59	2	no	—
252	#334	—	59	2	no	—
253	Q₈⋊C₈	—	59	1	no	—
254	Q₈⋊C₈	—	59	1	no	—
255	Q₈⋊C₈	—	59	2	no	—
256	Q₈⋊C₈	—	59	2	no	—
257	D₄⋊C₈	—	59	1	no	—
258	D₄⋊C₈	—	59	1	no	—
259	#322	—	59	2	no	—
260	C₈²	—	59	2	no	—
261	C₅₉	#18016	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
263	C₂×Q₁₆	—	59	2	no	—
264	C₂×SD₁₆	—	59	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	118	1	no	—
268	C₄⋊Q₈	—	59	1	no	—
269	C₄⋊Q₈	—	59	1	no	—
270	#125	—	118	1	no	—
271	C₂²⋊Q₈	—	59	2	no	—
272	C₂²⋊Q₈	—	118	1	no	—
273	C₄×Q₈	—	59	2	no	—
274	C₄×Q₈	—	118	1	no	—
275	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
276	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
280	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
281	#117	—	2	1	no	—
282	#117	—	118	1	no	—
283	#117	C₄×D₅₉	1	1	yes	characteristic
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
286	#107	—	59	2	no	—
287	#106	—	59	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	59	1	no	—
291	C₄⋊C₈	—	59	1	no	—
292	C₄⋊C₈	—	59	1	no	—
293	C₄⋊C₈	—	59	1	no	—
294	C₄⋊C₈	—	118	2	no	—
295	C₄⋊C₈	—	118	2	no	—
296	C₄⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
299	#103	—	59	2	no	—
300	#103	—	59	2	no	—
301	#103	—	59	2	no	—
302	#102	—	59	2	no	—
303	C₂²⋊C₈	—	2	2	no	—
304	C₂²⋊C₈	—	59	2	no	—
305	C₂²⋊C₈	—	118	1	no	—
306	C₂²⋊C₈	C₂²⋊D₅₉	1	2	yes	—
307	#97	—	2	2	no	—
308	#97	—	118	2	no	—
309	C₄×C₈	—	59	2	no	—
310	C₄×C₈	—	59	1	no	—
311	C₄×C₈	—	59	1	no	—
312	C₄×C₈	—	118	2	no	—
313	C₄×C₈	—	118	1	no	—
314	C₄×C₈	—	118	1	no	—
315	C₄×C₈	C₂²×D₅₉	1	2	yes	—
316	#41	—	2	2	no	—
317	#41	—	4	1	no	—
318	C₂×Q₈	—	59	2	no	—
319	C₂×Q₈	—	118	1	no	—
320	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
327	C₂²×C₄	#11745685	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
329	Q₁₆	—	236	2	no	—
330	SD₁₆	—	118	4	no	—
331	M₁₆	—	8	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	8	2	no	—
334	C₂×C₈	—	59	2	no	—
335	C₂×C₈	—	59	2	no	—
336	C₂×C₈	—	118	4	no	—
337	C₂×C₈	—	118	1	no	—
338	C₂×C₈	—	118	1	no	—
339	C₂×C₈	—	118	1	no	—
340	C₂×C₈	—	118	1	no	—
341	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
342	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	59	2	no	—
346	C₄⋊C₄	—	118	1	no	—
347	C₄⋊C₄	—	118	1	no	—
348	C₄⋊C₄	—	118	2	no	—
349	C₄⋊C₄	—	118	1	no	—
350	C₄⋊C₄	—	118	2	no	—
351	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
352	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	118	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	118	2	no	—
361	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
362	C₄²	#11745685	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
364	C₄²	C₂³×D₅₉	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	2	1	no	—
369	Q₈	—	118	2	no	—
370	Q₈	—	118	2	no	—
371	Q₈	—	236	2	no	—
372	D₄	—	2	1	no	—
373	D₄	—	4	2	no	—
374	D₄	#14273735	1	2	yes	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	118	2	no	—
388	C₂×C₄	—	118	2	no	—
389	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
391	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	118	2	no	—
399	C₈	—	118	2	no	—
400	C₈	—	118	2	no	—
401	C₈	—	118	2	no	—
402	C₈	—	236	1	no	—
403	C₈	—	236	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	236	2	no	—
418	C₄	—	236	2	no	—
419	C₄	#16837517	1	2	yes	—
420	C₄	C₂×#14273735	1	1	yes	characteristic
421	C₄	#16838168	1	1	yes	characteristic
422	C₄	#16838213	1	1	yes	characteristic
423	C₄	#16838217	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#21432821	1	1	yes	characteristic
427	C₂	#21432935	1	1	yes	characteristic
428	C₂	C₂×#16837517	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2990	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂×C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2990	D₅₉
hypocenter	C₅₉	#18016
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2990

Complements

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

N	H ≅ G/N	type
2. #21433197	C₂	semidirect
3. #21422991	C₂	semidirect
4. #21422965	C₂	semidirect
5. #21422953	C₂	semidirect
6. C₈×#11745670	C₂	semidirect
7. #21422887	C₂	semidirect
8. #21422550	C₂	semidirect
10. #21422380	C₂	semidirect
261. C₅₉	#18016	semidirect

Maximal subgroups

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

subgroup	index
#21434167	2
#21433197	2
#21422991	2
#21422965	2
#21422953	2
C₈×#11745670	2
#21422887	2
#21422550	2
#21422478	2
#21422380	2
C₅₉×#2990	2
#18016	59