Finite Group Databasebeta

← #14288946

Subgroups — #14288946

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
2C3×C5×#492C211yesmaximal, characteristic, complemented
3#11751176C211yesmaximal, characteristic, complemented
4#11751173C211yesmaximal, characteristic
5#11746367C211yesmaximal, characteristic, complemented
6#11746280C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10602057—31nomaximal, Hall
9C2×C3×C5×SD16—22no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C3×C5×#127C2211yescharacteristic
12#91835—22no—
13C2×#6716—21no—
14C2×#6715—21no—
15#91786—21no—
16#91782—21no—
17C4⋊C4×D15—21no—
18#91779—21no—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C3×C4×C5×C8C2211yescharacteristic
22#91116—21no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#71264—51nomaximal, Hall
27#66064—31no—
28C5×#492D311yescharacteristic, complemented
29#65364—31no—
30#65361—31no—
31#64766—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8D412yes—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×D60D411yescharacteristic
39C2×C4×D15—21no—
40C2×C4×D15—22no—
41C2×Dic30D411yescharacteristic
42C3×C5×SD16—44no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47#6716—42no—
48#6715—42no—
49#6714—22no—
50#6714—21no—
51C4⋊Dic15—22no—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D411yescharacteristic
54#6712—22no—
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5730—51no—
60C3×#492D511yescharacteristic, complemented
61#5075—51no—
62#5072—51no—
63#4546—51no—
64#4459—51no—
65#4456—51no—
66C2×C5×SD16—22no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C5×#127C2×D311yescharacteristic
69#4092—62no—
70C2×#687—61no—
71C2×#686—61no—
72#4043—61no—
73#4039—61no—
74D5×C4⋊C4—61no—
75#4036—61no—
76C4×D20—31no—
77C4×Dic10—31no—
78C4×C5×C8C2×D311yescharacteristic
79#3964—61no—
80#3964—61no—
81C4⋊#168—31no—
82C4⋊#168—31no—
83#1622—151noSylow
84C23×C3×C5—41no—
85C22×D15—21no—
86C3×C5×Q8—42no—
87C3×C5×D4—42no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C3×C4×C5C2×D411yescharacteristic
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×Dic15—21no—
97C2×Dic15—21no—
98C2×Dic15—21no—
99D60—21no—
100D60SD1612yescomplemented
101C4×D15—41no—
102C4×D15—41no—
103C4×D15—82no—
104Dic30—21no—
105Dic30—21no—
106C3×C5×C8—22no—
107C3⋊#168—41no—
108C3⋊#168—41no—
109C2×C3×SD16—22no—
110C3×C4⋊Q8C2×D511yescharacteristic
111C3×#127C2×D511yescharacteristic
112#946—102no—
113C2×#214—101no—
114C2×#213—101no—
115#897—101no—
116#893—101no—
117D3×C4⋊C4—101no—
118#890—101no—
119C4×D12—51no—
120C4×Dic6—51no—
121C3×C4×C8C2×D511yescharacteristic
122#832—101no—
123#832—101no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)—51no—
126C2×C5×Q8#6712yes—
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×C5×D4—21no—
130C2×D20—31no—
131C2×C4×D5—61no—
132C2×C4×D5—62no—
133C2×Dic10—31no—
134C5×SD16—44no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C42×C5C22×D311yescharacteristic
139#687—122no—
140#686—122no—
141#685—62no—
142#685—61no—
143C4⋊Dic5—31no—
144C4⋊Dic5—31no—
145C4⋊Dic5—62no—
146#683—62no—
147#683—61no—
148C4×Dic5—61no—
149C2×#168—61no—
150C2×#168—61no—
151#554—151no—
152#492D1511yescharacteristic, complemented
153#460—151no—
154#459—151no—
155#333—151no—
156Q8⋊C8—151no—
157D4⋊C8—151no—
158C22×C3×C5—81no—
159C22×C3×C5—81no—
160C22×C3×C5—81no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—22no—
163C2×D15—41no—
164C2×D15—41no—
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×Q8C22⋊D512yes—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×D12—51no—
179C2×C4×D3—101no—
180C2×C4×D3—102no—
181C2×Dic6—51no—
182C3×SD16—44no—
183C2×C3×C8—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C42C22×D511yescharacteristic
187#214—202no—
188#213—202no—
189(C2×D3)⋊C4—102no—
190(C2×D3)⋊C4—101no—
191C4⋊Dic3—51no—
192C4⋊Dic3—51no—
193C4⋊Dic3—102no—
194Dic3⋊C4—102no—
195Dic3⋊C4—101no—
196C4×Dic3—101no—
197C2×C3⋊C8—101no—
198C2×C3⋊C8—101no—
199C23×C5—41no—
200C22×D5—61no—
201C5×Q8—42no—
202C5×D4—42no—
203C5×D4—41no—
204C5×D4—41no—
205C5×D4—41no—
206C5×D4—41no—
