Finite Group Databasebeta

← C2×#11751958 #14417986

Subgroups — C2×#11751958 #14417986

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×#91990C211yesmaximal, characteristic, complemented
2C2×#91916C211yesmaximal, characteristic, complemented
3C2×#91492C211yesmaximal, characteristic
4C2×C3×#4008C211yesmaximal, characteristic, complemented
5#11751958C218yesmaximal, direct product factor
6C2×#91162C211yesmaximal, characteristic, complemented
7C2×#91158C211yesmaximal, characteristic, complemented
8C2×#91149C211yesmaximal, characteristic, complemented
9C2×#65737—31nomaximal, Hall
10C2×C3×#711C2211yescharacteristic
11C2×#6773C2211yescharacteristic
12C2×#6762—21no—
13C22×C3⋊#170—21no—
14#91990—22no—
15#91990C2214yescomplemented
16C2×#6758C2211yescharacteristic
17C2×D5⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
19C2×C3×#700C2211yescharacteristic
20C2×#6740—21no—
21C2×#6738—21no—
22#91916—22no—
23#91916C2214yescomplemented
24C2×#6715C411yescharacteristic, complemented
25C2×C5×#214C411yescharacteristic, complemented
26#91492C414yescomplemented
27#91492C2214yes—
28C2×#6661C411yescharacteristic, complemented
29C2×#6658C411yescharacteristic, complemented
30C2×D5×C3⋊C8C2211yescharacteristic
31C3×#4008C2214yescomplemented
32#91162C2214yescomplemented
33#91158C2214yescomplemented
34#91149C2214yescomplemented
35C2×#4823—51nomaximal, Hall
36C2×#4133—31no—
37C2×#4131—31no—
38C2×#4062—31no—
39C2×#4010—31no—
40C2×#4008D311yescharacteristic, complemented
41#65737—38no—
42C2×#3996—31no—
43C2×#3992—31no—
44C22×C3×AGL(1,𝔽5)—21no—
45C2×C3×C5×D4C2×C411yescharacteristic
46C2×D60C2×C411yescharacteristic
47C2×C5×Dic6C2×C411yescharacteristic
48C2×C3×C22⋊D5—21no—
49C22×C3×Dic5—21no—
50C3×#711—21no—
51C3×#711—21no—
52C3×#711C2×C412yes—
53C3×#711C2312yes—
54C2×C3×C4×D5C2311yescharacteristic
55C2×C3×Dic10C2×C411yescharacteristic
56C2×#1202—21no—
57C2×#1200—21no—
58#6773—21no—
59#6773—21no—
60#6773C2×C412yes—
61#6773C2312yes—
62#6762—24no—
63C2×C3⋊#170—21no—
64C2×C3⋊#170—24no—
65C2×C3⋊#170D411yescharacteristic
66C2×C3⋊#170D411yescharacteristic
67#6758—21no—
68#6758C2312yes—
69D5⋊(C3⋊C8)D412yes—
70D5⋊(C3⋊C8)C2312yes—
71C2×C3×#170—21no—
72C3×C4×AGL(1,𝔽5)—21no—
73C3×C4×AGL(1,𝔽5)C2312yes—
74C3×#700—21no—
75C3×#700C2312yes—
76#6740—24no—
77#6738—24no—
78#6715C2×C414yescomplemented
79C2×C3⋊#168C2×C411yescharacteristic
80C5×#214C2×C414yescomplemented
81C2×C5×C3⋊C8C2×C411yescharacteristic
82#6661C2×C414yescomplemented
83#6658C2×C414yescomplemented
84D5×C3⋊C8C2×C412yes—
85D5×C3⋊C8C2312yes—
86C2×#950—51no—
87C2×#948—51no—
88C2×#907—51no—
89C2×C3×#104—51no—
90C2×#822—51no—
91C2×#805—51no—
92C2×#803—51no—
93#4823—58no—
94C2×#713—31no—
95C2×#711C2×D311yescharacteristic
96C2×#704—61no—
97C22×#170—61no—
98#4133—34no—
99#4133—62no—
100#4131—34no—
101#4131—62no—
102C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
103C2×#700—31no—
104C2×#700—61no—
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×D5—31no—
115#4010—34no—
