Finite Group Databasebeta

← C2×C5×#5831 #14482799

Subgroups — C2×C5×#5831 #14482799

Order 1920.

3240 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C22×C5×D3×Q8C211yesmaximal, characteristic, complemented
3C5×#5831C2116yesmaximal, direct product factor
4C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
5C2×C5×#938C213yesmaximal, complemented
6C2×C5×#936C213yesmaximal, complemented
7C2×C4×C5×#67C213yesmaximal, complemented
8C2×C5×#924C213yesmaximal, complemented
9C2×C5×#548—31nomaximal, Hall
10C2×C3×C5×#41—28no—
11C2×C3×C5×#41C2218yescomplemented
12C22×C3×C5×Q8C2211yescharacteristic
13C22×C3×C5×D4C2213yes—
14C23×C3×C4×C5C2213yes—
15C22×C5×#67C2213yes—
16C2×C5×D3×Q8—28no—
17C2×C5×D3×Q8C2218yescomplemented
18C22×C4×C5×D3C2213yes—
19C22×C5×Dic6C2213yes—
20C2×C5×#217C2216yes—
21C2×C5×#217C2213yes—
22C5×Q8×Dic3C2218yescomplemented
23C5×#938C22124yescomplemented
24C5×#936C22124yescomplemented
25C4×C5×#67C22124yescomplemented
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×C4⋊Dic3C2213yes—
28C5×#924C22124yescomplemented
29C2×C5×Dic3⋊C4C2213yes—
30C2×C4×C5×Dic3C2213yes—
31C2×#5831C511yesmaximal, characteristic, direct product factor, Hall
32C22×C5×#41D311yescharacteristic, complemented
33C23×C5×Q8—31no—
34C5×#548—316no—
35C2×C5×#124—33no—
36C2×C5×C22⋊Q8—33no—
37C2×C5×#121—33no—
38C2×C4×C5×Q8—31no—
39C2×C4×C5×D4—33no—
40C24×C3×C5C2313yes—
41C23×C5×D3C2311yescharacteristic
42C3×C5×#41—232no—
43C2×C3×C5×Q8D418yescomplemented
44C2×C3×C5×Q8C2314yes—
45C2×C3×C5×D4—212no—
46C2×C3×C5×D4C23112yes—
47C22×C3×C4×C5—212no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×C4×C5C23112yes—
50C22×C3×C4×C5C2313yes—
51C2×C5×#67—212no—
52C2×C5×#67C23112yes—
53C22×C5×Dic3C2311yescharacteristic
54C22×C5×Dic3C2313yes—
55C22×C5×Dic3C2313yes—
56C5×D3×Q8—232no—
57C2×C4×C5×D3—212no—
58C2×C4×C5×D3C23112yes—
59C2×C5×Dic6—212no—
60C2×C5×Dic6C23112yes—
61C5×#217C23124yes—
62C5×#217C23112yes—
63C5×(C2×D3)⋊C4C2314yes—
64C5×C4⋊Dic3C23112yes—
65C5×Dic3⋊C4C23112yes—
66C4×C5×Dic3C23112yes—
67C22×C3×#41C2×C511yescharacteristic, complemented
68C22×D3×Q8C2×C511yescharacteristic, complemented
69#5831C2×C5116yesdirect product factor
70C2×Q8×Dic3C2×C511yescharacteristic, complemented
71C2×#938C2×C513yescomplemented
72C2×#936C2×C513yescomplemented
73C2×C4×#67C2×C513yescomplemented
74C2×#924C2×C513yescomplemented
75C2×C5×#41—28no—
