Subgroups — D₅₉×#2170 #28741913

Order 15104.

662 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	#504×D₅₉	C₂	1	2	yes	maximal, complemented
2	#443×D₅₉	C₂	1	1	yes	maximal, characteristic
3	#21425934	C₂	1	1	yes	maximal, characteristic, complemented
4	#21425933	C₂	1	1	yes	maximal, characteristic, complemented
5	#21425932	C₂	1	1	yes	maximal, characteristic, complemented
6	#21425931	C₂	1	2	yes	maximal, complemented
7	#21425930	C₂	1	2	yes	maximal, complemented
8	#364×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#350×D₅₉	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₉	C₄	1	1	yes	characteristic
13	#131×D₅₉	C₂²	1	2	yes	—
14	#16837820	—	2	2	no	—
15	#16837820	C₂²	1	2	yes	complemented
16	#16837819	C₂²	1	2	yes	complemented
17	#16837818	—	2	2	no	—
18	#16837818	C₂²	1	2	yes	complemented
19	M₃₂×D₅₉	—	2	2	no	—
20	M₃₂×D₅₉	C₂²	1	2	yes	—
21	C₂×C₁₆×D₅₉	—	2	2	no	—
22	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₅₉	C₂²	1	1	yes	characteristic
24	#16837520	C₂²	1	1	yes	characteristic
25	#16837519	C₄	1	1	yes	characteristic
26	#16837518	C₄	1	1	yes	characteristic
27	#16837517	C₂²	1	2	yes	—
28	#16837516	C₄	1	2	yes	—
29	#108×D₅₉	C₄	1	1	yes	characteristic
30	#104×D₅₉	C₄	1	2	yes	—
31	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
32	#16837223	C₂²	1	1	yes	characteristic, complemented
33	#16837222	C₂²	1	2	yes	complemented
34	#16837187	C₂²	1	2	yes	complemented
35	#16837186	C₂²	1	2	yes	complemented
36	#16837185	C₂²	1	2	yes	complemented
37	C₄×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₅₉	C₂²	1	1	yes	characteristic, complemented
40	C₅₉×#504	C₂²	1	2	yes	complemented
41	C₅₉×#443	C₂²	1	1	yes	characteristic
42	C₅₉×#364	C₂²	1	1	yes	characteristic, complemented
43	C₅₉×#350	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
45	#41×D₅₉	C₂×C₄	1	2	yes	—
46	#14273750	C₈	1	1	yes	characteristic
47	#14273749	C₂×C₄	1	1	yes	characteristic
48	#14273748	C₈	1	2	yes	—
49	#14273747	C₂×C₄	1	2	yes	—
50	#14273746	C₈	1	1	yes	characteristic
51	Q₁₆×D₅₉	C₈	1	1	yes	characteristic
52	SD₁₆×D₅₉	C₈	1	2	yes	—
53	D₈×D₅₉	C₈	1	1	yes	characteristic
54	#14273735	—	2	2	no	—
55	#14273735	C₂×C₄	1	2	yes	—
56	#14273734	C₂×C₄	1	2	yes	—
57	#14273733	—	2	2	no	—
58	#14273733	C₂³	1	2	yes	—
59	M₁₆×D₅₉	—	2	2	no	—
60	M₁₆×D₅₉	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₅₉	—	2	2	no	—
62	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₅₉	C₂³	1	1	yes	characteristic
64	C₄²×D₅₉	C₂×C₄	1	1	yes	characteristic
65	#14273667	—	2	2	no	—
66	#14273667	C₂³	1	2	yes	—
67	#14273666	—	2	2	no	—
68	#14273666	—	2	2	no	—
69	#14273666	—	2	2	no	—
70	C₂×C₅₉⋊C₁₆	—	2	2	no	—
71	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
73	C₁₆×D₅₉	—	2	2	no	—
74	C₁₆×D₅₉	—	2	1	no	—
75	C₁₆×D₅₉	—	2	1	no	—
76	C₁₆×D₅₉	—	2	2	no	—
77	C₁₆×D₅₉	—	2	2	no	—
78	C₁₆×D₅₉	D₄	1	1	yes	characteristic
