Finite Group Databasebeta

← #14514625

Subgroups — #14514625

Order 1920.

534 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 31 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
1C2×C5×C22⋊SL(2,𝔽3)C211yesmaximal, characteristic, complemented
2C5⋊#5931C211yesmaximal, characteristic, complemented
3C5⋊#5930C211yesmaximal, characteristic, complemented
4#10615790—31nomaximal, Hall
5C5×C22⋊SL(2,𝔽3)C2211yescharacteristic
6#91958—41nomaximal
7#91953—42nomaximal
8#87507—51nomaximal, Hall
9C23×C5×Q8D311yescharacteristic, complemented
10C2×#4088—32no—
11#66125—31no—
12#65517—31no—
13#65517—32no—
14#65517—31no—
15#65516—31no—
16#65516—32no—
17#65516—31no—
18#65514—32no—
19#65496—31no—
20C22×C5×A4—41no—
21C2×C5⋊S4—41no—
22C2×C5×SL(2,𝔽3)—42no—
23C2×C5×SL(2,𝔽3)—81no—
24A4⋊Dic5—41no—
25C5⋊GL(2,𝔽3)—42no—
26C5⋊#226—42no—
27C2×C22⋊SL(2,𝔽3)D511yescharacteristic, complemented
28#5931—51no—
29#5930—51no—
30C22×C5×Q8—31no—
31C22×C5×Q8—32no—
32C22×C5×Q8—32no—
33C22×C5×Q8—61no—
34C22×C5×Q8—61no—
35C22×C5×Q8C2×D311yescharacteristic
36C23×C4×C5—31no—
37C2×#709—31no—
38#4099—61no—
39C2×#689—32no—
40C2×#689—32no—
41#4088—62no—
42#4088—62no—
43#4088—62no—
44#4088—62no—
45C2×#688—32no—
46C2×#688—32no—
47#4076—31no—
48#4076—31no—
49#4075—61no—
50C4×C22⋊D5—61no—
51C4×C22⋊D5—61no—
52#4072—31no—
53#4070—31no—
54#4070—31no—
55C2×#681—32no—
56#3967—32no—
57#3967—32no—
58#3967—32no—
59#3967—32no—
60C22⋊#168—32no—
61C22⋊#168—31no—
62C22⋊#168—31no—
63#3004—151noSylow
64C2×C5×A4—41no—
65C2×C5×A4—81no—
66C5⋊S4—81no—
67#1220—161no—
68C5×SL(2,𝔽3)—42no—
69C5×SL(2,𝔽3)—81no—
70C22⋊SL(2,𝔽3)C2×D511yescharacteristic
71GL(2,ℤ/4)—201no—
72#983—202no—
73C24×C5S411yescharacteristic
74C2×C5×Q8—21no—
75C2×C5×Q8—32no—
76C2×C5×Q8—32no—
77C2×C5×Q8—32no—
78C2×C5×Q8—32no—
79C2×C5×Q8—32no—
80C2×C5×Q8—61no—
81C2×C5×Q8—61no—
82C2×C5×Q8—62no—
83C2×C5×Q8—62no—
84C2×C5×Q8—62no—
85C2×C5×Q8—61no—
86C2×C5×Q8—61no—
87C2×C5×Q8—61no—
88C2×C5×Q8—62no—
89C2×C5×Q8S412yescomplemented
90C22×C4×C5—31no—
91C22×C4×C5—31no—
92C22×C4×C5—31no—
93C22×C4×C5—31no—
94C22×C4×C5—31no—
95C22×C4×C5—31no—
96C22×C4×C5—62no—
97C22×C4×C5—62no—
98C2×C22⋊D5—61no—
99C2×C22⋊D5—61no—
100C2×C22⋊D5—61no—
101#709—62no—
102#709—62no—
103C2×D20—31no—
104C2×C4×D5—61no—
105C2×Dic10—31no—
106C22⋊Dic5—61no—
107C22⋊Dic5—61no—
108C22⋊Dic5—61no—
109#689—62no—
110#689—62no—
111#689—62no—
112#689—62no—
113#688—62no—
114#688—62no—
115#688—62no—
116#688—62no—
117#685—61no—
118#685—61no—
119C4⋊Dic5—31no—
120C4⋊Dic5—31no—
121#683—61no—
122#683—61no—
123C4×Dic5—61no—
