Finite Group Databasebeta

← #14289285

Subgroups — #14289285

Order 1920.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#556C211yesmaximal, characteristic, complemented
2#11751189C211yesmaximal, characteristic, complemented
3#11751128C211yesmaximal, characteristic, complemented
4#11751116C211yesmaximal, characteristic
5#11746368C211yesmaximal, characteristic, complemented
6#11746356C211yesmaximal, characteristic, complemented
7D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
8#10602724—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#126—22no—
11C3×C5×#124—21no—
12C3×C5×C22⋊Q8—21no—
13C3×C4×C5×Q8—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C5×#117—21no—
17C2×#6717—21no—
18C2×#6715—21no—
19#91763C2211yescharacteristic
20#91093—22no—
21#91093—21no—
22#91093—21no—
23C4⋊(C3⋊#168)C2211yescharacteristic
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71931—51nomaximal, Hall
27C5×#556D311yescharacteristic, complemented
28#65377—31no—
29#65316—31no—
30#65304—31no—
31#64767—31no—
32Q8⋊#168—31no—
33D4⋊#168—31no—
34C2×C3×C5×Q8—21no—
35C2×C3×C5×Q8D411yescharacteristic
36C2×C3×C5×D4D411yescharacteristic
37C22×C3×C4×C5—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C3×C5×C4⋊C4—22no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C4⋊C4D412yes—
47C3×C5×C22⋊C4—22no—
48C3×C5×C22⋊C4—22no—
49C3×C5×C22⋊C4—21no—
50C3×C42×C5—22no—
51C3×C42×C5—21no—
52C3×C42×C5C2311yescharacteristic
53#6717—42no—
54#6715—42no—
55C2×C3⋊#168—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C3×#556D511yescharacteristic, complemented
59#5088—51no—
60#5027—51no—
61#5015—51no—
62#4547—51no—
63#4535—51no—
64D4⋊(C3⋊C8)—51no—
65C5×C4⋊Q8C2×D311yescharacteristic
66C5×#126—22no—
67C5×#124—21no—
68C5×C22⋊Q8—21no—
69C4×C5×Q8—21no—
70C4×C5×Q8C2×D311yescharacteristic
71C4×C5×D4C2×D311yescharacteristic
72C5×#117—21no—
73C2×#688—61no—
74C2×#686—61no—
75#4020—31no—
76#3941—61no—
77#3941—61no—
78#3941—62no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81C4×#168—31no—
82#1628—151noSylow
83C23×C3×C5—21no—
84C22×D15—41no—
85C3×C5×Q8—21no—
86C3×C5×Q8—21no—
87C3×C5×Q8—41no—
88C3×C5×Q8—41no—
89C3×C5×D4—21no—
90C3×C5×D4—21no—
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×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100D60—42no—
101D60—41no—
102D60—41no—
103D60—41no—
104D60—41no—
105C3⋊#168—41no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C3×C4⋊Q8C2×D511yescharacteristic
109C3×#126—22no—
110C3×#124—21no—
111C3×C22⋊Q8—21no—
112C3×C4×Q8—21no—
113C3×C4×Q8C2×D511yescharacteristic
114C3×C4×D4C2×D511yescharacteristic
115C3×#117—21no—
116C2×#215—101no—
117C2×#213—101no—
118#874—51no—
119#809—101no—
120#809—101no—
121#809—102no—
122C4⋊(C3⋊C8)—51no—
123C4⋊(C3⋊C8)—51no—
124C4×C3⋊C8—51no—
125C2×C5×Q8—21no—
126C2×C5×Q8#6711yescharacteristic
127C2×C5×D4#6711yescharacteristic
128C22×C4×C5—21no—
129C2×D20—61no—
130C2×D20—61no—
131C2×D20—61no—
132C5×C4⋊C4—22no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6711yescharacteristic
136C5×C4⋊C4#6711yescharacteristic
137C5×C4⋊C4#6712yes—
138C5×C22⋊C4—22no—
139C5×C22⋊C4—22no—
140C5×C22⋊C4—21no—
141C42×C5—22no—
142C42×C5—21no—
143C42×C5C22×D311yescharacteristic
144#688—122no—
145#686—122no—
146C2×#168—61no—
147C2×#168—61no—
148C2×#168—61no—
149#556D1511yescharacteristic, complemented
150#486—151no—
151#460—151no—
152#459—151no—
153#332—151no—
154Q8⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5—41no—
157C22×C3×C5—41no—
158C22×C3×C5—41no—
159C22×C3×C5#12011yescharacteristic
160C2×D15—81no—
161C2×D15—81no—
162C2×D15—81no—
163C3×C4×C5—21no—
164C3×C4×C5—41no—
165C3×C4×C5—41no—
166C3×C4×C5—42no—
167C3×C4×C5—41no—
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C2×C3×Q8—21no—
173C2×C3×Q8C22⋊D511yescharacteristic
174C2×C3×D4C22⋊D511yescharacteristic
175C22×C3×C4—21no—
176C2×D12—101no—
177C2×D12—101no—
178C2×D12—101no—
179C3×C4⋊C4—22no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4C22⋊D511yescharacteristic
183C3×C4⋊C4C22⋊D511yescharacteristic
184C3×C4⋊C4C22⋊D512yes—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—21no—
188C3×C42—22no—
189C3×C42—21no—
190C3×C42C22×D511yescharacteristic
191#215—202no—
192#213—202no—
