Finite Group Databasebeta

← #14514628

Subgroups — #14514628

Order 1920.

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

normal subgroups only

This group has 586 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
1C5×#5948C211yesmaximal, characteristic, complemented
2C5⋊#5931C212yesmaximal, complemented
3#10615813—31nomaximal, Hall
4C5×C22⋊SL(2,𝔽3)C2211yescharacteristic, complemented
5#91956—42nomaximal
6C4⋊(C5⋊S4)—41nomaximal
7#87510—51nomaximal, Hall
8C22×C5×#41D311yescharacteristic, complemented
9C2×#4095—32no—
10C2×#4076—31no—
11#65527—34no—
12#65521—32no—
13#65516—32no—
14#65506—32no—
15#65496—31no—
16C2×C5⋊S4—42no—
17C5×#41⋊C3—42no—
18C5×#41⋊C3—81no—
19C4×C5×A4—41no—
20C5⋊GL(2,𝔽3)—44no—
21#5948D511yescharacteristic, complemented
22#5931—52no—
23C2×C5×#41—32no—
24C2×C5×#41—32no—
25C2×C5×#41—61no—
26C2×C5×#41—61no—
27C22×C5×Q8C2×D311yescharacteristic
28C22×C5×D4—31no—
29C23×C4×C5—31no—
30C22×C22⋊D5—61no—
31C22×D20—31no—
32#4095—62no—
33#4095—62no—
34#4095—62no—
35#4095—62no—
36C2×#688—34no—
37C2×#686—34no—
38#4076—32no—
39#4076—32no—
40#4076—61no—
41#4076—61no—
42C2×#685—61no—
43C2×C4⋊Dic5—31no—
44C2×#681—32no—
45#3967—34no—
46#3964—34no—
47C22⋊#168—32no—
48C22⋊#168—32no—
49#3006—151noSylow
50C2×C5×A4—41no—
51C5⋊S4—82no—
52D60—161no—
53C5×SL(2,𝔽3)—42no—
54C5×SL(2,𝔽3)—81no—
55C22⋊SL(2,𝔽3)C2×D511yescharacteristic, complemented
56#986—202no—
57C4⋊S4—201no—
58C24×C5—31no—
59C23×D5—61no—
60C5×#41—21no—
61C5×#41—32no—
62C5×#41—32no—
63C5×#41—32no—
64C5×#41—61no—
65C5×#41—62no—
66C5×#41—61no—
67C5×#41—61no—
68C5×#41—62no—
69C5×#41S412yescomplemented
70C2×C5×Q8—32no—
71C2×C5×Q8—61no—
72C2×C5×D4—32no—
73C2×C5×D4—61no—
74C2×C5×D4—62no—
75C2×C5×D4—62no—
76C22×C4×C5—31no—
77C22×C4×C5—31no—
78C22×C4×C5—31no—
79C22×C4×C5—31no—
80C22×C4×C5—31no—
81C22×C4×C5—62no—
82C22×C4×C5—62no—
83C22×C4×C5S411yescharacteristic
84C2×C22⋊D5—62no—
85C2×C22⋊D5—62no—
86C2×C22⋊D5—122no—
87C2×C22⋊D5—122no—
88C22×Dic5—61no—
89C2×D20—32no—
90C2×D20—62no—
91C2×D20—62no—
92C2×D20—61no—
93#688—64no—
94#688—64no—
95#686—64no—
96#686—64no—
97#685—62no—
98#685—62no—
99C4⋊Dic5—32no—
100C4⋊Dic5—61no—
101#681—62no—
102#681—62no—
103C2×#168—34no—
104C22×#41D1511yescharacteristic, complemented
105C2×AGL(1,ℤ/8)—152no—
106C2×#121—151no—
107#449—154no—
108#448—152no—
109#447—152no—
110#417—152no—
111#407—151no—
112C2×D15—162no—
113C5×A4—41no—
114C3×C4×C5—161no—
115C2×S4—202no—
116#41⋊C3—42no—
117#41⋊C3—81no—
118C4×A4—41no—
119GL(2,𝔽3)—204no—
120C23×C5—31no—
121C23×C5—31no—
122C23×C5—62no—
123C23×C5—61no—
124C23×C5—61no—
125C23×C5—121no—
126C23×C5C2×S411yescharacteristic
127C22×D5—62no—
128C22×D5—122no—
129C22×D5—122no—
130C22×D5—122no—
131C5×Q8—21no—
132C5×Q8—32no—
133C5×Q8—61no—
134C5×Q8C2×S412yes—
135C5×D4—32no—
136C5×D4—32no—
137C5×D4—62no—
138C5×D4—61no—
139C5×D4—62no—
140C5×D4—61no—
141C2×C4×C5—31no—
142C2×C4×C5—32no—
143C2×C4×C5—32no—
144C2×C4×C5—31no—
145C2×C4×C5—31no—
146C2×C4×C5—31no—
147C2×C4×C5—62no—
148C2×C4×C5—62no—
149C2×C4×C5—62no—
150C2×C4×C5—61no—
151C2×C4×C5—61no—
152C22⋊D5—122no—
153C22⋊D5—124no—
154C22⋊D5—122no—
155C2×Dic5—62no—
156C2×Dic5—122no—
157D20—64no—
158D20—121no—
159D20—121no—
160#168—64no—
161C2×#41—32no—
162C2×#41—32no—
163C2×#41—61no—
164C2×#41—61no—
165C22×Q8C2×D1511yescharacteristic
166C22×D4—31no—
167C22×D4—151no—
168C22×D4—301no—
169C23×C4—31no—
170AGL(1,ℤ/8)—302no—
171AGL(1,ℤ/8)—302no—
172AGL(1,ℤ/8)—302no—
