Finite Group Databasebeta

← C2×#11747107 #14417970

Subgroups — C2×#11747107 #14417970

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×#91297C211yesmaximal, characteristic
2C2×#91288C211yesmaximal, characteristic, complemented
3C2×#91284C211yesmaximal, characteristic, complemented
4C2×#91087C211yesmaximal, characteristic, complemented
5C2×C5×#805C211yesmaximal, characteristic, complemented
6C2×C3×#3937C211yesmaximal, characteristic, complemented
7C2×#90992C211yesmaximal, characteristic, complemented
8#11747107C218yesmaximal, direct product factor
9C2×#65112—31nomaximal, Hall
10C2×C5×#235C2211yescharacteristic
11C2×C3×#709C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C2×C5×#208C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17C2×#6661C411yescharacteristic, complemented
18C2×#6656C411yescharacteristic, complemented
19C2×#6655C411yescharacteristic, complemented
20#91297C414yescomplemented
21#91297C2214yes—
22C2×#6652C411yescharacteristic, complemented
23C2×#6650—21no—
24C2×#6649—21no—
25#91288—22no—
26#91288C2214yescomplemented
27C2×D3×#168—21no—
28#91284—22no—
29#91284C2214yescomplemented
30C2×D5×C3⋊C8—21no—
31#91087C2214yescomplemented
32C5×#805C2214yescomplemented
33C3×#3937C2214yescomplemented
34#90992C2214yescomplemented
35C2×#4823—51nomaximal, Hall
36C2×#4096—31no—
37C2×#4094—31no—
38C2×#4053—31no—
39C2×C5×#104—31no—
40C2×#3954—31no—
41C2×#3937D311yescharacteristic, complemented
42C2×#3935—31no—
43#65112—38no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×C5×#67—21no—
47C5×#235—21no—
48C5×#235—21no—
49C5×#235C2×C412yes—
50C5×#235C2312yes—
51C2×C5×D12C2×C411yescharacteristic
52C2×C4×C5×D3—21no—
53C2×C5×Dic6C2×C411yescharacteristic
54C2×C3×C22⋊D5—21no—
55C3×#709—21no—
56C3×#709—21no—
57C3×#709C2×C412yes—
58C3×#709C2312yes—
59C2×C3×D20C2×C411yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2×C411yescharacteristic
62C3×C42×C5—21no—
63C3×C42×C5C2312yes—
64C2×C3⋊#168C2×C411yescharacteristic
65C2×C3⋊#168C2×C412yes—
66C2×C3⋊#168C2×C411yescharacteristic
67C2×C3⋊#168D411yescharacteristic
68C2×C3⋊#168D412yes—
69C2×C3⋊#168D411yescharacteristic
70C2×C3⋊#168C2312yes—
71C2×C3⋊#168C2312yes—
72C5×#208—21no—
73C5×#208C2312yes—
74C2×C5×C3⋊C8—21no—
75C3×#681—21no—
76C3×#681C2312yes—
77C2×C3×#168—21no—
78#6661C2×C414yescomplemented
79#6656C2×C414yescomplemented
80#6655C2×C414yescomplemented
81#6652C2×C414yescomplemented
82#6650—24no—
83#6649—24no—
84D3×#168—24no—
85D5×C3⋊C8—24no—
86C2×#950—51no—
87C2×#948—51no—
88C2×#907—51no—
89C2×C3×#104—51no—
90C2×#822—51no—
91C2×#805D511yescharacteristic, complemented
92C2×#803—51no—
93#4823—58no—
94C2×C5×#41—31no—
95C2×#709C2×D311yescharacteristic
96C2×C5×M16—31no—
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—61no—
107C2×#681C2×D311yescharacteristic
108C22×#168—31no—
109C22×#168—31no—
110C22×#168—61no—
111#4053—34no—
112#4053—62no—
113C2×#676—61no—
114C2×C8×D5—61no—
115C5×#104—34no—
116#3954—34no—
