Finite Group Databasebeta

← #14309039

Subgroups — #14309039

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756276C211yesmaximal, characteristic, complemented
2C5×#5005C211yesmaximal, characteristic
3#11748625C211yesmaximal, characteristic
4C2×#90978C211yesmaximal, characteristic
5C3×#64751C211yesmaximal, characteristic, complemented
6#11745990C211yesmaximal, characteristic, complemented
7#11745973C211yesmaximal, characteristic, complemented
8#10601187—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C3×C5×#117C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13#91779—21no—
14#91777—21no—
15#91767—22no—
16C4×Dic30—22no—
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C5×#805—22no—
21#90996—22no—
22#90978—21no—
23#90978—21no—
24#68714—51nomaximal, Hall
25#65851—31no—
26C5×#421—31no—
27#65529—31no—
28C2×#3969—31no—
29#64776—31no—
30#64775—31no—
31#64751D311yescharacteristic, complemented
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—21no—
34C2×Dic30—22no—
35C2×C5×#67—21no—
36C5×#235—21no—
37C5×#235—21no—
38C5×#235—21no—
39C5×#235—21no—
40C2×C5×D12Q811yescharacteristic, complemented
41C2×C4×C5×D3—21no—
42C2×C5×Dic6Q811yescharacteristic, complemented
43C3×C5×C4⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5D412yes—
46#6719D412yes—
47C4⋊Dic15—22no—
48C4⋊Dic15—21no—
49#6712—22no—
50#6712—22no—
51C4×Dic15—21no—
52C4×Dic15—21no—
53C4×Dic15D411yescharacteristic
54C4×Dic15D411yescharacteristic
55C5×#208—21no—
56C5×#208—21no—
57C2×C5×C3⋊C8—21no—
58C3×C22⋊Dic5—21no—
59C3×C4⋊Dic5—21no—
60C3×C4×Dic5—21no—
61C3×#681—21no—
62C3×#681—21no—
63C2×C3×#168—21no—
64#5517—51no—
65C2×#825—51no—
66#5006—51no—
67#5005D511yescharacteristic
68C3×H(3,ℤ/4)—51no—
69#4559—51no—
70#4532—51no—
71C2×C5×#41—31no—
72C2×C5×M16—31no—
73C5×#117C2×D311yescharacteristic
74#4072—31no—
75#4072C2×D311yescharacteristic
76C2×C4×Dic5—31no—
77C2×#681C2×D311yescharacteristic
78#4036—61no—
79#4034—61no—
80#4024—62no—
81C4×Dic10—62no—
82C5×#104—62no—
83#3969—61no—
84#3969—61no—
85#3966—62no—
86#2031—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C5×D3—21no—
89C2×C3×C4×C5—22no—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×Q811yescharacteristic
93C2×C3×C4×C5#4111yescharacteristic
94C2×C3×C4×C5#4111yescharacteristic
95C2×C3×C4×C5#4111yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—22no—
99C2×Dic15—42no—
100Dic30—44no—
101C5×#67—41no—
102C5×#67—41no—
103C2×C5×Dic3—21no—
104C5×D12—21no—
105C5×D12—21no—
106C4×C5×D3—41no—
107C4×C5×D3—41no—
108C5×Dic6—21no—
109C5×Dic6—21no—
110C2×C3×Dic5—41no—
111C3×#168—41no—
112C5×C3⋊C8—41no—
113C2×#235C2×D511yescharacteristic
114C2×C3×M16—51no—
115C3×#117—51no—
116C3×#117C2×D511yescharacteristic
117#926—51no—
118C2×C4×Dic3—51no—
119C2×#208C2×D511yescharacteristic
120#890—101no—
121#888—101no—
122#878—102no—
123C4×Dic6—102no—
124#825—101no—
125#825—101no—
126#806—102no—
127#805—22no—
128C5×#41—61no—
129C5×#41—61no—
130C5×#41—61no—
131C5×#41—61no—
132C2×C5×Q8—31no—
133C2×C5×D4—31no—
134C2×C5×D4—61no—
135C22×C4×C5—61no—
136C22×C4×C5C22×D311yescharacteristic
137C22×Dic5—61no—
138C2×Dic10—62no—
139C5×M16—61no—
