Finite Group Databasebeta

← C2×#11752395 #14417846

Subgroups — C2×#11752395 #14417846

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91992C211yesmaximal, characteristic, complemented
2C2×#91990C211yesmaximal, characteristic, complemented
3C2×C3×#4062C211yesmaximal, characteristic
4C2×#91239C211yesmaximal, characteristic, complemented
5C2×#91237C211yesmaximal, characteristic, complemented
6#11752395C218yesmaximal, direct product factor
7C2×#91224C211yesmaximal, characteristic, complemented
8C2×C8×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
9C2×#65736—31nomaximal, Hall
10C2×C3×#713C2211yescharacteristic
11C2×C3×#711C2211yescharacteristic
12C2×#6762—21no—
13C22×C3⋊#170—21no—
14#91992—22no—
15#91992C2214yescomplemented
16#91990—22no—
17#91990C2214yescomplemented
18C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
19C2×#6758—21no—
20C2×#6758C2211yescharacteristic
21C2×#6758C2211yescharacteristic
22C2×D5⋊(C3⋊C8)—21no—
23C2×D5⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×C5×SD16C411yescharacteristic, complemented
25C2×C3×#689C411yescharacteristic, complemented
26C2×C3×#686C411yescharacteristic, complemented
27C3×#4062C414yescomplemented
28C3×#4062C2214yes—
29C2×C3×#677C411yescharacteristic, complemented
30C2×C3×C8×D5C2211yescharacteristic
31#91239C2214yescomplemented
32#91237C2214yescomplemented
33#91224C2214yescomplemented
34C8×ΓL(1,𝔽16)C2214yescomplemented
35C2×#5196—51nomaximal, Hall
36C2×#4133—31no—
37C2×#4131—31no—
38C2×#4062D311yescharacteristic
39C2×#4010—31no—
40C2×#4008—31no—
41#65736—38no—
42C2×#3995—31no—
43C2×C8×AGL(1,𝔽5)—31no—
44C22×ΓL(1,𝔽16)—21no—
45C2×C3×C5×Q8C2×C411yescharacteristic
46C2×C3×C5×D4C2×C411yescharacteristic
47C2×C3×C22⋊D5—21no—
48C22×C3×Dic5—21no—
49C3×#713—21no—
50C3×#713—21no—
51C3×#713C2×C412yes—
52C3×#713C2312yes—
53C3×#711—21no—
54C3×#711—21no—
55C3×#711C2×C412yes—
56C3×#711C2312yes—
57C2×C3×D20—21no—
58C2×C3×D20C2×C411yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×C4×D5C2311yescharacteristic
61C2×C3×Dic10C2×C411yescharacteristic
62#6762—24no—
63C2×C3⋊#170—21no—
64C2×C3⋊#170—21no—
65C2×C3⋊#170—24no—
66C2×C3⋊#170D411yescharacteristic
67C2×C3⋊#170D411yescharacteristic
68C4×ΓL(1,𝔽16)—21no—
69C4×ΓL(1,𝔽16)C2312yes—
70#6758—21no—
71#6758—21no—
72#6758—24no—
73#6758C2312yes—
74#6758C2312yes—
75D5⋊(C3⋊C8)—24no—
76D5⋊(C3⋊C8)D412yes—
77D5⋊(C3⋊C8)C2312yes—
78C3×C5×SD16C2×C414yescomplemented
79C2×C3×C5×C8C2×C411yescharacteristic
80C3×#689C2×C414yescomplemented
81C3×#686C2×C414yescomplemented
82C2×C3×#168C2×C411yescharacteristic
83C3×#677C2×C414yescomplemented
84C3×C8×D5C2×C412yes—
85C3×C8×D5C2312yes—
86C2×C3×#135—51no—
87C2×#948—51no—
88C2×#948—51no—
89C2×#837—51no—
