Finite Group Databasebeta

← #14288958

Subgroups — #14288958

Order 1920.

472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#11756489C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4#11750944C211yesmaximal, characteristic
5C3×C5×#333C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746304C211yesmaximal, characteristic, complemented
8#10599283—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835—22no—
11C2×#6717—22no—
12C2×D120—21no—
13C2×#6706—21no—
14#91786—21no—
15#91782—21no—
16C4⋊C4×D15—21no—
17#91779—21no—
18#91763C2211yescharacteristic
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×C4⋊C8C2211yescharacteristic
23#91105—21no—
24#91105—21no—
25C4×C3⋊#168C2211yescharacteristic
26#68490—51nomaximal, Hall
27#66064—31no—
28#65374—31no—
29#65137—31no—
30#65132—31no—
31C5×#333D311yescharacteristic, complemented
32#64704—31no—
33#64703—31no—
34C2×C3×C5×Q8D412yes—
35C2×D60—21no—
36C2×D60—21no—
37C2×D60—21no—
38C2×D60D411yescharacteristic
39C2×C4×D15—21no—
40C2×C4×D15—22no—
41C2×Dic30D411yescharacteristic
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6717—44no—
48#6714—22no—
49#6714—21no—
50C4⋊Dic15—22no—
51C4⋊Dic15D411yescharacteristic
52C4⋊Dic15D411yescharacteristic
53#6712—22no—
54#6712—21no—
55C4×Dic15—21no—
56C2×C3⋊#168—21no—
57D120—42no—
58#6706—42no—
59#5730—51no—
60#5085—51no—
61#4848—51no—
62#4843—51no—
63C3×#333D511yescharacteristic, complemented
64#4484—51no—
65#4483—51no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4092—62no—
68C2×#688—62no—
69C2×D40—61no—
70C2×#677—61no—
71#4043—61no—
72#4039—61no—
73D5×C4⋊C4—61no—
74#4036—61no—
75#4020—31no—
76C4×D20—31no—
77C4×Dic10—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×C4⋊C8C2×D311yescharacteristic
80#3953—61no—
81#3953—61no—
82C4×#168—31no—
83#1622—151noSylow
84C22×D15—21no—
85C22×D15—41no—
86C3×C5×Q8—42no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—21no—
94D60—21no—
95D60—42no—
96D60—41no—
97D60—41no—
98D60—41no—
99D60—41no—
100D60SD1612yescomplemented
101C4×D15—41no—
102C4×D15—41no—
103C4×D15—82no—
104Dic30—21no—
105Dic30—21no—
106C3×C5×C8—41no—
107C3×C5×C8—41no—
108C3⋊#168—22no—
109C3×C4⋊Q8C2×D511yescharacteristic
110#946—102no—
111C2×#215—102no—
112C2×D24—101no—
113C2×#204—101no—
114#897—101no—
115#893—101no—
116D3×C4⋊C4—101no—
117#890—101no—
118#874—51no—
119C4×D12—51no—
120C4×Dic6—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×C4⋊C8C2×D511yescharacteristic
123#821—101no—
124#821—101no—
125C4×C3⋊C8—51no—
126C2×C5×Q8D1212yes—
127C2×D20—31no—
128C2×D20—61no—
129C2×D20—61no—
130C2×D20—61no—
131C2×C4×D5—61no—
132C2×C4×D5—62no—
133C2×Dic10—31no—
134C2×C5×C8—21no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C42×C5C22×D311yescharacteristic
139#688—124no—
140#685—62no—
141#685—61no—
142C4⋊Dic5—31no—
143C4⋊Dic5—31no—
144C4⋊Dic5—62no—
145#683—62no—
146#683—61no—
147C4×Dic5—61no—
148C2×#168—61no—
149D40—122no—
150#677—122no—
151#554—151no—
152#492—151no—
153#460—151no—
154#459—151no—
155#333D1511yescharacteristic, complemented
156Q8⋊C8—151no—
157D4⋊C8—151no—
158C22×C3×C5#12011yescharacteristic
159C2×D15—22no—
160C2×D15—41no—
161C2×D15—41no—
162C2×D15—81no—
163C2×D15—81no—
164C2×D15—81no—
165C3×C4×C5—21no—
166C3×C4×C5—42no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5#13711yescharacteristic
171Dic15—41no—
172Dic15—41no—
173Dic15—41no—
174C2×C3×Q8D2012yes—
175C2×D12—51no—
176C2×D12—101no—
177C2×D12—101no—
178C2×D12—101no—
179C2×C4×D3—101no—
180C2×C4×D3—102no—
181C2×Dic6—51no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187#215—204no—
188(C2×D3)⋊C4—102no—
189(C2×D3)⋊C4—101no—
190C4⋊Dic3—51no—
191C4⋊Dic3—51no—
192C4⋊Dic3—102no—
193Dic3⋊C4—102no—
194Dic3⋊C4—101no—
195C4×Dic3—101no—
196C2×C3⋊C8—101no—
197D24—202no—
198#204—202no—
199C22×D5—61no—
200C22×D5—121no—
201C5×Q8—42no—
202C2×C4×C5—22no—
203C2×C4×C5C2×D1211yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×Dic5—61no—
207C2×Dic5—61no—
208C2×Dic5—61no—
209D20—32no—
210D20—61no—
211D20—122no—
212D20—121no—
213D20—121no—
214D20—121no—
215D20—121no—
