Finite Group Databasebeta

← #14411850

Subgroups — #14411850

Order 1920.

1548 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×#41C211yesmaximal, characteristic
2C2×#91837C211yesmaximal, characteristic, complemented
3C2×C3×#4094C211yesmaximal, characteristic, complemented
4#11748347C213yesmaximal, complemented
5#11748346C213yesmaximal, complemented
6#11748345C213yesmaximal, complemented
7C2×(C2×D3)⋊#168C213yesmaximal, complemented
8#10615806—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×D3×#41—24no—
11C5×D3×#41—24no—
12C2×C5×#239C411yescharacteristic
13C2×C5×D3×Q8C411yescharacteristic
14C2×C5×#237C413yes—
15C2×C5×D3×D4C413yes—
16C2×C5×#235C2213yes—
17C22×C4×C5×D3C2213yes—
18#91837—24no—
19C2×#6710C2213yescomplemented
20C22×C3⋊#168C2213yescomplemented
21C3×#4094—24no—
22C2×C3×#681C2213yescomplemented
23C22×C3×#168C2213yescomplemented
24(C2×D3)⋊#168C2211yescharacteristic
25(C2×D3)⋊#168C2213yes—
26(C2×D3)⋊#168C2213yescomplemented
27(C2×D3)⋊#168C2213yescomplemented
28(C2×D3)⋊#168C2216yescomplemented
29#83793—51nomaximal, Hall
30C22×C5×#41—31no—
31C2×#4094—31no—
32C2×#4094D311yescharacteristic, complemented
33#65523—33no—
34#65523—33no—
35#65496—33no—
36C2×C22⋊#168—33no—
37C23×C5×D3C2×C413yes—
38C3×C5×#41D414yes—
39C3×C5×#41D414yes—
40C2×C3×C5×Q8C2×C411yescharacteristic
41C2×C3×C5×D4C2×C413yes—
42C22×C3×C4×C5C2313yes—
43C2×C5×#67C2×C416yes—
44C22×C5×Dic3C2×C413yes—
45C5×#239—24no—
46C5×D3×Q8—24no—
47C5×#237—212no—
48C5×D3×D4—212no—
49C5×#235—26no—
50C5×#235—26no—
51C2×C5×D12C2×C413yes—
52C2×C4×C5×D3—26no—
53C2×C4×C5×D3—26no—
54C2×C4×C5×D3C2×C413yes—
55C2×C4×C5×D3C2×C413yes—
56C2×C4×C5×D3C2311yescharacteristic
57C2×C4×C5×D3C2313yes—
58C2×C5×Dic6C2×C413yes—
59#6710—26no—
60C2×C3⋊#168—26no—
61C2×C3⋊#168C2311yescharacteristic
62C2×C3⋊#168C2313yes—
63C3×#681—26no—
64C2×C3×#168—26no—
65C2×C3×#168C2311yescharacteristic
66C2×C3×#168C2313yes—
67C2×D3×#41D511yescharacteristic
68C2×C3×#131—51no—
69C2×#948—51no—
70#5129—53no—
71#5126—53no—
72#5110—53no—
73C2×(C2×D3)⋊C8—53no—
74C2×C5×#41—31no—
75C2×C5×#41—33no—
76C2×C5×#41—33no—
77C2×C5×#41—64no—
78C2×C5×#41—64no—
79C2×C5×#41C2×D311yescharacteristic
80C22×C5×Q8—31no—
81C22×C5×D4—33no—
82C23×C4×C5—33no—
83#4094—24no—
84#4094—64no—
85C2×#681—33no—
86C2×#681C2×D313yescomplemented
87C22×#168—33no—
88C22×#168C2×D313yescomplemented
89C22⋊#168—31no—
90C22⋊#168—33no—
91C22⋊#168—33no—
92C22⋊#168—33no—
93C22⋊#168—36no—
94#2880—151noSylow
95C23×C3×C5C22×C413yes—
96C22×C5×D3—26no—
97C22×C5×D3—26no—
98C22×C5×D3—43no—
99C22×C5×D3C22×C413yes—
100C22×C5×D3C22×C411yescharacteristic
101C3×C5×Q8C22⋊C414yes—
