Finite Group Databasebeta

← C2×#11750924 #14417921

Subgroups — C2×#11750924 #14417921

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×#91839C211yesmaximal, characteristic
2C2×#91837C211yesmaximal, characteristic, complemented
3C2×#91796C211yesmaximal, characteristic, complemented
4C2×C3×C5×#104C211yesmaximal, characteristic, complemented
5C2×#91106C211yesmaximal, characteristic, complemented
6C2×#91089C211yesmaximal, characteristic, complemented
7C2×#91087C211yesmaximal, characteristic, complemented
8#11750924C218yesmaximal, direct product factor
9C2×#65112—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C2×#6817C2211yescharacteristic
12C2×C3×C5×M16C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14#91839C414yescomplemented
15#91839C2214yes—
16#91837—22no—
17#91837C2214yescomplemented
18C2×#6718C411yescharacteristic, complemented
19C2×#6717C411yescharacteristic, complemented
20C2×#6716C411yescharacteristic, complemented
21C2×#6715C411yescharacteristic, complemented
22C2×#6710—21no—
23C2×#6710C2211yescharacteristic
24C22×C3⋊#168—21no—
25C22×C3⋊#168C2211yescharacteristic
26C22×C3⋊#168C2211yescharacteristic
27#91796—22no—
28#91796C2214yescomplemented
29C2×#6705—21no—
30C2×C8×D15—21no—
31C3×C5×#104C2214yescomplemented
32#91106C2214yescomplemented
33#91089C2214yescomplemented
34#91087C2214yescomplemented
35C2×#4823—51nomaximal, Hall
36C2×#4096—31no—
37C2×#4094—31no—
38C2×#4053—31no—
39C2×C5×#104D311yescharacteristic, complemented
40C2×#3954—31no—
41C2×#3937—31no—
42C2×#3935—31no—
43#65112—38no—
44C3×C5×#41—21no—
45C3×C5×#41—21no—
46C3×C5×#41C2×C412yes—
47C3×C5×#41C2312yes—
48C2×C3×C5×Q8C2×C411yescharacteristic
49C2×C3×C5×D4—21no—
50C2×C3×C5×D4C2×C411yescharacteristic
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5—21no—
53C22×C3×C4×C5C2311yescharacteristic
54C2×#1220—21no—
55#6817—21no—
56#6817—21no—
57#6817C2×C412yes—
58#6817C2312yes—
59C2×D60C2×C411yescharacteristic
60C2×C4×D15—21no—
61C2×Dic30C2×C411yescharacteristic
62C3×C5×M16—21no—
63C3×C5×M16C2312yes—
64C2×C3×C5×C8—21no—
65C3×C42×C5—21no—
66C3×C42×C5C2312yes—
67#6718C2×C414yescomplemented
68#6717C2×C414yescomplemented
69#6716C2×C414yescomplemented
70#6715C2×C414yescomplemented
71#6710—21no—
72#6710—24no—
73#6710C2312yes—
74C2×C3⋊#168—21no—
75C2×C3⋊#168—24no—
76C2×C3⋊#168C2×C411yescharacteristic
77C2×C3⋊#168C2×C411yescharacteristic
78C2×C3⋊#168C2×C412yes—
79C2×C3⋊#168D411yescharacteristic
80C2×C3⋊#168D411yescharacteristic
81C2×C3⋊#168D412yes—
82C2×C3⋊#168C2312yes—
83C2×C3⋊#168C2312yes—
84#6705—24no—
85C8×D15—24no—
86C2×#950—51no—
87C2×#948—51no—
88C2×#907—51no—
89C2×C3×#104D511yescharacteristic, complemented
90C2×#822—51no—
91C2×#805—51no—
92C2×#803—51no—
93#4823—58no—
94C2×C5×#41C2×D311yescharacteristic
95C2×#709—31no—
96C2×C5×M16C2×D311yescharacteristic
97C2×C42×C5C2×D311yescharacteristic
98#4096—34no—
99#4096—34no—
100#4094—34no—
101#4094—62no—
102C2×#689—31no—
103C2×#688—31no—
104C2×#687—31no—
105C2×#686—31no—
106C2×#681—31no—
107C2×#681—61no—
108C22×#168—31no—
109C22×#168—31no—
110C22×#168—61no—
111#4053—34no—
112#4053—62no—
113C2×#676—61no—
114C2×C8×D5—61no—
115C5×#104C2×D314yescomplemented
