Finite Group Databasebeta

← C22×C3×D5×C4⋊C4 #14478701

Subgroups — C22×C3×D5×C4⋊C4 #14478701

Order 1920.

4976 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C212yesmaximal
2C23×C3×C4×D5C211yesmaximal, characteristic
3C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
5C22×C3×#683C212yesmaximal, complemented
6C2×C3×D5×C4⋊C4C2124yesmaximal, direct product factor
7C22×D5×C4⋊C4C311yesmaximal, characteristic, direct product factor, Hall
8C24×C3×D5C2211yescharacteristic
9C23×C3×C4×C5C2212yes—
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×Dic5C2212yes—
12C23×C3×Dic5C2211yescharacteristic
13C22×C3×C4×D5—216no—
14C22×C3×C4×D5C4116yescomplemented
15C22×C3×C4×D5C22124yes—
16C22×C3×C4×D5C22112yes—
17C2×C3×C5×C4⋊C4C22112yescomplemented
18C2×C3×C4⋊Dic5C22112yescomplemented
19C2×C3×#683C22124yescomplemented
20C3×D5×C4⋊C4C22164yesdirect product factor
21C23×C3×C4⋊C4—51nomaximal, Hall
22C23×C4×D5C2×C312yes—
23C23×C4×D5C2×C311yescharacteristic
24C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
25C22×C4⋊Dic5C2×C311yescharacteristic, complemented
26C22×#683C2×C312yescomplemented
27C2×D5×C4⋊C4C2×C3124yesdirect product factor
28C24×C3×C5C2311yescharacteristic
29C23×C3×D5C2×C418yes—
30C23×C3×D5D418yes—
31C23×C3×D5Q818yes—
32C23×C3×D5C2316yes—
33C22×C3×C4×C5—28no—
34C22×C3×C4×C5C2×C418yescomplemented
35C22×C3×C4×C5C23112yes—
36C22×C3×C4×C5C2316yes—
37C22×C3×Dic5—28no—
38C22×C3×Dic5C2×C418yescomplemented
39C22×C3×Dic5C23112yes—
40C22×C3×Dic5C2316yes—
41C2×C3×C4×D5—296no—
42C2×C3×C4×D5C2×C4196yescomplemented
43C2×C3×C4×D5C23132yes—
44C2×C3×C4×D5C23116yes—
45C3×C5×C4⋊C4C23116yescomplemented
46C3×C4⋊Dic5C23116yescomplemented
47C3×#683C23132yescomplemented
48C24×C3×C4—51no—
49C24×C3×C4—52no—
50C22×C3×C4⋊C4—52no—
51C22×C3×C4⋊C4—51no—
52C22×C3×C4⋊C4—524no—
53C22×C3×C4⋊C4D511yescharacteristic, direct product factor
54C24×D5C22×C311yescharacteristic
55C23×C4×C5C22×C312yes—
56C23×C4×C5C22×C311yescharacteristic
57C23×Dic5C22×C312yes—
58C23×Dic5C22×C311yescharacteristic
59C22×C4×D5—216no—
60C22×C4×D5C3×C4116yescomplemented
61C22×C4×D5C22×C3124yes—
62C22×C4×D5C22×C3112yes—
63C2×C5×C4⋊C4C22×C3112yescomplemented
64C2×C4⋊Dic5C22×C3112yescomplemented
65C2×#683C22×C3124yescomplemented
66D5×C4⋊C4C22×C3164yesdirect product factor
67C23×C4⋊C4—51noSylow
68C23×C3×C5C22×C414yes—
69C23×C3×C5C2×D414yes—
70C23×C3×C5C2×Q814yes—
71C23×C3×C5C2413yes—
72C22×C3×D5C4⋊C4164yesdirect product factor
73C22×C3×D5C22×C4124yes—
74C22×C3×D5C2×D4124yes—
75C22×C3×D5C2×Q8124yes—
76C22×C3×D5C2414yes—
77C2×C3×C4×C5—224no—
78C2×C3×C4×C5C22×C4124yescomplemented
79C2×C3×C4×C5C2418yes—
80C2×C3×C4×C5C2414yes—
81C2×C3×Dic5—224no—
82C2×C3×Dic5C22×C4124yescomplemented
83C2×C3×Dic5C2418yes—
84C2×C3×Dic5C2414yes—
85C3×C4×D5—264no—
86C3×C4×D5C22×C4164yescomplemented