116#4008C2×D314yescomplemented
117#3996—34no—
118#3992—34no—
119C2×#444—151noSylow
120C23×C3×C5—21no—
121C22×D15—21no—
122C22×C3×D5#4111yescharacteristic
123C2×C3×AGL(1,𝔽5)—22no—
124C2×C3×AGL(1,𝔽5)—42no—
125C3×C5×D4—21no—
126C3×C5×D4C22×C412yes—
127C2×C3×C4×C5C22×C411yescharacteristic
128D60—21no—
129D60C22×C412yes—
130C2×C5×Dic3—21no—
131C5×Dic6—21no—
132C5×Dic6C22×C412yes—
133C3×C22⋊D5—22no—
134C3×C22⋊D5—22no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C2×D411yescharacteristic
139C3×C4×D5C22×C411yescharacteristic
140C3×C4×D5C2×D411yescharacteristic
141C3×C4×D5#4111yescharacteristic
142C3×C4×D5C2411yescharacteristic
143C3×Dic10—21no—
144C3×Dic10C22×C412yes—
145#1202—22no—
146#1202—22no—
147#1200—22no—
148#1200—22no—
149C3⋊#170—22no—
150C3⋊#170C2×D412yes—
151C3⋊#170C2×D412yes—
152C3×#170—22no—
153C3⋊#168C22×C412yes—
154C5×C3⋊C8C22×C412yes—
155C2×C3×#41—51no—
156C2×#235—51no—
157C2×C3×M16—51no—
158C2×C3×C42—51no—
159#950—54no—
160#950—54no—
161#948—54no—
162#948—102no—
163C2×#216—51no—
164C2×#215—51no—
165C2×#214AGL(1,𝔽5)11yescharacteristic, complemented
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×#104—54no—
177#822—54no—
178#805—54no—
179#803—54no—
180C22×AGL(1,𝔽5)—21no—
181C2×C5×Q8—31no—
182C2×C5×D4C4×D311yescharacteristic
183C2×C22⋊D5—21no—
184C22×Dic5—21no—
185#713—32no—
186#713—32no—
187#713—61no—
188#713—61no—
189#711—21no—
190#711—21no—
191#711C4×D312yes—
192#711C22×D312yes—
193C2×D20—31no—
194C2×D20—61no—
195C2×C4×D5—61no—
196C2×C4×D5C22×D311yescharacteristic
197C2×Dic10C4×D311yescharacteristic
198#704—64no—
199C2×#170—21no—
200C2×#170—31no—
201C2×#170—31no—
202C2×#170—64no—
203C2×#170—61no—
204C4×AGL(1,𝔽5)—21no—
205C4×AGL(1,𝔽5)C22×D312yes—
206#700—21no—
207#700—32no—
208#700—64no—
209#700—61no—
210#700C22×D312yes—
211D5⋊C8—32no—
212D5⋊C8—32no—
213D5⋊C8—64no—
214C5×SD16—34no—
215C2×C5×C8—31no—
216#689—34no—
217#686—34no—
218C2×#168—31no—
219#677—34no—
220C8×D5—32no—
221C8×D5—32no—
222C2×#135—151no—
223C2×#131—151no—
224C2×#131—151no—
225#444—158no—
226C2×#108—151no—
227C2×#104—51no—
228C2×#104—151no—
229C2×#97—151no—
230C22×C3×C5—22no—
231C22×C3×C5—42no—
232C22×C3×C5C4×D411yescharacteristic
233C2×D15—22no—
234C2×D15—42no—
235C2×C3×D5—22no—
236C2×C3×D5C4×D411yescharacteristic
237C2×C3×D5C2×#4111yescharacteristic
238C3×AGL(1,𝔽5)—42no—
239C3×C4×C5C4×D411yescharacteristic
240C3×C4×C5C23×C411yescharacteristic
241C3×Dic5—22no—
242C3×Dic5C4×D411yescharacteristic
243C3×Dic5C22×D411yescharacteristic
244C5×Dic3—22no—
245C3×#41—52no—
246C3×#41—52no—
247C3×#41—101no—
248C3×#41—101no—
249C2×C3×Q8—51no—
250C2×C3×D4—101no—
251C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
252C22×C3×C4—51no—
253C22×C3×C4—101no—
254C22×C3×C4—101no—
255C2×#67—101no—
256#235—52no—
257#235—52no—
258#235—101no—
259#235—101no—
260C2×D12—51no—
261C2×C4×D3—101no—
262C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
263C3×M16—52no—
264C3×M16—101no—
265C2×C3×C8—101no—
266C3×C42—52no—
267C3×C42—101no—
268#216—54no—
