Finite Group Databasebeta

← C2×#11749080 #14425971

Subgroups — C2×#11749080 #14425971

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6715C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#687C211yesmaximal, characteristic, complemented
4C2×#91374C211yesmaximal, characteristic, complemented
5#11749080C218yesmaximal, direct product factor
6C2×Dic3⋊#168C211yesmaximal, characteristic, complemented
7C2×#90970C211yesmaximal, characteristic, complemented
8C2×#90969C211yesmaximal, characteristic, complemented
9C2×#65305—31nomaximal, Hall
10C22×C3×C5×D4C2211yescharacteristic
11C22×D60C2211yescharacteristic
12C23×C5×Dic3—21no—
13C22×C3×Dic10C2211yescharacteristic
14C2×#6715—24no—
15C2×#6715C2214yes—
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×#217—21no—
18C5×D4×Dic3—22no—
19C5×D4×Dic3C2214yescomplemented
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×#687—24no—
23C2×C3×#687C2214yescomplemented
24C22×C3×#168C2211yescharacteristic
25C2×#6667—21no—
26C2×#6667—21no—
27#91374—22no—
28#91374C2214yescomplemented
29Dic3⋊#168C2214yescomplemented
30#90970C2214yescomplemented
31#90969C2214yescomplemented
32C2×#5165—51nomaximal, Hall
33C2×C4×C5×D4—31no—
34C22×#687D311yescharacteristic, complemented
35C22×#686—31no—
36C2×#4021—31no—
37#65305—38no—
38C2×#3942—31no—
39C2×#3941—31no—
40C2×C4⋊#168—31no—
41C24×C3×C5—21no—
42C23×D15—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—22no—
45C2×C3×C5×D4D414yes—
46C2×C3×C5×D4C2312yes—
47C22×C3×C4×C5C2311yescharacteristic
48C2×D60—22no—
49C2×D60—22no—
50C2×D60—21no—
51C2×D60C2312yes—
52C22×C5×Dic3—21no—
53C22×C5×Dic3—24no—
54C22×C5×Dic3—44no—
55C22×C5×Dic3D411yescharacteristic
56C22×C5×Dic3D411yescharacteristic
57C22×C3×Dic5—21no—
58C2×C3×Dic10—22no—
59C2×C3×Dic10—22no—
60C2×C3×Dic10—21no—
61C2×C3×Dic10C2312yes—
62#6715—28no—
63C2×C3⋊#168—22no—
64C2×C3⋊#168C2312yes—
65C5×#217—24no—
66C5×C4⋊Dic3—21no—
67C5×C4⋊Dic3C2312yes—
68C4×C5×Dic3D412yes—
69C4×C5×Dic3C2312yes—
70C3×#687—28no—
71C2×C3×#168—22no—
72C2×C3×#168C2312yes—
73#6667—24no—
74#6667—24no—
75C22×C3×SD16—51no—
76C2×#947—51no—
77C2×D4×Dic3D511yescharacteristic, complemented
78C22×#213—51no—
79C2×#835—51no—
80#5165—58no—
81C2×#821—51no—
82C2×Dic3⋊C8—51no—
83C22×C5×D4C2×D311yescharacteristic
84C23×C4×C5—61no—
85C22×D20—31no—
86C22×Dic10C2×D311yescharacteristic
87C4×C5×D4—34no—
88C4×C5×D4—62no—
89C2×C5×C4⋊C4—31no—
90C2×C5×C22⋊C4—61no—
91C2×C42×C5—31no—
92C2×#687—24no—
93C2×#687C2×D314yescomplemented
94C2×#686—34no—
95C2×#686—64no—
96C2×#685—61no—
97C2×#685—61no—
98C22×#168—31no—
99C22×#168C2×D311yescharacteristic
100#4021—34no—
101#4021—62no—
102#3942—34no—
103#3941—34no—
104C4⋊#168—34no—
105C2×#463—151noSylow
106C23×C3×C5—24no—
107C23×C3×C5—22no—
108C23×C3×C5—42no—
109C23×C3×C5—42no—
110C23×C3×C5C2×D411yescharacteristic
111C22×D15—22no—
112C22×D15—42no—
113C22×D15—42no—
114C22×D15—42no—
