Finite Group Databasebeta

← C2×#11748140 #14411723

Subgroups — C2×#11748140 #14411723

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6771C211yesmaximal, characteristic
2C22×C5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C22×D3×#168C211yesmaximal, characteristic, complemented
4C2×#91104C211yesmaximal, characteristic, complemented
5C2×C3×#3952C211yesmaximal, characteristic, complemented
6C2×#90957C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11748140C218yesmaximal, direct product factor
9C2×#65418—31nomaximal, Hall
10C22×C4×D15C2211yescharacteristic
11C22×C4×C5×D3C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C22×#1204C411yescharacteristic
14C22×#1203C411yescharacteristic
15C22×#1202C411yescharacteristic
16C22×#1201C411yescharacteristic
17C2×#6771—24no—
18C2×#6771—24no—
19C2×#6771C414yes—
20C2×#6771C2214yes—
21C22×C3×C5×C8C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×C5×ΓL(1,𝔽25)—24no—
25C2×C5×ΓL(1,𝔽25)C2214yescomplemented
26C22×C3×#168C2211yescharacteristic
27C2×D3×#168—24no—
28C2×D3×#168C2214yescomplemented
29#91104C2214yescomplemented
30C3×#3952C2214yescomplemented
31#90957C2214yescomplemented
32#90955C2214yescomplemented
33C2×#4727—51nomaximal, Hall
34C22×#709—31no—
35C22×C5×M16—31no—
36C23×#168—31no—
37#65418—38no—
38C2×#3952—31no—
39C2×#3952—31no—
40C2×#3952—31no—
41C2×#3952D311yescharacteristic, complemented
42C23×D15C2×C411yescharacteristic
43C23×C5×D3C2×C411yescharacteristic
44C23×C3×D5C2×C411yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15C2×C411yescharacteristic
47C2×C4×D15—22no—
48C2×C4×D15—22no—
49C2×C4×D15C2×C412yes—
50C2×C4×D15C2312yes—
51C22×C5×Dic3C2×C411yescharacteristic
52C2×C4×C5×D3C2×C412yes—
53C2×C4×C5×D3D414yes—
54C2×C4×C5×D3D414yes—
55C2×C4×C5×D3C2312yes—
56C22×C3×Dic5C2×C411yescharacteristic
57C2×C3×C4×D5—22no—
58C2×C3×C4×D5—22no—
59C2×C3×C4×D5C2×C412yes—
60C2×C3×C4×D5C2312yes—
61C2×#1204—24no—
62C2×#1204C2×C414yes—
63C2×#1203—24no—
64C2×#1203C2×C414yes—
65C2×#1202—24no—
66C2×#1202C2×C414yes—
67C2×#1201—24no—
68C2×#1201C2×C414yes—
69#6771—216no—
70#6771—28no—
71#6771—28no—
72C2×C3×C5×C8—22no—
73C2×C3×C5×C8C2312yes—
74C2×C3⋊#168—22no—
75C2×C3⋊#168C2312yes—
76C2×C5×C3⋊C8—22no—
77C2×C5×C3⋊C8C2312yes—
78C5×ΓL(1,𝔽25)—28no—
79C2×C3×#168—22no—
80C2×C3×#168C2312yes—
81D3×#168—28no—
82C22×#235—51no—
83C22×ΓL(1,𝔽25)D511yescharacteristic, complemented
84C22×D3×C8—51no—
85C2×C3×C22⋊C8—51no—
86C2×#830—51no—
87C2×(C2×D3)⋊C8—51no—
88C2×(C2×D3)⋊C8—51no—
89#4727—58no—
90C23×C4×C5—31no—
91C22×C22⋊D5—31no—
92C22×C22⋊D5—31no—
93C2×#709—34no—
94C2×#709—34no—
95C2×#709—64no—
96C2×#709—64no—
97C22×D20—31no—
