Finite Group Databasebeta

← C2×#11751952 #14417987

Subgroups — C2×#11751952 #14417987

Order 1920.

928 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×C3×#4131C211yesmaximal, characteristic, complemented
2C2×#91911C211yesmaximal, characteristic, complemented
3C2×#91490C211yesmaximal, characteristic
4C2×#91237C211yesmaximal, characteristic, complemented
5#11751952C218yesmaximal, direct product factor
6C2×#91161C211yesmaximal, characteristic, complemented
7C2×#91155C211yesmaximal, characteristic, complemented
8C2×#91150C211yesmaximal, characteristic, complemented
9C2×#65733—31nomaximal, Hall
10C2×C3×#711C2211yescharacteristic
11C2×#6772C2211yescharacteristic
12C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
13C2×#6758C2211yescharacteristic
14C2×C3×#704—21no—
15C22×C3×#170—21no—
16C3×#4131—22no—
17C3×#4131C2214yescomplemented
18C2×C3×#700C2211yescharacteristic
19C2×C3×D5⋊C8C2211yescharacteristic
20C2×#6739—21no—
21C2×D3×#170—21no—
22#91911—22no—
23#91911C2214yescomplemented
24C2×#6716C411yescharacteristic, complemented
25C2×C5×#213C411yescharacteristic, complemented
26#91490C414yescomplemented
27#91490C2214yes—
28C2×#6662C411yescharacteristic, complemented
29C2×#6656C411yescharacteristic, complemented
30C2×D5×C3⋊C8C2211yescharacteristic
31#91237C2214yescomplemented
32#91161C2214yescomplemented
33#91155C2214yescomplemented
34#91150C2214yescomplemented
35C2×#5145—51nomaximal, Hall
36C2×#4131—31no—
37C2×#4131D311yescharacteristic, complemented
38C2×#4058—31no—
39C2×#4008—31no—
40C2×#4008—31no—
41#65733—38no—
42C2×#3995—31no—
43C2×#3992—31no—
44C22×ΓL(1,𝔽16)—21no—
45C2×C3×C5×D4C2×C411yescharacteristic
46C2×Dic30C2×C411yescharacteristic
47C2×C5×D12C2×C411yescharacteristic
48C2×C3×C22⋊D5—21no—
49C22×C3×Dic5—21no—
50C3×#711—21no—
51C3×#711—21no—
52C3×#711C2×C412yes—
53C3×#711C2312yes—
54C2×C3×C4×D5C2311yescharacteristic
55C2×C3×Dic10C2×C411yescharacteristic
56C2×#1201—21no—
57C2×D3×Dic5—21no—
58#6772—21no—
59#6772—21no—
60#6772C2×C412yes—
61#6772C2312yes—
62C2×C3⋊#170—21no—
63C4×ΓL(1,𝔽16)—21no—
64C4×ΓL(1,𝔽16)C2312yes—
65#6758—21no—
66#6758C2312yes—
67C3×#704—24no—
68C2×C3×#170—21no—
69C2×C3×#170—24no—
70C2×C3×#170D411yescharacteristic
71C2×C3×#170D411yescharacteristic
72C3×#700—21no—
73C3×#700C2312yes—
74C3×D5⋊C8D412yes—
75C3×D5⋊C8C2312yes—
76#6739—24no—
77D3×#170—24no—
78#6716C2×C414yescomplemented
79C2×C3⋊#168C2×C411yescharacteristic
80C5×#213C2×C414yescomplemented
81C2×C5×C3⋊C8C2×C411yescharacteristic
82#6662C2×C414yescomplemented
83#6656C2×C414yescomplemented
84D5×C3⋊C8C2×C412yes—
85D5×C3⋊C8C2312yes—
86C2×C3×#131—51no—
87C2×#950—51no—
88C2×#901—51no—
89C2×#837—51no—
90#5145—58no—
91C2×#825—51no—
92C2×#822—51no—
93C2×#815—51no—
94C2×#711—31no—
95C2×#711C2×D311yescharacteristic
96C2×#704—21no—
97C2×#704—61no—
98C22×#170—21no—
99C22×#170—61no—
100#4131—22no—
101#4131—34no—
102#4131—62no—
103#4131C2×D314yescomplemented
104C2×C4×AGL(1,𝔽5)—31no—
105C2×#700—31no—
106C2×#700C2×D311yescharacteristic
107C2×D5⋊C8C2×D311yescharacteristic
108C2×C5×D8—31no—
109C2×#687—31no—
110C2×#687—31no—
111#4058—34no—
112#4058—34no—
