Finite Group Databasebeta

← #14299551

Subgroups — #14299551

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#681C211yesmaximal, characteristic
2C5×#5126C211yesmaximal, characteristic
3C2×#90992C211yesmaximal, characteristic, complemented
4C2×#90991C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊#168C211yesmaximal, characteristic
6#11746379C211yesmaximal, characteristic, complemented
7C3×#64778C211yesmaximal, characteristic, complemented
8#10600777—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×#681C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16C2×#6650—21no—
17D3×#681—22no—
18D3×#681—22no—
19C2×D3×#168—21no—
20C5×(C2×D3)⋊C8—21no—
21C5×(C2×D3)⋊C8—21no—
22#90992—22no—
23#90991—22no—
24(C2×D3)⋊#168C412yes—
25(C2×D3)⋊#168C412yes—
26#68941—51nomaximal, Hall
27C22×#681—31no—
28C5×#407—31no—
29C2×C22⋊#168—31no—
30C2×#3954—31no—
31C2×#3954—31no—
32#64778—31no—
33#64778D311yescharacteristic, complemented
34C23×C5×D3Q811yescharacteristic
35C22×C3×C4×C5C2311yescharacteristic
36C22×C5×Dic3Q811yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C4×C5×D3—21no—
39C2×C4×C5×D3—21no—
40C2×C4×C5×D3—21no—
41C2×C4×C5×D3C2×C411yescharacteristic
42C2×C4×C5×D3C2×C411yescharacteristic
43C2×C4×C5×D3D411yescharacteristic
44C2×C4×C5×D3D411yescharacteristic
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C2×C3×C5×C8—21no—
48#6710—21no—
49#6710D412yes—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168—21no—
53C2×C3⋊#168C2×C412yes—
54C5×#208—21no—
55C5×#208—21no—
56C2×C5×C3⋊C8—21no—
57C3×#681—21no—
58C3×#681D412yes—
59C2×C3×#168—21no—
60C2×C3×#168—21no—
61C2×C3×#168—21no—
62C2×C3×#168C2×C412yes—
63#6650—24no—
64D3×#168—24no—
65C2×D3×M16—51no—
66#5126D511yescharacteristic
67C2×#822—51no—
68C2×(C2×D3)⋊C8—51no—
69C2×#819—51no—
70C3×#341—51no—
71#4558—51no—
72C23×C4×C5—31no—
73C2×C5×M16—31no—
74C2×C5×M16C2×D311yescharacteristic
75C2×#681—31no—
76C2×#681—61no—
77C2×#681—62no—
78C2×#681—62no—
79C2×#681C2×D311yescharacteristic
80C22×#168—31no—
81C22×#168—61no—
82C22×#168C2×D311yescharacteristic
83C5×C22⋊C8—61no—
84C5×C22⋊C8—61no—
85C22⋊#168—32no—
86C22⋊#168—32no—
87#3954—62no—
88#3954—62no—
89#1855—151noSylow
90C23×C3×C5C2×Q811yescharacteristic
91C22×C5×D3—21no—
92C22×C5×D3—21no—
93C22×C5×D3—22no—
94C22×C5×D3—41no—
95C22×C5×D3C4⋊C411yescharacteristic
96C22×C5×D3C4⋊C411yescharacteristic
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3C4⋊C411yescharacteristic
106C2×C5×Dic3C4⋊C411yescharacteristic
107C4×C5×D3—21no—
108C4×C5×D3—21no—
109C4×C5×D3—21no—
110C4×C5×D3—21no—
111C4×C5×D3—21no—
112C4×C5×D3—21no—
113C4×C5×D3—21no—
114C4×C5×D3—21no—
115C3×C5×C8—41no—
116C3⋊#168—22no—
117C3⋊#168—22no—
118C3×#168—22no—
119C3×#168—22no—
120C5×C3⋊C8—41no—
121C22×C4×D3C2×D511yescharacteristic
122C2×C3×M16—51no—
123C2×C3×M16C2×D511yescharacteristic
124C22×C3×C8—51no—
125C2×#208—51no—
126C2×#208C2×D511yescharacteristic
127C22×C3⋊C8—51no—
128D3×M16—102no—
129D3×M16—102no—
130C2×ΓL(1,𝔽25)—101no—
131C2×D3×C8—101no—
132#822—102no—
133(C2×D3)⋊C8—21no—
134(C2×D3)⋊C8—21no—
135(C2×D3)⋊C8—52no—
136(C2×D3)⋊C8—52no—
137#819—102no—
138C24×C5—31no—
139C22×C4×C5—31no—
140C22×C4×C5—31no—
141C22×C4×C5—31no—
142C22×C4×C5—31no—
143C22×C4×C5—31no—
144C22×C4×C5—61no—
145C22×C4×C5—61no—
146C22×C4×C5—61no—
147C22×C4×C5—61no—
148C22×C4×C5C22×D311yescharacteristic
