Finite Group Databasebeta

← C2×#11755144 #14479036

Subgroups — C2×#11755144 #14479036

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×D3×Q8C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
4#11755144C2116yesmaximal, direct product factor
5C2×#91371C213yesmaximal
6C2×#91344C213yesmaximal, complemented
7C2×#91338C213yesmaximal
8C2×Dic5×Dic6C213yesmaximal, complemented
9C2×#66146—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×C5×D3×Q8C4116yescomplemented
12C2×C5×D3×Q8C2218yes—
13C22×C4×C5×D3C2213yes—
14C22×C5×Dic6C2213yes—
15Q8×Dic15C2218yescomplemented
16C2×C4⋊Dic15C2213yes—
17C2×C4×Dic15C2213yes—
18C3×Q8×Dic5C2218yescomplemented
19C2×C3×C4⋊Dic5C2213yes—
20C2×C3×C4×Dic5C2213yes—
21C2×Dic3⋊Dic5C2213yes—
22C2×Dic3⋊Dic5C2213yes—
23C2×(C2×D3)⋊Dic5C2211yescharacteristic
24C2×(C2×D3)⋊Dic5C2213yes—
25C2×Dic3×Dic5C2216yes—
26#91371C22124yes—
27#91344C22124yescomplemented
28#91338C22124yes—
29Dic5×Dic6C22124yescomplemented
30C2×#5572—51nomaximal, Hall
31C23×C5×Q8—31no—
32#66146—316no—
33C2×Q8×Dic5—33no—
34C2×Q8×Dic5—33no—
35C2×Q8×Dic5—31no—
36C2×Q8×Dic5D311yescharacteristic, complemented
37C2×#4072—33no—
38C2×#4072—33no—
39C23×C5×D3C2311yescharacteristic
40C2×C3×C5×Q8C2×C418yes—
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44C22×Dic15C2311yescharacteristic
45C22×C5×Dic3C2313yes—
46C5×D3×Q8C2×C4164yescomplemented
47C2×C4×C5×D3C2×C4124yes—
48C2×C4×C5×D3C23112yes—
49C2×C5×Dic6C2×C4124yes—
50C2×C5×Dic6C23112yes—
51C22×C3×Dic5C2313yes—
52C22×C3×Dic5C2311yescharacteristic
53C4⋊Dic15C23112yes—
54C4×Dic15C23112yes—
55C3×C4⋊Dic5C23112yes—
56C3×C4×Dic5C23112yes—
57Dic3⋊Dic5C23112yes—
58Dic3⋊Dic5C23112yes—
59(C2×D3)⋊Dic5C23112yes—
60(C2×D3)⋊Dic5C2314yes—
61Dic3×Dic5C23124yes—
62C22×D3×Q8D511yescharacteristic
63C2×C3×C4×Q8—51no—
64C2×Q8×Dic3—51no—
65#5572—516no—
66C2×#892—53no—
67C2×#887—53no—
68C2×#872—53no—
69C2×C4×Dic6—53no—
70C22×C5×Q8—316no—
71C22×C5×Q8—38no—
72C22×C5×Q8—33no—
73C22×C5×Q8C2×D311yescharacteristic
74C23×C4×C5—33no—
75C2×C22⋊Dic5—33no—
76C2×C22⋊Dic5—31no—
77Q8×Dic5—38no—
78Q8×Dic5—324no—
79Q8×Dic5—324no—
80Q8×Dic5C2×D318yescomplemented
81#4072—324no—
82#4072—324no—
83C2×C4⋊Dic5—33no—
84C2×C4⋊Dic5—33no—
85C2×C4⋊Dic5—33no—
86C2×C4⋊Dic5C2×D313yes—
87C2×C4×Dic5—33no—
88C2×C4×Dic5—36no—
89C2×C4×Dic5C2×D313yes—
90C2×#519—151noSylow
91C23×C3×C5C2411yescharacteristic
92C22×C5×D3—22no—
93C22×C5×D3—22no—
94C22×C5×D3C22×C414yes—
95C22×C5×D3C2412yes—
96C3×C5×Q8C22×C4116yes—
97C2×C3×C4×C5C22×C4112yes—
98C2×C3×C4×C5C2416yes—
99C2×Dic15—26no—
100C2×Dic15—22no—
101C2×Dic15C2416yes—
102C2×Dic15C2412yes—
103C2×C5×Dic3C22×C4112yes—
104C2×C5×Dic3C2416yes—
105C4×C5×D3C22×C4148yes—
106C5×Dic6C22×C4148yes—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—26no—
109C2×C3×Dic5C2416yes—
110C2×C3×Dic5C2412yes—
111C22×C3×Q8C2×D511yescharacteristic
112C2×D3×Q8Dic5116yescomplemented
113C2×D3×Q8C2×D518yes—
114C22×C4×D3C2×D513yes—
115C22×Dic6C2×D513yes—
116C3×C4×Q8—58no—
117C2×C3×C4⋊C4—53no—
118C2×C3×C42—53no—
119Q8×Dic3—58no—
