Finite Group Databasebeta

← C2×#11747207 #14431568

Subgroups — C2×#11747207 #14431568

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4041C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic, complemented
3C2×#91091C211yesmaximal, characteristic, complemented
4C2×C5×#808C211yesmaximal, characteristic, complemented
5C2×#90965C211yesmaximal, characteristic, complemented
6C2×#90964C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747207C218yesmaximal, direct product factor
9C2×#65155—31nomaximal, Hall
10C22×C3×D20—21no—
11C22×C3×D20C2211yescharacteristic
12C22×C3×C4×D5C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C22×C5×C3⋊C8C2211yescharacteristic
18C2×C3×#685—21no—
19C3×#4041—22no—
20C3×#4041C2214yes—
21C2×#6665—21no—
22C2×Dic3×Dic5—21no—
23#91358—22no—
24#91358C2214yescomplemented
25#91091C2214yescomplemented
26C5×#808C2214yescomplemented
27#90965C2214yescomplemented
28#90964C2214yescomplemented
29#90955C2214yescomplemented
30C2×#5035—51nomaximal, Hall
31C2×#4041D311yescharacteristic
32C2×#4038—31no—
33C2×C5×#106—31no—
34C2×#3953—31no—
35C2×#3952—31no—
36C2×#3941—31no—
37C2×#3939—31no—
38#65155—38no—
39C23×C3×D5—21no—
40C23×C3×D5D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×C5×Dic3—21no—
45C22×C3×Dic5D411yescharacteristic
46C2×C3×D20—22no—
47C2×C3×D20—22no—
48C2×C3×D20—24no—
49C2×C3×D20—21no—
50C2×C3×D20—44no—
51C2×C3×D20C2312yes—
52C2×C3×C4×D5—22no—
53C2×C3×C4×D5—22no—
54C2×C3×C4×D5D412yes—
55C2×C3×C4×D5C2312yes—
56C3×C5×C4⋊C4—21no—
57C3×C5×C4⋊C4C2312yes—
58C4⋊Dic15—21no—
59C4⋊Dic15C2312yes—
60C2×C3⋊#168—22no—
61C2×C3⋊#168C2312yes—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3C2312yes—
64C2×C5×C3⋊C8—22no—
65C2×C5×C3⋊C8C2312yes—
66C3×#685—24no—
67#6665—24no—
68Dic3×Dic5—24no—
69C2×C3×#121—51no—
70C2×#926—51no—
71C2×#832—51no—
72C2×#832—51no—
73C2×#830—51no—
74#5035—58no—
75C2×#808D511yescharacteristic, complemented
76C2×#807—51no—
77C22×D20—21no—
78C22×D20C2×D311yescharacteristic
79C22×C4×D5C2×D311yescharacteristic
80C22×C5×C8—31no—
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4C2×D311yescharacteristic
83C2×#685—21no—
84C2×#685—61no—
85C2×C4⋊Dic5—31no—
86C2×C4×Dic5—61no—
87C22×#168—31no—
88#4041—22no—
89#4041C2×D314yes—
90#4038—34no—
91#4038—62no—
92C5×#106—34no—
93#3953—34no—
94#3952—34no—
95#3941—34no—
96#3939—34no—
97C2×#482—151noSylow
98C23×C3×C5C2×D411yescharacteristic
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5—22no—
102C22×C3×D5—22no—
103C22×C3×D5—42no—
104C22×C3×D5—42no—
105C22×C3×D5—42no—
106C22×C3×D5C2×D412yes—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—42no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5#4112yes—
111C2×C3×C4×C5#4112yes—
112C2×C3×C4×C5C2411yescharacteristic
113C2×Dic15—22no—
114C2×Dic15—42no—
115C2×C5×Dic3—22no—
116C2×C5×Dic3—42no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5C2×D412yes—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20—48no—
122C3×D20—42no—
123C3×C4×D5—24no—
124C3×C4×D5—22no—
125C3×C4×D5—22no—
126C3⋊#168—22no—
127C5×C3⋊C8—22no—
128C22×C3×D4—51no—
129C22×C3×D4—101no—
130C23×C3×C4—51no—
131C3×#121—54no—
132C3×#121—102no—
133C2×C3×C4⋊C4C2×D511yescharacteristic
134C2×C3×C22⋊C4—101no—
135C2×#217—101no—
136#926—54no—
137#926—102no—
138C2×C4⋊Dic3—51no—
139C2×C4⋊Dic3C2×D511yescharacteristic
140C2×C4×Dic3—101no—
141C22×C3⋊C8—51no—
142C22×C3⋊C8C2×D511yescharacteristic
143#832—54no—
144#832—54no—
145#830—54no—
146#808C2×D514yescomplemented
147#807—54no—
148C23×D5—21no—
149C23×D5#6711yescharacteristic
150C22×C4×C5—21no—
