Finite Group Databasebeta

← C2×#11751978 #14417992

Subgroups — C2×#11751978 #14417992

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×#4133C211yesmaximal, characteristic, complemented
2C2×#91914C211yesmaximal, characteristic, complemented
3C2×#91516C211yesmaximal, characteristic
4C2×#91239C211yesmaximal, characteristic, complemented
5#11751978C218yesmaximal, direct product factor
6C2×#91161C211yesmaximal, characteristic, complemented
7C2×#91157C211yesmaximal, characteristic, complemented
8C2×#91150C211yesmaximal, characteristic, complemented
9C2×#65741—31nomaximal, Hall
10C2×C3×#713C2211yescharacteristic
11C2×#6773C2211yescharacteristic
12C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
13C2×#6758C2211yescharacteristic
14C3×#4133—22no—
15C3×#4133C2214yescomplemented
16C2×C3×#700—21no—
17C2×C3×#700C2211yescharacteristic
18C2×C3×D5⋊C8—21no—
19C2×C3×D5⋊C8C2211yescharacteristic
20C2×#6740—21no—
21C2×#6738—21no—
22#91914—22no—
23#91914C2214yescomplemented
24C2×#6717C411yescharacteristic, complemented
25C2×C5×#216C411yescharacteristic, complemented
26#91516C414yescomplemented
27#91516C2214yes—
28C2×#6655C411yescharacteristic, complemented
29C2×#6653C411yescharacteristic, complemented
30C2×D5×C3⋊C8C2211yescharacteristic
31#91239C2214yescomplemented
32#91161C2214yescomplemented
33#91157C2214yescomplemented
34#91150C2214yescomplemented
35C2×#5145—51nomaximal, Hall
36C2×#4133—31no—
37C2×#4133D311yescharacteristic, complemented
38C2×#4065—31no—
39C2×#4010—31no—
40C2×#4010—31no—
41#65741—38no—
42C2×#3995—31no—
43C2×#3992—31no—
44C22×ΓL(1,𝔽16)—21no—
45C2×C3×C5×Q8C2×C411yescharacteristic
46C2×D60C2×C411yescharacteristic
47C2×C5×Dic6C2×C411yescharacteristic
48C3×#713—21no—
49C3×#713—21no—
50C3×#713C2×C412yes—
51C3×#713C2312yes—
52C2×C3×D20—21no—
53C2×C3×D20C2×C411yescharacteristic
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5C2311yescharacteristic
56C2×#1202—21no—
57C2×#1200—21no—
58#6773—21no—
59#6773—21no—
60#6773C2×C412yes—
61#6773C2312yes—
62C2×C3⋊#170—21no—
63C4×ΓL(1,𝔽16)—21no—
64C4×ΓL(1,𝔽16)C2312yes—
65#6758—21no—
66#6758C2312yes—
67C2×C3×#170—21no—
68C2×C3×#170D411yescharacteristic
69C2×C3×#170D411yescharacteristic
70C3×#700—21no—
71C3×#700—24no—
72C3×#700C2312yes—
73C3×D5⋊C8—24no—
74C3×D5⋊C8D412yes—
75C3×D5⋊C8C2312yes—
76#6740—24no—
77#6738—24no—
78#6717C2×C414yescomplemented
79C2×C3⋊#168C2×C411yescharacteristic
80C5×#216C2×C414yescomplemented
81C2×C5×C3⋊C8C2×C411yescharacteristic
82#6655C2×C414yescomplemented
83#6653C2×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×#713—31no—
95C2×#713C2×D311yescharacteristic
96#4133—22no—
97#4133—34no—
98#4133—62no—
99#4133C2×D314yescomplemented
100C2×C4×AGL(1,𝔽5)—31no—
101C2×#700—21no—
102C2×#700—31no—
103C2×#700—61no—
104C2×#700C2×D311yescharacteristic
105C2×D5⋊C8—21no—
106C2×D5⋊C8—61no—
107C2×D5⋊C8C2×D311yescharacteristic
108C2×C5×Q16—31no—
109C2×#688—31no—
110C2×#688—31no—
111#4065—34no—
112#4065—34no—
113C2×D40—31no—
114C2×C8×D5—31no—
115#4010—34no—
116#4010—34no—
117#3995—34no—
118#3992—34no—
119C2×#444—151noSylow
120C22×D15—21no—
121C22×C3×D5—21no—
122C22×C3×D5#4111yescharacteristic
123C2×ΓL(1,𝔽16)—22no—
124C2×ΓL(1,𝔽16)—42no—
125C3×C5×Q8—21no—
126C3×C5×Q8C22×C412yes—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5C22×C411yescharacteristic
129D60—21no—
130D60C22×C412yes—
131C2×C5×Dic3—21no—
132C5×Dic6—21no—
133C5×Dic6C22×C412yes—
134C2×C3×Dic5C2×D411yescharacteristic
135C3×D20—22no—
136C3×D20—22no—
137C3×D20—21no—
