Finite Group Databasebeta

← C5×#83793 #14411803

Subgroups — C5×#83793 #14411803

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×C3×C5×#131C211yesmaximal, characteristic, complemented
3C2×C5×#948C211yesmaximal, characteristic, complemented
4C5×#5129C213yesmaximal, complemented
5C5×#5126C213yesmaximal, complemented
6C5×#5110C213yesmaximal, complemented
7C2×C5×(C2×D3)⋊C8C213yesmaximal, complemented
8C5×#2880—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—
18C3×C5×#131—24no—
19C2×C3×C5×M16C2213yescomplemented
20C22×C3×C5×C8C2213yescomplemented
21C5×#948—24no—
22C2×C5×#208C2213yescomplemented
23C22×C5×C3⋊C8C2213yescomplemented
24C5×(C2×D3)⋊C8C2211yescharacteristic
25C5×(C2×D3)⋊C8C2213yes—
26C5×(C2×D3)⋊C8C2213yescomplemented
27C5×(C2×D3)⋊C8C2213yescomplemented
28C5×(C2×D3)⋊C8C2216yescomplemented
29#83793C511yesmaximal, characteristic, direct product factor, Hall
30C22×C5×#41—31no—
31C2×C5×#131—31no—
32C2×C5×#131D311yescharacteristic, complemented
33C5×#408—33no—
34C5×#408—33no—
35C5×#407—33no—
36C2×C5×C22⋊C8—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—
59C3×C5×M16—26no—
60C2×C3×C5×C8—26no—
61C2×C3×C5×C8C2311yescharacteristic
62C2×C3×C5×C8C2313yes—
63C5×#208—26no—
64C2×C5×C3⋊C8—26no—
65C2×C5×C3⋊C8C2311yescharacteristic
66C2×C5×C3⋊C8C2313yes—
67C2×D3×#41C2×C511yescharacteristic
68C2×C3×#131C2×C511yescharacteristic, complemented
69C2×#948C2×C511yescharacteristic, complemented
70#5129C2×C513yescomplemented
71#5126C2×C513yescomplemented
72#5110C2×C513yescomplemented
73C2×(C2×D3)⋊C8C2×C513yescomplemented
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—
83C5×#131—24no—
84C5×#131—64no—
85C2×C5×M16—33no—
86C2×C5×M16C2×D313yescomplemented
87C22×C5×C8—33no—
88C22×C5×C8C2×D313yescomplemented
89C5×C22⋊C8—31no—
90C5×C22⋊C8—33no—
91C5×C22⋊C8—33no—
92C5×C22⋊C8—33no—
93C5×C22⋊C8—36no—
94#2880—31noSylow
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×C5×C8—21no—
120C3×C5×C8—23no—
121C5×C3⋊C8—21no—
122C5×C3⋊C8—23no—
123C2×C3×#41C22×C511yescharacteristic
124D3×#41—24no—
125D3×#41—24no—
126C2×#239C4×C511yescharacteristic
127C2×D3×Q8C4×C511yescharacteristic
128C2×#237C4×C513yes—
129C2×D3×D4C4×C513yes—
130C2×#235C22×C513yes—
131C22×C4×D3C22×C513yes—
132C3×#131—24no—
133C2×C3×M16C22×C513yescomplemented
134C22×C3×C8C22×C513yescomplemented
135#948—24no—
136C2×#208C22×C513yescomplemented
137C22×C3⋊C8C22×C513yescomplemented
138(C2×D3)⋊C8C22×C513yes—
139(C2×D3)⋊C8C22×C511yescharacteristic
140(C2×D3)⋊C8C22×C516yescomplemented
141(C2×D3)⋊C8C22×C513yescomplemented
142(C2×D3)⋊C8C22×C513yescomplemented
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—
165C5×M16—26no—
166C5×M16—66no—
167C2×C5×C8—26no—
168C2×C5×C8—31no—
169C2×C5×C8—33no—
170C2×C5×C8—66no—
171C2×C5×C8C22×D311yescharacteristic
172C2×C5×C8C22×D313yes—
173C22×#41—31no—
174C2×#131—31no—
175C2×#131C5×D311yescharacteristic, complemented
176#408—33no—
177#408—33no—
178#407—33no—
179C2×C22⋊C8—33no—
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×C4×C513yes—
197C3×#41C5×D414yes—
198C3×#41C5×D414yes—
199C2×C3×Q8C2×C4×C511yescharacteristic
200C2×C3×D4C2×C4×C513yes—
201C22×C3×C4C23×C513yes—
202C2×#67C2×C4×C516yes—
203C22×Dic3C2×C4×C513yes—
204#239—24no—
205D3×Q8—24no—
206#237—212no—
207D3×D4—212no—
208#235—26no—
209#235—26no—
210C2×D12C2×C4×C513yes—
211C2×C4×D3—26no—
212C2×C4×D3—26no—
213C2×C4×D3C2×C4×C513yes—
214C2×C4×D3C2×C4×C513yes—
215C2×C4×D3C23×C511yescharacteristic
216C2×C4×D3C23×C513yes—
217C2×Dic6C2×C4×C513yes—
218C3×M16—26no—
219C2×C3×C8—26no—
220C2×C3×C8C23×C511yescharacteristic
