Finite Group Databasebeta

← C2×C59×#2045 #28435626

Subgroups — C2×C59×#2045 #28435626

Order 15104.

1586 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D8×C59C211yesmaximal, characteristic
2C2×C59×#424C211yesmaximal, characteristic, complemented
3C2×C59×#418C212yesmaximal, complemented
4C22×#100×C59C212yesmaximal, complemented
5C59×#2045C218yesmaximal, direct product factor
6C2×C59×#341C211yesmaximal, characteristic, complemented
7C23×D4×C59C2212yes—
8C22×D8×C59—28no—
9C22×D8×C59—22no—
10C22×D8×C59—22no—
11C22×D8×C59C2214yes—
12C22×M16×C59C2212yes—
13C22×M16×C59C2211yescharacteristic
14C23×C8×C59C2211yescharacteristic
15C2×#117×C59C2211yescharacteristic
16C59×#424—22no—
17C59×#424C2214yescomplemented
18C2×C4⋊C8×C59—22no—
19C59×#418—24no—
20C59×#418C2218yescomplemented
21C2×#102×C59—24no—
22C2×#100×C59—28no—
23C2×#100×C59C2218yescomplemented
24C59×#341C2214yescomplemented
25C25×C59—22no—
26C22×D4×C59—22no—
27C22×D4×C59—22no—
28C22×D4×C59—24no—
29C22×D4×C59—22no—
30C22×D4×C59—22no—
31C22×D4×C59—24no—
32C22×D4×C59—22no—
33C22×D4×C59—24no—
34C22×D4×C59D418yes—
35C22×D4×C59C2314yes—
36C23×C4×C59C2311yescharacteristic
37C2×D8×C59—216no—
38C2×D8×C59—216no—
39C2×D8×C59—216no—
40C2×D8×C59—28no—
41C2×M16×C59—22no—
42C2×M16×C59—21no—
43C2×M16×C59—24no—
44C2×M16×C59—24no—
45C2×M16×C59—24no—
46C2×M16×C59C2314yes—
47C2×M16×C59C2312yes—
48C22×C8×C59—24no—
49C22×C8×C59—22no—
50C22×C8×C59—21no—
51C22×C8×C59D412yes—
52C22×C8×C59D412yes—
53C22×C8×C59C2312yes—
54#117×C59—21no—
55#117×C59—21no—
56#117×C59D412yes—
57#117×C59C2312yes—
58C2×C4⋊C4×C59D412yes—
59C2×C22⋊C4×C59—21no—
60C2×C42×C59—21no—
61C4⋊C8×C59—28no—
62#102×C59—216no—
63#100×C59—216no—
64C24×C59—28no—
65C24×C59—24no—
66C24×C59—42no—
67C24×C59—42no—
68C24×C59—44no—
69C24×C59—88no—
70C24×C59#4111yescharacteristic
71C2×D4×C59—28no—
72C2×D4×C59—28no—
73C2×D4×C59—28no—
74C2×D4×C59—28no—
75C2×D4×C59—28no—
76C2×D4×C59—24no—
77C2×D4×C59—24no—
78C2×D4×C59—24no—
79C2×D4×C59—24no—
80C2×D4×C59—24no—
81C2×D4×C59—44no—
82C2×D4×C59—44no—
83C2×D4×C59—42no—
84C2×D4×C59—42no—
85C2×D4×C59—44no—
86C2×D4×C59—44no—
87C2×D4×C59—44no—
88C2×D4×C59C2×D418yes—
89C22×C4×C59—22no—
90C22×C4×C59C2×D414yes—
91C22×C4×C59C2×D411yescharacteristic
92C22×C4×C59C2×D411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59#4111yescharacteristic
96C22×C4×C59#4114yes—
97C22×C4×C59C2411yescharacteristic
98D8×C59—232no—
99M16×C59—24no—
100M16×C59—24no—
101M16×C59—24no—
102M16×C59—42no—
103M16×C59—44no—
104C2×C8×C59—24no—
105C2×C8×C59—24no—
106C2×C8×C59—24no—
107C2×C8×C59—24no—
108C2×C8×C59—22no—
109C2×C8×C59—42no—
110C2×C8×C59—44no—
111C2×C8×C59C2×D414yes—
112C4⋊C4×C59—22no—
113C4⋊C4×C59C2×D414yes—
114C22⋊C4×C59—22no—
115C22⋊C4×C59—22no—
116C42×C59—22no—
117C42×C59—22no—
118C23×C59—24no—
119C23×C59—28no—
120C23×C59—44no—
121C23×C59—44no—
122C23×C59—48no—
123C23×C59—48no—
124C23×C59—88no—
125C23×C59—816no—
126C23×C59—88no—
127C23×C59—816no—
128C23×C59—88no—
129C23×C59#12111yescharacteristic
