Finite Group Databasebeta

← C2×#11747170 #14431652

Subgroups — C2×#11747170 #14431652

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C2×#91360C211yesmaximal, characteristic
3C2×#91094C211yesmaximal, characteristic, complemented
4C2×C5×#807C211yesmaximal, characteristic, complemented
5C2×#90986C211yesmaximal, characteristic, complemented
6C2×#90974C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic
8#11747170C218yesmaximal, direct product factor
9C2×#65177—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×#685—21no—
17C2×C3×C4⋊Dic5C2211yescharacteristic
18C2×C3×C4×Dic5—21no—
19C3×#4038—22no—
20C3×#4038C2214yes—
21C2×Dic3⋊Dic5—21no—
22C2×#6665—21no—
23#91360—22no—
24#91360C2214yes—
25#91094C2214yescomplemented
26C5×#807C2214yescomplemented
27#90986C2214yescomplemented
28#90974C2214yescomplemented
29#90955C2214yes—
30C2×#4996—51nomaximal, Hall
31C2×#4043—31no—
32C2×#4038D311yescharacteristic
33C2×C5×#107—31no—
34C2×#3952—31no—
35C2×#3948—31no—
36C2×#3942—31no—
37C2×#3940—31no—
38#65177—38no—
39C23×C3×D5D411yescharacteristic
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C2×Dic30—22no—
44C2×Dic30—22no—
45C2×Dic30—21no—
46C2×Dic30C2312yes—
47C22×C5×Dic3—21no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5D411yescharacteristic
50C2×C3×C4×D5—22no—
51C2×C3×C4×D5—22no—
52C2×C3×C4×D5D412yes—
53C2×C3×C4×D5C2312yes—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4C2312yes—
56C2×C3⋊#168—22no—
57C2×C3⋊#168C2312yes—
58C5×C4⋊Dic3—21no—
59C5×C4⋊Dic3C2312yes—
60C2×C5×C3⋊C8—22no—
61C2×C5×C3⋊C8C2312yes—
62C3×#685—24no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5C2312yes—
65C3×C4×Dic5—24no—
66Dic3⋊Dic5—24no—
67#6665—24no—
68C2×C3×#117—51no—
69C2×#924—51no—
70C2×#830—51no—
71#4996—58no—
72C2×#810—51no—
73C2×#810—51no—
74C2×#808—51no—
75C2×#807D511yescharacteristic, complemented
76C22×C4×D5C2×D311yescharacteristic
77C22×Dic10—31no—
78C22×C5×C8—31no—
79C2×C5×C4⋊C4—31no—
80C2×C5×C4⋊C4C2×D311yescharacteristic
81C2×#685—21no—
82C2×#685—61no—
83C2×C4⋊Dic5—61no—
84C2×C4⋊Dic5C2×D311yescharacteristic
85C2×C4×Dic5—21no—
86C22×#168—31no—
87#4043—34no—
88#4043—62no—
89#4038—22no—
90#4038C2×D314yes—
91C5×#107—34no—
92#3952—34no—
93#3948—34no—
94#3942—34no—
95#3940—34no—
96C2×#485—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×C3×D5—22no—
99C22×C3×D5—22no—
100C22×C3×D5—22no—
101C22×C3×D5C2×D412yes—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—42no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4112yes—
106C2×C3×C4×C5#4112yes—
107C2×C3×C4×C5C2411yescharacteristic
108C2×Dic15—22no—
109C2×Dic15—42no—
110Dic30—22no—
111Dic30—22no—
112Dic30—42no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3—42no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5C2×D412yes—
119C3×C4×D5—24no—
120C3×C4×D5—22no—
121C3×C4×D5—22no—
122C3⋊#168—22no—
123C5×C3⋊C8—22no—
124C23×C3×C4—51no—
125C22×Dic6—51no—
126C3×#117—54no—
127C3×#117—102no—
128C2×C3×C4⋊C4—51no—
129C2×C3×C4⋊C4C2×D511yescharacteristic
130C2×C3×C22⋊C4—101no—
131C2×C3×C42—101no—
132C2×#217—101no—
133C2×C4⋊Dic3C2×D511yescharacteristic
134#924—54no—
135#924—102no—
136C2×Dic3⋊C4—101no—
137C22×C3⋊C8—51no—
138C22×C3⋊C8C2×D511yescharacteristic
139#830—54no—
140#810—54no—
141#810—54no—
142#808—54no—
