Finite Group Databasebeta

← C2×#11752038 #14411726

Subgroups — C2×#11752038 #14411726

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×#6782C211yesmaximal, characteristic
2C22×#6739C211yesmaximal, characteristic, complemented
3C22×D3×#170C211yesmaximal, characteristic, complemented
4C2×#91241C211yesmaximal, characteristic, complemented
5C2×C3×C22⋊#170C211yesmaximal, characteristic, complemented
6#11752038C218yesmaximal, direct product factor
7C2×#91171C211yesmaximal, characteristic, complemented
8C2×#91171C211yesmaximal, characteristic, complemented
9C2×#65775—31nomaximal, Hall
10C22×#1220C411yescharacteristic
11C22×C5×#67C411yescharacteristic
12C23×C3×Dic5C2211yescharacteristic
13C22×#1204C411yescharacteristic
14C22×#1203C411yescharacteristic
15C22×#1200C2211yescharacteristic
16C2×#6782—24no—
17C2×#6782—24no—
18C2×#6782C414yes—
19C2×#6782C2214yes—
20C22×D3×Dic5C2211yescharacteristic
21C22×C3⋊#170C2211yescharacteristic
22C22×C3⋊#170C2211yescharacteristic
23C22×C3×#170C2211yescharacteristic
24C22×C3×#170C2211yescharacteristic
25C2×#6739—24no—
26C2×#6739C2214yescomplemented
27C2×D3×#170—24no—
28C2×D3×#170C2214yescomplemented
29#91241C2214yescomplemented
30C3×C22⋊#170C2214yescomplemented
31#91171C2214yescomplemented
32#91171C2214yescomplemented
33C2×#4727—51nomaximal, Hall
34C22×#711—31no—
35C22×#704—31no—
36C23×#170—31no—
37C2×C22⋊#170—31no—
38C2×C22⋊#170D311yescharacteristic, complemented
39#65775—38no—
40C2×#4003—31no—
41C2×#4003—31no—
42C24×C3×C5C2×C411yescharacteristic
43C23×D15C2×C411yescharacteristic
44C23×C5×D3C2×C411yescharacteristic
45C2×#1220—24no—
46C2×#1220C2×C414yes—
47C22×Dic15C2×C411yescharacteristic
48C2×C5×#67—24no—
49C2×C5×#67C2×C414yes—
50C22×C5×Dic3C2×C411yescharacteristic
51C22×C3×Dic5—22no—
52C22×C3×Dic5—22no—
53C22×C3×Dic5C2×C412yes—
54C22×C3×Dic5C2×C411yescharacteristic
55C22×C3×Dic5C2312yes—
56C22×C3×Dic5C2311yescharacteristic
57C2×#1204—24no—
58C2×#1204C2×C414yes—
59C2×#1203—24no—
60C2×#1203C2×C414yes—
61C2×#1200—22no—
62C2×#1200—22no—
63C2×#1200C2×C412yes—
64C2×#1200C2312yes—
65#6782—216no—
66#6782—28no—
67#6782—28no—
68C2×D3×Dic5C2×C412yes—
69C2×D3×Dic5D414yes—
70C2×D3×Dic5D414yes—
71C2×D3×Dic5C2312yes—
72C2×C3⋊#170—22no—
73C2×C3⋊#170—22no—
74C2×C3⋊#170C2312yes—
75C2×C3⋊#170C2312yes—
76C2×C3×#170—22no—
77C2×C3×#170—22no—
78C2×C3×#170C2312yes—
79C2×C3×#170C2312yes—
80#6739—28no—
81D3×#170—28no—
82C22×#235—51no—
83C22×ΓL(1,𝔽25)—51no—
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—
90C22×C5×D4—31no—
91C22×C22⋊D5—31no—
92C22×C22⋊D5—31no—
93C23×Dic5—31no—
94C23×Dic5C2×D311yescharacteristic
95C2×#711—34no—
96C2×#711—34no—
97C2×#711—64no—
98C2×#711—64no—
99C22×C4×D5—31no—
100C22×Dic10—31no—
101C2×#704—34no—
102C2×#704—64no—
103C22×#170—31no—
104C22×#170—31no—
105C22×#170—34no—
106C22×#170—64no—
107C22×#170C2×D311yescharacteristic
108C22×#170C2×D311yescharacteristic
109C22⋊#170—34no—
110C22⋊#170C2×D314yescomplemented
111#4003—34no—
