Finite Group Databasebeta

← C59×#14899 #28427008

Subgroups — C59×#14899 #28427008

Order 15104.

1326 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C59×#396C211yesmaximal, characteristic
2C2×C59×#376C211yesmaximal, characteristic, complemented
3C59×#1443C211yesmaximal, characteristic, complemented
4C59×#1442C213yesmaximal, complemented
5C59×#1440C213yesmaximal
6C59×#1437C213yesmaximal
7C59×#1436C213yesmaximal, complemented
8C22×C4⋊C4×C59C2213yes—
9C22×C22⋊C4×C59C2211yescharacteristic
10C22×C22⋊C4×C59C2213yes—
11C22×C22⋊C4×C59C2213yes—
12C22×C42×C59C2213yes—
13C59×#396—24no—
14C59×#376—24no—
15C2×#95×C59C2213yes—
16C2×#95×C59C2213yes—
17C2×#95×C59C2213yes—
18C2×#95×C59C2213yes—
19C2×#95×C59C2213yes—
20C2×#95×C59C2213yes—
21C2×#95×C59C2213yes—
22C2×#95×C59C2211yescharacteristic
23C25×C59C2311yescharacteristic
24C23×C4×C59C2313yes—
25C23×C4×C59C2311yescharacteristic
26C23×C4×C59C2313yes—
27C23×C4×C59C2313yes—
28C23×C4×C59C2313yes—
29C23×C4×C59C2311yescharacteristic
30C2×C4⋊C4×C59—26no—
31C2×C4⋊C4×C59—26no—
32C2×C4⋊C4×C59—43no—
33C2×C22⋊C4×C59—26no—
34C2×C22⋊C4×C59—26no—
35C2×C22⋊C4×C59—26no—
36C2×C22⋊C4×C59—26no—
37C2×C22⋊C4×C59—26no—
38C2×C22⋊C4×C59—43no—
39C2×C22⋊C4×C59—43no—
40C2×C42×C59—26no—
41C2×C42×C59—26no—
42C2×C42×C59—26no—
43#95×C59—26no—
44#95×C59—26no—
45#95×C59—26no—
46#95×C59—26no—
47#95×C59—43no—
48#95×C59—43no—
49#95×C59—43no—
50#95×C59D414yes—
51C24×C59—21no—
52C24×C59—23no—
53C24×C59—23no—
54C24×C59—23no—
55C24×C59—23no—
56C24×C59—21no—
57C24×C59#4112yes—
58C24×C59C2411yescharacteristic
59C22×C4×C59—21no—
60C22×C4×C59—23no—
61C22×C4×C59—23no—
62C22×C4×C59—23no—
63C22×C4×C59—23no—
64C22×C4×C59—23no—
65C22×C4×C59—23no—
66C22×C4×C59—23no—
67C22×C4×C59—23no—
68C22×C4×C59—23no—
69C22×C4×C59—23no—
70C22×C4×C59—23no—
71C22×C4×C59—23no—
72C22×C4×C59—23no—
73C22×C4×C59—23no—
74C22×C4×C59—23no—
75C22×C4×C59—23no—
76C22×C4×C59—23no—
77C22×C4×C59—23no—
78C22×C4×C59—23no—
79C22×C4×C59—23no—
80C22×C4×C59—23no—
81C22×C4×C59—23no—
82C22×C4×C59—23no—
83C22×C4×C59—23no—
84C22×C4×C59—23no—
85C22×C4×C59—23no—
86C22×C4×C59—23no—
87C22×C4×C59—23no—
88C22×C4×C59—21no—
89C22×C4×C59C2×D416yes—
90C22×C4×C59#4116yes—
91C22×C4×C59#4116yes—
92C22×C4×C59#4116yes—
93C4⋊C4×C59—412no—
94C22⋊C4×C59—412no—
95C22⋊C4×C59—412no—
96C22⋊C4×C59—44no—
97C42×C59—224no—
98C23×C59—26no—
99C23×C59—22no—
100C23×C59—26no—
101C23×C59—43no—
102C23×C59—41no—
103C23×C59—43no—
104C23×C59—43no—
105C23×C59—43no—
106C23×C59—43no—
107C23×C59—43no—
108C23×C59—43no—
109C23×C59—43no—
