Finite Group Databasebeta

← C59×#29387 #28441496

Subgroups — C59×#29387 #28441496

Order 15104.

646 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#2956C211yesmaximal, characteristic, complemented
2C59×#2923C211yesmaximal, characteristic, complemented
3C59×#2103C211yesmaximal, characteristic, complemented
4C59×#2098C211yesmaximal, characteristic, complemented
5C59×#2053C211yesmaximal, characteristic, complemented
6C59×#2017C211yesmaximal, characteristic
7C59×#1938C212yesmaximal, complemented
8C59×#1906C212yesmaximal, complemented
9C59×#1881C212yesmaximal, complemented
10C59×#1868C212yesmaximal, complemented
11C59×#1841C211yesmaximal, characteristic, complemented
12C59×#575C2211yescharacteristic
13C59×#575C2212yes—
14C59×#568C2212yes—
15C4×#41×C59C2211yescharacteristic
16C59×#444—22no—
17C59×#443—22no—
18C59×#433—22no—
19C59×#432—22no—
20C59×#430C2211yescharacteristic
21C59×#424C2211yescharacteristic
22C59×#424C2211yescharacteristic
23C59×#424C2212yes—
24C59×#421C2212yes—
25C2×#104×C59C2212yes—
26C59×#416C2212yes—
27C59×#410C2212yes—
28C59×#408C2211yescharacteristic
29C59×#408C2211yescharacteristic
30C59×#408C2212yes—
31C4×M16×C59C2211yescharacteristic
32C2×#97×C59C2211yescharacteristic
33C59×#344C2212yes—
34C59×#344C2212yes—
35C59×#341C2212yes—
36C59×#339C2212yes—
37C59×#338C2211yescharacteristic
38C59×H(3,ℤ/4)C2211yescharacteristic
39C2×#41×C59C2311yescharacteristic
40C2×#41×C59C2312yes—
41#137×C59—22no—
42#137×C59—22no—
43#137×C59—22no—
44AGL(1,ℤ/8)×C59—22no—
45AGL(1,ℤ/8)×C59—22no—
46AGL(1,ℤ/8)×C59—22no—
47#135×C59—22no—
48#135×C59—42no—
49#131×C59—24no—
50#131×C59—42no—
51C2×M16×C59—42no—
52C2×M16×C59C2312yes—
53C2×M16×C59C2312yes—
54C2×M16×C59C2311yescharacteristic
55C2×M16×C59C2311yescharacteristic
56C22×C8×C59C2311yescharacteristic
57C22×C8×C59C2311yescharacteristic
58C4×Q8×C59—21no—
59C4×D4×C59—21no—
60C4×D4×C59—22no—
61#117×C59—21no—
62#117×C59C2312yes—
63#117×C59C2311yescharacteristic
64C2×C42×C59—21no—
65C2×C42×C59C2311yescharacteristic
66#108×C59—22no—
67C4⋊C8×C59—22no—
68C4⋊C8×C59—22no—
69C4⋊C8×C59—42no—
70#104×C59—22no—
71#104×C59—22no—
72#104×C59—42no—
73#103×C59—22no—
74#102×C59—22no—
75#99×C59—24no—
76C22⋊C8×C59—22no—
77C22⋊C8×C59—22no—
78C22⋊C8×C59—42no—
79#97×C59—21no—
80#97×C59—21no—
81#97×C59D412yes—
82C4×C8×C59D412yes—
83#41×C59—22no—
84#41×C59—22no—
85#41×C59—22no—
86#41×C59—22no—
87#41×C59—22no—
88#41×C59—22no—
89C2×Q8×C59#4112yes—
90C2×Q8×C59#4111yescharacteristic
91C2×D4×C59—22no—
92C2×D4×C59—21no—
93C2×D4×C59#4112yes—
94C2×D4×C59#4111yescharacteristic
95C22×C4×C59—22no—
96C22×C4×C59—21no—
97C22×C4×C59—21no—
98C22×C4×C59—22no—
99C22×C4×C59C2411yescharacteristic
100Q16×C59—22no—
101Q16×C59—42no—
102SD16×C59—24no—
103SD16×C59—42no—
104SD16×C59—42no—
105D8×C59—22no—
106D8×C59—42no—
107M16×C59—22no—
108M16×C59—22no—
109M16×C59—22no—
110M16×C59—22no—
111M16×C59—22no—
112M16×C59—22no—
113M16×C59—44no—
114C2×C8×C59—21no—
115C2×C8×C59—21no—
116C2×C8×C59—22no—
117C2×C8×C59—22no—
118C2×C8×C59—22no—
119C2×C8×C59—22no—
120C2×C8×C59—44no—
121C2×C8×C59C2×D412yes—