221C2×C3×C8C23×C513yes—
222#208—26no—
223C2×C3⋊C8—26no—
224C2×C3⋊C8C23×C511yescharacteristic
225C2×C3⋊C8C23×C513yes—
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
250C5×C8—21no—
251C5×C8—23no—
252C5×C8—61no—
253C5×C8—63no—
254C2×#41—31no—
255C2×#41—33no—
256C2×#41—33no—
257C2×#41—64no—
258C2×#41—64no—
259C2×#41C2×C5×D311yescharacteristic
260C22×Q8—31no—
261C22×D4—33no—
262C23×C4—33no—
263#131—24no—
264#131—64no—
265C2×M16—33no—
266C2×M16C2×C5×D313yescomplemented
267C22×C8—33no—
268C22×C8C2×C5×D313yescomplemented
269C22⋊C8—31no—
270C22⋊C8—33no—
271C22⋊C8—33no—
272C22⋊C8—33no—
273C22⋊C8—36no—
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×C4×C513yes—
281C22×D3—26no—
282C22×D3—26no—
283C22×D3—43no—
284C22×D3C22×C4×C513yes—
285C22×D3C22×C4×C511yescharacteristic
286C3×Q8C5×C22⋊C414yes—
287C3×D4C5×C22⋊C4112yes—
288C2×C3×C4C22×C4×C513yes—
289C2×C3×C4C2×C5×D416yes—
290C2×C3×C4C2×C5×D416yes—
291C2×C3×C4C24×C511yescharacteristic
292#67—212no—
293C2×Dic3—26no—
294C2×Dic3C22×C4×C513yes—
295C2×Dic3C22×C4×C511yescharacteristic
296D12—26no—
297C4×D3—26no—
298C4×D3—26no—
299C4×D3—21no—
300C4×D3—21no—
301C4×D3—23no—
302C4×D3—23no—
303Dic6—26no—
304C3×C8—21no—
305C3×C8—23no—
306C3⋊C8—21no—
307C3⋊C8—23no—
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#41C5×D1214yes—
330#41C5×#6714yes—
331C2×Q8—33no—
332C2×Q8—64no—
333C2×Q8C4×C5×D311yescharacteristic
334C2×D4—36no—
335C2×D4—33no—
336C2×D4—612no—
337C2×D4C4×C5×D313yes—
338C22×C4—33no—
339C22×C4—33no—
340C22×C4—33no—
341C22×C4—31no—
342C22×C4—33no—
343C22×C4—66no—
344C22×C4—66no—
345C22×C4C22×C5×D313yes—
346M16—26no—
347M16—66no—
348C2×C8—26no—
349C2×C8—31no—
350C2×C8—33no—
351C2×C8—66no—
352C2×C8C22×C5×D311yescharacteristic
353C2×C8C22×C5×D313yes—
354C3×C5#288011yescharacteristic, complemented, Hall
355C22×C3—23no—
356C22×C3—23no—
357C22×C3C2×C5×C22⋊C416yes—
358C22×C3C23×C4×C511yescharacteristic
359C2×D3—21no—
360C2×D3—21no—
361C2×D3—23no—
362C2×D3—23no—
363C2×D3—23no—
364C2×D3—412no—
365C2×D3C5×#13112yescomplemented
366C3×C4C2×C5×C22⋊C416yes—
367C3×C4C22×C5×D411yescharacteristic
368C3×C4C22×C5×D411yescharacteristic
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×C4×C5×D313yes—
383Q8—66no—
384Q8C5×(C2×D3)⋊C414yes—
385D4—612no—
386D4—66no—
387D4C5×(C2×D3)⋊C4112yes—
388C2×C4—31no—
389C2×C4—33no—
390C2×C4—66no—
391C2×C4—66no—
392C2×C4—66no—
393C2×C4—61no—
394C2×C4—63no—
395C2×C4—61no—
396C2×C4—63no—
397C2×C4C2×C4×C5×D313yes—
398C2×C4C2×C5×D1216yes—
399C2×C4C2×C5×#6716yes—
400C2×C4C23×C5×D311yescharacteristic
401C8—21no—
402C8—23no—
403C8—61no—
404C8—63no—
405C2×C3—26no—
406C2×C3C22×C5×C22⋊C411yescharacteristic
407C2×C3C2×C5×#13111yescharacteristic
408C2×C3C5×#56811yescharacteristic
409D3—22no—
410D3—43no—
411C5#8379311yescharacteristic, direct product factor, Sylow
412C22—23no—
413C22—23no—
414C22—32no—
415C22—61no—
416C22—61no—
417C22—63no—
418C22—63no—
419C22—63no—
420C22—1212no—
421C22C2×C5×(C2×D3)⋊C416yes—
422C22C22×C4×C5×D311yescharacteristic
423C4—61no—
424C4—63no—
425C4C2×C5×(C2×D3)⋊C416yes—
426C4C22×C5×D1211yescharacteristic
427C4C22×C5×#6711yescharacteristic
428C3C5×#288011yescharacteristic, complemented, Sylow
429C2—26no—
430C2—62no—
431C2—123no—
432C2C5×D3×#13111yescharacteristic
433C2C5×#575011yescharacteristic
434C2C22×C5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#131C2
socleC22×C3×C5C23×C4
prime radicalC2×C5×D3×#41C2
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#131D3
hypocenterC3C5×#2880
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×#131

