Finite Group Databasebeta

← #14303068

Subgroups — #14303068

Order 1920.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5525C211yesmaximal, characteristic
2#11754125C211yesmaximal, characteristic, complemented
3#11748355C211yesmaximal, characteristic, complemented
4C2×#90959C211yesmaximal, characteristic, complemented
5C2×#90959C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7C3×#64753C211yesmaximal, characteristic, complemented
8#10602648—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#895—22no—
15C5×#882C414yes—
16C5×#875—21no—
17C5×#874—21no—
18C2×C3×#681C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91288—22no—
21D3×#681—22no—
22#91286—22no—
23#90962—21no—
24#90959—21no—
25#90959—22no—
26#90959—22no—
27#69040—51nomaximal, Hall
28C5×#535—31no—
29#66153—31no—
30#65526—31no—
31C2×#3965—31no—
32C2×#3965—31no—
33#64753—31no—
34#64753D311yescharacteristic, complemented
35C23×C5×D3C2×C412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×C5×#67C2×C412yes—
38C5×#235—21no—
39C5×#235—21no—
40C5×#235—21no—
41C5×#235—21no—
42C2×C5×D12—21no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—24no—
49C2×C5×D12D411yescharacteristic
50C2×C4×C5×D3D412yes—
51C2×C5×Dic6D411yescharacteristic
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4C2×C412yes—
54C3×C42×C5—21no—
55#6710—21no—
56#6710—21no—
57#6710—21no—
58#6710D412yescomplemented
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C5×(C2×D3)⋊C4—24no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C3×#681D412yescomplemented
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68#6650—24no—
69D3×#168—24no—
70#5745—51no—
71#5525D511yescharacteristic
72#5132—51no—
73C2×#823—51no—
74C2×#823—51no—
75C3×#344—51no—
76#4533—51no—
77C2×C5×#41—31no—
78C22×C5×D4—31no—
79C5×#127—61no—
80C5×#124—61no—
81C5×#121—62no—
82C5×#120—34no—
83C5×#117C2×D311yescharacteristic
84#4094—62no—
85#4094—62no—
86C2×#681—31no—
87C2×#681—31no—
88C2×#681—62no—
89C2×#681C2×D311yescharacteristic
90C2×#681C2×D311yescharacteristic
91#3968—61no—
92#3965—62no—
93#3965—61no—
94#3965—62no—
95#1914—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C5×D3—22no—
98C22×C5×D3—22no—
99C22×C5×D3—22no—
100C22×C5×D3—82no—
101C22×C5×D3C22⋊C412yes—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109C5×#67—22no—
110C5×#67—22no—
111C2×C5×Dic3C22⋊C412yes—
112C5×D12—21no—
113C5×D12—21no—
114C5×D12—41no—
115C5×D12—41no—
116C5×D12—41no—
117C5×D12—41no—
118C5×D12—84no—
119C4×C5×D3—22no—
120C4×C5×D3—22no—
121C5×Dic6—21no—
122C5×Dic6—21no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C3×#168—22no—
126C3×#168—41no—
127C2×#235C2×D511yescharacteristic
128C22×D12C2×D511yescharacteristic
129C2×C3×M16—51no—
130C2×C3×M16—51no—
131C3×#117C2×D511yescharacteristic
132C2×#208—51no—
133C2×#208—51no—
134#907—102no—
135D3×M16—102no—
136#901—102no—
137#895—22no—
138#882Dic514yes—
139#875—21no—
140#874—21no—
141#824—101no—
142#823—102no—
143#823—102no—
144#823—101no—
145C24×C5—32no—
146C5×#41—61no—
147C5×#41—61no—
148C5×#41—61no—
149C5×#41—61no—
150C2×C5×Q8—31no—
151C2×C5×D4—32no—
152C2×C5×D4—31no—
153C2×C5×D4—64no—
154C2×C5×D4—61no—
155C2×C5×D4—61no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C2×C5×D4—61no—