116#3954—34no—
117#3937—34no—
118#3935—34no—
119C2×#444—151noSylow
120C23×C3×C5—21no—
121C23×C3×C5#4111yescharacteristic
122C22×D15—21no—
123C3×C5×Q8—21no—
124C3×C5×Q8C22×C412yes—
125C3×C5×D4—22no—
126C3×C5×D4—22no—
127C3×C5×D4—21no—
128C3×C5×D4C22×C412yes—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—42no—
134C2×C3×C4×C5C22×C411yescharacteristic
135C2×C3×C4×C5C22×C411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5#4111yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140#1220—22no—
141#1220—22no—
142C2×Dic15—21no—
143D60—21no—
144D60C22×C412yes—
145C4×D15—22no—
146C4×D15—22no—
147Dic30—21no—
148Dic30C22×C412yes—
149C3×C5×C8—22no—
150C3⋊#168—22no—
151C3⋊#168C22×C412yes—
152C3⋊#168C22×C412yes—
153C3⋊#168C2×D412yes—
154C3⋊#168C2×D412yes—
155C2×C3×#41C2×D511yescharacteristic
156C2×#235—51no—
157C2×C3×M16C2×D511yescharacteristic
158C2×C3×C42C2×D511yescharacteristic
159#950—54no—
160#950—54no—
161#948—54no—
162#948—102no—
163C2×#216—51no—
164C2×#215—51no—
165C2×#214—51no—
166C2×#213—51no—
167C2×#208—51no—
168C2×#208—101no—
169C22×C3⋊C8—51no—
170C22×C3⋊C8—51no—
171C22×C3⋊C8—101no—
172#907—54no—
173#907—102no—
174C2×ΓL(1,𝔽25)—101no—
175C2×D3×C8—101no—
176C3×#104C2×D514yescomplemented
177#822—54no—
178#805—54no—
179#803—54no—
180C5×#41—21no—
181C5×#41—21no—
182C5×#41C4×D312yes—
183C5×#41C22×D312yes—
184C2×C5×Q8C4×D311yescharacteristic
185C2×C5×D4—21no—
186C2×C5×D4C4×D311yescharacteristic
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—61no—
191#709—32no—
192#709—32no—
193#709—61no—
194#709—61no—
195C2×D20—31no—
196C2×C4×D5—61no—
197C2×Dic10—31no—
198C5×M16—21no—
199C5×M16C22×D312yes—
200C2×C5×C8—21no—
201C42×C5—21no—
202C42×C5C22×D312yes—
203#689—34no—
204#688—34no—
205#687—34no—
206#686—34no—
207#681—32no—
208#681—64no—
209#681—61no—
210C2×#168—32no—
211C2×#168—31no—
212C2×#168—31no—
213C2×#168—31no—
214C2×#168—31no—
215C2×#168—32no—
216C2×#168—32no—
217C2×#168—32no—
218C2×#168—64no—
219C2×#168—61no—
220#676—64no—
221C8×D5—64no—
222C2×#135—151no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—151no—
228C2×#104D1511yescharacteristic, complemented
229C2×#97—151no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—42no—
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5C4×D411yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C2×D15—22no—
237C2×D15—42no—
238C3×C4×C5—22no—
239C3×C4×C5—42no—
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C4×D411yescharacteristic
242C3×C4×C5C23×C411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—22no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41C4×D512yes—
248C3×#41C22×D512yes—
249C2×C3×Q8C4×D511yescharacteristic
250C2×C3×D4—21no—
251C2×C3×D4C4×D511yescharacteristic
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C22×D511yescharacteristic
255C2×#67—101no—
256#235—52no—
257#235—52no—
258#235—101no—
259#235—101no—
260C2×D12—51no—
261C2×C4×D3—101no—
262C2×Dic6—51no—
263C3×M16—21no—
264C3×M16C22×D512yes—
265C2×C3×C8—21no—
266C3×C42—21no—
267C3×C42C22×D512yes—
268#216—54no—
269#215—54no—
270#214—54no—
271#213—54no—
272#208—52no—
273#208—104no—
274#208—101no—
275C2×C3⋊C8—51no—