140C5×M16—61no—
141C2×C5×C8—61no—
142C5×C4⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5D1212yes—
145C22⋊Dic5—21no—
146C22⋊Dic5—32no—
147C4⋊Dic5—21no—
148C4⋊Dic5—62no—
149C4⋊Dic5—61no—
150#683—62no—
151#683—62no—
152C4×Dic5—21no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—61no—
156C4×Dic5—61no—
157#681—21no—
158#681—21no—
159C2×#168—21no—
160#533—151no—
161#421—31no—
162C2×#104—151no—
163#410—151no—
164#344—151no—
165#339—151no—
166H(3,ℤ/4)—51no—
167C22×C3×C5—41no—
168C22×C3×C5#12011yescharacteristic
169C22×C3×C5C22⋊Q811yescharacteristic
170C22×C3×C5#12411yescharacteristic
171C2×C5×D3—41no—
172C2×C5×D3—81no—
173C3×C4×C5—42no—
174C3×C4×C5C22⋊Q811yescharacteristic
175C3×C4×C5C22⋊Q811yescharacteristic
176C3×C4×C5#12411yescharacteristic
177C3×C4×C5#12411yescharacteristic
178Dic15—22no—
179Dic15—42no—
180Dic15—41no—
181C3×Dic5—81no—
182C5×Dic3—41no—
183C22×C3×C4C22×D511yescharacteristic
184C2×#67—21no—
185C22×Dic3—101no—
186#235—21no—
187#235—21no—
188#235—21no—
189#235—21no—
190C2×D12Dic1011yescharacteristic, complemented
191C2×C4×D3—21no—
192C2×Dic6—102no—
193C2×Dic6Dic1011yescharacteristic, complemented
194C3×M16—101no—
195C3×M16—101no—
196C2×C3×C8—101no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—101no—
199C3×C22⋊C4—21no—
200C3×C22⋊C4—101no—
201C3×C42—101no—
202C3×C42C22⋊D512yes—
203#217—52no—
204C4⋊Dic3—102no—
205C4⋊Dic3—101no—
206Dic3⋊C4—102no—
207Dic3⋊C4—102no—
208C4×Dic3—51no—
209C4×Dic3—51no—
210C4×Dic3—101no—
211C4×Dic3—101no—
212#208—21no—
213#208—21no—
214C2×C3⋊C8—21no—
215C23×C5—61no—
216C23×C5D3×D411yescharacteristic
217C5×Q8—61no—
218C5×Q8—61no—
219C5×D4—61no—
220C5×D4—61no—
221C5×D4—121no—
222C5×D4—121no—
223C2×C4×C5—22no—
224C2×C4×C5—61no—
225C2×C4×C5—121no—
226C2×C4×C5—121no—
227C2×C4×C5C2×D1211yescharacteristic
228C2×C4×C5#23511yescharacteristic
229C2×C4×C5#23511yescharacteristic
230C2×C4×C5D3×D411yescharacteristic
231C2×C4×C5#23711yescharacteristic
232C2×C4×C5D3×Q811yescharacteristic
233C2×Dic5—41no—
234C2×Dic5—61no—
235C2×Dic5—61no—
236C2×Dic5—62no—
237C2×Dic5—122no—
238Dic10—124no—
239C5×C8—121no—
240#168—41no—
241C2×#41—31no—
242C2×M16—31no—
243C2×M16—51no—
244C4⋊Q8—301no—
245#125—301no—
246C22⋊Q8—302no—
247C4×Q8—302no—
248#117—51no—
249#117—151no—
250#117D3×D511yescharacteristic
251C2×C42—151no—
252#104—62no—
253#104—301no—
254#104—301no—
255#99—302no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—21no—
259C2×C3×C5#39311yescharacteristic
260C5×D3—81no—
261C23×C3D4×D511yescharacteristic
262C22×D3—21no—
263C2×C3×C4—22no—
264C2×C3×C4—201no—
265C2×C3×C4C2×Dic1011yescharacteristic
266C2×C3×C4#70911yescharacteristic
267C2×C3×C4D4×D511yescharacteristic
268C2×C3×C4#71111yescharacteristic
269C2×C3×C4#71111yescharacteristic
270C2×C3×C4C2×C22⋊D511yescharacteristic
271#67—41no—
272#67—41no—
273C2×Dic3—21no—
274C2×Dic3—101no—
275C2×Dic3—101no—
276C2×Dic3—102no—
277C2×Dic3—202no—
278D12—21no—
279D12—21no—
280C4×D3—41no—
281C4×D3—41no—
282Dic6—21no—
283Dic6—21no—
284Dic6—204no—
285C3×C8—201no—
286C3⋊C8—41no—
287C22×C5—41no—
288C22×C5—121no—
289C22×C5—241no—
290C22×C5#88211yescharacteristic
291C22×C5#88511yescharacteristic