76C2×C5×#41C2×D318yescomplemented
77C22×C5×Q8—38no—
78C22×C5×Q8—33no—
79C22×C5×Q8—68no—
80C22×C5×Q8C2×D311yescharacteristic
81C22×C5×D4—33no—
82C22×C5×D4C2×D313yes—
83C23×C4×C5—33no—
84C23×C4×C5C2×D313yes—
85C5×#124—324no—
86C5×C22⋊Q8—324no—
87C5×#121—324no—
88C4×C5×Q8—38no—
89C4×C5×D4—324no—
90C2×C5×C4⋊C4—33no—
91C2×C5×C4⋊C4—33no—
92C2×C5×C22⋊C4—33no—
93C2×C5×C22⋊C4—36no—
94C2×C5×C22⋊C4—31no—
95C2×C42×C5—33no—
96C2×#548—31noSylow
97C23×C3×C5—26no—
98C23×C3×C5—26no—
99C23×C3×C5—26no—
100C23×C3×C5C2416yes—
101C23×C3×C5C2411yescharacteristic
102C22×C5×D3—22no—
103C22×C5×D3—22no—
104C22×C5×D3#4114yescomplemented
105C22×C5×D3C2412yes—
106C3×C5×Q8C2×D4116yescomplemented
107C3×C5×D4—224no—
108C2×C3×C4×C5—22no—
109C2×C3×C4×C5—224no—
110C2×C3×C4×C5C2×D4112yes—
111C2×C3×C4×C5C2412yes—
112C2×C3×C4×C5C2416yes—
113C5×#67—224no—
114C2×C5×Dic3—26no—
115C2×C5×Dic3—26no—
116C2×C5×Dic3—22no—
117C2×C5×Dic3C2412yes—
118C2×C5×Dic3C2416yes—
119C2×C5×Dic3C2416yes—
120C4×C5×D3—224no—
121C5×Dic6—224no—
122C2×C3×#41—28no—
123C2×C3×#41C22×C518yescomplemented
124C22×C3×Q8C22×C511yescharacteristic
125C22×C3×D4C22×C513yes—
126C23×C3×C4C22×C513yes—
127C22×#67C22×C513yes—
128C2×D3×Q8—28no—
129C2×D3×Q8C22×C518yescomplemented
130C22×C4×D3C22×C513yes—
131C22×Dic6C22×C513yes—
132C2×#217C22×C516yes—
133C2×#217C22×C513yes—
134Q8×Dic3C22×C518yescomplemented
135#938C22×C5124yescomplemented
136#936C22×C5124yescomplemented
137C4×#67C22×C5124yescomplemented
138C2×(C2×D3)⋊C4C22×C511yescharacteristic
139C2×C4⋊Dic3C22×C513yes—
140#924C22×C5124yescomplemented
141C2×Dic3⋊C4C22×C513yes—
142C2×C4×Dic3C22×C513yes—
143C24×C5—31no—
144C24×C5C22×D313yes—
145C5×#41—232no—
146C2×C5×Q8—312no—
147C2×C5×Q8—632no—
148C2×C5×Q8—612no—
149C2×C5×Q8#6718yescomplemented
150C2×C5×Q8C22×D314yes—
151C2×C5×D4—212no—
152C2×C5×D4—312no—
153C2×C5×D4—612no—
154C2×C5×D4C22×D3112yes—
155C22×C4×C5—212no—
156C22×C4×C5—31no—
157C22×C4×C5—33no—
158C22×C4×C5—33no—
159C22×C4×C5—312no—
160C22×C4×C5—612no—
161C22×C4×C5C22×D3112yes—
162C22×C4×C5C22×D311yescharacteristic
163C22×C4×C5C22×D313yes—
164C5×C4⋊C4—312no—
165C5×C4⋊C4—312no—
166C5×C22⋊C4—312no—
167C5×C22⋊C4—324no—
168C5×C22⋊C4—34no—
169C42×C5—312no—
170C22×#41C5×D311yescharacteristic, complemented
171C23×Q8—31no—
172#548—316no—
173C2×#124—33no—
174C2×C22⋊Q8—33no—
175C2×#121—33no—
176C2×C4×Q8—31no—
177C2×C4×D4—33no—
178C22×C3×C5—26no—
179C22×C3×C5—26no—