102C3×C5×D4C22⋊C4112yes—
103C2×C3×C4×C5C22×C413yes—
104C2×C3×C4×C5C2×D416yes—
105C2×C3×C4×C5C2×D416yes—
106C2×C3×C4×C5C2411yescharacteristic
107C5×#67—212no—
108C2×C5×Dic3—26no—
109C2×C5×Dic3C22×C413yes—
110C2×C5×Dic3C22×C411yescharacteristic
111C5×D12—26no—
112C4×C5×D3—26no—
113C4×C5×D3—26no—
114C4×C5×D3—21no—
115C4×C5×D3—21no—
116C4×C5×D3—23no—
117C4×C5×D3—23no—
118C5×Dic6—26no—
119C3⋊#168—21no—
120C3⋊#168—23no—
121C3×#168—21no—
122C3×#168—23no—
123C2×C3×#41C2×D511yescharacteristic
124D3×#41—24no—
125D3×#41—24no—
126C2×#239Dic511yescharacteristic
127C2×D3×Q8Dic511yescharacteristic
128C2×#237Dic513yes—
129C2×D3×D4Dic513yes—
130C2×#235C2×D513yes—
131C22×C4×D3C2×D513yes—
132C3×#131—104no—
133C2×C3×M16—53no—
134C22×C3×C8—53no—
135#948—104no—
136C2×#208—53no—
137C22×C3⋊C8—53no—
138(C2×D3)⋊C8—53no—
139(C2×D3)⋊C8—56no—
140(C2×D3)⋊C8—53no—
141(C2×D3)⋊C8—51no—
142(C2×D3)⋊C8—53no—
143C24×C5—33no—
144C5×#41—64no—
145C5×#41—612no—
146C5×#41—66no—
147C5×#41—66no—
148C5×#41D1214yes—
149C5×#41#6714yes—
150C2×C5×Q8—33no—
151C2×C5×Q8—64no—
152C2×C5×Q8C4×D311yescharacteristic
153C2×C5×D4—36no—
154C2×C5×D4—33no—
155C2×C5×D4—612no—
156C2×C5×D4C4×D313yes—
157C22×C4×C5—33no—
158C22×C4×C5—33no—
159C22×C4×C5—33no—
160C22×C4×C5—31no—
161C22×C4×C5—33no—
162C22×C4×C5—66no—
163C22×C4×C5—66no—
164C22×C4×C5C22×D313yes—
165#681—26no—
166#681—66no—
167C2×#168—26no—
168C2×#168—31no—
169C2×#168—33no—
170C2×#168—66no—
171C2×#168C22×D311yescharacteristic
172C2×#168C22×D313yes—
173C22×#41—31no—
174C2×#131—51no—
175C2×#131—151no—
176#408—153no—
177#408—153no—
178#407—153no—
179C2×C22⋊C8—153no—
180C22×C3×C5—23no—
181C22×C3×C5—23no—
182C22×C3×C5C2×C22⋊C416yes—
183C22×C3×C5C23×C411yescharacteristic
184C2×C5×D3—21no—
185C2×C5×D3—21no—
186C2×C5×D3—23no—
187C2×C5×D3—23no—
188C2×C5×D3—23no—
189C2×C5×D3—412no—
190C2×C5×D3#13112yescomplemented
191C3×C4×C5C2×C22⋊C416yes—
192C3×C4×C5C22×D411yescharacteristic
193C3×C4×C5C22×D411yescharacteristic
194C5×Dic3—23no—
195C5×Dic3—21no—
196C23×D3C2×Dic513yes—
197C3×#41C22⋊D514yes—
198C3×#41C22⋊D514yes—
199C2×C3×Q8C2×Dic511yescharacteristic
200C2×C3×D4C2×Dic513yes—
201C22×C3×C4C22×D513yes—
202C2×#67C2×Dic516yes—
203C22×Dic3C2×Dic513yes—
204#239—24no—
205D3×Q8—24no—
206#237—212no—
207D3×D4—212no—
208#235—26no—
209#235—26no—
210C2×D12C2×Dic513yes—
211C2×C4×D3—26no—
212C2×C4×D3—26no—
213C2×C4×D3C2×Dic513yes—
214C2×C4×D3C2×Dic513yes—
215C2×C4×D3C22×D511yescharacteristic
216C2×C4×D3C22×D513yes—
217C2×Dic6C2×Dic513yes—
218C3×M16—106no—
219C2×C3×C8—51no—
220C2×C3×C8—53no—
221C2×C3×C8—106no—
222#208—106no—
223C2×C3⋊C8—51no—
224C2×C3⋊C8—53no—
