Finite Group Databasebeta

← #14300243

Subgroups — #14300243

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×#91288C211yesmaximal, characteristic
2#11751220C211yesmaximal, characteristic, complemented
3C2×C5×#825C211yesmaximal, characteristic
4C2×C3×#3954C211yesmaximal, characteristic, complemented
5#11748388C211yesmaximal, characteristic
6#11745976C211yesmaximal, characteristic, complemented
7#11745967C211yesmaximal, characteristic, complemented
8#10601169—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C4×C5×Dic3C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×#6650—21no—
17#91288—22no—
18#91288—22no—
19C2×D3×#168—21no—
20#91098—21no—
21#91098—21no—
22C5×#825—22no—
23C3×#3954—22no—
24#90973C411yescharacteristic, complemented
25#90973C411yescharacteristic, complemented
26#90967C411yescharacteristic, complemented
27#90967C411yescharacteristic, complemented
28#70722—51nomaximal, Hall
29C2×#4094—31no—
30C2×C5×#104—31no—
31#65522—31no—
32C2×#3954D311yescharacteristic, complemented
33#65408—31no—
34#64744—31no—
35#64743—31no—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C5×#67—21no—
38C22×C5×Dic3—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×C5×M16—21no—
47C3×C5×M16—21no—
48C2×C3×C5×C8—21no—
49#6719—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C4⋊Dic15C2×C411yescharacteristic
52C4×Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D411yescharacteristic
56C2×C3⋊#168D411yescharacteristic
57C4×C5×Dic3—21no—
58C4×C5×Dic3—21no—
59C3×#681—21no—
60C3×#681D412yes—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168—21no—
64C2×C3×#168C2×C411yescharacteristic
65C2×C3×#168C2×C411yescharacteristic
66#6650—24no—
67D3×#168—24no—
68C2×#907—51no—
69C2×C3×#108—51no—
70C2×#825D511yescharacteristic
71#5119—51no—
72#5113—51no—
73#4555—51no—
74#4550—51no—
75C2×C5×#41—31no—
76C2×C5×M16C2×D311yescharacteristic
77C2×C42×C5—31no—
78#4094—62no—
79#4094—62no—
80#4072—31no—
81C2×#681—61no—
82C2×#681C2×D311yescharacteristic
83C22×#168—31no—
84C22×#168—61no—
85C22×#168C2×D311yescharacteristic
86C5×#104—62no—
87#3967—31no—
88#3967—31no—
89#3964—31no—
90#3964—31no—
91#3954—22no—
92#3946—61no—
93#3946—61no—
94#1866—151noSylow
95C23×C3×C5#4111yescharacteristic
96C22×C5×D3—21no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—21no—
105C5×#67—22no—
106C5×#67—22no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C5×D12—21no—
112C5×D12C4⋊C412yes—
113C4×C5×D3—22no—
114C4×C5×D3—22no—
115C5×Dic6—21no—
116C5×Dic6C4⋊C412yes—
117C3×C5×C8—41no—
118C3⋊#168—21no—
119C3⋊#168—21no—
120C3×#168—21no—
121C3×#168—21no—
122C3×#168—22no—
123C2×#235C2×D511yescharacteristic
124C2×C3×M16—51no—
125C2×C3×M16C2×D511yescharacteristic
126C22×C3×C8—51no—
127#926—51no—
128C2×C4×Dic3C2×D511yescharacteristic
129C22×C3⋊C8—51no—
130#907—102no—
131#907—102no—
132C2×ΓL(1,𝔽25)—101no—
133C2×D3×C8—101no—
134C3×#108—102no—
135#825—22no—
136#821—51no—
137#821—51no—
138#816—51no—
139#816—51no—
140Dic3⋊C8—101no—
141Dic3⋊C8—101no—
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—61no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C5×M16—21no—
153C5×M16—21no—
154C2×C5×C8—21no—
155C42×C5—61no—
156C42×C5—61no—
157C22⋊Dic5—61no—
158C4⋊Dic5—31no—
159C4⋊Dic5—31no—
160C4×Dic5—61no—
161#681—21no—
162#681—64no—
163#681#6712yes—
164C2×#168—21no—
165C2×#168—21no—
166C2×#168—21no—
167C2×#168—31no—
168C2×#168—31no—
169C2×#168—64no—
170C2×#168—61no—
171C2×#168—61no—
172C2×#168C4×D311yescharacteristic
173C2×#168C4×D311yescharacteristic
174C2×#131—151no—
175C2×#108—51no—
176#424—151no—
177C2×#104—31no—
178#416—151no—
179#339—151no—
180#336—151no—
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×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193Dic15—41no—
194Dic15—41no—
195C5×Dic3—22no—
196C5×Dic3—42no—
197C22×C3×C4C22×D511yescharacteristic
198C2×#67—21no—
199C22×Dic3—21no—
200#235—21no—
201#235—21no—
202#235Dic1012yes—
203#235C22⋊D512yes—
204C2×D12C4×D511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C4×D511yescharacteristic
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—52no—
210C3×M16—101no—
211C2×C3×C8—21no—
212C2×C3×C8—51no—
213C2×C3×C8—51no—
214C2×C3×C8—101no—
215C2×C3×C8—101no—
216C2×C3×C8—101no—
217#217—101no—
218C4⋊Dic3—51no—
219C4⋊Dic3—51no—
220C4×Dic3—21no—
221C4×Dic3—21no—
222C4×Dic3—101no—
223C2×C3⋊C8—51no—
224C2×C3⋊C8—51no—
225C2×C3⋊C8—101no—
226C2×C3⋊C8—101no—
227ΓL(1,𝔽25)—104no—
228D3×C8—104no—
229C23×C5—61no—