138C3×D20C22×C412yes—
139C3×C4×D5—22no—
140C3×C4×D5—22no—
141C3×C4×D5C22×C411yescharacteristic
142C3×C4×D5C2×D411yescharacteristic
143C3×C4×D5#4111yescharacteristic
144C3×C4×D5C2411yescharacteristic
145#1202—22no—
146#1202—22no—
147#1200—22no—
148#1200—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×#216AGL(1,𝔽5)11yescharacteristic, complemented
166C2×#215—51no—
167C2×#214—51no—
168C2×#213—51no—
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×Q8—31no—
182C2×C5×Q8C4×D311yescharacteristic
183#713—21no—
184#713—21no—
185#713—32no—
186#713—32no—
187#713—61no—
188#713—61no—
189#713C4×D312yes—
190#713C22×D312yes—
191C2×D20—21no—
192C2×D20—31no—
193C2×D20—61no—
194C2×D20C4×D311yescharacteristic
195C2×C4×D5—21no—
196C2×C4×D5—61no—
197C2×C4×D5C22×D311yescharacteristic
198C2×#170—21no—
199C2×#170—61no—
200C2×#170#6711yescharacteristic
201C2×#170#6711yescharacteristic
202C4×AGL(1,𝔽5)—32no—
203C4×AGL(1,𝔽5)—61no—
204#700—21no—
205#700—24no—
206#700—32no—
207#700—61no—
208#700—64no—
209#700C22×D312yes—
210D5⋊C8—24no—
211D5⋊C8—64no—
212D5⋊C8#6712yes—
213D5⋊C8C22×D312yes—
214C5×Q16—34no—
215C2×C5×C8—31no—
216#688—34no—
217#688—34no—
218C2×#168—31no—
219D40—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×C5C4×D411yescharacteristic
231C2×D15—22no—
232C2×D15—42no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5—42no—
236C2×C3×D5C4×D411yescharacteristic
237C2×C3×D5C2×#4111yescharacteristic
238ΓL(1,𝔽16)—42no—
239C3×C4×C5—22no—
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×Dic5C4×D411yescharacteristic
243C3×Dic5C22×D411yescharacteristic
244C5×Dic3—22no—
245C3×#41—52no—
246C3×#41—52no—
247C3×#41—101no—
248C3×#41—101no—
249C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
250C2×C3×D4—51no—
251C2×C3×D4—101no—
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×D12—51no—
261C2×C4×D3—101no—
262C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
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#216C2×AGL(1,𝔽5)14yescomplemented
273#215—54no—
274#214—54no—
275#213—54no—
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—
287C22×D5—21no—
288C22×D5—61no—
289C22×D5#23511yescharacteristic
290C2×AGL(1,𝔽5)—62no—
291C2×AGL(1,𝔽5)—122no—
292C5×Q8—21no—
293C5×Q8—32no—
294C5×Q8—61no—
295C5×Q8C2×C4×D312yes—
296C2×C4×C5—21no—
297C2×C4×C5—61no—
298C2×C4×C5C2×C4×D311yescharacteristic
299C2×Dic5C2×#6711yescharacteristic
300D20—22no—
301D20—22no—
302D20—21no—
303D20—32no—
304D20—62no—
305D20—62no—
306D20—61no—
307D20C2×C4×D312yes—
308C4×D5—22no—
309C4×D5—22no—
310C4×D5—62no—
311C4×D5—62no—
312C4×D5C2×C4×D311yescharacteristic
313C4×D5#23511yescharacteristic
314C4×D5C2×#6711yescharacteristic
315C4×D5C23×D311yescharacteristic
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—31no—
327C2×SD16—151no—
328C2×SD16—151no—
329C2×D8—151no—
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#44412yescomplemented
348C2×C3×C5C2×C4×D411yescharacteristic
349D15—42no—
350C3×D5—21no—
351C3×D5—21no—
352C3×D5—42no—
353C23×C3—51no—
354C23×C3—101no—
355C22×D3—101no—
356C3×Q8—21no—
357C3×Q8C22×AGL(1,𝔽5)12yes—
358C3×D4—52no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—101no—
362C2×C3×C4—21no—
363C2×C3×C4—51no—
364C2×C3×C4—51no—
365C2×C3×C4—51no—
366C2×C3×C4—51no—
367C2×C3×C4—51no—
368C2×C3×C4—102no—
369C2×C3×C4—102no—
370C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
371#67—102no—
372#67—102no—
373C2×Dic3—21no—
374C2×Dic3—102no—
375C2×Dic3—202no—
376D12—52no—
377D12—101no—
378C4×D3—102no—