207C2×C4×C5—22no—
208C2×C4×C5D3×D411yescharacteristic
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5C2×#6711yescharacteristic
211C2×Dic5—61no—
212C2×Dic5—61no—
213C2×Dic5—61no—
214D20—32no—
215D20—61no—
216C4×D5—121no—
217C4×D5—121no—
218C4×D5—242no—
219Dic10—61no—
220Dic10—61no—
221C5×C8—22no—
222#168—121no—
223#168—121no—
224C2×SD16—22no—
225C2×SD16—301no—
226C2×D8—301no—
227C4⋊Q8C2×D1511yescharacteristic
228#127C2×D1511yescharacteristic
229#125—301no—
230C22⋊Q8—301no—
231C22⋊Q8—302no—
232C4×Q8—151no—
233C4×D4—151no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—151no—
237C4⋊C8—151no—
238#102—301no—
239#102—301no—
240C4×C8C2×D1511yescharacteristic
241C2×C3×C5—161no—
242C2×C3×C5#44811yescharacteristic
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45311yescharacteristic
245D15—42no—
246C23×C3—41no—
247C22×D3—101no—
248C3×Q8—42no—
249C3×D4—42no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C2×C3×C4—22no—
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C2×Dic3—101no—
259C2×Dic3—101no—
260C2×Dic3—101no—
261D12—52no—
262D12—101no—
263C4×D3—201no—
264C4×D3—201no—
265C4×D3—402no—
266Dic6—101no—
267Dic6—101no—
268C3×C8—22no—
269C3⋊C8—201no—
270C3⋊C8—201no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—81no—
274C22×C5#93711yescharacteristic
275C2×D5—62no—
276C2×D5—121no—
277C2×D5—121no—
278C4×C5—21no—
279C4×C5—42no—
280C4×C5D3×SD1611yescharacteristic
281C4×C5#91411yescharacteristic
282C4×C5#91511yescharacteristic
283C4×C5#91611yescharacteristic
284Dic5—121no—
285Dic5—121no—
286Dic5—121no—
287C2×Q8—151no—
288C2×Q8#122012yes—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—151no—
293C22×C4—302no—
294C22×C4—301no—
295SD16—44no—
296SD16—602no—
297D8—602no—
298C2×C8—21no—
299C2×C8—301no—
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—81no—
314C22×C3—81no—
315C22×C3—81no—
316C22×C3#408311yescharacteristic
317C2×D3—102no—
318C2×D3—201no—
319C2×D3—201no—
320C3×C4—21no—
321C3×C4—42no—
322C3×C4D5×SD1611yescharacteristic
323C3×C4#406011yescharacteristic
324C3×C4#406111yescharacteristic
325C3×C4#406211yescharacteristic
326Dic3—201no—
327Dic3—201no—
328Dic3—201no—
329C2×C5—161no—
330C2×C5#507711yescharacteristic
331C2×C5#517011yescharacteristic
332C2×C5#517211yescharacteristic
333D5—122no—
334C23—41no—
335C23—301no—
336Q8—42no—
337Q8—301no—
338Q8—301no—
339D4—42no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—152no—
345D4—301no—
346C2×C4—22no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4—301no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4—1202no—
353C2×C4D4×D1511yescharacteristic
354C2×C4D4×D1511yescharacteristic
355C2×C4C2×#122011yescharacteristic
356C8—22no—
357C8—601no—
358C8—601no—
359C2×C3—161no—
360C2×C3#6536611yescharacteristic
361C2×C3#6545911yescharacteristic
362C2×C3#6546111yescharacteristic
363D3—202no—
364C5#7126411yescharacteristic, complemented, Sylow
365C22—81no—
366C22—81no—
367C22—81no—
368C22—302no—
369C22—601no—
370C22—601no—
371C22#9182611yescharacteristic
372C4—21no—
373C4—42no—
374C4—601no—
375C4—601no—
376C4—601no—
377C4SD16×D1511yescharacteristic
378C4#9180311yescharacteristic
379C4#9180411yescharacteristic
380C4#9180511yescharacteristic
381C3#1060205711yescharacteristic, complemented, Sylow
382C2—161no—
383C2—602no—
384C2#1175117811yescharacteristic
385C2#1175127111yescharacteristic
386C2#1175127311yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#492C2
socleC22×C3×C5#120
prime radical#11751173C2
hypercenter#492D15
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #11756489C2semidirect
2. C3×C5×#492C2semidirect
3. #11751176C2semidirect
5. #11746367C2semidirect
6. #11746280C2semidirect
7. #11746277C2semidirect
28. C5×#492D3semidirect
60. C3×#492D5semidirect
100. D60SD16semidirect
152. #492D15semidirect
312. C3×C5#1622semidirect
364. C5#71264semidirect
381. C3#10602057semidirect

Maximal subgroups

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

subgroupindex
#117564892
C3×C5×#4922
#117511762
#117511732
#117463672
#117462802
#117462772
#106020573
#712645