98C22×C4×D5—31no—
99C22×C4×D5C2×D311yescharacteristic
100C22×Dic10—31no—
101C2×C5×M16—34no—
102C2×C5×M16—64no—
103C22×C5×C8—31no—
104C22×C5×C8C2×D311yescharacteristic
105C22×#168—31no—
106C22×#168—34no—
107C22×#168—64no—
108C22×#168C2×D311yescharacteristic
109#3952—34no—
110#3952—34no—
111#3952—34no—
112#3952C2×D314yescomplemented
113C2×#408—151noSylow
114C23×C3×C5C22×C411yescharacteristic
115C22×D15—22no—
116C22×D15—22no—
117C22×D15—22no—
118C22×D15C22×C412yes—
119C22×C5×D3—22no—
120C22×C5×D3—22no—
121C22×C5×D3C22⋊C414yes—
122C22×C5×D3C22×C412yes—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5C22×C412yes—
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×C3×C4×C5C2×D412yes—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2411yescharacteristic
131C2×Dic15—22no—
132C2×Dic15C22×C412yes—
133C4×D15—24no—
134C4×D15—22no—
135C4×D15—22no—
136C2×C5×Dic3C22⋊C414yes—
137C2×C5×Dic3C22×C412yes—
138C4×C5×D3C22⋊C418yes—
139C4×C5×D3C2×D414yes—
140C4×C5×D3C2×D414yes—
141C2×C3×Dic5—22no—
142C2×C3×Dic5C22×C412yes—
143C3×C4×D5—24no—
144C3×C4×D5—22no—
145C3×C4×D5—22no—
146#1204—28no—
147#1203—28no—
148#1202—28no—
149#1201—28no—
150C3×C5×C8—22no—
151C3⋊#168—22no—
152C3×#168—22no—
153C5×C3⋊C8—22no—
154C23×C3×C4—51no—
155C22×#67—51no—
156C22×#67—51no—
157C2×#235—54no—
158C2×#235—54no—
159C2×#235—104no—
160C2×#235—104no—
161C22×D12—51no—
162C22×C4×D3—51no—
163C22×C4×D3C2×D511yescharacteristic
164C22×Dic6—51no—
165C22×C3×C8—51no—
166C22×C3×C8C2×D511yescharacteristic
167C22×C3⋊C8—51no—
168C22×C3⋊C8C2×D511yescharacteristic
169C2×ΓL(1,𝔽25)—24no—
170C2×ΓL(1,𝔽25)C2×D514yescomplemented
171C2×D3×C8—54no—
172C2×D3×C8—104no—
173C3×C22⋊C8—54no—
174#830—54no—
175(C2×D3)⋊C8—54no—
176(C2×D3)⋊C8—54no—
177C24×C5—31no—
178C23×D5—31no—
179C23×D5C4×D311yescharacteristic
180C22×C4×C5—31no—
181C22×C4×C5—32no—
182C22×C4×C5—34no—
183C22×C4×C5—34no—
184C22×C4×C5—32no—
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—34no—
187C2×C22⋊D5—34no—
188C2×C22⋊D5—64no—
189C2×C22⋊D5—64no—
190C22×Dic5—31no—
191C22×Dic5C4×D311yescharacteristic
192#709—616no—
193#709—68no—
194#709—68no—
195C2×D20—34no—
196C2×D20—64no—
197C2×C4×D5—22no—
198C2×C4×D5—22no—
199C2×C4×D5—32no—
200C2×C4×D5—32no—
201C2×C4×D5—62no—
202C2×C4×D5—62no—
203C2×C4×D5C4×D312yes—
204C2×C4×D5C22×D312yes—
205C2×Dic10—34no—
206C2×Dic10—64no—
207C5×M16—68no—
208C2×C5×C8—22no—
209C2×C5×C8—32no—
210C2×C5×C8—62no—
211C2×C5×C8C22×D312yes—
212C2×#168—22no—
213C2×#168—32no—
214C2×#168—68no—
215C2×#168—62no—
216C2×#168C22×D312yes—
217C22×#41—151no—
218C22×M16—31no—
219C23×C8—151no—
220#408—158no—
221C2×C22⋊C8—51no—
222C2×C22⋊C8—151no—