120C2×(C2×D3)⋊C4—51no—
121C2×(C2×D3)⋊C4—53no—
122C2×C4⋊Dic3—53no—
123C2×Dic3⋊C4—53no—
124C2×Dic3⋊C4—53no—
125C2×C4×Dic3—53no—
126C2×C4×Dic3—56no—
127#892—524no—
128#887—524no—
129#872—524no—
130C4×Dic6—524no—
131C24×C5—31no—
132C2×C5×Q8—364no—
133C2×C5×Q8—324no—
134C2×C5×Q8—312no—
135C2×C5×Q8C4×D318yes—
136C2×C5×Q8C22×D314yes—
137C22×C4×C5—33no—
138C22×C4×C5—324no—
139C22×C4×C5—312no—
140C22×C4×C5C22×D313yes—
141C22×Dic5—33no—
142C22×Dic5—31no—
143C22×Dic5C22×D313yes—
144C22×Dic5C22×D311yescharacteristic
145C22⋊Dic5—312no—
146C22⋊Dic5—34no—
147C4⋊Dic5—312no—
148C4⋊Dic5—312no—
149C4⋊Dic5—312no—
150C4⋊Dic5C22×D3112yes—
151C4×Dic5—312no—
152C4×Dic5—324no—
153C4×Dic5C22×D3112yes—
154C23×Q8—31no—
155#519—1516no—
156C2×C4×Q8—51no—
157C2×C4×Q8—153no—
158C2×C4×Q8—153no—
159C2×C4×Q8—151no—
160C2×#117—153no—
161C2×#117—153no—
162C22×C3×C5C23×C412yes—
163C22×C3×C52−1+412yes—
164C22×C3×C52−1+412yes—
165C22×C3×C5C2511yescharacteristic
166C2×C5×D3—28no—
167C2×C5×D3—22no—
168C2×C5×D3—22no—
169C2×C5×D3C23×C414yes—
170C3×C4×C5C23×C4112yes—
171Dic15—26no—
172Dic15—22no—
173C3×Dic5—22no—
174C3×Dic5—26no—
175C5×Dic3C23×C4112yes—
176C23×D3C22×D511yescharacteristic
177C2×C3×Q8C2×Dic518yes—
178C2×C3×Q8C22×D514yes—
179C22×C3×C4—53no—
180C22×C3×C4—51no—
181C22×C3×C4C22×D513yes—
182C22×Dic3—51no—
183C22×Dic3—53no—
184C22×Dic3C22×D513yes—
185D3×Q8C2×Dic5164yescomplemented
186C2×C4×D3C2×Dic5124yes—
187C2×C4×D3C22×D5112yes—
188C2×Dic6C2×Dic5124yes—
189C2×Dic6C22×D5112yes—
190C3×C4⋊C4—512no—
191C3×C42—512no—
192(C2×D3)⋊C4—54no—
193(C2×D3)⋊C4—512no—
194C4⋊Dic3—512no—
195Dic3⋊C4—512no—
196Dic3⋊C4—512no—
197C4×Dic3—512no—
198C4×Dic3—524no—
199C23×C5—34no—
200C23×C5—32no—
201C23×C5—62no—
202C23×C5—62no—
203C23×C5C23×D311yescharacteristic
204C5×Q8—348no—
205C5×Q8C2×C4×D3116yes—
206C2×C4×C5—312no—
207C2×C4×C5—36no—
208C2×C4×C5—348no—
209C2×C4×C5C2×C4×D3112yes—
210C2×C4×C5C23×D316yes—
211C2×Dic5—22no—
212C2×Dic5—26no—
213C2×Dic5—36no—
214C2×Dic5—32no—
215C2×Dic5—66no—
216C2×Dic5—62no—
217C2×Dic5C23×D316yes—
218C2×Dic5C23×D312yes—
219C22×Q8—316no—
220C22×Q8—38no—
221C22×Q8—33no—
222C22×Q8D3×D511yescharacteristic
223C23×C4—33no—
224C4×Q8—58no—
225C4×Q8—1524no—
226C4×Q8—1524no—
227C4×Q8—158no—
228#117—1524no—
229#117—1524no—
230C2×C4⋊C4—53no—
231C2×C4⋊C4—153no—
232C2×C4⋊C4—153no—
233C2×C4⋊C4—153no—
234C2×C22⋊C4—151no—
235C2×C22⋊C4—153no—
236C2×C42—53no—
237C2×C42—156no—
238C2×C42—153no—
239C2×C3×C5#51914yescomplemented
240C2×C3×C5C24×C411yescharacteristic
241C2×C3×C5C2×2−1+411yescharacteristic
242C2×C3×C5C2×2−1+411yescharacteristic
243C5×D3—24no—
244C23×C3C23×D511yescharacteristic
245C22×D3—22no—
246C22×D3—22no—
247C22×D3C22×Dic514yes—
248C22×D3C23×D512yes—
249C3×Q8C22×Dic5116yes—
250C2×C3×C4—56no—
251C2×C3×C4—52no—
252C2×C3×C4—106no—
253C2×C3×C4—102no—
254C2×C3×C4C22×Dic5112yes—
255C2×C3×C4C23×D516yes—
256C2×Dic3—52no—
257C2×Dic3—56no—
258C2×Dic3—102no—
259C2×Dic3—106no—
260C2×Dic3C22×Dic5112yes—
261C2×Dic3C23×D516yes—
262C4×D3C22×Dic5148yes—
263Dic6C22×Dic5148yes—