113C2×Dic20—31no—
114C2×C8×D5—31no—
115#4008—34no—
116#4008—34no—
117#3995—34no—
118#3992—34no—
119C2×#444—151noSylow
120C23×C3×C5—21no—
121C22×C5×D3—21no—
122C22×C3×D5#4111yescharacteristic
123C2×ΓL(1,𝔽16)—22no—
124C2×ΓL(1,𝔽16)—42no—
125C3×C5×D4—21no—
126C3×C5×D4C22×C412yes—
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×Dic15—21no—
129Dic30—21no—
130Dic30C22×C412yes—
131C5×D12—21no—
132C5×D12C22×C412yes—
133C3×C22⋊D5—22no—
134C3×C22⋊D5—22no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C2×D411yescharacteristic
139C3×C4×D5C22×C411yescharacteristic
140C3×C4×D5C2×D411yescharacteristic
141C3×C4×D5#4111yescharacteristic
142C3×C4×D5C2411yescharacteristic
143C3×Dic10—21no—
144C3×Dic10C22×C412yes—
145#1201—22no—
146#1201—22no—
147D3×Dic5—22no—
148D3×Dic5—22no—
149C3⋊#170—22no—
150C3×#170—22no—
151C3×#170C2×D412yes—
152C3×#170C2×D412yes—
153C3⋊#168C22×C412yes—
154C5×C3⋊C8C22×C412yes—
155C2×C3×#41—51no—
156C2×#235—51no—
157C3×#131—54no—
158C3×#131—102no—
159C2×C3×M16—51no—
160C2×C3×M16—101no—
161C22×C3×C8—51no—
162C22×C3×C8—101no—
163#950—54no—
164#950—54no—
165C2×#216—51no—
166C2×#215—51no—
167C2×#214—51no—
168C2×#213AGL(1,𝔽5)11yescharacteristic, complemented
169C2×C4×Dic3—51no—
170C2×#208—51no—
171C22×C3⋊C8—51no—
172#901—54no—
173#901—102no—
174C2×ΓL(1,𝔽25)—101no—
175C2×D3×C8—101no—
176#837—54no—
177#825—54no—
178#822—54no—
179#815—54no—
180C22×AGL(1,𝔽5)—61no—
181C2×C5×D4—31no—
182C2×C5×D4C4×D311yescharacteristic
183C2×C22⋊D5—21no—
184C2×C22⋊D5—61no—
185C22×Dic5—21no—
186C22×Dic5—61no—
187#711—21no—
188#711—21no—
189#711—32no—
190#711—32no—
191#711—61no—
192#711—61no—
193#711C4×D312yes—
194#711C22×D312yes—
195C2×C4×D5C22×D311yescharacteristic
196C2×Dic10—31no—
197C2×Dic10C4×D311yescharacteristic
198#704—24no—
199#704—64no—
200C2×#170—21no—
201C2×#170—24no—
202C2×#170—61no—
203C2×#170—64no—
204C2×#170#6711yescharacteristic
205C2×#170#6711yescharacteristic
206C4×AGL(1,𝔽5)—32no—
207C4×AGL(1,𝔽5)—61no—
208#700—21no—
209#700—32no—
210#700—61no—
211#700C22×D312yes—
212D5⋊C8#6712yes—
213D5⋊C8C22×D312yes—
214C5×D8—34no—
215C2×C5×C8—31no—
216#687—34no—
217#687—34no—
218C2×#168—31no—
219Dic20—34no—
220C8×D5—32no—
221C8×D5—32no—
222C2×#135—151no—
223C2×#131—51no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—151no—
228C2×#104—151no—
229C2×#97—151no—
230C22×C3×C5—22no—
231C22×C3×C5—42no—
232C22×C3×C5C4×D411yescharacteristic
233C2×C5×D3—22no—
234C2×C5×D3—42no—
235C2×C3×D5—22no—
236C2×C3×D5C4×D411yescharacteristic
237C2×C3×D5C2×#4111yescharacteristic
238ΓL(1,𝔽16)—42no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C23×C411yescharacteristic
241Dic15—22no—
242C3×Dic5—22no—
243C3×Dic5C4×D411yescharacteristic
244C3×Dic5C22×D411yescharacteristic
245C3×#41—52no—
246C3×#41—52no—
247C3×#41—101no—
248C3×#41—101no—
249C2×C3×Q8—51no—
250C2×C3×D4—101no—
251C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
252C22×C3×C4—51no—
253C22×C3×C4—101no—
254C2×#67—101no—
255C22×Dic3—101no—
256#235—52no—
257#235—52no—
258#235—101no—
259#235—101no—
260C2×D12C2×AGL(1,𝔽5)11yescharacteristic
261C2×C4×D3—101no—
262C2×Dic6—51no—
263C3×M16—52no—
