Finite Group Databasebeta

← #14300268

Subgroups — #14300268

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91286C211yesmaximal, characteristic
2C2×C5×#805C211yesmaximal, characteristic
3C2×#90991C211yesmaximal, characteristic, complemented
4#11748435C211yesmaximal, characteristic, complemented
5#11748388C211yesmaximal, characteristic
6#11746344C211yesmaximal, characteristic, complemented
7C3×#64744C211yesmaximal, characteristic, complemented
8#10601169—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C42×C5C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C22×C3×#168C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×#6650—21no—
17#91286—22no—
18#91286—22no—
19C2×D3×#168—21no—
20C5×#805—22no—
21#90991—22no—
22#90983—21no—
23#90983—21no—
24#90973C411yescharacteristic, complemented
25#90973C411yescharacteristic, complemented
26#90967C411yescharacteristic, complemented
27#90967C411yescharacteristic, complemented
28#68694—51nomaximal, Hall
29C2×#4094—31no—
30C2×C5×#104—31no—
31#65522—31no—
32C2×#3954—31no—
33#65408—31no—
34#64744D311yescharacteristic, complemented
35#64743—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×C5×#67—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235D412yes—
42C5×#235Q812yes—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5—21no—
48#6719—21no—
49C4⋊Dic15C2×C411yescharacteristic
50C4⋊Dic15C2×C411yescharacteristic
51C4×Dic15—21no—
52#6710—21no—
53#6710D412yes—
54C2×C3⋊#168—21no—
55C5×#208—21no—
56C5×#208—21no—
57C2×C5×C3⋊C8—21no—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62C2×C3×#168C2×C411yescharacteristic
63C2×C3×#168C2×C411yescharacteristic
64C2×C3×#168D411yescharacteristic
65C2×C3×#168D411yescharacteristic
66#6650—24no—
67D3×#168—24no—
68C2×#901—51no—
69#5113—51no—
70C2×#819—51no—
71#5102—51no—
72C2×#805D511yescharacteristic
73C3×#336—51no—
74#4523—51no—
75C2×C5×#41—31no—
76C2×C5×M16—31no—
77C2×C42×C5C2×D311yescharacteristic
78#4094—62no—
79#4094—62no—
80#4072—31no—
81C2×#681—31no—
82C2×#681—61no—
83C22×#168—61no—
84C22×#168C2×D311yescharacteristic
85C22×#168C2×D311yescharacteristic
86C5×#104—62no—
87#3967—31no—
88#3967—31no—
89#3964—31no—
90#3964—31no—
91#3954—62no—
92#3946—61no—
93#3946—61no—
94#1866—151noSylow
95C23×C3×C5#4111yescharacteristic
96C22×C5×D3—21no—
97C2×C3×C4×C5—22no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×Q811yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—21no—
107C2×Dic15—21no—
108C5×#67—22no—
109C5×#67—22no—
110C2×C5×Dic3—21no—
111C5×D12—21no—
112C5×D12C4⋊C412yes—
113C4×C5×D3—22no—
114C4×C5×D3—22no—
115C5×Dic6—21no—
116C5×Dic6C4⋊C412yes—
117C3⋊#168—22no—
118C3×#168—21no—
119C3×#168—21no—
120C3×#168—21no—
121C3×#168—21no—
122C5×C3⋊C8—41no—
123C2×#235C2×D511yescharacteristic
124C22×C3×C8—51no—
125C22×C3×C8—51no—
126C2×C3×C42C2×D511yescharacteristic
127#926—51no—
128C2×#208—51no—
129C2×#208C2×D511yescharacteristic
130#901—102no—
131#901—102no—
132C2×ΓL(1,𝔽25)—101no—
133C2×D3×C8—101no—
134#821—51no—
135#821—51no—
136#819—102no—
137#816—51no—
138#816—51no—
139Dic3⋊C8—101no—
140Dic3⋊C8—101no—
141#805—22no—
142C5×#41—32no—
143C5×#41—32no—
144C5×#41—61no—
145C5×#41—61no—
146C2×C5×Q8—31no—