149C5×M16—21no—
150C5×M16—21no—
151C5×M16—61no—
152C5×M16—61no—
153C2×C5×C8—21no—
154C2×C5×C8—61no—
155#681—21no—
156#681—32no—
157#681—64no—
158#681—61no—
159#681D1212yes—
160C2×#168—21no—
161C2×#168—21no—
162C2×#168—21no—
163C2×#168—32no—
164C2×#168—64no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#168—61no—
168C2×#168C4×D312yes—
169C22×M16—151no—
170C2×#108—151no—
171C2×#108—151no—
172#407—31no—
173C2×C22⋊C8—151no—
174#341—51no—
175#341—151no—
176C22×C3×C5—21no—
177C22×C3×C5—21no—
178C22×C3×C5C2×C4⋊C411yescharacteristic
179C22×C3×C5C22⋊Q811yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C2×C5×D3—21no—
182C2×C5×D3—21no—
183C2×C5×D3—21no—
184C2×C5×D3—21no—
185C2×C5×D3—21no—
186C2×C5×D3—42no—
187C2×C5×D3—42no—
188C2×C5×D3#10812yescomplemented
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12011yescharacteristic
192C3×C4×C5#12311yescharacteristic
193C5×Dic3—21no—
194C5×Dic3—21no—
195C23×D3Dic1011yescharacteristic
196C22×C3×C4C22×D511yescharacteristic
197C22×Dic3Dic1011yescharacteristic
198C2×C4×D3—21no—
199C2×C4×D3—21no—
200C2×C4×D3—21no—
201C2×C4×D3—21no—
202C2×C4×D3C4×D511yescharacteristic
203C2×C4×D3C4×D511yescharacteristic
204C2×C4×D3C22⋊D511yescharacteristic
205C2×C4×D3C22⋊D511yescharacteristic
206C3×M16—21no—
207C3×M16—21no—
208C3×M16—52no—
209C3×M16—101no—
210C2×C3×C8—21no—
211C2×C3×C8—52no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C2×C3×C8—101no—
215#208—21no—
216#208—21no—
217#208—52no—
218#208—101no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—52no—
221C2×C3⋊C8—101no—
222C2×C3⋊C8—101no—
223C2×C3⋊C8—101no—
224ΓL(1,𝔽25)—104no—
225D3×C8—104no—
226C23×C5—31no—
227C23×C5—31no—
228C23×C5—62no—
229C23×C5—61no—
230C23×C5—61no—
231C23×C5—121no—
232C23×C5D3×Q811yescharacteristic
233C2×C4×C5—31no—
234C2×C4×C5—31no—
235C2×C4×C5—61no—
236C2×C4×C5—61no—
237C2×C4×C5—61no—
238C2×C4×C5—61no—
239C2×C4×C5—61no—
240C2×C4×C5—61no—
241C2×C4×C5—61no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—61no—
245C2×C4×C5C2×C4×D311yescharacteristic
246C2×C4×C5C2×D1211yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23711yescharacteristic
251C5×C8—41no—
252C5×C8—121no—
253#168—22no—
254#168—22no—
255#168—62no—
256#168—62no—
257C23×C4—31no—
258C2×M16—31no—
259C2×M16—51no—
260C2×M16—151no—
261C2×M16—301no—
262C2×M16—302no—
263C2×M16—302no—
264C2×M16D3×D511yescharacteristic
265C22×C8—51no—
266C22×C8—151no—
267C22×C8—301no—
268#108—302no—
269#108—302no—
270C22⋊C8—61no—
271C22⋊C8—61no—
272C22⋊C8—152no—
273C22⋊C8—152no—
274C2×C3×C5—21no—
275C2×C3×C5—21no—
276C2×C3×C5#38511yescharacteristic
277C2×C3×C5C2×#10811yescharacteristic
278C2×C3×C5#43011yescharacteristic
279C5×D3—22no—
280C5×D3—41no—
281C23×C3C2×Dic1011yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—22no—
285C22×D3—41no—
286C22×D3#68311yescharacteristic
287C22×D3#68311yescharacteristic
288C2×C3×C4C2×C4×D511yescharacteristic
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4#71111yescharacteristic
293C2×C3×C4C2×C22⋊D511yescharacteristic
294C2×Dic3—21no—
295C2×Dic3—21no—
296C2×Dic3#68311yescharacteristic
297C2×Dic3#68311yescharacteristic
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—21no—
301C4×D3—21no—
302C4×D3—21no—
303C4×D3—21no—
304C4×D3—21no—
305C4×D3—21no—
306C3×C8—41no—
307C3×C8—102no—
308C3×C8—102no—
309C3⋊C8—41no—
310C3⋊C8—102no—