79	C₁₆×D₅₉	D₄	1	1	yes	characteristic
80	C₁₆×D₅₉	D₄	1	1	yes	characteristic
81	C₁₆×D₅₉	D₄	1	1	yes	characteristic
82	#14273663	C₂×C₄	1	1	yes	characteristic
83	#14273662	C₂×C₄	1	2	yes	—
84	#14273655	C₂×C₄	1	2	yes	—
85	#14273654	C₂×C₄	1	2	yes	—
86	#14273653	C₂×C₄	1	2	yes	—
87	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₅₉	C₂³	1	1	yes	characteristic
90	#135×C₅₉	C₂×C₄	1	1	yes	characteristic
91	#131×C₅₉	C₂³	1	2	yes	—
92	M₃₂×C₅₉	—	2	2	no	—
93	M₃₂×C₅₉	C₂³	1	2	yes	—
94	C₂×C₁₆×C₅₉	—	2	2	no	—
95	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
97	#108×C₅₉	C₂×C₄	1	1	yes	characteristic
98	#104×C₅₉	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
100	#41×C₅₉	C₂²×C₄	1	2	yes	—
101	#11745689	C₂×C₈	1	2	yes	—
102	Q₈×D₅₉	C₂×C₈	1	2	yes	—
103	#11745687	—	2	2	no	—
104	#11745687	C₂×C₈	1	2	yes	—
105	D₄×D₅₉	—	2	2	no	—
106	D₄×D₅₉	C₂×C₈	1	2	yes	—
107	#11745685	—	2	2	no	—
108	#11745685	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₅₉	—	2	1	no	—
110	C₂×C₄×D₅₉	—	2	2	no	—
111	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
112	Q₁₆×C₅₉	C₂×C₈	1	1	yes	characteristic
113	SD₁₆×C₅₉	C₂×C₈	1	2	yes	—
114	D₈×C₅₉	C₂×C₈	1	1	yes	characteristic
115	M₁₆×C₅₉	—	2	2	no	—
116	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₅₉	—	2	2	no	—
118	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
120	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	#11745672	C₂×C₈	1	2	yes	—
122	#11745671	C₂×C₈	1	2	yes	—
123	#11745670	C₂×C₈	1	2	yes	—
124	#11745669	C₂×C₈	1	2	yes	—
125	C₄×Dic₅₉	—	2	1	no	—
126	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
127	#11745664	—	2	2	no	—
128	#11745664	C₂²×C₄	1	2	yes	—
129	C₂×C₅₉⋊C₈	—	2	2	no	—
130	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	Dic₂₃₆	C₂×C₈	1	1	yes	characteristic
133	D₄₇₂	C₂×C₈	1	1	yes	characteristic
134	#11745660	C₂×C₈	1	2	yes	—
135	#11745659	—	2	2	no	—
136	#11745659	—	2	2	no	—
137	#11745659	—	2	2	no	—
138	C₈×D₅₉	—	2	2	no	—
139	C₈×D₅₉	—	2	2	no	—
140	C₈×D₅₉	—	2	2	no	—
141	C₈×D₅₉	C₂×C₈	1	1	yes	characteristic
142	C₈×D₅₉	C₂×C₈	1	1	yes	characteristic
143	C₈×D₅₉	C₂×C₈	1	1	yes	characteristic
144	C₈×D₅₉	C₂×C₈	1	1	yes	characteristic
145	C₈×D₅₉	C₂×D₄	1	1	yes	characteristic
146	C₈×D₅₉	C₂×D₄	1	1	yes	characteristic
147	C₈×D₅₉	#41	1	1	yes	characteristic
148	C₈×D₅₉	#41	1	1	yes	characteristic
149	C₁₆×C₅₉	—	2	2	no	—
150	C₁₆×C₅₉	—	2	1	no	—
151	C₁₆×C₅₉	C₂×D₄	1	1	yes	characteristic
152	C₁₆×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₅₉⋊C₁₆	—	2	2	no	—
154	C₅₉⋊C₁₆	—	2	1	no	—
155	C₅₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
156	C₅₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
157	C₂²×D₅₉	—	2	2	no	—
158	C₂²×D₅₉	#131	1	1	yes	characteristic
159	Q₈×C₅₉	C₂²×C₈	1	2	yes	—
160	D₄×C₅₉	—	2	2	no	—
161	D₄×C₅₉	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₅₉	—	2	1	no	—
163	C₂×C₄×C₅₉	—	2	2	no	—
