Finite Group Databasebeta

← C2×#11751688 #14417998

Subgroups — C2×#11751688 #14417998

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×#91916C211yesmaximal, characteristic, complemented
2C2×#91913C211yesmaximal, characteristic, complemented
3C2×#91269C211yesmaximal, characteristic
4C2×#91221C211yesmaximal, characteristic, complemented
5C2×C3×#3996C211yesmaximal, characteristic, complemented
6C2×#91157C211yesmaximal, characteristic, complemented
7C2×#91155C211yesmaximal, characteristic, complemented
8#11751688C218yesmaximal, direct product factor
9C2×#65737—31nomaximal, Hall
10C2×#6773C2211yescharacteristic
11C2×#6772C2211yescharacteristic
12C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
13C2×D5⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#700C2211yescharacteristic
15C2×C3×#700C2211yescharacteristic
16C2×#6740—21no—
17C2×#6739—21no—
18C2×#6738—21no—
19C2×D3×#170—21no—
20#91916—22no—
21#91916C2214yescomplemented
22#91913—22no—
23#91913C2214yescomplemented
24C2×#6706C411yescharacteristic, complemented
25C2×C5×#204C411yescharacteristic, complemented
26C2×C3×C8×D5C2211yescharacteristic
27C2×#6663C411yescharacteristic, complemented
28C2×#6654C411yescharacteristic, complemented
29#91269C414yescomplemented
30#91269C2214yes—
31#91221C2214yescomplemented
32C3×#3996C2214yescomplemented
33#91157C2214yescomplemented
34#91155C2214yescomplemented
35C2×#4894—51nomaximal, Hall
36C2×#4133—31no—
37C2×#4131—31no—
38C2×#4062—31no—
39C2×#4010—31no—
40C2×#4008—31no—
41#65737—38no—
42C2×#3996D311yescharacteristic, complemented
43C2×#3992—31no—
44C22×ΓL(1,𝔽16)—21no—
45C2×D60C2×C411yescharacteristic
46C2×Dic30C2×C411yescharacteristic
47C2×C5×D12C2×C411yescharacteristic
48C2×C5×Dic6C2×C411yescharacteristic
49C2×C3×C4×D5C2311yescharacteristic
50C2×#1202—21no—
51C2×#1201—21no—
52C2×#1200—21no—
53C2×D3×Dic5—21no—
54#6773—21no—
55#6773—21no—
56#6773C2×C412yes—
57#6773C2312yes—
58#6772—21no—
59#6772—21no—
60#6772C2×C412yes—
61#6772C2312yes—
62C2×C3⋊#170D411yescharacteristic
63C2×C3⋊#170D411yescharacteristic
64C4×ΓL(1,𝔽16)—21no—
65C4×ΓL(1,𝔽16)C2312yes—
66D5⋊(C3⋊C8)D412yes—
67D5⋊(C3⋊C8)C2312yes—
68C2×C3×#170—21no—
69C2×C3×#170—21no—
70C3×#700—21no—
71C3×#700—21no—
72C3×#700C2312yes—
73C3×#700C2312yes—
74#6740—24no—
75#6739—24no—
76#6738—24no—
77D3×#170—24no—
78C2×C3×C5×C8C2×C411yescharacteristic
79#6706C2×C414yescomplemented
80C5×#204C2×C414yescomplemented
81C2×C3×#168C2×C411yescharacteristic
82C3×C8×D5C2×C412yes—
83C3×C8×D5C2312yes—
84#6663C2×C414yescomplemented
85#6654C2×C414yescomplemented
86C2×#907—51no—
87C2×#907—51no—
88C2×#904—51no—
89C2×C3×#108—51no—
90C2×#825—51no—
91C2×#825—51no—
92C2×#815—51no—
93#4894—58no—
94C2×#713—31no—
95C2×#711—31no—
96C2×#704—61no—
97C22×#170—61no—
98#4133—34no—
99#4133—62no—
100#4131—34no—
101#4131—62no—
102C2×C4×AGL(1,𝔽5)—31no—
103C2×#700—61no—
104C2×#700C2×D311yescharacteristic
105C2×#700C2×D311yescharacteristic
106C2×D5⋊C8—31no—
107C2×D5⋊C8—61no—
108C2×C5×SD16—31no—
109C2×#689—31no—
110C2×#686—31no—
111#4062—34no—
112#4062—34no—
113C2×#677—31no—