117#3937C2×D314yescomplemented
118#3935—34no—
119C2×#444—151noSylow
120C23×C3×C5#4111yescharacteristic
121C22×C5×D3—21no—
122C22×C3×D5—21no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—42no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C22×C411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5C2411yescharacteristic
131C5×#67—22no—
132C5×#67—22no—
133C2×C5×Dic3—21no—
134C5×D12—21no—
135C5×D12C22×C412yes—
136C4×C5×D3—22no—
137C4×C5×D3—22no—
138C5×Dic6—21no—
139C5×Dic6C22×C412yes—
140C3×C22⋊D5—22no—
141C3×C22⋊D5—22no—
142C2×C3×Dic5—21no—
143C3×D20—21no—
144C3×D20C22×C412yes—
145C3×C4×D5—22no—
146C3×C4×D5—22no—
147C3×Dic10—21no—
148C3×Dic10C22×C412yes—
149C3⋊#168C22×C412yes—
150C3⋊#168C22×C412yes—
151C3⋊#168C2×D412yes—
152C3⋊#168C2×D412yes—
153C3×#168—22no—
154C5×C3⋊C8—22no—
155C2×C3×#41—51no—
156C2×#235C2×D511yescharacteristic
157C2×C3×M16—51no—
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—101no—
168C2×#208C2×D511yescharacteristic
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×#104—54no—
177#822—54no—
178#805C2×D514yescomplemented
179#803—54no—
180C5×#41—32no—
181C5×#41—32no—
182C5×#41—61no—
183C5×#41—61no—
184C2×C5×Q8—31no—
185C2×C5×D4—31no—
186C2×C5×D4—61no—
187C22×C4×C5—21no—
188C22×C4×C5—61no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—21no—
191#709—21no—
192#709—21no—
193#709C4×D312yes—
194#709C22×D312yes—
195C2×D20C4×D311yescharacteristic
196C2×C4×D5—21no—
197C2×Dic10C4×D311yescharacteristic
198C5×M16—32no—
199C5×M16—61no—
200C2×C5×C8—61no—
201C42×C5—21no—
202C42×C5C22×D312yes—
203#689—34no—
204#688—34no—
205#687—34no—
206#686—34no—
207#681—21no—
208#681—64no—
209#681C22×D312yes—
210C2×#168—21no—
211C2×#168—32no—
212C2×#168—31no—
213C2×#168—31no—
214C2×#168—31no—
215C2×#168—31no—
216C2×#168—32no—
217C2×#168—32no—
218C2×#168—32no—
219C2×#168—64no—
220#676—64no—
221C8×D5—64no—
222C2×#135—151no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—31no—
228C2×#104—51no—
229C2×#97—151no—
230C22×C3×C5—22no—
231C22×C3×C5C4×D411yescharacteristic
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C2×C5×D3—22no—
235C2×C5×D3—42no—
236C2×C3×D5—22no—
237C2×C3×D5—42no—
238C3×C4×C5—42no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C4×D411yescharacteristic
241C3×C4×C5C23×C411yescharacteristic
242C3×C4×C5C22×D411yescharacteristic
243C3×Dic5—22no—
244C5×Dic3—22no—
245C3×#41—52no—
246C3×#41—52no—
247C3×#41—101no—
248C3×#41—101no—
249C2×C3×Q8—51no—
250C2×C3×D4—51no—
251C2×C3×D4—101no—
252C22×C3×C4—21no—
253C22×C3×C4—101no—
254C22×C3×C4C22×D511yescharacteristic
255C2×#67—21no—
256#235—21no—
257#235—21no—
258#235C4×D512yes—
259#235C22×D512yes—
260C2×D12C4×D511yescharacteristic
261C2×C4×D3—21no—
262C2×Dic6C4×D511yescharacteristic
263C3×M16—52no—
264C3×M16—101no—
265C2×C3×C8—101no—
266C3×C42—21no—
267C3×C42C22×D512yes—
268#216—54no—
269#215—54no—
270#214—54no—
271#213—54no—
272#208—21no—
273#208—104no—
