Finite Group Databasebeta

← C2×#11748498 #14411713

Subgroups — C2×#11748498 #14411713

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×#6817C211yesmaximal, characteristic
2C22×#6651C211yesmaximal, characteristic, complemented
3C22×#6648C211yesmaximal, characteristic, complemented
4C2×C5×#830C211yesmaximal, characteristic, complemented
5C2×C3×C22⋊#168C211yesmaximal, characteristic, complemented
6#11748498C218yesmaximal, direct product factor
7C2×#90957C211yesmaximal, characteristic, complemented
8C2×#90957C211yesmaximal, characteristic, complemented
9C2×#65016—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×#1220C411yescharacteristic
12C22×#1220C411yescharacteristic
13C2×#6817—24no—
14C2×#6817—24no—
15C2×#6817C414yes—
16C2×#6817C2214yes—
17C22×D60C411yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×Dic30C411yescharacteristic
21C22×C5×C3⋊C8C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C22×C3×#168C2211yescharacteristic
24C22×C3×#168C2211yescharacteristic
25C2×#6651—24no—
26C2×#6651C2214yescomplemented
27C2×#6648—24no—
28C2×#6648C2214yescomplemented
29C5×#830C2214yescomplemented
30C3×C22⋊#168C2214yescomplemented
31#90957C2214yescomplemented
32#90957C2214yescomplemented
33C2×#4727—51nomaximal, Hall
34C22×#709—31no—
35C22×#676—31no—
36C22×C8×D5—31no—
37C2×C5×C22⋊C8—31no—
38C2×C22⋊#168D311yescharacteristic, complemented
39C2×#3952—31no—
40C2×#3952—31no—
41#65016—38no—
42C24×C3×C5C2×C411yescharacteristic
43C23×D15C2×C411yescharacteristic
44C23×D15C2×C411yescharacteristic
45C22×C3×C4×C5—22no—
46C22×C3×C4×C5—22no—
47C22×C3×C4×C5C2×C411yescharacteristic
48C22×C3×C4×C5C2×C412yes—
49C22×C3×C4×C5C2312yes—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—24no—
52C2×#1220—24no—
53C2×#1220C2×C414yes—
54C2×#1220C2×C414yes—
55C22×Dic15C2×C411yescharacteristic
56C22×Dic15C2×C411yescharacteristic
57#6817—216no—
58#6817—28no—
59#6817—28no—
60C2×D60—24no—
61C2×D60C2×C414yes—
62C2×C4×D15—22no—
63C2×C4×D15—22no—
64C2×C4×D15C2×C412yes—
65C2×C4×D15C2×C412yes—
66C2×C4×D15D414yes—
67C2×C4×D15D414yes—
68C2×C4×D15C2312yes—
69C2×C4×D15C2312yes—
70C2×Dic30—24no—
71C2×Dic30C2×C414yes—
72C2×C5×C3⋊C8—22no—
73C2×C5×C3⋊C8—22no—
74C2×C5×C3⋊C8C2312yes—
75C2×C5×C3⋊C8C2312yes—
76C2×C3×#168—22no—
77C2×C3×#168—22no—
78C2×C3×#168C2312yes—
79C2×C3×#168C2312yes—
80#6651—28no—
81#6648—28no—
82C22×#235—51no—
83C22×ΓL(1,𝔽25)—51no—
84C22×D3×C8—51no—
85C2×C3×C22⋊C8—51no—
86C2×#830D511yescharacteristic, complemented
87C2×(C2×D3)⋊C8—51no—
88C2×(C2×D3)⋊C8—51no—
89#4727—58no—
90C23×C4×C5C2×D311yescharacteristic
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×D5—31no—
100C22×Dic10—31no—
101C22×C5×C8—31no—
102C22×C5×C8—31no—
103C22×#168C2×D311yescharacteristic
104C22×#168C2×D311yescharacteristic
105C2×#676—34no—
106C2×#676—64no—
107C2×C8×D5—34no—
108C2×C8×D5—64no—
109C5×C22⋊C8—34no—
110C22⋊#168C2×D314yescomplemented
111#3952—34no—
112#3952—34no—
113C2×#408—151noSylow
114C23×C3×C5—22no—
115C23×C3×C5—22no—
116C23×C3×C5—22no—
117C23×C3×C5C22×C412yes—
118C23×C3×C5C22×C411yescharacteristic
119C22×D15—22no—
120C22×D15—22no—
121C22×D15—22no—
122C22×D15—22no—
123C22×D15—22no—
