Finite Group Databasebeta

← C22×#91345 #14479762

Subgroups — C22×#91345 #14479762

Order 1920.

2640 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6714C211yesmaximal, characteristic
2C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
4C22×#6668C211yesmaximal, characteristic, complemented
5C22×#6667C211yesmaximal, characteristic
6C22×#6667C211yesmaximal, characteristic
7C22×Dic3×Dic5C211yesmaximal, characteristic, complemented
8C2×#91345C2124yesmaximal, direct product factor
9C22×#4044—31nomaximal, Hall
10C24×D15C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C23×C3×Dic5C2211yescharacteristic
17C2×#6714C22112yes—
18C2×C5×Dic3⋊C4C22112yescomplemented
19C2×C3×C4⋊Dic5C22112yescomplemented
20C2×#6668C22112yescomplemented
21C2×#6667C22112yes—
22C2×#6667C22112yes—
23C2×Dic3×Dic5C22112yescomplemented
24#91345C22164yesdirect product factor
25C22×#898—51nomaximal, Hall
26C22×C5×C4⋊C4—31no—
27C22×#685—31no—
28C22×#685—31no—
29C22×#685—31no—
30C22×C4⋊Dic5D311yescharacteristic, complemented
31C22×#683—31no—
32C22×C4×Dic5—31no—
33C2×#4044—324no—
34C24×C3×C5C2311yescharacteristic
35C23×D15—24no—
36C23×D15—24no—
37C23×D15—24no—
38C23×D15C2316yes—
39C22×C3×C4×C5—24no—
40C22×C3×C4×C5C2316yes—
41C22×Dic15—24no—
42C22×Dic15C2316yes—
43C22×C5×Dic3—24no—
44C22×C5×Dic3—24no—
45C22×C5×Dic3C2316yes—
46C22×C5×Dic3C2316yes—
47C22×C3×Dic5—24no—
48C22×C3×Dic5—24no—
49C22×C3×Dic5C2316yes—
50C22×C3×Dic5C2316yes—
51#6714C23116yes—
52C5×Dic3⋊C4C23116yescomplemented
53C3×C4⋊Dic5C23116yescomplemented
54#6668C23116yescomplemented
55#6667C23116yes—
56#6667C23116yes—
57Dic3×Dic5C23116yescomplemented
58C22×C3×C4⋊C4—51no—
59C22×(C2×D3)⋊C4—51no—
60C22×(C2×D3)⋊C4—51no—
61C22×(C2×D3)⋊C4—51no—
62C22×C4⋊Dic3—51no—
63C22×Dic3⋊C4D511yescharacteristic, complemented
64C22×C4×Dic3—51no—
65C2×#898—524no—
66C24×D5—31no—
67C23×C4×C5—31no—
68C23×C4×C5—31no—
69C23×C4×C5C2×D311yescharacteristic
70C23×Dic5—31no—
71C23×Dic5C2×D311yescharacteristic
72C23×Dic5C2×D311yescharacteristic
73C2×C5×C4⋊C4—312no—
74C2×#685—312no—
75C2×#685—312no—
76C2×#685—312no—
77C2×C4⋊Dic5C2×D3112yescomplemented
78C2×#683—312no—
79C2×C4×Dic5—312no—
80#4044—364no—
81C22×#126—151noSylow
82C23×C3×C5#4114yes—
83C23×C3×C5#4114yes—
84C23×C3×C5#4114yes—
85C23×C3×C5C2413yes—
86C22×D15—212no—
87C22×D15—212no—
88C22×D15—212no—
89C22×D15—416no—
90C22×D15C2414yes—
91C2×C3×C4×C5—212no—
92C2×C3×C4×C5C2414yes—
93C2×Dic15—212no—
94C2×Dic15C2414yes—
95C2×C5×Dic3—212no—
96C2×C5×Dic3—212no—
97C2×C5×Dic3C2414yes—
98C2×C5×Dic3C2414yes—
99C2×C3×Dic5—212no—
100C2×C3×Dic5—212no—
101C2×C3×Dic5C2414yes—
102C2×C3×Dic5C2414yes—
103C24×D3—51no—
104C23×C3×C4—51no—
105C23×C3×C4—51no—
106C23×C3×C4C2×D511yescharacteristic
107C23×Dic3—51no—
108C23×Dic3C2×D511yescharacteristic
109C23×Dic3C2×D511yescharacteristic
110C2×C3×C4⋊C4—512no—
111C2×(C2×D3)⋊C4—512no—
112C2×(C2×D3)⋊C4—512no—
113C2×(C2×D3)⋊C4—512no—
114C2×C4⋊Dic3—512no—
115C2×Dic3⋊C4C2×D5112yescomplemented
116C2×C4×Dic3—512no—
117#898—564no—
118C24×C5C22×D311yescharacteristic
119C23×D5—36no—
120C23×D5—64no—
121C23×D5—64no—
122C23×D5—64no—