264C3×M16—104no—
265C3×M16—101no—
266C2×C3×C8—52no—
267C2×C3×C8—52no—
268C2×C3×C8—51no—
269C2×C3×C8—51no—
270C2×C3×C8—104no—
271C2×C3×C8—101no—
272#216—54no—
273#215—54no—
274#214—54no—
275#213C2×AGL(1,𝔽5)14yescomplemented
276C4×Dic3—52no—
277C4×Dic3—101no—
278#208—52no—
279#208—101no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—101no—
284C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287C23×C5—21no—
288C23×C5—61no—
289C22×D5#23511yescharacteristic
290C2×AGL(1,𝔽5)—62no—
291C2×AGL(1,𝔽5)—122no—
292C5×D4—21no—
293C5×D4—32no—
294C5×D4—61no—
295C5×D4C2×C4×D312yes—
296C2×C4×C5C2×C4×D311yescharacteristic
297C22⋊D5—22no—
298C22⋊D5—22no—
299C22⋊D5—62no—
300C22⋊D5—62no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—61no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5C2×#6711yescharacteristic
308C4×D5C2×C4×D311yescharacteristic
309C4×D5#23511yescharacteristic
310C4×D5C2×#6711yescharacteristic
311C4×D5C23×D311yescharacteristic
312Dic10—21no—
313Dic10—32no—
314Dic10—61no—
315Dic10C2×C4×D312yes—
316#170—22no—
317#170—62no—
318#170C2×#6712yes—
319#170C2×#6712yes—
320C5×C8—32no—
321#168—32no—
322C2×#41—51no—
323C2×#41—151no—
324#135—154no—
325#135—154no—
326C2×Q16—151no—
327C2×SD16—151no—
328C2×SD16—151no—
329C2×D8—31no—
330#131—54no—
331#131—102no—
332#131—154no—
333#131—302no—
334C2×M16—51no—
335C2×M16—101no—
336C2×M16—151no—
337C2×M16—301no—
338C22×C8—51no—
339C22×C8—101no—
340C22×C8—151no—
341C22×C8—301no—
342C2×C42—151no—
343#108—154no—
344#104—154no—
345#104—154no—
346#97—154no—
347C2×C3×C5—42no—
348C2×C3×C5#44412yescomplemented
349C2×C3×C5C2×C4×D411yescharacteristic
350C3×D5—21no—
351C3×D5—21no—
352C5×D3—42no—
353C23×C3—21no—
354C23×C3—51no—
355C22×D3—21no—
356C3×Q8—52no—
357C3×Q8—101no—
358C3×D4—21no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4C22×AGL(1,𝔽5)12yes—
362C2×C3×C4—51no—
363C2×C3×C4—51no—
364C2×C3×C4—51no—
365C2×C3×C4—51no—
366C2×C3×C4—51no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—101no—
370C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
371#67—102no—
372#67—102no—
373C2×Dic3—101no—
374C2×Dic3—102no—
375C2×Dic3—202no—
376D12—21no—
377D12C22×AGL(1,𝔽5)12yes—
378C4×D3—102no—
379C4×D3—102no—
380Dic6—52no—
381Dic6—101no—
382C3×C8—52no—
383C3×C8—52no—
384C3×C8—102no—
385C3⋊C8—52no—
386C3⋊C8—102no—
387C3⋊C8C22×AGL(1,𝔽5)12yes—
388C22×C5—22no—
389C22×C5—42no—
390C22×C5—62no—
391C22×C5—122no—
392C22×C5C4×#6711yescharacteristic
393C2×D5—22no—
394C2×D5C4×#6711yescharacteristic
395C2×D5C2×#23511yescharacteristic
396AGL(1,𝔽5)—122no—
397C4×C5C4×#6711yescharacteristic
398C4×C5C22×C4×D311yescharacteristic
399Dic5—22no—
400Dic5—62no—
401Dic5C4×#6711yescharacteristic
402Dic5C22×#6711yescharacteristic
403#41—52no—
404#41—52no—
405#41—101no—
406#41—101no—
407#41—152no—
408#41—152no—
409#41—301no—
410#41—301no—
411C2×Q8—51no—
412C2×Q8—151no—
413C2×D4—31no—
414C2×D4—101no—
415C2×D4—301no—
416C2×D4D3×AGL(1,𝔽5)11yescharacteristic
417C22×C4—51no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4—301no—
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—34no—
425M16—52no—
426M16—104no—