264C22×C5—34no—
265C22×C5—62no—
266C22×C5—62no—
267C22×C5—68no—
268C22×C5C22×C4×D312yes—
269C22×C5#100712yes—
270C22×C5#101012yes—
271C22×C5C24×D311yescharacteristic
272C4×C5—312no—
273C4×C5C22×C4×D3112yes—
274Dic5—22no—
275Dic5—26no—
276Dic5—66no—
277Dic5—62no—
278C24—31no—
279C2×Q8—364no—
280C2×Q8—324no—
281C2×Q8—312no—
282C2×Q8D3×Dic518yes—
283C2×Q8C2×D3×D514yes—
284C22×C4—33no—
285C22×C4—324no—
286C22×C4—312no—
287C22×C4—51no—
288C22×C4—53no—
289C22×C4—151no—
290C22×C4—153no—
291C22×C4C2×D3×D513yes—
292C4⋊C4—512no—
293C4⋊C4—1512no—
294C4⋊C4—1512no—
295C4⋊C4—1512no—
296C22⋊C4—154no—
297C22⋊C4—1512no—
298C42—512no—
299C42—1524no—
300C42—1512no—
301C3×C5C2×#51911yescharacteristic, complemented, Hall
302C22×C3#414712yes—
303C22×C3#414712yes—
304C22×C3C23×Dic512yes—
305C22×C3C24×D511yescharacteristic
306C2×D3—28no—
307C2×D3—22no—
308C2×D3—22no—
309C2×D3C23×Dic514yes—
310C3×C4—106no—
311C3×C4—102no—
312C3×C4C23×Dic5112yes—
313Dic3—102no—
314Dic3—106no—
315Dic3C23×Dic5112yes—
316C2×C5—64no—
317C2×C5#557214yescomplemented
318C2×C5C23×C4×D311yescharacteristic
319C2×C5C2×#100711yescharacteristic
320C2×C5C2×#101011yescharacteristic
321C23—34no—
322C23—32no—
323C23—62no—
324C23—62no—
325C23C22×D3×D511yescharacteristic
326Q8—348no—
327Q8C2×D3×Dic5116yes—
328C2×C4—312no—
329C2×C4—36no—
330C2×C4—348no—
331C2×C4—52no—
332C2×C4—56no—
333C2×C4—106no—
334C2×C4—102no—
335C2×C4—152no—
336C2×C4—156no—
337C2×C4—302no—
338C2×C4—306no—
339C2×C4C2×D3×Dic5112yes—
340C2×C4C22×D3×D516yes—
341C2×C3#6614614yescomplemented
342C2×C3C2×#414711yescharacteristic
343C2×C3C2×#414711yescharacteristic
344C2×C3C24×Dic511yescharacteristic
345D3—24no—
346C5C2×#557211yescharacteristic, complemented, Sylow
347C22—34no—
348C22—68no—
349C22—62no—
350C22—62no—
351C22#9202812yes—
352C22#9202912yes—
353C22C22×D3×Dic512yes—
354C22C23×D3×D511yescharacteristic
355C4—312no—
356C4—106no—
357C4—102no—
358C4—302no—
359C4—306no—
360C4C22×D3×Dic5112yes—
361C3C2×#6614611yescharacteristic, complemented, Sylow
362C2—64no—
363C2#1175514414yesdirect product factor
364C2C2×#9202811yescharacteristic
365C2C2×#9202911yescharacteristic
366C2C23×D3×Dic511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
cosocleC22×C3×C5C25
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
3. C2×C3×Q8×Dic5C2semidirect
4. #11755144C2direct (N × H)
6. C2×#91344C2semidirect
8. C2×Dic5×Dic6C2semidirect
11. C2×C5×D3×Q8C4semidirect
15. Q8×Dic15C22semidirect
18. C3×Q8×Dic5C22semidirect
27. #91344C22semidirect
29. Dic5×Dic6C22semidirect
36. C2×Q8×Dic5D3semidirect
46. C5×D3×Q8C2×C4semidirect
80. Q8×Dic5C2×D3semidirect
112. C2×D3×Q8Dic5semidirect
185. D3×Q8C2×Dic5semidirect
239. C2×C3×C5#519semidirect
301. C3×C5C2×#519semidirect
317. C2×C5#5572semidirect
341. C2×C3#66146semidirect
346. C5C2×#5572semidirect
361. C3C2×#66146semidirect
363. C2#11755144direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×D3×Q82
C2×Q8×Dic152
C2×C3×Q8×Dic52
#117551442
C2×#913712
C2×#913442
C2×#913382
C2×Dic5×Dic62
C2×#661463
C2×#55725