Finite Group Databasebeta

← C2×#11751619 #14513386

Subgroups — C2×#11751619 #14513386

Order 1920.

514 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 59 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×#91954C211yesmaximal, characteristic, complemented
2C2×C5×#986C211yesmaximal, characteristic
3C2×#4094⋊C3C211yesmaximal, characteristic, complemented
4#11751619C214yesmaximal, direct product factor
5C2×#65489—31nomaximal, Hall
6C2×C5×#41⋊C3C2211yescharacteristic
7#91954—21no—
8#91954C2212yescomplemented
9C2×C5⋊#226—21no—
10C5×#986—21no—
11C5×#986C2212yes—
12C2×C5×GL(2,𝔽3)—21no—
13C2×#6659—41nomaximal
14#4094⋊C3C2212yescomplemented
15C2×#5406—51nomaximal, Hall
16C2×C5×AGL(1,ℤ/8)—31no—
17C2×#4097—31no—
18C2×#4094D311yescharacteristic, complemented
19C22×#687—31no—
20C2×#3965—31no—
21#65489—34no—
22#65489—34no—
23C2×#3956—31no—
24C2×#3954—31no—
25C2×Dic30—41no—
26C2×C5×D12—41no—
27C5×#41⋊C3D411yescharacteristic
28C5×#41⋊C3C2311yescharacteristic
29C2×C5×SL(2,𝔽3)D411yescharacteristic
30C5⋊#226—22no—
31C5×GL(2,𝔽3)—22no—
32C2×C3×#168—41no—
33#6659—44no—
34C2×#986D511yescharacteristic
35C2×#984—51no—
36C2×#131⋊C3—51no—
37#5406—54no—
38C2×C5×#41C2×D311yescharacteristic
39C22×C5×D4—31no—
40C22×Dic10—31no—
41C5×AGL(1,ℤ/8)—32no—
42C5×AGL(1,ℤ/8)—32no—
43C5×AGL(1,ℤ/8)—61no—
44C5×AGL(1,ℤ/8)—61no—
45C2×C5×SD16—61no—
46C2×C5×D8—61no—
47C2×C5×M16—31no—
48#4097—32no—
49#4097—32no—
50#4097—61no—
51#4097—61no—
52#4094—32no—
53#4094C2×D312yescomplemented
54C2×#689—61no—
55C2×#687—34no—
56C2×#687—61no—
57C2×#687—62no—
58C2×#687—61no—
59C2×#687—61no—
60C2×#681—31no—
61C2×#681—31no—
62C22×#168—31no—
63#3965—34no—
64#3956—34no—
65#3954—34no—
66C2×#471—151noSylow
67C22×C5×D3—81no—
68C2×C3×C4×C5—41no—
69C2×Dic15—81no—
70Dic30—42no—
71Dic30—81no—
72C5×D12—42no—
73C5×D12—81no—
74C5×SL(2,𝔽3)C2×D411yescharacteristic
75C3×#168—42no—
76C2×#41⋊C3C2×D511yescharacteristic
77#986—21no—
78#986C2×D512yes—
79#984—52no—
80#984—101no—
81C2×GL(2,𝔽3)—21no—
82C2×#226—101no—
83C2×#204—201no—
84#131⋊C3—52no—
85C24×C5—61no—
86C5×#41—31no—
87C5×#41—31no—
88C5×#41D1211yescharacteristic
89C5×#41C22×D311yescharacteristic
90C2×C5×Q8D1211yescharacteristic
91C2×C5×D4—31no—
92C2×C5×D4—32no—
93C2×C5×D4—61no—
94C2×C5×D4—61no—
95C2×C5×D4—61no—
96C2×C5×D4—61no—
97C2×C5×D4—61no—
98C22×C4×C5—31no—
99C22×Dic5—61no—
100C2×Dic10—32no—
101C2×Dic10—61no—
102C2×Dic10—61no—
103C2×Dic10—61no—
104C2×Dic10—61no—
105C2×Dic10—61no—
106C5×SD16—62no—
107C5×SD16—62no—
108C5×D8—62no—
109C5×D8—62no—
110C5×M16—32no—
111C5×M16—61no—
112C2×C5×C8—61no—
113#689—62no—
114#689—62no—
115#687—64no—
116#687—62no—
117#687—62no—
118#687—64no—
119#681—32no—
120#681—32no—
121#681—61no—
122#681—61no—
123C2×#168—31no—
124C2×#168—32no—
125C2×#168—32no—
126C2×#168—61no—
127C2×#168S411yescharacteristic
128C2×#137—151no—
129C2×AGL(1,ℤ/8)—31no—
130C22×SD16—151no—
131C2×#131—51no—
132#471—154no—
133#471—154no—
134C2×#108—151no—
135C2×#101—151no—
136C2×#100—151no—
137C22×C3×C5—41no—
138C2×C5×D3—82no—
139C2×C5×D3—162no—
140C3×C4×C5—41no—
141C3×C4×C5—41no—
142Dic15—82no—
143C2×D12—41no—
144C2×Dic6—201no—
145#41⋊C3C22⋊D511yescharacteristic
146#41⋊C3C22×D511yescharacteristic
147C2×SL(2,𝔽3)C22⋊D511yescharacteristic
148GL(2,𝔽3)—22no—
149#226—102no—
150C2×C3×C8—201no—
151#204—204no—
152C23×C5—31no—
153C23×C5—62no—
154C23×C5—121no—
155C23×C5—121no—
156C23×C5—242no—
157C5×Q8—31no—
158C5×Q8C2×D1211yescharacteristic
159C5×D4—31no—
160C5×D4—31no—
161C5×D4—61no—
162C5×D4—62no—
163C5×D4—62no—
164C5×D4—121no—
165C5×D4—121no—
166C2×C4×C5—31no—
167C2×C4×C5—31no—
168C2×C4×C5—31no—
169C2×C4×C5—31no—
170C2×C4×C5—31no—
