Finite Group Databasebeta

← C2×#11749379 #14429455

Subgroups — C2×#11749379 #14429455

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91831C211yesmaximal, characteristic
2C22×C5×#216C211yesmaximal, characteristic, complemented
3C2×#91321C211yesmaximal, characteristic
4C2×#91291C211yesmaximal, characteristic
5C2×C3×#3968C211yesmaximal, characteristic, complemented
6#11749379C218yesmaximal, direct product factor
7C2×#90993C211yesmaximal, characteristic, complemented
8C2×#90962C211yesmaximal, characteristic, complemented
9C2×#65481—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×#6817C2211yescharacteristic
12C22×C5×Dic6C2211yescharacteristic
13C2×#6718—21no—
14#91831—22no—
15#91831C2214yes—
16C2×#6717—21no—
17C2×#6710C2211yescharacteristic
18C2×C5×#216—21no—
19C2×C5×#216—22no—
20C2×C5×#216—21no—
21C2×C5×#216C2214yescomplemented
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×#681C2211yescharacteristic
24C2×C3×#681C2211yescharacteristic
25#91321—22no—
26#91321C2214yes—
27C2×#6663—21no—
28C2×#6660—21no—
29C2×#6651—21no—
30#91291—22no—
31#91291C2214yes—
32C2×#6648—21no—
33C3×#3968C2214yescomplemented
34#90993C2214yescomplemented
35#90962C2214yescomplemented
36C2×#4755—51nomaximal, Hall
37C22×C5×Q16—31no—
38C2×#4088—31no—
39C2×#4088—31no—
40C2×#4047—31no—
41C2×#3968—31no—
42C2×#3968D311yescharacteristic, complemented
43#65481—38no—
44C2×#3951—31no—
45C2×C3×C5×Q8—21no—
46C2×C3×C5×Q8—21no—
47C2×C3×C5×Q8—21no—
48C2×C3×C5×Q8—21no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8C2312yes—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2311yescharacteristic
53C2×#1220—21no—
54#6817—21no—
55#6817—21no—
56#6817D412yes—
57#6817C2312yes—
58C2×D60D411yescharacteristic
59C2×C4×D15—21no—
60C2×Dic30D411yescharacteristic
61C22×C5×Dic3—21no—
62C2×C5×Dic6—21no—
63C2×C5×Dic6—21no—
64C2×C5×Dic6—21no—
65C2×C5×Dic6—21no—
66C2×C5×Dic6—21no—
67C2×C5×Dic6C2312yes—
68#6718—24no—
69#6717—24no—
70#6710—21no—
71#6710C2312yes—
72C2×C3⋊#168—21no—
73C5×#216—24no—
74C5×#216—24no—
75C2×C5×C3⋊C8D411yescharacteristic
76C2×C5×C3⋊C8D412yes—
77C2×C5×C3⋊C8D411yescharacteristic
78C2×C5×C3⋊C8C2312yes—
79C3×#681—21no—
80C3×#681—21no—
81C3×#681C2312yes—
82C3×#681C2312yes—
83C2×C3×#168—21no—
84C2×C3×#168—21no—
85#6663—24no—
86#6660—24no—
87#6651—24no—
88#6648—24no—
89C22×#216D511yescharacteristic, complemented
90C2×#942—51no—
91C2×#909—51no—
92C2×#907—51no—
93C2×C3×#101—51no—
94C2×#824—51no—
95C2×#822—51no—
96#4755—58no—
97C22×C5×Q8—31no—
98C22×C5×Q8C2×D311yescharacteristic
99C2×#709—31no—
100C2×C5×Q16—34no—
101C2×C5×Q16—61no—
102C2×C5×Q16—61no—
103C2×C5×Q16—62no—
104C22×C5×C8—31no—
105C2×#689—61no—
106C2×#689—61no—
107#4088—34no—
108#4088—34no—
109#4088—62no—
110#4088—62no—
111C2×#688—61no—
112C2×#688—61no—
113C2×#681—31no—
114C2×#681C2×D311yescharacteristic
115C2×#681C2×D311yescharacteristic
116#4047—34no—
117#4047—62no—
118C2×#676—61no—
119C2×C8×D5—61no—
120#3968—34no—
121#3968C2×D314yescomplemented