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C22×C4×C5—21no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C5×M16—61no—
153C5×M16—61no—
154C2×C5×C8—61no—
155C42×C5—21no—
156C42×C5—21no—
157C22⋊Dic5—61no—
158C4⋊Dic5—31no—
159C4⋊Dic5—31no—
160C4×Dic5—61no—
161#681—32no—
162#681—64no—
163#681—61no—
164C2×#168—21no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168—21no—
168C2×#168—64no—
169C2×#168—61no—
170C2×#168C4×D311yescharacteristic
171C2×#168C4×D311yescharacteristic
172C2×#168D1211yescharacteristic
173C2×#168D1211yescharacteristic
174C2×#131—151no—
175C2×#108—151no—
176#424—151no—
177C2×#104—31no—
178#416—151no—
179#339—151no—
180#336—51no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5C22⋊Q811yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C5×D3—22no—
187C2×C5×D3—41no—
188C2×C5×D3—41no—
189C3×C4×C5—42no—
190C3×C4×C5C2×C4⋊C411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5#12011yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194Dic15—41no—
195Dic15—41no—
196C5×Dic3—22no—
197C22×C3×C4—21no—
198C22×C3×C4C22×D511yescharacteristic
199C2×#67—21no—
200#235—21no—
201#235—21no—
202#235Dic1012yes—
203#235C22⋊D512yes—
204C2×D12C4×D511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C4×D511yescharacteristic
207C2×C3×C8—51no—
208C2×C3×C8—51no—
209C2×C3×C8—51no—
210C2×C3×C8—51no—
211C2×C3×C8—101no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215C3×C42—21no—
216C3×C42—21no—
217#217—101no—
218C4⋊Dic3—51no—
219C4⋊Dic3—51no—
220C4×Dic3—101no—
221#208—21no—
222#208—21no—
223#208—52no—
224#208—101no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—101no—
227ΓL(1,𝔽25)—104no—
228D3×C8—104no—
229C23×C5—61no—
230C23×C5#23511yescharacteristic
231C5×Q8—32no—
232C5×Q8—61no—
233C5×D4—32no—
234C5×D4—62no—
235C5×D4—62no—
236C5×D4—61no—
237C2×C4×C5—22no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—61no—
241C2×C4×C5—62no—
242C2×C4×C5—62no—
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5C2×D1211yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5D3×Q811yescharacteristic
249C2×Dic5—61no—
250C2×Dic5—61no—
251C5×C8—121no—
252#168—21no—
253#168—21no—
254#168—21no—
255#168—21no—
256#168—62no—
257C2×#41—31no—
258#131—302no—
259#131—302no—
260C2×M16—31no—
261C2×M16—151no—
262C2×M16—301no—
263C22×C8—51no—
264C22×C8—51no—
265C22×C8—301no—
266#117—151no—
267C2×C42D3×D511yescharacteristic
268#108—302no—
269C4⋊C8—301no—
270C4⋊C8—301no—
271#104—62no—
272#103—151no—
273#103—151no—
274#102—151no—
275#102—151no—
276C2×C3×C5—21no—
277C2×C3×C5—21no—
278C2×C3×C5#38511yescharacteristic
279C2×C3×C5#44311yescharacteristic
280C2×C3×C5#44411yescharacteristic
281C5×D3—42no—
282C23×C3#71111yescharacteristic
283C22×D3—21no—
284C2×C3×C4—22no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4C2×Dic1011yescharacteristic
288C2×C3×C4C2×C4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4C2×C22⋊D511yescharacteristic
293#67—22no—
294#67—22no—
295C2×Dic3—21no—
296C2×Dic3—101no—
297C2×Dic3—101no—
298D12—21no—
299D12#68312yes—
300C4×D3—22no—
301C4×D3—22no—
302Dic6—21no—
303Dic6#68312yes—
304C3×C8—101no—
305C3×C8—101no—
306C3×C8—101no—
307C3×C8—101no—
308C3⋊C8—41no—
309C3⋊C8—102no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—62no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5C4×D1211yescharacteristic
