Finite Group Databasebeta

← #14438935

Subgroups — #14438935

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5477C211yesmaximal, characteristic, complemented
2C3×#65811C211yesmaximal, characteristic, complemented
3C2×#91297C214yesmaximal, complemented
4C2×C4×C3⋊#168C211yesmaximal, characteristic, complemented
5#11747103C211yesmaximal, characteristic, complemented
6#11747081C211yesmaximal, characteristic, complemented
7#11747079C211yesmaximal, characteristic, complemented
8#11747040C214yesmaximal, complemented
9#11747039C211yesmaximal, characteristic, complemented
10#10615016—31nomaximal, Hall
11C2×C5×#235C2212yes—
12C2×C3×#709C2212yes—
13C2×C3×C42×C5C2211yescharacteristic
14C22×C3⋊#168C2212yes—
15C5×#930—22no—
16C5×#875C2212yes—
17C5×#874C2211yescharacteristic
18C4×C5×D12—22no—
19C5×#869C2211yescharacteristic
20C3×#4076—22no—
21C3×#4021C2212yes—
22C3×#4020C2211yescharacteristic
23C3×C4×D20—22no—
24C3×#4015C2211yescharacteristic
25C2×#6661C2214yes—
26C2×#6656C2214yes—
27C2×#6655C2214yes—
28#91297—216no—
29C2×#6652C2214yes—
30C4×C3⋊#168C2211yescharacteristic
31C4×C3⋊#168C2211yescharacteristic
32C4×C3⋊#168C2212yes—
33#83285—51nomaximal, Hall
34C5×#532—31no—
35C2×#4096—34no—
36#65811D311yescharacteristic, complemented
37#65381—31no—
38#65374—31no—
39#65365—31no—
40#65362—31no—
41#65348—34no—
42C2×C4×#168—31no—
43C22×C3×C4×C5D412yes—
44C22×C3×C4×C5C2311yescharacteristic
45C2×C5×#67—22no—
46C5×#235—28no—
47C2×C5×D12—22no—
48C2×C5×D12C2312yes—
49C2×C4×C5×D3—22no—
50C2×C5×Dic6C2312yes—
51C2×C3×C22⋊D5—22no—
52C3×#709—28no—
53C2×C3×D20—22no—
54C2×C3×D20C2312yes—
55C2×C3×C4×D5—22no—
56C2×C3×Dic10C2312yes—
57C3×C42×C5D412yes—
58C3×C42×C5C2311yescharacteristic
59C3×C42×C5C2311yescharacteristic
60C2×C3⋊#168D418yescomplemented
61C2×C3⋊#168C2312yes—
62C2×C3⋊#168C2312yes—
63C5×(C2×D3)⋊C4—24no—
64C5×C4⋊Dic3—22no—
65C3×#685—24no—
66C3×C4⋊Dic5—22no—
67#6661—28no—
68#6656—28no—
69#6655—28no—
70#6652—28no—
71C3×#532—51no—
72C2×#950—54no—
73#5477D511yescharacteristic, complemented
74#5092—51no—
75#5085—51no—
76#5076—51no—
77#5073—51no—
78#5059—54no—
79C2×C4×C3⋊C8—51no—
80C2×C5×#41—32no—
81C2×#709C2×D312yes—
82C5×C4⋊Q8—31no—
83C5×#127—31no—
84C5×#124—32no—
85C5×#121—62no—
86C4×C5×D4—62no—
87C2×C42×C5C2×D311yescharacteristic
88#4096—616no—
89C2×#689—34no—
90C2×#688—34no—
91C2×#687—34no—
92C2×#686—34no—
93#4076—22no—
94C22×#168—32no—
95#4021C2×D312yes—
96#4020C2×D311yescharacteristic
97C4×D20—22no—
98#4015C2×D311yescharacteristic
99C4×#168—32no—
100C4×#168—31no—
101C4×#168—31no—
102#3147—151noSylow
103C23×C3×C5C2×D411yescharacteristic
104C22×C5×D3—22no—
105C22×C3×D5—22no—
106C2×C3×C4×C5—24no—
107C2×C3×C4×C5C2×D412yes—
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D414yes—
110C2×C3×C4×C5C2×D412yes—
111C2×C3×C4×C5C2411yescharacteristic
112C5×#67—44no—
113C2×C5×Dic3—22no—
114C5×D12—24no—
115C5×D12—44no—
116C4×C5×D3—44no—
117C5×Dic6—24no—
118C3×C22⋊D5—44no—
119C2×C3×Dic5—22no—
120C3×D20—24no—
121C3×D20—44no—
122C3×C4×D5—44no—
123C3×Dic10—24no—
124C3⋊#168C2×D414yes—
125C3⋊#168C2×D414yes—
126C2×C3×#41—52no—
127C2×#235C2×D512yes—
128C3×C4⋊Q8—51no—
129C3×#127—51no—