159C2×C5×D4—61no—
160C22×C4×C5—32no—
161C22×C4×C5C22×D311yescharacteristic
162C5×C4⋊C4—21no—
163C5×C22⋊C4—64no—
164C5×C22⋊C4C4×D312yes—
165C42×C5—21no—
166#681—21no—
167#681—21no—
168#681—21no—
169#681—32no—
170#681—64no—
171#681—61no—
172#681—61no—
173#681—61no—
174#681D1212yescomplemented
175C2×#168—21no—
176C2×#168—21no—
177C2×#168—64no—
178C2×#168—61no—
179C2×#168—61no—
180#568—151no—
181#535—31no—
182#413—151no—
183C2×#100—151no—
184C2×#100—151no—
185#344—51no—
186#344—151no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5C4×D411yescharacteristic
190C22×C3×C5C4×D411yescharacteristic
191C2×C5×D3—22no—
192C2×C5×D3—42no—
193C2×C5×D3—44no—
194C2×C5×D3—42no—
195C2×C5×D3—82no—
196C2×C5×D3—82no—
197C3×C4×C5—42no—
198C3×C4×C5#12011yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201C3×C4×C5#12311yescharacteristic
202C5×Dic3—22no—
203C23×D3C2×Dic512yes—
204C22×C3×C4C22×D511yescharacteristic
205C2×#67C2×Dic512yes—
206#235—21no—
207#235—21no—
208#235—21no—
209#235—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—24no—
217C2×D12C22⋊D511yescharacteristic
218C2×C4×D3C22⋊D512yes—
219C2×Dic6C22⋊D511yescharacteristic
220C3×M16—52no—
221C3×M16—101no—
222C3×M16—101no—
223C3×M16—101no—
224C2×C3×C8—101no—
225C2×C3×C8—101no—
226C3×C4⋊C4—21no—
227C3×C22⋊C4C2×Dic512yes—
228C3×C42—21no—
229(C2×D3)⋊C4—24no—
230#208—52no—
231#208—101no—
232#208—101no—
233#208—101no—
234C2×C3⋊C8—101no—
235C2×C3⋊C8—101no—
236ΓL(1,𝔽25)—104no—
237D3×C8—104no—
238C23×C5—32no—
239C23×C5—62no—
240C23×C5—62no—
241C23×C5—62no—
242C23×C5—242no—
243C23×C5C2×C4×D311yescharacteristic
244C5×Q8—61no—
245C5×Q8—61no—
246C5×D4—62no—
247C5×D4—62no—
248C5×D4—61no—
249C5×D4—61no—
250C5×D4—121no—
251C5×D4—121no—
252C5×D4—121no—
253C5×D4—121no—
254C5×D4—244no—
255C2×C4×C5—22no—
256C2×C4×C5—32no—
257C2×C4×C5—62no—
258C2×C4×C5—62no—
259C2×C4×C5C2×D1211yescharacteristic
260C2×C4×C5#23511yescharacteristic
261C2×C4×C5D3×D411yescharacteristic
262C2×C4×C5D3×D411yescharacteristic
263C2×C4×C5D3×D411yescharacteristic
264C2×C4×C5#23911yescharacteristic
265#168—22no—
266#168—41no—
267#168—62no—
268#168—121no—
269C2×#41—31no—
270C22×D4—31no—
271#131—302no—
272#131—302no—
273C2×M16—51no—
274C2×M16—51no—
275C2×M16—151no—
276C2×M16—151no—
277C2×M16—302no—
278#127—61no—
279#124—61no—
280#121—62no—
281#120—34no—
282#117D3×D511yescharacteristic
283#101—301no—
284#100—302no—
285#100—302no—
286#100—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291C5×D3—42no—
292C5×D3—82no—
293C23×C3C22×Dic511yescharacteristic
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—82no—
298C22×D3C22⋊Dic512yes—
299C2×C3×C4—22no—
300C2×C3×C4D4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4#71111yescharacteristic
303C2×C3×C4#71111yescharacteristic
304C2×C3×C4C2×C22⋊D511yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306#67—22no—
307#67—22no—
308C2×Dic3C22⋊Dic512yes—
309D12—21no—
310D12—21no—
311D12—41no—
312D12—41no—
313D12—41no—
314D12—41no—
315D12—84no—
316C4×D3—22no—
317C4×D3—22no—
318Dic6—21no—
319Dic6—21no—
320C3×C8—102no—
321C3×C8—201no—
322C3⋊C8—102no—
323C3⋊C8—201no—
324C22×C5—41no—
325C22×C5—62no—
326C22×C5—122no—
327C22×C5—124no—
328C22×C5—122no—
329C22×C5—242no—
