Finite Group Databasebeta

← C2×#11748189 #14429345

Subgroups — C2×#11748189 #14429345

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#908C211yesmaximal, characteristic
2C2×#91322C211yesmaximal, characteristic, complemented
3C22×#6659C211yesmaximal, characteristic, complemented
4C2×#91286C211yesmaximal, characteristic, complemented
5C2×#91108C211yesmaximal, characteristic, complemented
6C2×C3×#3954C211yesmaximal, characteristic, complemented
7C2×#90959C211yesmaximal, characteristic, complemented
8#11748189C218yesmaximal, direct product factor
9C2×#65489—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C2×C5×#235C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C2×#6710C2211yescharacteristic
15C5×#908—22no—
16C5×#908C2214yes—
17C2×C5×D24—21no—
18C2×C5×#204—21no—
19C2×C3×#681C2211yescharacteristic
20C22×C3×#168C2211yescharacteristic
21#91322—22no—
22#91322C2214yescomplemented
23C2×#6663—21no—
24C2×#6659—21no—
25C2×#6659—21no—
26C2×#6659—22no—
27C2×#6659—21no—
28C2×#6659C2214yescomplemented
29C2×#6650—21no—
30#91286—22no—
31#91286C2214yescomplemented
32C2×D3×#168—21no—
33#91108C2214yescomplemented
34C3×#3954C2214yescomplemented
35#90959C2214yescomplemented
36C2×#4898—51nomaximal, Hall
37C2×C5×AGL(1,ℤ/8)—31no—
38C2×#4097—31no—
39C2×#4094—31no—
40C22×#687—31no—
41C2×#3965—31no—
42#65489—38no—
43C2×#3956—31no—
44C2×#3954D311yescharacteristic, complemented
45C23×C5×D3—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C2×Dic30—21no—
49C2×Dic30—21no—
50C2×Dic30—21no—
51C2×Dic30—21no—
52C2×Dic30—21no—
53C2×Dic30C2312yes—
54C2×C5×#67—21no—
55C5×#235—21no—
56C5×#235—21no—
57C5×#235D412yes—
58C5×#235C2312yes—
59C2×C5×D12—21no—
60C2×C5×D12—21no—
61C2×C5×D12—21no—
62C2×C5×D12—21no—
63C2×C5×D12—21no—
64C2×C5×D12D411yescharacteristic
65C2×C5×D12C2312yes—
66C2×C4×C5×D3—21no—
67C2×C5×Dic6D411yescharacteristic
68C3×C5×M16—21no—
69C3×C5×M16C2312yes—
70C2×C3×C5×C8—21no—
71#6710—21no—
72#6710C2312yes—
73C2×C3⋊#168—21no—
74C5×D24—24no—
75C5×#204—24no—
76C3×#681—21no—
77C3×#681C2312yes—
78C2×C3×#168—21no—
79C2×C3×#168D411yescharacteristic
80C2×C3×#168D412yes—
81C2×C3×#168D411yescharacteristic
82C2×C3×#168C2312yes—
83#6663—24no—
84#6659—24no—
85#6659—24no—
86#6659—24no—
87#6650—24no—
88D3×#168—24no—
89C2×#909—51no—
90C2×#908D511yescharacteristic
91C22×#204—51no—
92C2×#901—51no—
93C2×C3×#108—51no—
94C2×#824—51no—
95C2×#823—51no—
96#4898—58no—
97C2×C5×#41—31no—
98C22×C5×D4—31no—
99C22×Dic10—31no—
100C5×AGL(1,ℤ/8)—34no—
101C5×AGL(1,ℤ/8)—62no—
102C2×C5×SD16—61no—
103C2×C5×D8—61no—
104C2×C5×M16C2×D311yescharacteristic
105#4097—34no—
106#4097—62no—
107#4094—34no—
108#4094—62no—
109C2×#689—61no—
110C2×#687—34no—
111C2×#687—61no—
112C2×#687—61no—
113C2×#687—61no—
114C2×#687—62no—
115C2×#681—31no—
116C2×#681—61no—
117C2×#681C2×D311yescharacteristic
118C22×#168—61no—
119C22×#168C2×D311yescharacteristic
120#3965—34no—
121#3956—34no—
122#3954C2×D314yescomplemented
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×C5×D3—21no—