274#208C22×D512yes—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—51no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—52no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—51no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—52no—
283C2×C3⋊C8—52no—
284C2×C3⋊C8—104no—
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287C23×C5—61no—
288C23×C5#23711yescharacteristic
289C22×D5—21no—
290C5×Q8—32no—
291C5×Q8—61no—
292C5×D4—32no—
293C5×D4—62no—
294C5×D4—62no—
295C5×D4—61no—
296C2×C4×C5—22no—
297C2×C4×C5—42no—
298C2×C4×C5—61no—
299C2×C4×C5—62no—
300C2×C4×C5—62no—
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—22no—
308C22⋊D5—22no—
309C2×Dic5—21no—
310D20—21no—
311D20C2×C4×D312yes—
312C4×D5—22no—
313C4×D5—22no—
314Dic10—21no—
315Dic10C2×C4×D312yes—
316C5×C8—62no—
317#168—22no—
318#168—32no—
319#168—32no—
320#168—32no—
321#168—32no—
322C2×#41—31no—
323C2×#41—51no—
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—31no—
335C2×M16—51no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—151no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42D3×D511yescharacteristic
343#108—154no—
344#104—34no—
345#104—54no—
346#97—154no—
347C2×C3×C5—21no—
348C2×C3×C5—21no—
349C2×C3×C5#44412yescomplemented
350C2×C3×C5C2×C4×D411yescharacteristic
351C3×D5—42no—
352C5×D3—42no—
353C23×C3—101no—
354C23×C3#71111yescharacteristic
355C22×D3—21no—
356C3×Q8—52no—
357C3×Q8—101no—
358C3×D4—52no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4—101no—
362C2×C3×C4—22no—
363C2×C3×C4—42no—
364C2×C3×C4—101no—
365C2×C3×C4—102no—
366C2×C3×C4—102no—
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—22no—
374#67—22no—
375C2×Dic3—21no—
376D12—21no—
377D12C2×C4×D512yes—
378C4×D3—22no—
379C4×D3—22no—
380Dic6—21no—
381Dic6C2×C4×D512yes—
382C3×C8—102no—
383C3⋊C8—22no—
384C3⋊C8—52no—
385C3⋊C8—52no—
386C3⋊C8—52no—
387C3⋊C8—52no—
388C22×C5—22no—
389C22×C5—62no—
390C22×C5—122no—
391C22×C5#67⋊C411yescharacteristic
392C22×C5#67⋊C411yescharacteristic
393C22×C5C2×#23711yescharacteristic
394C2×D5—22no—
395C2×D5—42no—
396C4×C5—42no—
397C4×C5—62no—
398C4×C5#67⋊C411yescharacteristic
399C4×C5#67⋊C411yescharacteristic
400C4×C5C22×C4×D311yescharacteristic
401C4×C5C2×D3×D411yescharacteristic
402Dic5—22no—
403#41—32no—
404#41—32no—
405#41—52no—
406#41—52no—
407#41—61no—
408#41—61no—
409#41—101no—
410#41—101no—
411C2×Q8—31no—
412C2×Q8—51no—
413C2×D4—31no—
414C2×D4—51no—
415C2×D4—61no—
416C2×D4—101no—
417C22×C4—21no—
418C22×C4—61no—
419C22×C4—101no—
420C22×C4C2×D3×D511yescharacteristic
421Q16—154no—
422SD16—154no—
423SD16—154no—
424D8—154no—
425M16—32no—
426M16—52no—
427M16—61no—
428M16—101no—
429M16—304no—
430M16—304no—
431C2×C8—61no—
432C2×C8—101no—
433C2×C8—151no—
434C2×C8—151no—
435C2×C8—152no—
436C2×C8—152no—
437C2×C8—151no—
438C2×C8—151no—
439C2×C8—152no—
440C2×C8—152no—
441C2×C8—304no—
442C2×C8—304no—
443C42—21no—
444C42C2×D3×D512yes—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—102no—
