Finite Group Databasebeta

← #14290042

Subgroups — #14290042

Order 1920.

500 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752536C211yesmaximal, characteristic
2C3×#65138C211yesmaximal, characteristic, complemented
3#11746971C211yesmaximal, characteristic, complemented
4#11746901C211yesmaximal, characteristic, complemented
5#11746304C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10599200—31nomaximal, Hall
9C2×#6768—21no—
10C4×D60C2211yescharacteristic
11C5×#874C2211yescharacteristic
12C2×C3×Dic20—21no—
13C3×#4015C2211yescharacteristic
14C3×C4×Dic10C2211yescharacteristic
15#91466—21no—
16#91451—21no—
17#91416—22no—
18Dic5×D12—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3948—21no—
23#90990—21no—
24#90968—21no—
25#90966—22no—
26#71061—51nomaximal, Hall
27#66052—31no—
28#65359—31no—
29#65138D311yescharacteristic, complemented
30#65135—31no—
31C5×#331—31no—
32#64704—31no—
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12D412yes—
39C2×C3×Dic10—21no—
40C2×C3×Dic10D411yescharacteristic
41C2×#1203—22no—
42C2×#1203—22no—
43C2×D3×Dic5—22no—
44#6768—42no—
45#6768—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48#6714—21no—
49C4⋊Dic15D411yescharacteristic
50C2×C3⋊#168—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×Dic20—42no—
58(C2×D3)⋊Dic5—22no—
59#5577—51no—
60C3×#462—51no—
61#5088—51no—
62#5087—51no—
63#4535—51no—
64#4485D511yescharacteristic, complemented
65#4483—51no—
66C2×#711—61no—
67C5×#127—31no—
68#4086—61no—
69#4085—62no—
70#4084—61no—
71D4×Dic5—61no—
72C2×Dic20—21no—
73C4×D20—31no—
74#4015C2×D311yescharacteristic
75C4×Dic10C2×D311yescharacteristic
76C5×C4⋊C8—31no—
77C5×C4⋊C8C2×D311yescharacteristic
78#3964—62no—
79#3953—61no—
80#3950—61no—
81#3948—21no—
82C4×#168—31no—
83#1641—151noSylow
84C22×D15—21no—
85C22×C5×D3—22no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90D60—21no—
91D60—21no—
92C4×D15—41no—
93C4×D15—41no—
94C5×D12—42no—
95C5×D12—41no—
96C5×D12—41no—
97C5×D12—41no—
98C5×D12—41no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—41no—
102C3×Dic10—21no—
103C3×Dic10—41no—
104C3×Dic10—41no—
105C3×Dic10D812yes—
106#1203—44no—
107#1203—82no—
108D3×Dic5—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C5×C3⋊C8—41no—
112C2×#239—101no—
113C2×C3×Q16—101no—
114C3×C4⋊Q8—51no—
115C3×C4×Q8—51no—
116#895—101no—
117#895—102no—
118#874—101no—
119#874C2×D511yescharacteristic
120C4×D12—51no—
121C4×D12—101no—
122C3×C4⋊C8C2×D511yescharacteristic
123C3×#103—101no—
124#809—101no—
125#809—102no—
126#807—101no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C4×C3⋊C8—51no—
129C2×C5×D4—32no—
130C2×C5×D4—61no—
131C2×C5×D4—61no—
132C2×C22⋊D5—62no—
133C2×C22⋊D5—62no—
134C22×Dic5—62no—
135#711—122no—
136#711—122no—
137C2×D20—31no—
138C2×C4×D5—61no—
139C2×Dic10—21no—
140C2×Dic10#6711yescharacteristic
141C2×C5×C8—21no—
142C2×C5×C8—61no—
143C42×C5C22×D311yescharacteristic
144C22⋊Dic5—62no—
145#685—61no—
146C4⋊Dic5—21no—
147C4⋊Dic5—21no—
148C4⋊Dic5—31no—
149C4⋊Dic5#6711yescharacteristic
150#683—21no—
151C4×Dic5—21no—
152C2×#168—61no—
153Dic20—42no—
154#550—151no—
155#486—151no—
156#474—151no—
157#462—51no—
158#331—31no—
159Q8⋊C8—151no—
160D4⋊C8—151no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—41no—
163C2×D15—41no—
164C2×D15—41no—
165C2×C5×D3—42no—
166C2×C5×D3—42no—
167C2×C5×D3—42no—
168C3×C4×C5—21no—
169C3×C4×C5C2×D811yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—41no—
174C3×Dic5—22no—
175C3×Dic5—41no—
176C3×Dic5—81no—
177C2×C3×Q8—51no—
178C2×C3×Q8—101no—
179#239—202no—
180#239—202no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—51no—
184C2×D12—102no—
185C2×D12—102no—
186C2×D12D2012yes—
187C2×C4×D3—102no—
188C2×C4×D3—101no—
189C3×Q16—202no—
190C2×C3×C8—21no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—101no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C42—101no—
196C3×C42C22×D511yescharacteristic
197(C2×D3)⋊C4—102no—
198(C2×D3)⋊C4—101no—
199C4⋊Dic3—51no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—101no—
202C23×C5—62no—
203C22×D5—61no—
204C5×D4—122no—
205C5×D4—121no—
206C5×D4—121no—
207C5×D4—121no—
208C5×D4—121no—
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C22⋊D5—124no—
