Finite Group Databasebeta

← #14290040

Subgroups — #14290040

Order 1920.

500 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752554C211yesmaximal, characteristic
2C3×#64983C211yesmaximal, characteristic, complemented
3#11747104C211yesmaximal, characteristic, complemented
4#11746900C211yesmaximal, characteristic, complemented
5#11746277C211yesmaximal, characteristic, complemented
6C5×#4459C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10598983—31nomaximal, Hall
9C2×#6765—21no—
10C4×Dic30C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91463—21no—
15#91456—21no—
16#91434—21no—
17#91408—22no—
18C2×#6662—21no—
19C3×C4×C5×C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×#3953—22no—
23#90989—21no—
24#90971—21no—
25#90966—21no—
26#71207—51nomaximal, Hall
27#65887—31no—
28#65296—31no—
29#65138—31no—
30#64983D311yescharacteristic, complemented
31C5×D4⋊C8—31no—
32#64705—31no—
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20D412yes—
40C2×C3×Dic10—21no—
41C2×#1201—22no—
42C2×#1201—22no—
43C2×D5×Dic3—22no—
44#6765—42no—
45#6765—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48C4⋊Dic15D411yescharacteristic
49#6712—21no—
50C4×Dic15—21no—
51C2×C3⋊#168—21no—
52C5×(C2×D3)⋊C4—21no—
53C5×C4⋊Dic3D411yescharacteristic
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57#6665—22no—
58#6662—42no—
59#5718—51no—
60C3×#486—51no—
61#5090—51no—
62#5087—51no—
63#4544—51no—
64#4459D511yescharacteristic, complemented
65#4456—51no—
66C2×#709—61no—
67C4×C5×D4—31no—
68#4086—61no—
69#4076—61no—
70C2×Dic20—61no—
71#4039—61no—
72#4030—62no—
73#4020C2×D311yescharacteristic
74#4015C2×D311yescharacteristic
75C4×Dic10—31no—
76C5×C4⋊C8—31no—
77C4×C5×C8C2×D311yescharacteristic
78#3964—61no—
79#3953—22no—
80#3948—61no—
81#3939—61no—
82C4⋊#168—31no—
83#1641—151noSylow
84C22×C5×D3—21no—
85C22×C3×D5—22no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30D812yes—
93C2×C5×Dic3—21no—
94C5×D12—21no—
95C5×D12—21no—
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C2×C3×Dic5—41no—
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×Dic10—41no—
105C3×Dic10—41no—
106#1201—44no—
107#1201—82no—
108D5×Dic3—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C5×C3⋊C8—41no—
112C2×#237—101no—
113C3×C4⋊Q8—51no—
114C3×#127—51no—
115C2×#216—101no—
116#940—101no—
117#939—102no—
118#938—101no—
119D4×Dic3—101no—
120C4×D12C2×D511yescharacteristic
121C4×Dic6—51no—
122C3×#102—102no—
123C3×C4×C8C2×D511yescharacteristic
124#835—101no—
125#809—101no—
126#807—101no—
127C4⋊(C3⋊C8)—51no—
128C4⋊(C3⋊C8)C2×D511yescharacteristic
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133#709—122no—
134#709—122no—
135C2×D20—21no—
136C2×D20—21no—
137C2×D20#6712yes—
138C2×C4×D5—62no—
139C2×Dic10—21no—
140C2×Dic10—31no—
141C2×C5×C8—21no—
142C2×C5×C8—61no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#685—62no—
147C4⋊Dic5—21no—
148C4⋊Dic5—21no—
149C4⋊Dic5—31no—
150#683—61no—
151C4×Dic5—61no—
152C2×#168—61no—
153Dic20—122no—
154#550—151no—
155#486—51no—
156#474—151no—
157#462—151no—
158#331—151no—
159Q8⋊C8—151no—
160D4⋊C8—31no—
161C22×C3×C5#12011yescharacteristic
162C2×C5×D3—41no—
163C2×C5×D3—41no—
164C2×C5×D3—41no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C2×C3×D5—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—22no—
174Dic15—41no—
175C3×Dic5—81no—
176C5×Dic3—41no—
177C2×C3×Q8—101no—
178C2×C3×D4—52no—
179C2×C3×D4—101no—
180C2×C3×D4—101no—
181C2×#67—102no—
182C2×#67—102no—
183C22×Dic3—102no—
184#237—202no—
185#237—202no—
186C2×D12D2011yescharacteristic
187C2×C4×D3—21no—
188C2×Dic6—51no—
189C2×C3×C8—21no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C42C22×D511yescharacteristic
193#217—102no—
194#216—202no—
195(C2×D3)⋊C4—21no—
196C4⋊Dic3—51no—
197C4⋊Dic3D2011yescharacteristic
198Dic3⋊C4—101no—
199C4×Dic3—101no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—101no—
202C23×C5—61no—
203C22×D5—22no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—61no—
207C2×C4×C5—121no—
208C2×C4×C5—121no—
209C2×C4×C5D3×D411yescharacteristic
