Finite Group Databasebeta

← #14305870

Subgroups — #14305870

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#936C211yesmaximal, characteristic
2C2×#91116C211yesmaximal, characteristic
3C2×C3×#3964C211yesmaximal, characteristic
4#11748619C211yesmaximal, characteristic, complemented
5C2×#90973C211yesmaximal, characteristic, complemented
6C2×#90972C211yesmaximal, characteristic, complemented
7C2×Dic3×#168C211yesmaximal, characteristic, complemented
8#10602518—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×#217—22no—
14C5×#936—22no—
15C5×#936C414yescomplemented
16C2×C4×C5×Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19#91116—22no—
20C3×#3964—22no—
21#90994—22no—
22#90973—22no—
23#90972—22no—
24Dic3×#168—22no—
25#70158—51nomaximal, Hall
26C2×C5×#124—31no—
27C2×#3967—31no—
28C2×#3967—31no—
29C2×#3964—31no—
30C2×#3964D311yescharacteristic
31#65225—31no—
32C2×C4×#168—31no—
33C24×C3×C5—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2×C412yes—
40C22×C3×C4×C5C2311yescharacteristic
41C22×Dic15—21no—
42C22×C5×Dic3—21no—
43C22×C5×Dic3D412yes—
44C2×C5×Dic6—21no—
45C2×C5×Dic6—21no—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6C2×C412yes—
50C22×C3×Dic5—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15—21no—
53C2×C3⋊#168—21no—
54C2×C3⋊#168—21no—
55C2×C3⋊#168D412yes—
56C5×#217—28no—
57C4×C5×Dic3C2×C412yes—
58C4×C5×Dic3D412yes—
59C3×C4⋊Dic5—21no—
60C3×C4⋊Dic5—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63C2×C3×#168D412yes—
64C2×#936D511yescharacteristic
65C2×C3×#102—51no—
66C2×#832—51no—
67C2×#816—51no—
68C2×C8×Dic3—51no—
69#4977—51no—
70C2×#810—51no—
71C22×C5×Q8—31no—
72C22×C5×D4C2×D311yescharacteristic
73C5×#124—34no—
74C5×#124—62no—
75C2×C5×C22⋊C4—62no—
76C2×C42×C5—31no—
77C2×C4⋊Dic5—31no—
78C2×C4⋊Dic5C2×D311yescharacteristic
79C22×#168—31no—
80C22×#168C2×D311yescharacteristic
81#3967—62no—
82#3967—62no—
83#3964—22no—
84#3964—62no—
85#3963—62no—
86C4×#168—62no—
87#1958—151noSylow
88C23×C3×C5—22no—
89C23×C3×C5—41no—
90C23×C3×C5—41no—
91C23×C3×C5—42no—
92C23×C3×C5—42no—
93C23×C3×C5C2×D411yescharacteristic
94C3×C5×D4—22no—
95C3×C5×D4—22no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—41no—
105C2×Dic15—42no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—22no—
108C2×C5×Dic3—22no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3C22⋊C414yes—
112C5×Dic6—22no—
113C5×Dic6—22no—
114C5×Dic6—41no—
115C5×Dic6—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—42no—
118C3⋊#168—22no—
119C3×#168—22no—
120C22×C3×D4C2×D511yescharacteristic
121C22×Dic6C2×D511yescharacteristic
122C22×C3×C8—51no—
123C2×C3×C4⋊C4—51no—
124C2×#217—22no—
125#936—22no—
126#936Dic514yescomplemented
127C2×C4⋊Dic3—51no—
128C2×C4×Dic3C2×D511yescharacteristic
129C22×C3⋊C8—51no—
130C3×#102—102no—
131#832—102no—
132C3⋊#95—102no—
133#816—102no—
134C8×Dic3—102no—
135#810—102no—
136C24×C5—21no—
137C2×C5×Q8—32no—
138C2×C5×Q8—61no—
139C2×C5×Q8—61no—
140C2×C5×Q8—61no—
141C2×C5×Q8—61no—
142C2×C5×Q8—61no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4C4×D312yes—
149C22×C4×C5—32no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C22×Dic5—21no—
153C22×Dic5—61no—