130C3×#124—52no—
131C3×#121—102no—
132C3×C4×D4—102no—
133C2×C3×C42C2×D511yescharacteristic
134#950—1016no—
135C2×#216—54no—
136C2×#215—54no—
137C2×#214—54no—
138C2×#213—54no—
139#930—22no—
140C22×C3⋊C8—52no—
141#875C2×D512yes—
142#874C2×D511yescharacteristic
143C4×D12—22no—
144#869C2×D511yescharacteristic
145C4×C3⋊C8—52no—
146C4×C3⋊C8—51no—
147C4×C3⋊C8—51no—
148C5×#41—68no—
149C2×C5×Q8—32no—
150C2×C5×D4—32no—
151C2×C5×D4—62no—
152C2×C5×D4—62no—
153C22×C4×C5—62no—
154C22×C4×C5#6712yes—
155C22×C4×C5C22×D311yescharacteristic
156C2×C22⋊D5—22no—
157#709—28no—
158C2×D20—22no—
159C2×D20C22×D312yes—
160C2×C4×D5—22no—
161C2×Dic10C22×D312yes—
162C5×C4⋊C4—62no—
163C5×C22⋊C4—64no—
164C42×C5#6712yes—
165C42×C5C22×D311yescharacteristic
166C42×C5C22×D311yescharacteristic
167#689—68no—
168#688—68no—
169#687—68no—
170#686—68no—
171#685—24no—
172C4⋊Dic5—22no—
173C2×#168—38no—
174C2×#168—32no—
175C2×#168—32no—
176C2×#135—154no—
177#532—31no—
178#532—51no—
179#495—154no—
180#494—151no—
181#493—151no—
182#492—151no—
183#492—151no—
184C2×C4×C8—151no—
185C22×C3×C5—22no—
186C22×C3×C5#12712yes—
187C22×C3×C5C22×D411yescharacteristic
188C2×C5×D3—42no—
189C2×C5×D3—44no—
190C2×C3×D5—42no—
191C2×C3×D5—44no—
192C3×C4×C5—22no—
193C3×C4×C5#12712yes—
194C3×C4×C5#13514yescomplemented
195C3×C4×C5C22×D412yes—
196C3×Dic5—42no—
197C5×Dic3—42no—
198C3×#41—108no—
199C2×C3×Q8—52no—
200C2×C3×D4—52no—
201C2×C3×D4—102no—
202C2×C3×D4—102no—
203C22×C3×C4—102no—
204C22×C3×C4C22⋊D512yes—
205C22×C3×C4C22×D511yescharacteristic
206C2×#67—22no—
207#235—28no—
208C2×D12—22no—
209C2×D12C22×D512yes—
210C2×C4×D3—22no—
211C2×Dic6C22×D512yes—
212C3×C4⋊C4—102no—
213C3×C22⋊C4—104no—
214C3×C42C22⋊D512yes—
215C3×C42C22×D511yescharacteristic
216C3×C42C22×D511yescharacteristic
217#216—108no—
218#215—108no—
219#214—108no—
220#213—108no—
221(C2×D3)⋊C4—24no—
222C4⋊Dic3—22no—
223C2×C3⋊C8—58no—
224C2×C3⋊C8—52no—
225C2×C3⋊C8—52no—
226C23×C5—62no—
227C23×C5C2×#6711yescharacteristic
228C22×D5—22no—
229C5×Q8—64no—
230C5×D4—64no—
231C5×D4—124no—
232C5×D4—124no—
233C2×C4×C5—24no—
234C2×C4×C5—62no—
235C2×C4×C5—124no—
236C2×C4×C5D3×D414yes—
237C2×C4×C5C2×#6712yes—
238C2×C4×C5C2×#6712yes—
239C2×C4×C5C2×#6711yescharacteristic
240C2×C4×C5C23×D311yescharacteristic
241C22⋊D5—44no—
242C2×Dic5—22no—
243D20—24no—
244D20—44no—
245C4×D5—44no—
246Dic10—24no—
247#168—34no—
248#168—34no—
249C2×#41—32no—
250C2×#41—52no—
251#135—3016no—
252C2×Q16—154no—
253C2×SD16—154no—
254C2×SD16—154no—
255C2×D8—154no—
256C22×C8—152no—
257C4⋊Q8—31no—
258C4⋊Q8—51no—
259#127—31no—
260#127—51no—
261#124—32no—
262#124—52no—
263#121—62no—
264#121—102no—
265C4×D4—62no—
266C4×D4—102no—
267C2×C42D3×D511yescharacteristic
268C4×C8—151no—
269C4×C8—151no—
270C4×C8—152no—
271C2×C3×C5—22no—
272C2×C3×C5C2×#12711yescharacteristic
273C2×C3×C5C2×#13512yes—
274C3×D5—82no—
275C5×D3—82no—
276C23×C3—102no—
277C23×C3C2×C22⋊D511yescharacteristic
278C22×D3—22no—
279C3×Q8—104no—
280C3×D4—104no—
281C3×D4—204no—
282C3×D4—204no—
283C2×C3×C4—24no—
284C2×C3×C4—102no—
285C2×C3×C4—204no—
286C2×C3×C4D4×D514yes—
287C2×C3×C4C2×C22⋊D512yes—
288C2×C3×C4C2×C22⋊D512yes—