223C2×C22⋊C8—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5C2×C22⋊C412yes—
226C22×C3×C5#13112yes—
227C22×C3×C5#13112yes—
228C22×C3×C5C23×C411yescharacteristic
229C2×D15—22no—
230C2×D15—22no—
231C2×D15—22no—
232C2×D15—44no—
233C2×C5×D3—22no—
234C2×C5×D3—22no—
235C2×C5×D3—28no—
236C2×C5×D3C2×C22⋊C414yes—
237C2×C3×D5—22no—
238C2×C3×D5—22no—
239C2×C3×D5—22no—
240C2×C3×D5—44no—
241C3×C4×C5C2×C22⋊C412yes—
242C3×C4×C5C22×D411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—22no—
245C3×Dic5—22no—
246C5×Dic3C2×C22⋊C414yes—
247C24×C3—51no—
248C23×D3—51no—
249C23×D3C4×D511yescharacteristic
250C22×C3×C4—51no—
251C22×C3×C4—52no—
252C22×C3×C4—52no—
253C22×C3×C4—102no—
254C22×C3×C4—102no—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—54no—
257C2×#67—54no—
258C2×#67—104no—
259C2×#67—104no—
260C22×Dic3—51no—
261C22×Dic3C4×D511yescharacteristic
262#235—1016no—
263#235—108no—
264#235—108no—
265C2×D12—54no—
266C2×D12—104no—
267C2×C4×D3—52no—
268C2×C4×D3—52no—
269C2×C4×D3—102no—
270C2×C4×D3—102no—
271C2×C4×D3C4×D512yes—
272C2×C4×D3D2014yes—
273C2×C4×D3C22⋊D514yes—
274C2×C4×D3C22×D512yes—
275C2×Dic6—54no—
276C2×Dic6—104no—
277C2×C3×C8—22no—
278C2×C3×C8—52no—
279C2×C3×C8—102no—
280C2×C3×C8C22×D512yes—
281C2×C3⋊C8—22no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—102no—
284C2×C3⋊C8C22×D512yes—
285ΓL(1,𝔽25)—28no—
286D3×C8—108no—
287C23×C5—34no—
288C23×C5—32no—
289C23×C5—62no—
290C23×C5—62no—
291C23×C5C2×C4×D311yescharacteristic
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—32no—
296C22×D5—62no—
297C22×D5—62no—
298C22×D5—62no—
299C22×D5C2×C4×D312yes—
300C2×C4×C5—34no—
301C2×C4×C5—32no—
302C2×C4×C5—38no—
303C2×C4×C5—34no—
304C2×C4×C5—34no—
305C2×C4×C5C2×C4×D311yescharacteristic
306C2×C4×C5D3×D412yes—
307C2×C4×C5D3×D412yes—
308C2×C4×C5C23×D311yescharacteristic
309C22⋊D5—68no—
310C22⋊D5—68no—
311C2×Dic5—22no—
312C2×Dic5—32no—
313C2×Dic5—62no—
314C2×Dic5C2×C4×D312yes—
315D20—68no—
316C4×D5—24no—
317C4×D5—22no—
318C4×D5—22no—
319C4×D5—64no—
320C4×D5—62no—
321C4×D5—62no—
322Dic10—68no—
323C5×C8—22no—
324C5×C8—62no—
325#168—22no—
326#168—62no—
327C2×#41—154no—
328C2×#41—154no—
329C2×#41—304no—
330C2×#41—304no—
331C22×Q8—151no—
332C22×D4—151no—
333C22×D4—151no—
334C22×D4—151no—
335C23×C4—31no—
336C23×C4—51no—
337C23×C4—151no—
338C2×M16—34no—
339C2×M16—64no—
340C22×C8—31no—
341C22×C8—51no—
342C22×C8—154no—
343C22×C8—151no—
344C22×C8—304no—
345C22×C8D3×D511yescharacteristic
346C22⋊C8—54no—
347C22⋊C8—154no—
348C22⋊C8—154no—
349C22⋊C8—154no—
350C2×C3×C5#40814yescomplemented
351C2×C3×C5C22×C22⋊C411yescharacteristic
352C2×C3×C5C2×#13111yescharacteristic
