Finite Group Databasebeta

← C22×#91899 #14514522

Subgroups — C22×#91899 #14514522

Order 1920.

1734 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1734 conjugacy classes of subgroups — too many to draw. Only its 191 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
1C22×A4×Dic5C211yesmaximal, characteristic
2C22×A4⋊Dic5C211yesmaximal, characteristic
3C22×C5×SL(2,ℤ/4)C211yesmaximal, characteristic
4C2×#91899C2112yesmaximal, direct product factor
5C22×#4024—31nomaximal, Hall
6C23×C5×A4C2211yescharacteristic
7C22×#1204—41nomaximal
8C2×A4×Dic5C2216yes—
9C2×A4⋊Dic5C2216yes—
10C2×C5×SL(2,ℤ/4)C2216yes—
11#91899C22116yesdirect product factor
12C22×A4⋊Q8—51nomaximal, Hall
13C24×Dic5D311yescharacteristic
14C23×Dic10—31no—
15C22×C5×C22⋊C4—31no—
16C22×C22⋊Dic5—31no—
17C22×C4⋊Dic5—31no—
18C22×#683—31no—
19C22×#683—31no—
20C2×#4024—312no—
21C2×#4024—312no—
22C22×C5×A4Q814yescomplemented
23C22×C5×A4C2313yes—
24C22×Dic15—41no—
25C22×C5×Dic3—41no—
26C22×C3×Dic5—41no—
27C2×#1204—412no—
28A4×Dic5C2314yes—
29A4⋊Dic5C2314yes—
30C5×SL(2,ℤ/4)C2314yes—
31C22×C4×A4—51no—
32C22×SL(2,ℤ/4)—51no—
33C22×SL(2,ℤ/4)D511yescharacteristic
34C2×A4⋊Q8—512no—
35C25×C5C2×D311yescharacteristic
36C23×C4×C5—31no—
37C23×C4×C5—31no—
38C23×Dic5—31no—
39C23×Dic5—36no—
40C23×Dic5—31no—
41C23×Dic5—31no—
42C23×Dic5—31no—
43C23×Dic5C2×D316yes—
44C22×Dic10—312no—
45C22×Dic10—61no—
46C22×Dic10—66no—
47C22×Dic10—61no—
48C2×C5×C22⋊C4—36no—
49C2×C5×C22⋊C4—36no—
50C2×C22⋊Dic5—36no—
51C2×C22⋊Dic5—36no—
52C2×C4⋊Dic5—312no—
53C2×#683—312no—
54C2×#683—312no—
55#4024—348no—
56#4024—316no—
57C22×C22⋊Q8—151noSylow
58C23×C3×C5—41no—
59C2×C5×A4C2×Q816yescomplemented
60C2×C5×A4C2411yescharacteristic
61C2×Dic15—46no—
62C2×C5×Dic3—46no—
63C2×C3×Dic5—46no—
64#1204—416no—
65C23×A4C2×D511yescharacteristic
66C22×Dic6—201no—
67C2×C4×A4—56no—
68C2×SL(2,ℤ/4)—56no—
69C2×SL(2,ℤ/4)C2×D516yes—
70A4⋊Q8—516no—
71C24×C5—31no—
72C24×C5—33no—
73C24×C5—34no—
74C24×C5Dic614yescomplemented
75C24×C5C22×D313yes—
76C22×C4×C5—36no—
77C22×C4×C5—36no—
78C22×C4×C5—63no—
79C22×C4×C5—64no—
80C22×C4×C5—61no—
81C22×Dic5—31no—
82C22×Dic5—36no—
83C22×Dic5—36no—
84C22×Dic5—312no—
85C22×Dic5—36no—
86C22×Dic5—36no—
87C22×Dic5—36no—
88C22×Dic5—64no—
89C22×Dic5—63no—
90C22×Dic5—63no—
91C22×Dic5—64no—
92C22×Dic5—61no—
93C22×Dic5S411yescharacteristic
94C22×Dic5C22×D314yes—
95C2×Dic10—316no—
96C2×Dic10—612no—
97C2×Dic10—624no—
98C2×Dic10—612no—
99C5×C22⋊C4—312no—