126C22×C5×D3—22no—
127C22×C5×D3—41no—
128C22×C5×D3—41no—
129C22×C5×D3—82no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136C2×Dic15—22no—
137C2×Dic15—41no—
138C2×Dic15—41no—
139Dic30—22no—
140Dic30—22no—
141Dic30—41no—
142Dic30—41no—
143C5×#67—22no—
144C5×#67—22no—
145C2×C5×Dic3—21no—
146C5×D12—21no—
147C5×D12—22no—
148C5×D12—22no—
149C5×D12—41no—
150C5×D12—41no—
151C5×D12C2×D412yes—
152C4×C5×D3—22no—
153C4×C5×D3—22no—
154C5×Dic6—21no—
155C5×Dic6C2×D412yes—
156C3×C5×C8—22no—
157C3⋊#168—22no—
158C3×#168—22no—
159C3×#168C2×D412yes—
160C3×#168C2×D412yes—
161C2×#235C2×D511yescharacteristic
162C22×D12C2×D511yescharacteristic
163C22×Dic6—51no—
164C2×C3×M16—51no—
165C2×C3×M16C2×D511yescharacteristic
166C22×C3×C8—51no—
167C2×#208—51no—
168#909—54no—
169#909—102no—
170#908—22no—
171#908C2×D514yes—
172C2×Dic12—101no—
173C2×D24—21no—
174C2×#204—21no—
175C2×#204—54no—
176C2×#204—101no—
177C2×#204—101no—
178C2×#204—102no—
179C2×#204—101no—
180#901—54no—
181#901—102no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184C3×#108—54no—
185#824—54no—
186#823—54no—
187C24×C5—61no—
188C5×#41—32no—
189C5×#41—32no—
190C5×#41—61no—
191C5×#41—61no—
192C2×C5×Q8—31no—
193C2×C5×D4—31no—
194C2×C5×D4—32no—
195C2×C5×D4—61no—
196C2×C5×D4—61no—
197C2×C5×D4—61no—
198C2×C5×D4—61no—
199C2×C5×D4—61no—
200C2×C5×D4—61no—
201C22×C4×C5—61no—
202C22×C4×C5C22×D311yescharacteristic
203C22×Dic5—61no—
204C2×Dic10—32no—
205C2×Dic10—61no—
206C2×Dic10—61no—
207C2×Dic10—61no—
208C2×Dic10—61no—
209C2×Dic10—61no—
210C5×SD16—64no—
211C5×D8—64no—
212C5×M16—21no—
213C5×M16C22×D312yes—
214C2×C5×C8—21no—
215#689—64no—
216#687—64no—
217#687—64no—
218#687—64no—
219#681—21no—
220#681—32no—
221#681—61no—
222#681—64no—
223#681C22×D312yes—
224C2×#168—21no—
225C2×#168—61no—
226C2×#168—64no—
227C2×#168D1211yescharacteristic
228C2×#168D1211yescharacteristic
229C2×#168D1212yes—
230C2×#168C22×D312yes—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—31no—
233C22×SD16—151no—
234C2×#131—151no—
235#471—158no—
236C2×#108—51no—
237C2×#101—151no—
238C2×#100—151no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×C5×D3—22no—
244C2×C5×D3—42no—
245C2×C5×D3—42no—
246C2×C5×D3—82no—
247C2×C5×D3—82no—
248C2×C5×D3—82no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253Dic15—42no—
254C5×Dic3—22no—
255C23×D3—21no—
256C22×C3×C4C22×D511yescharacteristic
257C2×#67—21no—
258C22×Dic3—101no—
259#235—21no—
260#235—21no—
261#235C22⋊D512yes—
262#235C22×D512yes—
263C2×D12—21no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12C22⋊D511yescharacteristic
269C2×D12C22×D512yes—
270C2×C4×D3—21no—
271C2×Dic6—52no—
272C2×Dic6—101no—
273C2×Dic6—101no—
274C2×Dic6—101no—
275C2×Dic6—101no—
276C2×Dic6—101no—
277C2×Dic6C22⋊D511yescharacteristic
278C3×M16—21no—
279C3×M16—52no—
280C3×M16—101no—
281C3×M16C22×D512yes—
282C2×C3×C8—21no—
283C2×C3×C8—51no—
284C2×C3×C8—51no—
285C2×C3×C8—52no—
286C2×C3×C8—52no—
287C2×C3×C8—101no—
288#208—52no—
289#208—101no—
290C2×C3⋊C8—101no—
291Dic12—104no—