448C22×C3—202no—
449C22×C3#402711yescharacteristic
450C22×C3#402711yescharacteristic
451C22×C3C2×#71111yescharacteristic
452C2×D3—22no—
453C2×D3—42no—
454C3×C4—42no—
455C3×C4—102no—
456C3×C4#402711yescharacteristic
457C3×C4#402711yescharacteristic
458C3×C4C22×C4×D511yescharacteristic
459C3×C4C2×D4×D511yescharacteristic
460Dic3—22no—
461C2×C5—21no—
462C2×C5—21no—
463C2×C5—122no—
464C2×C5#482312yescomplemented
465C2×C5C2×#67⋊C411yescharacteristic
466D5—42no—
467C23—61no—
468C23—101no—
469C23#678011yescharacteristic
470Q8—32no—
471Q8—52no—
472Q8—61no—
473Q8—101no—
474D4—32no—
475D4—52no—
476D4—62no—
477D4—62no—
478D4—61no—
479D4—102no—
480D4—102no—
481D4—101no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—101no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4C4×D3×D511yescharacteristic
491C2×C4C4×D3×D511yescharacteristic
492C2×C4#677711yescharacteristic
493C2×C4#677711yescharacteristic
494C2×C4#678011yescharacteristic
495C2×C4C22×D3×D511yescharacteristic
496C8—62no—
497C8—102no—
498C8—152no—
499C8—152no—
500C8—152no—
501C8—152no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—202no—
505C2×C3#6511212yescomplemented
506C2×C3C2×#402711yescharacteristic
507D3—42no—
508C5C2×#482311yescharacteristic, complemented, Sylow
509C22—22no—
510C22—62no—
511C22—102no—
512C22—122no—
513C22—202no—
514C22#9144211yescharacteristic
515C22#9144211yescharacteristic
516C22C2×#678011yescharacteristic
517C4—42no—
518C4—62no—
519C4—102no—
520C4#9144211yescharacteristic
521C4#9144211yescharacteristic
522C4C2×C4×D3×D511yescharacteristic
523C4C2×#677711yescharacteristic
524C3C2×#6511211yescharacteristic, complemented, Sylow
525C2—21no—
526C2—21no—
527C2—122no—
528C2—202no—
529C2#1174710712yesdirect product factor
530C2C2×#9144211yescharacteristic
subgroupG/H
centerC2×C4#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C4×D4
prime radicalC2×#91297C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#91288C2semidirect
3. C2×#91284C2semidirect
4. C2×#91087C2semidirect
5. C2×C5×#805C2semidirect
6. C2×C3×#3937C2semidirect
7. C2×#90992C2semidirect
8. #11747107C2direct (N × H)
17. C2×#6661C4semidirect
18. C2×#6656C4semidirect
19. C2×#6655C4semidirect
20. #91297C4semidirect
22. C2×#6652C4semidirect
26. #91288C22semidirect
29. #91284C22semidirect
31. #91087C22semidirect
32. C5×#805C22semidirect
33. C3×#3937C22semidirect
34. #90992C22semidirect
41. C2×#3937D3semidirect
78. #6661C2×C4semidirect
79. #6656C2×C4semidirect
80. #6655C2×C4semidirect
81. #6652C2×C4semidirect
91. C2×#805D5semidirect
117. #3937C2×D3semidirect
178. #805C2×D5semidirect
349. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
464. C2×C5#4823semidirect
505. C2×C3#65112semidirect
508. C5C2×#4823semidirect
524. C3C2×#65112semidirect
529. C2#11747107direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#912972
C2×#912882
C2×#912842
C2×#910872
C2×C5×#8052
C2×C3×#39372
C2×#909922
#117471072
C2×#651123
C2×#48235