173AGL(1,ℤ/8)—302no—
174C2×SD16—154no—
175C2×D8—154no—
176C2×M16—152no—
177#121—152no—
178#121—152no—
179#121—301no—
180#121—301no—
181C2×C4⋊C4—151no—
182C2×C22⋊C4—301no—
183#103—154no—
184#102—154no—
185C22⋊C8—152no—
186C22⋊C8—152no—
187C2×C3×C5—161no—
188D15—322no—
189C2×A4—41no—
190S4—402no—
191D12—801no—
192SL(2,𝔽3)—42no—
193SL(2,𝔽3)—81no—
194C22×C5—31no—
195C22×C5—31no—
196C22×C5—32no—
197C22×C5—61no—
198C22×C5—61no—
199C22×C5—61no—
200C22×C5—61no—
201C22×C5—61no—
202C22×C5—122no—
203C22×C5—122no—
204C22×C5#98611yescharacteristic, complemented
205C2×D5—122no—
206C2×D5—122no—
207C2×D5—122no—
208C2×D5—244no—
209C4×C5—32no—
210C4×C5—31no—
211C4×C5—61no—
212C4×C5#102011yescharacteristic
213Dic5—122no—
214C24—31no—
215C24—301no—
216#41—21no—
217#41—32no—
218#41—32no—
219#41—32no—
220#41—61no—
221#41—62no—
222#41—61no—
223#41—61no—
224#41—62no—
225#41C5⋊S412yescomplemented
226C2×Q8—32no—
227C2×Q8—61no—
228C2×D4—32no—
229C2×D4—61no—
230C2×D4—62no—
231C2×D4—62no—
232C2×D4—152no—
233C2×D4—302no—
234C2×D4—302no—
235C2×D4—301no—
236C2×D4—302no—
237C2×D4—302no—
238C2×D4—602no—
239C2×D4—602no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—31no—
244C22×C4—31no—
245C22×C4—62no—
246C22×C4—62no—
247C22×C4—301no—
248C22×C4C5⋊S411yescharacteristic
249SD16—304no—
250SD16—304no—
251D8—304no—
252D8—304no—
253M16—302no—
254M16—302no—
255C2×C8—154no—
256C4⋊C4—152no—
257C4⋊C4—301no—
258C22⋊C4—302no—
259C22⋊C4—302no—
260C3×C5—161noHall
261C2×D3—802no—
262A4—41no—
263C3×C4—161no—
264C2×C5—31no—
265C2×C5—31no—
266C2×C5—62no—
267C2×C5—121no—
268C2×C5C2×#102011yescharacteristic
269D5—242no—
270C23—31no—
271C23—31no—
272C23—62no—
273C23—61no—
274C23—61no—
275C23—121no—
276C23—302no—
277C23—602no—
278C23—602no—
279C23—602no—
280C23C2×C5⋊S411yescharacteristic
281Q8—21no—
282Q8—32no—
283Q8—61no—
284Q8C2×C5⋊S412yes—
285D4—32no—
286D4—32no—
287D4—62no—
288D4—61no—
289D4—62no—
290D4—61no—
291D4—304no—
292D4—601no—
293D4—602no—
294D4—604no—
295D4—602no—
296D4—601no—
297C2×C4—31no—
298C2×C4—32no—
299C2×C4—31no—
300C2×C4—32no—
301C2×C4—31no—
302C2×C4—31no—
303C2×C4—62no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—302no—
309C2×C4—602no—
310C8—304no—
311C2×C3—161no—
312D3—1602no—
313C5#8751011yescharacteristic, complemented, Sylow
314C22—31no—
315C22—31no—
316C22—32no—
317C22—61no—
318C22—61no—
319C22—61no—
320C22—61no—
321C22—61no—
322C22—122no—
323C22—122no—
324C22—602no—
325C22—602no—
326C22—602no—
327C22—1204no—
328C22#9195611yescharacteristic, complemented
329C4—32no—
330C4—31no—
331C4—61no—
332C4—602no—
333C4C5⋊#102011yescharacteristic
334C3—161noSylow
335C2—31no—
336C2—31no—
337C2—62no—
338C2—121no—
339C2—1202no—
340C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, FrattiniC2C2×C5⋊#1020
commutator, cosocle, hypocenterC5×C22⋊SL(2,𝔽3)C22
FittingC22×C5×#41D3
socleC23×C5C2×S4
hypercenterC4C5⋊#1020
LCSG ▷ C5×C22⋊SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C5×#5948C2semidirect
2. C5⋊#5931C2semidirect
4. C5×C22⋊SL(2,𝔽3)C22semidirect
8. C22×C5×#41D3semidirect
21. #5948D5semidirect
55. C22⋊SL(2,𝔽3)C2×D5semidirect
69. C5×#41S4semidirect
104. C22×#41D15semidirect
204. C22×C5#986semidirect
225. #41C5⋊S4semidirect
313. C5#87510semidirect
328. C22#91956semidirect

Maximal subgroups

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

subgroupindex
C5×#59482
C5⋊#59312
#106158133
#919564
C4⋊(C5⋊S4)4
#875105