Finite Group Databasebeta

← C2×#11748083 #14429327

Subgroups — C2×#11748083 #14429327

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#901C211yesmaximal, characteristic, complemented
2C22×C3×#677C211yesmaximal, characteristic, complemented
3C2×#91309C211yesmaximal, characteristic, complemented
4C2×#91298C211yesmaximal, characteristic
5C2×#91103C211yesmaximal, characteristic, complemented
6C2×#90961C211yesmaximal, characteristic, complemented
7C2×#90958C211yesmaximal, characteristic, complemented
8#11748083C218yesmaximal, direct product factor
9C2×#65430—31nomaximal, Hall
10C2×C5×#235C2211yescharacteristic
11C22×C3×D20C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C22×C3×C5×C8C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C2×#6710C2211yescharacteristic
16C2×C5×#208C2211yescharacteristic
17C5×#901—22no—
18C5×#901C2214yescomplemented
19C2×C5×ΓL(1,𝔽25)—21no—
20C2×C5×D3×C8—21no—
21C2×C3×#677—21no—
22C2×C3×#677—21no—
23C2×C3×#677—22no—
24C2×C3×#677C2214yescomplemented
25C2×#6661—21no—
26#91309—22no—
27#91309C2214yescomplemented
28C2×#6656—21no—
29C2×#6655—21no—
30#91298—22no—
31#91298C2214yes—
32C2×#6652—21no—
33#91103C2214yescomplemented
34#90961C2214yescomplemented
35#90958C2214yescomplemented
36C2×#5177—51nomaximal, Hall
37C2×C5×#131—31no—
38C2×#4097—31no—
39C2×#4095—31no—
40C22×#677D311yescharacteristic, complemented
41#65430—38no—
42C2×#3956—31no—
43C2×#3955—31no—
44C2×#3951—31no—
45C23×C3×D5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×C5×#67—21no—
48C5×#235—21no—
49C5×#235—21no—
50C5×#235D412yes—
51C5×#235C2312yes—
52C2×C5×D12D411yescharacteristic
53C2×C4×C5×D3—21no—
54C2×C5×Dic6D411yescharacteristic
55C22×C3×Dic5—21no—
56C2×C3×D20—21no—
57C2×C3×D20—21no—
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20—21no—
61C2×C3×D20C2312yes—
62C2×C3×Dic10—21no—
63C2×C3×Dic10—21no—
64C2×C3×Dic10—21no—
65C2×C3×Dic10—21no—
66C2×C3×Dic10—21no—
67C2×C3×Dic10C2312yes—
68C2×C3×C5×C8D411yescharacteristic
69C2×C3×C5×C8D411yescharacteristic
70C2×C3×C5×C8D412yes—
71C2×C3×C5×C8C2312yes—
72#6710—21no—
73#6710—21no—
74#6710C2312yes—
75#6710C2312yes—
76C2×C3⋊#168—21no—
77C2×C3⋊#168—21no—
78C5×#208—21no—
79C5×#208C2312yes—
80C2×C5×C3⋊C8—21no—
81C5×ΓL(1,𝔽25)—24no—
82C5×D3×C8—24no—
83C3×#677—24no—
84C3×#677—24no—
85#6661—24no—
86#6656—24no—
87#6655—24no—
88#6652—24no—
89C22×C3×SD16—51no—
90C2×#942—51no—
91C2×#932—51no—
92C2×#901D511yescharacteristic, complemented
93C2×#836—51no—
94C2×#833—51no—
95#5177—58no—
96C2×#819—51no—
97C2×C5×#41—31no—
98C22×D20C2×D311yescharacteristic
99C22×Dic10C2×D311yescharacteristic
100C5×#131—34no—
101C5×#131—62no—
102C2×C5×M16—31no—
103C2×C5×M16—61no—
104C22×C5×C8—61no—
105C22×C5×C8C2×D311yescharacteristic
106#4097—34no—
107#4097—62no—
108#4095—34no—
109#4095—62no—
110C2×#689—61no—
111C2×#688—61no—
112C2×#687—61no—
113C2×#686—61no—
114C2×#681—31no—
115C2×#681—31no—
116C2×#677—21no—
117C2×#677—21no—
118C2×#677—22no—
119C2×#677C2×D314yescomplemented
120#3956—34no—
121#3955—34no—
122#3951—34no—