164	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₅₉	—	2	2	no	—
166	C₂²⋊D₅₉	—	2	2	no	—
167	C₂²⋊D₅₉	—	2	2	no	—
168	C₂×Dic₅₉	—	2	1	no	—
169	C₂×Dic₅₉	—	2	2	no	—
170	C₂×Dic₅₉	#131	1	1	yes	characteristic
171	D₂₃₆	—	2	2	no	—
172	D₂₃₆	C₂²×C₈	1	2	yes	—
173	C₄×D₅₉	—	2	4	no	—
174	C₄×D₅₉	—	2	2	no	—
175	C₄×D₅₉	—	2	2	no	—
176	C₄×D₅₉	—	2	2	no	—
177	C₄×D₅₉	C₄×D₄	1	1	yes	characteristic
178	C₄×D₅₉	C₄×D₄	1	1	yes	characteristic
179	C₄×D₅₉	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₅₉	C₂²×C₈	1	1	yes	characteristic
181	Dic₁₁₈	—	2	2	no	—
182	Dic₁₁₈	C₂²×C₈	1	2	yes	—
183	C₈×C₅₉	—	2	2	no	—
184	C₈×C₅₉	C₂²×C₈	1	1	yes	characteristic
185	C₈×C₅₉	C₂²×C₈	1	1	yes	characteristic
186	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
188	C₅₉⋊C₈	—	2	2	no	—
189	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
190	C₅₉⋊C₈	C₄×D₄	1	1	yes	characteristic
191	C₅₉⋊C₈	C₂²×C₈	1	1	yes	characteristic
192	C₅₉⋊C₈	C₂²×C₈	1	1	yes	characteristic
193	C₂×#2170	—	59	1	no	maximal, Sylow
194	C₂²×C₅₉	—	2	2	no	—
195	C₂²×C₅₉	C₂×#131	1	1	yes	characteristic
196	C₂×D₅₉	—	2	2	no	—
197	C₂×D₅₉	—	2	2	no	—
198	C₂×D₅₉	—	4	4	no	—
199	C₂×D₅₉	C₈×D₄	1	1	yes	characteristic
200	C₂×D₅₉	C₈×D₄	1	1	yes	characteristic
201	C₄×C₅₉	—	2	2	no	—
202	C₄×C₅₉	—	2	2	no	—
203	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₅₉	C₂³×C₈	1	1	yes	characteristic
205	Dic₅₉	—	2	2	no	—
206	Dic₅₉	—	2	2	no	—
207	Dic₅₉	C₈×D₄	1	1	yes	characteristic
208	Dic₅₉	C₈×D₄	1	1	yes	characteristic
209	C₂×#504	—	59	2	no	—
210	C₂×#443	—	59	1	no	—
211	#2170	—	59	2	no	—
212	#2170	—	59	1	no	—
213	#2170	—	59	1	no	—
214	#2170	—	59	2	no	—
215	#2170	—	59	1	no	—
216	#2170	D₅₉	1	1	yes	characteristic, direct product factor
217	C₂×#364	—	59	1	no	—
218	C₂×#350	—	59	2	no	—
219	C₂×C₄×C₁₆	—	59	1	no	—
220	C₂×C₅₉	—	2	1	no	—
221	C₂×C₅₉	—	4	2	no	—
222	C₂×C₅₉	C₂×C₈×D₄	1	1	yes	characteristic
223	D₅₉	—	2	1	no	—
224	D₅₉	—	4	2	no	—
225	D₅₉	#2170	1	2	yes	direct product factor
226	C₂×#135	—	59	1	no	—
227	C₂×#131	—	59	2	no	—
228	#504	—	59	2	no	—
229	#504	—	59	2	no	—
230	#504	—	59	2	no	—
231	#504	—	118	2	no	—
232	#504	—	118	2	no	—
233	#504	C₂×D₅₉	1	2	yes	complemented
234	C₂×M₃₂	—	59	2	no	—
235	C₂×M₃₂	—	118	2	no	—
236	C₂²×C₁₆	—	59	1	no	—
237	C₂²×C₁₆	—	59	1	no	—
238	C₂²×C₁₆	—	118	2	no	—
239	#443	—	59	1	no	—
240	#443	—	59	2	no	—
241	#443	—	59	1	no	—
242	#443	—	59	2	no	—
243	#443	—	59	1	no	—
244	#443	C₂×D₅₉	1	1	yes	characteristic
245	C₂×#108	—	59	1	no	—
246	C₂×#104	—	59	2	no	—
247	C₂×C₄×C₈	—	59	1	no	—
248	#364	—	59	2	no	—
249	#364	—	59	1	no	—
250	#364	C₂×D₅₉	1	1	yes	characteristic, complemented
251	#350	—	59	2	no	—
252	#350	—	59	2	no	—
253	#350	—	59	2	no	—
254	#350	C₂×D₅₉	1	2	yes	complemented
255	C₄×C₁₆	—	59	1	no	—
256	C₄×C₁₆	—	59	1	no	—
257	C₄×C₁₆	—	59	1	no	—
258	C₄×C₁₆	C₂×D₅₉	1	1	yes	characteristic, complemented