193C2×C3⋊C8—101no—
194C2×C3⋊C8—101no—
195C2×C3⋊C8—101no—
196C23×C5—21no—
197C22×D5—121no—
198C5×Q8—21no—
199C5×Q8—21no—
200C5×Q8—41no—
201C5×Q8—41no—
202C5×D4—21no—
203C5×D4—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—22no—
208C2×C4×C5—41no—
209C2×C4×C5—41no—
210C2×C4×C5C2×#6711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213D20—122no—
214D20—121no—
215D20—121no—
216D20—121no—
217D20—121no—
218#168—121no—
219#168—121no—
220#168—121no—
221C2×SD16—301no—
222C2×D8—301no—
223C4⋊Q8C2×D1511yescharacteristic
224#127—151no—
225#126—22no—
226#124—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8C2×D1511yescharacteristic
230C4×D4C2×D1511yescharacteristic
231#117—21no—
232C4⋊C8—151no—
233C4⋊C8—151no—
234#102—301no—
235#102—301no—
236#102—302no—
237C4×C8—151no—
238C2×C3×C5—81no—
239C2×C3×C5#44911yescharacteristic
240C2×C3×C5#44911yescharacteristic
241C2×C3×C5#45411yescharacteristic
242D15—161no—
243C23×C3—21no—
244C22×D3—201no—
245C3×Q8—21no—
246C3×Q8—21no—
247C3×Q8—41no—
248C3×Q8—41no—
249C3×D4—21no—
250C3×D4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260D12—202no—
261D12—201no—
262D12—201no—
263D12—201no—
264D12—201no—
265C3⋊C8—201no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—41no—
269C22×C5—41no—
270C22×C5—41no—
271C22×C5#95311yescharacteristic
272C2×D5—241no—
273C2×D5—241no—
274C2×D5—241no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—42no—
279C4×C5—41no—
280C4×C5#94911yescharacteristic
281C4×C5#94911yescharacteristic
282C4×C5#95011yescharacteristic
283C4×C5#95011yescharacteristic
284C2×Q8—21no—
285C2×Q8#122011yescharacteristic
286C2×D4—301no—
287C2×D4—301no—
288C2×D4—301no—
289C2×D4#122011yescharacteristic
290C22×C4—21no—
291SD16—602no—
292D8—602no—
293C2×C8—301no—
294C2×C8—301no—
295C2×C8—301no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4#122011yescharacteristic
300C4⋊C4#122011yescharacteristic
301C4⋊C4#122012yes—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—21no—
305C42—22no—
306C42—21no—
307C42C22×D1511yescharacteristic
308C3×C5#162811yescharacteristic, complemented, Hall
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3#409911yescharacteristic
313C2×D3—401no—
314C2×D3—401no—
315C2×D3—401no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—41no—
319C3×C4—42no—
320C3×C4—41no—
321C3×C4#409511yescharacteristic
322C3×C4#409511yescharacteristic
323C3×C4#409611yescharacteristic
324C3×C4#409611yescharacteristic
325C2×C5—81no—
326C2×C5#523811yescharacteristic
327C2×C5#523811yescharacteristic
328C2×C5#524511yescharacteristic
329D5—481no—
330C23—21no—
331C23—601no—
332Q8—21no—
333Q8—21no—
334Q8—41no—
335Q8—41no—
336D4—21no—
337D4—21no—
338D4—602no—
339D4—601no—
340D4—601no—
341D4—601no—
342D4—601no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4C2×#122011yescharacteristic
350C2×C4C2×#122011yescharacteristic
351C2×C4C2×#122011yescharacteristic
352C8—601no—
353C8—601no—
354C8—601no—
355C2×C3—81no—
356C2×C3#6552711yescharacteristic
357C2×C3#6552711yescharacteristic
358C2×C3#6553411yescharacteristic
359D3—801no—
360C5#7193111yescharacteristic, complemented, Sylow
361C22—41no—
362C22—41no—
363C22—41no—
364C22—1201no—
365C22—1201no—
366C22—1201no—
367C22#9184211yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—42no—
372C4—41no—
373C4#9183811yescharacteristic
374C4#9183811yescharacteristic
375C4#9183911yescharacteristic
376C4#9183911yescharacteristic
377C3#1060272411yescharacteristic, complemented, Sylow
378C2—81no—
379C2—2401no—
380C2#1175133911yescharacteristic
381C2#1175133911yescharacteristic
382C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#556C2
socleC22×C3×C5#120
prime radical#11751116C2
hypercenter#556D15
hypocenterC3×C5#1628
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C3×C5×#556C2semidirect
2. #11751189C2semidirect
3. #11751128C2semidirect
5. #11746368C2semidirect
6. #11746356C2semidirect
7. D4⋊(C3⋊#168)C2semidirect
27. C5×#556D3semidirect
58. C3×#556D5semidirect
149. #556D15semidirect
308. C3×C5#1628semidirect
360. C5#71931semidirect
377. C3#10602724semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5562
#117511892
#117511282
#117511162
#117463682
#117463562
D4⋊(C3⋊#168)2
#106027243
#719315