Finite Group Databasebeta

← #14290867

Subgroups — #14290867

Order 1920.

480 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#65889C211yesmaximal, characteristic
2C5×#5007C211yesmaximal, characteristic, complemented
3#11747059C211yesmaximal, characteristic, complemented
4#11746947C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745856C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601904—31nomaximal, Hall
9C2×C3×#711—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4076—21no—
13C2×C3×C4⋊Dic5—21no—
14C3×#4043—21no—
15C3×#4032—22no—
16C3×C4×D20C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6655—21no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#832—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90986—22no—
25#90972—21no—
26#71913—51nomaximal, Hall
27#65889D311yescharacteristic
28C5×#474—31no—
29#65372—31no—
30#65368—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64702—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C2×C3×C22⋊D5—22no—
38C22×C3×Dic5—22no—
39C3×#711—42no—
40C3×#711—42no—
41C2×C3×D20D411yescharacteristic
42C2×C3×C4×D5—21no—
43C2×C3×Dic10—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C42×C5C2311yescharacteristic
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—22no—
53C3×#685—21no—
54C3×C4⋊Dic5—22no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5D411yescharacteristic
57C3×C4⋊Dic5D412yes—
58#6655—42no—
59C3×#547—51no—
60#5080—51no—
61#5019—51no—
62#5007D511yescharacteristic, complemented
63#4547—51no—
64D4⋊(C3⋊C8)—51no—
65D4⋊(C3⋊C8)—51no—
66C2×#711—21no—
67C5×C4⋊Q8—31no—
68C4×C5×D4C2×D311yescharacteristic
69C2×#688—61no—
70#4076—21no—
71C2×C4⋊Dic5—21no—
72#4043—21no—
73#4032—22no—
74C4×D20C2×D311yescharacteristic
75#4015C2×D311yescharacteristic
76C5×#107—61no—
77C5×C4⋊C8—31no—
78C5×#102—61no—
79#3967—61no—
80#3940—62no—
81C4⋊#168—31no—
82C4×#168—31no—
83#1654—151noSylow
84C23×C3×C5—21no—
85C22×C3×D5—21no—
86C3×C5×D4—21no—
87C3×C5×D4SD1612yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—41no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×C5×Dic3—41no—
95C5×Dic6—41no—
96C5×Dic6—41no—
97C3×C22⋊D5—44no—
98C2×C3×Dic5—22no—
99C2×C3×Dic5—21no—
100C2×C3×Dic5—44no—
101C3×D20—21no—
102C3×D20—21no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105C3×Dic10—41no—
106C3×Dic10—41no—
107C3⋊#168—22no—
108C3⋊#168—41no—
109C5×C3⋊C8—41no—
110C2×C3×#41—101no—
111C3×C4⋊Q8—51no—
112C3×#123—102no—
113C3×C22⋊Q8—101no—
114C3×#121—101no—
115C3×C4×D4—51no—
116C3×C4×D4C2×D511yescharacteristic
117C2×C3×C4⋊C4—101no—
118C2×#214—101no—
119#869C2×D511yescharacteristic
120#832—21no—
121#810—101no—
122#808—102no—
123#807—21no—
124C4⋊(C3⋊C8)—51no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C4×C3⋊C8—51no—
127C2×C5×Q8—61no—
128C2×C5×D4#6711yescharacteristic
129C22×C4×C5—21no—
130C2×C22⋊D5—22no—
131C22×Dic5—22no—
132#711—42no—
133#711—42no—
134C2×D20#6711yescharacteristic
135C2×C4×D5—21no—
136C2×Dic10—21no—
137C2×C5×C8—61no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C22⋊C4—21no—
142C42×C5C22×D311yescharacteristic
143#688—122no—
144#685—22no—
145#685—21no—
146C4⋊Dic5—22no—
147C4⋊Dic5—21no—
148C4⋊Dic5#6712yes—
149C4⋊Dic5#6711yescharacteristic
150C2×#168—61no—
151C2×#168—61no—
152#547—51no—
153#498—151no—
154#474—31no—
155#461—151no—
156#332—151no—
157D4⋊C8—151no—
158D4⋊C8—151no—
159C22×C3×C5—22no—
160C22×C3×C5—41no—
161C22×C3×C5—41no—
162C22×C3×C5#12011yescharacteristic
163C2×C3×D5—41no—
164C2×C3×D5—41no—
165C2×C3×D5—41no—
166C3×C4×C5—21no—
167C3×C4×C5—41no—
168C3×C4×C5C2×SD1611yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×Dic5—42no—
173C3×Dic5—41no—
174C5×Dic3—81no—
175C3×#41—202no—
176C3×#41—202no—
177C2×C3×Q8—101no—
178C2×C3×D4—51no—
179C2×C3×D4—102no—
180C2×C3×D4C22⋊D511yescharacteristic
181C22×C3×C4—21no—
182C22×C3×C4—102no—
183C22×C3×C4—101no—
184C2×Dic6—21no—
185C3×C4⋊C4—52no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—102no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4C22⋊D511yescharacteristic
190C3×C22⋊C4—21no—
191C3×C22⋊C4—102no—
192C3×C22⋊C4—101no—
193C3×C42C22×D511yescharacteristic
194#214—202no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—101no—
199C2×C3⋊C8—101no—
200C23×C5—21no—
201C22×D5—21no—
202C5×Q8—121no—
203C5×Q8—121no—
204C5×D4—21no—
205C5×D4#21412yescomplemented
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5—41no—
209C2×C4×C5—121no—
210C2×C4×C5C2×#6711yescharacteristic