124C22×D15C22⋊C414yes—
125C22×D15C22×C412yes—
126C22×D15C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—24no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C22×C412yes—
132C2×C3×C4×C5C22×C411yescharacteristic
133C2×C3×C4×C5C2×D412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2411yescharacteristic
136#1220—28no—
137#1220—28no—
138C2×Dic15—22no—
139C2×Dic15C22⋊C414yes—
140C2×Dic15C22×C412yes—
141C2×Dic15C22×C412yes—
142D60—28no—
143C4×D15—24no—
144C4×D15—22no—
145C4×D15—22no—
146C4×D15C22⋊C418yes—
147C4×D15C2×D414yes—
148C4×D15C2×D414yes—
149Dic30—28no—
150C3×#168—22no—
151C3×#168—22no—
152C5×C3⋊C8—22no—
153C5×C3⋊C8—22no—
154C23×C3×C4C2×D511yescharacteristic
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×D3—51no—
164C22×Dic6—51no—
165C22×C3×C8—51no—
166C22×C3×C8—51no—
167C22×C3⋊C8C2×D511yescharacteristic
168C22×C3⋊C8C2×D511yescharacteristic
169C2×ΓL(1,𝔽25)—54no—
170C2×ΓL(1,𝔽25)—104no—
171C2×D3×C8—54no—
172C2×D3×C8—104no—
173C3×C22⋊C8—54no—
174#830C2×D514yescomplemented
175(C2×D3)⋊C8—54no—
176(C2×D3)⋊C8—54no—
177C24×C5C4×D311yescharacteristic
178C23×D5—31no—
179C23×D5—31no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5C4×D311yescharacteristic
183C22×C4×C5C4×D312yes—
184C22×C4×C5C22×D312yes—
185C22×C4×C5C22×D311yescharacteristic
186C2×C22⋊D5—34no—
187C2×C22⋊D5—34no—
188C2×C22⋊D5—64no—
189C2×C22⋊D5—64no—
190C22×Dic5—31no—
191C22×Dic5—31no—
192#709—616no—
193#709—68no—
194#709—68no—
195C2×D20—34no—
196C2×D20—64no—
197C2×C4×D5—32no—
198C2×C4×D5—34no—
199C2×C4×D5—34no—
200C2×C4×D5—32no—
201C2×C4×D5—32no—
202C2×C4×D5—32no—
203C2×C4×D5—62no—
204C2×C4×D5—62no—
205C2×Dic10—34no—
206C2×Dic10—64no—
207C2×C5×C8—32no—
208C2×C5×C8—32no—
209C2×C5×C8—62no—
210C2×C5×C8—62no—
211C2×#168—22no—
212C2×#168—22no—
213C2×#168C22×D312yes—
214C2×#168C22×D312yes—
215#676—68no—
216C8×D5—68no—
217C22×#41—151no—
218C22×M16—151no—
219C23×C8—151no—
220#408—158no—
221C2×C22⋊C8—31no—
222C2×C22⋊C8—51no—
223C2×C22⋊C8—151no—
224C2×C22⋊C8—151no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—44no—
229C22×C3×C5C2×C22⋊C412yes—
230C22×C3×C5#13112yes—
231C22×C3×C5#13112yes—
232C22×C3×C5C23×C411yescharacteristic
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—28no—
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—22no—
239C2×D15—44no—
240C2×D15C2×C22⋊C414yes—
241C3×C4×C5—22no—
242C3×C4×C5C2×C22⋊C412yes—
243C3×C4×C5C22×D411yescharacteristic
244C3×C4×C5C22×D411yescharacteristic
245Dic15—22no—
246Dic15C2×C22⋊C414yes—
247C24×C3C4×D511yescharacteristic
248C23×D3—51no—
249C23×D3—51no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4C4×D511yescharacteristic
253C22×C3×C4C4×D512yes—
254C22×C3×C4C22×D512yes—
255C22×C3×C4C22×D511yescharacteristic
256C2×#67—54no—
257C2×#67—54no—
258C2×#67—104no—
259C2×#67—104no—
260C22×Dic3—51no—
261C22×Dic3—51no—
262#235—108no—
263#235—108no—
264#235—1016no—
265C2×D12—54no—
266C2×D12—104no—
267C2×C4×D3—52no—
268C2×C4×D3—54no—
269C2×C4×D3—54no—
270C2×C4×D3—52no—
271C2×C4×D3—52no—
272C2×C4×D3—52no—
273C2×C4×D3—102no—
274C2×C4×D3—102no—
275C2×Dic6—54no—
276C2×Dic6—104no—
277C2×C3×C8—52no—
278C2×C3×C8—52no—
279C2×C3×C8—102no—
