Finite Group Databasebeta

← #14288892

Subgroups — #14288892

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#550C211yesmaximal, characteristic, complemented
2#11751174C211yesmaximal, characteristic, complemented
3#11751128C211yesmaximal, characteristic, complemented
4#11751116C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602711—31nomaximal, Hall
9C2×C3×C5×#41—21no—
10C3×C5×#127—21no—
11C3×C5×#127C2211yescharacteristic
12C3×C5×#121—22no—
13C3×C5×#121—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4C2211yescharacteristic
17C2×#6717—21no—
18C2×#6715—22no—
19C2×#6715—21no—
20#91763C2211yescharacteristic
21#91093—21no—
22#91093—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71918—51nomaximal, Hall
27C5×#550D311yescharacteristic, complemented
28#65362—31no—
29#65316—31no—
30#65304—31no—
31#64764—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C3×C5×#41—42no—
35C3×C5×#41—42no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—22no—
38C2×C3×C5×D4—22no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4D411yescharacteristic
42C2×C3×C5×D4D412yes—
43C22×C3×C4×C5—22no—
44C22×C3×C4×C5—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C4⋊C4D411yescharacteristic
51C3×C5×C22⋊C4—22no—
52C3×C5×C22⋊C4—21no—
53C3×C42×C5—21no—
54C3×C42×C5C2311yescharacteristic
55#6717—42no—
56#6715—44no—
57#6715—42no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C3×#550D511yescharacteristic, complemented
62#5073—51no—
63#5027—51no—
64#5015—51no—
65#4544—51no—
66#4535—51no—
67D4⋊(C3⋊C8)—51no—
68C2×C5×#41—21no—
69C5×#127—21no—
70C5×#127C2×D311yescharacteristic
71C5×#121—22no—
72C5×#121—21no—
73C4×C5×Q8C2×D311yescharacteristic
74C4×C5×D4—21no—
75C4×C5×D4C2×D311yescharacteristic
76C2×#688—61no—
77C2×#686—61no—
78C2×#686—62no—
79#4020—31no—
80#3941—61no—
81#3941—61no—
82C4⋊#168—31no—
83C4⋊#168—31no—
84C4×#168—31no—
85#1621—151noSylow
86C23×C3×C5—21no—
87C23×C3×C5—22no—
88C22×D15—41no—
89C3×C5×Q8—21no—
90C3×C5×Q8D812yescomplemented
91C3×C5×D4—21no—
92C3×C5×D4—21no—
93C3×C5×D4—44no—
94C3×C5×D4—42no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C3×C5×D4—82no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—44no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109D60—42no—
110D60—41no—
111D60—41no—
112D60—41no—
113D60—41no—
114C3⋊#168—22no—
115C3⋊#168—41no—
116C3⋊#168—41no—
117C2×C3×#41—21no—
118C3×#127—21no—
119C3×#127C2×D511yescharacteristic
120C3×#121—22no—
121C3×#121—21no—
122C3×C4×Q8C2×D511yescharacteristic
123C3×C4×D4—21no—
124C3×C4×D4C2×D511yescharacteristic
125C2×#215—101no—
126C2×#213—101no—
127C2×#213—102no—
128#874—51no—
129#809—101no—
130#809—101no—
131C4⋊(C3⋊C8)—51no—
132C4⋊(C3⋊C8)—51no—
133C4×C3⋊C8—51no—
134C5×#41—42no—
135C5×#41—42no—
136C2×C5×Q8#6711yescharacteristic
137C2×C5×D4—22no—
138C2×C5×D4—22no—
139C2×C5×D4—21no—
140C2×C5×D4—21no—
141C2×C5×D4#6711yescharacteristic
142C2×C5×D4#6712yes—
143C22×C4×C5—22no—
144C22×C4×C5—21no—
145C2×D20—61no—
146C2×D20—61no—
147C2×D20—61no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4#6711yescharacteristic
150C5×C4⋊C4#6711yescharacteristic
151C5×C22⋊C4—22no—
152C5×C22⋊C4—21no—