90C2×#837—51no—
91#5196—58no—
92C2×#819—51no—
93C2×C8×Dic3—51no—
94C2×#713C2×D311yescharacteristic
95C2×#711C2×D311yescharacteristic
96C2×#704—61no—
97C22×#170—61no—
98#4133—34no—
99#4133—62no—
100#4131—34no—
101#4131—62no—
102C2×C4×AGL(1,𝔽5)—31no—
103C2×#700—31no—
104C2×#700—31no—
105C2×#700—61no—
106C2×D5⋊C8—31no—
107C2×D5⋊C8—61no—
108C2×C5×SD16Dic311yescharacteristic, complemented
109C2×#689Dic311yescharacteristic, complemented
110C2×#686Dic311yescharacteristic, complemented
111#4062Dic314yescomplemented
112#4062C2×D314yes—
113C2×#677Dic311yescharacteristic, complemented
114C2×C8×D5C2×D311yescharacteristic
115#4010—34no—
116#4008—34no—
117#3995—34no—
118C8×AGL(1,𝔽5)—34no—
119C2×#443—151noSylow
120C23×C3×C5—21no—
121C22×C3×D5—21no—
122C22×C3×D5#4111yescharacteristic
123C2×ΓL(1,𝔽16)—24no—
124C2×ΓL(1,𝔽16)—22no—
125C3×C5×Q8—21no—
126C3×C5×Q8C22×C412yes—
127C3×C5×D4—21no—
128C3×C5×D4C22×C412yes—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5C22×C411yescharacteristic
131C3×C22⋊D5—22no—
132C3×C22⋊D5—22no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—22no—
136C2×C3×Dic5C2×D411yescharacteristic
137C3×D20—22no—
138C3×D20—22no—
139C3×D20—21no—
140C3×D20C22×C412yes—
141C3×C4×D5—22no—
142C3×C4×D5—22no—
143C3×C4×D5C22×C411yescharacteristic
144C3×C4×D5C2×D411yescharacteristic
145C3×C4×D5#4111yescharacteristic
146C3×C4×D5C2411yescharacteristic
147C3×Dic10—21no—
148C3×Dic10C22×C412yes—
149C3⋊#170—22no—
150C3⋊#170—22no—
151C3⋊#170C2×D412yes—
152C3⋊#170C2×D412yes—
153C3×C5×C8C22×C412yes—
154C3×#168C22×C412yes—
155C2×C3×#41—51no—
156C2×C3×#41—51no—
157C3×#135—54no—
158C3×#135—54no—
159C2×C3×Q16—51no—
160C2×C3×SD16—51no—
161C2×C3×SD16AGL(1,𝔽5)11yescharacteristic, complemented
162C2×C3×D8—51no—
163C22×C3×C8—51no—
164#948—54no—
165#948—54no—
166#948—102no—
167#948—102no—
168C2×C4×Dic3—51no—
169C2×#208—51no—
170C2×#208—51no—
171C2×#208—101no—
172C2×#208—101no—
173C22×C3⋊C8—51no—
174C22×C3⋊C8—101no—
175C22×C3⋊C8—101no—
176#837—54no—
177#837—54no—
178#819—54no—
179C8×Dic3—54no—
180C22×AGL(1,𝔽5)—61no—
181C2×C5×Q8C2×Dic311yescharacteristic
182C2×C5×D4C2×Dic311yescharacteristic
183C2×C22⋊D5—21no—
184C22×Dic5—21no—
185#713—21no—
186#713—21no—
187#713C2×Dic312yes—
188#713C22×D312yes—
189#711—21no—
190#711—21no—
191#711C2×Dic312yes—
192#711C22×D312yes—
193C2×D20—21no—
194C2×D20C2×Dic311yescharacteristic
195C2×C4×D5—21no—
196C2×C4×D5C22×D311yescharacteristic
197C2×Dic10C2×Dic311yescharacteristic
198#704—64no—
199C2×#170—31no—
200C2×#170—31no—
201C2×#170—64no—
202C2×#170—61no—
203C2×#170—61no—
204C4×AGL(1,𝔽5)—32no—
205C4×AGL(1,𝔽5)—61no—
206#700—32no—
207#700—32no—
208#700—64no—
209#700—61no—
210#700—61no—
211D5⋊C8—32no—
212D5⋊C8—32no—