292C22×C5#89611yescharacteristic
293C4×C5—42no—
294C4×C5—121no—
295C4×C5#87511yescharacteristic
296C4×C5#88511yescharacteristic
297C4×C5#89611yescharacteristic
298C4×C5#89711yescharacteristic
299Dic5—62no—
300Dic5—81no—
301Dic5—122no—
302Dic5—121no—
303#41—61no—
304#41—61no—
305#41—61no—
306#41—61no—
307C2×Q8—31no—
308C2×Q8—302no—
309C2×D4—31no—
310C2×D4—61no—
311C22×C4—61no—
312C22×C4—301no—
313C22×C4C2×D3×D511yescharacteristic
314M16—61no—
315M16—61no—
316M16—101no—
317M16—101no—
318C2×C8—61no—
319C2×C8—101no—
320C4⋊C4—21no—
321C4⋊C4—101no—
322C4⋊C4—302no—
323C4⋊C4—302no—
324C4⋊C4—302no—
325C4⋊C4—301no—
326C22⋊C4—21no—
327C22⋊C4—101no—
328C22⋊C4—152no—
329C42—101no—
330C42—151no—
331C42—151no—
332C42—301no—
333C42—301no—
334C42#120312yes—
335C3×C5#203111yescharacteristic, complemented, Hall
336C22×C3—41no—
337C22×C3#402411yescharacteristic
338C22×C3#403111yescharacteristic
339C22×C3#408311yescharacteristic
340C2×D3—41no—
341C2×D3—81no—
342C3×C4—42no—
343C3×C4—401no—
344C3×C4#402411yescharacteristic
345C3×C4#403111yescharacteristic
346C3×C4#407011yescharacteristic
347C3×C4#408211yescharacteristic
348Dic3—41no—
349Dic3—102no—
350Dic3—202no—
351Dic3—201no—
352C2×C5—21no—
353C2×C5—21no—
354C2×C5—21no—
355C2×C5—241no—
356C2×C5#467311yescharacteristic
357C23—61no—
358C23#679011yescharacteristic
359Q8—61no—
360Q8—61no—
361Q8—604no—
362D4—61no—
363D4—61no—
364D4—121no—
365D4—121no—
366C2×C4—22no—
367C2×C4—61no—
368C2×C4—121no—
369C2×C4—121no—
370C2×C4—201no—
371C2×C4—301no—
372C2×C4—301no—
373C2×C4—302no—
374C2×C4—602no—
375C2×C4#676511yescharacteristic
376C2×C4D3×Dic1011yescharacteristic
377C2×C4#677211yescharacteristic
378C2×C4#677211yescharacteristic
379C2×C4C2×#120311yescharacteristic
380C2×C4#679011yescharacteristic
381C8—121no—
382C8—201no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3#6523611yescharacteristic
387D3—81no—
388C5#6871411yescharacteristic, complemented, Sylow
389C22—41no—
390C22—121no—
391C22—241no—
392C22#9143211yescharacteristic
393C22#9146211yescharacteristic
394C22#9157311yescharacteristic
395C4—42no—
396C4—121no—
397C4—302no—
398C4—401no—
399C4—601no—
400C4—602no—
401C4#9136511yescharacteristic
402C4#9137311yescharacteristic
403C4#9143211yescharacteristic
404C4#9146211yescharacteristic
405C3#1060118711yescharacteristic, complemented, Sylow
406C2—21no—
407C2—21no—
408C2—21no—
409C2—241no—
410C2#1174879511yescharacteristic
subgroupG/H
centerC4#91373
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#393
prime radicalC2×C5×#235C22
hypercenter#117D3×D5
hypocenterC3×C5#2031
LCSG ▷ C22×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756276C2semidirect
5. C3×#64751C2semidirect
6. #11745990C2semidirect
7. #11745973C2semidirect
31. #64751D3semidirect
40. C2×C5×D12Q8semidirect
42. C2×C5×Dic6Q8semidirect
190. C2×D12Dic10semidirect
193. C2×Dic6Dic10semidirect
335. C3×C5#2031semidirect
388. C5#68714semidirect
405. C3#10601187semidirect

Maximal subgroups

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

subgroupindex
#117562762
C5×#50052
#117486252
C2×#909782
C3×#647512
#117459902
#117459732
#106011873
#687145