122#3951—34no—
123C2×#473—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×D15—21no—
126C3×C5×Q8—22no—
127C3×C5×Q8—22no—
128C3×C5×Q8—41no—
129C3×C5×Q8—41no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5#4111yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139#1220—22no—
140#1220—22no—
141C2×Dic15—21no—
142D60—21no—
143D60C2×D412yes—
144C4×D15—22no—
145C4×D15—22no—
146Dic30—21no—
147Dic30C2×D412yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—41no—
150C2×C5×Dic3—41no—
151C5×Dic6—22no—
152C5×Dic6—22no—
153C5×Dic6—41no—
154C5×Dic6—41no—
155C3⋊#168—22no—
156C3×#168—22no—
157C3×#168—22no—
158C5×C3⋊C8C2×D412yes—
159C5×C3⋊C8C2×D412yes—
160C22×C3×Q8C2×D511yescharacteristic
161C2×#235—51no—
162C22×Dic6C2×D511yescharacteristic
163C2×C3×M16—51no—
164C2×C3×M16—51no—
165C2×#216—21no—
166C2×#216—21no—
167C2×#216—22no—
168C2×#216—101no—
169C2×#216C2×D514yescomplemented
170#942—54no—
171#942—102no—
172C2×#215—101no—
173C2×#208—51no—
174C22×C3⋊C8C2×D511yescharacteristic
175#909—54no—
176#909—102no—
177#907—54no—
178#907—102no—
179C2×Dic12—101no—
180C2×#204—101no—
181C2×ΓL(1,𝔽25)—101no—
182C2×D3×C8—101no—
183C3×#101—54no—
184#824—54no—
185#822—54no—
186C2×C5×Q8—21no—
187C2×C5×Q8—21no—
188C2×C5×Q8—21no—
189C2×C5×Q8—21no—
190C2×C5×Q8—21no—
191C2×C5×Q8—32no—
192C2×C5×Q8—61no—
193C2×C5×Q8—61no—
194C2×C5×Q8—61no—
195C2×C5×Q8—61no—
196C2×C5×Q8—61no—
197C2×C5×Q8C22×D312yes—
198C22×C4×C5—21no—
199C22×C4×C5—61no—
200C22×C4×C5C22×D311yescharacteristic
201C2×C22⋊D5—61no—
202#709—32no—
203#709—32no—
204#709—61no—
205#709—61no—
206C2×D20—31no—
207C2×C4×D5—61no—
208C2×Dic10—31no—
209C5×Q16—64no—
210C5×Q16—64no—
211C2×C5×C8—31no—
212C2×C5×C8—31no—
213C2×C5×C8—32no—
214C2×C5×C8—32no—
215#689—64no—
216#689—64no—
217#688—64no—
218#688—64no—
219#681—21no—
220#681—21no—
221#681—32no—
222#681—61no—
223#681C22×D312yes—
224#681C22×D312yes—
225C2×#168—21no—
226C2×#168—21no—
227C2×#168—61no—
228#676—64no—
229C8×D5—64no—
230C2×#137—151no—
231C2×#137—151no—
232C22×Q16—31no—
233C2×#131—151no—
234#473—158no—
235C2×#108—151no—
236C2×#101—51no—
237C2×#101—151no—
238C22×C3×C5—22no—
239C22×C3×C5#12111yescharacteristic
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C2×D15—22no—
243C2×D15—42no—
244C3×C4×C5—42no—
245C3×C4×C5#12111yescharacteristic
246C3×C4×C5#12111yescharacteristic
247C3×C4×C5C22×D411yescharacteristic
248C3×C4×C5C22×D411yescharacteristic
249Dic15—22no—
250C5×Dic3—42no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8C22×D512yes—
257C22×C3×C4—21no—
258C22×C3×C4C22×D511yescharacteristic
259C2×#67—101no—
260C22×Dic3—21no—
261#235—52no—
262#235—52no—
263#235—101no—
264#235—101no—
265C2×D12—51no—
266C2×C4×D3—101no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—51no—
273C2×Dic6C22×D512yes—
274C3×M16—52no—
275C3×M16—52no—
276C3×M16—101no—
277C3×M16—101no—
278C2×C3×C8—101no—
279C2×C3×C8—101no—
280#216—24no—
281#216—24no—
282#216—104no—
283#215—104no—
284#208—52no—