180C22×C3×C5—26no—
181C22×C3×C5—412no—
182C22×C3×C5C22×D412yes—
183C22×C3×C5C2×#4112yes—
184C22×C3×C52−1+412yes—
185C22×C3×C5C2511yescharacteristic
186C2×C5×D3—28no—
187C2×C5×D3—22no—
188C2×C5×D3—22no—
189C2×C5×D3C2×#4114yescomplemented
190C3×C4×C5—22no—
191C3×C4×C5C22×D4112yes—
192C5×Dic3—26no—
193C5×Dic3—26no—
194C5×Dic3—22no—
195C24×C3C23×C513yes—
196C23×D3C23×C511yescharacteristic
197C3×#41—232no—
198C2×C3×Q8C5×D418yescomplemented
199C2×C3×Q8C23×C514yes—
200C2×C3×D4—212no—
201C2×C3×D4C23×C5112yes—
202C22×C3×C4—212no—
203C22×C3×C4C23×C511yescharacteristic
204C22×C3×C4C23×C5112yes—
205C22×C3×C4C23×C513yes—
206C2×#67—212no—
207C2×#67C23×C5112yes—
208C22×Dic3C23×C511yescharacteristic
209C22×Dic3C23×C513yes—
210C22×Dic3C23×C513yes—
211D3×Q8—232no—
212C2×C4×D3—212no—
213C2×C4×D3C23×C5112yes—
214C2×Dic6—212no—
215C2×Dic6C23×C5112yes—
216#217C23×C5124yes—
217#217C23×C5112yes—
218(C2×D3)⋊C4C23×C514yes—
219C4⋊Dic3C23×C5112yes—
220Dic3⋊C4C23×C5112yes—
221C4×Dic3C23×C5112yes—
222C23×C5—26no—
223C23×C5—26no—
224C23×C5—26no—
225C23×C5—34no—
226C23×C5—32no—
227C23×C5—62no—
228C23×C5—62no—
229C23×C5C23×D316yes—
230C23×C5C23×D311yescharacteristic
231C5×Q8—624no—
232C5×Q8C2×#67116yescomplemented
233C5×D4—224no—
234C5×D4—624no—
235C2×C4×C5—22no—
236C2×C4×C5—224no—
237C2×C4×C5—32no—
238C2×C4×C5—36no—
239C2×C4×C5—36no—
240C2×C4×C5—66no—
241C2×C4×C5—62no—
242C2×C4×C5—66no—
243C2×C4×C5—624no—
244C2×C4×C5C2×#67112yes—
245C2×C4×C5C23×D312yes—
246C2×C4×C5C23×D316yes—
247C2×#41—28no—
248C2×#41C2×C5×D318yescomplemented
249C22×Q8—38no—
250C22×Q8—33no—
251C22×Q8—68no—
252C22×Q8C2×C5×D311yescharacteristic
253C22×D4—33no—
254C22×D4C2×C5×D313yes—
255C23×C4—33no—
256C23×C4C2×C5×D313yes—
257#124—324no—
258C22⋊Q8—324no—
259#121—324no—
260C4×Q8—38no—
261C4×D4—324no—
262C2×C4⋊C4—33no—
263C2×C4⋊C4—33no—
264C2×C22⋊C4—33no—
265C2×C22⋊C4—36no—
266C2×C22⋊C4—31no—
267C2×C42—33no—
268C2×C3×C5—46no—
269C2×C3×C5#54814yescomplemented
270C2×C3×C5C23×D411yescharacteristic
271C2×C3×C5C22×#4111yescharacteristic
272C2×C3×C5C2×2−1+411yescharacteristic
273C5×D3—24no—
274C23×C3—26no—
275C23×C3—26no—
276C23×C3—26no—
277C23×C3C24×C516yes—
278C23×C3C24×C511yescharacteristic
279C22×D3—22no—
280C22×D3—22no—
281C22×D3C5×#4114yescomplemented
282C22×D3C24×C512yes—
283C3×Q8C2×C5×D4116yescomplemented
284C3×D4—224no—
285C2×C3×C4—22no—
286C2×C3×C4—224no—
287C2×C3×C4C2×C5×D4112yes—