230C23×C5#23911yescharacteristic
231C5×Q8—32no—
232C5×Q8—61no—
233C5×D4—32no—
234C5×D4—62no—
235C5×D4—62no—
236C5×D4—61no—
237C2×C4×C5—61no—
238C2×C4×C5—62no—
239C2×C4×C5—62no—
240C2×C4×C5—62no—
241C2×C4×C5—121no—
242C2×C4×C5—121no—
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×Q811yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C2×Dic5—61no—
250C2×Dic5—61no—
251C5×C8—41no—
252#168—21no—
253#168—21no—
254#168—22no—
255#168—61no—
256#168—61no—
257C2×#41—31no—
258#131—302no—
259#131—302no—
260C2×M16—51no—
261C2×M16—301no—
262C2×M16D3×D511yescharacteristic
263C22×C8—51no—
264C22×C8—151no—
265C22×C8—301no—
266#117—151no—
267C2×C42—31no—
268#108—102no—
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×C4C2×Dic1011yescharacteristic
285C2×C3×C4C2×C4×D511yescharacteristic
286C2×C3×C4D4×D511yescharacteristic
287C2×C3×C4D4×D511yescharacteristic
288C2×C3×C4#71111yescharacteristic
289C2×C3×C4C2×C22⋊D511yescharacteristic
290#67—22no—
291#67—22no—
292C2×Dic3—21no—
293C2×Dic3—22no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—101no—
297C2×Dic3—101no—
298D12—21no—
299D12#68312yes—
300C4×D3—22no—
301C4×D3—22no—
302Dic6—21no—
303Dic6#68312yes—
304C3×C8—41no—
305C3×C8—101no—
306C3×C8—101no—
307C3×C8—102no—
308C3⋊C8—101no—
309C3⋊C8—101no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—62no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5#89311yescharacteristic
316C22×C5#89411yescharacteristic
317C22×C5#94611yescharacteristic
318C4×C5—62no—
319C4×C5—122no—
320C4×C5D3×C4⋊C411yescharacteristic
321C4×C5#89611yescharacteristic
322C4×C5C4×#6711yescharacteristic
323C4×C5#93711yescharacteristic
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—61no—
334C22×C4—61no—
335C22×C4C2×D3×D511yescharacteristic
336M16—21no—
337M16—21no—
338M16—52no—
339M16—101no—
340M16—304no—
341C2×C8—21no—
342C2×C8—51no—
343C2×C8—51no—
344C2×C8—101no—
345C2×C8—101no—
346C2×C8—101no—
347C2×C8—151no—
348C2×C8—151no—
349C2×C8—304no—
350C2×C8—301no—
351C2×C8—301no—
352C4⋊C4—151no—
353C4⋊C4—151no—
354C22⋊C4—301no—
355C42—61no—
356C42—61no—
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#402411yescharacteristic
368C3×C4#402711yescharacteristic
369C3×C4C2×#68311yescharacteristic
370C3×C4#408311yescharacteristic
371Dic3—22no—
372Dic3—42no—
373Dic3—201no—
374Dic3—201no—
375C2×C5—21no—
376C2×C5—21no—
377C2×C5—122no—
378C2×C5#489411yescharacteristic
379C2×C5#489511yescharacteristic
380C2×C5#498911yescharacteristic
381C23—61no—
382C23#676811yescharacteristic
383Q8—32no—
384Q8—61no—
385D4—32no—
386D4—62no—
387D4—62no—
388D4—61no—
389C2×C4—61no—
390C2×C4—62no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—121no—
394C2×C4—121no—
395C2×C4—301no—
396C2×C4—301no—
397C2×C4D3×Dic1011yescharacteristic
398C2×C4#677211yescharacteristic
399C2×C4C4×D3×D511yescharacteristic
400C2×C4D5×#6711yescharacteristic
401C2×C4D3×C22⋊D511yescharacteristic
402C2×C4#679011yescharacteristic
403C8—41no—
404C8—101no—
405C8—101no—
406C8—102no—
407C8—301no—
408C8—301no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3#6511211yescharacteristic
412C2×C3#6511311yescharacteristic
413C2×C3#6523511yescharacteristic
414D3—42no—
415C5#7072211yescharacteristic, complemented, Sylow
416C22—21no—
417C22—21no—
418C22—62no—
419C22—121no—
420C22—121no—
421C22#9140611yescharacteristic
422C22#9141011yescharacteristic
423C22#9142311yescharacteristic
424C4—62no—
425C4—122no—
426C4—601no—
427C4—601no—
428C4D3×#68311yescharacteristic
429C4#9143211yescharacteristic
430C4#9144011yescharacteristic
431C4#9157711yescharacteristic
432C3#1060116911yescharacteristic, complemented, Sylow
433C2—21no—
434C2—21no—
435C2—122no—
436C2#1174817611yescharacteristic
437C2#1174817711yescharacteristic
438C2#1174889211yescharacteristic
subgroupG/H
centerC2×C4#6790
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C4×D4
prime radicalC2×C5×#235C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1866
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11751220C2semidirect
4. C2×C3×#3954C2semidirect
6. #11745976C2semidirect
7. #11745967C2semidirect
24. #90973C4semidirect
25. #90973C4semidirect
26. #90967C4semidirect
27. #90967C4semidirect
32. C2×#3954D3semidirect
358. C3×C5#1866semidirect
415. C5#70722semidirect
432. C3#10601169semidirect

Maximal subgroups

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

subgroupindex
C2×#912882
#117512202
C2×C5×#8252
C2×C3×#39542
#117483882
#117459762
#117459672
#106011693
#707225