259	C₅₉	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	59	2	no	—
261	#135	—	59	2	no	—
262	#135	—	59	1	no	—
263	#135	—	59	2	no	—
264	#135	—	59	1	no	—
265	#135	—	59	1	no	—
266	#135	C₄×D₅₉	1	1	yes	characteristic
267	C₂×Q₁₆	—	59	1	no	—
268	C₂×SD₁₆	—	59	2	no	—
269	C₂×D₈	—	59	1	no	—
270	#131	—	59	2	no	—
271	#131	—	59	2	no	—
272	#131	—	59	2	no	—
273	#131	—	118	2	no	—
274	#131	—	118	2	no	—
275	#131	C₂²×D₅₉	1	2	yes	—
276	C₂×M₁₆	—	59	2	no	—
277	C₂×M₁₆	—	118	2	no	—
278	C₂²×C₈	—	59	1	no	—
279	C₂²×C₈	—	59	1	no	—
280	C₂²×C₈	—	118	2	no	—
281	C₂×C₄²	—	59	1	no	—
282	M₃₂	—	2	2	no	—
283	M₃₂	—	59	2	no	—
284	M₃₂	—	118	2	no	—
285	M₃₂	—	118	2	no	—
286	M₃₂	—	118	2	no	—
287	M₃₂	—	118	2	no	—
288	M₃₂	C₂²×D₅₉	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	59	1	no	—
291	C₂×C₁₆	—	59	1	no	—
292	C₂×C₁₆	—	59	1	no	—
293	C₂×C₁₆	—	59	1	no	—
294	C₂×C₁₆	—	59	1	no	—
295	C₂×C₁₆	—	59	1	no	—
296	C₂×C₁₆	—	118	2	no	—
297	C₂×C₁₆	—	118	1	no	—
298	C₂×C₁₆	—	118	1	no	—
299	C₂×C₁₆	—	118	2	no	—
300	C₂×C₁₆	—	118	2	no	—
301	C₂×C₁₆	—	118	2	no	—
302	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₅₉	1	1	yes	characteristic
304	#108	—	59	2	no	—
305	#108	—	59	1	no	—
306	#108	C₄×D₅₉	1	1	yes	characteristic
307	#104	—	59	2	no	—
308	#104	—	59	2	no	—
309	#104	—	59	2	no	—
310	#104	C₄×D₅₉	1	2	yes	—
311	C₄×C₈	—	59	1	no	—
312	C₄×C₈	—	59	1	no	—
313	C₄×C₈	—	59	1	no	—
314	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
315	#41	—	59	2	no	—
316	#41	—	59	2	no	—
317	#41	—	59	2	no	—
318	#41	—	118	2	no	—
319	#41	—	118	2	no	—
320	#41	C₂×C₄×D₅₉	1	2	yes	—
321	C₂×Q₈	—	59	2	no	—
322	C₂×D₄	—	59	2	no	—
323	C₂×D₄	—	118	2	no	—
324	C₂²×C₄	—	59	1	no	—
325	C₂²×C₄	—	118	2	no	—
326	C₂²×C₄	—	118	1	no	—
327	Q₁₆	—	59	2	no	—
328	Q₁₆	—	59	1	no	—
329	Q₁₆	C₈×D₅₉	1	1	yes	characteristic
330	SD₁₆	—	59	2	no	—
331	SD₁₆	—	59	2	no	—
332	SD₁₆	—	59	2	no	—
333	SD₁₆	C₈×D₅₉	1	2	yes	—
334	D₈	—	59	2	no	—
335	D₈	—	59	1	no	—
336	D₈	C₈×D₅₉	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	59	2	no	—
339	M₁₆	—	118	2	no	—
340	M₁₆	—	118	2	no	—
341	M₁₆	—	118	2	no	—
342	M₁₆	—	118	2	no	—
343	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	59	1	no	—
346	C₂×C₈	—	59	1	no	—
347	C₂×C₈	—	59	1	no	—
348	C₂×C₈	—	59	1	no	—
349	C₂×C₈	—	59	1	no	—
350	C₂×C₈	—	59	1	no	—
351	C₂×C₈	—	59	1	no	—
352	C₂×C₈	—	59	1	no	—
353	C₂×C₈	—	59	1	no	—
354	C₂×C₈	—	59	1	no	—
355	C₂×C₈	—	118	2	no	—
356	C₂×C₈	—	118	2	no	—
357	C₂×C₈	—	118	2	no	—
358	C₂×C₈	—	118	2	no	—
359	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
361	C₄²	—	59	1	no	—
362	C₄²	—	118	1	no	—
363	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	1	no	—
366	C₁₆	—	59	1	no	—
367	C₁₆	—	59	1	no	—
368	C₁₆	—	118	2	no	—
369	C₁₆	—	118	1	no	—
370	C₁₆	D₄×D₅₉	1	1	yes	characteristic
371	C₁₆	D₄×D₅₉	1	1	yes	characteristic
372	C₂³	—	59	1	no	—
373	C₂³	—	118	2	no	—
374	Q₈	—	59	2	no	—
375	Q₈	—	118	2	no	—
