Finite Group Databasebeta

← #14284054

Subgroups — #14284054

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×D3×#124C211yesmaximal, characteristic
2#11747005C211yesmaximal, characteristic, complemented
3#11746878C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6#11745847C211yesmaximal, characteristic, complemented
7#11745847C211yesmaximal, characteristic, complemented
8#10602511—31nomaximal, Hall
9C2×C5×D3×Q8C411yescharacteristic
10C2×C5×D3×D4C411yescharacteristic
11C3×C5×#124C2211yescharacteristic
12C5×#947C411yescharacteristic
13C5×#936C411yescharacteristic
14C5×#885—21no—
15C5×#885—21no—
16C5×D3×C22⋊C4—21no—
17C5×D3×C22⋊C4—21no—
18C5×#875C2211yescharacteristic
19C42×C5×D3C2211yescharacteristic
20C2×#6650—21no—
21#91087C2211yescharacteristic, complemented
22#91087C2211yescharacteristic, complemented
23C3×#3935C2211yescharacteristic, complemented
24C3×#3935C2211yescharacteristic, complemented
25Dic3⋊#168—21no—
26(C2×D3)⋊#168—21no—
27Dic3×#168—21no—
28#68343—51nomaximal, Hall
29C2×C5×#124—31no—
30#65215—31no—
31C4×#681—31no—
32#64760—31no—
33#64760—31no—
34#64760—31no—
35#64760D311yescharacteristic, complemented
36C23×C5×D3—21no—
37C2×C3×C5×Q8C2×C411yescharacteristic
38C2×C3×C5×D4C2×C411yescharacteristic
39C2×C5×#67—21no—
40C5×D3×Q8—42no—
41C5×D3×D4—42no—
42C2×C5×D12C2×C411yescharacteristic
43C2×C4×C5×D3—21no—
44C2×C4×C5×D3C2×C411yescharacteristic
45C2×C4×C5×D3D411yescharacteristic
46C2×C4×C5×D3D411yescharacteristic
47C2×C5×Dic6—21no—
48C2×C5×Dic6C2×C411yescharacteristic
49C3×C5×C22⋊C4—21no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5C2311yescharacteristic
52C2×C3⋊#168—21no—
53C2×C3⋊#168—21no—
54C5×#217—21no—
55C5×#217—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×(C2×D3)⋊C4—21no—
59C5×(C2×D3)⋊C4—21no—
60C4×C5×Dic3C2×C411yescharacteristic
61C4×C5×Dic3D411yescharacteristic
62C4×C5×Dic3D411yescharacteristic
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65#6650—24no—
66D3×#124D511yescharacteristic
67#4707—51no—
68#4705—51no—
69C3×#329—51no—
70#4540—51no—
71#4464—51no—
72#4464—51no—
73C22×C5×Q8—31no—
74C22×C5×D4—31no—
75C5×#124—31no—
76C5×#124—31no—
77C5×#124—31no—
78C5×#124—61no—
79C5×#124—61no—
80C5×#124C2×D311yescharacteristic
81C2×C5×C22⋊C4—61no—
82C2×C5×C22⋊C4—61no—
83C2×C42×C5—31no—
84C2×#681—61no—
85C22⋊#168—61no—
86C4⋊#168—61no—
87#3935—31no—
88#3935—31no—
89#3935C2×D311yescharacteristic, complemented
90#3935C2×D311yescharacteristic, complemented
91C4×#168—61no—
92#1527—151noSylow
93C23×C3×C5—21no—
94C22×C5×D3—21no—
95C22×C5×D3—42no—
96C22×C5×D3—42no—
97C22×C5×D3—42no—
98C22×C5×D3C22⋊C411yescharacteristic
99C3×C5×Q8—41no—
100C3×C5×D4—41no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C5×#67—42no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3C22⋊C411yescharacteristic
108C2×C5×Dic3C22⋊C411yescharacteristic
109C2×C5×Dic3C22⋊C411yescharacteristic
110C5×D12—41no—
111C4×C5×D3—22no—
112C4×C5×D3—22no—
113C4×C5×D3—41no—
114C4×C5×D3—42no—
115C5×Dic6—42no—
116C5×Dic6—41no—
117C3⋊#168—22no—
118C3⋊#168—41no—
119C3×#168—22no—
120C3×#168—41no—
121C2×D3×Q8Dic511yescharacteristic
122C2×D3×D4Dic511yescharacteristic
123C3×#124C2×D511yescharacteristic
124#947Dic511yescharacteristic
125#936Dic511yescharacteristic
126C2×ΓL(1,𝔽25)—101no—
127#885—21no—
128#885—21no—
129D3×C22⋊C4—21no—
130D3×C22⋊C4—21no—
