Finite Group Databasebeta

← #14290045

Subgroups — #14290045

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#11752677C211yesmaximal, characteristic
2C5×#4849C211yesmaximal, characteristic, complemented
3#11746912C211yesmaximal, characteristic, complemented
4#11746886C211yesmaximal, characteristic, complemented
5#11746306C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745843C211yesmaximal, characteristic, complemented
8#10601854—31nomaximal, Hall
9C2×#6773—21no—
10#91763C2211yescharacteristic
11C2×C5×Dic12—21no—
12C5×#869C2211yescharacteristic
13C4×C5×Dic6C2211yescharacteristic
14C3×C4×D20C2211yescharacteristic
15#91459—22no—
16#91458—21no—
17#91450—21no—
18#91428—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#816—21no—
22C3×C4×#168C2211yescharacteristic
23#90989—21no—
24#90969—22no—
25#90964—21no—
26#68190—51nomaximal, Hall
27#65911—31no—
28C5×#462—31no—
29#65377—31no—
30#65376—31no—
31Q8⋊#168—31no—
32#64705—31no—
33#64703D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60D412yes—
37C2×C5×Dic6—21no—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×D20D411yescharacteristic
40C2×C3×C4×D5—21no—
41C2×#1202—22no—
42C2×#1202—22no—
43C2×#1200—22no—
44#6773—42no—
45#6773—42no—
46C2×C3×C5×C8—21no—
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3—21no—
54C5×Dic12—42no—
55C3×#685—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C2×C3×#168—21no—
58#6667—22no—
59#5553—51no—
60#5007—51no—
61#4849D511yescharacteristic, complemented
62#4694—51no—
63C3×D4⋊C8—51no—
64#4485—51no—
65#4456—51no—
66C2×#713—61no—
67C2×C5×Q16—61no—
68C5×C4⋊Q8—31no—
69C4×C5×Q8—31no—
70#4041—62no—
71#4041—61no—
72#4020—31no—
73#4020—61no—
74C4×D20—61no—
75C4×D20C2×D311yescharacteristic
76C5×C4⋊C8C2×D311yescharacteristic
77C5×#103—61no—
78#3941—62no—
79#3941—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1641—151noSylow
84C22×D15—22no—
85C22×C3×D5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89D60—42no—
90D60—41no—
91D60—41no—
92D60—41no—
93D60—41no—
94C2×C5×Dic3—21no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—41no—
97C5×Dic6—21no—
98C5×Dic6—41no—
99C5×Dic6—41no—
100C5×Dic6D812yes—
101C2×C3×Dic5—21no—
102C3×D20—21no—
103C3×D20—21no—
104C3×C4×D5—41no—
105C3×C4×D5—41no—
106#1202—44no—
107#1202—82no—
108#1200—44no—
109C3×C5×C8—41no—
110C3⋊#168—41no—
111C3×#168—41no—
112C2×#235—101no—
113C3×C4×D4—51no—
114#940—101no—
115#930—101no—
116C2×Dic12—21no—
117#893—101no—
118#884—102no—
119#874—51no—
120#869C2×D511yescharacteristic
121C4×Dic6C2×D511yescharacteristic
122C3×C4⋊C8C2×D511yescharacteristic
123C3×C4×C8—51no—
124#832—101no—
125#821—102no—
126#816—21no—
127#807—101no—
128C4⋊(C3⋊C8)—51no—
129C2×C5×Q8—31no—
130C2×C5×Q8—61no—
131#713—122no—
132#713—122no—
133C2×D20—32no—
134C2×D20—62no—
135C2×D20—61no—
136C2×D20—61no—
137C2×D20—62no—
138C2×D20D1211yescharacteristic
139C2×C4×D5—21no—
140C2×C4×D5—62no—
141C5×Q16—122no—
142C2×C5×C8—21no—
143C5×C4⋊C4—31no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C5×C4⋊C4—61no—
147C42×C5—61no—
148C42×C5C22×D311yescharacteristic
149#685—21no—
150#685—62no—
151C4⋊Dic5D1211yescharacteristic
152C2×#168—21no—
153C2×#168—61no—
154#550—151no—
155#486—151no—
156#474—151no—
157#462—31no—
158#331—151no—
159Q8⋊C8—151no—
160D4⋊C8—51no—
161C22×C3×C5#12011yescharacteristic
162C2×D15—42no—
163C2×D15—42no—
164C2×D15—42no—
165C2×C3×D5—41no—
166C2×C3×D5—41no—
167C2×C3×D5—41no—
168C3×C4×C5—21no—
169C3×C4×C5C2×D811yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173C3×Dic5—41no—
174C5×Dic3—22no—
175C5×Dic3—41no—
176C5×Dic3—81no—
177C2×C3×D4—51no—
178C22×C3×C4—101no—
179C2×#67—102no—
180C2×#67—102no—
181#235—202no—
182#235—202no—
183C2×D12—52no—
184C2×D12—101no—
185C2×D12—101no—
186C2×C4×D3—102no—
187C2×Dic6—21no—
188C2×Dic6C22⋊D511yescharacteristic
189C2×C3×C8—21no—
190C2×C3×C8—101no—
191C3×C4⋊C4—51no—
192C3×C22⋊C4—101no—
193C3×C42C22×D511yescharacteristic
194(C2×D3)⋊C4—102no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3C22⋊D511yescharacteristic
198Dic3⋊C4—21no—
199C4×Dic3—21no—
200C2×C3⋊C8—101no—
201Dic12—42no—
202C22×D5—21no—
203C22×D5—62no—
204C5×Q8—32no—
205C5×Q8—61no—
