Finite Group Databasebeta

← #14411583

Subgroups — #14411583

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91913C212yesmaximal
2C4×#6772C211yesmaximal, characteristic
3#11752335C211yesmaximal, characteristic, complemented
4C3×C4×#700C211yesmaximal, characteristic, complemented
5#11751907C212yesmaximal, complemented
6D3×#4002C212yesmaximal, complemented
7#11751868C214yesmaximal, complemented
8#11751782C212yesmaximal, complemented
9#10617136—31nomaximal, Hall
10C2×#6772C2211yescharacteristic
11C2×D5⋊(C3⋊C8)C2212yes—
12C2×C3×#700C2212yes—
13C2×#6739C2214yes—
14C2×D3×#170C2214yes—
15#91913C4116yescomplemented
16C4×Dic30C411yescharacteristic
17C4×C5×D12C411yescharacteristic
18C3×C42×D5C2211yescharacteristic
19#91440C412yes—
20C4×#1201C412yes—
21Dic5×D12C411yescharacteristic
22#91398C2212yes—
23C4×D3×Dic5C2212yes—
24#91358C2211yescharacteristic
25#91333C411yescharacteristic
26#91231C2212yes—
27#91231C2211yescharacteristic
28#91231C2211yescharacteristic
29C3×#4002C2212yes—
30C3×C4×#170C2212yes—
31#91169C2214yes—
32Dic3×#170C2214yes—
33#78516—51nomaximal, Hall
34C2×#4131—32no—
35C4×#711—31no—
36C4×#704—32no—
37C2×#4002—32no—
38#65701—32no—
39#65691—34no—
40C4×#700D311yescharacteristic, complemented
41#65676—31no—
42C2×Dic30C2×C411yescharacteristic
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3C2×C412yes—
45C2×C3×C4×D5C2×C411yescharacteristic
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5C2311yescharacteristic
48C2×#1201C2×C412yes—
49C2×D3×Dic5C2×C412yes—
50C2×D3×Dic5C2312yes—
51#6772C2×C418yes—
52C2×C3⋊#170C2312yes—
53C2×C3⋊#170C2312yes—
54D5⋊(C3⋊C8)C2×C418yescomplemented
55C2×C3×#170C2314yes—
56C3×#700C2×C418yescomplemented
57#6739C2×C4116yescomplemented
58D3×#170C2×C4116yescomplemented
59C3×C42×C5C2×C411yescharacteristic
60C4⋊Dic15C2×C411yescharacteristic
61#6712C2×C412yes—
62C4×Dic15C2×C412yes—
63C5×(C2×D3)⋊C4C2×C412yes—
64C5×C4⋊Dic3C2×C411yescharacteristic
65C3×C4×Dic5C2×C411yescharacteristic
66C3×C4×Dic5C2311yescharacteristic
67C3×C4×Dic5C2311yescharacteristic
68#6669C2×C412yes—
69(C2×D3)⋊Dic5C2×C412yes—
70#6665C2×C412yes—
71Dic3×Dic5C2×C412yes—
72Dic3×Dic5C2312yes—
73C2×#907—52no—
74C4×#235—51no—
75C3×C4×M16—51no—
76#5122—52no—
77C2×#803—51no—
78#4707—52no—
79D3×#97—52no—
80#4689—54no—
81C2×#711—31no—
82C2×#704—34no—
83C22×#170—34no—
84#4131—316no—
85C2×#700C2×D312yes—
86C2×D5⋊C8—32no—
87C4×C5×D4—31no—
88D4×Dic5—31no—
89C4×C22⋊D5—32no—
90C2×C4×Dic5—32no—
91#4038—31no—
92#4033—31no—
93#4027—32no—
94#4023—32no—
95C42×D5C2×D311yescharacteristic
96C4×Dic10—31no—
97#4002—34no—
98#4002—32no—
99#4002—31no—
100#4002—31no—
101#4002C2×D312yes—
102C4×#170—34no—
103C4×#170C2×D312yes—
104#2875—151noSylow
105C22×C5×D3C22×C412yes—
106C22×C3×D5C22×C411yescharacteristic
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C22×C411yescharacteristic
110C2×Dic15C22×C412yes—
111C2×Dic15C22×C412yes—
112Dic30C4214yes—
113C2×C5×Dic3C22×C412yes—
114C5×D12C4214yes—
115C4×C5×D3—42no—
116C2×C3×Dic5C22×C411yescharacteristic
117C2×C3×Dic5C22×C411yescharacteristic
118C2×C3×Dic5C2411yescharacteristic
119C3×C4×D5—41no—
120C3×C4×D5—41no—
121C3×C4×D5C22×C414yes—
122#1201C4218yes—
123D3×Dic5—42no—
124D3×Dic5C22×C418yes—
125C3⋊#170C22×C414yes—
126C3⋊#170C22×C414yes—
127C3×#170C22×C418yes—
128C2×#235—51no—
129C2×C3×M16—52no—
130C2×C3×C42—51no—
131C4×#67—52no—
132C4×#67—52no—
133#926—51no—
134C22×C3⋊C8—52no—
135#907—516no—
136C2×ΓL(1,𝔽25)—54no—
137C2×D3×C8—54no—