154C5×C22⋊C4—68no—
155C42×C5—32no—
156C42×C5—32no—
157C4⋊Dic5—21no—
158C4⋊Dic5—21no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161C2×#168—21no—
162C2×#168—21no—
163C2×#168—32no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168#6712yes—
167C2×#124—31no—
168C2×#103—151no—
169C2×#103—151no—
170C2×#102—51no—
171C2×#102—151no—
172C2×C4×C8—151no—
173#382—151no—
174C22×C3×C5—42no—
175C22×C3×C5—44no—
176C22×C3×C5—82no—
177C22×C3×C5—81no—
178C22×C3×C5—81no—
179C22×C3×C5C2×C22⋊C411yescharacteristic
180C22×C3×C5#12411yescharacteristic
181C22×C3×C5#12711yescharacteristic
182C22×C3×C5#13512yes—
183C22×C3×C5#13512yes—
184C3×C4×C5C4×D411yescharacteristic
185C3×C4×C5C4×D411yescharacteristic
186C3×C4×C5#12111yescharacteristic
187C3×C4×C5#12111yescharacteristic
188Dic15—81no—
189C3×Dic5—81no—
190C5×Dic3—24no—
191C5×Dic3—42no—
192C24×C3—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4C2×Dic512yes—
199C22×C3×C4—101no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—21no—
202C22×Dic3—101no—
203C22×Dic3C22⋊D512yes—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6C2×Dic512yes—
210C2×C3×C8—52no—
211C2×C3×C8—101no—
212C2×C3×C8—101no—
213C3×C4⋊C4—101no—
214C3×C4⋊C4—101no—
215#217—28no—
216C4⋊Dic3—101no—
217C4⋊Dic3—101no—
218C4×Dic3C2×Dic512yes—
219C4×Dic3C22⋊D512yes—
220C2×C3⋊C8—52no—
221C2×C3⋊C8—101no—
222C2×C3⋊C8—101no—
223C23×C5—22no—
224C23×C5—41no—
225C23×C5—42no—
226C23×C5—42no—
227C23×C5—41no—
228C23×C5D3×D411yescharacteristic
229C5×Q8—62no—
230C5×Q8—62no—
231C5×Q8—121no—
232C5×Q8—121no—
233C5×D4—22no—
234C5×D4—22no—
235C5×D4—41no—
236C5×D4—41no—
237C2×C4×C5—34no—
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×C5#23711yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C2×Dic5—42no—
250C2×Dic5—41no—
251C2×Dic5—122no—
252C2×Dic5—121no—
253#168—22no—
254#168—62no—
255C22×Q8—31no—
256C22×D4D3×D511yescharacteristic
257C22×C8—51no—
258C22×C8—151no—
259#124—34no—
260#124—62no—
261C2×C4⋊C4—51no—
262C2×C4⋊C4—151no—
263C2×C22⋊C4—62no—
264C2×C42—31no—
265#103—302no—
266#103—302no—
267#102—102no—
268#102—302no—
269C4×C8—302no—
270#95—302no—
271C2×C3×C5—82no—
272C2×C3×C5#39011yescharacteristic
273C2×C3×C5#41612yes—
274C2×C3×C5#48812yes—
275C2×C3×C5#49511yescharacteristic
276C2×C3×C5#49511yescharacteristic
277C23×C3—22no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3C2×C22⋊D511yescharacteristic
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—41no—
286C3×D4—41no—
287C2×C3×C4—202no—
288C2×C3×C4—201no—
289C2×C3×C4D4×D511yescharacteristic
290C2×C3×C4D4×D511yescharacteristic
291C2×C3×C4#71111yescharacteristic
292C2×C3×C4#71111yescharacteristic
293C2×C3×C4C22×Dic511yescharacteristic
294C2×C3×C4C2×C22⋊D511yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—202no—
301C2×Dic3—201no—
302C2×Dic3C22⋊Dic514yes—
303Dic6—22no—
304Dic6—22no—
305Dic6—41no—
306Dic6—41no—
307C3×C8—102no—
308C3⋊C8—102no—
309C22×C5—42no—
310C22×C5—44no—
311C22×C5—81no—
312C22×C5—81no—
313C22×C5—82no—
314C22×C5D3×C22⋊C411yescharacteristic
315C22×C5#88511yescharacteristic
316C22×C5#91212yes—
317C22×C5#91612yes—
318C22×C5#94011yescharacteristic
319C4×C5—64no—
320C4×C5—122no—