376	Q₈	C₂×C₈×D₅₉	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	59	2	no	—
379	D₄	—	118	2	no	—
380	D₄	—	118	2	no	—
381	D₄	—	118	2	no	—
382	D₄	—	118	2	no	—
383	D₄	C₂×C₈×D₅₉	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	59	1	no	—
387	C₂×C₄	—	59	1	no	—
388	C₂×C₄	—	59	1	no	—
389	C₂×C₄	—	59	1	no	—
390	C₂×C₄	—	59	1	no	—
391	C₂×C₄	—	118	2	no	—
392	C₂×C₄	—	118	2	no	—
393	C₂×C₄	—	118	4	no	—
394	C₂×C₄	—	118	2	no	—
395	C₂×C₄	—	118	1	no	—
396	C₂×C₄	—	118	2	no	—
397	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	59	1	no	—
400	C₈	—	59	1	no	—
401	C₈	—	59	1	no	—
402	C₈	—	59	1	no	—
403	C₈	—	118	2	no	—
404	C₈	C₂×C₈×D₅₉	1	1	yes	characteristic
405	C₈	C₂×C₈×D₅₉	1	1	yes	characteristic
406	C₈	C₂×D₄×D₅₉	1	1	yes	characteristic
407	C₈	#41×D₅₉	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	59	1	no	—
410	C₂²	—	59	1	no	—
411	C₂²	—	118	2	no	—
412	C₂²	—	118	2	no	—
413	C₂²	—	236	4	no	—
414	C₂²	#131×D₅₉	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	59	1	no	—
418	C₄	—	59	1	no	—
419	C₄	—	118	2	no	—
420	C₄	—	118	2	no	—
421	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₅₉	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	59	2	no	—
426	C₂	—	118	1	no	—
427	C₂	—	236	2	no	—
428	C₂	C₈×D₄×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₅₉
commutator	C₄×C₅₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#2170	C₂
socle	C₂×C₅₉	C₂×C₈×D₄
prime radical	#135×D₅₉	C₄
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	#2170	D₅₉
hypocenter	C₅₉	C₂×#2170
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #504×D₅₉	C₂	semidirect
3. #21425934	C₂	semidirect
4. #21425933	C₂	semidirect
5. #21425932	C₂	semidirect
6. #21425931	C₂	semidirect
7. #21425930	C₂	semidirect
8. #364×D₅₉	C₂	semidirect
9. #350×D₅₉	C₂	semidirect
10. C₄×C₁₆×D₅₉	C₂	semidirect
11. C₅₉×#2170	C₂	semidirect
15. #16837820	C₂²	semidirect
16. #16837819	C₂²	semidirect
18. #16837818	C₂²	semidirect
32. #16837223	C₂²	semidirect
33. #16837222	C₂²	semidirect
34. #16837187	C₂²	semidirect
35. #16837186	C₂²	semidirect
36. #16837185	C₂²	semidirect
37. C₄×C₅₉⋊C₁₆	C₂²	semidirect
38. C₁₆×Dic₅₉	C₂²	semidirect
39. C₁₆×Dic₅₉	C₂²	semidirect
40. C₅₉×#504	C₂²	semidirect
42. C₅₉×#364	C₂²	semidirect
43. C₅₉×#350	C₂²	semidirect
44. C₄×C₁₆×C₅₉	C₂²	semidirect
216. #2170	D₅₉	direct (N × H)
225. D₅₉	#2170	direct (N × H)
233. #504	C₂×D₅₉	semidirect
250. #364	C₂×D₅₉	semidirect
254. #350	C₂×D₅₉	semidirect
258. C₄×C₁₆	C₂×D₅₉	semidirect
259. C₅₉	C₂×#2170	semidirect

Maximal subgroups

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

subgroup	index
#504×D₅₉	2
#443×D₅₉	2
#21425934	2
#21425933	2
#21425932	2
#21425931	2
#21425930	2
#364×D₅₉	2
#350×D₅₉	2
C₄×C₁₆×D₅₉	2
C₅₉×#2170	2
C₂×#2170	59

Subgroups — D59×#2170 #28741913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×#2170 #28741913