100C5×C22⋊C4—34no—
101C22⋊Dic5—312no—
102C22⋊Dic5—34no—
103C4⋊Dic5—316no—
104#683—316no—
105#683—316no—
106C23×Q8—151no—
107C24×C4—51no—
108C2×C22⋊Q8—1512no—
109C2×C22⋊Q8—1512no—
110C22×C4⋊C4—151no—
111C22×C4⋊C4—151no—
112C22×C4⋊C4—151no—
113C22×C22⋊C4—31no—
114C22×C22⋊C4—151no—
115C22×C3×C5—44no—
116C22×C3×C5—43no—
117C5×A4C22×Q811yescharacteristic, complemented
118Dic15—44no—
119C3×Dic5—44no—
120C5×Dic3—44no—
121C22×A4Dic1014yescomplemented
122C22×A4C22×D513yes—
123C22×C3×C4—201no—
124C22×Dic3—41no—
125C22×Dic3—201no—
126C2×Dic6—2012no—
127C4×A4—54no—
128SL(2,ℤ/4)—54no—
129SL(2,ℤ/4)C22×D514yes—
130C23×C5—34no—
131C23×C5—34no—
132C23×C5—33no—
133C23×C5—33no—
134C23×C5—33no—
135C23×C5—312no—
136C23×C5—36no—
137C23×C5—61no—
138C23×C5—66no—
139C23×C5C2×Dic616yescomplemented
140C23×C5C2×S411yescharacteristic
141C23×C5C23×D311yescharacteristic
142C2×C4×C5—34no—
143C2×C4×C5—34no—
144C2×C4×C5—66no—
145C2×C4×C5—612no—
146C2×C4×C5—66no—
147C2×Dic5—36no—
148C2×Dic5—34no—
149C2×Dic5—312no—
150C2×Dic5—34no—
151C2×Dic5—34no—
152C2×Dic5—34no—
153C2×Dic5—66no—
154C2×Dic5—66no—
155C2×Dic5—612no—
156C2×Dic5—66no—
157C2×Dic5C2×S416yes—
158Dic10—616no—
159Dic10—616no—
160C25D3×D511yescharacteristic
161C22×Q8—1512no—
162C22×Q8—301no—
163C22×Q8—306no—
164C22×Q8—301no—
165C23×C4—31no—
166C23×C4—31no—
167C23×C4—56no—
168C23×C4—151no—
169C23×C4—151no—
170C23×C4—156no—
171C23×C4—151no—
172C23×C4—151no—
173C22⋊Q8—1516no—
174C22⋊Q8—1548no—
175C2×C4⋊C4—1512no—
176C2×C4⋊C4—1512no—
177C2×C4⋊C4—1512no—
178C2×C22⋊C4—36no—
179C2×C22⋊C4—36no—
180C2×C22⋊C4—156no—
181C2×C22⋊C4—156no—
182C2×C3×C5—46no—
183C2×C3×C5—41no—
184C23×C3—41no—
185C2×A4C2×Dic1016yescomplemented
186C2×A4C23×D511yescharacteristic
187C2×C3×C4—206no—
188C2×Dic3—46no—
189C2×Dic3—206no—
190Dic6—2016no—
191C22×C5—36no—
192C22×C5—31no—
193C22×C5—36no—
194C22×C5—36no—
195C22×C5—312no—
196C22×C5—31no—
197C22×C5—33no—
198C22×C5—63no—
199C22×C5—64no—
200C22×C5A4⋊Q814yescomplemented
201C22×C5C22×Dic611yescharacteristic, complemented
202C22×C5C22×S413yes—
203C4×C5—64no—
204C4×C5—64no—
205Dic5—34no—
206Dic5—64no—
207Dic5—64no—
208Dic5C22×S414yes—
209C24—31no—
210C24—33no—
211C24—34no—
212C24#120414yescomplemented
213C24C2×D3×D513yes—
214C2×Q8—1516no—
215C2×Q8—3012no—
216C2×Q8—3024no—
217C2×Q8—3012no—
218C22×C4—36no—
219C22×C4—36no—
220C22×C4—51no—
221C22×C4—54no—
222C22×C4—63no—
223C22×C4—64no—
224C22×C4—61no—
225C22×C4—156no—
226C22×C4—156no—
227C22×C4—151no—