131#875C2×D511yescharacteristic
132C42×D3C2×D511yescharacteristic
133C3×#97—51no—
134C3×#97—51no—
135(C2×D3)⋊C8—101no—
136Dic3⋊C8—101no—
137C8×Dic3—101no—
138#803—51no—
139#803—51no—
140C24×C5—61no—
141C2×C5×Q8—31no—
142C2×C5×Q8—61no—
143C2×C5×Q8—122no—
144C2×C5×Q8C4×D311yescharacteristic
145C2×C5×D4—31no—
146C2×C5×D4—61no—
147C2×C5×D4—122no—
148C2×C5×D4C4×D311yescharacteristic
149C22×C4×C5—31no—
150C22×C4×C5—31no—
151C22×C4×C5—31no—
152C22×C4×C5—61no—
153C5×C22⋊C4—21no—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—61no—
161C42×C5—31no—
162C42×C5—31no—
163C42×C5—31no—
164C42×C5C22×D311yescharacteristic
165#681—64no—
166C2×#168—21no—
167C2×#168—21no—
168C2×#168—61no—
169C2×#168—61no—
170C2×#124—31no—
171#432—151no—
172C4×M16—151no—
173#329—51no—
174#329—151no—
175#329—151no—
176#329—151no—
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C2×C5×D3—21no—
182C2×C5×D3—21no—
183C2×C5×D3—41no—
184C2×C5×D3—41no—
185C2×C5×D3—41no—
186C2×C5×D3—84no—
187C2×C5×D3#10412yes—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C5×Dic3—21no—
193C5×Dic3—21no—
194C5×Dic3—41no—
195C5×Dic3#10012yes—
196C23×D3—21no—
197C2×C3×Q8C2×Dic511yescharacteristic
198C2×C3×D4C2×Dic511yescharacteristic
199C2×#67—21no—
200D3×Q8—42no—
201D3×D4—42no—
202C2×D12C2×Dic511yescharacteristic
203C2×C4×D3—21no—
204C2×C4×D3C2×Dic511yescharacteristic
205C2×C4×D3C22⋊D511yescharacteristic
206C2×C4×D3C22⋊D511yescharacteristic
207C2×Dic6—21no—
208C2×Dic6C2×Dic511yescharacteristic
209C2×C3×C8—101no—
210C2×C3×C8—101no—
211C3×C22⋊C4—21no—
212C3×C22⋊C4—21no—
213C3×C42C22×D511yescharacteristic
214#217—21no—
215#217—21no—
216(C2×D3)⋊C4—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—21no—
220C4×Dic3C2×Dic511yescharacteristic
221C4×Dic3C22⋊D511yescharacteristic
222C4×Dic3C22⋊D511yescharacteristic
223C2×C3⋊C8—101no—
224C2×C3⋊C8—101no—
225ΓL(1,𝔽25)—104no—
226C23×C5—21no—
227C23×C5—31no—
228C23×C5—61no—
229C23×C5—122no—
230C23×C5—122no—
231C23×C5—122no—
232C5×Q8—41no—
233C5×Q8—121no—
234C5×Q8—122no—
235C5×D4—41no—
236C5×D4—121no—
237C5×D4—122no—
238C2×C4×C5—21no—
239C2×C4×C5—31no—
240C2×C4×C5—31no—
241C2×C4×C5—31no—
242C2×C4×C5—62no—
243C2×C4×C5—62no—
244C2×C4×C5—61no—
245C2×C4×C5—121no—
246C2×C4×C5—122no—
247C2×C4×C5C2×C4×D311yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250#168—22no—
251#168—41no—
252#168—62no—
253#168—121no—
254C22×Q8—31no—
255C22×D4—31no—
256C2×M16—301no—
257#124—31no—
258#124—31no—
259#124—31no—
260#124—61no—
261#124—61no—
262#124D3×D511yescharacteristic
263C2×C22⋊C4—61no—
264C2×C22⋊C4—61no—
265C2×C42—31no—
266C4⋊C8—301no—
267C22⋊C8—301no—
268#97—51no—
269#97—51no—
270#97—151no—
271#97—151no—
272C4×C8—301no—
273C2×C3×C5—81no—
274C2×C3×C5C2×#10011yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C2×C3×C5#42111yescharacteristic
277C5×D3—22no—
278C5×D3—81no—
279C23×C3—21no—
280C22×D3—21no—
281C22×D3—42no—
282C22×D3—42no—
283C22×D3—42no—
284C22×D3C22⋊Dic511yescharacteristic
285C3×Q8—41no—
286C3×D4—41no—
287C2×C3×C4—21no—
288C2×C3×C4C22×Dic511yescharacteristic
289C2×C3×C4C2×C22⋊D511yescharacteristic
290C2×C3×C4C2×C22⋊D511yescharacteristic
291#67—42no—
292C2×Dic3—21no—
293C2×Dic3C22⋊Dic511yescharacteristic
294C2×Dic3C22⋊Dic511yescharacteristic
295C2×Dic3C22⋊Dic511yescharacteristic
296D12—41no—
297C4×D3—22no—
298C4×D3—22no—
299C4×D3—41no—
300C4×D3—42no—
301Dic6—42no—