171C2×C4×C5C2×S411yescharacteristic
172C2×Dic5—62no—
173C2×Dic5—121no—
174C2×Dic5—121no—
175Dic10—62no—
176Dic10—62no—
177Dic10—121no—
178Dic10—121no—
179C5×C8—62no—
180#168—32no—
181#168—62no—
182#168C2×S412yes—
183C2×#41D3×D511yescharacteristic
184C22×Q8—151no—
185C22×D4—31no—
186#137—152no—
187#137—152no—
188#137—301no—
189#137—301no—
190AGL(1,ℤ/8)—32no—
191AGL(1,ℤ/8)—32no—
192AGL(1,ℤ/8)—61no—
193AGL(1,ℤ/8)—61no—
194C2×Q16—301no—
195C2×SD16—61no—
196C2×SD16—154no—
197C2×SD16—301no—
198C2×SD16—302no—
199C2×SD16—301no—
200C2×SD16—301no—
201C2×D8—61no—
202#131—52no—
203#131—152no—
204C2×M16—31no—
205C2×M16—151no—
206C2×M16—151no—
207C22×C8—151no—
208#108—154no—
209#101—154no—
210#100—154no—
211C2×C3×C5—41no—
212C2×C3×C5—42no—
213C5×D3—162no—
214C22×D3—81no—
215C2×C3×C4—41no—
216C2×Dic3—401no—
217D12—42no—
218D12—81no—
219Dic6—202no—
220Dic6—401no—
221SL(2,𝔽3)C2×C22⋊D511yescharacteristic
222C3×C8—202no—
223C22×C5—31no—
224C22×C5—31no—
225C22×C5—62no—
226C22×C5—122no—
227C22×C5—242no—
228C22×C5—242no—
229C22×C5—242no—
230C22×C5C4⋊S411yescharacteristic
231C4×C5—31no—
232C4×C5—31no—
233C4×C5C4⋊S411yescharacteristic
234C4×C5C22×S411yescharacteristic
235Dic5—122no—
236C24—61no—
237#41—31no—
238#41—31no—
239#41#120311yescharacteristic
240#41C2×D3×D511yescharacteristic
241C2×Q8—152no—
242C2×Q8—301no—
243C2×Q8—301no—
244C2×Q8—301no—
245C2×Q8—301no—
246C2×Q8—301no—
247C2×Q8#120311yescharacteristic
248C2×D4—31no—
249C2×D4—32no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—61no—
255C22×C4—31no—
256C22×C4—301no—
257Q16—302no—
258Q16—302no—
259SD16—62no—
260SD16—62no—
261SD16—304no—
262SD16—304no—
263SD16—302no—
264SD16—302no—
265D8—62no—
266D8—62no—
267M16—32no—
268M16—61no—
269M16—152no—
270M16—152no—
271M16—301no—
272M16—301no—
273C2×C8—51no—
274C2×C8—61no—
275C2×C8—152no—
276C2×C8—152no—
277C2×C8—151no—
278C2×C8—301no—
279C3×C5—41noHall
280C22×C3—41no—
281C2×D3—82no—
282C2×D3—162no—
283C3×C4—41no—
284C3×C4—41no—
285Dic3—402no—
286C2×C5—61no—
287C2×C5—61no—
288C2×C5—242no—
289C2×C5#540612yescomplemented
290C2×C5C2×C4⋊S411yescharacteristic
291C23—31no—
292C23—62no—
293C23—121no—
294C23—121no—
295C23—242no—
296Q8—31no—
297Q8—302no—
298Q8—302no—
299Q8—601no—
300Q8—601no—
301Q8C2×#120311yescharacteristic
302D4—31no—
303D4—31no—
304D4—61no—
305D4—62no—
306D4—62no—
307D4—121no—
308D4—121no—
309C2×C4—31no—
310C2×C4—31no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—302no—
315C2×C4—601no—
316C2×C4—601no—
317C2×C4D5×S411yescharacteristic
318C8—52no—
319C8—62no—
320C8—152no—
321C8—302no—
322C2×C3—42no—
323C2×C3—41no—
324D3—162no—
325C5C2×#540611yescharacteristic, complemented, Sylow
326C22—31no—
327C22—31no—
328C22—62no—
329C22—122no—
330C22—242no—
331C22—242no—
332C22—242no—
333C22#9190211yescharacteristic
334C4—31no—
335C4—31no—
336C4—602no—
337C4#9190211yescharacteristic
338C4C2×D5×S411yescharacteristic
339C3—41noSylow
340C2—61no—
341C2—61no—
342C2—242no—
343C2#1175161912yesdirect product factor
344C2C2×#9190211yescharacteristic
subgroupG/H
centerC22#91902
commutator, cosocleC5×#41⋊C3C23
FrattiniC4C2×D5×S4
FittingC2×C5×#41C2×D3
socleC22×C5C4⋊S4
prime radicalC2×C5×#986C2
hypercenterC2×C4D5×S4
hypocenterC5×SL(2,𝔽3)C2×D4
LCSG ▷ C5×#41⋊C3 ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91954C2semidirect
3. C2×#4094⋊C3C2semidirect
4. #11751619C2direct (N × H)
8. #91954C22semidirect
14. #4094⋊C3C22semidirect
18. C2×#4094D3semidirect
53. #4094C2×D3semidirect
289. C2×C5#5406semidirect
325. C5C2×#5406semidirect
343. C2#11751619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919542
C2×C5×#9862
C2×#4094⋊C32
#117516192
C2×#654893
C2×#66594
C2×#54065