114C2×C8×D5C2×D311yescharacteristic
115#4010—34no—
116#4008—34no—
117#3996C2×D314yescomplemented
118#3992—34no—
119C2×#444—151noSylow
120C22×D15—21no—
121C22×C5×D3—21no—
122C22×C3×D5#4111yescharacteristic
123C2×ΓL(1,𝔽16)—22no—
124C2×ΓL(1,𝔽16)—42no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×Dic15—21no—
127D60—21no—
128D60C22×C412yes—
129Dic30—21no—
130Dic30C22×C412yes—
131C2×C5×Dic3—21no—
132C5×D12—21no—
133C5×D12C22×C412yes—
134C5×Dic6—21no—
135C5×Dic6C22×C412yes—
136C2×C3×Dic5C2×D411yescharacteristic
137C3×C4×D5C22×C411yescharacteristic
138C3×C4×D5C2×D411yescharacteristic
139C3×C4×D5#4111yescharacteristic
140C3×C4×D5C2411yescharacteristic
141#1202—22no—
142#1202—22no—
143#1201—22no—
144#1201—22no—
145#1200—22no—
146#1200—22no—
147D3×Dic5—22no—
148D3×Dic5—22no—
149C3⋊#170C2×D412yes—
150C3⋊#170C2×D412yes—
151C3×#170—22no—
152C3×#170—22no—
153C3×C5×C8C22×C412yes—
154C3×#168C22×C412yes—
155C2×#235—51no—
156C2×#235—51no—
157C2×C3×M16—51no—
158C2×C3×M16—51no—
159C22×C3×C8—51no—
160C2×C4×Dic3—51no—
161C22×C3⋊C8—51no—
162#907—54no—
163#907—54no—
164#907—102no—
165#907—102no—
166C2×Dic12—51no—
167#904—54no—
168#904—54no—
169C2×D24—51no—
170C2×#204—51no—
171C2×#204AGL(1,𝔽5)11yescharacteristic, complemented
172C2×ΓL(1,𝔽25)—101no—
173C2×ΓL(1,𝔽25)—101no—
174C2×D3×C8—101no—
175C2×D3×C8—101no—
176C3×#108—54no—
177#825—54no—
178#825—54no—
179#815—54no—
180C22×AGL(1,𝔽5)—61no—
181C2×C5×Q8—31no—
182C2×C5×D4—31no—
183C2×C22⋊D5—61no—
184C22×Dic5—61no—
185#713—32no—
186#713—32no—
187#713—61no—
188#713—61no—
189#711—32no—
190#711—32no—
191#711—61no—
192#711—61no—
193C2×D20—31no—
194C2×D20—61no—
195C2×C4×D5—61no—
196C2×C4×D5C22×D311yescharacteristic
197C2×Dic10—31no—
198#704—64no—
199C2×#170—21no—
200C2×#170—21no—
201C2×#170—31no—
202C2×#170—31no—
203C2×#170—64no—
204C4×AGL(1,𝔽5)—32no—
205C4×AGL(1,𝔽5)—61no—
206#700—21no—
207#700—21no—
208#700—64no—
209#700C22×D312yes—
210#700C22×D312yes—
211D5⋊C8—32no—
212D5⋊C8—32no—
213D5⋊C8—64no—
214C5×SD16—34no—
215C2×C5×C8C4×D311yescharacteristic
216#689—34no—
217#686—34no—
218C2×#168C4×D311yescharacteristic
219#677—34no—
220C8×D5C4×D312yes—
221C8×D5C22×D312yes—
222C2×#135—151no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—51no—
227C2×#104—151no—
228C2×#104—151no—
229C2×#97—151no—
230C22×C3×C5C4×D411yescharacteristic
231C2×D15—22no—
232C2×D15—42no—
233C2×C5×D3—22no—
234C2×C5×D3—42no—
235C2×C3×D5—22no—
236C2×C3×D5C4×D411yescharacteristic
237C2×C3×D5C2×#4111yescharacteristic
238ΓL(1,𝔽16)—42no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C23×C411yescharacteristic
241Dic15—22no—
242C3×Dic5C4×D411yescharacteristic
243C3×Dic5C22×D411yescharacteristic
244C5×Dic3—22no—
245C22×C3×C4—51no—
246C2×#67—101no—
247C2×#67—101no—
248C22×Dic3—101no—
249#235—52no—
250#235—52no—
251#235—52no—
252#235—52no—
253#235—101no—
254#235—101no—
255#235—101no—
256#235—101no—
257C2×D12—51no—
258C2×D12C2×AGL(1,𝔽5)11yescharacteristic
259C2×C4×D3—101no—
260C2×C4×D3—101no—
261C2×Dic6—51no—
262C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
263C3×M16—52no—