276C2×C3⋊C8—51no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—52no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—104no—
284C2×C3⋊C8—101no—
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287C23×C5—21no—
288C23×C5#23711yescharacteristic
289C22×D5—61no—
290C5×Q8—21no—
291C5×Q8C2×C4×D312yes—
292C5×D4—22no—
293C5×D4—22no—
294C5×D4—21no—
295C5×D4C2×C4×D312yes—
296C2×C4×C5—21no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—42no—
301C2×C4×C5C2×C4×D311yescharacteristic
302C2×C4×C5C2×C4×D311yescharacteristic
303C2×C4×C5D3×D411yescharacteristic
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5#23711yescharacteristic
306C2×C4×C5C23×D311yescharacteristic
307C22⋊D5—62no—
308C22⋊D5—62no—
309C2×Dic5—61no—
310D20—32no—
311D20—61no—
312C4×D5—62no—
313C4×D5—62no—
314Dic10—32no—
315Dic10—61no—
316C5×C8—22no—
317#168—32no—
318#168—32no—
319#168—32no—
320#168—32no—
321#168—62no—
322C2×#41—151no—
323C2×#41C2×D1511yescharacteristic
324#135—154no—
325#135—154no—
326C2×Q16—151no—
327C2×SD16—151no—
328C2×SD16—151no—
329C2×D8—151no—
330#131—154no—
331#131—154no—
332#131—302no—
333#131—302no—
334C2×M16—151no—
335C2×M16—301no—
336C2×M16—301no—
337C2×M16C2×D1511yescharacteristic
338C22×C8—151no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42C2×D1511yescharacteristic
343#108—154no—
344#104—154no—
345#104C2×D1514yescomplemented
346#97—154no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5—42no—
350C2×C3×C5#44412yescomplemented
351C2×C3×C5C2×C4×D411yescharacteristic
352D15—42no—
353C23×C3—21no—
354C23×C3#71111yescharacteristic
355C22×D3—101no—
356C3×Q8—21no—
357C3×Q8C2×C4×D512yes—
358C3×D4—22no—
359C3×D4—22no—
360C3×D4—21no—
361C3×D4C2×C4×D512yes—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—42no—
367C2×C3×C4C2×C4×D511yescharacteristic
368C2×C3×C4C2×C4×D511yescharacteristic
369C2×C3×C4D4×D511yescharacteristic
370C2×C3×C4D4×D511yescharacteristic
371C2×C3×C4#71111yescharacteristic
372C2×C3×C4C23×D511yescharacteristic
373#67—102no—
374#67—102no—
375C2×Dic3—101no—
376D12—52no—
377D12—101no—
378C4×D3—102no—
379C4×D3—102no—
380Dic6—52no—
381Dic6—101no—
382C3×C8—22no—
383C3⋊C8—52no—
384C3⋊C8—52no—
385C3⋊C8—52no—
386C3⋊C8—52no—
387C3⋊C8—102no—
388C22×C5—22no—
389C22×C5—22no—
390C22×C5—42no—
391C22×C5#67⋊C411yescharacteristic
392C22×C5#67⋊C411yescharacteristic
393C22×C5C2×#23711yescharacteristic
394C2×D5—62no—
395C2×D5—122no—
396C4×C5—22no—
397C4×C5—42no—
398C4×C5#67⋊C411yescharacteristic
399C4×C5#67⋊C411yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×D3×D411yescharacteristic
402Dic5—62no—
403#41—21no—
404#41—21no—
405#41—152no—
406#41—152no—
407#41—301no—
408#41—301no—
409#41C4×D1512yes—
410#41C22×D1512yes—
411C2×Q8—151no—
412C2×Q8C4×D1511yescharacteristic
413C2×D4—21no—
414C2×D4—151no—
415C2×D4—301no—
416C2×D4C4×D1511yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—301no—
420C22×C4C22×D1511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—21no—
426M16—152no—
427M16—304no—
428M16—304no—
429M16—301no—
430M16C22×D1512yes—
431C2×C8—21no—
432C2×C8—151no—
433C2×C8—151no—
434C2×C8—152no—
435C2×C8—152no—
436C2×C8—151no—
437C2×C8—151no—
438C2×C8—152no—
439C2×C8—152no—
440C2×C8—304no—