353C2×C3×C5C2×#13111yescharacteristic
354D15—42no—
355C3×D5—42no—
356C5×D3—24no—
357C23×C3—52no—
358C23×C3—102no—
359C23×C3—102no—
360C23×C3—102no—
361C23×C3C2×C4×D511yescharacteristic
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—52no—
365C22×D3—102no—
366C22×D3—102no—
367C22×D3—102no—
368C22×D3#68514yes—
369C22×D3C2×C4×D512yes—
370C2×C3×C4—52no—
371C2×C3×C4—102no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—104no—
375C2×C3×C4C2×C4×D511yescharacteristic
376C2×C3×C4C2×D2012yes—
377C2×C3×C4C2×C22⋊D512yes—
378C2×C3×C4C23×D511yescharacteristic
379#67—108no—
380#67—108no—
381C2×Dic3—52no—
382C2×Dic3—102no—
383C2×Dic3#68514yes—
384C2×Dic3C2×C4×D512yes—
385D12—108no—
386C4×D3—102no—
387C4×D3—102no—
388C4×D3—104no—
389C4×D3#68518yes—
390C4×D3C2×D2014yes—
391C4×D3C2×C22⋊D514yes—
392Dic6—108no—
393C3×C8—22no—
394C3×C8—102no—
395C3⋊C8—22no—
396C3⋊C8—102no—
397C22×C5—34no—
398C22×C5—62no—
399C22×C5—62no—
400C22×C5—68no—
401C22×C5D3×C22⋊C412yes—
402C22×C5#90112yes—
403C22×C5#90712yes—
404C22×C5C22×C4×D311yescharacteristic
405C2×D5—22no—
406C2×D5—22no—
407C2×D5—22no—
408C2×D5—44no—
409C2×D5—62no—
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—124no—
413C4×C5—34no—
414C4×C5D3×C22⋊C412yes—
415C4×C5C2×D3×D411yescharacteristic
416C4×C5C2×D3×D411yescharacteristic
417Dic5—22no—
418Dic5—62no—
419C24—31no—
420C24—51no—
421C24—151no—
422#41—3016no—
423#41—308no—
424#41—308no—
425C2×Q8—154no—
426C2×Q8—304no—
427C2×D4—154no—
428C2×D4—154no—
429C2×D4—154no—
430C2×D4—304no—
431C2×D4—304no—
432C2×D4—304no—
433C22×C4—31no—
434C22×C4—32no—
435C22×C4—34no—
436C22×C4—34no—
437C22×C4—32no—
438C22×C4—51no—
439C22×C4—52no—
440C22×C4—52no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—151no—
444C22×C4—152no—
445C22×C4—152no—
446C22×C4—302no—
447C22×C4—302no—
448C22×C4C2×D3×D511yescharacteristic
449M16—68no—
450C2×C8—22no—
451C2×C8—32no—
452C2×C8—52no—
453C2×C8—62no—
454C2×C8—102no—
455C2×C8—152no—
456C2×C8—308no—
457C2×C8—302no—
458C2×C8C2×D3×D512yes—
459C3×C5C2×#40811yescharacteristic, complemented, Hall
460C22×C3—102no—
461C22×C3—102no—
462C22×C3—102no—
463C22×C3—204no—
464C22×C3#405312yes—
465C22×C3#405312yes—
466C22×C3C2×#68512yes—
467C22×C3C22×C4×D511yescharacteristic
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—28no—
471C2×D3—102no—
472C2×D3—102no—
473C2×D3—102no—
474C2×D3—204no—
475C2×D3C2×#68514yes—
476C3×C4—102no—
477C3×C4C2×#68512yes—
478C3×C4C22×D2011yescharacteristic
479C3×C4C22×C22⋊D511yescharacteristic
480Dic3—102no—
481Dic3C2×#68514yes—
482C2×C5—64no—
483C2×C5#472714yescomplemented
484C2×C5C2×D3×C22⋊C411yescharacteristic