264C3×M16—52no—
265C3×M16—101no—
266C3×M16—101no—
267C2×C3×C8—51no—
268C2×C3×C8—52no—
269C2×C3×C8—52no—
270C2×C3×C8—101no—
271C2×C3×C8—101no—
272C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
273C4×Dic3—52no—
274C4×Dic3—101no—
275C2×C3⋊C8—52no—
276C2×C3⋊C8—52no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279Dic12—54no—
280D24—54no—
281#204—54no—
282#204C2×AGL(1,𝔽5)14yescomplemented
283ΓL(1,𝔽25)—104no—
284ΓL(1,𝔽25)—104no—
285D3×C8—104no—
286D3×C8—104no—
287C23×C5—61no—
288C22×D5—61no—
289C22×D5#23911yescharacteristic
290C2×AGL(1,𝔽5)—62no—
291C2×AGL(1,𝔽5)—122no—
292C5×Q8—32no—
293C5×Q8—61no—
294C5×D4—32no—
295C5×D4—61no—
296C2×C4×C5—61no—
297C2×C4×C5C2×C4×D311yescharacteristic
298C22⋊D5—62no—
299C22⋊D5—62no—
300C2×Dic5—61no—
301C2×Dic5—62no—
302C2×Dic5—62no—
303C2×Dic5D3×D411yescharacteristic
304D20—32no—
305D20—62no—
306D20—62no—
307D20—61no—
308C4×D5—62no—
309C4×D5—62no—
310C4×D5C2×C4×D311yescharacteristic
311C4×D5D3×D411yescharacteristic
312C4×D5#23911yescharacteristic
313C4×D5C23×D311yescharacteristic
314Dic10—32no—
315Dic10—61no—
316#170—22no—
317#170—22no—
318#170—32no—
319#170—32no—
320C5×C8C2×C4×D312yes—
321#168C2×C4×D312yes—
322C2×#41—151no—
323C2×#41—151no—
324#135—154no—
325#135—154no—
326C2×Q16—151no—
327C2×SD16—31no—
328C2×SD16—151no—
329C2×D8—151no—
330#131—154no—
331#131—154no—
332#131—302no—
333#131—302no—
334C2×M16—51no—
335C2×M16—51no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—51no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42—151no—
343#108—54no—
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—
352C5×D3—42no—
353C23×C3—51no—
354C22×D3—21no—
355C22×D3—101no—
356C2×C3×C4—51no—
357C2×C3×C4—51no—
358C2×C3×C4—51no—
359C2×C3×C4—51no—
360C2×C3×C4—51no—
361C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
362#67—102no—
363#67—102no—
364#67—102no—
365#67—102no—
366C2×Dic3—21no—
367C2×Dic3—101no—
368C2×Dic3—102no—
369C2×Dic3—202no—
370D12—21no—
371D12—52no—
372D12—101no—
373D12C22×AGL(1,𝔽5)12yes—
374C4×D3—102no—
375C4×D3—102no—
376C4×D3—102no—
377C4×D3—102no—
378Dic6—21no—
379Dic6—52no—
380Dic6—101no—
381Dic6C22×AGL(1,𝔽5)12yes—
382C3×C8—52no—
383C3×C8—102no—
384C3×C8—102no—
385C3×C8C22×AGL(1,𝔽5)12yes—
386C3⋊C8—52no—
387C3⋊C8—52no—
388C22×C5—62no—
389C22×C5—122no—
390C22×C5#89311yescharacteristic
391C2×D5—22no—
392C2×D5—62no—
393C2×D5—122no—
394C2×D5#89311yescharacteristic
395C2×D5C2×#23911yescharacteristic
396AGL(1,𝔽5)—122no—
397C4×C5—62no—
398C4×C5#89311yescharacteristic
399C4×C5C22×C4×D311yescharacteristic
400Dic5—62no—
401Dic5#89311yescharacteristic
402Dic5C2×D3×D411yescharacteristic
403#41—152no—
404#41—152no—
405#41—152no—
406#41—152no—
407#41—301no—
408#41—301no—
409#41—301no—
410#41—301no—
411C2×Q8—31no—
412C2×Q8—151no—
413C2×D4—31no—
414C2×D4—151no—
415C2×D4—301no—
416C2×D4—301no—
417C22×C4—51no—
418C22×C4—301no—
419C22×C4—301no—
420C22×C4—301no—
421Q16—154no—
422SD16—34no—
423SD16—154no—
424D8—154no—
425M16—52no—
426M16—52no—
427M16—101no—
428M16—101no—
429M16—304no—
430M16—304no—
431C2×C8—51no—
432C2×C8—52no—