87C25×C3—51no—
88C23×C3×C4—51no—
89C23×C3×C4—516no—
90C23×C3×C4—512no—
91C23×C3×C4—52no—
92C23×C3×C4—524no—
93C23×C3×C4—1016no—
94C23×C3×C4C2×D512yes—
95C23×C3×C4C2×D511yescharacteristic
96C2×C3×C4⋊C4—524no—
97C2×C3×C4⋊C4—512no—
98C2×C3×C4⋊C4—564no—
99C2×C3×C4⋊C4C2×D5112yesdirect product factor
100C24×C5C23×C311yescharacteristic
101C23×D5C2×C3×C418yes—
102C23×D5C3×D418yes—
103C23×D5C3×Q818yes—
104C23×D5C23×C316yes—
105C22×C4×C5—28no—
106C22×C4×C5C2×C3×C418yescomplemented
107C22×C4×C5C23×C3112yes—
108C22×C4×C5C23×C316yes—
109C22×Dic5—28no—
110C22×Dic5C2×C3×C418yescomplemented
111C22×Dic5C23×C3112yes—
112C22×Dic5C23×C316yes—
113C2×C4×D5—296no—
114C2×C4×D5C2×C3×C4196yescomplemented
115C2×C4×D5C23×C3132yes—
116C2×C4×D5C23×C3116yes—
117C5×C4⋊C4C23×C3116yescomplemented
118C4⋊Dic5C23×C3116yescomplemented
119#683C23×C3132yescomplemented
120C24×C4—51no—
121C24×C4—52no—
122C22×C4⋊C4—52no—
123C22×C4⋊C4—51no—
124C22×C4⋊C4—524no—
125C22×C4⋊C4C3×D511yescharacteristic, direct product factor
126C22×C3×C5C2×C4⋊C4116yescomplemented
127C22×C3×C5C23×C416yes—
128C22×C3×C5C22×D416yes—
129C22×C3×C5C22×Q816yes—
130C22×C3×C5C2511yescharacteristic
131C2×C3×D5C2×C4⋊C4196yesdirect product factor
132C2×C3×D5C23×C418yes—
133C2×C3×D5C22×D418yes—
134C2×C3×D5C22×Q818yes—
135C3×C4×C5—28no—
136C3×C4×C5C23×C418yescomplemented
137C3×Dic5—28no—
138C3×Dic5C23×C418yescomplemented
139C24×C3—58no—
140C24×C3—58no—
141C24×C3—58no—
142C24×C3—56no—
143C24×C3C22×D511yescharacteristic
144C22×C3×C4—28no—
145C22×C3×C4—58no—
146C22×C3×C4—56no—
147C22×C3×C4—596no—
148C22×C3×C4—516no—
149C22×C3×C4—512no—
150C22×C3×C4—532no—
151C22×C3×C4—1096no—
152C22×C3×C4—108no—
153C22×C3×C4C4×D518yescomplemented
154C22×C3×C4C22×D5112yes—
155C22×C3×C4C22×D516yes—
156C3×C4⋊C4—532no—
157C3×C4⋊C4—516no—
158C3×C4⋊C4C22×D5116yesdirect product factor
159C23×C5C22×C3×C414yes—
160C23×C5C2×C3×D414yes—
161C23×C5C2×C3×Q814yes—
162C23×C5C24×C313yes—
163C22×D5C3×C4⋊C4164yesdirect product factor
164C22×D5C22×C3×C4124yes—
165C22×D5C2×C3×D4124yes—
166C22×D5C2×C3×Q8124yes—
167C22×D5C24×C314yes—
168C2×C4×C5—224no—
169C2×C4×C5C22×C3×C4124yescomplemented
170C2×C4×C5C24×C318yes—
171C2×C4×C5C24×C314yes—
172C2×Dic5—224no—
173C2×Dic5C22×C3×C4124yescomplemented
174C2×Dic5C24×C318yes—
175C2×Dic5C24×C314yes—
176C4×D5—264no—
177C4×D5C22×C3×C4164yescomplemented
178C25—51no—
179C23×C4—51no—
180C23×C4—516no—
181C23×C4—512no—
182C23×C4—52no—
183C23×C4—524no—
184C23×C4—1016no—
185C23×C4C2×C3×D512yes—
186C23×C4C2×C3×D511yescharacteristic
187C2×C4⋊C4—524no—
188C2×C4⋊C4—512no—
189C2×C4⋊C4—564no—
190C2×C4⋊C4C2×C3×D5112yesdirect product factor
191C2×C3×C5C22×C4⋊C4112yescomplemented
192C2×C3×C5C24×C411yescharacteristic
193C2×C3×C5C23×D411yescharacteristic
194C2×C3×C5C23×Q811yescharacteristic
