Finite Group Databasebeta

← #14288955

Subgroups — #14288955

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#554C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11751128C211yesmaximal, characteristic, complemented
4#11751116C211yesmaximal, characteristic
5#11746367C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602716—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#125—21no—
11C3×C5×C22⋊Q8—21no—
12C3×C5×C22⋊Q8—22no—
13C3×C4×C5×Q8C2211yescharacteristic
14C3×C4×C5×D4—21no—
15C3×C4×C5×D4C2211yescharacteristic
16C2×C3×C5×C4⋊C4—21no—
17C2×#6717—22no—
18C2×#6717—21no—
19C2×#6715—21no—
20#91763C2211yescharacteristic
21#91093—21no—
22#91093—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71923—51nomaximal, Hall
27C5×#554D311yescharacteristic, complemented
28#65374—31no—
29#65316—31no—
30#65304—31no—
31#64766—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C3×C5×Q8D412yes—
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—22no—
38C22×C3×C4×C5—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C3×C5×C4⋊C4—22no—
43C3×C5×C4⋊C4—22no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4D411yescharacteristic
48C3×C5×C4⋊C4D411yescharacteristic
49C3×C5×C22⋊C4—22no—
50C3×C5×C22⋊C4—21no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53#6717—44no—
54#6717—42no—
55#6715—42no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C3×#554D511yescharacteristic, complemented
60#5085—51no—
61#5027—51no—
62#5015—51no—
63#4546—51no—
64#4535—51no—
65D4⋊(C3⋊C8)—51no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C5×#125—21no—
68C5×C22⋊Q8—21no—
69C5×C22⋊Q8—22no—
70C4×C5×Q8C2×D311yescharacteristic
71C4×C5×D4—21no—
72C4×C5×D4C2×D311yescharacteristic
73C2×C5×C4⋊C4—21no—
74C2×#688—61no—
75C2×#688—62no—
76C2×#686—61no—
77#4020—31no—
78#3941—61no—
79#3941—61no—
80C4⋊#168—31no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1622—151noSylow
84C23×C3×C5—21no—
85C22×D15—41no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C3×C5×Q8—42no—
89C3×C5×D4—21no—
90C3×C5×D4SD1612yescomplemented
91C2×C3×C4×C5—21no—
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—22no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—82no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101D60—42no—
102D60—41no—
103D60—41no—
104D60—41no—
105D60—41no—
106C3⋊#168—22no—
107C3⋊#168—41no—
108C3⋊#168—41no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×#125—21no—
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8—22no—
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4—21no—
115C3×C4×D4C2×D511yescharacteristic
116C2×C3×C4⋊C4—21no—
117C2×#215—101no—
118C2×#215—102no—
119C2×#213—101no—
120#874—51no—
121#809—101no—
122#809—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)—51no—
125C4×C3⋊C8—51no—
126C2×C5×Q8#6711yescharacteristic
127C2×C5×Q8#6712yes—
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—22no—
130C22×C4×C5—21no—
131C2×D20—61no—
132C2×D20—61no—
133C2×D20—61no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—22no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—21no—
139C5×C4⋊C4#6711yescharacteristic
140C5×C4⋊C4#6711yescharacteristic
141C5×C22⋊C4—22no—
142C5×C22⋊C4—21no—
143C42×C5—21no—
144C42×C5C22×D311yescharacteristic
145#688—124no—
146#688—122no—
147#686—122no—
148C2×#168—61no—
149C2×#168—61no—
150C2×#168—61no—
151#554D1511yescharacteristic, complemented
152#492—151no—
153#460—151no—
154#459—151no—
155#333—151no—
156Q8⋊C8—151no—
157D4⋊C8—151no—
158C22×C3×C5—22no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—81no—
163C2×D15—81no—
164C2×D15—81no—
165C3×C4×C5—21no—
166C3×C4×C5—41no—
167C3×C4×C5—41no—
168C3×C4×C5—41no—
169C3×C4×C5—42no—
170C3×C4×C5C2×SD1611yescharacteristic
171C3×C4×C5#13511yescharacteristic
172C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C3×C4×C5#13711yescharacteristic
174C2×C3×Q8C22⋊D511yescharacteristic
175C2×C3×Q8C22⋊D512yes—
176C2×C3×D4C22⋊D511yescharacteristic
177C22×C3×C4—22no—
178C22×C3×C4—21no—
179C2×D12—101no—
180C2×D12—101no—
181C2×D12—101no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4C22⋊D511yescharacteristic
188C3×C4⋊C4C22⋊D511yescharacteristic
189C3×C22⋊C4—22no—
190C3×C22⋊C4—21no—
191C3×C42—21no—
192C3×C42C22×D511yescharacteristic
193#215—204no—
194#215—202no—
195#213—202no—
196C2×C3⋊C8—101no—
197C2×C3⋊C8—101no—
198C2×C3⋊C8—101no—