379C4×D3—102no—
380Dic6—21no—
381Dic6C22×AGL(1,𝔽5)12yes—
382C3×C8—52no—
383C3×C8—52no—
384C3×C8—102no—
385C3⋊C8—52no—
386C3⋊C8—102no—
387C3⋊C8C22×AGL(1,𝔽5)12yes—
388C22×C5C4×#6711yescharacteristic
389C2×D5—22no—
390C2×D5—22no—
391C2×D5—42no—
392C2×D5—62no—
393C2×D5—122no—
394C2×D5C4×#6711yescharacteristic
395C2×D5C2×#23511yescharacteristic
396AGL(1,𝔽5)—122no—
397C4×C5—22no—
398C4×C5—62no—
399C4×C5C4×#6711yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
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—31no—
412C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
413C2×D4—51no—
414C2×D4—101no—
415C2×D4—151no—
416C2×D4—301no—
417C22×C4—51no—
418C22×C4—101no—
419C22×C4—301no—
420C22×C4—301no—
421Q16—34no—
422SD16—154no—
423SD16—154no—
424D8—154no—
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—51no—
447C22×C3—51no—
448C22×C3—102no—
449C22×C3—102no—
450C22×C3—202no—
451C22×C3D4×AGL(1,𝔽5)11yescharacteristic
452C2×D3—102no—
453C2×D3—202no—
454C3×C4—22no—
455C3×C4—51no—
456C3×C4—51no—
457C3×C4D4×AGL(1,𝔽5)11yescharacteristic
458C3×C4C23×AGL(1,𝔽5)11yescharacteristic
459Dic3—22no—
460Dic3—202no—
461C2×C5#514512yescomplemented
462C2×C5C2×C4×#6711yescharacteristic
463D5—21no—
464D5—21no—
465D5—42no—
466D5—122no—
467C23—51no—
468C23—101no—
469C23—301no—
470Q8—21no—
471Q8—32no—
472Q8—61no—
473Q8C2×D3×AGL(1,𝔽5)12yes—
474D4—52no—
475D4—102no—
476D4—102no—
477D4—101no—
478D4—152no—
479D4—302no—
480D4—302no—
481D4—301no—
482C2×C4—21no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—51no—
488C2×C4—61no—
489C2×C4—102no—
490C2×C4—102no—
491C2×C4—302no—
492C2×C4—302no—
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—101no—
503C2×C3—101no—
504C2×C3—202no—
505C2×C3#6574112yescomplemented
506C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
507D3—202no—
508C5C2×#514511yescharacteristic, complemented, Sylow
509C22—51no—
510C22—51no—
511C22—102no—
512C22—102no—
513C22—202no—
514C22—302no—
515C22—602no—
516C22AGL(1,𝔽5)×#6711yescharacteristic
517C4—22no—
518C4—51no—
519C4—51no—
520C4—62no—
521C4—602no—
522C4AGL(1,𝔽5)×#6711yescharacteristic
523C4C22×D3×AGL(1,𝔽5)11yescharacteristic
524C3C2×#6574111yescharacteristic, complemented, Sylow
525C2—101no—
526C2—101no—
527C2—202no—
528C2—602no—
529C2#1175197812yesdirect 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×Q8C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×#91516C2
cosocleC3×C4×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4133C2semidirect
2. C2×#91914C2semidirect
4. C2×#91239C2semidirect
5. #11751978C2direct (N × H)
6. C2×#91161C2semidirect
7. C2×#91157C2semidirect
8. C2×#91150C2semidirect
15. C3×#4133C22semidirect
23. #91914C22semidirect
24. C2×#6717C4semidirect
25. C2×C5×#216C4semidirect
26. #91516C4semidirect
28. C2×#6655C4semidirect
29. C2×#6653C4semidirect
31. #91239C22semidirect
32. #91161C22semidirect
33. #91157C22semidirect
34. #91150C22semidirect
37. C2×#4133D3semidirect
78. #6717C2×C4semidirect
80. C5×#216C2×C4semidirect
82. #6655C2×C4semidirect
83. #6653C2×C4semidirect
99. #4133C2×D3semidirect
165. C2×#216AGL(1,𝔽5)semidirect
272. #216C2×AGL(1,𝔽5)semidirect
347. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
461. C2×C5#5145semidirect
505. C2×C3#65741semidirect
508. C5C2×#5145semidirect
524. C3C2×#65741semidirect
529. C2#11751978direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#41332
C2×#919142
C2×#915162
C2×#912392
#117519782
C2×#911612
C2×#911572
C2×#911502
C2×#657413
C2×#51455