213C22⋊D5—242no—
214C2×Dic5—21no—
215C2×Dic5—21no—
216C2×Dic5—41no—
217C2×Dic5—61no—
218C2×Dic5—124no—
219D20—61no—
220D20—61no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—21no—
224Dic10—41no—
225Dic10—41no—
226Dic10#21312yes—
227C5×C8—41no—
228C5×C8—121no—
229#168—121no—
230C2×#41—301no—
231C2×Q16—101no—
232C4⋊Q8—51no—
233#127—31no—
234#127—301no—
235#121—301no—
236#121—302no—
237C4×Q8—51no—
238C4×D4—151no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8—31no—
242C4⋊C8D3×D511yescharacteristic
243#103—101no—
244#102—301no—
245#102—302no—
246C4×C8—151no—
247C2×C3×C5#44711yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45511yescharacteristic
250D15—81no—
251C5×D3—82no—
252C22×D3—22no—
253C22×D3—101no—
254C3×Q8—52no—
255C3×Q8—101no—
256C3×Q8—201no—
257C3×Q8—201no—
258C2×C3×C4—101no—
259C2×C3×C4—101no—
260C2×C3×C4—201no—
261C2×C3×C4C2×D2011yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×Dic3—101no—
265D12—42no—
266D12—41no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—101no—
271D12—101no—
272D12—204no—
273D12—402no—
274C4×D3—204no—
275C4×D3—201no—
276C4×D3—201no—
277C3×C8—41no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—122no—
281C22×C5—122no—
282C22×C5—122no—
283C22×C5#93711yescharacteristic
284C2×D5—121no—
285C2×D5—121no—
286C2×D5—121no—
287C4×C5—21no—
288C4×C5#91811yescharacteristic
289C4×C5#91911yescharacteristic
290C4×C5C2×#21311yescharacteristic
291C4×C5#94911yescharacteristic
292Dic5—22no—
293Dic5—41no—
294Dic5—81no—
295Dic5—121no—
296#41—602no—
297#41—602no—
298C2×Q8—51no—
299C2×Q8—101no—
300C2×D4—32no—
301C2×D4—61no—
302C2×D4—61no—
303C2×D4—151no—
304C2×D4—302no—
305C2×D4—302no—
306C22×C4—302no—
307C22×C4—301no—
308Q16—202no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—301no—
312C4⋊C4—51no—
313C4⋊C4—101no—
314C4⋊C4—101no—
315C4⋊C4—101no—
316C4⋊C4—151no—
317C22⋊C4—302no—
318C22⋊C4—301no—
319C42—101no—
320C42C2×D3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3#402811yescharacteristic
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—42no—
326C2×D3—201no—
327C2×D3—201no—
328C2×D3—201no—
329C3×C4—21no—
330C3×C4—102no—
331C3×C4—201no—
332C3×C4—401no—
333C3×C4D5×D811yescharacteristic
334C3×C4#405811yescharacteristic
335C3×C4#406011yescharacteristic
336C3×C4#406111yescharacteristic
337Dic3—201no—
338C2×C5—242no—
339C2×C5#503611yescharacteristic
340C2×C5#518711yescharacteristic
341C2×C5#520211yescharacteristic
342D5—241no—
343C23—62no—
344C23—301no—
345Q8—52no—
346Q8—101no—
347Q8—201no—
348Q8—201no—
349D4—122no—
350D4—121no—
351D4—121no—
352D4—121no—
353D4—121no—
354D4—301no—
355D4—301no—
356D4—604no—
357D4—1202no—
358C2×C4—101no—
359C2×C4—101no—
360C2×C4—201no—
361C2×C4—301no—
362C2×C4—604no—
363C2×C4—601no—
364C2×C4—601no—
365C2×C4D3×D2011yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C8—41no—
369C8—121no—
370C8—601no—
371C2×C3#6503511yescharacteristic
372C2×C3#6506211yescharacteristic
373C2×C3#6507211yescharacteristic
374D3—82no—
375D3—401no—
376C5#7106111yescharacteristic, complemented, Sylow
377C22—122no—
378C22—122no—
379C22—122no—
380C22—601no—
381C22—601no—
382C22—601no—
383C22#9147411yescharacteristic
384C4—21no—
385C4—102no—
386C4—201no—
387C4—401no—
388C4—601no—
389C4#9127911yescharacteristic
390C4#9128011yescharacteristic
391C4D5×#21311yescharacteristic
392C4#9150211yescharacteristic
393C3#1059920011yescharacteristic, complemented, Sylow
394C2—242no—
395C2—1201no—
396C2#1174748011yescharacteristic
397C2#1174815111yescharacteristic
398C2#1174824111yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752536C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1641
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#65138C2semidirect
3. #11746971C2semidirect
4. #11746901C2semidirect
5. #11746304C2semidirect
6. C5×#4485C2semidirect
7. #11745840C2semidirect
29. #65138D3semidirect
64. #4485D5semidirect
321. C3×C5#1641semidirect
376. C5#71061semidirect
393. C3#10599200semidirect

Maximal subgroups

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

subgroupindex
#117525362
C3×#651382
#117469712
#117469012
#117463042
C5×#44852
#117458402
#105992003
#710615