112#4003—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×D15C22×C412yes—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3C22⋊C414yes—
126C22×C5×D3C22×C412yes—
127#1220—28no—
128C2×Dic15C22⋊C414yes—
129C2×Dic15C22×C412yes—
130C5×#67—28no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3C22×C412yes—
133C2×C3×Dic5—22no—
134C2×C3×Dic5—24no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5C22×C412yes—
138C2×C3×Dic5C22×C411yescharacteristic
139C2×C3×Dic5C2×D412yes—
140C2×C3×Dic5C2×D412yes—
141C2×C3×Dic5C2411yescharacteristic
142#1204—28no—
143#1203—28no—
144#1200—24no—
145#1200—22no—
146#1200—22no—
147D3×Dic5C22⋊C418yes—
148D3×Dic5C2×D414yes—
149D3×Dic5C2×D414yes—
150C3⋊#170—22no—
151C3⋊#170—22no—
152C3×#170—22no—
153C3×#170—22no—
154C23×C3×C4—51no—
155C22×#67—51no—
156C22×#67AGL(1,𝔽5)11yescharacteristic
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⋊C8—51no—
168C22×C3⋊C8—51no—
169C2×ΓL(1,𝔽25)—54no—
170C2×ΓL(1,𝔽25)—104no—
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—
178C24×C5C4×D311yescharacteristic
179C23×D5—31no—
180C2×C5×D4—34no—
181C2×C5×D4—64no—
182C22×C4×C5—31no—
183C2×C22⋊D5—34no—
184C2×C22⋊D5—34no—
185C2×C22⋊D5—64no—
186C2×C22⋊D5—64no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—31no—
190C22×Dic5—32no—
191C22×Dic5—34no—
192C22×Dic5—34no—
193C22×Dic5—32no—
194C22×Dic5C4×D311yescharacteristic
195C22×Dic5C4×D312yes—
196C22×Dic5C22×D312yes—
197C22×Dic5C22×D311yescharacteristic
198#711—616no—
199#711—68no—
200#711—68no—
201C2×C4×D5—32no—
202C2×C4×D5—32no—
203C2×C4×D5—62no—
204C2×C4×D5—62no—
205C2×Dic10—34no—
206C2×Dic10—64no—
207#704—68no—
208C2×#170—22no—
209C2×#170—22no—
210C2×#170—32no—
211C2×#170—32no—
212C2×#170—68no—
213C2×#170—62no—
214C2×#170—62no—
215C2×#170C22×D312yes—
216C2×#170C22×D312yes—
217C22×#41—151no—
218C22×M16—151no—
219C23×C8—151no—
220#408—158no—
221C2×C22⋊C8—51no—
222C2×C22⋊C8—151no—
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—22no—
236C2×D15—44no—
237C2×C5×D3—22no—
238C2×C5×D3—22no—
239C2×C5×D3—28no—
240C2×C5×D3C2×C22⋊C414yes—
241Dic15C2×C22⋊C414yes—
242C3×Dic5—22no—
243C3×Dic5C2×C22⋊C412yes—
244C3×Dic5C22×D411yescharacteristic
245C3×Dic5C22×D411yescharacteristic
246C5×Dic3—22no—
247C24×C3C2×AGL(1,𝔽5)11yescharacteristic
248C23×D3—51no—
249C23×D3C2×AGL(1,𝔽5)11yescharacteristic
250C22×C3×C4—51no—
251C22×C3×C4—52no—
252C22×C3×C4—51no—
253C22×C3×C4—52no—
254C22×C3×C4—102no—
255C22×C3×C4—102no—
256C2×#67—24no—
257C2×#67—54no—
258C2×#67—104no—
259C2×#67C2×AGL(1,𝔽5)14yes—
260C22×Dic3—51no—
261C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
262#235—1016no—
263#235—108no—
264#235—108no—
265C2×D12—54no—
266C2×D12—104no—
267C2×C4×D3—54no—
268C2×C4×D3—54no—
269C2×C4×D3—52no—
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—52no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—102no—
284C2×C3⋊C8—102no—
285ΓL(1,𝔽25)—108no—
286D3×C8—108no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—22no—
290C23×C5—34no—
291C23×C5—32no—
292C23×C5—62no—
293C23×C5—62no—
294C23×C5C2×C4×D312yes—