427M16—101no—
428M16—152no—
429M16—304no—
430M16—301no—
431C2×C8—31no—
432C2×C8—52no—
433C2×C8—51no—
434C2×C8—51no—
435C2×C8—52no—
436C2×C8—104no—
437C2×C8—101no—
438C2×C8—152no—
439C2×C8—152no—
440C2×C8—151no—
441C2×C8—304no—
442C2×C8—301no—
443C42—152no—
444C42—301no—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—42no—
448C22×C3—51no—
449C22×C3—51no—
450C22×C3—102no—
451C22×C3D4×AGL(1,𝔽5)11yescharacteristic
452C2×D3—22no—
453C2×D3—42no—
454C3×C4—51no—
455C3×C4—51no—
456C3×C4—102no—
457C3×C4D4×AGL(1,𝔽5)11yescharacteristic
458C3×C4C23×AGL(1,𝔽5)11yescharacteristic
459Dic3—102no—
460Dic3—202no—
461C2×C5—42no—
462C2×C5—122no—
463C2×C5#514512yescomplemented
464C2×C5C2×C4×#6711yescharacteristic
465D5—21no—
466D5—21no—
467C23—21no—
468C23—51no—
469C23—61no—
470Q8—52no—
471Q8—101no—
472Q8—152no—
473Q8—301no—
474D4—21no—
475D4—32no—
476D4—61no—
477D4—102no—
478D4—102no—
479D4—302no—
480D4—302no—
481D4C2×D3×AGL(1,𝔽5)12yes—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—102no—
488C2×C4—102no—
489C2×C4—101no—
490C2×C4—302no—
491C2×C4—302no—
492C2×C4—301no—
493C2×C4—302no—
494C2×C4—602no—
495C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
496C8—32no—
497C8—52no—
498C8—52no—
499C8—102no—
500C8—152no—
501C8—302no—
502C2×C3—42no—
503C2×C3—101no—
504C2×C3—101no—
505C2×C3#6573312yescomplemented
506C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
507D3—42no—
508C5C2×#514511yescharacteristic, complemented, Sylow
509C22—22no—
510C22—42no—
511C22—51no—
512C22—51no—
513C22—62no—
514C22—102no—
515C22—122no—
516C22AGL(1,𝔽5)×#6711yescharacteristic
517C4—51no—
518C4—51no—
519C4—102no—
520C4—302no—
521C4—602no—
522C4AGL(1,𝔽5)×#6711yescharacteristic
523C4C22×D3×AGL(1,𝔽5)11yescharacteristic
524C3C2×#6573311yescharacteristic, complemented, Sylow
525C2—42no—
526C2—101no—
527C2—101no—
528C2—122no—
529C2#1175195212yesdirect product factor
530C2C2×AGL(1,𝔽5)×#6711yescharacteristic
subgroupG/H
centerC22AGL(1,𝔽5)×#67
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×#91490C2
cosocleC3×C4×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4131C2semidirect
2. C2×#91911C2semidirect
4. C2×#91237C2semidirect
5. #11751952C2direct (N × H)
6. C2×#91161C2semidirect
7. C2×#91155C2semidirect
8. C2×#91150C2semidirect
17. C3×#4131C22semidirect
23. #91911C22semidirect
24. C2×#6716C4semidirect
25. C2×C5×#213C4semidirect
26. #91490C4semidirect
28. C2×#6662C4semidirect
29. C2×#6656C4semidirect
31. #91237C22semidirect
32. #91161C22semidirect
33. #91155C22semidirect
34. #91150C22semidirect
37. C2×#4131D3semidirect
78. #6716C2×C4semidirect
80. C5×#213C2×C4semidirect
82. #6662C2×C4semidirect
83. #6656C2×C4semidirect
103. #4131C2×D3semidirect
168. C2×#213AGL(1,𝔽5)semidirect
275. #213C2×AGL(1,𝔽5)semidirect
348. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
463. C2×C5#5145semidirect
505. C2×C3#65733semidirect
508. C5C2×#5145semidirect
524. C3C2×#65733semidirect
529. C2#11751952direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41312
C2×#919112
C2×#914902
C2×#912372
#117519522
C2×#911612
C2×#911552
C2×#911502
C2×#657333
C2×#51455