316C22×C5#88311yescharacteristic
317C22×C5#89611yescharacteristic
318C4×C5—42no—
319C4×C5—62no—
320C4×C5#67⋊C411yescharacteristic
321C4×C5#88211yescharacteristic
322C4×C5D3×C4⋊C411yescharacteristic
323C4×C5#89711yescharacteristic
324Dic5—121no—
325Dic5—121no—
326#41—32no—
327#41—32no—
328#41—61no—
329#41—61no—
330C2×Q8—31no—
331C2×D4—31no—
332C2×D4—61no—
333C22×C4—21no—
334C22×C4—61no—
335C22×C4C2×D3×D511yescharacteristic
336M16—61no—
337M16—61no—
338M16—152no—
339M16—304no—
340M16—301no—
341C2×C8—51no—
342C2×C8—51no—
343C2×C8—51no—
344C2×C8—51no—
345C2×C8—61no—
346C2×C8—101no—
347C2×C8—101no—
348C2×C8—101no—
349C2×C8—101no—
350C2×C8—304no—
351C2×C8—301no—
352C4⋊C4—151no—
353C4⋊C4—151no—
354C22⋊C4—301no—
355C42—21no—
356C42—21no—
357C42—301no—
358C3×C5#186611yescharacteristic, complemented, Hall
359C22×C3—21no—
360C22×C3—21no—
361C22×C3#402411yescharacteristic
362C22×C3#402711yescharacteristic
363C22×C3#408111yescharacteristic
364C2×D3—22no—
365C2×D3—41no—
366C2×D3—41no—
367C3×C4—42no—
368C3×C4#402411yescharacteristic
369C3×C4#402711yescharacteristic
370C3×C4C2×#68311yescharacteristic
371C3×C4#408311yescharacteristic
372Dic3—22no—
373Dic3—201no—
374Dic3—201no—
375C2×C5—21no—
376C2×C5—21no—
377C2×C5—122no—
378C2×C5#466811yescharacteristic
379C2×C5#470011yescharacteristic
380C2×C5#471711yescharacteristic
381C23—61no—
382C23#678211yescharacteristic
383Q8—32no—
384Q8—61no—
385D4—32no—
386D4—62no—
387D4—62no—
388D4—61no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—61no—
393C2×C4—62no—
394C2×C4—62no—
395C2×C4—301no—
396C2×C4—301no—
397C2×C4D3×Dic1011yescharacteristic
398C2×C4C4×D3×D511yescharacteristic
399C2×C4D5×D1211yescharacteristic
400C2×C4#677711yescharacteristic
401C2×C4#678011yescharacteristic
402C2×C4D3×C22⋊D511yescharacteristic
403C8—101no—
404C8—101no—
405C8—101no—
406C8—101no—
407C8—121no—
408C8—302no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3#6511211yescharacteristic
412C2×C3#6511311yescharacteristic
413C2×C3#6523511yescharacteristic
414D3—42no—
415C5#6869411yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—62no—
419C22—121no—
420C22—121no—
421C22#9140511yescharacteristic
422C22#9143611yescharacteristic
423C22#9155511yescharacteristic
424C4—42no—
425C4—62no—
426C4—601no—
427C4—601no—
428C4D3×#68311yescharacteristic
429C4#9141711yescharacteristic
430C4#9144211yescharacteristic
431C4#9147511yescharacteristic
432C3#1060116911yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—122no—
436C2#1174701811yescharacteristic
437C2#1174701911yescharacteristic
438C2#1174889311yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1866
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×#90991C2semidirect
4. #11748435C2semidirect
6. #11746344C2semidirect
7. C3×#64744C2semidirect
24. #90973C4semidirect
25. #90973C4semidirect
26. #90967C4semidirect
27. #90967C4semidirect
34. #64744D3semidirect
358. C3×C5#1866semidirect
415. C5#68694semidirect
432. C3#10601169semidirect

Maximal subgroups

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

subgroupindex
C2×#912862
C2×C5×#8052
C2×#909912
#117484352
#117483882
#117463442
C3×#647442
#106011693
#686945