441C2×C8—304no—
442C2×C8—301no—
443C42—21no—
444C42C22×D1512yes—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—42no—
449C22×C3#402711yescharacteristic
450C22×C3#402711yescharacteristic
451C22×C3C2×#71111yescharacteristic
452C2×D3—102no—
453C2×D3—202no—
454C3×C4—22no—
455C3×C4—42no—
456C3×C4#402711yescharacteristic
457C3×C4#402711yescharacteristic
458C3×C4C22×C4×D511yescharacteristic
459C3×C4C2×D4×D511yescharacteristic
460Dic3—102no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—42no—
464C2×C5#482312yescomplemented
465C2×C5C2×#67⋊C411yescharacteristic
466D5—122no—
467C23—21no—
468C23—301no—
469C23#681911yescharacteristic
470Q8—21no—
471Q8—152no—
472Q8—301no—
473Q8C2×C4×D1512yes—
474D4—22no—
475D4—22no—
476D4—21no—
477D4—152no—
478D4—302no—
479D4—302no—
480D4—301no—
481D4C2×C4×D1512yes—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—42no—
487C2×C4—301no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4C2×C4×D1511yescharacteristic
491C2×C4C2×C4×D1511yescharacteristic
492C2×C4D4×D1511yescharacteristic
493C2×C4D4×D1511yescharacteristic
494C2×C4#681911yescharacteristic
495C2×C4C23×D1511yescharacteristic
496C8—22no—
497C8—152no—
498C8—152no—
499C8—152no—
500C8—152no—
501C8—302no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—42no—
505C2×C3#6511212yescomplemented
506C2×C3C2×#402711yescharacteristic
507D3—202no—
508C5C2×#482311yescharacteristic, complemented, Sylow
509C22—22no—
510C22—22no—
511C22—42no—
512C22—302no—
513C22—602no—
514C22#9177011yescharacteristic
515C22#9177011yescharacteristic
516C22C2×#681911yescharacteristic
517C4—22no—
518C4—42no—
519C4—302no—
520C4#9177011yescharacteristic
521C4#9177011yescharacteristic
522C4C22×C4×D1511yescharacteristic
523C4C2×D4×D1511yescharacteristic
524C3C2×#6511211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—42no—
528C2—602no—
529C2#1175092412yesdirect product factor
530C2C2×#9177011yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5C4×D4
prime radicalC2×#91839C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#104D15
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#91837C2semidirect
3. C2×#91796C2semidirect
4. C2×C3×C5×#104C2semidirect
5. C2×#91106C2semidirect
6. C2×#91089C2semidirect
7. C2×#91087C2semidirect
8. #11750924C2direct (N × H)
14. #91839C4semidirect
17. #91837C22semidirect
18. C2×#6718C4semidirect
19. C2×#6717C4semidirect
20. C2×#6716C4semidirect
21. C2×#6715C4semidirect
28. #91796C22semidirect
31. C3×C5×#104C22semidirect
32. #91106C22semidirect
33. #91089C22semidirect
34. #91087C22semidirect
39. C2×C5×#104D3semidirect
67. #6718C2×C4semidirect
68. #6717C2×C4semidirect
69. #6716C2×C4semidirect
70. #6715C2×C4semidirect
89. C2×C3×#104D5semidirect
115. C5×#104C2×D3semidirect
176. C3×#104C2×D5semidirect
228. C2×#104D15semidirect
345. #104C2×D15semidirect
350. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
464. C2×C5#4823semidirect
505. C2×C3#65112semidirect
508. C5C2×#4823semidirect
524. C3C2×#65112semidirect
529. C2#11750924direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918392
C2×#918372
C2×#917962
C2×C3×C5×#1042
C2×#911062
C2×#910892
C2×#910872
#117509242
C2×#651123
C2×#48235