292D24—24no—
293#204—24no—
294#204—104no—
295#204—104no—
296#204—104no—
297ΓL(1,𝔽25)—104no—
298D3×C8—104no—
299C23×C5—61no—
300C23×C5—62no—
301C23×C5—121no—
302C23×C5—121no—
303C23×C5—242no—
304C23×C5#23911yescharacteristic
305C5×Q8—32no—
306C5×Q8—61no—
307C5×D4—32no—
308C5×D4—62no—
309C5×D4—62no—
310C5×D4—61no—
311C5×D4—62no—
312C5×D4—62no—
313C5×D4—121no—
314C5×D4—121no—
315C2×C4×C5—61no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5C2×D1211yescharacteristic
319C2×C4×C5C2×D1211yescharacteristic
320C2×C4×C5D3×D411yescharacteristic
321C2×C4×C5D3×D411yescharacteristic
322C2×C4×C5#23911yescharacteristic
323C2×C4×C5C23×D311yescharacteristic
324C2×Dic5—62no—
325C2×Dic5—121no—
326C2×Dic5—121no—
327Dic10—62no—
328Dic10—62no—
329Dic10—121no—
330Dic10—121no—
331C5×C8—22no—
332#168—22no—
333#168—62no—
334#168C2×D1212yes—
335#168C2×D1212yes—
336C2×#41—31no—
337C22×Q8—151no—
338C22×D4—31no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—34no—
342AGL(1,ℤ/8)—62no—
343C2×Q16—301no—
344C2×SD16—61no—
345C2×SD16—154no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—302no—
349C2×SD16—301no—
350C2×D8—61no—
351#131—154no—
352#131—302no—
353C2×M16—51no—
354C2×M16—151no—
355C2×M16—301no—
356C2×M16D3×D511yescharacteristic
357C22×C8—51no—
358C22×C8—301no—
359#108—54no—
360#101—154no—
361#100—154no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366C5×D3—42no—
367C5×D3—82no—
368C23×C3#71111yescharacteristic
369C22×D3—21no—
370C22×D3—22no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—82no—
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4D4×D511yescharacteristic
376C2×C3×C4#71111yescharacteristic
377C2×C3×C4C2×C22⋊D511yescharacteristic
378C2×C3×C4C2×C22⋊D511yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380#67—22no—
381#67—22no—
382C2×Dic3—21no—
383C2×Dic3—102no—
384C2×Dic3—201no—
385C2×Dic3—201no—
386D12—22no—
387D12—22no—
388D12—21no—
389D12—41no—
390D12—41no—
391D12C2×C22⋊D512yes—
392C4×D3—22no—
393C4×D3—22no—
394Dic6—21no—
395Dic6—102no—
396Dic6—102no—
397Dic6—201no—
398Dic6—201no—
399Dic6C2×C22⋊D512yes—
400C3×C8—22no—
401C3×C8—52no—
402C3×C8—52no—
403C3×C8—102no—
404C3⋊C8—102no—
405C22×C5—22no—
406C22×C5—62no—
407C22×C5—122no—
408C22×C5—122no—
409C22×C5—242no—
410C22×C5—242no—
411C22×C5—242no—
412C22×C5#89511yescharacteristic
413C22×C5#89511yescharacteristic
414C22×C5C2×#23911yescharacteristic
415C4×C5—62no—
416C4×C5#89511yescharacteristic
417C4×C5#89511yescharacteristic
418C4×C5C22×D1211yescharacteristic
419C4×C5C2×D3×D411yescharacteristic
420Dic5—122no—
421C24—61no—
422#41—32no—
423#41—32no—
424#41—61no—
425#41—61no—
426C2×Q8—31no—
427C2×Q8—152no—
428C2×Q8—301no—
429C2×Q8—301no—
430C2×Q8—301no—
431C2×Q8—301no—
432C2×Q8—301no—
433C2×D4—31no—
434C2×D4—32no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—61no—
441C22×C4—61no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—64no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—64no—
450M16—21no—
451M16—52no—
452M16—101no—
453M16—152no—