225C2×C3⋊C8—106no—
226C23×C5—31no—
227C23×C5—33no—
228C23×C5—66no—
229C23×C5—66no—
230C23×C5—123no—
231C23×C5C2×C4×D313yes—
232C5×Q8—66no—
233C5×Q8(C2×D3)⋊C414yes—
234C5×D4—612no—
235C5×D4—66no—
236C5×D4(C2×D3)⋊C4112yes—
237C2×C4×C5—31no—
238C2×C4×C5—33no—
239C2×C4×C5—66no—
240C2×C4×C5—66no—
241C2×C4×C5—66no—
242C2×C4×C5—61no—
243C2×C4×C5—63no—
244C2×C4×C5—61no—
245C2×C4×C5—63no—
246C2×C4×C5C2×C4×D313yes—
247C2×C4×C5C2×D1216yes—
248C2×C4×C5C2×#6716yes—
249C2×C4×C5C23×D311yescharacteristic
250#168—21no—
251#168—23no—
252#168—61no—
253#168—63no—
254C2×#41—31no—
255C2×#41—33no—
256C2×#41—33no—
257C2×#41—64no—
258C2×#41—64no—
259C2×#41D3×D511yescharacteristic
260C22×Q8—31no—
261C22×D4—33no—
262C23×C4—33no—
263#131—104no—
264#131—304no—
265C2×M16—53no—
266C2×M16—153no—
267C22×C8—53no—
268C22×C8—153no—
269C22⋊C8—151no—
270C22⋊C8—153no—
271C22⋊C8—153no—
272C22⋊C8—153no—
273C22⋊C8—156no—
274C2×C3×C5—26no—
275C2×C3×C5C22×C22⋊C411yescharacteristic
276C2×C3×C5C2×#13111yescharacteristic
277C2×C3×C5#56811yescharacteristic
278C5×D3—22no—
279C5×D3—43no—
280C23×C3C22×Dic513yes—
281C22×D3—26no—
282C22×D3—26no—
283C22×D3—43no—
284C22×D3C22×Dic513yes—
285C22×D3C22×Dic511yescharacteristic
286C3×Q8C22⋊Dic514yes—
287C3×D4C22⋊Dic5112yes—
288C2×C3×C4C22×Dic513yes—
289C2×C3×C4C2×C22⋊D516yes—
290C2×C3×C4C2×C22⋊D516yes—
291C2×C3×C4C23×D511yescharacteristic
292#67—212no—
293C2×Dic3—26no—
294C2×Dic3C22×Dic513yes—
295C2×Dic3C22×Dic511yescharacteristic
296D12—26no—
297C4×D3—26no—
298C4×D3—26no—
299C4×D3—21no—
300C4×D3—21no—
301C4×D3—23no—
302C4×D3—23no—
303Dic6—26no—
304C3×C8—101no—
305C3×C8—103no—
306C3⋊C8—101no—
307C3⋊C8—103no—
308C22×C5—23no—
309C22×C5—23no—
310C22×C5—32no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5—63no—
314C22×C5—63no—
315C22×C5—63no—
316C22×C5—1212no—
317C22×C5C2×(C2×D3)⋊C416yes—
318C22×C5C22×C4×D311yescharacteristic
319C4×C5—61no—
320C4×C5—63no—
321C4×C5C2×(C2×D3)⋊C416yes—
322C4×C5C22×D1211yescharacteristic
323C4×C5C22×#6711yescharacteristic
324C24—33no—
325#41—64no—
326#41—612no—
327#41—66no—
328#41—66no—
329#41#120114yes—
330#41#120314yes—
331C2×Q8—33no—
332C2×Q8—64no—
333C2×Q8D3×Dic511yescharacteristic
334C2×D4—36no—
335C2×D4—33no—
336C2×D4—612no—
337C2×D4D3×Dic513yes—
338C22×C4—33no—
339C22×C4—33no—
340C22×C4—33no—
341C22×C4—31no—
342C22×C4—33no—
343C22×C4—66no—
344C22×C4—66no—
345C22×C4C2×D3×D513yes—
346M16—106no—
347M16—306no—
348C2×C8—51no—
349C2×C8—53no—
350C2×C8—106no—
351C2×C8—151no—
352C2×C8—153no—
353C2×C8—306no—
354C3×C5#288011yescharacteristic, complemented, Hall
355C22×C3—23no—
356C22×C3—23no—
357C22×C3C2×C22⋊Dic516yes—