153C42×C5—21no—
154C42×C5C22×D311yescharacteristic
155#688—122no—
156#686—124no—
157#686—122no—
158C2×#168—61no—
159C2×#168—61no—
160C2×#168—61no—
161#550D1511yescharacteristic, complemented
162#493—151no—
163#460—151no—
164#459—151no—
165#331—151no—
166Q8⋊C8—151no—
167D4⋊C8—151no—
168C22×C3×C5—42no—
169C22×C3×C5—41no—
170C22×C3×C5—41no—
171C22×C3×C5—42no—
172C22×C3×C5—42no—
173C22×C3×C5—41no—
174C22×C3×C5#12011yescharacteristic
175C2×D15—81no—
176C2×D15—81no—
177C2×D15—81no—
178C3×C4×C5—22no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5C2×D811yescharacteristic
183C3×C4×C5#13511yescharacteristic
184C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
185C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
186C3×#41—42no—
187C3×#41—42no—
188C2×C3×Q8C22⋊D511yescharacteristic
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4C22⋊D511yescharacteristic
194C2×C3×D4C22⋊D512yes—
195C22×C3×C4—22no—
196C22×C3×C4—21no—
197C2×D12—101no—
198C2×D12—101no—
199C2×D12—101no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4C22⋊D511yescharacteristic
202C3×C4⋊C4C22⋊D511yescharacteristic
203C3×C22⋊C4—22no—
204C3×C22⋊C4—21no—
205C3×C42—21no—
206C3×C42C22×D511yescharacteristic
207#215—202no—
208#213—204no—
209#213—202no—
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212C2×C3⋊C8—101no—
213C23×C5—21no—
214C23×C5—22no—
215C22×D5—121no—
216C5×Q8—21no—
217C5×Q8#21312yescomplemented
218C5×D4—21no—
219C5×D4—21no—
220C5×D4—42no—
221C5×D4—44no—
222C5×D4—41no—
223C5×D4—41no—
224C5×D4—41no—
225C5×D4—41no—
226C5×D4—82no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—21no—
230C2×C4×C5—44no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5C2×#6711yescharacteristic
234C2×C4×C5C2×#6711yescharacteristic
235C2×C4×C5C2×#6711yescharacteristic
236D20—122no—
237D20—121no—
238D20—121no—
239D20—121no—
240D20—121no—
241#168—62no—
242#168—121no—
243#168—121no—
244C2×#41—21no—
245C2×SD16—301no—
246C2×D8—301no—
247C2×D8—302no—
248#127—21no—
249#127—151no—
250#127C2×D1511yescharacteristic
251#121—22no—
252#121—21no—
253C4×Q8C2×D1511yescharacteristic
254C4×D4—21no—
255C4×D4C2×D1511yescharacteristic
256C4⋊C8—151no—
257C4⋊C8—151no—
258#102—301no—
259#102—301no—
260C4×C8—151no—
261C2×C3×C5—81no—
262C2×C3×C5—82no—
263C2×C3×C5#44711yescharacteristic
264C2×C3×C5#44911yescharacteristic
265C2×C3×C5#45311yescharacteristic
266D15—161no—
267C23×C3—21no—
268C23×C3—22no—
269C22×D3—201no—
270C3×Q8—21no—
271C3×Q8#68612yescomplemented
272C3×D4—21no—
273C3×D4—21no—
274C3×D4—42no—
275C3×D4—44no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—82no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—44no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4C2×C22⋊D511yescharacteristic
288C2×C3×C4C2×C22⋊D511yescharacteristic
289C2×C3×C4C2×C22⋊D511yescharacteristic
290D12—202no—
291D12—201no—
292D12—201no—
293D12—201no—
294D12—201no—
295C3⋊C8—102no—
296C3⋊C8—201no—
297C3⋊C8—201no—
298C22×C5—42no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—42no—
302C22×C5—42no—
303C22×C5—41no—
304C22×C5#95311yescharacteristic
305C2×D5—241no—
306C2×D5—241no—
307C2×D5—241no—
308C4×C5—22no—