138C4×D12—51no—
139C4×D12AGL(1,𝔽5)11yescharacteristic
140#872—52no—
141C42×D3—52no—
142C4×Dic6—51no—
143C4×Dic6—51no—
144C3×#97—52no—
145C3×C4×C8—52no—
146#815—54no—
147C8×Dic3—54no—
148#803—52no—
149#803—51no—
150#803—51no—
151C2×C5×D4—31no—
152C22×C4×C5—32no—
153C2×C22⋊D5—32no—
154C22×Dic5—32no—
155C22×Dic5—32no—
156#711—38no—
157C2×C4×D5C4×D311yescharacteristic
158C2×C4×D5C4×D311yescharacteristic
159C2×C4×D5C22×D311yescharacteristic
160C2×Dic10—31no—
161#704—316no—
162C2×#170—32no—
163C2×#170—32no—
164C2×#170—316no—
165C2×#170C22×D314yes—
166#700C4×D318yescomplemented
167D5⋊C8—38no—
168C5×C4⋊C4—31no—
169C5×C22⋊C4—32no—
170C42×C5C4×D311yescharacteristic
171C22⋊Dic5—32no—
172#685—32no—
173C4⋊Dic5—31no—
174#683—32no—
175#683—32no—
176C4×Dic5—32no—
177C4×Dic5—32no—
178C4×Dic5—32no—
179C4×Dic5C4×D311yescharacteristic
180C4×Dic5C22×D311yescharacteristic
181C4×Dic5C22×D311yescharacteristic
182C2×#131—152no—
183C4×#41—151no—
184#405—154no—
185#405—152no—
186C4×M16—51no—
187C4×M16—152no—
188C2×#97—152no—
189C2×#97—151no—
190C22×C3×C5C23×C411yescharacteristic
191C2×C5×D3—22no—
192C2×C5×D3—22no—
193C2×C5×D3C2×C4214yes—
194C2×C3×D5—21no—
195C2×C3×D5—21no—
196C2×C3×D5C2×C4212yes—
197C3×C4×C5—21no—
198C3×C4×C5—21no—
199C3×C4×C5C2×C4212yes—
200Dic15—22no—
201Dic15C2×C4214yes—
202C3×Dic5—21no—
203C3×Dic5—21no—
204C3×Dic5C23×C412yes—
205C5×Dic3—22no—
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4—51no—
209C2×#67—52no—
210#235—58no—
211C2×D12C2×AGL(1,𝔽5)11yescharacteristic
212C2×C4×D3—52no—
213C2×C4×D3—52no—
214C2×C4×D3C2×AGL(1,𝔽5)12yes—
215C2×Dic6—51no—
216C3×M16—58no—
217C2×C3×C8—54no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42C2×AGL(1,𝔽5)11yescharacteristic
222#217—52no—
223(C2×D3)⋊C4—52no—
224(C2×D3)⋊C4C2×AGL(1,𝔽5)12yes—
225C4⋊Dic3—51no—
226C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
227Dic3⋊C4—52no—
228Dic3⋊C4—52no—
229C4×Dic3—52no—
230C4×Dic3—52no—
231C4×Dic3—52no—
232C2×C3⋊C8—52no—
233C2×C3⋊C8—52no—
234C2×C3⋊C8—58no—
235ΓL(1,𝔽25)—516no—
236D3×C8—516no—
237C23×C5—32no—
238C22×D5C2×C4×D311yescharacteristic
239C5×D4—34no—
240C2×C4×C5—32no—
241C2×C4×C5—122no—
242C2×C4×C5C2×C4×D311yescharacteristic
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5C2×C4×D311yescharacteristic
245C22⋊D5—38no—
246C2×Dic5—32no—
247C2×Dic5—38no—
248C2×Dic5—32no—
249C2×Dic5—122no—
250C2×Dic5C2×C4×D311yescharacteristic
251C2×Dic5C2×C4×D311yescharacteristic
252C2×Dic5C23×D311yescharacteristic
253C4×D5—41no—
254C4×D5—41no—
255C4×D5C2×C4×D314yes—
256Dic10—34no—
257#170—34no—
258#170—34no—
259#170C2×C4×D318yes—
260C2×#41—151no—
261#131—1516no—
262C2×M16—52no—
263C2×M16—154no—
264C22×C8—154no—
265C22×C8—152no—
266C4×Q8—151no—
267C4×Q8—151no—
268C4×D4—31no—
269C4×D4—151no—
270C4×D4—152no—
271C4×D4—152no—
272#117—152no—
273#117—151no—
274C2×C42—51no—
275C2×C42—152no—
276#97—52no—
277#97—151no—
278#97—151no—
279#97—152no—
280#97—154no—
281C4×C8—52no—
282C4×C8—154no—
283C2×C3×C5C22×C4211yescharacteristic
284C2×C3×C5#56811yescharacteristic
285C2×C3×C5#56811yescharacteristic
286C3×D5—22no—
287C5×D3—24no—
288C23×C3—51no—
289C22×D3C22×AGL(1,𝔽5)12yes—
290C2×C3×C4—51no—
291C2×C3×C4—54no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—201no—
295C2×C3×C4—201no—
296C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
297C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
298C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
299#67—58no—
300C2×Dic3—52no—