213D5⋊C8—64no—
214C5×SD16C2×Dic314yescomplemented
215C2×C5×C8C2×Dic311yescharacteristic
216#689C2×Dic314yescomplemented
217#686C2×Dic314yescomplemented
218C2×#168C2×Dic311yescharacteristic
219#677C2×Dic314yescomplemented
220C8×D5C2×Dic312yes—
221C8×D5C22×D312yes—
222C2×#135—51no—
223C2×#131—151no—
224C2×#131—151no—
225#443—158no—
226C2×#108—151no—
227C2×#104—151no—
228C2×#104—151no—
229C2×C4×C8—151no—
230C22×C3×C5—22no—
231C22×C3×C5—42no—
232C22×C3×C5C4×D411yescharacteristic
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—42no—
236C2×C3×D5C4×D411yescharacteristic
237C2×C3×D5C2×#4111yescharacteristic
238ΓL(1,𝔽16)—24no—
239C3×C4×C5—22no—
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×Dic5—22no—
243C3×Dic5C4×D411yescharacteristic
244C3×Dic5C22×D411yescharacteristic
245C3×#41—52no—
246C3×#41—52no—
247C3×#41—52no—
248C3×#41—52no—
249C3×#41—101no—
250C3×#41—101no—
251C3×#41—101no—
252C3×#41—101no—
253C2×C3×Q8—51no—
254C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
255C2×C3×D4—51no—
256C2×C3×D4—101no—
257C2×C3×D4—101no—
258C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
259C22×C3×C4—51no—
260C22×C3×C4—101no—
261C22×C3×C4—101no—
262C22×Dic3—101no—
263C3×Q16—54no—
264C3×SD16—54no—
265C3×SD16C2×AGL(1,𝔽5)14yescomplemented
266C3×D8—54no—
267C2×C3×C8—51no—
268C2×C3×C8—52no—
269C2×C3×C8—52no—
270C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
271C4×Dic3—52no—
272C4×Dic3—101no—
273#208—52no—
274#208—52no—
275#208—104no—
276#208—104no—
277#208—101no—
278#208—101no—
279C2×C3⋊C8—52no—
280C2×C3⋊C8—52no—
281C2×C3⋊C8—51no—
282C2×C3⋊C8—51no—
283C2×C3⋊C8—104no—
284C2×C3⋊C8—104no—
285C2×C3⋊C8—101no—
286C2×C3⋊C8—101no—
287C23×C5—21no—
288C22×D5—21no—
289C22×D5#23711yescharacteristic
290C2×AGL(1,𝔽5)—64no—
291C2×AGL(1,𝔽5)—62no—
292C5×Q8—21no—
293C5×Q8C22×Dic312yes—
294C5×D4—21no—
295C5×D4C22×Dic312yes—
296C2×C4×C5—21no—
297C2×C4×C5C22×Dic311yescharacteristic
298C22⋊D5—22no—
299C22⋊D5—22no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5D3×D411yescharacteristic
304D20—22no—
305D20—22no—
306D20—21no—
307D20C22×Dic312yes—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5D3×D411yescharacteristic
311C4×D5#23711yescharacteristic
312C4×D5C22×Dic311yescharacteristic
313C4×D5C23×D311yescharacteristic
314Dic10—21no—
315Dic10C22×Dic312yes—
316#170—32no—
317#170—32no—
318#170—62no—
319#170—62no—
320C5×C8C22×Dic312yes—
321#168C22×Dic312yes—
322C2×#41—51no—
323C2×#41—51no—
324#135—54no—
325#135—54no—
326C2×Q16—51no—
327C2×SD16—51no—
328C2×SD16ΓL(1,𝔽16)11yescharacteristic, complemented
329C2×D8—51no—
330#131—154no—
331#131—154no—
332#131—302no—
333#131—302no—
334C2×M16—151no—