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×C5×D3—21no—
126C22×C3×D5—22no—
127C22×C3×D5—41no—
128C22×C3×D5—41no—
129C22×C3×D5—82no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C5×#67—22no—
137C5×#67—22no—
138C2×C5×Dic3—21no—
139C5×D12—21no—
140C5×D12C2×D412yes—
141C4×C5×D3—22no—
142C4×C5×D3—22no—
143C5×Dic6—21no—
144C5×Dic6C2×D412yes—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—41no—
147C2×C3×Dic5—41no—
148C3×D20—22no—
149C3×D20—22no—
150C3×D20—41no—
151C3×D20—41no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154C3×Dic10—41no—
155C3×Dic10—41no—
156C3×C5×C8C2×D412yes—
157C3×C5×C8C2×D412yes—
158C3⋊#168—22no—
159C3⋊#168—22no—
160C5×C3⋊C8—22no—
161C22×C3×Q8—51no—
162C22×C3×D4—51no—
163C2×#235C2×D511yescharacteristic
164C2×C3×SD16—54no—
165C2×C3×SD16—101no—
166C2×C3×SD16—101no—
167C2×C3×SD16—102no—
168C22×C3×C8C2×D511yescharacteristic
169C2×#216—101no—
170#942—54no—
171#942—102no—
172C2×#215—101no—
173C2×#214—101no—
174#932—54no—
175#932—102no—
176C2×#213—101no—
177C2×#208—51no—
178C2×#208—51no—
179C2×#208C2×D511yescharacteristic
180#901—22no—
181#901C2×D514yescomplemented
182C2×ΓL(1,𝔽25)—21no—
183C2×D3×C8—21no—
184#836—54no—
185#833—54no—
186#819—54no—
187C23×D5—21no—
188C5×#41—32no—
189C5×#41—32no—
190C5×#41—61no—
191C5×#41—61no—
192C2×C5×Q8—31no—
193C2×C5×D4—31no—
194C2×C5×D4—61no—
195C22×C4×C5—61no—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—21no—
198C2×D20—21no—
199C2×D20—21no—
200C2×D20—21no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20C22×D312yes—
204C2×Dic10—21no—
205C2×Dic10—21no—
206C2×Dic10—21no—
207C2×Dic10—21no—
208C2×Dic10—21no—
209C2×Dic10C22×D312yes—
210C5×M16—32no—
211C5×M16—61no—
212C5×M16—64no—
213C2×C5×C8—61no—
214C2×C5×C8—64no—
215C2×C5×C8#6711yescharacteristic
216C2×C5×C8#6711yescharacteristic
217C2×C5×C8#6712yes—
218C2×C5×C8C22×D312yes—
219#689—64no—
220#688—64no—
221#687—64no—
222#686—64no—
223#681—32no—
224#681—32no—
225#681—61no—
226#681—61no—
227C2×#168—61no—
228C2×#168—61no—
229#677—24no—
230#677—24no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—51no—
234C2×#131—31no—
235#471—158no—
236C2×#108—151no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×C5×D3—22no—
244C2×C5×D3—42no—
245C2×C3×D5—42no—
246C2×C3×D5—82no—
247C2×C3×D5—82no—
248C2×C3×D5—82no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253C3×Dic5—42no—
254C5×Dic3—22no—
255C24×C3—101no—
256C2×C3×Q8—52no—
257C2×C3×Q8—101no—
258C2×C3×Q8—101no—
259C2×C3×Q8—101no—
260C2×C3×Q8—101no—
261C2×C3×Q8—101no—
262C2×C3×D4—52no—
263C2×C3×D4—101no—
264C2×C3×D4—101no—
265C2×C3×D4—101no—
266C2×C3×D4—101no—
267C2×C3×D4—101no—
268C22×C3×C4—101no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—21no—
271#235—21no—
272#235—21no—
273#235D2012yes—
274#235C22×D512yes—
275C2×D12D2011yescharacteristic
276C2×C4×D3—21no—
277C2×Dic6D2011yescharacteristic
278C3×SD16—104no—
279C3×SD16—104no—
280C2×C3×C8C22⋊D511yescharacteristic
281C2×C3×C8C22⋊D511yescharacteristic
282C2×C3×C8C22⋊D512yes—
283C2×C3×C8C22×D512yes—
284#216—104no—
285#215—104no—
286#214—104no—
287#213—104no—