151C22×C4×C5—61no—
152C22×C4×C5C22×D311yescharacteristic
153C22×Dic5—61no—
154C22×Dic5#6711yescharacteristic
155C2×D20—22no—
156C2×D20—22no—
157C2×D20—24no—
158C2×D20—21no—
159C2×D20—44no—
160C2×D20C22×D312yes—
161C2×C4×D5—22no—
162C2×C4×D5—22no—
163C2×C4×D5#6712yes—
164C2×C4×D5C22×D312yes—
165C2×C5×C8—32no—
166C2×C5×C8—62no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—32no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4C22×D312yes—
171#685—24no—
172#685—64no—
173C4⋊Dic5—32no—
174C4⋊Dic5—61no—
175C4×Dic5—64no—
176C2×#168—32no—
177C2×#168—62no—
178C2×#121—51no—
179C2×#117—151no—
180#482—158no—
181C2×#107—151no—
182C2×#106—31no—
183C2×#102—151no—
184C2×#102—151no—
185C2×C22⋊C8—151no—
186C22×C3×C5#12312yes—
187C22×C3×C5#13512yes—
188C22×C3×C5AGL(1,ℤ/8)12yes—
189C22×C3×C5C22×D411yescharacteristic
190C2×C3×D5—22no—
191C2×C3×D5—22no—
192C2×C3×D5—22no—
193C2×C3×D5—44no—
194C2×C3×D5—42no—
195C2×C3×D5—42no—
196C2×C3×D5—42no—
197C2×C3×D5—84no—
198C3×C4×C5—42no—
199C3×C4×C5#12312yes—
200C3×C4×C5C2×#4111yescharacteristic
201C3×C4×C5C2×#4111yescharacteristic
202Dic15—42no—
203C3×Dic5—22no—
204C5×Dic3—42no—
205C24×C3—51no—
206C24×C3—101no—
207C2×C3×D4—52no—
208C2×C3×D4—104no—
209C2×C3×D4—102no—
210C2×C3×D4—101no—
211C2×C3×D4—102no—
212C2×C3×D4—204no—
213C22×C3×C4—21no—
214C22×C3×C4—51no—
215C22×C3×C4—52no—
216C22×C3×C4—52no—
217C22×C3×C4—102no—
218C22×C3×C4—102no—
219C22×C3×C4C22×D511yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—101no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4C22×D512yes—
224C3×C22⋊C4—104no—
225#217—104no—
226C4⋊Dic3—21no—
227C4⋊Dic3—52no—
228C4⋊Dic3—101no—
229C4⋊Dic3C22×D512yes—
230C4×Dic3—104no—
231C2×C3⋊C8—22no—
232C2×C3⋊C8—52no—
233C2×C3⋊C8—102no—
234C2×C3⋊C8C22×D512yes—
235C23×C5C2×#6711yescharacteristic
236C22×D5—22no—
237C22×D5—22no—
238C22×D5—22no—
239C22×D5—22no—
240C22×D5—42no—
241C22×D5—42no—
242C22×D5—42no—
243C22×D5C2×#6712yes—
244C2×C4×C5—22no—
245C2×C4×C5—42no—
246C2×C4×C5—62no—
247C2×C4×C5—122no—
248C2×C4×C5#23712yes—
249C2×C4×C5#23712yes—
250C2×C4×C5C2×#6711yescharacteristic
251C2×C4×C5C23×D311yescharacteristic
252C2×Dic5—22no—
253C2×Dic5—62no—
254C2×Dic5—122no—
255C2×Dic5C2×#6712yes—
256D20—22no—
257D20—22no—
258D20—48no—
259D20—42no—
260C4×D5—24no—
261C4×D5—22no—
262C4×D5—22no—
263C5×C8—62no—
264#168—62no—
265C22×D4—51no—
266C22×D4—101no—
267C23×C4—51no—
268C22×C8—31no—
269C22×C8—151no—
270#121—54no—
271#121—102no—
272#117—154no—
273#117—302no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—151no—
276C2×C4⋊C4D3×D511yescharacteristic
277C2×C22⋊C4—101no—
278C2×C22⋊C4—301no—
279C2×C42—301no—
280#107—154no—
281#106—34no—
282#102—154no—
283#102—154no—
284C22⋊C8—154no—
285C2×C3×C5#48214yescomplemented
286C2×C3×C5C2×#12311yescharacteristic
287C2×C3×C5C2×#13511yescharacteristic
288C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
289C3×D5—42no—
290C3×D5—82no—
291C23×C3—52no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—102no—
295C23×C3—102no—
296C23×C3—202no—
297C23×C3—202no—
298C23×C3—202no—
299C23×C3D4×D511yescharacteristic
300C3×D4—102no—
301C3×D4—102no—
302C3×D4—208no—
303C3×D4—202no—
304C2×C3×C4—22no—
305C2×C3×C4—42no—
306C2×C3×C4—52no—
307C2×C3×C4—102no—
308C2×C3×C4—102no—
309C2×C3×C4—102no—
310C2×C3×C4—104no—
311C2×C3×C4#70912yes—
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4#71312yes—
314C2×C3×C4C23×D511yescharacteristic
315C2×Dic3—22no—
316C2×Dic3—42no—
317C2×Dic3—102no—
318C2×Dic3—202no—
319C3⋊C8—22no—
320C3⋊C8—102no—
321C22×C5#93212yes—
322C22×C5#93512yes—