285#208—101no—
286C2×C3⋊C8—101no—
287C2×C3⋊C8C22⋊D511yescharacteristic
288C2×C3⋊C8C22⋊D511yescharacteristic
289C2×C3⋊C8C22⋊D512yes—
290C2×C3⋊C8C22×D512yes—
291Dic12—104no—
292#204—104no—
293ΓL(1,𝔽25)—104no—
294D3×C8—104no—
295C23×C5#23511yescharacteristic
296C22×D5—61no—
297C5×Q8—22no—
298C5×Q8—22no—
299C5×Q8—41no—
300C5×Q8—41no—
301C5×Q8—62no—
302C5×Q8—62no—
303C5×Q8—121no—
304C5×Q8—121no—
305C2×C4×C5—22no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—62no—
309C2×C4×C5—121no—
310C2×C4×C5—121no—
311C2×C4×C5#23511yescharacteristic
312C2×C4×C5D3×D411yescharacteristic
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5C23×D311yescharacteristic
317C22⋊D5—62no—
318C22⋊D5—62no—
319C2×Dic5—61no—
320D20—32no—
321D20—61no—
322C4×D5—62no—
323C4×D5—62no—
324Dic10—32no—
325Dic10—61no—
326C5×C8—32no—
327C5×C8—32no—
328#168—22no—
329#168—22no—
330#168—62no—
331C2×#41—151no—
332C22×Q8—31no—
333C22×Q8D3×D511yescharacteristic
334#137—154no—
335#137—154no—
336#137—302no—
337#137—302no—
338C2×Q16—34no—
339C2×Q16—61no—
340C2×Q16—61no—
341C2×Q16—62no—
342C2×Q16—301no—
343C2×Q16—301no—
344C2×SD16—301no—
345C2×SD16—301no—
346#131—154no—
347#131—302no—
348C2×M16—51no—
349C2×M16—51no—
350C2×M16—151no—
351C2×M16—301no—
352C22×C8—31no—
353C22×C8—301no—
354#108—154no—
355#101—54no—
356#101—154no—
357C2×C3×C5—21no—
358C2×C3×C5—21no—
359C2×C3×C5#47312yescomplemented
360C2×C3×C5C2×#12111yescharacteristic
361D15—42no—
362C23×C3#71111yescharacteristic
363C22×D3—101no—
364C3×Q8—22no—
365C3×Q8—22no—
366C3×Q8—41no—
367C3×Q8—41no—
368C2×C3×C4—22no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4D4×D511yescharacteristic
372C2×C3×C4D4×D511yescharacteristic
373C2×C3×C4#71111yescharacteristic
374C2×C3×C4C2×C22⋊D511yescharacteristic
375C2×C3×C4C2×C22⋊D511yescharacteristic
376C2×C3×C4C23×D511yescharacteristic
377#67—102no—
378#67—102no—
379C2×Dic3—22no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—101no—
383D12—52no—
384D12—101no—
385C4×D3—102no—
386C4×D3—102no—
387Dic6—22no—
388Dic6—22no—
389Dic6—41no—
390Dic6—41no—
391Dic6—52no—
392Dic6—101no—
393C3×C8—102no—
394C3×C8—102no—
395C3⋊C8—102no—
396C3⋊C8C2×C22⋊D512yes—
397C3⋊C8C2×C22⋊D512yes—
398C22×C5—22no—
399C22×C5#88411yescharacteristic
400C22×C5#88411yescharacteristic
401C22×C5C2×#23511yescharacteristic
402C2×D5—62no—
403C2×D5—122no—
404C4×C5—42no—
405C4×C5—122no—
406C4×C5#88411yescharacteristic
407C4×C5#88411yescharacteristic
408C4×C5C2×D3×D411yescharacteristic
409C4×C5C2×D3×D411yescharacteristic
410Dic5—62no—
411#41—152no—
412#41—152no—
413#41—301no—
414#41—301no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—32no—
421C2×Q8—61no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×Q8—61no—
426C2×Q8—151no—
427C2×Q8C2×D3×D512yes—
428C2×D4—151no—
429C2×D4—301no—
430C22×C4—21no—
431C22×C4—61no—
432C22×C4—301no—
433C22×C4C2×D3×D511yescharacteristic
434Q16—64no—
435Q16—64no—
436Q16—304no—
437Q16—304no—
438SD16—304no—
439SD16—304no—