454M16—304no—
455M16—301no—
456M16C2×D3×D512yes—
457C2×C8—21no—
458C2×C8—51no—
459C2×C8—51no—
460C2×C8—52no—
461C2×C8—52no—
462C2×C8—101no—
463C2×C8—304no—
464C2×C8—301no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3#408511yescharacteristic
468C22×C3#408511yescharacteristic
469C22×C3C2×#71111yescharacteristic
470C2×D3—22no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—82no—
474C2×D3—82no—
475C2×D3—82no—
476C3×C4#408511yescharacteristic
477C3×C4#408511yescharacteristic
478C3×C4C2×D4×D511yescharacteristic
479C3×C4C22×C22⋊D511yescharacteristic
480Dic3—22no—
481Dic3—202no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5—122no—
485C2×C5—242no—
486C2×C5#489812yescomplemented
487C2×C5C2×#89511yescharacteristic
488C23—61no—
489C23—62no—
490C23—121no—
491C23—121no—
492C23—242no—
493C23#676811yescharacteristic
494Q8—32no—
495Q8—61no—
496Q8—302no—
497Q8—302no—
498Q8—601no—
499Q8—601no—
500D4—32no—
501D4—62no—
502D4—62no—
503D4—61no—
504D4—62no—
505D4—62no—
506D4—121no—
507D4—121no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—302no—
512C2×C4—601no—
513C2×C4—601no—
514C2×C4#676811yescharacteristic
515C2×C4D5×D1211yescharacteristic
516C2×C4D5×D1211yescharacteristic
517C2×C4D3×C22⋊D511yescharacteristic
518C2×C4D3×C22⋊D511yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—22no—
521C8—52no—
522C8—52no—
523C8—102no—
524C8—302no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3#6548912yescomplemented
528C2×C3C2×#408511yescharacteristic
529D3—42no—
530D3—82no—
531C5C2×#489811yescharacteristic, complemented, Sylow
532C22—22no—
533C22—62no—
534C22—122no—
535C22—122no—
536C22—242no—
537C22—242no—
538C22—242no—
539C22#9141611yescharacteristic
540C22#9141611yescharacteristic
541C22C2×#676811yescharacteristic
542C4—62no—
543C4—602no—
544C4#9141611yescharacteristic
545C4#9141611yescharacteristic
546C4C2×D5×D1211yescharacteristic
547C4C2×D3×C22⋊D511yescharacteristic
548C3C2×#6548911yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—122no—
552C2—242no—
553C2#1174818912yesdirect product factor
554C2C2×#9141611yescharacteristic
subgroupG/H
centerC22#91416
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#121
prime radicalC2×C5×#908C2
hypercenterC2×M16D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#91322C2semidirect
3. C22×#6659C2semidirect
4. C2×#91286C2semidirect
5. C2×#91108C2semidirect
6. C2×C3×#3954C2semidirect
7. C2×#90959C2semidirect
8. #11748189C2direct (N × H)
22. #91322C22semidirect
28. C2×#6659C22semidirect
31. #91286C22semidirect
33. #91108C22semidirect
34. C3×#3954C22semidirect
35. #90959C22semidirect
44. C2×#3954D3semidirect
122. #3954C2×D3semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
486. C2×C5#4898semidirect
527. C2×C3#65489semidirect
531. C5C2×#4898semidirect
548. C3C2×#65489semidirect
553. C2#11748189direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#9082
C2×#913222
C22×#66592
C2×#912862
C2×#911082
C2×C3×#39542
C2×#909592
#117481892
C2×#654893
C2×#48985