228C22×C4—156no—
229C22×C4—1512no—
230C22×C4—156no—
231C22×C4—156no—
232C22×C4—304no—
233C22×C4—303no—
234C22×C4—303no—
235C22×C4—304no—
236C22×C4—301no—
237C4⋊C4—1516no—
238C4⋊C4—1516no—
239C4⋊C4—1516no—
240C22⋊C4—312no—
241C22⋊C4—34no—
242C22⋊C4—1512no—
243C22⋊C4—154no—
244C3×C5—41noHall
245C22×C3—43no—
246C22×C3—44no—
247A4C22×Dic1011yescharacteristic, complemented
248C3×C4—204no—
249Dic3—44no—
250Dic3—204no—
251C2×C5—31no—
252C2×C5—31no—
253C2×C5—36no—
254C2×C5C2×A4⋊Q816yescomplemented
255C2×C5C23×S411yescharacteristic
256C23—33no—
257C23—33no—
258C23—34no—
259C23—34no—
260C23—33no—
261C23—312no—
262C23—36no—
263C23—61no—
264C23—66no—
265C23C2×#120416yescomplemented
266C23D5×S411yescharacteristic
267C23C22×D3×D511yescharacteristic
268Q8—3016no—
269Q8—3016no—
270C2×C4—34no—
271C2×C4—34no—
272C2×C4—56no—
273C2×C4—66no—
274C2×C4—612no—
275C2×C4—66no—
276C2×C4—154no—
277C2×C4—1512no—
278C2×C4—156no—
279C2×C4—154no—
280C2×C4—154no—
281C2×C4—154no—
282C2×C4—306no—
283C2×C4—306no—
284C2×C4—3012no—
285C2×C4—306no—
286C2×C3—41no—
287C2×C3—46no—
288C5C22×A4⋊Q811yescharacteristic, complemented, Sylow
289C22—36no—
290C22—31no—
291C22—31no—
292C22—33no—
293C22—36no—
294C22—36no—
295C22—312no—
296C22—63no—
297C22—64no—
298C22#9189914yesdirect product factor
299C22C22×#120411yescharacteristic, complemented
300C22C2×D5×S413yes—
301C4—54no—
302C4—64no—
303C4—64no—
304C4—154no—
305C4—304no—
306C4—304no—
307C3—41noSylow
308C2—31no—
309C2—31no—
310C2—36no—
311C2C2×#9189916yesdirect product factor
312C2C22×D5×S411yescharacteristic
subgroupG/H
center, hypercenterC23D5×S4
commutator, cosocleC2×C5×A4C24
FrattiniC2C22×D5×S4
Fitting, socleC25×C5C2×D3
prime radicalC23×C5×A4C22
hypocenterC5×A4C22×Q8
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
4. C2×#91899C2direct (N × H)
11. #91899C22direct (N × H)
22. C22×C5×A4Q8semidirect
59. C2×C5×A4C2×Q8semidirect
74. C24×C5Dic6semidirect
117. C5×A4C22×Q8semidirect
121. C22×A4Dic10semidirect
139. C23×C5C2×Dic6semidirect
185. C2×A4C2×Dic10semidirect
200. C22×C5A4⋊Q8semidirect
201. C22×C5C22×Dic6semidirect
212. C24#1204semidirect
247. A4C22×Dic10semidirect
254. C2×C5C2×A4⋊Q8semidirect
265. C23C2×#1204semidirect
288. C5C22×A4⋊Q8semidirect
298. C22#91899direct (N × H)
299. C22C22×#1204semidirect
311. C2C2×#91899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×A4×Dic52
C22×A4⋊Dic52
C22×C5×SL(2,ℤ/4)2
C2×#918992
C22×#40243
C22×#12044
C22×A4⋊Q85