309C4×C5—21no—
310C4×C5—41no—
311C4×C5—41no—
312C4×C5C2×#21311yescharacteristic
313C4×C5#93211yescharacteristic
314C4×C5#94911yescharacteristic
315C4×C5#95011yescharacteristic
316#41—42no—
317#41—42no—
318C2×Q8#122011yescharacteristic
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—301no—
324C2×D4—301no—
325C2×D4—301no—
326C2×D4#122011yescharacteristic
327C2×D4#122012yes—
328C22×C4—22no—
329C22×C4—21no—
330SD16—602no—
331D8—604no—
332D8—602no—
333C2×C8—301no—
334C2×C8—301no—
335C2×C8—301no—
336C4⋊C4—21no—
337C4⋊C4#122011yescharacteristic
338C4⋊C4#122011yescharacteristic
339C22⋊C4—22no—
340C22⋊C4—21no—
341C42—21no—
342C42C22×D1511yescharacteristic
343C3×C5#162111yescharacteristic, complemented, Hall
344C22×C3—42no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—41no—
350C22×C3#409911yescharacteristic
351C2×D3—401no—
352C2×D3—401no—
353C2×D3—401no—
354C3×C4—22no—
355C3×C4—21no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4C2×#68611yescharacteristic
359C3×C4#407811yescharacteristic
360C3×C4#409511yescharacteristic
361C3×C4#409611yescharacteristic
362C2×C5—81no—
363C2×C5—82no—
364C2×C5#521711yescharacteristic
365C2×C5#523811yescharacteristic
366C2×C5#524111yescharacteristic
367D5—481no—
368C23—21no—
369C23—22no—
370C23—601no—
371Q8—21no—
372Q8#671512yescomplemented
373D4—21no—
374D4—21no—
375D4—42no—
376D4—44no—
377D4—41no—
378D4—41no—
379D4—41no—
380D4—41no—
381D4—82no—
382D4—602no—
383D4—601no—
384D4—601no—
385D4—601no—
386D4—601no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4C2×#122011yescharacteristic
394C2×C4C2×#122011yescharacteristic
395C2×C4C2×#122011yescharacteristic
396C8—302no—
397C8—601no—
398C8—601no—
399C2×C3—81no—
400C2×C3—82no—
401C2×C3#6550611yescharacteristic
402C2×C3#6552711yescharacteristic
403C2×C3#6553011yescharacteristic
404D3—801no—
405C5#7191811yescharacteristic, complemented, Sylow
406C22—42no—
407C22—41no—
408C22—41no—
409C22—42no—
410C22—42no—
411C22—41no—
412C22—1201no—
413C22—1201no—
414C22—1201no—
415C22#9184211yescharacteristic
416C4—22no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4C2×#671511yescharacteristic
421C4#9182111yescharacteristic
422C4#9183811yescharacteristic
423C4#9183911yescharacteristic
424C3#1060271111yescharacteristic, complemented, Sylow
425C2—81no—
426C2—82no—
427C2—2401no—
428C2#1175131811yescharacteristic
429C2#1175133911yescharacteristic
430C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#550C2
socleC22×C3×C5#120
hypercenter#550D15
hypocenterC3×C5#1621
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C3×C5×#550C2semidirect
2. #11751174C2semidirect
3. #11751128C2semidirect
4. #11751116C2semidirect
5. #11746365C2semidirect
6. #11746356C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
27. C5×#550D3semidirect
61. C3×#550D5semidirect
90. C3×C5×Q8D8semidirect
161. #550D15semidirect
217. C5×Q8#213semidirect
271. C3×Q8#686semidirect
343. C3×C5#1621semidirect
372. Q8#6715semidirect
405. C5#71918semidirect
424. C3#10602711semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5502
#117511742
#117511282
#117511162
#117463652
#117463562
D4⋊(C3⋊#168)2
#106027113
#719185