115C3×C5×D4—24no—
116C3×C5×D4—22no—
117C3×C5×D4C2×D414yes—
118C2×C3×C4×C5C2×D411yescharacteristic
119C2×C3×C4×C5C2×D412yes—
120C2×C3×C4×C5#4112yes—
121C2×C3×C4×C5C2411yescharacteristic
122D60—22no—
123D60—22no—
124D60—42no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—48no—
129C2×C5×Dic3—42no—
130C2×C5×Dic3C2×D412yes—
131C2×C5×Dic3C2×D412yes—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—42no—
134C3×Dic10—22no—
135C3×Dic10—22no—
136C3×Dic10—42no—
137C3⋊#168—22no—
138C3×#168—22no—
139C22×C3×Q8—51no—
140C22×C3×D4C2×D511yescharacteristic
141C23×Dic3—21no—
142C22×D12—51no—
143C2×C3×SD16—54no—
144C2×C3×SD16—104no—
145C22×C3×C8—51no—
146C2×#217—21no—
147#947—54no—
148#947—102no—
149D4×Dic3—22no—
150D4×Dic3C2×D514yescomplemented
151C2×#213—54no—
152C2×#213—104no—
153C2×(C2×D3)⋊C4—101no—
154C2×(C2×D3)⋊C4—101no—
155C2×C4⋊Dic3C2×D511yescharacteristic
156C2×C4×Dic3C2×D511yescharacteristic
157C22×C3⋊C8—51no—
158#835—54no—
159#821—54no—
160Dic3⋊C8—54no—
161C24×C5—21no—
162C23×D5—61no—
163C2×C5×D4—21no—
164C2×C5×D4—22no—
165C2×C5×D4#6714yes—
166C2×C5×D4C22×D312yes—
167C22×C4×C5—31no—
168C22×C4×C5—31no—
169C22×C4×C5—64no—
170C22×C4×C5—61no—
171C22×C4×C5—124no—
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—21no—
174C2×D20—32no—
175C2×D20—62no—
176C2×D20—62no—
177C2×D20—61no—
178C2×Dic10—22no—
179C2×Dic10—22no—
180C2×Dic10—21no—
181C2×Dic10C22×D312yes—
182C5×C4⋊C4—32no—
183C5×C4⋊C4—61no—
184C5×C22⋊C4—64no—
185C42×C5—32no—
186C42×C5—32no—
187#687—28no—
188#686—68no—
189#685—64no—
190#685—64no—
191C2×#168—22no—
192C2×#168—32no—
193C2×#168—62no—
194C2×#168C22×D312yes—
195C22×SD16—51no—
196C22×D8—151no—
197C2×#124—151no—
198C2×C4×D4—31no—
199#463—158no—
200C2×C4⋊C8—151no—
201C2×#103—151no—
202C2×#102—151no—
203C22×C3×C5—24no—
204C22×C3×C5—42no—
205C22×C3×C5—42no—
206C22×C3×C5—48no—
207C22×C3×C5#12112yes—
208C22×C3×C5#13512yes—
209C22×C3×C5AGL(1,ℤ/8)12yes—
210C22×C3×C5C22×D411yescharacteristic
211C2×D15—42no—
212C2×D15—42no—
213C2×D15—42no—
214C2×D15—84no—
215C3×C4×C5#12112yes—
216C3×C4×C5C22×D411yescharacteristic
217C3×C4×C5C2×#4111yescharacteristic
218C3×Dic5—42no—
219C5×Dic3—22no—
220C5×Dic3—22no—
221C5×Dic3—42no—
222C24×C3—21no—
223C23×D3—101no—
224C2×C3×Q8—52no—
225C2×C3×Q8—101no—
226C2×C3×Q8—102no—
227C2×C3×Q8—102no—
228C2×C3×D4—22no—
229C2×C3×D4—21no—
230C2×C3×D4D2014yes—
231C2×C3×D4C22×D512yes—
232C22×C3×C4—101no—
233C22×C3×C4C22×D511yescharacteristic
234C22×Dic3—21no—
235C22×Dic3—24no—
236C22×Dic3—44no—
237C22×Dic3C22⋊D511yescharacteristic
238C22×Dic3C22⋊D511yescharacteristic
239C2×D12—52no—
240C2×D12—102no—
241C2×D12—102no—
242C2×D12—101no—
243C3×SD16—108no—
244C2×C3×C8—52no—
245C2×C3×C8—102no—
246#217—24no—
247#213—108no—
248(C2×D3)⋊C4—104no—
249(C2×D3)⋊C4—104no—
250C4⋊Dic3—21no—
251C4⋊Dic3C22×D512yes—
252C4×Dic3C22⋊D512yes—
253C4×Dic3C22×D512yes—
254C2×C3⋊C8—52no—