269#215—54no—
270#214C2×AGL(1,𝔽5)14yescomplemented
271#213—54no—
272#208—52no—
273#208—104no—
274#208—101no—
275C2×C3⋊C8—52no—
276C2×C3⋊C8—52no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—51no—
280C2×C3⋊C8—52no—
281C2×C3⋊C8—52no—
282C2×C3⋊C8—104no—
283C2×C3⋊C8—101no—
284C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
285ΓL(1,𝔽25)—104no—
286D3×C8—104no—
287C23×C5—21no—
288C22×D5—61no—
289C22×D5#23711yescharacteristic
290C2×AGL(1,𝔽5)—22no—
291C2×AGL(1,𝔽5)—42no—
292C5×Q8—32no—
293C5×Q8—61no—
294C5×D4—21no—
295C5×D4C2×C4×D312yes—
296C2×C4×C5—61no—
297C2×C4×C5C2×C4×D311yescharacteristic
298C22⋊D5—22no—
299C22⋊D5—22no—
300C2×Dic5—21no—
301C2×Dic5—22no—
302C2×Dic5—22no—
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#23711yescharacteristic
313C4×D5C23×D311yescharacteristic
314Dic10—21no—
315Dic10C2×C4×D312yes—
316#170—22no—
317#170—32no—
318#170—32no—
319#170—62no—
320C5×C8—32no—
321#168—32no—
322C2×#41—51no—
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—151no—
336C2×M16—301no—
337C2×M16—301no—
338C22×C8—151no—
339C22×C8—151no—
340C22×C8—301no—
341C22×C8—301no—
342C2×C42—51no—
343#108—154no—
344#104—54no—
345#104—154no—
346#97—154no—
347C2×C3×C5—42no—
348C2×C3×C5#44412yescomplemented
349C2×C3×C5C2×C4×D411yescharacteristic
350D15—42no—
351C3×D5—21no—
352C3×D5—21no—
353C23×C3—21no—
354C23×C3—51no—
355C22×D3—101no—
356C3×Q8—52no—
357C3×Q8—101no—
358C3×D4—21no—
359C3×D4—102no—
360C3×D4—102no—
361C3×D4C22×AGL(1,𝔽5)12yes—
362C2×C3×C4—51no—
363C2×C3×C4—51no—
364C2×C3×C4—51no—
365C2×C3×C4—51no—
366C2×C3×C4—51no—
367C2×C3×C4—102no—
368C2×C3×C4—102no—
369C2×C3×C4—101no—
370C2×C3×C4—102no—
371C2×C3×C4—202no—
372C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
373#67—102no—
374#67—102no—
375C2×Dic3—21no—
376D12—52no—
377D12—101no—
378C4×D3—102no—
379C4×D3—102no—
380Dic6—21no—
381Dic6C22×AGL(1,𝔽5)12yes—
382C3×C8—102no—
383C3⋊C8—52no—
384C3⋊C8—52no—
385C3⋊C8—52no—
386C3⋊C8—102no—
387C3⋊C8C22×AGL(1,𝔽5)12yes—
388C22×C5—22no—
389C22×C5—42no—
390C22×C5#67⋊C411yescharacteristic
391C2×D5—22no—
392C2×D5—62no—
393C2×D5—122no—
394C2×D5#67⋊C411yescharacteristic
395C2×D5C2×#23711yescharacteristic
396AGL(1,𝔽5)—42no—
397C4×C5—62no—
398C4×C5#67⋊C411yescharacteristic
399C4×C5C22×C4×D311yescharacteristic
400Dic5—22no—
401Dic5#67⋊C411yescharacteristic
402Dic5C2×D3×D411yescharacteristic
403#41—52no—
404#41—52no—
405#41—101no—
406#41—101no—
407#41—152no—
408#41—152no—
409#41—301no—
410#41—301no—
411C2×Q8—31no—
412C2×Q8—51no—
413C2×D4—101no—
414C2×D4—151no—
415C2×D4—301no—
416C2×D4D3×AGL(1,𝔽5)11yescharacteristic
417C22×C4—51no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—301no—
421Q16—154no—
422SD16—34no—
423SD16—154no—
424D8—154no—
425M16—52no—
426M16—101no—
427M16—152no—
428M16—304no—
429M16—304no—
430M16—301no—
431C2×C8—31no—
432C2×C8—101no—
433C2×C8—152no—
434C2×C8—152no—
435C2×C8—152no—
436C2×C8—151no—
437C2×C8—151no—
438C2×C8—152no—
439C2×C8—151no—
440C2×C8—304no—
441C2×C8—304no—
442C2×C8—301no—