195C3×D5C22×C4⋊C4116yesdirect product factor
196C23×C3—524no—
197C23×C3—524no—
198C23×C3—524no—
199C23×C3—54no—
200C23×C3—564no—
201C23×C3C2×C4×D514yes—
202C23×C3D4×D514yes—
203C23×C3Q8×D514yes—
204C23×C3C23×D513yes—
205C2×C3×C4—224no—
206C2×C3×C4—524no—
207C2×C3×C4—54no—
208C2×C3×C4—564no—
209C2×C3×C4—58no—
210C2×C3×C4—1064no—
211C2×C3×C4—1024no—
212C2×C3×C4C2×C4×D5124yescomplemented
213C2×C3×C4C23×D518yes—
214C2×C3×C4C23×D514yes—
215C22×C5C2×C3×C4⋊C4116yescomplemented
216C22×C5C23×C3×C416yes—
217C22×C5C22×C3×D416yes—
218C22×C5C22×C3×Q816yes—
219C22×C5C25×C311yescharacteristic
220C2×D5C2×C3×C4⋊C4196yesdirect product factor
221C2×D5C23×C3×C418yes—
222C2×D5C22×C3×D418yes—
223C2×D5C22×C3×Q818yes—
224C4×C5—28no—
225C4×C5C23×C3×C418yescomplemented
226Dic5—28no—
227Dic5C23×C3×C418yescomplemented
228C24—58no—
229C24—58no—
230C24—58no—
231C24—56no—
232C24C22×C3×D511yescharacteristic
233C22×C4—28no—
234C22×C4—58no—
235C22×C4—56no—
236C22×C4—596no—
237C22×C4—516no—
238C22×C4—512no—
239C22×C4—532no—
240C22×C4—1096no—
241C22×C4—108no—
242C22×C4C3×C4×D518yescomplemented
243C22×C4C22×C3×D5112yes—
244C22×C4C22×C3×D516yes—
245C4⋊C4—532no—
246C4⋊C4—516no—
247C4⋊C4C22×C3×D5116yesdirect product factor
248C3×C5C23×C4⋊C411yescharacteristic, complemented, Hall
249C22×C3—596no—
250C22×C3—58no—
251C22×C3—58no—
252C22×C3—58no—
253C22×C3D5×C4⋊C4116yesdirect product factor
254C22×C3C22×C4×D516yes—
255C22×C3C2×D4×D516yes—
256C22×C3C2×Q8×D516yes—
257C22×C3C24×D511yescharacteristic
258C3×C4—28no—
259C3×C4—58no—
260C3×C4—108no—
261C3×C4C22×C4×D518yescomplemented
262C2×C5C22×C3×C4⋊C4112yescomplemented
263C2×C5C24×C3×C411yescharacteristic
264C2×C5C23×C3×D411yescharacteristic
265C2×C5C23×C3×Q811yescharacteristic
266D5C22×C3×C4⋊C4116yesdirect product factor
267C23—524no—
268C23—524no—
269C23—524no—
270C23—564no—
271C23—54no—
272C23C2×C3×C4×D514yes—
273C23C3×D4×D514yes—
274C23C3×Q8×D514yes—
275C23C23×C3×D513yes—
276C2×C4—224no—
277C2×C4—524no—
278C2×C4—54no—
279C2×C4—564no—
280C2×C4—58no—
281C2×C4—1064no—
282C2×C4—1024no—
283C2×C4C2×C3×C4×D5124yescomplemented
284C2×C4C23×C3×D518yes—
285C2×C4C23×C3×D514yes—
286C2×C3—516no—
287C2×C3C2×D5×C4⋊C4112yesdirect product factor
288C2×C3C23×C4×D511yescharacteristic
289C2×C3C22×D4×D511yescharacteristic
290C2×C3C22×Q8×D511yescharacteristic
291C5C23×C3×C4⋊C411yescharacteristic, complemented, Sylow
292C22—58no—
293C22—58no—
294C22—58no—
295C22—596no—
296C22C3×D5×C4⋊C4116yesdirect product factor
297C22C22×C3×C4×D516yes—
298C22C2×C3×D4×D516yes—
299C22C2×C3×Q8×D516yes—
300C22C24×C3×D511yescharacteristic
301C4—28no—
302C4—58no—
303C4—108no—
304C4C22×C3×C4×D518yescomplemented
305C3C22×D5×C4⋊C411yescharacteristic, direct product factor, Sylow
306C2—516no—
307C2C2×C3×D5×C4⋊C4112yesdirect product factor