122C2×C8×C59C2×D412yes—
123C4⋊C4×C59—22no—
124C4⋊C4×C59—21no—
125C4⋊C4×C59—22no—
126C22⋊C4×C59—22no—
127C22⋊C4×C59—22no—
128C22⋊C4×C59#4112yes—
129C42×C59—22no—
130C42×C59—21no—
131C42×C59—21no—
132C42×C59—22no—
133C42×C59C2×D411yescharacteristic
134C42×C59C2×D411yescharacteristic
135C23×C59—21no—
136C23×C59—22no—
137C23×C59C2×#4111yescharacteristic
138Q8×C59—22no—
139Q8×C59—22no—
140Q8×C59—22no—
141D4×C59—22no—
142D4×C59—22no—
143D4×C59—22no—
144D4×C59—42no—
145D4×C59—42no—
146D4×C59—42no—
147C2×C4×C59—21no—
148C2×C4×C59—22no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—22no—
152C2×C4×C59—41no—
153C2×C4×C59—42no—
154C2×C4×C59—41no—
155C2×C4×C59—42no—
156C2×C4×C59—42no—
157C2×C4×C59—81no—
158C2×C4×C59—82no—
159C2×C4×C59C22×D411yescharacteristic
160C2×C4×C59C2×#4112yes—
161C2×C4×C59C2×#4111yescharacteristic
162C2×C4×C59H(5,𝔽2)12yes—
163C8×C59—22no—
164C8×C59—22no—
165C8×C59—41no—
166C8×C59—41no—
167C8×C59—42no—
168C8×C59—42no—
169#29387C5911yesmaximal, characteristic, direct product factor, Sylow
170C22×C59—41no—
171C22×C59—42no—
172C22×C59—41no—
173C22×C59—42no—
174C22×C59—82no—
175C22×C59#52511yescharacteristic
176C22×C59#55312yes—
177C4×C59—42no—
178C4×C59—41no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—42no—
182C4×C59—82no—
183C4×C59#52511yescharacteristic
184C4×C59#53511yescharacteristic
185C4×C59#55112yes—
186#2956C2×C5911yescharacteristic, complemented
187#2923C2×C5911yescharacteristic, complemented
188#2103C2×C5911yescharacteristic, complemented
189#2098C2×C5911yescharacteristic, complemented
190#2053C2×C5911yescharacteristic, complemented
191#2017C2×C5911yescharacteristic
192#1938C2×C5912yescomplemented
193#1906C2×C5912yescomplemented
194#1881C2×C5912yescomplemented
195#1868C2×C5912yescomplemented
196#1841C2×C5911yescharacteristic, complemented
197C2×C59—21no—
198C2×C59—22no—
199C2×C59—81no—
200C2×C59—82no—
201C2×C59#259811yescharacteristic
202#575C22×C5911yescharacteristic
203#575C22×C5912yes—
204#568C22×C5912yes—
205C4×#41C22×C5911yescharacteristic
206#444—22no—
207#443—22no—
208#433—22no—
209#432—22no—
210#430C22×C5911yescharacteristic
211#424C22×C5911yescharacteristic
212#424C22×C5911yescharacteristic
213#424C22×C5912yes—
214#421C22×C5912yes—
215C2×#104C22×C5912yes—
216#416C22×C5912yes—
217#410C22×C5912yes—
218#408C22×C5911yescharacteristic
219#408C22×C5911yescharacteristic
220#408C22×C5912yes—
221C4×M16C22×C5911yescharacteristic
222C2×#97C22×C5911yescharacteristic
223#344C22×C5912yes—
224#344C22×C5912yes—
225#341C22×C5912yes—
226#339C22×C5912yes—
227#338C22×C5911yescharacteristic
228H(3,ℤ/4)C22×C5911yescharacteristic
229C59#2938711yescharacteristic, direct product factor, Sylow
230C2×#41C23×C5911yescharacteristic
231C2×#41C23×C5912yes—
232#137—22no—
233#137—22no—
234#137—22no—
235AGL(1,ℤ/8)—22no—
236AGL(1,ℤ/8)—22no—
237AGL(1,ℤ/8)—22no—
238#135—22no—
239#135—42no—
240#131—24no—
241#131—42no—
242C2×M16—42no—
243C2×M16C23×C5912yes—
244C2×M16C23×C5912yes—
245C2×M16C23×C5911yescharacteristic
246C2×M16C23×C5911yescharacteristic
247C22×C8C23×C5911yescharacteristic