130C23×C59#12111yescharacteristic
131C23×C59#12314yes—
132C23×C59C2×#4111yescharacteristic
133D4×C59—28no—
134D4×C59—28no—
135D4×C59—44no—
136D4×C59—44no—
137D4×C59—48no—
138D4×C59—48no—
139C2×C4×C59—24no—
140C2×C4×C59—44no—
141C2×C4×C59#12012yes—
142C2×C4×C59#12012yes—
143C2×C4×C59#12114yes—
144C2×C4×C59#12114yes—
145C2×C4×C59#12111yescharacteristic
146C2×C4×C59#12111yescharacteristic
147C2×C4×C59#12314yes—
148C2×C4×C59#12412yes—
149C2×C4×C59#12412yes—
150C2×C4×C59C22×D412yes—
151C2×C4×C59C22×D411yescharacteristic
152C2×C4×C59C22×D411yescharacteristic
153C2×C4×C59C2×#4112yes—
154C8×C59—24no—
155C8×C59—42no—
156C8×C59—44no—
157C2×#2045C5911yesmaximal, characteristic, direct product factor, Sylow
158C22×C59—22no—
159C22×C59—22no—
160C22×C59—28no—
161C22×C59—48no—
162C22×C59—88no—
163C22×C59—88no—
164C22×C59—816no—
165C22×C59—88no—
166C22×C59—816no—
167C22×C59#39412yes—
168C22×C59#39412yes—
169C22×C59#47214yes—
170C22×C59C2×#12111yescharacteristic
171C22×C59C2×#12312yes—
172C4×C59—44no—
173C4×C59#39412yes—
174C4×C59#39412yes—
175C4×C59C2×#12011yescharacteristic
176C4×C59C2×#12112yes—
177C4×C59C2×#12411yescharacteristic
178C23×D8C2×C5911yescharacteristic
179C2×#424C2×C5911yescharacteristic, complemented
180C2×#418C2×C5912yescomplemented
181C22×#100C2×C5912yescomplemented
182#2045C2×C5918yesdirect product factor
183C2×#341C2×C5911yescharacteristic, complemented
184C2×C59—22no—
185C2×C59—22no—
186C2×C59—88no—
187C2×C59#204514yesdirect product factor
188C2×C59C2×#39411yescharacteristic
189C2×C59C2×#47212yes—
190C23×D4C22×C5912yes—
191C22×D8—28no—
192C22×D8—22no—
193C22×D8—22no—
194C22×D8C22×C5914yes—
195C22×M16C22×C5911yescharacteristic
196C22×M16C22×C5912yes—
197C23×C8C22×C5911yescharacteristic
198C2×#117C22×C5911yescharacteristic
199#424—22no—
200#424C22×C5914yescomplemented
201C2×C4⋊C8—22no—
202#418—24no—
203#418C22×C5918yescomplemented
204C2×#102—24no—
205C2×#100—28no—
206C2×#100C22×C5918yescomplemented
207#341C22×C5914yescomplemented
208C59C2×#204511yescharacteristic, direct product factor, Sylow
209C25—22no—
210C22×D4—24no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—24no—
216C22×D4—22no—
217C22×D4—24no—
218C22×D4D4×C5918yes—
219C22×D4C23×C5914yes—
220C23×C4C23×C5911yescharacteristic
221C2×D8—216no—
222C2×D8—216no—
223C2×D8—216no—
224C2×D8—28no—
225C2×M16—22no—
226C2×M16—21no—
227C2×M16—24no—
228C2×M16—24no—
229C2×M16—24no—
230C2×M16C23×C5914yes—
231C2×M16C23×C5912yes—
232C22×C8—24no—
233C22×C8—22no—
234C22×C8—21no—
235C22×C8D4×C5912yes—
236C22×C8D4×C5912yes—
237C22×C8C23×C5912yes—
238#117—21no—
239#117—21no—
240#117D4×C5912yes—
241#117C23×C5912yes—
242C2×C4⋊C4D4×C5912yes—
243C2×C22⋊C4—21no—
244C2×C42—21no—
245C4⋊C8—28no—
246#102—216no—
247#100—216no—
248C24—28no—
249C24—24no—
250C24—42no—
251C24—42no—
252C24—44no—
253C24—88no—
254C24#41×C5911yescharacteristic
255C2×D4—28no—
256C2×D4—28no—
257C2×D4—28no—
258C2×D4—28no—
259C2×D4—28no—
260C2×D4—24no—
261C2×D4—24no—
262C2×D4—24no—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—44no—
