Finite Group Databasebeta

← #14288952

Subgroups — #14288952

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#11756338C211yesmaximal, characteristic, complemented
2C3×C5×#460C211yesmaximal, characteristic, complemented
3#11751177C211yesmaximal, characteristic, complemented
4#11751173C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11746304C211yesmaximal, characteristic, complemented
7#11746302C211yesmaximal, characteristic, complemented
8#10601821—31nomaximal, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12#91835—21no—
13C2×#6716—22no—
14C2×#6715—21no—
15#91785—22no—
16C4⋊C4×D15—21no—
17C4×D60—21no—
18C4×D60C2211yescharacteristic
19#91759—21no—
20#91758C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C5×#102—21no—
23#91116—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4×C3⋊#168C2211yescharacteristic
26#71028—51nomaximal, Hall
27#65913—31no—
28C5×#460D311yescharacteristic, complemented
29#65365—31no—
30#65361—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8D411yescharacteristic
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×Dic30D412yes—
42C3×C5×SD16—42no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5C2311yescharacteristic
48#6716—44no—
49#6715—42no—
50#6714—22no—
51#6714—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15D411yescharacteristic
55#6712—22no—
56#6712—22no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59#5579—51no—
60C3×#460D511yescharacteristic, complemented
61#5076—51no—
62#5072—51no—
63#4535—51no—
64#4483—51no—
65#4481—51no—
66C2×C5×SD16—21no—
67C5×#127C2×D311yescharacteristic
68C4×C5×Q8C2×D311yescharacteristic
69#4092—61no—
70C2×#687—62no—
71C2×#686—61no—
72#4042—62no—
73D5×C4⋊C4—61no—
74C4×D20—31no—
75C4×D20—61no—
76#4016—61no—
77#4015—31no—
78C5×C4⋊C8C2×D311yescharacteristic
79C5×#102—21no—
80#3964—61no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1622—151noSylow
84C23×C3×C5—41no—
85C22×D15—21no—
86C3×C5×Q8—21no—
87C3×C5×Q8—21no—
88C3×C5×D4—42no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—22no—
100D60—21no—
101D60SD1612yescomplemented
102C4×D15—41no—
103C4×D15—41no—
104C4×D15—82no—
105Dic30—42no—
106C3×C5×C8—41no—
107C3⋊#168—22no—
108C3⋊#168—41no—
109C2×C3×SD16—21no—
110C3×#127C2×D511yescharacteristic
111C3×C4×Q8C2×D511yescharacteristic
112#946—101no—
113C2×#214—102no—
114C2×#213—101no—
115#896—102no—
116D3×C4⋊C4—101no—
117C4×D12—51no—
118C4×D12—101no—
119#870—101no—
120#869—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122C3×#102—21no—
123#832—101no—
124C4⋊(C3⋊C8)—51no—
125C4×C3⋊C8—51no—
126C2×C5×Q8#6711yescharacteristic
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—32no—
134C5×SD16—42no—
135C2×C5×C8—21no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4#6711yescharacteristic
138C42×C5—21no—
139C42×C5C22×D311yescharacteristic
140#687—124no—
141#686—122no—
142#685—62no—
143#685—61no—
144C4⋊Dic5—31no—
145C4⋊Dic5—61no—
146C4⋊Dic5—61no—
147#683—62no—
148#683—62no—
149C2×#168—61no—
150C2×#168—61no—
151#554—151no—
152#492—151no—
153#460D1511yescharacteristic, complemented
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—41no—
167C3×C4×C5—41no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5#13711yescharacteristic
172Dic15—41no—
173Dic15—42no—
174C2×C3×Q8C22⋊D511yescharacteristic
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—52no—
182C3×SD16—42no—
183C2×C3×C8—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4C22⋊D511yescharacteristic
186C3×C42—21no—
187C3×C42C22×D511yescharacteristic
188#214—204no—
189#213—202no—
190(C2×D3)⋊C4—102no—
191(C2×D3)⋊C4—101no—
192C4⋊Dic3—51no—
193C4⋊Dic3—101no—
194C4⋊Dic3—101no—
195Dic3⋊C4—102no—
196Dic3⋊C4—102no—
197C2×C3⋊C8—101no—
198C2×C3⋊C8—101no—
199C23×C5—41no—
200C22×D5—61no—
201C5×Q8—21no—
202C5×Q8—21no—