295C23×C5C2×C4×D311yescharacteristic
296C22×D5—32no—
297C22×D5—62no—
298C22×D5—62no—
299C22×D5—62no—
300C5×D4—68no—
301C2×C4×C5—32no—
302C2×C4×C5—62no—
303C22⋊D5—68no—
304C22⋊D5—68no—
305C2×Dic5—22no—
306C2×Dic5—24no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—34no—
310C2×Dic5—32no—
311C2×Dic5—38no—
312C2×Dic5—34no—
313C2×Dic5—34no—
314C2×Dic5C2×C4×D312yes—
315C2×Dic5C2×C4×D311yescharacteristic
316C2×Dic5D3×D412yes—
317C2×Dic5D3×D412yes—
318C2×Dic5C23×D311yescharacteristic
319C4×D5—64no—
320C4×D5—62no—
321C4×D5—62no—
322Dic10—68no—
323#170—22no—
324#170—22no—
325#170—62no—
326#170—62no—
327C2×#41—154no—
328C2×#41—154no—
329C2×#41—304no—
330C2×#41—304no—
331C22×Q8—151no—
332C22×D4—31no—
333C22×D4—151no—
334C22×D4—151no—
335C23×C4—51no—
336C23×C4—151no—
337C23×C4—151no—
338C2×M16—154no—
339C2×M16—304no—
340C22×C8—51no—
341C22×C8—51no—
342C22×C8—154no—
343C22×C8—151no—
344C22×C8—151no—
345C22×C8—304no—
346C22⋊C8—54no—
347C22⋊C8—154no—
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—42no—
356C5×D3—24no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3C22×AGL(1,𝔽5)12yes—
361C23×C3C22×AGL(1,𝔽5)11yescharacteristic
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—52no—
365C22×D3—102no—
366C22×D3—102no—
367C22×D3—102no—
368C22×D3C22⋊AGL(1,𝔽5)14yes—
369C22×D3C22×AGL(1,𝔽5)12yes—
370C2×C3×C4—52no—
371C2×C3×C4—52no—
372C2×C3×C4—51no—
373C2×C3×C4—51no—
374C2×C3×C4—52no—
375C2×C3×C4—104no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379#67—28no—
380#67—108no—
381C2×Dic3—22no—
382C2×Dic3—54no—
383C2×Dic3—52no—
384C2×Dic3C22×AGL(1,𝔽5)12yes—
385D12—108no—
386C4×D3—58no—
387C4×D3—54no—
388C4×D3—54no—
389C4×D3—104no—
390C4×D3—102no—
391C4×D3—102no—
392Dic6—108no—
393C3×C8—102no—
394C3×C8—102no—
395C3⋊C8—102no—
396C3⋊C8—102no—
397C22×C5—22no—
398C22×C5—22no—
399C22×C5—22no—
400C22×C5—34no—
401C22×C5—44no—
402C22×C5—62no—
403C22×C5—62no—
404C22×C5—68no—
405C22×C5D3×C22⋊C412yes—
406C22×C5#90112yes—
407C22×C5#90712yes—
408C22×C5C22×C4×D311yescharacteristic
409C2×D5—62no—
410C2×D5—62no—
411C2×D5—62no—
412C2×D5—124no—
413C4×C5—62no—
414Dic5—22no—
415Dic5—34no—
416Dic5D3×C22⋊C412yes—
417Dic5C2×D3×D411yescharacteristic
418Dic5C2×D3×D411yescharacteristic
419C24—31no—
420C24—151no—
421C24D3×AGL(1,𝔽5)11yescharacteristic
422#41—308no—
423#41—308no—
424#41—3016no—
425C2×Q8—154no—
426C2×Q8—304no—
427C2×D4—34no—
428C2×D4—64no—
429C2×D4—154no—
430C2×D4—154no—
431C2×D4—304no—
432C2×D4—304no—
433C22×C4—31no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—51no—
438C22×C4—102no—
439C22×C4—102no—
440C22×C4—152no—
441C22×C4—152no—
442C22×C4—152no—
443C22×C4—154no—
444C22×C4—154no—
445C22×C4—152no—
446C22×C4—151no—
447C22×C4—302no—
448C22×C4—302no—
449M16—308no—
450C2×C8—52no—
451C2×C8—52no—
452C2×C8—102no—
453C2×C8—102no—
454C2×C8—152no—
455C2×C8—152no—
456C2×C8—308no—
457C2×C8—302no—
458C2×C8—302no—
459C3×C5C2×#40811yescharacteristic, complemented, Hall
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—44no—