123C22×C4×C5—24no—
124C22×C4×C5—36no—
125C22×C4×C5—36no—
126C22×C4×C5—64no—
127C22×C4×C5—64no—
128C22×C4×C5C22×D316yes—
129C22×Dic5—24no—
130C22×Dic5—24no—
131C22×Dic5—36no—
132C22×Dic5—64no—
133C22×Dic5C22×D316yes—
134C22×Dic5C22×D316yes—
135C5×C4⋊C4—316no—
136#685—316no—
137#685—316no—
138#685—316no—
139C4⋊Dic5C22×D3116yescomplemented
140#683—316no—
141C4×Dic5—316no—
142C2×#126—1524no—
143C22×C4⋊C4—31no—
144C22×C4⋊C4—51no—
145C22×C4⋊C4—151no—
146C22×C22⋊C4—151no—
147C22×C22⋊C4—151no—
148C22×C22⋊C4—151no—
149C22×C42—151no—
150C22×C3×C5#126116yescomplemented
151C22×C3×C5C2×#4116yes—
152C22×C3×C5C2×#4116yes—
153C22×C3×C5C2×#4116yes—
154C22×C3×C5C2511yescharacteristic
155C2×D15—24no—
156C2×D15—24no—
157C2×D15—24no—
158C2×D15—424no—
159C3×C4×C5—24no—
160Dic15—24no—
161C3×Dic5—24no—
162C3×Dic5—24no—
163C5×Dic3—24no—
164C5×Dic3—24no—
165C24×C3C22×D511yescharacteristic
166C23×D3—56no—
167C23×D3—104no—
168C23×D3—104no—
169C23×D3—104no—
170C22×C3×C4—24no—
171C22×C3×C4—56no—
172C22×C3×C4—56no—
173C22×C3×C4—104no—
174C22×C3×C4—104no—
175C22×C3×C4C22×D516yes—
176C22×Dic3—24no—
177C22×Dic3—24no—
178C22×Dic3—56no—
179C22×Dic3—104no—
180C22×Dic3C22×D516yes—
181C22×Dic3C22×D516yes—
182C3×C4⋊C4—516no—
183(C2×D3)⋊C4—516no—
184(C2×D3)⋊C4—516no—
185(C2×D3)⋊C4—516no—
186C4⋊Dic3—516no—
187Dic3⋊C4C22×D5116yescomplemented
188C4×Dic3—516no—
189C23×C5#23514yes—
190C23×C5#23714yes—
191C23×C5#23914yes—
192C23×C5C23×D313yes—
193C22×D5—34no—
194C22×D5—612no—
195C22×D5—612no—
196C22×D5—612no—
197C22×D5—1216no—
198C2×C4×C5—212no—
199C2×C4×C5—34no—
200C2×C4×C5—34no—
201C2×C4×C5—612no—
202C2×C4×C5—612no—
203C2×C4×C5C23×D314yes—
204C2×Dic5—212no—
205C2×Dic5—212no—
206C2×Dic5—34no—
207C2×Dic5—612no—
208C2×Dic5C23×D314yes—
209C2×Dic5C23×D314yes—
210C25—151no—
211C23×C4—31no—
212C23×C4—31no—
213C23×C4—51no—
214C23×C4—51no—
215C23×C4—151no—
216C23×C4D3×D511yescharacteristic
217#126—1564no—
218C2×C4⋊C4—312no—
219C2×C4⋊C4—512no—
220C2×C4⋊C4—1512no—
221C2×C22⋊C4—1512no—
222C2×C22⋊C4—1512no—
223C2×C22⋊C4—1512no—
224C2×C42—1512no—
225C2×C3×C5C2×#126112yescomplemented
226C2×C3×C5C22×#4111yescharacteristic
227C2×C3×C5C22×#4111yescharacteristic
228C2×C3×C5C22×#4111yescharacteristic
229D15—44no—
230C23×C3#70914yes—
231C23×C3#71114yes—
232C23×C3#71314yes—
233C23×C3C23×D513yes—
234C22×D3—54no—
235C22×D3—1012no—
236C22×D3—1012no—
237C22×D3—1012no—
238C22×D3—2016no—
239C2×C3×C4—212no—
240C2×C3×C4—54no—
241C2×C3×C4—54no—
242C2×C3×C4—1012no—
243C2×C3×C4—1012no—
244C2×C3×C4C23×D514yes—
245C2×Dic3—212no—
246C2×Dic3—212no—
247C2×Dic3—54no—
248C2×Dic3—1012no—
249C2×Dic3C23×D514yes—
250C2×Dic3C23×D514yes—
251C22×C5#898116yescomplemented
252C22×C5C2×#23516yes—
253C22×C5C2×#23716yes—
254C22×C5C2×#23916yes—
255C22×C5C24×D311yescharacteristic
256C2×D5—64no—
257C2×D5—64no—
258C2×D5—64no—
259C2×D5—1224no—
260C4×C5—24no—
261C4×C5—64no—
262C4×C5—64no—
263Dic5—24no—
264Dic5—24no—
265Dic5—64no—
266C24—156no—
267C24—304no—
268C24—304no—
269C24—304no—
270C24C2×D3×D511yescharacteristic
271C22×C4—24no—
272C22×C4—36no—
273C22×C4—36no—
274C22×C4—56no—