110C23×C59—43no—
111C23×C59C22×D411yescharacteristic
112C23×C59C2×#4113yes—
113C23×C59C2×#4113yes—
114C23×C59C2×#4113yes—
115C23×C59C2×#4111yescharacteristic
116C23×C59H(5,𝔽2)13yes—
117C23×C592−1+411yescharacteristic
118C2×C4×C59—26no—
119C2×C4×C59—26no—
120C2×C4×C59—26no—
121C2×C4×C59—26no—
122C2×C4×C59—26no—
123C2×C4×C59—26no—
124C2×C4×C59—26no—
125C2×C4×C59—26no—
126C2×C4×C59—26no—
127C2×C4×C59—26no—
128C2×C4×C59—26no—
129C2×C4×C59—43no—
130C2×C4×C59—43no—
131C2×C4×C59—43no—
132C2×C4×C59—43no—
133C2×C4×C59—43no—
134C2×C4×C59—43no—
135C2×C4×C59—43no—
136C2×C4×C59—43no—
137C2×C4×C59—43no—
138C2×C4×C59—43no—
139C2×C4×C59—43no—
140C2×C4×C59—43no—
141C2×C4×C59—41no—
142C2×C4×C59—43no—
143C2×C4×C59—43no—
144C2×C4×C59—43no—
145C2×C4×C59—43no—
146C2×C4×C59—43no—
147C2×C4×C59—43no—
148C2×C4×C59—43no—
149C2×C4×C59—43no—
150C2×C4×C59—43no—
151C2×C4×C59#12614yes—
152#14899C5911yesmaximal, characteristic, direct product factor, Sylow
153C22×C59—42no—
154C22×C59—46no—
155C22×C59—46no—
156C22×C59—81no—
157C22×C59—81no—
158C22×C59—83no—
159C22×C59—83no—
160C22×C59#52513yes—
161C22×C59C2×#12611yescharacteristic
162C22×C59#52913yes—
163C22×C59#52913yes—
164C22×C59#52913yes—
165C22×C59#54013yes—
166C22×C59#54213yes—
167C22×C59#54613yes—
168C22×C59#54811yescharacteristic
169C22×C59#55113yes—
170C22×C59#55213yes—
171C22×C59#55313yes—
172C22×C59#55513yes—
173C4×C59—24no—
174C4×C59—46no—
175C4×C59—46no—
176C4×C59—46no—
177C4×C59—81no—
178C4×C59—83no—
179C2×#396C2×C5911yescharacteristic
180C2×#376C2×C5911yescharacteristic, complemented
181#1443C2×C5911yescharacteristic, complemented
182#1442C2×C5913yescomplemented
183#1440C2×C5913yes—
184#1437C2×C5913yes—
185#1436C2×C5913yescomplemented
186C2×C59—82no—
187C2×C59#240111yescharacteristic
188C2×C59#247613yes—
189C2×C59#247713yes—
190C2×C59#252613yes—
191C2×C59#252913yes—
192C2×C59#264411yescharacteristic
193C2×C59#285211yescharacteristic
194C22×C4⋊C4C22×C5913yes—
195C22×C22⋊C4C22×C5911yescharacteristic
196C22×C22⋊C4C22×C5913yes—
197C22×C22⋊C4C22×C5913yes—
198C22×C42C22×C5913yes—
199#396—24no—
200#376—24no—
201C2×#95C22×C5913yes—
202C2×#95C22×C5913yes—
203C2×#95C22×C5913yes—
204C2×#95C22×C5913yes—
205C2×#95C22×C5913yes—
206C2×#95C22×C5913yes—
207C2×#95C22×C5913yes—
208C2×#95C22×C5911yescharacteristic
209C59#1489911yescharacteristic, direct product factor, Sylow
210C25C23×C5911yescharacteristic
211C23×C4C23×C5913yes—
212C23×C4C23×C5911yescharacteristic
213C23×C4C23×C5913yes—
214C23×C4C23×C5913yes—
215C23×C4C23×C5913yes—