143#807C2×D514yescomplemented
144C23×D5#6711yescharacteristic
145C22×C4×C5—21no—
146C22×C4×C5—61no—
147C22×C4×C5C22×D311yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—61no—
150C22×Dic5#6711yescharacteristic
151C2×C4×D5—22no—
152C2×C4×D5—22no—
153C2×C4×D5#6712yes—
154C2×C4×D5C22×D312yes—
155C2×Dic10—32no—
156C2×Dic10—62no—
157C2×Dic10—62no—
158C2×Dic10—61no—
159C2×C5×C8—32no—
160C2×C5×C8—62no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—32no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4C22×D312yes—
165#685—24no—
166#685—64no—
167C4⋊Dic5—21no—
168C4⋊Dic5—64no—
169C4⋊Dic5C22×D312yes—
170C4×Dic5—24no—
171C2×#168—32no—
172C2×#168—62no—
173C2×C22⋊Q8—151no—
174C2×#117—51no—
175#485—158no—
176C2×#107—31no—
177C2×#106—151no—
178C2×#103—151no—
179C2×#103—151no—
180C2×C22⋊C8—151no—
181C22×C3×C5#12312yes—
182C22×C3×C5#13512yes—
183C22×C3×C5#13712yes—
184C22×C3×C5C22×D411yescharacteristic
185C2×C3×D5—22no—
186C2×C3×D5—22no—
187C2×C3×D5—22no—
188C2×C3×D5—44no—
189C3×C4×C5—42no—
190C3×C4×C5#12312yes—
191C3×C4×C5C2×#4111yescharacteristic
192C3×C4×C5C2×#4111yescharacteristic
193Dic15—42no—
194C3×Dic5—22no—
195C3×Dic5—42no—
196C5×Dic3—42no—
197C24×C3—51no—
198C22×C3×C4—21no—
199C22×C3×C4—51no—
200C22×C3×C4—52no—
201C22×C3×C4—52no—
202C22×C3×C4—102no—
203C22×C3×C4—102no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—101no—
208C2×Dic6—52no—
209C2×Dic6—102no—
210C2×Dic6—102no—
211C2×Dic6—101no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—52no—
214C3×C4⋊C4—101no—
215C3×C4⋊C4C22×D512yes—
216C3×C22⋊C4—104no—
217C3×C42—104no—
218#217—104no—
219C4⋊Dic3—21no—
220C4⋊Dic3C22×D512yes—
221Dic3⋊C4—104no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—102no—
225C2×C3⋊C8C22×D512yes—
226C23×C5C2×#6711yescharacteristic
227C22×D5—22no—
228C22×D5—22no—
229C22×D5—22no—
230C22×D5C2×#6712yes—
231C2×C4×C5—22no—
232C2×C4×C5—42no—
233C2×C4×C5—62no—
234C2×C4×C5—122no—
235C2×C4×C5#23512yes—
236C2×C4×C5#23512yes—
237C2×C4×C5C2×#6711yescharacteristic
238C2×C4×C5C23×D311yescharacteristic
239C2×Dic5—22no—
240C2×Dic5—22no—
241C2×Dic5—42no—
242C2×Dic5—62no—
243C2×Dic5—122no—
244C2×Dic5C2×#6712yes—
245C4×D5—24no—
246C4×D5—22no—
247C4×D5—22no—
248Dic10—62no—
249Dic10—62no—
250Dic10—122no—
251C5×C8—62no—
252#168—62no—
253C22×Q8—151no—
254C23×C4—51no—
255C22×C8—31no—
256C22×C8—151no—
257C22⋊Q8—154no—
258C22⋊Q8—302no—
259#117—54no—
260#117—102no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—301no—
264C2×C4⋊C4D3×D511yescharacteristic
265C2×C22⋊C4—101no—
266C2×C22⋊C4—301no—
267C2×C42—101no—
268#107—34no—
269#106—154no—
270#103—154no—
271#103—154no—
272C22⋊C8—154no—
273C2×C3×C5#48514yescomplemented
274C2×C3×C5C2×#12311yescharacteristic
275C2×C3×C5C2×#13511yescharacteristic
276C2×C3×C5C2×#13711yescharacteristic
277C3×D5—42no—
278C23×C3—52no—
279C23×C3—102no—
280C23×C3—102no—
281C23×C3—102no—
282C23×C3D4×D511yescharacteristic
283C2×C3×C4—22no—
284C2×C3×C4—42no—
285C2×C3×C4—52no—
286C2×C3×C4—102no—
287C2×C3×C4—102no—
288C2×C3×C4—102no—
289C2×C3×C4—104no—
290C2×C3×C4—102no—
291C2×C3×C4—202no—
292C2×C3×C4#70912yes—
293C2×C3×C4D4×D511yescharacteristic
294C2×C3×C4#71312yes—
295C2×C3×C4C23×D511yescharacteristic
296C2×Dic3—22no—
297C2×Dic3—42no—
298C2×Dic3—102no—
299C2×Dic3—202no—
300Dic6—102no—
