Finite Group Databasebeta

← #14290878

Subgroups — #14290878

Order 1920.

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

normal subgroups only

This group has 480 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#11752676C211yesmaximal, characteristic
2C5×#4846C211yesmaximal, characteristic, complemented
3#11747059C211yesmaximal, characteristic, complemented
4#11746941C211yesmaximal, characteristic, complemented
5#11746303C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601904—31nomaximal, Hall
9C2×#6772—21no—
10#91758C2211yescharacteristic
11C4×C5×D12C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91457—22no—
15#91456—21no—
16D3×C4⋊Dic5—21no—
17#91360—21no—
18C2×#6655—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#821—21no—
22C5×#818—21no—
23C3×C4×#168C2211yescharacteristic
24#90985—22no—
25#90972—21no—
26#68211—51nomaximal, Hall
27#65889—31no—
28C5×#474—31no—
29#65372—31no—
30#65368—31no—
31D4⋊#168—31no—
32#64703D311yescharacteristic, complemented
33#64702—31no—
34C2×Dic30—21no—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C5×Dic6—21no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1201—22no—
41C2×D3×Dic5—22no—
42#6772—42no—
43#6772—42no—
44C2×C3×C5×C8—21no—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C2×C3⋊#168—21no—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D411yescharacteristic
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—22no—
57#6665—22no—
58#6655—42no—
59#5551—51no—
60#5019—51no—
61#4846D511yescharacteristic, complemented
62#4680—51no—
63C3×D4⋊C8—51no—
64#4482—51no—
65#4459—51no—
66C2×#711—61no—
67C5×C4⋊Q8—31no—
68C4×C5×D4—31no—
69C2×#688—61no—
70#4076—61no—
71C2×C4⋊Dic5—61no—
72#4043—61no—
73#4032—62no—
74C4×D20C2×D311yescharacteristic
75#4015—31no—
76C5×#107—61no—
77C5×C4⋊C8C2×D311yescharacteristic
78C5×#102—61no—
79#3967—61no—
80#3940—62no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1654—151noSylow
84C22×C5×D3—21no—
85C22×C3×D5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90Dic30—41no—
91Dic30—41no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—41no—
94C5×D12—21no—
95C5×D12SD1612yescomplemented
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C5×Dic6—41no—
99C5×Dic6—41no—
100C2×C3×Dic5—21no—
101C3×D20—21no—
102C3×D20—21no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105#1201—44no—
106D3×Dic5—44no—
107C3×C5×C8—41no—
108C3⋊#168—41no—
109C3×#168—22no—
110C2×#235—101no—
111C3×C4×D4—51no—
112#938—101no—
113C2×#214—101no—
114#924—101no—
115D3×C4⋊C4—101no—
116#883—102no—
117C4×D12C2×D511yescharacteristic
118#869—51no—
119#869C2×D511yescharacteristic
120C3×C4⋊C8C2×D511yescharacteristic
121C3×C4×C8—51no—
122#821—21no—
123#818—21no—
124#817—102no—
125#810—101no—
126C4⋊(C3⋊C8)—51no—
127C2×C5×Q8—61no—
128C2×C5×D4—31no—
129C22×C4×C5—61no—
130C2×C22⋊D5—62no—
131C22×Dic5—62no—
132#711—122no—
133#711—122no—
134C2×D20D1211yescharacteristic
135C2×C4×D5—21no—
136C2×Dic10—61no—
137C2×C5×C8—21no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4—61no—
141C5×C22⋊C4—61no—
142C42×C5C22×D311yescharacteristic
143#688—122no—
144#685—21no—
145#685—62no—
146C4⋊Dic5—32no—
147C4⋊Dic5—62no—
148C4⋊Dic5—61no—
149C4⋊Dic5D1211yescharacteristic
150C2×#168—21no—
151C2×#168—61no—
152#547—151no—
153#498—151no—
154#474—31no—
155#461—151no—
156#332—151no—
157D4⋊C8—51no—
158D4⋊C8—151no—
159C22×C3×C5#12011yescharacteristic
160C2×C5×D3—22no—
161C2×C5×D3—41no—
162C2×C5×D3—41no—
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C3×C4×C5—21no—
167C3×C4×C5C2×SD1611yescharacteristic
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171Dic15—42no—
172C3×Dic5—41no—
173C5×Dic3—41no—
174C5×Dic3—81no—
175C2×C3×D4—51no—
176C22×C3×C4—101no—
177C2×#67—102no—
178#235—202no—
179#235—202no—
180C2×D12C22⋊D511yescharacteristic
181C2×C4×D3—21no—
182C2×C4×D3—102no—
183C2×Dic6—21no—
184C2×Dic6—101no—
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C3×C4⋊C4—51no—
188C3×C22⋊C4—101no—
189C3×C42C22×D511yescharacteristic
190#217—102no—
191#214—202no—
192(C2×D3)⋊C4—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—52no—
196C4⋊Dic3—101no—
197C4⋊Dic3C22⋊D511yescharacteristic
198Dic3⋊C4—102no—
199C2×C3⋊C8—101no—
200C23×C5—61no—
201C22×D5—21no—
202C5×Q8—121no—
203C5×Q8—121no—