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C22⋊D5—124no—
213C22⋊D5—242no—
214C2×Dic5—41no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—124no—
223Dic10—32no—
224Dic10—41no—
225Dic10—41no—
226Dic10—61no—
227C5×C8—41no—
228C5×C8—121no—
229#168—121no—
230C2×#41—301no—
231C2×Q16—301no—
232C4⋊Q8—51no—
233#127—51no—
234#127—301no—
235#121—302no—
236#121—301no—
237C4×Q8—151no—
238C4×D4—31no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8—31no—
242C4⋊C8—151no—
243#103—301no—
244#102—102no—
245#102—301no—
246C4×C8D3×D511yescharacteristic
247C2×C3×C5#44711yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45511yescharacteristic
250C3×D5—82no—
251C5×D3—81no—
252C23×C3—102no—
253C22×D3—21no—
254C3×Q8—201no—
255C3×Q8—201no—
256C3×D4—202no—
257C3×D4—201no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C2×C3×C4—201no—
262C2×C3×C4C2×D2011yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4D4×D511yescharacteristic
265#67—204no—
266#67—402no—
267C2×Dic3—21no—
268C2×Dic3—101no—
269C2×Dic3—101no—
270C2×Dic3—204no—
271D12—21no—
272D12—21no—
273C4×D3—41no—
274C4×D3—41no—
275Dic6—52no—
276Dic6—101no—
277C3×C8—41no—
278C3⋊C8—41no—
279C3⋊C8—201no—
280C22×C5—121no—
281C22×C5—121no—
282C22×C5—121no—
283C22×C5#93711yescharacteristic
284C2×D5—42no—
285C2×D5—42no—
286C2×D5—42no—
287C4×C5—21no—
288C4×C5—121no—
289C4×C5D3×D811yescharacteristic
290C4×C5#91111yescharacteristic
291C4×C5#91511yescharacteristic
292C4×C5#91611yescharacteristic
293Dic5—62no—
294Dic5—81no—
295Dic5—121no—
296#41—602no—
297#41—602no—
298C2×Q8—101no—
299C2×Q8—151no—
300C2×D4—31no—
301C2×D4—52no—
302C2×D4—101no—
303C2×D4—101no—
304C2×D4—302no—
305C2×D4—302no—
306C22×C4—61no—
307C22×C4—302no—
308Q16—602no—
309C2×C8—21no—
310C2×C8—61no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—101no—
314C4⋊C4—101no—
315C4⋊C4—151no—
316C4⋊C4—301no—
317C22⋊C4—61no—
318C22⋊C4—302no—
319C42—301no—
320C42C2×D3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3#402811yescharacteristic
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C3×C4—21no—
330C3×C4—401no—
331C3×C4#405011yescharacteristic
332C3×C4#405511yescharacteristic
333C3×C4D5×D811yescharacteristic
334C3×C4#406011yescharacteristic
335Dic3—41no—
336Dic3—102no—
337Dic3—201no—
338C2×C5—241no—
339C2×C5#506111yescharacteristic
340C2×C5#515611yescharacteristic
341C2×C5#517311yescharacteristic
342D5—82no—
343C23—61no—
344C23—102no—
345Q8—152no—
346Q8—201no—
347Q8—201no—
348Q8—301no—
349D4—61no—
350D4—61no—
351D4—202no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356D4—604no—
357D4—1202no—
358C2×C4—61no—
359C2×C4—121no—
360C2×C4—121no—
361C2×C4—201no—
362C2×C4—301no—
363C2×C4—301no—
364C2×C4—604no—
365C2×C4D3×D2011yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C8—41no—
369C8—121no—
370C8—601no—
371C2×C3—402no—
372C2×C3#6502211yescharacteristic
373C2×C3#6506211yescharacteristic
374C2×C3#6511411yescharacteristic
375D3—81no—
376C5#7120711yescharacteristic, complemented, Sylow
377C22—121no—
378C22—121no—
379C22—121no—
380C22—202no—
381C22—202no—
382C22—202no—
383C22#9147411yescharacteristic
384C4—21no—
385C4—121no—
386C4—302no—
387C4—401no—
388C4—601no—
389C4#9125611yescharacteristic
390C4#9125811yescharacteristic
391C4#9127211yescharacteristic
392C4#9127411yescharacteristic
393C3#1059898311yescharacteristic, complemented, Sylow
394C2—241no—
395C2—402no—
396C2#1174711511yescharacteristic
397C2#1174811311yescharacteristic
398C2#1174814711yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#11752554C2
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×#64983C2semidirect
3. #11747104C2semidirect
4. #11746900C2semidirect
5. #11746277C2semidirect
6. C5×#4459C2semidirect
7. #11745852C2semidirect
30. #64983D3semidirect
64. #4459D5semidirect
321. C3×C5#1641semidirect
376. C5#71207semidirect
393. C3#10598983semidirect

Maximal subgroups

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

subgroupindex
#117525542
C3×#649832
#117471042
#117469002
#117462772
C5×#44592
#117458522
#105989833
#712075