288C2×C3×C4C24×C512yes—
289C2×C3×C4C24×C516yes—
290#67—224no—
291C2×Dic3—26no—
292C2×Dic3—26no—
293C2×Dic3—22no—
294C2×Dic3C24×C512yes—
295C2×Dic3C24×C516yes—
296C2×Dic3C24×C516yes—
297C4×D3—224no—
298Dic6—224no—
299C22×C5—26no—
300C22×C5—26no—
301C22×C5—26no—
302C22×C5—34no—
303C22×C5—412no—
304C22×C5—62no—
305C22×C5—62no—
306C22×C5—68no—
307C22×C5D3×#4112yes—
308C22×C5#101012yes—
309C22×C5C22×#6712yes—
310C22×C5C24×D311yescharacteristic
311C4×C5—22no—
312C4×C5—66no—
313C4×C5—62no—
314C4×C5—66no—
315C4×C5C22×#67112yes—
316C24—31no—
317C24C22×C5×D313yes—
318#41—232no—
319C2×Q8—312no—
320C2×Q8—632no—
321C2×Q8—612no—
322C2×Q8C5×#6718yescomplemented
323C2×Q8C22×C5×D314yes—
324C2×D4—212no—
325C2×D4—312no—
326C2×D4—612no—
327C2×D4C22×C5×D3112yes—
328C22×C4—212no—
329C22×C4—31no—
330C22×C4—33no—
331C22×C4—33no—
332C22×C4—312no—
333C22×C4—612no—
334C22×C4C22×C5×D311yescharacteristic
335C22×C4C22×C5×D3112yes—
336C22×C4C22×C5×D313yes—
337C4⋊C4—312no—
338C4⋊C4—312no—
339C22⋊C4—312no—
340C22⋊C4—324no—
341C22⋊C4—34no—
342C42—312no—
343C3×C5C2×#54811yescharacteristic, complemented, Hall
344C22×C3—26no—
345C22×C3—26no—
346C22×C3—26no—
347C22×C3—412no—
348C22×C3C22×C5×D412yes—
349C22×C3C2×C5×#4112yes—
350C22×C3C5×2−1+412yes—
351C22×C3C25×C511yescharacteristic
352C2×D3—28no—
353C2×D3—22no—
354C2×D3—22no—
355C2×D3C2×C5×#4114yescomplemented
356C3×C4—22no—
357C3×C4C22×C5×D4112yes—
358Dic3—26no—
359Dic3—26no—
360Dic3—22no—
361C2×C5—46no—
362C2×C5—64no—
363C2×C5#583114yesdirect product factor
364C2×C5C2×D3×#4111yescharacteristic
365C2×C5C2×#101011yescharacteristic
366C2×C5C23×#6711yescharacteristic
367C23—26no—
368C23—26no—
369C23—26no—
370C23—34no—
371C23—32no—
372C23—62no—
373C23—62no—
374C23C23×C5×D316yes—
375C23C23×C5×D311yescharacteristic
376Q8—624no—
377Q8C2×C5×#67116yescomplemented
378D4—224no—
379D4—624no—
380C2×C4—22no—
381C2×C4—224no—
382C2×C4—32no—
383C2×C4—36no—
384C2×C4—36no—
385C2×C4—66no—
386C2×C4—62no—
387C2×C4—66no—
388C2×C4—624no—
389C2×C4C2×C5×#67112yes—
390C2×C4C23×C5×D312yes—
391C2×C4C23×C5×D316yes—
392C2×C3—46no—
393C2×C3C5×#54814yescomplemented
394C2×C3C23×C5×D411yescharacteristic
395C2×C3C22×C5×#4111yescharacteristic
396C2×C3C2×C5×2−1+411yescharacteristic
397D3—24no—
398C5C2×#583111yescharacteristic, direct product factor, Sylow
399C22—26no—
400C22—26no—
401C22—26no—
402C22—34no—
403C22—412no—