248C22×C8C23×C5911yescharacteristic
249C4×Q8—21no—
250C4×D4—21no—
251C4×D4—22no—
252#117—21no—
253#117C23×C5912yes—
254#117C23×C5911yescharacteristic
255C2×C42—21no—
256C2×C42C23×C5911yescharacteristic
257#108—22no—
258C4⋊C8—22no—
259C4⋊C8—22no—
260C4⋊C8—42no—
261#104—22no—
262#104—22no—
263#104—42no—
264#103—22no—
265#102—22no—
266#99—24no—
267C22⋊C8—22no—
268C22⋊C8—22no—
269C22⋊C8—42no—
270#97—21no—
271#97—21no—
272#97D4×C5912yes—
273C4×C8D4×C5912yes—
274#41—22no—
275#41—22no—
276#41—22no—
277#41—22no—
278#41—22no—
279#41—22no—
280C2×Q8#41×C5912yes—
281C2×Q8#41×C5911yescharacteristic
282C2×D4—22no—
283C2×D4—21no—
284C2×D4#41×C5912yes—
285C2×D4#41×C5911yescharacteristic
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—22no—
290C22×C4C24×C5911yescharacteristic
291Q16—22no—
292Q16—42no—
293SD16—24no—
294SD16—42no—
295SD16—42no—
296D8—22no—
297D8—42no—
298M16—22no—
299M16—22no—
300M16—22no—
301M16—22no—
302M16—22no—
303M16—22no—
304M16—44no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—44no—
312C2×C8C2×D4×C5912yes—
313C2×C8C2×D4×C5912yes—
314C4⋊C4—22no—
315C4⋊C4—21no—
316C4⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4#41×C5912yes—
320C42—22no—
321C42—21no—
322C42—21no—
323C42—22no—
324C42C2×D4×C5911yescharacteristic
325C42C2×D4×C5911yescharacteristic
326C23—21no—
327C23—22no—
328C23C2×#41×C5911yescharacteristic
329Q8—22no—
330Q8—22no—
331Q8—22no—
332D4—22no—
333D4—22no—
334D4—22no—
335D4—42no—
336D4—42no—
337D4—42no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4C22×D4×C5911yescharacteristic
351C2×C4C2×#41×C5912yes—
352C2×C4C2×#41×C5911yescharacteristic
353C2×C4H(5,𝔽2)×C5912yes—
354C8—22no—
355C8—22no—
356C8—41no—
357C8—41no—
358C8—42no—
359C8—42no—
360C22—41no—
361C22—42no—
362C22—41no—
363C22—42no—
364C22—82no—
365C22C59×#52511yescharacteristic
366C22C59×#55312yes—
367C4—41no—
368C4—42no—
369C4—41no—
370C4—41no—
371C4—42no—
372C4—82no—
373C4C59×#52511yescharacteristic
374C4C59×#53511yescharacteristic
375C4C59×#55112yes—
376C2—21no—
377C2—22no—
378C2—81no—
379C2—82no—
380C2C59×#259811yescharacteristic
subgroupG/H
centerC4×C59#535
commutator, Frattini, cosocleC22×C4C24×C59
socleC2×C59#2598
prime radicalC59×#2017C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C59 ◁ C22×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#2956C2semidirect
2. C59×#2923C2semidirect
3. C59×#2103C2semidirect
4. C59×#2098C2semidirect
5. C59×#2053C2semidirect
7. C59×#1938C2semidirect
8. C59×#1906C2semidirect
9. C59×#1881C2semidirect
10. C59×#1868C2semidirect
11. C59×#1841C2semidirect
169. #29387C59direct (N × H)
186. #2956C2×C59semidirect
187. #2923C2×C59semidirect
188. #2103C2×C59semidirect
189. #2098C2×C59semidirect
190. #2053C2×C59semidirect
192. #1938C2×C59semidirect
193. #1906C2×C59semidirect
194. #1881C2×C59semidirect
195. #1868C2×C59semidirect
196. #1841C2×C59semidirect
229. C59#29387direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#29562
C59×#29232
C59×#21032
C59×#20982
C59×#20532
C59×#20172
C59×#19382
C59×#19062
C59×#18812
C59×#18682
C59×#18412
#2938759