255C2×C3⋊C8—102no—
256C23×C5—24no—
257C23×C5—22no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5D3×D411yescharacteristic
261C22×D5—62no—
262C22×D5—122no—
263C22×D5—122no—
264C22×D5—122no—
265C5×D4—24no—
266C5×D4—22no—
267C5×D4C2×#6714yes—
268C2×C4×C5—32no—
269C2×C4×C5—32no—
270C2×C4×C5—62no—
271C2×C4×C5—62no—
272C2×C4×C5—62no—
273C2×C4×C5—128no—
274C2×C4×C5—122no—
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5#23712yes—
277C2×C4×C5C2×#6712yes—
278C2×C4×C5C23×D311yescharacteristic
279C2×Dic5—22no—
280C2×Dic5—42no—
281D20—62no—
282D20—62no—
283D20—122no—
284Dic10—22no—
285Dic10—22no—
286Dic10—42no—
287#168—22no—
288#168—62no—
289C22×Q8—51no—
290C22×D4—151no—
291C22×D4D3×D511yescharacteristic
292C23×C4—61no—
293C2×SD16—54no—
294C2×SD16—104no—
295C2×D8—154no—
296C2×D8—304no—
297C22×C8—51no—
298C22×C8—151no—
299#124—154no—
300#124—302no—
301C4×D4—34no—
302C4×D4—62no—
303C2×C4⋊C4—31no—
304C2×C22⋊C4—61no—
305C2×C22⋊C4—301no—
306C2×C22⋊C4—301no—
307C2×C42—31no—
308C4⋊C8—154no—
309#103—154no—
310#102—154no—
311C2×C3×C5—44no—
312C2×C3×C5#46314yescomplemented
313C2×C3×C5C2×#12111yescharacteristic
314C2×C3×C5C2×#13511yescharacteristic
315C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
316D15—82no—
317C23×C3—22no—
318C23×C3—24no—
319C23×C3—42no—
320C23×C3—42no—
321C23×C3C2×C22⋊D511yescharacteristic
322C22×D3—102no—
323C22×D3—202no—
324C22×D3—202no—
325C22×D3—202no—
326C3×Q8—102no—
327C3×Q8—102no—
328C3×Q8—202no—
329C3×D4—22no—
330C3×D4—24no—
331C3×D4C2×D2014yes—
332C2×C3×C4—102no—
333C2×C3×C4—202no—
334C2×C3×C4C2×D2012yes—
335C2×C3×C4#70912yes—
336C2×C3×C4C2×C22⋊D511yescharacteristic
337C2×C3×C4C23×D511yescharacteristic
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—48no—
342C2×Dic3—42no—
343C2×Dic3C2×C22⋊D512yes—
344C2×Dic3C2×C22⋊D512yes—
345D12—102no—
346D12—102no—
347D12—202no—
348C3×C8—102no—
349C3⋊C8—102no—
350C22×C5—24no—
351C22×C5—48no—
352C22×C5—42no—
353C22×C5—42no—
354C22×C5#91412yes—
355C22×C5#91612yes—
356C22×C5#93912yes—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—122no—
359C2×D5—122no—
360C2×D5—122no—
361C2×D5—244no—
362C4×C5—62no—
363C4×C5—62no—
364C4×C5—122no—
365C4×C5#93912yes—
366C4×C5C2×#23711yescharacteristic
367C4×C5C22×#6711yescharacteristic
368Dic5—42no—
369C24—21no—
370C24—301no—
371C2×Q8—52no—
372C2×Q8—101no—
373C2×Q8—102no—
374C2×Q8—102no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—152no—
378C2×D4—302no—
379C2×D4—302no—
380C2×D4—301no—
381C2×D4#120214yes—
382C2×D4C2×D3×D512yes—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—64no—
386C22×C4—61no—
387C22×C4—101no—
388C22×C4—124no—
389C22×C4C2×D3×D511yescharacteristic
390SD16—108no—
391D8—308no—
392C2×C8—52no—
393C2×C8—102no—
394C2×C8—152no—
395C2×C8—302no—
396C4⋊C4—32no—
397C4⋊C4—61no—
398C22⋊C4—64no—
399C22⋊C4—304no—
400C22⋊C4—304no—
401C42—32no—
402C42—32no—