280C2×C3×C8—102no—
281C2×C3⋊C8—22no—
282C2×C3⋊C8—22no—
283C2×C3⋊C8C22×D512yes—
284C2×C3⋊C8C22×D512yes—
285ΓL(1,𝔽25)—108no—
286D3×C8—108no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—22no—
290C23×C5C2×C4×D312yes—
291C23×C5C2×C4×D311yescharacteristic
292C22×D5—34no—
293C22×D5—32no—
294C22×D5—32no—
295C22×D5—62no—
296C22×D5—62no—
297C22×D5—62no—
298C22×D5—62no—
299C22×D5—62no—
300C2×C4×C5—22no—
301C2×C4×C5—24no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5C2×C4×D312yes—
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—34no—
312C2×Dic5—32no—
313C2×Dic5—32no—
314C2×Dic5—62no—
315D20—68no—
316C4×D5—38no—
317C4×D5—34no—
318C4×D5—34no—
319C4×D5—64no—
320C4×D5—62no—
321C4×D5—62no—
322Dic10—68no—
323C5×C8—62no—
324C5×C8—62no—
325#168—22no—
326#168—22no—
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—151no—
336C23×C4—151no—
337C23×C4D3×D511yescharacteristic
338C2×M16—154no—
339C2×M16—304no—
340C22×C8—31no—
341C22×C8—31no—
342C22×C8—51no—
343C22×C8—51no—
344C22×C8—154no—
345C22×C8—304no—
346C22⋊C8—34no—
347C22⋊C8—54no—
348C22⋊C8—154no—
349C22⋊C8—154no—
350C2×C3×C5—42no—
351C2×C3×C5#40814yescomplemented
352C2×C3×C5C22×C22⋊C411yescharacteristic
353C2×C3×C5C2×#13111yescharacteristic
354C2×C3×C5C2×#13111yescharacteristic
355D15—24no—
356D15—42no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3C2×C4×D512yes—
361C23×C3C2×C4×D511yescharacteristic
362C22×D3—52no—
363C22×D3—54no—
364C22×D3—52no—
365C22×D3—102no—
366C22×D3—102no—
367C22×D3—102no—
368C22×D3—102no—
369C22×D3—102no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—24no—
374C2×C3×C4C2×C4×D512yes—
375C2×C3×C4C2×C4×D511yescharacteristic
376C2×C3×C4D4×D512yes—
377C2×C3×C4D4×D512yes—
378C2×C3×C4C23×D511yescharacteristic
379#67—108no—
380#67—108no—
381C2×Dic3—52no—
382C2×Dic3—54no—
383C2×Dic3—52no—
384C2×Dic3—102no—
385D12—108no—
386C4×D3—54no—
387C4×D3—54no—
388C4×D3—58no—
389C4×D3—102no—
390C4×D3—102no—
391C4×D3—104no—
392Dic6—108no—
393C3×C8—102no—
394C3×C8—102no—
395C3⋊C8—22no—
396C3⋊C8—22no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—22no—
400C22×C5—44no—
401C22×C5D3×C22⋊C412yes—
402C22×C5#90112yes—
403C22×C5#90712yes—
404C22×C5C22×C4×D311yescharacteristic
405C2×D5—34no—
406C2×D5—62no—
407C2×D5—62no—
408C2×D5—68no—
409C2×D5—62no—
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—124no—
413C4×C5—22no—
414C4×C5D3×C22⋊C412yes—
415C4×C5C2×D3×D411yescharacteristic
416C4×C5C2×D3×D411yescharacteristic
417Dic5—34no—
418Dic5—62no—
419C24—151no—
420C24—151no—
421C24#120011yescharacteristic
422#41—308no—
423#41—308no—
424#41—3016no—
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—22no—
434C22×C4—22no—
435C22×C4—151no—
436C22×C4—152no—
437C22×C4—154no—
438C22×C4—154no—
439C22×C4—152no—
440C22×C4—151no—
441C22×C4—152no—
442C22×C4—152no—
443C22×C4—302no—
444C22×C4—302no—
445C22×C4#120011yescharacteristic
446C22×C4#120012yes—
447C22×C4C2×D3×D512yes—
448C22×C4C2×D3×D511yescharacteristic
449M16—308no—
450C2×C8—32no—
451C2×C8—32no—
452C2×C8—52no—
453C2×C8—52no—
454C2×C8—62no—
455C2×C8—62no—
456C2×C8—102no—
457C2×C8—102no—
458C2×C8—308no—
459C3×C5C2×#40811yescharacteristic, complemented, Hall