199C23×C5—21no—
200C22×D5—121no—
201C5×Q8—21no—
202C5×Q8—21no—
203C5×Q8—42no—
204C5×D4—21no—
205C5×D4#21512yescomplemented
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—22no—
210C2×C4×C5—41no—
211C2×C4×C5—41no—
212C2×C4×C5—82no—
213C2×C4×C5C2×#6711yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216D20—122no—
217D20—121no—
218D20—121no—
219D20—121no—
220D20—121no—
221#168—62no—
222#168—121no—
223#168—121no—
224C2×SD16—301no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8C2×D1511yescharacteristic
228#127—151no—
229#125—21no—
230C22⋊Q8—21no—
231C22⋊Q8—22no—
232C4×Q8C2×D1511yescharacteristic
233C4×D4—21no—
234C4×D4C2×D1511yescharacteristic
235C2×C4⋊C4—21no—
236C4⋊C8—151no—
237C4⋊C8—151no—
238#102—301no—
239#102—301no—
240C4×C8—151no—
241C2×C3×C5—42no—
242C2×C3×C5#44811yescharacteristic
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45311yescharacteristic
245D15—161no—
246C23×C3—21no—
247C22×D3—201no—
248C3×Q8—21no—
249C3×Q8—21no—
250C3×Q8—42no—
251C3×D4—21no—
252C3×D4#68812yescomplemented
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—22no—
257C2×C3×C4—41no—
258C2×C3×C4—41no—
259C2×C3×C4—82no—
260C2×C3×C4C2×C22⋊D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263D12—202no—
264D12—201no—
265D12—201no—
266D12—201no—
267D12—201no—
268C3⋊C8—102no—
269C3⋊C8—201no—
270C3⋊C8—201no—
271C22×C5—22no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5#95311yescharacteristic
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—41no—
280C4×C5—41no—
281C4×C5—41no—
282C4×C5—42no—
283C4×C5C2×#21511yescharacteristic
284C4×C5#94211yescharacteristic
285C4×C5#94911yescharacteristic
286C4×C5#95011yescharacteristic
287C2×Q8#122011yescharacteristic
288C2×Q8#122012yes—
289C2×D4—301no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4#122011yescharacteristic
293C22×C4—22no—
294C22×C4—21no—
295SD16—604no—
296SD16—602no—
297D8—602no—
298C2×C8—301no—
299C2×C8—301no—
300C2×C8—301no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4#122011yescharacteristic
307C4⋊C4#122011yescharacteristic
308C22⋊C4—22no—
309C22⋊C4—21no—
310C42—21no—
311C42C22×D1511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3—22no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3#409911yescharacteristic
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—42no—
325C3×C4C2×#68811yescharacteristic
326C3×C4#408811yescharacteristic
327C3×C4#409511yescharacteristic
328C3×C4#409611yescharacteristic
329C2×C5—42no—
330C2×C5#522711yescharacteristic
331C2×C5#523811yescharacteristic
332C2×C5#524111yescharacteristic
333D5—481no—
334C23—21no—
335C23—601no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339D4—21no—
340D4—602no—
341D4—601no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4#671712yescomplemented
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—82no—
353C2×C4C2×#122011yescharacteristic
354C2×C4C2×#122011yescharacteristic
355C2×C4C2×#122011yescharacteristic
356C8—302no—
357C8—601no—
358C8—601no—
359C2×C3—42no—
360C2×C3#6551611yescharacteristic
361C2×C3#6552711yescharacteristic
362C2×C3#6553011yescharacteristic
363D3—801no—
364C5#7192311yescharacteristic, complemented, Sylow
365C22—22no—
366C22—41no—
367C22—41no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9184211yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—42no—
377C4C2×#671711yescharacteristic
378C4#9183111yescharacteristic
379C4#9183811yescharacteristic
380C4#9183911yescharacteristic
381C3#1060271611yescharacteristic, complemented, Sylow
382C2—42no—
383C2—2401no—
384C2#1175132811yescharacteristic
385C2#1175133911yescharacteristic
386C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#554C2
socleC22×C3×C5#120
prime radical#11751116C2
hypercenter#554D15
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×C5×#554C2semidirect
2. #11751186C2semidirect
3. #11751128C2semidirect
5. #11746367C2semidirect
6. #11746356C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
27. C5×#554D3semidirect
59. C3×#554D5semidirect
90. C3×C5×D4SD16semidirect
151. #554D15semidirect
205. C5×D4#215semidirect
252. C3×D4#688semidirect
312. C3×C5#1622semidirect
345. D4#6717semidirect
364. C5#71923semidirect
381. C3#10602716semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5542
#117511862
#117511282
#117511162
#117463672
#117463562
D4⋊(C3⋊#168)2
#106027163
#719235