204C5×D4—32no—
205C5×D4—61no—
206C2×C4×C5—61no—
207C2×C4×C5—121no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5C2×D1211yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C22⋊D5—124no—
214C2×Dic5—21no—
215C2×Dic5—62no—
216C2×Dic5—124no—
217D20—21no—
218D20—21no—
219C4×D5—41no—
220C4×D5—41no—
221Dic10—121no—
222Dic10—121no—
223C5×C8—41no—
224#168—22no—
225#168—121no—
226C2×#41—301no—
227C2×SD16—301no—
228C4⋊Q8—31no—
229C4⋊Q8—151no—
230#123—302no—
231C22⋊Q8—301no—
232#121—301no—
233C4×D4—31no—
234C4×D4—51no—
235C2×C4⋊C4—301no—
236#107—61no—
237#106—302no—
238C4⋊C8—151no—
239C4⋊C8D3×D511yescharacteristic
240#103—301no—
241#102—61no—
242C4×C8—51no—
243C2×C3×C5#44911yescharacteristic
244C2×C3×C5#45011yescharacteristic
245C2×C3×C5#45611yescharacteristic
246C3×D5—81no—
247C5×D3—42no—
248C23×C3—101no—
249C22×D3—21no—
250C3×D4—101no—
251C3×D4—101no—
252C2×C3×C4—101no—
253C2×C3×C4—201no—
254C2×C3×C4—201no—
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258#67—204no—
259C2×Dic3—21no—
260C2×Dic3—41no—
261C2×Dic3—102no—
262D12—21no—
263D12#68812yescomplemented
264C4×D3—41no—
265C4×D3—41no—
266C4×D3—204no—
267Dic6—41no—
268Dic6—41no—
269Dic6—201no—
270Dic6—201no—
271C3×C8—41no—
272C3×C8—102no—
273C3⋊C8—201no—
274C22×C5—62no—
275C22×C5—121no—
276C22×C5—121no—
277C22×C5#88211yescharacteristic
278C2×D5—41no—
279C2×D5—41no—
280C2×D5—41no—
281C4×C5—21no—
282C4×C5—121no—
283C4×C5—241no—
284C4×C5#90411yescharacteristic
285C4×C5#90811yescharacteristic
286C4×C5#91111yescharacteristic
287C4×C5D3×SD1611yescharacteristic
288Dic5—41no—
289Dic5—122no—
290#41—602no—
291#41—602no—
292C2×Q8—61no—
293C2×Q8—301no—
294C2×D4—31no—
295C2×D4—51no—
296C2×D4—302no—
297C22×C4—61no—
298C22×C4—101no—
299C22×C4—302no—
300SD16—602no—
301C2×C8—21no—
302C2×C8—101no—
303C2×C8—301no—
304C4⋊C4—31no—
305C4⋊C4—51no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—152no—
309C4⋊C4—302no—
310C4⋊C4—301no—
311C22⋊C4—61no—
312C22⋊C4—101no—
313C22⋊C4—302no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3—201no—
317C22×C3—201no—
318C22×C3—201no—
319C22×C3#408311yescharacteristic
320C2×D3—22no—
321C2×D3—41no—
322C2×D3—41no—
323C3×C4—21no—
324C3×C4—201no—
325C3×C4#405711yescharacteristic
326C3×C4#405811yescharacteristic
327C3×C4C2×#68811yescharacteristic
328C3×C4#409511yescharacteristic
329Dic3—41no—
330Dic3—81no—
331Dic3—202no—
332C2×C5—122no—
333C2×C5#473411yescharacteristic
334C2×C5#477611yescharacteristic
335C2×C5#482611yescharacteristic
336D5—81no—
337C23—61no—
338C23—101no—
339Q8—121no—
340Q8—121no—
341Q8—601no—
342Q8—601no—
343D4—32no—
344D4—61no—
345D4—101no—
346D4—101no—
347D4—604no—
348C2×C4—61no—
349C2×C4—101no—
350C2×C4—121no—
351C2×C4—121no—
352C2×C4—121no—
353C2×C4—201no—
354C2×C4—201no—
355C2×C4—302no—
356C2×C4—604no—
357C2×C4D5×D1211yescharacteristic
358C2×C4#677711yescharacteristic
359C2×C4D3×C22⋊D511yescharacteristic
360C8—41no—
361C8—102no—
362C8—601no—
363C2×C3—401no—
364C2×C3#6533511yescharacteristic
365C2×C3#6544711yescharacteristic
366C2×C3#6549411yescharacteristic
367D3—42no—
368C5#6821111yescharacteristic, complemented, Sylow
369C22—62no—
370C22—121no—
371C22—121no—
372C22—201no—
373C22—201no—
374C22—201no—
375C22#9147511yescharacteristic
376C4—21no—
377C4—121no—
378C4—201no—
379C4—241no—
380C4—602no—
381C4#9125011yescharacteristic
382C4#9127011yescharacteristic
383C4#9148011yescharacteristic
384C4D3×#68811yescharacteristic
385C3#1060190411yescharacteristic, complemented, Sylow
386C2—122no—
387C2—401no—
388C2#1174748311yescharacteristic
389C2#1174815611yescharacteristic
390C2#1174825711yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radical#11752676C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1654
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×#4846C2semidirect
3. #11747059C2semidirect
4. #11746941C2semidirect
5. #11746303C2semidirect
6. C3×#64703C2semidirect
7. #11745837C2semidirect
32. #64703D3semidirect
61. #4846D5semidirect
95. C5×D12SD16semidirect
263. D12#688semidirect
315. C3×C5#1654semidirect
368. C5#68211semidirect
385. C3#10601904semidirect

Maximal subgroups

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

subgroupindex
#117526762
C5×#48462
#117470592
#117469412
#117463032
C3×#647032
#117458372
#106019043
#682115