275C22×C4—56no—
276C22×C4—64no—
277C22×C4—64no—
278C22×C4—104no—
279C22×C4—104no—
280C22×C4—156no—
281C22×C4—304no—
282C22×C4C2×D3×D516yes—
283C4⋊C4—316no—
284C4⋊C4—516no—
285C4⋊C4—1516no—
286C22⋊C4—1516no—
287C22⋊C4—1516no—
288C22⋊C4—1516no—
289C42—1516no—
290C3×C5C22×#12611yescharacteristic, complemented, Hall
291C22×C3#4044116yescomplemented
292C22×C3C2×#70916yes—
293C22×C3C2×#71116yes—
294C22×C3C2×#71316yes—
295C22×C3C24×D511yescharacteristic
296C2×D3—104no—
297C2×D3—104no—
298C2×D3—104no—
299C2×D3—2024no—
300C3×C4—24no—
301C3×C4—104no—
302C3×C4—104no—
303Dic3—24no—
304Dic3—24no—
305Dic3—104no—
306C2×C5C2×#898112yescomplemented
307C2×C5C22×#23511yescharacteristic
308C2×C5C22×#23711yescharacteristic
309C2×C5C22×#23911yescharacteristic
310D5—124no—
311C23—154no—
312C23—3012no—
313C23—3012no—
314C23—3012no—
315C23—6016no—
316C23#676614yes—
317C23#676914yes—
318C23#678214yes—
319C23C22×D3×D513yes—
320C2×C4—212no—
321C2×C4—34no—
322C2×C4—34no—
323C2×C4—54no—
324C2×C4—54no—
325C2×C4—612no—
326C2×C4—612no—
327C2×C4—1012no—
328C2×C4—1012no—
329C2×C4—154no—
330C2×C4—3012no—
331C2×C4C22×D3×D514yes—
332C2×C3C2×#4044112yescomplemented
333C2×C3C22×#70911yescharacteristic
334C2×C3C22×#71111yescharacteristic
335C2×C3C22×#71311yescharacteristic
336D3—204no—
337C5C22×#89811yescharacteristic, complemented, Sylow
338C22—304no—
339C22—304no—
340C22—304no—
341C22—6024no—
342C22#91345116yesdirect product factor
343C22C2×#676616yes—
344C22C2×#676916yes—
345C22C2×#678216yes—
346C22C23×D3×D511yescharacteristic
347C4—24no—
348C4—64no—
349C4—64no—
350C4—104no—
351C4—104no—
352C4—304no—
353C3C22×#404411yescharacteristic, complemented, Sylow
354C2—604no—
355C2C2×#91345112yesdirect product factor
356C2C22×#676611yescharacteristic
357C2C22×#676911yescharacteristic
358C2C22×#678211yescharacteristic
subgroupG/H
centerC24C2×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC24×C3×C5C23
prime radicalC24×D15C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C22×#126
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C5×Dic3⋊C4C2semidirect
3. C22×C3×C4⋊Dic5C2semidirect
4. C22×#6668C2semidirect
7. C22×Dic3×Dic5C2semidirect
8. C2×#91345C2direct (N × H)
18. C2×C5×Dic3⋊C4C22semidirect
19. C2×C3×C4⋊Dic5C22semidirect
20. C2×#6668C22semidirect
23. C2×Dic3×Dic5C22semidirect
24. #91345C22direct (N × H)
30. C22×C4⋊Dic5D3semidirect
52. C5×Dic3⋊C4C23semidirect
53. C3×C4⋊Dic5C23semidirect
54. #6668C23semidirect
57. Dic3×Dic5C23semidirect
63. C22×Dic3⋊C4D5semidirect
77. C2×C4⋊Dic5C2×D3semidirect
115. C2×Dic3⋊C4C2×D5semidirect
139. C4⋊Dic5C22×D3semidirect
150. C22×C3×C5#126semidirect
187. Dic3⋊C4C22×D5semidirect
225. C2×C3×C5C2×#126semidirect
251. C22×C5#898semidirect
290. C3×C5C22×#126semidirect
291. C22×C3#4044semidirect
306. C2×C5C2×#898semidirect
332. C2×C3C2×#4044semidirect
337. C5C22×#898semidirect
342. C22#91345direct (N × H)
353. C3C22×#4044semidirect
355. C2C2×#91345direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67142
C22×C5×Dic3⋊C42
C22×C3×C4⋊Dic52
C22×#66682
C22×#66672
C22×Dic3×Dic52
C2×#913452
C22×#40443
C22×#8985