289C2×C3×C4C2×C22⋊D511yescharacteristic
290C2×C3×C4C23×D511yescharacteristic
291#67—44no—
292C2×Dic3—22no—
293D12—24no—
294D12—44no—
295C4×D3—44no—
296Dic6—24no—
297C3⋊C8—54no—
298C3⋊C8—54no—
299C22×C5—22no—
300C22×C5—122no—
301C22×C5—124no—
302C22×C5#94012yes—
303C22×C5C22×#6711yescharacteristic
304C2×D5—42no—
305C2×D5—44no—
306C4×C5—22no—
307C4×C5—122no—
308C4×C5#94012yes—
309C4×C5#95014yescomplemented
310C4×C5C2×D3×D412yes—
311Dic5—42no—
312#41—68no—
313#41—108no—
314C2×Q8—32no—
315C2×Q8—52no—
316C2×D4—32no—
317C2×D4—52no—
318C2×D4—62no—
319C2×D4—62no—
320C2×D4—102no—
321C2×D4—102no—
322C22×C4—62no—
323C22×C4—102no—
324C22×C4#120112yes—
325C22×C4C2×D3×D511yescharacteristic
326Q16—308no—
327SD16—308no—
328SD16—308no—
329D8—308no—
330C2×C8—158no—
331C2×C8—152no—
332C2×C8—152no—
333C4⋊C4—62no—
334C4⋊C4—102no—
335C22⋊C4—64no—
336C22⋊C4—104no—
337C42#120112yes—
338C42C2×D3×D511yescharacteristic
339C42C2×D3×D511yescharacteristic
340C3×C5#314711yescharacteristic, complemented, Hall
341C22×C3—22no—
342C22×C3—202no—
343C22×C3—204no—
344C22×C3#408612yes—
345C22×C3C22×C22⋊D511yescharacteristic
346C2×D3—42no—
347C2×D3—44no—
348C3×C4—22no—
349C3×C4—202no—
350C3×C4#408612yes—
351C3×C4#409614yescomplemented
352C3×C4C2×D4×D512yes—
353Dic3—42no—
354C2×C5—22no—
355C2×C5—242no—
356C2×C5C2×#94011yescharacteristic
357C2×C5C2×#95012yes—
358D5—82no—
359C23—62no—
360C23—102no—
361C23C2×#120111yescharacteristic
362Q8—64no—
363Q8—104no—
364D4—64no—
365D4—104no—
366D4—124no—
367D4—124no—
368D4—204no—
369D4—204no—
370C2×C4—24no—
371C2×C4—62no—
372C2×C4—102no—
373C2×C4—124no—
374C2×C4—204no—
375C2×C4#677714yes—
376C2×C4C2×#120112yes—
377C2×C4C2×#120112yes—
378C2×C4C2×#120111yescharacteristic
379C2×C4C22×D3×D511yescharacteristic
380C8—154no—
381C8—154no—
382C2×C3—22no—
383C2×C3—402no—
384C2×C3C2×#408611yescharacteristic
385C2×C3C2×#409612yes—
386D3—82no—
387C5#8328511yescharacteristic, complemented, Sylow
388C22—22no—
389C22—122no—
390C22—124no—
391C22—202no—
392C22—204no—
393C22#9146312yes—
394C22C22×#120111yescharacteristic
395C4—22no—
396C4—122no—
397C4—202no—
398C4#9129714yescomplemented
399C4#9146312yes—
400C4C2×#677712yes—
401C3#1061501611yescharacteristic, complemented, Sylow
402C2—22no—
403C2—242no—
404C2—402no—
405C2C2×#9129712yes—
406C2C2×#9146311yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C22×D4
hypercenterC2×C42D3×D5
hypocenterC3×C5#3147
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C5×#5477C2semidirect
2. C3×#65811C2semidirect
3. C2×#91297C2semidirect
4. C2×C4×C3⋊#168C2semidirect
5. #11747103C2semidirect
6. #11747081C2semidirect
7. #11747079C2semidirect
8. #11747040C2semidirect
9. #11747039C2semidirect
36. #65811D3semidirect
60. C2×C3⋊#168D4semidirect
73. #5477D5semidirect
194. C3×C4×C5#135semidirect
309. C4×C5#950semidirect
340. C3×C5#3147semidirect
351. C3×C4#4096semidirect
387. C5#83285semidirect
398. C4#91297semidirect
401. C3#10615016semidirect

Maximal subgroups

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

subgroupindex
C5×#54772
C3×#658112
C2×#912972
C2×C4×C3⋊#1682
#117471032
#117470812
#117470792
#117470402
#117470392
#106150163
#832855