443C42—52no—
444C42—101no—
445C3×C5C2×#44411yescharacteristic, complemented, Hall
446C22×C3—22no—
447C22×C3—42no—
448C22×C3—51no—
449C22×C3—51no—
450C22×C3—102no—
451C22×C3D4×AGL(1,𝔽5)11yescharacteristic
452C2×D3—102no—
453C2×D3—202no—
454C3×C4—51no—
455C3×C4—51no—
456C3×C4—102no—
457C3×C4—202no—
458C3×C4D4×AGL(1,𝔽5)11yescharacteristic
459C3×C4C23×AGL(1,𝔽5)11yescharacteristic
460Dic3—22no—
461C2×C5—42no—
462C2×C5#482312yescomplemented
463C2×C5C2×#67⋊C411yescharacteristic
464D5—21no—
465D5—21no—
466D5—122no—
467C23—21no—
468C23—51no—
469C23—301no—
470Q8—32no—
471Q8—52no—
472Q8—61no—
473Q8—101no—
474D4—21no—
475D4—102no—
476D4—102no—
477D4—152no—
478D4—302no—
479D4—302no—
480D4—301no—
481D4C2×D3×AGL(1,𝔽5)12yes—
482C2×C4—51no—
483C2×C4—51no—
484C2×C4—51no—
485C2×C4—51no—
486C2×C4—51no—
487C2×C4—61no—
488C2×C4—102no—
489C2×C4—102no—
490C2×C4—101no—
491C2×C4—102no—
492C2×C4—202no—
493C2×C4—302no—
494C2×C4—302no—
495C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
496C8—32no—
497C8—102no—
498C8—152no—
499C8—152no—
500C8—152no—
501C8—302no—
502C2×C3—42no—
503C2×C3—101no—
504C2×C3—101no—
505C2×C3#6573712yescomplemented
506C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
507D3—202no—
508C5C2×#482311yescharacteristic, complemented, Sylow
509C22—22no—
510C22—42no—
511C22—51no—
512C22—51no—
513C22—102no—
514C22—302no—
515C22—602no—
516C22#67⋊AGL(1,𝔽5)11yescharacteristic
517C4—51no—
518C4—51no—
519C4—62no—
520C4—102no—
521C4—202no—
522C4#67⋊AGL(1,𝔽5)11yescharacteristic
523C4C22×D3×AGL(1,𝔽5)11yescharacteristic
524C3C2×#6573711yescharacteristic, complemented, Sylow
525C2—42no—
526C2—101no—
527C2—101no—
528C2—602no—
529C2#1175195812yesdirect product factor
530C2C2×#67⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22#67⋊AGL(1,𝔽5)
commutatorC3×C4×C5C23×C4
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C4×D4
prime radicalC2×#91492C2
cosocleC3×C4×D5C24
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#91990C2semidirect
2. C2×#91916C2semidirect
4. C2×C3×#4008C2semidirect
5. #11751958C2direct (N × H)
6. C2×#91162C2semidirect
7. C2×#91158C2semidirect
8. C2×#91149C2semidirect
15. #91990C22semidirect
23. #91916C22semidirect
24. C2×#6715C4semidirect
25. C2×C5×#214C4semidirect
26. #91492C4semidirect
28. C2×#6661C4semidirect
29. C2×#6658C4semidirect
31. C3×#4008C22semidirect
32. #91162C22semidirect
33. #91158C22semidirect
34. #91149C22semidirect
40. C2×#4008D3semidirect
78. #6715C2×C4semidirect
80. C5×#214C2×C4semidirect
82. #6661C2×C4semidirect
83. #6658C2×C4semidirect
116. #4008C2×D3semidirect
165. C2×#214AGL(1,𝔽5)semidirect
270. #214C2×AGL(1,𝔽5)semidirect
348. C2×C3×C5#444semidirect
445. C3×C5C2×#444semidirect
462. C2×C5#4823semidirect
505. C2×C3#65737semidirect
508. C5C2×#4823semidirect
524. C3C2×#65737semidirect
529. C2#11751958direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919902
C2×#919162
C2×#914922
C2×C3×#40082
#117519582
C2×#911622
C2×#911582
C2×#911492
C2×#657373
C2×#48235