216C4×D5—121no—
217C4×D5—121no—
218C4×D5—242no—
219Dic10—61no—
220Dic10—61no—
221C5×C8—41no—
222C5×C8—41no—
223#168—62no—
224C2×SD16—301no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8C2×D1511yescharacteristic
228#127—151no—
229#125—301no—
230C22⋊Q8—301no—
231C22⋊Q8—302no—
232C4×Q8—151no—
233C4×D4—151no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8C2×D1511yescharacteristic
237C4⋊C8C2×D1511yescharacteristic
238#102—301no—
239#102—301no—
240C4×C8—151no—
241C2×C3×C5#44811yescharacteristic
242C2×C3×C5#44911yescharacteristic
243C2×C3×C5#45311yescharacteristic
244D15—42no—
245D15—161no—
246C22×D3—101no—
247C22×D3—201no—
248C3×Q8—42no—
249C2×C3×C4—22no—
250C2×C3×C4C2×D2011yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×Dic3—101no—
254C2×Dic3—101no—
255C2×Dic3—101no—
256D12—52no—
257D12—101no—
258D12—202no—
259D12—201no—
260D12—201no—
261D12—201no—
262D12—201no—
263C4×D3—201no—
264C4×D3—201no—
265C4×D3—402no—
266Dic6—101no—
267Dic6—101no—
268C3×C8—41no—
269C3×C8—41no—
270C3⋊C8—102no—
271C22×C5#88211yescharacteristic
272C2×D5—62no—
273C2×D5—121no—
274C2×D5—121no—
275C2×D5—241no—
276C2×D5—241no—
277C2×D5—241no—
278C4×C5—21no—
279C4×C5—42no—
280C4×C5D3×SD1611yescharacteristic
281C4×C5#91411yescharacteristic
282C4×C5#91811yescharacteristic
283C4×C5#91911yescharacteristic
284Dic5—121no—
285Dic5—121no—
286Dic5—121no—
287C2×Q8—151no—
288C2×Q8D6012yes—
289C2×D4—151no—
290C2×D4—301no—
291C2×D4—301no—
292C2×D4—301no—
293C22×C4—302no—
294C22×C4—301no—
295SD16—602no—
296SD16—604no—
297D8—602no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—301no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—151no—
304C4⋊C4—151no—
305C4⋊C4—302no—
306C4⋊C4—302no—
307C4⋊C4—301no—
308C22⋊C4—302no—
309C22⋊C4—301no—
310C42—301no—
311C42C22×D1511yescharacteristic
312C3×C5#162211yescharacteristic, complemented, Hall
313C22×C3#402811yescharacteristic
314C2×D3—102no—
315C2×D3—201no—
316C2×D3—201no—
317C2×D3—401no—
318C2×D3—401no—
319C2×D3—401no—
320C3×C4—21no—
321C3×C4—42no—
322C3×C4D5×SD1611yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406411yescharacteristic
325C3×C4#406511yescharacteristic
326Dic3—201no—
327Dic3—201no—
328Dic3—201no—
329C2×C5#474711yescharacteristic
330C2×C5#480611yescharacteristic
331C2×C5#481011yescharacteristic
332D5—122no—
333D5—481no—
334C23—301no—
335C23—601no—
336Q8—42no—
337Q8—301no—
338Q8—301no—
339D4—152no—
340D4—301no—
341D4—602no—
342D4—601no—
343D4—601no—
344D4—601no—
345D4—601no—
346C2×C4—22no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4—301no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4—1202no—
353C2×C4C2×D6011yescharacteristic
354C2×C4D4×D1511yescharacteristic
355C2×C4D4×D1511yescharacteristic
356C8—41no—
357C8—41no—
358C8—302no—
359C2×C3#6503611yescharacteristic
360C2×C3#6509511yescharacteristic
361C2×C3#6510011yescharacteristic
362D3—202no—
363D3—801no—
364C5#6849011yescharacteristic, complemented, Sylow
365C22—302no—
366C22—601no—
367C22—601no—
368C22—1201no—
369C22—1201no—
370C22—1201no—
371C22#9177111yescharacteristic
372C4—21no—
373C4—42no—
374C4—601no—
375C4—601no—
376C4—601no—
377C4SD16×D1511yescharacteristic
378C4#9180311yescharacteristic
379C4#9180711yescharacteristic
380C4#9180811yescharacteristic
381C3#1059928311yescharacteristic, complemented, Sylow
382C2—602no—
383C2—2401no—
384C2#1175084811yescharacteristic
385C2#1175090711yescharacteristic
386C2#1175091111yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5#120
prime radical#11750944C2
hypercenter#333D15
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
2. #11751186C2semidirect
3. #11750949C2semidirect
5. C3×C5×#333C2semidirect
6. #11746305C2semidirect
7. #11746304C2semidirect
31. C5×#333D3semidirect
63. C3×#333D5semidirect
100. D60SD16semidirect
155. #333D15semidirect
312. C3×C5#1622semidirect
364. C5#68490semidirect
381. C3#10599283semidirect

Maximal subgroups

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

subgroupindex
#117564892
#117511862
#117509492
#117509442
C3×C5×#3332
#117463052
#117463042
#105992833
#684905