288#208—21no—
289#208—52no—
290#208—52no—
291#208—101no—
292#208—101no—
293#208C22×D512yes—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—101no—
296C2×C3⋊C8—101no—
297ΓL(1,𝔽25)—24no—
298D3×C8—24no—
299C23×C5—61no—
300C23×C5#23711yescharacteristic
301C22×D5—22no—
302C22×D5—41no—
303C22×D5—41no—
304C22×D5—82no—
305C5×Q8—32no—
306C5×Q8—61no—
307C5×D4—32no—
308C5×D4—62no—
309C5×D4—62no—
310C5×D4—61no—
311C2×C4×C5—61no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5#23711yescharacteristic
317C2×C4×C5C2×#6711yescharacteristic
318C2×C4×C5C2×#6711yescharacteristic
319C2×C4×C5C23×D311yescharacteristic
320C2×Dic5—22no—
321C2×Dic5—41no—
322C2×Dic5—41no—
323D20—22no—
324D20—22no—
325D20—41no—
326D20—41no—
327Dic10—22no—
328Dic10—22no—
329Dic10—41no—
330Dic10—41no—
331C5×C8—62no—
332C5×C8C2×#6712yes—
333C5×C8C2×#6712yes—
334#168—62no—
335#168—62no—
336C2×#41—31no—
337C22×Q8—51no—
338C22×D4—51no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—301no—
344C2×SD16—54no—
345C2×SD16—101no—
346C2×SD16—101no—
347C2×SD16—102no—
348C2×SD16—301no—
349C2×SD16—301no—
350C2×D8—301no—
351#131—34no—
352#131—62no—
353C2×M16—31no—
354C2×M16—61no—
355C2×M16—151no—
356C2×M16—151no—
357C22×C8—61no—
358C22×C8D3×D511yescharacteristic
359#108—154no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366C3×D5—82no—
367C5×D3—42no—
368C23×C3—102no—
369C23×C3—201no—
370C23×C3—201no—
371C23×C3—402no—
372C23×C3#70911yescharacteristic
373C22×D3—21no—
374C3×Q8—102no—
375C3×Q8—102no—
376C3×Q8—201no—
377C3×Q8—201no—
378C3×D4—102no—
379C3×D4—102no—
380C3×D4—201no—
381C3×D4—201no—
382C2×C3×C4—102no—
383C2×C3×C4—201no—
384C2×C3×C4—201no—
385C2×C3×C4C2×D2011yescharacteristic
386C2×C3×C4C2×D2011yescharacteristic
387C2×C3×C4#70911yescharacteristic
388C2×C3×C4C2×C22⋊D511yescharacteristic
389C2×C3×C4C2×C22⋊D511yescharacteristic
390C2×C3×C4C23×D511yescharacteristic
391#67—22no—
392#67—22no—
393C2×Dic3—21no—
394D12—21no—
395D12C2×D2012yes—
396C4×D3—22no—
397C4×D3—22no—
398Dic6—21no—
399Dic6C2×D2012yes—
400C3×C8C2×C22⋊D512yes—
401C3×C8C2×C22⋊D512yes—
402C3⋊C8—22no—
403C3⋊C8—102no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5—62no—
407C22×C5—122no—
408C22×C5#93811yescharacteristic
409C22×C5#93811yescharacteristic
410C22×C5C2×#23711yescharacteristic
411C2×D5—42no—
412C2×D5—82no—
413C2×D5—82no—
414C2×D5—82no—
415C4×C5—62no—
416C4×C5#93811yescharacteristic
417C4×C5#93811yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419C4×C5C22×#6711yescharacteristic
420Dic5—42no—
421C24—101no—
422#41—32no—
423#41—32no—
424#41—61no—
425#41—61no—
426C2×Q8—31no—
427C2×Q8—52no—
428C2×Q8—101no—
429C2×Q8—101no—
430C2×Q8—101no—
431C2×Q8—101no—
432C2×Q8—101no—
433C2×D4—31no—
434C2×D4—52no—
435C2×D4—61no—
436C2×D4—101no—
437C2×D4—101no—
438C2×D4—101no—
439C2×D4—101no—
440C2×D4—101no—
441C22×C4—61no—
442C22×C4—101no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—104no—
446SD16—104no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—32no—
451M16—61no—
452M16—64no—
453M16—152no—
454M16—152no—
455M16—301no—