206C5×Q8—121no—
207C5×Q8—121no—
208C2×C4×C5—61no—
209C2×C4×C5—61no—
210C2×C4×C5—121no—
211C2×C4×C5C2×D1211yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×Dic5—21no—
215D20—21no—
216D20—21no—
217D20—122no—
218D20—124no—
219D20—121no—
220D20—121no—
221D20—121no—
222D20—121no—
223D20—242no—
224C4×D5—41no—
225C4×D5—41no—
226C4×D5—124no—
227C5×C8—41no—
228#168—41no—
229#168—121no—
230C2×#41—301no—
231C2×Q16—61no—
232C4⋊Q8—31no—
233#127—151no—
234#127—301no—
235#121—302no—
236#121—301no—
237C4×Q8—31no—
238C4×D4—51no—
239C4×D4—301no—
240#107—301no—
241C4⋊C8—151no—
242C4⋊C8D3×D511yescharacteristic
243#103—61no—
244#102—302no—
245#102—301no—
246C4×C8—51no—
247C2×C3×C5#44711yescharacteristic
248C2×C3×C5#45211yescharacteristic
249C2×C3×C5#45511yescharacteristic
250D15—82no—
251C3×D5—81no—
252C23×C3—101no—
253C22×D3—102no—
254C3×D4—101no—
255C3×D4—101no—
256C2×C3×C4—101no—
257C2×C3×C4—201no—
258C2×C3×C4—201no—
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—41no—
267D12—202no—
268D12—201no—
269D12—201no—
270D12—201no—
271D12—201no—
272C4×D3—204no—
273Dic6—21no—
274Dic6—41no—
275Dic6—41no—
276Dic6#68612yes—
277C3×C8—41no—
278C3×C8—201no—
279C3⋊C8—201no—
280C22×C5#88211yescharacteristic
281C2×D5—41no—
282C2×D5—41no—
283C2×D5—41no—
284C2×D5—122no—
285C2×D5—122no—
286C2×D5—122no—
287C4×C5—21no—
288C4×C5—62no—
289C4×C5—121no—
290C4×C5—241no—
291C4×C5#90411yescharacteristic
292C4×C5#90911yescharacteristic
293C4×C5D3×D811yescharacteristic
294C4×C5#91411yescharacteristic
295Dic5—41no—
296#41—602no—
297#41—602no—
298C2×Q8—31no—
299C2×Q8—61no—
300C2×D4—51no—
301C2×D4—152no—
302C2×D4—302no—
303C2×D4—302no—
304C2×D4—301no—
305C2×D4—301no—
306C22×C4—101no—
307C22×C4—302no—
308Q16—122no—
309C2×C8—21no—
310C2×C8—101no—
311C2×C8—301no—
312C4⋊C4—31no—
313C4⋊C4—51no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C22⋊C4—101no—
318C22⋊C4—302no—
319C42—61no—
320C42C2×D3×D511yescharacteristic
321C3×C5#164111yescharacteristic, complemented, Hall
322C22×C3—201no—
323C22×C3—201no—
324C22×C3—201no—
325C22×C3#408311yescharacteristic
326C2×D3—202no—
327C2×D3—202no—
328C2×D3—202no—
329C3×C4—21no—
330C3×C4—201no—
331C3×C4#406411yescharacteristic
332C3×C4#406511yescharacteristic
333C3×C4C2×#68611yescharacteristic
334C3×C4#409511yescharacteristic
335Dic3—22no—
336Dic3—41no—
337Dic3—81no—
338C2×C5#473311yescharacteristic
339C2×C5#477311yescharacteristic
340C2×C5#482511yescharacteristic
341D5—81no—
342D5—242no—
343C23—101no—
344C23—302no—
345Q8—32no—
346Q8—61no—
347Q8—121no—
348Q8—121no—
349D4—101no—
350D4—101no—
351D4—602no—
352D4—604no—
353D4—601no—
354D4—601no—
355D4—601no—
356D4—601no—
357D4—1202no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—101no—
361C2×C4—121no—
362C2×C4—201no—
363C2×C4—201no—
364C2×C4—604no—
365C2×C4D5×D1211yescharacteristic
366C2×C4#677711yescharacteristic
367C2×C4D3×C22⋊D511yescharacteristic
368C8—41no—
369C8—201no—
370C8—601no—
371C2×C3—401no—
372C2×C3#6532511yescharacteristic
373C2×C3#6547611yescharacteristic
374C2×C3#6549111yescharacteristic
375D3—402no—
376C5#6819011yescharacteristic, complemented, Sylow
377C22—201no—
378C22—201no—
379C22—201no—
380C22—602no—
381C22—602no—
382C22—602no—
383C22#9147511yescharacteristic
384C4—21no—
385C4—62no—
386C4—121no—
387C4—201no—
388C4—241no—
389C4#9126111yescharacteristic
390C4#9127111yescharacteristic
391C4D3×#68611yescharacteristic
392C4#9150411yescharacteristic
393C3#1060185411yescharacteristic, complemented, Sylow
394C2—401no—
395C2—1202no—
396C2#1174748211yescharacteristic
397C2#1174815711yescharacteristic
398C2#1174824511yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752677C2
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. C5×#4849C2semidirect
3. #11746912C2semidirect
4. #11746886C2semidirect
5. #11746306C2semidirect
6. C3×#64703C2semidirect
7. #11745843C2semidirect
33. #64703D3semidirect
61. #4849D5semidirect
321. C3×C5#1641semidirect
376. C5#68190semidirect
393. C3#10601854semidirect

Maximal subgroups

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

subgroupindex
#117526772
C5×#48492
#117469122
#117468862
#117463062
C3×#647032
#117458432
#106018543
#681905