404C22—62no—
405C22—62no—
406C22—68no—
407C22C5×D3×#4112yes—
408C22C5×#101012yes—
409C22C22×C5×#6712yes—
410C22C24×C5×D311yescharacteristic
411C4—22no—
412C4—66no—
413C4—62no—
414C4—66no—
415C4C22×C5×#67112yes—
416C3C2×C5×#54811yescharacteristic, complemented, Sylow
417C2—46no—
418C2—64no—
419C2C5×#583114yesdirect product factor
420C2C2×C5×D3×#4111yescharacteristic
421C2C2×C5×#101011yescharacteristic
422C2C23×C5×#6711yescharacteristic
subgroupG/H
centerC23×C5C23×D3
commutator, cosocleC22×C3C25×C5
FrattiniC22C24×C5×D3
FittingC22×C3×C5×#41C2
socleC23×C3×C5C24
hypercenterC22×C5×#41D3
hypocenterC3C2×C5×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C5×#41

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C22×C5×D3×Q8C2semidirect
3. C5×#5831C2direct (N × H)
4. C2×C5×Q8×Dic3C2semidirect
5. C2×C5×#938C2semidirect
6. C2×C5×#936C2semidirect
7. C2×C4×C5×#67C2semidirect
8. C2×C5×#924C2semidirect
11. C2×C3×C5×#41C22semidirect
17. C2×C5×D3×Q8C22semidirect
22. C5×Q8×Dic3C22semidirect
23. C5×#938C22semidirect
24. C5×#936C22semidirect
25. C4×C5×#67C22semidirect
28. C5×#924C22semidirect
31. C2×#5831C5direct (N × H)
32. C22×C5×#41D3semidirect
43. C2×C3×C5×Q8D4semidirect
67. C22×C3×#41C2×C5semidirect
68. C22×D3×Q8C2×C5semidirect
69. #5831C2×C5direct (N × H)
70. C2×Q8×Dic3C2×C5semidirect
71. C2×#938C2×C5semidirect
72. C2×#936C2×C5semidirect
73. C2×C4×#67C2×C5semidirect
74. C2×#924C2×C5semidirect
76. C2×C5×#41C2×D3semidirect
104. C22×C5×D3#41semidirect
106. C3×C5×Q8C2×D4semidirect
123. C2×C3×#41C22×C5semidirect
129. C2×D3×Q8C22×C5semidirect
134. Q8×Dic3C22×C5semidirect
135. #938C22×C5semidirect
136. #936C22×C5semidirect
137. C4×#67C22×C5semidirect
140. #924C22×C5semidirect
149. C2×C5×Q8#67semidirect
170. C22×#41C5×D3semidirect
189. C2×C5×D3C2×#41semidirect
198. C2×C3×Q8C5×D4semidirect
232. C5×Q8C2×#67semidirect
248. C2×#41C2×C5×D3semidirect
269. C2×C3×C5#548semidirect
281. C22×D3C5×#41semidirect
283. C3×Q8C2×C5×D4semidirect
322. C2×Q8C5×#67semidirect
343. C3×C5C2×#548semidirect
355. C2×D3C2×C5×#41semidirect
363. C2×C5#5831direct (N × H)
377. Q8C2×C5×#67semidirect
393. C2×C3C5×#548semidirect
398. C5C2×#5831direct (N × H)
416. C3C2×C5×#548semidirect
419. C2C5×#5831direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C22×C5×D3×Q82
C5×#58312
C2×C5×Q8×Dic32
C2×C5×#9382
C2×C5×#9362
C2×C4×C5×#672
C2×C5×#9242
C2×C5×#5483
C2×#58315