456M16—301no—
457C2×C8—61no—
458C2×C8—64no—
459C2×C8—301no—
460C2×C8—301no—
461C2×C8#120111yescharacteristic
462C2×C8#120111yescharacteristic
463C2×C8#120112yes—
464C2×C8C2×D3×D512yes—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—202no—
468C22×C3—402no—
469C22×C3—402no—
470C22×C3—402no—
471C22×C3#407611yescharacteristic
472C22×C3#407611yescharacteristic
473C22×C3C2×#70911yescharacteristic
474C2×D3—22no—
475C2×D3—42no—
476C3×C4—202no—
477C3×C4#407611yescharacteristic
478C3×C4#407611yescharacteristic
479C3×C4C22×D2011yescharacteristic
480C3×C4C22×C22⋊D511yescharacteristic
481Dic3—22no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—122no—
485C2×C5#517712yescomplemented
486C2×C5C2×#93811yescharacteristic
487D5—82no—
488C23—61no—
489C23—102no—
490C23—201no—
491C23—201no—
492C23—402no—
493C23#676511yescharacteristic
494Q8—32no—
495Q8—61no—
496Q8—102no—
497Q8—102no—
498Q8—201no—
499Q8—201no—
500D4—32no—
501D4—62no—
502D4—62no—
503D4—61no—
504D4—102no—
505D4—102no—
506D4—201no—
507D4—201no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—102no—
512C2×C4—201no—
513C2×C4—201no—
514C2×C4#676511yescharacteristic
515C2×C4D3×D2011yescharacteristic
516C2×C4D3×D2011yescharacteristic
517C2×C4C2×#120111yescharacteristic
518C2×C4C2×#120111yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—62no—
521C8—302no—
522C8—302no—
523C8C2×#120112yes—
524C8C2×#120112yes—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—402no—
528C2×C3#6543012yescomplemented
529C2×C3C2×#407611yescharacteristic
530D3—42no—
531C5C2×#517711yescharacteristic, complemented, Sylow
532C22—22no—
533C22—62no—
534C22—122no—
535C22—202no—
536C22—402no—
537C22—402no—
538C22—402no—
539C22#9145611yescharacteristic
540C22#9145611yescharacteristic
541C22C2×#676511yescharacteristic
542C4—62no—
543C4—202no—
544C4#9145611yescharacteristic
545C4#9145611yescharacteristic
546C4C2×D3×D2011yescharacteristic
547C4C22×#120111yescharacteristic
548C3C2×#6543011yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—122no—
552C2—402no—
553C2#1174808312yesdirect product factor
554C2C2×#9145611yescharacteristic
subgroupG/H
centerC22#91456
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5#121
prime radicalC2×#91298C2
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C5×#901C2semidirect
2. C22×C3×#677C2semidirect
3. C2×#91309C2semidirect
5. C2×#91103C2semidirect
6. C2×#90961C2semidirect
7. C2×#90958C2semidirect
8. #11748083C2direct (N × H)
18. C5×#901C22semidirect
24. C2×C3×#677C22semidirect
27. #91309C22semidirect
33. #91103C22semidirect
34. #90961C22semidirect
35. #90958C22semidirect
40. C22×#677D3semidirect
92. C2×#901D5semidirect
119. C2×#677C2×D3semidirect
181. #901C2×D5semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
485. C2×C5#5177semidirect
528. C2×C3#65430semidirect
531. C5C2×#5177semidirect
548. C3C2×#65430semidirect
553. C2#11748083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#9012
C22×C3×#6772
C2×#913092
C2×#912982
C2×#911032
C2×#909612
C2×#909582
#117480832
C2×#654303
C2×#51775