335C2×M16—151no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—51no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42—151no—
343#108—154no—
344#104—154no—
345#104—154no—
346C4×C8—154no—
347C2×C3×C5—42no—
348C2×C3×C5#44312yescomplemented
349C2×C3×C5C2×C4×D411yescharacteristic
350C3×D5—21no—
351C3×D5—21no—
352C3×D5—42no—
353C23×C3—21no—
354C23×C3—51no—
355C23×C3—101no—
356C3×Q8—21no—
357C3×Q8—52no—
358C3×Q8—101no—
359C3×Q8C22×AGL(1,𝔽5)12yes—
360C3×D4—21no—
361C3×D4—52no—
362C3×D4—102no—
363C3×D4—102no—
364C3×D4—102no—
365C3×D4—102no—
366C3×D4—101no—
367C3×D4C22×AGL(1,𝔽5)12yes—
368C2×C3×C4—21no—
369C2×C3×C4—51no—
370C2×C3×C4—51no—
371C2×C3×C4—51no—
372C2×C3×C4—51no—
373C2×C3×C4—51no—
374C2×C3×C4—102no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—101no—
379C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
380C2×Dic3—102no—
381C2×Dic3—104no—
382C3×C8—52no—
383C3×C8C22×AGL(1,𝔽5)12yes—
384C3⋊C8—52no—
385C3⋊C8—52no—
386C3⋊C8—102no—
387C3⋊C8—102no—
388C22×C5—22no—
389C22×C5—42no—
390C22×C5D4×Dic311yescharacteristic
391C2×D5—22no—
392C2×D5—22no—
393C2×D5—42no—
394C2×D5D4×Dic311yescharacteristic
395C2×D5C2×#23711yescharacteristic
396AGL(1,𝔽5)—64no—
397C4×C5—22no—
398C4×C5D4×Dic311yescharacteristic
399C4×C5C23×Dic311yescharacteristic
400Dic5—22no—
401Dic5D4×Dic311yescharacteristic
402Dic5C2×D3×D411yescharacteristic
403#41—52no—
404#41—52no—
405#41—52no—
406#41—52no—
407#41—101no—
408#41—101no—
409#41—101no—
410#41—101no—
411C2×Q8—51no—
412C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
413C2×D4—51no—
414C2×D4—101no—
415C2×D4—101no—
416C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
417C22×C4—51no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—301no—
421Q16—54no—
422SD16—54no—
423SD16C2×ΓL(1,𝔽16)14yescomplemented
424D8—54no—
425M16—152no—
426M16—152no—
427M16—304no—
428M16—304no—
429M16—301no—
430M16—301no—
431C2×C8—51no—
432C2×C8—52no—
433C2×C8—52no—
434C2×C8—152no—
435C2×C8—151no—
436C2×C8—151no—
437C2×C8—152no—
438C2×C8—304no—
439C2×C8—304no—
440C2×C8—301no—
441C2×C8—301no—
442C2×C8C2×ΓL(1,𝔽16)11yescharacteristic
443C42—152no—
444C42—301no—
445C3×C5C2×#44311yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—42no—
448C22×C3—51no—
449C22×C3—51no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3—202no—
453C22×C3D4×AGL(1,𝔽5)11yescharacteristic
454C3×C4—22no—
455C3×C4—51no—
456C3×C4—51no—
457C3×C4—102no—
458C3×C4D4×AGL(1,𝔽5)11yescharacteristic
459C3×C4C23×AGL(1,𝔽5)11yescharacteristic
460Dic3—104no—
461C2×C5—42no—
462C2×C5#519612yescomplemented
463C2×C5C2×D4×Dic311yescharacteristic
464D5—21no—
465D5—21no—
466D5—42no—
467C23—21no—
468C23—51no—
469C23—101no—
470Q8—21no—
471Q8—52no—
472Q8—101no—
473Q8C22×ΓL(1,𝔽16)12yes—