403C3×C5C2×#46311yescharacteristic, complemented, Hall
404C22×C3—24no—
405C22×C3—48no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3#407612yes—
409C22×C3#407812yes—
410C22×C3#409612yes—
411C22×C3C22×C22⋊D511yescharacteristic
412C2×D3—202no—
413C2×D3—202no—
414C2×D3—202no—
415C2×D3—404no—
416C3×C4—202no—
417C3×C4#407612yes—
418C3×C4C22×D2011yescharacteristic
419C3×C4C2×#70911yescharacteristic
420Dic3—22no—
421Dic3—22no—
422Dic3—42no—
423C2×C5—44no—
424C2×C5#516514yescomplemented
425C2×C5C2×#91411yescharacteristic
426C2×C5C2×#91611yescharacteristic
427C2×C5C2×#93911yescharacteristic
428D5—242no—
429C23—22no—
430C23—24no—
431C23—42no—
432C23—42no—
433C23—302no—
434C23—602no—
435C23—602no—
436C23—602no—
437C23D3×C22⋊D511yescharacteristic
438Q8—102no—
439Q8—102no—
440Q8—202no—
441D4—22no—
442D4—24no—
443D4—302no—
444D4—302no—
445D4—602no—
446D4C2×#120214yes—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—102no—
453C2×C4—128no—
454C2×C4—122no—
455C2×C4—202no—
456C2×C4#677912yes—
457C2×C4C2×#120212yes—
458C2×C4D3×C22⋊D511yescharacteristic
459C2×C4C22×D3×D511yescharacteristic
460C8—102no—
461C8—302no—
462C2×C3—44no—
463C2×C3#6530514yescomplemented
464C2×C3C2×#407611yescharacteristic
465C2×C3C2×#407811yescharacteristic
466C2×C3C2×#409611yescharacteristic
467D3—402no—
468C5C2×#516511yescharacteristic, complemented, Sylow
469C22—24no—
470C22—48no—
471C22—42no—
472C22—42no—
473C22—602no—
474C22—602no—
475C22—602no—
476C22—1204no—
477C22#9149512yes—
478C22#9149612yes—
479C22#9156912yes—
480C22C2×D3×C22⋊D511yescharacteristic
481C4—62no—
482C4—62no—
483C4—122no—
484C4—202no—
485C4#9156912yes—
486C4C2×#677911yescharacteristic
487C4C22×#120211yescharacteristic
488C3C2×#6530511yescharacteristic, complemented, Sylow
489C2—44no—
490C2—1202no—
491C2#1174908014yesdirect product factor
492C2C2×#9149511yescharacteristic
493C2C2×#9149611yescharacteristic
494C2C2×#9156911yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6715C2
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#463
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C5×D4×Dic3C2semidirect
3. C22×C3×#687C2semidirect
4. C2×#91374C2semidirect
5. #11749080C2direct (N × H)
6. C2×Dic3⋊#168C2semidirect
7. C2×#90970C2semidirect
8. C2×#90969C2semidirect
19. C5×D4×Dic3C22semidirect
23. C2×C3×#687C22semidirect
28. #91374C22semidirect
29. Dic3⋊#168C22semidirect
30. #90970C22semidirect
31. #90969C22semidirect
34. C22×#687D3semidirect
77. C2×D4×Dic3D5semidirect
93. C2×#687C2×D3semidirect
150. D4×Dic3C2×D5semidirect
312. C2×C3×C5#463semidirect
403. C3×C5C2×#463semidirect
424. C2×C5#5165semidirect
463. C2×C3#65305semidirect
468. C5C2×#5165semidirect
488. C3C2×#65305semidirect
491. C2#11749080direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67152
C2×C5×D4×Dic32
C22×C3×#6872
C2×#913742
#117490802
C2×Dic3⋊#1682
C2×#909702
C2×#909692
C2×#653053
C2×#51655