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—44no—
464C22×C3D5×C22⋊C412yes—
465C22×C3#404712yes—
466C22×C3#405312yes—
467C22×C3C22×C4×D511yescharacteristic
468C2×D3—54no—
469C2×D3—102no—
470C2×D3—102no—
471C2×D3—108no—
472C2×D3—102no—
473C2×D3—102no—
474C2×D3—102no—
475C2×D3—204no—
476C3×C4—22no—
477C3×C4D5×C22⋊C412yes—
478C3×C4C2×D4×D511yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480Dic3—54no—
481Dic3—102no—
482C2×C5—42no—
483C2×C5#472714yescomplemented
484C2×C5C2×D3×C22⋊C411yescharacteristic
485C2×C5C2×#90111yescharacteristic
486C2×C5C2×#90711yescharacteristic
487D5—64no—
488D5—122no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—152no—
493C23—154no—
494C23—152no—
495C23—302no—
496C23—302no—
497C23—302no—
498C23—302no—
499C23—302no—
500C23C2×#120012yes—
501C23C2×#120011yescharacteristic
502Q8—308no—
503D4—308no—
504D4—308no—
505D4—308no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—152no—
511C2×C4—154no—
512C2×C4—154no—
513C2×C4—154no—
514C2×C4—158no—
515C2×C4—152no—
516C2×C4—302no—
517C2×C4—302no—
518C2×C4—302no—
519C2×C4—304no—
520C2×C4C2×#120012yes—
521C2×C4C2×#120011yescharacteristic
522C2×C4#679012yes—
523C2×C4#679012yes—
524C2×C4C22×D3×D511yescharacteristic
525C8—62no—
526C8—62no—
527C8—102no—
528C8—102no—
529C2×C3—42no—
530C2×C3#6501614yescomplemented
531C2×C3C2×D5×C22⋊C411yescharacteristic
532C2×C3C2×#404711yescharacteristic
533C2×C3C2×#405311yescharacteristic
534D3—104no—
535D3—202no—
536C5C2×#472711yescharacteristic, complemented, Sylow
537C22—22no—
538C22—22no—
539C22—22no—
540C22—44no—
541C22—154no—
542C22—302no—
543C22—302no—
544C22—308no—
545C22—302no—
546C22—302no—
547C22—302no—
548C22—604no—
549C22#9129012yes—
550C22#9129112yes—
551C22#9156112yes—
552C22C22×#120011yescharacteristic
553C4—22no—
554C4—154no—
555C4—302no—
556C4#9156112yes—
557C4C2×#679011yescharacteristic
558C4C2×#679011yescharacteristic
559C3C2×#6501611yescharacteristic, complemented, Sylow
560C2—42no—
561C2—304no—
562C2—602no—
563C2#1174849814yesdirect product factor
564C2C2×#9129011yescharacteristic
565C2C2×#9129111yescharacteristic
566C2C2×#9156111yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C22×C4
prime radicalC22×#6817C2
cosocleC2×C3×C4×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#408
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#6651C2semidirect
3. C22×#6648C2semidirect
4. C2×C5×#830C2semidirect
5. C2×C3×C22⋊#168C2semidirect
6. #11748498C2direct (N × H)
7. C2×#90957C2semidirect
8. C2×#90957C2semidirect
26. C2×#6651C22semidirect
28. C2×#6648C22semidirect
29. C5×#830C22semidirect
30. C3×C22⋊#168C22semidirect
31. #90957C22semidirect
32. #90957C22semidirect
38. C2×C22⋊#168D3semidirect
86. C2×#830D5semidirect
110. C22⋊#168C2×D3semidirect
174. #830C2×D5semidirect
351. C2×C3×C5#408semidirect
459. C3×C5C2×#408semidirect
483. C2×C5#4727semidirect
530. C2×C3#65016semidirect
536. C5C2×#4727semidirect
559. C3C2×#65016semidirect
563. C2#11748498direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68172
C22×#66512
C22×#66482
C2×C5×#8302
C2×C3×C22⋊#1682
#117484982
C2×#909572
C2×#650163
C2×#47275