216C23×C4C23×C5911yescharacteristic
217C2×C4⋊C4—26no—
218C2×C4⋊C4—26no—
219C2×C4⋊C4—43no—
220C2×C22⋊C4—26no—
221C2×C22⋊C4—26no—
222C2×C22⋊C4—26no—
223C2×C22⋊C4—26no—
224C2×C22⋊C4—26no—
225C2×C22⋊C4—43no—
226C2×C22⋊C4—43no—
227C2×C42—26no—
228C2×C42—26no—
229C2×C42—26no—
230#95—26no—
231#95—26no—
232#95—26no—
233#95—26no—
234#95—43no—
235#95—43no—
236#95—43no—
237#95D4×C5914yes—
238C24—21no—
239C24—23no—
240C24—23no—
241C24—23no—
242C24—23no—
243C24—21no—
244C24#41×C5912yes—
245C24C24×C5911yescharacteristic
246C22×C4—21no—
247C22×C4—23no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—23no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—21no—
276C22×C4C2×D4×C5916yes—
277C22×C4#41×C5916yes—
278C22×C4#41×C5916yes—
279C22×C4#41×C5916yes—
280C4⋊C4—412no—
281C22⋊C4—412no—
282C22⋊C4—412no—
283C22⋊C4—44no—
284C42—224no—
285C23—26no—
286C23—22no—
287C23—26no—
288C23—43no—
289C23—41no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23—43no—
296C23—43no—
297C23—43no—
298C23C22×D4×C5911yescharacteristic
299C23C2×#41×C5913yes—
300C23C2×#41×C5913yes—
301C23C2×#41×C5913yes—
302C23C2×#41×C5911yescharacteristic
303C23H(5,𝔽2)×C5913yes—
304C232−1+4×C5911yescharacteristic
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—41no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4#126×C5914yes—
339C22—46no—
340C22—42no—
341C22—46no—
342C22—83no—
343C22—81no—
344C22—81no—
345C22—83no—
346C22C59×#52513yes—
347C22C2×#126×C5911yescharacteristic
348C22C59×#52913yes—
349C22C59×#52913yes—
350C22C59×#52913yes—
351C22C59×#54013yes—
352C22C59×#54213yes—
353C22C59×#54613yes—
354C22C59×#54811yescharacteristic
355C22C59×#55113yes—
356C22C59×#55213yes—
357C22C59×#55313yes—
358C22C59×#55513yes—
359C4—24no—
360C4—46no—
361C4—46no—
362C4—46no—
363C4—83no—
364C4—81no—
365C2—82no—
366C2C59×#240111yescharacteristic
367C2C59×#247613yes—
368C2C59×#247713yes—
369C2C59×#252613yes—
370C2C59×#252913yes—
371C2C59×#264411yescharacteristic
372C2C59×#285211yescharacteristic
subgroupG/H
center, socleC24×C59C24
commutator, Frattini, cosocleC24C24×C59
prime radicalC25×C59C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#376C2semidirect
3. C59×#1443C2semidirect
4. C59×#1442C2semidirect
7. C59×#1436C2semidirect
152. #14899C59direct (N × H)
180. C2×#376C2×C59semidirect
181. #1443C2×C59semidirect
182. #1442C2×C59semidirect
185. #1436C2×C59semidirect
209. C59#14899direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C59×#3962
C2×C59×#3762
C59×#14432
C59×#14422
C59×#14402
C59×#14372
C59×#14362
#1489959