485C2×C5C2×#90111yescharacteristic
486C2×C5C2×#90711yescharacteristic
487D5—42no—
488D5—122no—
489C23—34no—
490C23—32no—
491C23—52no—
492C23—62no—
493C23—62no—
494C23—102no—
495C23—102no—
496C23—102no—
497C23—152no—
498C23—302no—
499C23—302no—
500C23—302no—
501C23C4×D3×D511yescharacteristic
502Q8—308no—
503D4—308no—
504D4—308no—
505D4—308no—
506C2×C4—34no—
507C2×C4—32no—
508C2×C4—38no—
509C2×C4—34no—
510C2×C4—34no—
511C2×C4—52no—
512C2×C4—102no—
513C2×C4—104no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—152no—
517C2×C4—302no—
518C2×C4—304no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4C4×D3×D511yescharacteristic
522C2×C4D3×D2012yes—
523C2×C4D3×C22⋊D512yes—
524C2×C4C22×D3×D511yescharacteristic
525C8—22no—
526C8—62no—
527C8—102no—
528C8—302no—
529C2×C3—202no—
530C2×C3#6541814yescomplemented
531C2×C3C2×#405311yescharacteristic
532C2×C3C2×#405311yescharacteristic
533C2×C3C22×#68511yescharacteristic
534D3—24no—
535D3—202no—
536C5C2×#472711yescharacteristic, complemented, Sylow
537C22—34no—
538C22—62no—
539C22—62no—
540C22—68no—
541C22—102no—
542C22—102no—
543C22—102no—
544C22—204no—
545C22—302no—
546C22—302no—
547C22—302no—
548C22—604no—
549C22#9126612yes—
550C22#9126812yes—
551C22D3×#68512yes—
552C22C2×C4×D3×D511yescharacteristic
553C4—34no—
554C4—102no—
555C4—302no—
556C4D3×#68512yes—
557C4C2×D3×D2011yescharacteristic
558C4C2×D3×C22⋊D511yescharacteristic
559C3C2×#6541811yescharacteristic, complemented, Sylow
560C2—64no—
561C2—202no—
562C2—602no—
563C2#1174814014yesdirect product factor
564C2C2×#9126611yescharacteristic
565C2C2×#9126811yescharacteristic
566C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C22×C4
prime radicalC22×#6771C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#408
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C5×ΓL(1,𝔽25)C2semidirect
3. C22×D3×#168C2semidirect
4. C2×#91104C2semidirect
5. C2×C3×#3952C2semidirect
6. C2×#90957C2semidirect
7. C2×#90955C2semidirect
8. #11748140C2direct (N × H)
25. C2×C5×ΓL(1,𝔽25)C22semidirect
28. C2×D3×#168C22semidirect
29. #91104C22semidirect
30. C3×#3952C22semidirect
31. #90957C22semidirect
32. #90955C22semidirect
41. C2×#3952D3semidirect
83. C22×ΓL(1,𝔽25)D5semidirect
112. #3952C2×D3semidirect
170. C2×ΓL(1,𝔽25)C2×D5semidirect
350. C2×C3×C5#408semidirect
459. C3×C5C2×#408semidirect
483. C2×C5#4727semidirect
530. C2×C3#65418semidirect
536. C5C2×#4727semidirect
559. C3C2×#65418semidirect
563. C2#11748140direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67712
C22×C5×ΓL(1,𝔽25)2
C22×D3×#1682
C2×#911042
C2×C3×#39522
C2×#909572
C2×#909552
#117481402
C2×#654183
C2×#47275