301C2×Dic3—52no—
302C2×Dic3C22×AGL(1,𝔽5)12yes—
303D12C4×AGL(1,𝔽5)14yes—
304C4×D3—42no—
305C4×D3—58no—
306C4×D3—202no—
307Dic6—54no—
308C3×C8—58no—
309C3⋊C8—54no—
310C3⋊C8—54no—
311C22×C5—34no—
312C22×C5—62no—
313C22×C5—62no—
314C22×C5C22×C4×D311yescharacteristic
315C2×D5—21no—
316C2×D5—21no—
317C2×D5C42×D312yes—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—62no—
321C4×C5C42×D312yes—
322Dic5—21no—
323Dic5—21no—
324Dic5—34no—
325Dic5—62no—
326Dic5C22×C4×D312yes—
327#41—158no—
328C2×Q8—151no—
329C2×D4—31no—
330C2×D4—152no—
331C22×C4—32no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—152no—
336C22×C4—152no—
337M16—58no—
338M16—1516no—
339C2×C8—54no—
340C2×C8—1516no—
341C2×C8—152no—
342C2×C8—152no—
343C2×C8—158no—
344C4⋊C4—31no—
345C4⋊C4—152no—
346C4⋊C4—152no—
347C4⋊C4—151no—
348C22⋊C4—32no—
349C22⋊C4—152no—
350C22⋊C4—152no—
351C42—51no—
352C42—51no—
353C42—51no—
354C42—152no—
355C42—152no—
356C42—152no—
357C42D3×AGL(1,𝔽5)11yescharacteristic
358C3×C5#287511yescharacteristic, complemented, Hall
359C22×C3—52no—
360C22×C3—101no—
361C22×C3—101no—
362C22×C3C23×AGL(1,𝔽5)11yescharacteristic
363C2×D3—22no—
364C2×D3—22no—
365C2×D3C2×C4×AGL(1,𝔽5)14yes—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—52no—
369C3×C4—101no—
370C3×C4—101no—
371C3×C4C2×C4×AGL(1,𝔽5)12yes—
372Dic3—22no—
373Dic3—54no—
374Dic3—102no—
375C2×C5—64no—
376C2×C5C2×C42×D311yescharacteristic
377C2×C5#574511yescharacteristic
378C2×C5#574511yescharacteristic
379D5—22no—
380C23—32no—
381C23—51no—
382Q8—154no—
383D4—34no—
384D4—158no—
385C2×C4—32no—
386C2×C4—51no—
387C2×C4—54no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—122no—
391C2×C4—158no—
392C2×C4—152no—
393C2×C4—152no—
394C2×C4—201no—
395C2×C4—201no—
396C2×C4—602no—
397C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
398C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
399C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
400C8—58no—
401C8—154no—
402C8—154no—
403C2×C3—102no—
404C2×C3C22×C4×AGL(1,𝔽5)11yescharacteristic
405C2×C3#6625611yescharacteristic
406C2×C3#6626411yescharacteristic
407D3—24no—
408C5#7851611yescharacteristic, complemented, Sylow
409C22—34no—
410C22—52no—
411C22—62no—
412C22—62no—
413C22—101no—
414C22—101no—
415C22C22×D3×AGL(1,𝔽5)11yescharacteristic
416C4—21no—
417C4—21no—
418C4—52no—
419C4—62no—
420C4—101no—
421C4—101no—
422C4—154no—
423C4—302no—
424C4C4×D3×AGL(1,𝔽5)12yes—
425C3#1061713611yescharacteristic, complemented, Sylow
426C2—64no—
427C2—102no—
428C2#1175682111yescharacteristic
429C2#1175682211yescharacteristic
430C2C2×C4×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FittingC3×C42×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×#6772C22
cosocleC2×C3×Dic5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2875
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
3. #11752335C2semidirect
4. C3×C4×#700C2semidirect
5. #11751907C2semidirect
6. D3×#4002C2semidirect
7. #11751868C2semidirect
8. #11751782C2semidirect
15. #91913C4semidirect
40. C4×#700D3semidirect
54. D5⋊(C3⋊C8)C2×C4semidirect
56. C3×#700C2×C4semidirect
57. #6739C2×C4semidirect
58. D3×#170C2×C4semidirect
166. #700C4×D3semidirect
358. C3×C5#2875semidirect
408. C5#78516semidirect
425. C3#10617136semidirect

Maximal subgroups

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

subgroupindex
C2×#919132
C4×#67722
#117523352
C3×C4×#7002
#117519072
D3×#40022
#117518682
#117517822
#106171363
#785165