124#681—62no—
125#681—62no—
126C2×#168—32no—
127C2×#168—32no—
128C23×Q8D1511yescharacteristic, complemented
129C2×#137—152no—
130#525—151no—
131#451—151no—
132#451—152no—
133#451—151no—
134#448—151no—
135#448—152no—
136#448—151no—
137#419—152no—
138#407—151no—
139C22×C3×C5—161no—
140C2×D15—161no—
141C5×A4—41no—
142Dic15—161no—
143C22×A4—41no—
144C2×S4—201no—
145C2×SL(2,𝔽3)—42no—
146C2×SL(2,𝔽3)—81no—
147SL(2,ℤ/4)—201no—
148GL(2,𝔽3)—202no—
149#226—202no—
150C23×C5—21no—
151C23×C5—31no—
152C23×C5—31no—
153C23×C5—61no—
154C23×C5C2×S411yescharacteristic
155C22×D5—61no—
156C5×Q8—21no—
157C5×Q8—32no—
158C5×Q8—32no—
159C5×Q8—32no—
160C5×Q8—61no—
161C5×Q8—62no—
162C5×Q8—61no—
163C5×Q8—62no—
164C5×Q8—61no—
165C5×Q8C2×S412yes—
166C2×C4×C5—31no—
167C2×C4×C5—32no—
168C2×C4×C5—31no—
169C2×C4×C5—32no—
170C2×C4×C5—31no—
171C2×C4×C5—31no—
172C2×C4×C5—62no—
173C2×C4×C5—62no—
174C2×C4×C5—62no—
175C2×C4×C5—62no—
176C2×C4×C5—61no—
177C2×C4×C5—61no—
178C22⋊D5—121no—
179C22⋊D5—121no—
180C22⋊D5—122no—
181C22⋊D5—121no—
182C22⋊D5—121no—
183C2×Dic5—61no—
184C2×Dic5—61no—
185C2×Dic5—61no—
186D20—62no—
187C4×D5—122no—
188Dic10—62no—
189#168—62no—
190#168—62no—
191C2×#41—151no—
192C22×Q8—31no—
193C22×Q8—32no—
194C22×Q8—32no—
195C22×Q8—61no—
196C22×Q8—61no—
197C22×Q8C2×D1511yescharacteristic
198C23×C4—31no—
199#137—302no—
200#137—302no—
201#137—302no—
202#137—302no—
203C2×Q16—152no—
204C2×Q16—152no—
205C2×SD16—152no—
206C2×SD16—152no—
207C2×M16—152no—
208#123—301no—
209C22⋊Q8—151no—
210C22⋊Q8—151no—
211#121—151no—
212#121—151no—
213#120—301no—
214C4×D4—301no—
215C4×D4—301no—
216#117—151no—
217#103—152no—
218#103—152no—
219#103—152no—
220#103—152no—
221C22⋊C8—152no—
222C22⋊C8—151no—
223C22⋊C8—151no—
224C2×C3×C5—161no—
225C2×C3×C5—321no—
226D15—321no—
227C2×A4—41no—
228C2×A4—81no—
229S4—401no—
230#67—801no—
231SL(2,𝔽3)—42no—
232SL(2,𝔽3)—81no—
233C22×C5—31no—
234C22×C5—31no—
235C22×C5—32no—
236C22×C5—31no—
237C22×C5—61no—
238C22×C5—61no—
239C22×C5—61no—
240C22×C5#98311yescharacteristic, complemented
241C22×C5#102011yescharacteristic
242C2×D5—121no—
243C2×D5—121no—
244C2×D5—121no—
245C4×C5—32no—
246C4×C5—32no—
247C4×C5—61no—
248C4×C5—61no—
249Dic5—121no—
250Dic5—121no—
251Dic5—121no—
252C24C5⋊S411yescharacteristic
253#41—302no—
254#41—302no—
255C2×Q8—21no—
256C2×Q8—32no—
257C2×Q8—32no—
258C2×Q8—32no—
259C2×Q8—32no—
260C2×Q8—32no—
261C2×Q8—61no—
262C2×Q8—61no—
263C2×Q8—62no—
264C2×Q8—62no—
265C2×Q8—62no—
266C2×Q8—61no—
267C2×Q8—61no—
268C2×Q8—61no—
269C2×Q8—62no—
270C2×Q8—151no—
271C2×Q8C5⋊S412yescomplemented