323C22×C5#95012yes—
324C22×C5C22×#6711yescharacteristic
325C2×D5—22no—
326C2×D5—22no—
327C2×D5—22no—
328C2×D5—44no—
329C2×D5—42no—
330C2×D5—42no—
331C2×D5—42no—
332C2×D5—84no—
333C4×C5—42no—
334C4×C5—122no—
335C4×C5#93512yes—
336C4×C5C2×#23711yescharacteristic
337C4×C5C2×#23711yescharacteristic
338Dic5—22no—
339Dic5—122no—
340C24—51no—
341C24—101no—
342C2×D4—52no—
343C2×D4—104no—
344C2×D4—102no—
345C2×D4—102no—
346C2×D4—101no—
347C2×D4—204no—
348C22×C4—21no—
349C22×C4—51no—
350C22×C4—52no—
351C22×C4—52no—
352C22×C4—61no—
353C22×C4—102no—
354C22×C4—102no—
355C22×C4—301no—
356C22×C4C2×D3×D511yescharacteristic
357C2×C8—32no—
358C2×C8—62no—
359C2×C8—152no—
360C2×C8—302no—
361C4⋊C4—21no—
362C4⋊C4—32no—
363C4⋊C4—61no—
364C4⋊C4—152no—
365C4⋊C4—301no—
366C4⋊C4C2×D3×D512yes—
367C22⋊C4—104no—
368C22⋊C4—304no—
369C42—304no—
370C3×C5C2×#48211yescharacteristic, complemented, Hall
371C22×C3—102no—
372C22×C3—102no—
373C22×C3—102no—
374C22×C3—204no—
375C22×C3—202no—
376C22×C3—202no—
377C22×C3—202no—
378C22×C3—404no—
379C22×C3#404012yes—
380C22×C3#406012yes—
381C22×C3#406212yes—
382C22×C3C2×D4×D511yescharacteristic
383C3×C4—42no—
384C3×C4—102no—
385C3×C4#404012yes—
386C3×C4C2×#70911yescharacteristic
387C3×C4C2×#71311yescharacteristic
388Dic3—42no—
389Dic3—202no—
390C2×C5#503514yescomplemented
391C2×C5C2×#93211yescharacteristic
392C2×C5C2×#93511yescharacteristic
393C2×C5C2×#95011yescharacteristic
394D5—42no—
395D5—82no—
396C23—52no—
397C23—102no—
398C23—102no—
399C23—102no—
400C23—102no—
401C23—202no—
402C23—202no—
403C23—202no—
404C23D5×#6711yescharacteristic
405D4—102no—
406D4—102no—
407D4—208no—
408D4—202no—
409C2×C4—22no—
410C2×C4—42no—
411C2×C4—52no—
412C2×C4—62no—
413C2×C4—102no—
414C2×C4—104no—
415C2×C4—102no—
416C2×C4—102no—
417C2×C4—122no—
418C2×C4—302no—
419C2×C4—602no—
420C2×C4#676512yes—
421C2×C4#676612yes—
422C2×C4D5×#6711yescharacteristic
423C2×C4C22×D3×D511yescharacteristic
424C8—62no—
425C8—302no—
426C2×C3—202no—
427C2×C3—402no—
428C2×C3#6515514yescomplemented
429C2×C3C2×#404011yescharacteristic
430C2×C3C2×#406011yescharacteristic
431C2×C3C2×#406211yescharacteristic
432C5C2×#503511yescharacteristic, complemented, Sylow
433C22—102no—
434C22—102no—
435C22—102no—
436C22—204no—
437C22—202no—
438C22—202no—
439C22—202no—
440C22—404no—
441C22#9140712yes—
442C22#9149112yes—
443C22#9151412yes—
444C22C2×D5×#6711yescharacteristic
445C4—42no—
446C4—102no—
447C4—122no—
448C4—602no—
449C4#9140712yes—
450C4C2×#676511yescharacteristic
451C4C2×#676611yescharacteristic
452C3C2×#6515511yescharacteristic, complemented, Sylow
453C2—202no—
454C2—402no—
455C2#1174720714yesdirect product factor
456C2C2×#9140711yescharacteristic
457C2C2×#9149111yescharacteristic
458C2C2×#9151411yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4041C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91358C2semidirect
3. C2×#91091C2semidirect
4. C2×C5×#808C2semidirect
5. C2×#90965C2semidirect
6. C2×#90964C2semidirect
7. C2×#90955C2semidirect
8. #11747207C2direct (N × H)
24. #91358C22semidirect
25. #91091C22semidirect
26. C5×#808C22semidirect
27. #90965C22semidirect
28. #90964C22semidirect
29. #90955C22semidirect
75. C2×#808D5semidirect
146. #808C2×D5semidirect
285. C2×C3×C5#482semidirect
370. C3×C5C2×#482semidirect
390. C2×C5#5035semidirect
428. C2×C3#65155semidirect
432. C5C2×#5035semidirect
452. C3C2×#65155semidirect
455. C2#11747207direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40412
C2×#913582
C2×#910912
C2×C5×#8082
C2×#909652
C2×#909642
C2×#909552
#117472072
C2×#651553
C2×#50355