311C3⋊C8—102no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—32no—
315C22×C5—61no—
316C22×C5—61no—
317C22×C5—61no—
318C22×C5—61no—
319C22×C5—61no—
320C22×C5—122no—
321C22×C5—122no—
322C22×C5D3×C4⋊C411yescharacteristic
323C22×C5#89611yescharacteristic
324C22×C5#89711yescharacteristic
325C4×C5—61no—
326C4×C5—61no—
327C4×C5C4×D1211yescharacteristic
328C4×C5#67⋊C411yescharacteristic
329C4×C5#88211yescharacteristic
330C4×C5#88311yescharacteristic
331C24—31no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—61no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4C2×D3×D511yescharacteristic
342M16—21no—
343M16—21no—
344M16—52no—
345M16—61no—
346M16—61no—
347M16—101no—
348M16—152no—
349M16—304no—
350M16—301no—
351C2×C8—21no—
352C2×C8—52no—
353C2×C8—61no—
354C2×C8—101no—
355C2×C8—101no—
356C2×C8—101no—
357C2×C8—152no—
358C2×C8—304no—
359C2×C8—301no—
360C2×C8—301no—
361C2×C8—301no—
362C3×C5#185511yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#402411yescharacteristic
366C22×C3#402411yescharacteristic
367C22×C3C2×#68311yescharacteristic
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—21no—
372C2×D3—21no—
373C2×D3—42no—
374C2×D3—42no—
375C2×D3#395412yescomplemented
376C3×C4#402711yescharacteristic
377C3×C4#402711yescharacteristic
378C3×C4#408111yescharacteristic
379C3×C4#408311yescharacteristic
380Dic3—21no—
381Dic3—21no—
382C2×C5—21no—
383C2×C5—21no—
384C2×C5—62no—
385C2×C5—121no—
386C2×C5#466811yescharacteristic
387C2×C5D3×#10811yescharacteristic
388C2×C5#489311yescharacteristic
389C23—31no—
390C23—31no—
391C23—62no—
392C23—61no—
393C23—61no—
394C23—121no—
395C23D3×Dic1011yescharacteristic
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4C4×D3×D511yescharacteristic
409C2×C4D5×D1211yescharacteristic
410C2×C4#677711yescharacteristic
411C2×C4#678011yescharacteristic
412C2×C4#678211yescharacteristic
413C2×C4D3×C22⋊D511yescharacteristic
414C8—41no—
415C8—102no—
416C8—102no—
417C8—121no—
418C8—302no—
419C8—302no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3#6523511yescharacteristic
423C2×C3C2×#395411yescharacteristic
424C2×C3#6541311yescharacteristic
425D3—22no—
426D3—41no—
427C5#6894111yescharacteristic, complemented, Sylow
428C22—21no—
429C22—21no—
430C22—32no—
431C22—61no—
432C22—61no—
433C22—61no—
434C22—61no—
435C22—61no—
436C22—122no—
437C22—122no—
438C22D3×#68311yescharacteristic
439C22#9141711yescharacteristic
440C22#9143611yescharacteristic
441C4—61no—
442C4—61no—
443C4#9140511yescharacteristic
444C4#9144211yescharacteristic
445C4#9147511yescharacteristic
446C4#9155511yescharacteristic
447C3#1060077711yescharacteristic, complemented, Sylow
448C2—21no—
449C2—21no—
450C2—62no—
451C2—121no—
452C2D3×#395411yescharacteristic
453C2#1174817211yescharacteristic
454C2#1174889311yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C5×D3Q8
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1855
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
3. C2×#90992C2semidirect
4. C2×#90991C2semidirect
6. #11746379C2semidirect
7. C3×#64778C2semidirect
33. #64778D3semidirect
188. C2×C5×D3#108semidirect
362. C3×C5#1855semidirect
375. C2×D3#3954semidirect
427. C5#68941semidirect
447. C3#10600777semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6812
C5×#51262
C2×#909922
C2×#909912
C2×(C2×D3)⋊#1682
#117463792
C3×#647782
#106007773
#689415