272C2×D4—151no—
273C2×D4—301no—
274C2×D4—301no—
275C2×D4—301no—
276C22×C4—31no—
277C22×C4—31no—
278C22×C4—31no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—62no—
283C22×C4—62no—
284C22×C4—301no—
285Q16—302no—
286Q16—302no—
287Q16—302no—
288Q16—302no—
289SD16—302no—
290SD16—302no—
291SD16—302no—
292SD16—302no—
293M16—302no—
294M16—302no—
295C2×C8—152no—
296C2×C8—152no—
297C4⋊C4—151no—
298C4⋊C4—151no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C22⋊C4—301no—
302C22⋊C4—301no—
303C22⋊C4—301no—
304C22⋊C4—301no—
305C22⋊C4—301no—
306C42—301no—
307C3×C5—161noHall
308C22×C3—161no—
309C2×D3—801no—
310A4—41no—
311Dic3—801no—
312C2×C5—21no—
313C2×C5—31no—
314C2×C5—31no—
315C2×C5—61no—
316C2×C5C2×#102011yescharacteristic
317D5—241no—
318C23—21no—
319C23—31no—
320C23—31no—
321C23—61no—
322C23—301no—
323C23C2×C5⋊S411yescharacteristic
324Q8—21no—
325Q8—32no—
326Q8—32no—
327Q8—32no—
328Q8—61no—
329Q8—62no—
330Q8—61no—
331Q8—62no—
332Q8—61no—
333Q8—302no—
334Q8C2×C5⋊S412yes—
335D4—302no—
336D4—601no—
337D4—601no—
338D4—602no—
339D4—601no—
340D4—601no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—32no—
344C2×C4—32no—
345C2×C4—31no—
346C2×C4—31no—
347C2×C4—62no—
348C2×C4—62no—
349C2×C4—62no—
350C2×C4—62no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—301no—
354C2×C4—301no—
355C2×C4—301no—
356C2×C4—602no—
357C8—302no—
358C8—302no—
359C2×C3—161no—
360C2×C3—321no—
361D3—1601no—
362C5#8750711yescharacteristic, complemented, Sylow
363C22—31no—
364C22—31no—
365C22—32no—
366C22—31no—
367C22—61no—
368C22—61no—
369C22—61no—
370C22—601no—
371C22—601no—
372C22—601no—
373C22#9195311yescharacteristic, complemented
374C22C5⋊#102011yescharacteristic
375C4—32no—
376C4—32no—
377C4—61no—
378C4—61no—
379C4—601no—
380C4—601no—
381C4—601no—
382C3—161noSylow
383C2—21no—
384C2—31no—
385C2—31no—
386C2—61no—
387C2—1201no—
388C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, FrattiniC2C2×C5⋊#1020
commutator, cosocle, hypocenterC5×C22⋊SL(2,𝔽3)C22
FittingC23×C5×Q8D3
socleC23×C5C2×S4
hypercenterC22C5⋊#1020
LCSG ▷ C5×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C2×C5×C22⋊SL(2,𝔽3)C2semidirect
2. C5⋊#5931C2semidirect
3. C5⋊#5930C2semidirect
9. C23×C5×Q8D3semidirect
27. C2×C22⋊SL(2,𝔽3)D5semidirect
89. C2×C5×Q8S4semidirect
128. C23×Q8D15semidirect
240. C22×C5#983semidirect
271. C2×Q8C5⋊S4semidirect
362. C5#87507semidirect
373. C22#91953semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C22⋊SL(2,𝔽3)2
C5⋊#59312
C5⋊#59302
#106157903
#919584
#919534
#875075