464C22×C3#413112yes—
465C22×C3#413112yes—
466C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
467C22×C3C23×AGL(1,𝔽5)11yescharacteristic
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—28no—
471C2×D3—102no—
472C2×D3—102no—
473C2×D3—102no—
474C2×D3—204no—
475C2×D3C2×C22⋊AGL(1,𝔽5)14yes—
476C3×C4—52no—
477C3×C4—51no—
478C3×C4—51no—
479C3×C4—102no—
480Dic3—22no—
481Dic3—54no—
482C2×C5—42no—
483C2×C5—64no—
484C2×C5#472714yescomplemented
485C2×C5C2×D3×C22⋊C411yescharacteristic
486C2×C5C2×#90111yescharacteristic
487C2×C5C2×#90711yescharacteristic
488D5—122no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—34no—
493C23—32no—
494C23—62no—
495C23—62no—
496C23—152no—
497C23—302no—
498C23—302no—
499C23—302no—
500C23C2×D3×AGL(1,𝔽5)12yes—
501C23C2×D3×AGL(1,𝔽5)11yescharacteristic
502Q8—308no—
503D4—68no—
504D4—308no—
505D4—308no—
506C2×C4—32no—
507C2×C4—52no—
508C2×C4—52no—
509C2×C4—51no—
510C2×C4—51no—
511C2×C4—52no—
512C2×C4—62no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—104no—
516C2×C4—102no—
517C2×C4—154no—
518C2×C4—154no—
519C2×C4—158no—
520C2×C4—154no—
521C2×C4—152no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—304no—
525C8—102no—
526C8—102no—
527C8—302no—
528C8—302no—
529C2×C3—42no—
530C2×C3#6577514yescomplemented
531C2×C3C2×#413111yescharacteristic
532C2×C3C2×#413111yescharacteristic
533C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
534D3—24no—
535D3—202no—
536C5C2×#472711yescharacteristic, complemented, Sylow
537C22—22no—
538C22—22no—
539C22—22no—
540C22—34no—
541C22—44no—
542C22—62no—
543C22—62no—
544C22—68no—
545C22—302no—
546C22—302no—
547C22—302no—
548C22—604no—
549C22#9192712yes—
550C22#9192912yes—
551C22D3×C22⋊AGL(1,𝔽5)12yes—
552C22C22×D3×AGL(1,𝔽5)11yescharacteristic
553C4—51no—
554C4—51no—
555C4—52no—
556C4—62no—
557C4—102no—
558C4—154no—
559C3C2×#6577511yescharacteristic, complemented, Sylow
560C2—42no—
561C2—64no—
562C2—602no—
563C2#1175203814yesdirect product factor
564C2C2×#9192711yescharacteristic
565C2C2×#9192911yescharacteristic
566C2C2×D3×C22⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC22×#6782C2
cosocleC2×C3×Dic5C24
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#408
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C22×#6739C2semidirect
3. C22×D3×#170C2semidirect
4. C2×#91241C2semidirect
5. C2×C3×C22⋊#170C2semidirect
6. #11752038C2direct (N × H)
7. C2×#91171C2semidirect
8. C2×#91171C2semidirect
26. C2×#6739C22semidirect
28. C2×D3×#170C22semidirect
29. #91241C22semidirect
30. C3×C22⋊#170C22semidirect
31. #91171C22semidirect
32. #91171C22semidirect
38. C2×C22⋊#170D3semidirect
110. C22⋊#170C2×D3semidirect
351. C2×C3×C5#408semidirect
459. C3×C5C2×#408semidirect
484. C2×C5#4727semidirect
530. C2×C3#65775semidirect
536. C5C2×#4727semidirect
559. C3C2×#65775semidirect
563. C2#11752038direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C22×#67392
C22×D3×#1702
C2×#912412
C2×C3×C22⋊#1702
#117520382
C2×#911712
C2×#657753
C2×#47275