268C2×D4—44no—
269C2×D4—44no—
270C2×D4—44no—
271C2×D4—44no—
272C2×D4C2×D4×C5918yes—
273C22×C4—22no—
274C22×C4C2×D4×C5914yes—
275C22×C4C2×D4×C5911yescharacteristic
276C22×C4C2×D4×C5911yescharacteristic
277C22×C4C2×D4×C5911yescharacteristic
278C22×C4C2×D4×C5911yescharacteristic
279C22×C4#41×C5911yescharacteristic
280C22×C4#41×C5914yes—
281C22×C4C24×C5911yescharacteristic
282D8—232no—
283M16—24no—
284M16—24no—
285M16—24no—
286M16—42no—
287M16—44no—
288C2×C8—24no—
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—24no—
292C2×C8—22no—
293C2×C8—42no—
294C2×C8—44no—
295C2×C8C2×D4×C5914yes—
296C4⋊C4—22no—
297C4⋊C4C2×D4×C5914yes—
298C22⋊C4—22no—
299C22⋊C4—22no—
300C42—22no—
301C42—22no—
302C23—24no—
303C23—28no—
304C23—48no—
305C23—48no—
306C23—44no—
307C23—44no—
308C23—88no—
309C23—816no—
310C23—88no—
311C23—816no—
312C23—88no—
313C23#121×C5911yescharacteristic
314C23#121×C5911yescharacteristic
315C23#123×C5914yes—
316C23C2×#41×C5911yescharacteristic
317D4—28no—
318D4—28no—
319D4—48no—
320D4—48no—
321D4—44no—
322D4—44no—
323C2×C4—24no—
324C2×C4—44no—
325C2×C4#120×C5912yes—
326C2×C4#120×C5912yes—
327C2×C4#121×C5911yescharacteristic
328C2×C4#121×C5911yescharacteristic
329C2×C4#121×C5914yes—
330C2×C4#121×C5914yes—
331C2×C4#123×C5914yes—
332C2×C4#124×C5912yes—
333C2×C4#124×C5912yes—
334C2×C4C22×D4×C5912yes—
335C2×C4C22×D4×C5911yescharacteristic
336C2×C4C22×D4×C5911yescharacteristic
337C2×C4C2×#41×C5912yes—
338C8—24no—
339C8—42no—
340C8—44no—
341C22—22no—
342C22—22no—
343C22—28no—
344C22—48no—
345C22—88no—
346C22—816no—
347C22—88no—
348C22—88no—
349C22—816no—
350C22C59×#39412yes—
351C22C59×#39412yes—
352C22C59×#47214yes—
353C22C2×#121×C5911yescharacteristic
354C22C2×#123×C5912yes—
355C4—44no—
356C4C59×#39412yes—
357C4C59×#39412yes—
358C4C2×#120×C5911yescharacteristic
359C4C2×#121×C5912yes—
360C4C2×#124×C5911yescharacteristic
361C2—22no—
362C2—22no—
363C2—88no—
364C2C59×#204514yesdirect product factor
365C2C2×C59×#39411yescharacteristic
366C2C2×C59×#47212yes—
subgroupG/H
center, socleC23×C59#121
commutator, Frattini, cosocleC22×C4C24×C59
prime radicalC23×D8×C59C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C59 ◁ C23×C4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C59×#424C2semidirect
3. C2×C59×#418C2semidirect
4. C22×#100×C59C2semidirect
5. C59×#2045C2direct (N × H)
6. C2×C59×#341C2semidirect
17. C59×#424C22semidirect
20. C59×#418C22semidirect
23. C2×#100×C59C22semidirect
24. C59×#341C22semidirect
157. C2×#2045C59direct (N × H)
179. C2×#424C2×C59semidirect
180. C2×#418C2×C59semidirect
181. C22×#100C2×C59semidirect
182. #2045C2×C59direct (N × H)
183. C2×#341C2×C59semidirect
187. C2×C59#2045direct (N × H)
200. #424C22×C59semidirect
203. #418C22×C59semidirect
206. C2×#100C22×C59semidirect
207. #341C22×C59semidirect
208. C59C2×#2045direct (N × H)
364. C2C59×#2045direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D8×C592
C2×C59×#4242
C2×C59×#4182
C22×#100×C592
C59×#20452
C2×C59×#3412
C2×#204559