474D4—21no—
475D4—52no—
476D4—102no—
477D4—102no—
478D4—102no—
479D4—102no—
480D4—101no—
481D4C22×ΓL(1,𝔽16)12yes—
482C2×C4—21no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—51no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—101no—
493C2×C4—302no—
494C2×C4—304no—
495C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
496C8—52no—
497C8—152no—
498C8—152no—
499C8—302no—
500C8—302no—
501C8C22×ΓL(1,𝔽16)12yes—
502C2×C3—42no—
503C2×C3—101no—
504C2×C3—101no—
505C2×C3—202no—
506C2×C3#6573612yescomplemented
507C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
508C5C2×#519611yescharacteristic, complemented, Sylow
509C22—22no—
510C22—42no—
511C22—51no—
512C22—51no—
513C22—102no—
514C22—102no—
515C22—202no—
516C22D4×ΓL(1,𝔽16)11yescharacteristic
517C4—22no—
518C4—51no—
519C4—51no—
520C4—102no—
521C4—304no—
522C4D4×ΓL(1,𝔽16)11yescharacteristic
523C4C23×ΓL(1,𝔽16)11yescharacteristic
524C3C2×#6573611yescharacteristic, complemented, Sylow
525C2—42no—
526C2—101no—
527C2—101no—
528C2—202no—
529C2#1175239512yesdirect product factor
530C2C2×D4×ΓL(1,𝔽16)11yescharacteristic
subgroupG/H
centerC22D4×ΓL(1,𝔽16)
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC2×C3×C5×SD16C4
socleC22×C3×C5C4×D4
prime radicalC2×C3×#4062C2
cosocleC3×C4×D5C24
hypercenterC2×SD16ΓL(1,𝔽16)
hypocenterC3×C5C2×#443
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#91992C2semidirect
2. C2×#91990C2semidirect
4. C2×#91239C2semidirect
5. C2×#91237C2semidirect
6. #11752395C2direct (N × H)
7. C2×#91224C2semidirect
8. C2×C8×ΓL(1,𝔽16)C2semidirect
15. #91992C22semidirect
17. #91990C22semidirect
24. C2×C3×C5×SD16C4semidirect
25. C2×C3×#689C4semidirect
26. C2×C3×#686C4semidirect
27. C3×#4062C4semidirect
29. C2×C3×#677C4semidirect
31. #91239C22semidirect
32. #91237C22semidirect
33. #91224C22semidirect
34. C8×ΓL(1,𝔽16)C22semidirect
78. C3×C5×SD16C2×C4semidirect
80. C3×#689C2×C4semidirect
81. C3×#686C2×C4semidirect
83. C3×#677C2×C4semidirect
108. C2×C5×SD16Dic3semidirect
109. C2×#689Dic3semidirect
110. C2×#686Dic3semidirect
111. #4062Dic3semidirect
113. C2×#677Dic3semidirect
161. C2×C3×SD16AGL(1,𝔽5)semidirect
214. C5×SD16C2×Dic3semidirect
216. #689C2×Dic3semidirect
217. #686C2×Dic3semidirect
219. #677C2×Dic3semidirect
265. C3×SD16C2×AGL(1,𝔽5)semidirect
328. C2×SD16ΓL(1,𝔽16)semidirect
348. C2×C3×C5#443semidirect
423. SD16C2×ΓL(1,𝔽16)semidirect
445. C3×C5C2×#443semidirect
462. C2×C5#5196semidirect
506. C2×C3#65736semidirect
508. C5C2×#5196semidirect
524. C3C2×#65736semidirect
529. C2#11752395direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919922
C2×#919902
C2×C3×#40622
C2×#912392
C2×#912372
#117523952
C2×#912242
C2×C8×ΓL(1,𝔽16)2
C2×#657363
C2×#51965