211C2×C4×C5C2×#6711yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—44no—
214C2×Dic5—22no—
215C2×Dic5—21no—
216C2×Dic5—44no—
217D20—21no—
218D20—21no—
219C4×D5—41no—
220C4×D5—41no—
221Dic10—41no—
222Dic10—41no—
223C5×C8—121no—
224#168—62no—
225#168—121no—
226C2×#41—101no—
227C2×SD16—301no—
228C4⋊Q8—31no—
229C4⋊Q8—51no—
230#123—102no—
231C22⋊Q8—101no—
232#121—101no—
233C4×D4—51no—
234C4×D4D3×D511yescharacteristic
235C2×C4⋊C4—101no—
236#107—61no—
237#106—302no—
238C4⋊C8—31no—
239C4⋊C8—151no—
240#103—301no—
241#102—61no—
242C4×C8—151no—
243C2×C3×C5—42no—
244C2×C3×C5#44911yescharacteristic
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45611yescharacteristic
247C3×D5—81no—
248C23×C3—21no—
249C23×C3—101no—
250C3×Q8—201no—
251C3×Q8—201no—
252C3×D4—21no—
253C3×D4—101no—
254C3×D4—101no—
255C3×D4—204no—
256C3×D4#68812yescomplemented
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—41no—
260C2×C3×C4—101no—
261C2×C3×C4—102no—
262C2×C3×C4—204no—
263C2×C3×C4—201no—
264C2×C3×C4—201no—
265C2×C3×C4D4×D511yescharacteristic
266C2×C3×C4D4×D511yescharacteristic
267C2×C3×C4C2×C22⋊D511yescharacteristic
268C2×Dic3—41no—
269Dic6—41no—
270Dic6—41no—
271C3⋊C8—41no—
272C3⋊C8—102no—
273C3⋊C8—201no—
274C22×C5—22no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5#95311yescharacteristic
278C2×D5—41no—
279C2×D5—41no—
280C2×D5—41no—
281C4×C5—21no—
282C4×C5—41no—
283C4×C5—241no—
284C4×C5#93211yescharacteristic
285C4×C5C2×#21411yescharacteristic
286C4×C5#94911yescharacteristic
287C4×C5#95011yescharacteristic
288Dic5—42no—
289Dic5—41no—
290#41—202no—
291#41—202no—
292C2×Q8—61no—
293C2×Q8—101no—
294C2×D4—51no—
295C2×D4—102no—
296C2×D4#120111yescharacteristic
297C22×C4—21no—
298C22×C4—102no—
299C22×C4—101no—
300SD16—602no—
301C2×C8—61no—
302C2×C8—301no—
303C2×C8—301no—
304C4⋊C4—51no—
305C4⋊C4—52no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—102no—
309C4⋊C4—101no—
310C4⋊C4#120111yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—102no—
313C22⋊C4—101no—
314C42C2×D3×D511yescharacteristic
315C3×C5#165411yescharacteristic, complemented, Hall
316C22×C3—22no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—201no—
320C22×C3—201no—
321C22×C3—201no—
322C22×C3#408311yescharacteristic
323C3×C4—21no—
324C3×C4—41no—
325C3×C4—201no—
326C3×C4—202no—
327C3×C4#405711yescharacteristic
328C3×C4#405811yescharacteristic
329C3×C4C2×#68811yescharacteristic
330C3×C4#409511yescharacteristic
331Dic3—81no—
332C2×C5—42no—
333C2×C5#521811yescharacteristic
334C2×C5#523811yescharacteristic
335C2×C5#524611yescharacteristic
336D5—81no—
337C23—21no—
338C23—101no—
339Q8—121no—
340Q8—121no—
341Q8—201no—
342Q8—201no—
343D4—21no—
344D4—101no—
345D4—101no—
346D4—204no—
347D4#665512yescomplemented
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—101no—
352C2×C4—102no—
353C2×C4—121no—
354C2×C4—204no—
355C2×C4—201no—
356C2×C4—201no—
357C2×C4C2×#120111yescharacteristic
358C2×C4D5×#6711yescharacteristic
359C2×C4D5×#6711yescharacteristic
360C8—121no—
361C8—302no—
362C8—601no—
363C2×C3—42no—
364C2×C3—401no—
365C2×C3#6533511yescharacteristic
366C2×C3#6544711yescharacteristic
367C2×C3#6549411yescharacteristic
368C5#7191311yescharacteristic, complemented, Sylow
369C22—22no—
370C22—41no—
371C22—41no—
372C22—201no—
373C22—201no—
374C22—201no—
375C22#9156311yescharacteristic
376C4—21no—
377C4—41no—
378C4—201no—
379C4—202no—
380C4—241no—
381C4#9129811yescharacteristic
382C4C2×#665511yescharacteristic
383C4#9147811yescharacteristic
384C4#9149011yescharacteristic
385C3#1060190411yescharacteristic, complemented, Sylow
386C2—42no—
387C2—401no—
388C2#1174852711yescharacteristic
389C2#1174902411yescharacteristic
390C2#1174946211yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×#65889C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1654
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C5×#5007C2semidirect
3. #11747059C2semidirect
4. #11746947C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745856C2semidirect
7. #11745834C2semidirect
62. #5007D5semidirect
87. C3×C5×D4SD16semidirect
205. C5×D4#214semidirect
256. C3×D4#688semidirect
315. C3×C5#1654semidirect
347. D4#6655semidirect
368. C5#71913semidirect
385. C3#10601904semidirect

Maximal subgroups

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

subgroupindex
C3×#658892
C5×#50072
#117470592
#117469472
D4⋊(C3⋊#168)2
#117458562
#117458342
#106019043
#719135