302Dic6—41no—
303C3×C8—102no—
304C3×C8—201no—
305C3⋊C8—102no—
306C3⋊C8—201no—
307C22×C5—32no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5—41no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5—121no—
314C22×C5—121no—
315C22×C5—121no—
316C22×C5—244no—
317C22×C5D3×C22⋊C411yescharacteristic
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—32no—
322C4×C5—41no—
323C4×C5—61no—
324C4×C5—61no—
325C4×C5—121no—
326C24—61no—
327C2×Q8—31no—
328C2×Q8—61no—
329C2×Q8—122no—
330C2×Q8D3×Dic511yescharacteristic
331C2×D4—31no—
332C2×D4—61no—
333C2×D4—122no—
334C2×D4D3×Dic511yescharacteristic
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—61no—
339M16—304no—
340C2×C8—101no—
341C2×C8—101no—
342C2×C8—301no—
343C2×C8—301no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C22⋊C4—61no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C42—31no—
353C42—31no—
354C42—31no—
355C42C2×D3×D511yescharacteristic
356C3×C5#152711yescharacteristic, complemented, Hall
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3C2×C22⋊Dic511yescharacteristic
361C2×D3—21no—
362C2×D3—21no—
363C2×D3—41no—
364C2×D3—41no—
365C2×D3—41no—
366C2×D3—84no—
367C2×D3#396912yes—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372Dic3—21no—
373Dic3—21no—
374Dic3—41no—
375Dic3#396512yes—
376C2×C5—62no—
377C2×C5—81no—
378C2×C5—241no—
379C2×C5D3×#10011yescharacteristic
380C2×C5D3×#10411yescharacteristic
381C2×C5#482111yescharacteristic
382C23—21no—
383C23—31no—
384C23—61no—
385C23—122no—
386C23—122no—
387C23—122no—
388Q8—41no—
389Q8—121no—
390Q8—122no—
391D4—41no—
392D4—121no—
393D4—122no—
394C2×C4—21no—
395C2×C4—31no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—61no—
401C2×C4—121no—
402C2×C4—122no—
403C2×C4C2×D3×Dic511yescharacteristic
404C2×C4D3×C22⋊D511yescharacteristic
405C2×C4D3×C22⋊D511yescharacteristic
406C8—102no—
407C8—201no—
408C8—302no—
409C8—601no—
410C2×C3—81no—
411C2×C3C2×#396511yescharacteristic
412C2×C3C2×#396911yescharacteristic
413C2×C3#6552511yescharacteristic
414D3—22no—
415D3—81no—
416C5#6834311yescharacteristic, complemented, Sylow
417C22—32no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—61no—
422C22—61no—
423C22—121no—
424C22—121no—
425C22—121no—
426C22—244no—
427C22D3×C22⋊Dic511yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—32no—
432C4—41no—
433C4—61no—
434C4—61no—
435C4—121no—
436C3#1060251111yescharacteristic, complemented, Sylow
437C2—62no—
438C2—81no—
439C2—241no—
440C2D3×#396511yescharacteristic
441C2D3×#396911yescharacteristic
442C2#1174942911yescharacteristic
subgroupG/H
centerC22D3×C22⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×D3×D4C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1527
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11747005C2semidirect
3. #11746878C2semidirect
4. #11746361C2semidirect
5. C3×#64760C2semidirect
6. #11745847C2semidirect
7. #11745847C2semidirect
21. #91087C22semidirect
22. #91087C22semidirect
23. C3×#3935C22semidirect
24. C3×#3935C22semidirect
35. #64760D3semidirect
89. #3935C2×D3semidirect
90. #3935C2×D3semidirect
356. C3×C5#1527semidirect
416. C5#68343semidirect
436. C3#10602511semidirect

Maximal subgroups

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

subgroupindex
C5×D3×#1242
#117470052
#117468782
#117463612
C3×#647602
#117458472
#106025113
#683435