433C2×C8—52no—
434C2×C8—101no—
435C2×C8—101no—
436C2×C8—152no—
437C2×C8—151no—
438C2×C8—151no—
439C2×C8—152no—
440C2×C8—304no—
441C2×C8—304no—
442C2×C8D3×AGL(1,𝔽5)11yescharacteristic
443C42—152no—
444C42—301no—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—51no—
447C22×C3—51no—
448C22×C3—102no—
449C22×C3D4×AGL(1,𝔽5)11yescharacteristic
450C2×D3—22no—
451C2×D3—42no—
452C2×D3—102no—
453C2×D3—202no—
454C3×C4—51no—
455C3×C4—51no—
456C3×C4D4×AGL(1,𝔽5)11yescharacteristic
457C3×C4C23×AGL(1,𝔽5)11yescharacteristic
458Dic3—22no—
459Dic3—102no—
460Dic3—202no—
461C2×C5—122no—
462C2×C5#489412yescomplemented
463C2×C5C2×#89311yescharacteristic
464D5—21no—
465D5—21no—
466D5—122no—
467C23—51no—
468C23—61no—
469C23—301no—
470Q8—32no—
471Q8—61no—
472Q8—152no—
473Q8—301no—
474D4—32no—
475D4—61no—
476D4—152no—
477D4—302no—
478D4—302no—
479D4—302no—
480D4—302no—
481D4—301no—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—61no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4—302no—
491C2×C4—302no—
492C2×C4—301no—
493C2×C4—302no—
494C2×C4—602no—
495C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
496C8—52no—
497C8—102no—
498C8—102no—
499C8—152no—
500C8—152no—
501C8C2×D3×AGL(1,𝔽5)12yes—
502C2×C3—101no—
503C2×C3—101no—
504C2×C3#6573712yescomplemented
505C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
506D3—42no—
507D3—202no—
508C5C2×#489411yescharacteristic, complemented, Sylow
509C22—51no—
510C22—51no—
511C22—62no—
512C22—102no—
513C22—122no—
514C22—302no—
515C22—602no—
516C22#9192111yescharacteristic
517C4—51no—
518C4—51no—
519C4—62no—
520C4—302no—
521C4—602no—
522C4#9192111yescharacteristic
523C4C22×D3×AGL(1,𝔽5)11yescharacteristic
524C3C2×#6573711yescharacteristic, complemented, Sylow
525C2—101no—
526C2—101no—
527C2—122no—
528C2—602no—
529C2#1175168812yesdirect product factor
530C2C2×#9192111yescharacteristic
subgroupG/H
centerC22#91921
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×#91269C2
cosocleC3×C4×D5C24
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#91916C2semidirect
2. C2×#91913C2semidirect
4. C2×#91221C2semidirect
5. C2×C3×#3996C2semidirect
6. C2×#91157C2semidirect
7. C2×#91155C2semidirect
8. #11751688C2direct (N × H)
21. #91916C22semidirect
23. #91913C22semidirect
24. C2×#6706C4semidirect
25. C2×C5×#204C4semidirect
27. C2×#6663C4semidirect
28. C2×#6654C4semidirect
29. #91269C4semidirect
31. #91221C22semidirect
32. C3×#3996C22semidirect
33. #91157C22semidirect
34. #91155C22semidirect
42. C2×#3996D3semidirect
79. #6706C2×C4semidirect
80. C5×#204C2×C4semidirect
84. #6663C2×C4semidirect
85. #6654C2×C4semidirect
117. #3996C2×D3semidirect
171. C2×#204AGL(1,𝔽5)semidirect
282. #204C2×AGL(1,𝔽5)semidirect
347. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
462. C2×C5#4894semidirect
504. C2×C3#65737semidirect
508. C5C2×#4894semidirect
524. C3C2×#65737semidirect
529. C2#11751688direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919162
C2×#919132
C2×#912692
C2×#912212
C2×C3×#39962
C2×#911572
C2×#911552
#117516882
C2×#657373
C2×#48945