330C22×C5—242no—
331C22×C5C4×D1211yescharacteristic
332C22×C5D3×C22⋊C411yescharacteristic
333C22×C5#89311yescharacteristic
334C4×C5—42no—
335C4×C5—62no—
336C4×C5#88211yescharacteristic
337C4×C5#88411yescharacteristic
338C4×C5#89411yescharacteristic
339C4×C5#89511yescharacteristic
340C24—32no—
341#41—61no—
342#41—61no—
343#41—61no—
344#41—61no—
345C2×Q8—31no—
346C2×D4—32no—
347C2×D4—31no—
348C2×D4—64no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C22×C4—32no—
356C22×C4C2×D3×D511yescharacteristic
357M16—52no—
358M16—101no—
359M16—101no—
360M16—101no—
361M16—152no—
362M16—304no—
363M16—301no—
364M16—301no—
365M16—301no—
366C2×C8—101no—
367C2×C8—101no—
368C2×C8—304no—
369C2×C8—301no—
370C2×C8—301no—
371C4⋊C4—21no—
372C22⋊C4—64no—
373C22⋊C4D3×Dic512yes—
374C42—21no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3D4×Dic511yescharacteristic
378C22×C3D4×Dic511yescharacteristic
379C22×C3C2×C22⋊Dic511yescharacteristic
380C2×D3—22no—
381C2×D3—42no—
382C2×D3—44no—
383C2×D3—42no—
384C2×D3—82no—
385C2×D3—82no—
386C3×C4—42no—
387C3×C4#408111yescharacteristic
388C3×C4#408311yescharacteristic
389C3×C4#408511yescharacteristic
390C3×C4#408511yescharacteristic
391Dic3—22no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5—122no—
396C2×C5—242no—
397C2×C5#466511yescharacteristic
398C23—32no—
399C23—62no—
400C23—62no—
401C23—62no—
402C23—242no—
403C23C2×D3×Dic511yescharacteristic
404Q8—61no—
405Q8—61no—
406D4—62no—
407D4—62no—
408D4—61no—
409D4—61no—
410D4—121no—
411D4—121no—
412D4—121no—
413D4—121no—
414D4—244no—
415C2×C4—22no—
416C2×C4—32no—
417C2×C4—62no—
418C2×C4—62no—
419C2×C4#676811yescharacteristic
420C2×C4#677211yescharacteristic
421C2×C4D5×D1211yescharacteristic
422C2×C4#677711yescharacteristic
423C2×C4D3×C22⋊D511yescharacteristic
424C2×C4D3×C22⋊D511yescharacteristic
425C8—102no—
426C8—201no—
427C8—302no—
428C8—601no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3#6550911yescharacteristic
433D3—42no—
434D3—82no—
435C5#6904011yescharacteristic, complemented, Sylow
436C22—41no—
437C22—62no—
438C22—122no—
439C22—124no—
440C22—122no—
441C22—242no—
442C22—242no—
443C22Dic5×D1211yescharacteristic
444C22#9143511yescharacteristic
445C22D3×C22⋊Dic511yescharacteristic
446C4—42no—
447C4—62no—
448C4#9141611yescharacteristic
449C4#9142311yescharacteristic
450C4#9145311yescharacteristic
451C4#9147511yescharacteristic
452C3#1060264811yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—122no—
457C2—242no—
458C2#1174890111yescharacteristic
subgroupG/H
centerC2#11748901
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC5×#5525C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1914
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754125C2semidirect
3. #11748355C2semidirect
4. C2×#90959C2semidirect
5. C2×#90959C2semidirect
6. #11746354C2semidirect
7. C3×#64753C2semidirect
34. #64753D3semidirect
58. #6710D4semidirect
65. C3×#681D4semidirect
174. #681D12semidirect
375. C3×C5#1914semidirect
435. C5#69040semidirect
452. C3#10602648semidirect

Maximal subgroups

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

subgroupindex
C5×#55252
#117541252
#117483552
C2×#909592
#117463542
C3×#647532
#106026483
#690405