308C2C23×C3×C4×D511yescharacteristic
309C2C22×C3×D4×D511yescharacteristic
310C2C22×C3×Q8×D511yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutatorC2×C5C24×C3×C4
FrattiniC22C24×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC24×C3×C5C23
prime radicalC24×C3×D5C22
cosocleC22×C5C25×C3
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C23×C3×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×C3×C5×C4⋊C4C2semidirect
4. C22×C3×C4⋊Dic5C2semidirect
5. C22×C3×#683C2semidirect
6. C2×C3×D5×C4⋊C4C2direct (N × H)
7. C22×D5×C4⋊C4C3direct (N × H)
14. C22×C3×C4×D5C4semidirect
17. C2×C3×C5×C4⋊C4C22semidirect
18. C2×C3×C4⋊Dic5C22semidirect
19. C2×C3×#683C22semidirect
20. C3×D5×C4⋊C4C22direct (N × H)
24. C22×C5×C4⋊C4C2×C3semidirect
25. C22×C4⋊Dic5C2×C3semidirect
26. C22×#683C2×C3semidirect
27. C2×D5×C4⋊C4C2×C3direct (N × H)
34. C22×C3×C4×C5C2×C4semidirect
38. C22×C3×Dic5C2×C4semidirect
42. C2×C3×C4×D5C2×C4semidirect
45. C3×C5×C4⋊C4C23semidirect
46. C3×C4⋊Dic5C23semidirect
47. C3×#683C23semidirect
53. C22×C3×C4⋊C4D5direct (N × H)
60. C22×C4×D5C3×C4semidirect
63. C2×C5×C4⋊C4C22×C3semidirect
64. C2×C4⋊Dic5C22×C3semidirect
65. C2×#683C22×C3semidirect
66. D5×C4⋊C4C22×C3direct (N × H)
72. C22×C3×D5C4⋊C4direct (N × H)
78. C2×C3×C4×C5C22×C4semidirect
82. C2×C3×Dic5C22×C4semidirect
86. C3×C4×D5C22×C4semidirect
99. C2×C3×C4⋊C4C2×D5direct (N × H)
106. C22×C4×C5C2×C3×C4semidirect
110. C22×Dic5C2×C3×C4semidirect
114. C2×C4×D5C2×C3×C4semidirect
117. C5×C4⋊C4C23×C3semidirect
118. C4⋊Dic5C23×C3semidirect
119. #683C23×C3semidirect
125. C22×C4⋊C4C3×D5direct (N × H)
126. C22×C3×C5C2×C4⋊C4semidirect
131. C2×C3×D5C2×C4⋊C4direct (N × H)
136. C3×C4×C5C23×C4semidirect
138. C3×Dic5C23×C4semidirect
153. C22×C3×C4C4×D5semidirect
158. C3×C4⋊C4C22×D5direct (N × H)
163. C22×D5C3×C4⋊C4direct (N × H)
169. C2×C4×C5C22×C3×C4semidirect
173. C2×Dic5C22×C3×C4semidirect
177. C4×D5C22×C3×C4semidirect
190. C2×C4⋊C4C2×C3×D5direct (N × H)
191. C2×C3×C5C22×C4⋊C4semidirect
195. C3×D5C22×C4⋊C4direct (N × H)
212. C2×C3×C4C2×C4×D5semidirect
215. C22×C5C2×C3×C4⋊C4semidirect
220. C2×D5C2×C3×C4⋊C4direct (N × H)
225. C4×C5C23×C3×C4semidirect
227. Dic5C23×C3×C4semidirect
242. C22×C4C3×C4×D5semidirect
247. C4⋊C4C22×C3×D5direct (N × H)
248. C3×C5C23×C4⋊C4semidirect
253. C22×C3D5×C4⋊C4direct (N × H)
261. C3×C4C22×C4×D5semidirect
262. C2×C5C22×C3×C4⋊C4semidirect
266. D5C22×C3×C4⋊C4direct (N × H)
283. C2×C4C2×C3×C4×D5semidirect
287. C2×C3C2×D5×C4⋊C4direct (N × H)
291. C5C23×C3×C4⋊C4semidirect
296. C22C3×D5×C4⋊C4direct (N × H)
304. C4C22×C3×C4×D5semidirect
305. C3C22×D5×C4⋊C4direct (N × H)
307. C2C2×C3×D5×C4⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C22×C3×C5×C4⋊C42
C22×C3×C4⋊Dic52
C22×C3×#6832
C2×C3×D5×C4⋊C42
C22×D5×C4⋊C43
C23×C3×C4⋊C45