440M16—52no—
441M16—52no—
442M16—101no—
443M16—101no—
444M16—152no—
445M16—304no—
446M16—301no—
447C2×C8—31no—
448C2×C8—31no—
449C2×C8—32no—
450C2×C8—32no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—304no—
454C2×C8—301no—
455C3×C5C2×#47311yescharacteristic, complemented, Hall
456C22×C3—22no—
457C22×C3#408411yescharacteristic
458C22×C3#408411yescharacteristic
459C22×C3C2×#71111yescharacteristic
460C2×D3—102no—
461C2×D3—202no—
462C3×C4—42no—
463C3×C4#408411yescharacteristic
464C3×C4#408411yescharacteristic
465C3×C4C2×D4×D511yescharacteristic
466C3×C4C22×C22⋊D511yescharacteristic
467Dic3—42no—
468Dic3—102no—
469C2×C5—21no—
470C2×C5—21no—
471C2×C5#475512yescomplemented
472C2×C5C2×#88411yescharacteristic
473D5—122no—
474C23—301no—
475C23#678211yescharacteristic
476Q8—22no—
477Q8—22no—
478Q8—41no—
479Q8—41no—
480Q8—62no—
481Q8—62no—
482Q8—121no—
483Q8—121no—
484Q8—152no—
485Q8—301no—
486D4—152no—
487D4—302no—
488D4—302no—
489D4—301no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—62no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—301no—
497C2×C4—302no—
498C2×C4—302no—
499C2×C4#678211yescharacteristic
500C2×C4D3×C22⋊D511yescharacteristic
501C2×C4D3×C22⋊D511yescharacteristic
502C2×C4#679011yescharacteristic
503C2×C4#679011yescharacteristic
504C2×C4C22×D3×D511yescharacteristic
505C8—32no—
506C8—32no—
507C8—102no—
508C8—102no—
509C8—302no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3#6548112yescomplemented
513C2×C3C2×#408411yescharacteristic
514D3—202no—
515C5C2×#475511yescharacteristic, complemented, Sylow
516C22—22no—
517C22—302no—
518C22—602no—
519C22#9155711yescharacteristic
520C22#9155711yescharacteristic
521C22C2×#678211yescharacteristic
522C4—42no—
523C4—122no—
524C4—302no—
525C4#9155711yescharacteristic
526C4#9155711yescharacteristic
527C4C2×D3×C22⋊D511yescharacteristic
528C4C2×#679011yescharacteristic
529C3C2×#6548111yescharacteristic, complemented, Sylow
530C2—21no—
531C2—21no—
532C2—602no—
533C2#1174937912yesdirect product factor
534C2C2×#9155711yescharacteristic
subgroupG/H
centerC22#91557
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC22×C3×C5#121
prime radicalC2×#6817C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#473
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C5×#216C2semidirect
5. C2×C3×#3968C2semidirect
6. #11749379C2direct (N × H)
7. C2×#90993C2semidirect
8. C2×#90962C2semidirect
21. C2×C5×#216C22semidirect
33. C3×#3968C22semidirect
34. #90993C22semidirect
35. #90962C22semidirect
42. C2×#3968D3semidirect
89. C22×#216D5semidirect
121. #3968C2×D3semidirect
169. C2×#216C2×D5semidirect
359. C2×C3×C5#473semidirect
455. C3×C5C2×#473semidirect
471. C2×C5#4755semidirect
512. C2×C3#65481semidirect
515. C5C2×#4755semidirect
529. C3C2×#65481semidirect
533. C2#11749379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918312
C22×C5×#2162
C2×#913212
C2×#912912
C2×C3×#39682
#117493792
C2×#909932
C2×#909622
C2×#654813
C2×#47555