301Dic6—102no—
302Dic6—202no—
303C3⋊C8—22no—
304C3⋊C8—102no—
305C22×C5#92912yes—
306C22×C5#95012yes—
307C22×C5#95112yes—
308C22×C5C22×#6711yescharacteristic
309C2×D5—22no—
310C2×D5—22no—
311C2×D5—22no—
312C2×D5—44no—
313C4×C5—42no—
314C4×C5—122no—
315C4×C5#92912yes—
316C4×C5C2×#23511yescharacteristic
317C4×C5C2×#23511yescharacteristic
318Dic5—22no—
319Dic5—42no—
320Dic5—122no—
321C24—51no—
322C2×Q8—152no—
323C2×Q8—301no—
324C2×Q8—302no—
325C2×Q8—302no—
326C22×C4—21no—
327C22×C4—51no—
328C22×C4—52no—
329C22×C4—52no—
330C22×C4—61no—
331C22×C4—102no—
332C22×C4—102no—
333C22×C4—101no—
334C22×C4—301no—
335C22×C4C2×D3×D511yescharacteristic
336C2×C8—32no—
337C2×C8—62no—
338C2×C8—152no—
339C2×C8—302no—
340C4⋊C4—21no—
341C4⋊C4—32no—
342C4⋊C4—52no—
343C4⋊C4—61no—
344C4⋊C4—101no—
345C4⋊C4—304no—
346C4⋊C4C2×D3×D512yes—
347C22⋊C4—104no—
348C22⋊C4—304no—
349C42—104no—
350C3×C5C2×#48511yescharacteristic, complemented, Hall
351C22×C3—102no—
352C22×C3—102no—
353C22×C3—102no—
354C22×C3—204no—
355C22×C3#404012yes—
356C22×C3#405812yes—
357C22×C3#406412yes—
358C22×C3C2×D4×D511yescharacteristic
359C3×C4—42no—
360C3×C4—102no—
361C3×C4—202no—
362C3×C4#404012yes—
363C3×C4C2×#70911yescharacteristic
364C3×C4C2×#71311yescharacteristic
365Dic3—42no—
366Dic3—202no—
367C2×C5#499614yescomplemented
368C2×C5C2×#92911yescharacteristic
369C2×C5C2×#95011yescharacteristic
370C2×C5C2×#95111yescharacteristic
371D5—42no—
372C23—52no—
373C23—102no—
374C23—102no—
375C23—102no—
376C23D5×#6711yescharacteristic
377Q8—302no—
378Q8—302no—
379Q8—602no—
380C2×C4—22no—
381C2×C4—42no—
382C2×C4—52no—
383C2×C4—62no—
384C2×C4—102no—
385C2×C4—102no—
386C2×C4—102no—
387C2×C4—104no—
388C2×C4—102no—
389C2×C4—122no—
390C2×C4—202no—
391C2×C4—302no—
392C2×C4—602no—
393C2×C4#677112yes—
394C2×C4#677312yes—
395C2×C4D5×#6711yescharacteristic
396C2×C4C22×D3×D511yescharacteristic
397C8—62no—
398C8—302no—
399C2×C3—202no—
400C2×C3#6517714yescomplemented
401C2×C3C2×#404011yescharacteristic
402C2×C3C2×#405811yescharacteristic
403C2×C3C2×#406411yescharacteristic
404C5C2×#499611yescharacteristic, complemented, Sylow
405C22—102no—
406C22—102no—
407C22—102no—
408C22—204no—
409C22#9134812yes—
410C22#9149012yes—
411C22#9150812yes—
412C22C2×D5×#6711yescharacteristic
413C4—42no—
414C4—102no—
415C4—122no—
416C4—202no—
417C4—602no—
418C4#9134812yes—
419C4C2×#677111yescharacteristic
420C4C2×#677311yescharacteristic
421C3C2×#6517711yescharacteristic, complemented, Sylow
422C2—202no—
423C2#1174717014yesdirect product factor
424C2C2×#9134811yescharacteristic
425C2C2×#9149011yescharacteristic
426C2C2×#9150811yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#91094C2semidirect
4. C2×C5×#807C2semidirect
5. C2×#90986C2semidirect
6. C2×#90974C2semidirect
8. #11747170C2direct (N × H)
25. #91094C22semidirect
26. C5×#807C22semidirect
27. #90986C22semidirect
28. #90974C22semidirect
75. C2×#807D5semidirect
143. #807C2×D5semidirect
273. C2×C3×C5#485semidirect
350. C3×C5C2×#485semidirect
367. C2×C5#4996semidirect
400. C2×C3#65177semidirect
404. C5C2×#4996semidirect
421. C3C2×#65177semidirect
423. C2#11747170direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C2×#913602
C2×#910942
C2×C5×#8072
C2×#909862
C2×#909742
C2×#909552
#117471702
C2×#651773
C2×#49965