203C5×D4—42no—
204C5×D4—41no—
205C5×D4—41no—
206C5×D4—41no—
207C5×D4—41no—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C2×Dic5—61no—
214C2×Dic5—62no—
215D20—32no—
216D20—61no—
217C4×D5—121no—
218C4×D5—121no—
219C4×D5—242no—
220Dic10—122no—
221C5×C8—41no—
222#168—62no—
223#168—121no—
224C2×SD16—21no—
225C2×SD16—302no—
226C2×D8—301no—
227C4⋊Q8—151no—
228#127C2×D1511yescharacteristic
229#125—301no—
230C22⋊Q8—302no—
231C22⋊Q8—301no—
232C4×Q8C2×D1511yescharacteristic
233C4×D4—151no—
234C4×D4—301no—
235C2×C4⋊C4—301no—
236C4⋊C8—151no—
237C4⋊C8C2×D1511yescharacteristic
238#102—21no—
239#102—301no—
240C4×C8—151no—
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—21no—
249C3×Q8—21no—
250C3×D4—42no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C3×D4—41no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260C2×Dic3—101no—
261C2×Dic3—102no—
262D12—52no—
263D12—101no—
264C4×D3—201no—
265C4×D3—201no—
266C4×D3—402no—
267Dic6—202no—
268C3×C8—41no—
269C3⋊C8—102no—
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—41no—
280C4×C5—41no—
281C4×C5D3×SD1611yescharacteristic
282C4×C5#91511yescharacteristic
283C4×C5#93211yescharacteristic
284C4×C5#95011yescharacteristic
285Dic5—122no—
286Dic5—121no—
287C2×Q8—152no—
288C2×Q8#122011yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—151no—
293C22×C4—302no—
294C22×C4—301no—
295SD16—42no—
296SD16—604no—
297D8—602no—
298C2×C8—21no—
299C2×C8—301no—
300C2×C8—301no—
301C4⋊C4—21no—
302C4⋊C4—151no—
303C4⋊C4—302no—
304C4⋊C4—302no—
305C4⋊C4—301no—
306C4⋊C4—301no—
307C4⋊C4#122011yescharacteristic
308C22⋊C4—302no—
309C22⋊C4—301no—
310C42—21no—
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—41no—
322C3×C4—41no—
323C3×C4D5×SD1611yescharacteristic
324C3×C4#406111yescharacteristic
325C3×C4#407811yescharacteristic
326C3×C4#409611yescharacteristic
327Dic3—201no—
328Dic3—202no—
329C2×C5—161no—
330C2×C5#503711yescharacteristic
331C2×C5#517011yescharacteristic
332C2×C5#519811yescharacteristic
333D5—122no—
334C23—41no—
335C23—301no—
336Q8—21no—
337Q8—21no—
338Q8—602no—
339D4—42no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—152no—
345D4—301no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—301no—
349C2×C4—302no—
350C2×C4—601no—
351C2×C4—601no—
352C2×C4—1202no—
353C2×C4D4×D1511yescharacteristic
354C2×C4D4×D1511yescharacteristic
355C2×C4C2×#122011yescharacteristic
356C8—41no—
357C8—302no—
358C8—601no—
359C2×C3—161no—
360C2×C3#6532611yescharacteristic
361C2×C3#6545911yescharacteristic
362C2×C3#6548711yescharacteristic
363D3—202no—
364C5#7102811yescharacteristic, complemented, Sylow
365C22—81no—
366C22—81no—
367C22—81no—
368C22—302no—
369C22—601no—
370C22—601no—
371C22#9182611yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—602no—
376C4—601no—
377C4SD16×D1511yescharacteristic
378C4#9180411yescharacteristic
379C4#9182111yescharacteristic
380C4#9183911yescharacteristic
381C3#1060182111yescharacteristic, complemented, Sylow
382C2—161no—
383C2—602no—
384C2#1175113811yescharacteristic
385C2#1175127111yescharacteristic
386C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#460C2
socleC22×C3×C5#120
prime radical#11751173C2
hypercenter#460D15
hypocenterC3×C5#1622
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #11756338C2semidirect
2. C3×C5×#460C2semidirect
3. #11751177C2semidirect
5. #11746356C2semidirect
6. #11746304C2semidirect
7. #11746302C2semidirect
28. C5×#460D3semidirect
60. C3×#460D5semidirect
101. D60SD16semidirect
153. #460D15semidirect
312. C3×C5#1622semidirect
364. C5#71028semidirect
381. C3#10601821semidirect

Maximal subgroups

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

subgroupindex
#117563382
C3×C5×#4602
#117511772
#117511732
#117463562
#117463042
#117463022
#106018213
#710285