358C22×C3C23×Dic511yescharacteristic
359C2×D3—21no—
360C2×D3—21no—
361C2×D3—23no—
362C2×D3—23no—
363C2×D3—23no—
364C2×D3—412no—
365C2×D3#409412yescomplemented
366C3×C4C2×C22⋊Dic516yes—
367C3×C4C22×C22⋊D511yescharacteristic
368C3×C4C22×C22⋊D511yescharacteristic
369Dic3—23no—
370Dic3—21no—
371C2×C5—26no—
372C2×C5—62no—
373C2×C5—123no—
374C2×C5D3×#13111yescharacteristic
375C2×C5#575011yescharacteristic
376C2×C5C22×(C2×D3)⋊C411yescharacteristic
377C23—31no—
378C23—33no—
379C23—66no—
380C23—66no—
381C23—123no—
382C23C2×D3×Dic513yes—
383Q8—66no—
384Q8(C2×D3)⋊Dic514yes—
385D4—612no—
386D4—66no—
387D4(C2×D3)⋊Dic5112yes—
388C2×C4—31no—
389C2×C4—33no—
390C2×C4—66no—
391C2×C4—61no—
392C2×C4—63no—
393C2×C4—61no—
394C2×C4—63no—
395C2×C4—66no—
396C2×C4—66no—
397C2×C4C2×D3×Dic513yes—
398C2×C4C2×#120116yes—
399C2×C4C2×#120316yes—
400C2×C4C22×D3×D511yescharacteristic
401C8—101no—
402C8—103no—
403C8—301no—
404C8—303no—
405C2×C3—26no—
406C2×C3C2×#409411yescharacteristic
407C2×C3#6615311yescharacteristic
408C2×C3C22×C22⋊Dic511yescharacteristic
409D3—22no—
410D3—43no—
411C5#8379311yescharacteristic, complemented, Sylow
412C22—23no—
413C22—23no—
414C22—32no—
415C22—61no—
416C22—61no—
417C22—63no—
418C22—63no—
419C22—63no—
420C22—1212no—
421C22C2×(C2×D3)⋊Dic516yes—
422C22C22×D3×Dic511yescharacteristic
423C4—61no—
424C4—63no—
425C4C2×(C2×D3)⋊Dic516yes—
426C4C22×#120111yescharacteristic
427C4C22×#120311yescharacteristic
428C3#1061580611yescharacteristic, complemented, Sylow
429C2—26no—
430C2—62no—
431C2—123no—
432C2D3×#409411yescharacteristic
433C2#1175529811yescharacteristic
434C2C22×(C2×D3)⋊Dic511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D3×D5
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×#41C22
prime radicalC2×C5×D3×#41C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2880
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91837C2semidirect
3. C2×C3×#4094C2semidirect
4. #11748347C2semidirect
5. #11748346C2semidirect
6. #11748345C2semidirect
7. C2×(C2×D3)⋊#168C2semidirect
19. C2×#6710C22semidirect
20. C22×C3⋊#168C22semidirect
22. C2×C3×#681C22semidirect
23. C22×C3×#168C22semidirect
26. (C2×D3)⋊#168C22semidirect
27. (C2×D3)⋊#168C22semidirect
28. (C2×D3)⋊#168C22semidirect
32. C2×#4094D3semidirect
86. C2×#681C2×D3semidirect
88. C22×#168C2×D3semidirect
190. C2×C5×D3#131semidirect
354. C3×C5#2880semidirect
365. C2×D3#4094semidirect
411. C5#83793semidirect
428. C3#10615806semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×#412
C2×#918372
C2×C3×#40942
#117483472
#117483462
#117483452
C2×(C2×D3)⋊#1682
#106158063
#837935