321C4×C5#67⋊C411yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5C4×#6711yescharacteristic
324C4×C5#93911yescharacteristic
325Dic5—81no—
326Dic5—241no—
327C24—21no—
328C2×Q8—32no—
329C2×Q8—61no—
330C2×Q8—61no—
331C2×Q8—61no—
332C2×Q8—61no—
333C2×Q8—61no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—21no—
337C2×D4—21no—
338C2×D4—21no—
339C2×D4D3×Dic512yes—
340C22×C4—32no—
341C22×C4—61no—
342C22×C4—101no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345C2×C8—52no—
346C2×C8—101no—
347C2×C8—101no—
348C2×C8—152no—
349C2×C8—301no—
350C2×C8—301no—
351C4⋊C4—101no—
352C4⋊C4—101no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C22⋊C4—68no—
356C42—32no—
357C42—32no—
358C3×C5#195811yescharacteristic, complemented, Hall
359C22×C3—42no—
360C22×C3—44no—
361C22×C3—82no—
362C22×C3—81no—
363C22×C3—81no—
364C22×C3#408211yescharacteristic
365C22×C3#408611yescharacteristic
366C22×C3#409612yes—
367C22×C3#409612yes—
368C22×C3C2×C22⋊Dic511yescharacteristic
369C3×C4—401no—
370C3×C4D4×Dic511yescharacteristic
371C3×C4D4×Dic511yescharacteristic
372C3×C4#408411yescharacteristic
373C3×C4#408411yescharacteristic
374Dic3—24no—
375Dic3—42no—
376Dic3—401no—
377C2×C5—82no—
378C2×C5#476812yes—
379C2×C5#477212yes—
380C2×C5#495711yescharacteristic
381C2×C5#515511yescharacteristic
382C2×C5#516811yescharacteristic
383C23—22no—
384C23—42no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23D3×C22⋊D511yescharacteristic
389Q8—62no—
390Q8—62no—
391Q8—121no—
392Q8—121no—
393D4—22no—
394D4—22no—
395D4—41no—
396D4—41no—
397C2×C4—34no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—202no—
404C2×C4—201no—
405C2×C4—602no—
406C2×C4—601no—
407C2×C4#678011yescharacteristic
408C2×C4C2×D3×Dic511yescharacteristic
409C2×C4#678211yescharacteristic
410C2×C4D5×#6711yescharacteristic
411C2×C4D3×C22⋊D511yescharacteristic
412C2×C4#679011yescharacteristic
413C8—102no—
414C8—302no—
415C2×C3—82no—
416C2×C3#6534512yes—
417C2×C3#6534811yescharacteristic
418C2×C3#6534811yescharacteristic
419C2×C3#6551011yescharacteristic
420C2×C3#6552212yes—
421C5#7015811yescharacteristic, complemented, Sylow
422C22—44no—
423C22—42no—
424C22—82no—
425C22—81no—
426C22—81no—
427C22#9149312yes—
428C22#9149512yes—
429C22#9152511yescharacteristic
430C22D3×C22⋊Dic511yescharacteristic
431C22#9156711yescharacteristic
432C4—64no—
433C4—122no—
434C4—401no—
435C4—1201no—
436C4#9154911yescharacteristic
437C4Dic5×#6711yescharacteristic
438C4#9155711yescharacteristic
439C4#67⋊Dic511yescharacteristic
440C3#1060251811yescharacteristic, complemented, Sylow
441C2—82no—
442C2#1174894212yes—
443C2#1174896512yes—
444C2#1174907411yescharacteristic
445C2#1174907811yescharacteristic
446C2#1174948211yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1958
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11748619C2semidirect
5. C2×#90973C2semidirect
6. C2×#90972C2semidirect
7. C2×Dic3×#168C2semidirect
15. C5×#936C4semidirect
126. #936Dic5semidirect
358. C3×C5#1958semidirect
421. C5#70158semidirect
440. C3#10602518semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9362
C2×#911162
C2×C3×#39642
#117486192
C2×#909732
C2×#909722
C2×Dic3×#1682
#106025183
#701585