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#131C2semidirect
3. C2×C5×#948C2semidirect
4. C5×#5129C2semidirect
5. C5×#5126C2semidirect
6. C5×#5110C2semidirect
7. C2×C5×(C2×D3)⋊C8C2semidirect
19. C2×C3×C5×M16C22semidirect
20. C22×C3×C5×C8C22semidirect
22. C2×C5×#208C22semidirect
23. C22×C5×C3⋊C8C22semidirect
26. C5×(C2×D3)⋊C8C22semidirect
27. C5×(C2×D3)⋊C8C22semidirect
28. C5×(C2×D3)⋊C8C22semidirect
29. #83793C5direct (N × H)
32. C2×C5×#131D3semidirect
68. C2×C3×#131C2×C5semidirect
69. C2×#948C2×C5semidirect
70. #5129C2×C5semidirect
71. #5126C2×C5semidirect
72. #5110C2×C5semidirect
73. C2×(C2×D3)⋊C8C2×C5semidirect
86. C2×C5×M16C2×D3semidirect
88. C22×C5×C8C2×D3semidirect
133. C2×C3×M16C22×C5semidirect
134. C22×C3×C8C22×C5semidirect
136. C2×#208C22×C5semidirect
137. C22×C3⋊C8C22×C5semidirect
140. (C2×D3)⋊C8C22×C5semidirect
141. (C2×D3)⋊C8C22×C5semidirect
142. (C2×D3)⋊C8C22×C5semidirect
175. C2×#131C5×D3semidirect
190. C2×C5×D3#131semidirect
266. C2×M16C2×C5×D3semidirect
268. C22×C8C2×C5×D3semidirect
354. C3×C5#2880semidirect
365. C2×D3C5×#131semidirect
411. C5#83793direct (N × H)
428. C3C5×#2880semidirect

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×C3×C5×#1312
C2×C5×#9482
C5×#51292
C5×#51262
C5×#51102
C2×C5×(C2×D3)⋊C82
C5×#28803
#837935