Finite Group Databasebeta

← C2×#11749209 #14431639

Subgroups — C2×#11749209 #14431639

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×#4092C211yesmaximal, characteristic
2C2×#91358C211yesmaximal, characteristic
3C2×#91119C211yesmaximal, characteristic, complemented
4C2×C5×#835C211yesmaximal, characteristic, complemented
5#11749209C218yesmaximal, direct product factor
6C2×#90990C211yesmaximal, characteristic, complemented
7C2×#90986C211yesmaximal, characteristic, complemented
8C2×#90955C211yesmaximal, characteristic
9C2×#65103—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C3×#4092—22no—
17C3×#4092C2214yes—
18C2×C3×#685—21no—
19C2×C3×C4⋊Dic5C2211yescharacteristic
20C2×C3×#683—21no—
21C2×#6665—21no—
22C2×Dic3×Dic5—21no—
23#91358—22no—
24#91358C2214yes—
25#91119C2214yescomplemented
26C5×#835C2214yescomplemented
27#90990C2214yescomplemented
28#90986C2214yescomplemented
29#90955C2214yes—
30C2×#5045—51nomaximal, Hall
31C2×#4092D311yescharacteristic
32C2×#4038—31no—
33C2×C5×#103—31no—
34C2×#3967—31no—
35C2×#3952—31no—
36C2×#3950—31no—
37C2×#3940—31no—
38#65103—38no—
39C23×C3×D5D411yescharacteristic
40C2×C3×C5×Q8—21no—
41C2×C3×C5×Q8—22no—
42C2×C3×C5×Q8—22no—
43C2×C3×C5×Q8C2312yes—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
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—
54C4⋊Dic15—21no—
55C4⋊Dic15C2312yes—
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×#683—24no—
66#6665—24no—
67Dic3×Dic5—24no—
68C2×C3×C22⋊Q8—51no—
69C2×#926—51no—
70C2×#835—51no—
71C2×#835D511yescharacteristic, complemented
72C2×#830—51no—
73#5045—58no—
74C2×#808—51no—
75C2×#807—51no—
76C22×C5×Q8C2×D311yescharacteristic
77C22×C4×D5C2×D311yescharacteristic
78C22×C5×C8—31no—
79C2×C5×C4⋊C4—31no—
80#4092—22no—
81#4092C2×D314yes—
82C2×#685—21no—
83C2×#685—61no—
84C2×C4⋊Dic5—31no—
85C2×C4⋊Dic5C2×D311yescharacteristic
86C2×#683—21no—
87C2×C4×Dic5—61no—
88C22×#168—31no—
89#4038—34no—
90#4038—62no—
91C5×#103—34no—
92#3967—34no—
93#3952—34no—
94#3950—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—
102C3×C5×Q8—22no—
103C3×C5×Q8—22no—
104C3×C5×Q8—42no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4112yes—
109C2×C3×C4×C5#4112yes—
110C2×C3×C4×C5C2411yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—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—
124C22×C3×Q8C2×D511yescharacteristic
125C23×C3×C4—51no—
126C3×C22⋊Q8—54no—
127C3×C22⋊Q8—102no—
128C2×C3×C4⋊C4—51no—
129C2×C3×C4⋊C4—101no—
130C2×C3×C22⋊C4—101no—
131C2×#217—101no—
132#926—54no—
133#926—102no—
134C2×C4⋊Dic3—51no—
135C2×C4⋊Dic3C2×D511yescharacteristic
136C2×C4×Dic3—101no—
137C22×C3⋊C8—51no—
138C22×C3⋊C8C2×D511yescharacteristic
139#835—54no—
140#835C2×D514yescomplemented
141#830—54no—
142#808—54no—
143#807—54no—
144C23×D5#6711yescharacteristic
145C2×C5×Q8—21no—
146C2×C5×Q8—22no—
147C2×C5×Q8—22no—
148C2×C5×Q8C22×D312yes—
149C22×C4×C5—21no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C22×Dic5—21no—
153C22×Dic5—61no—
154C22×Dic5#6711yescharacteristic
155C2×C4×D5—22no—
156C2×C4×D5—22no—
157C2×C4×D5#6712yes—
158C2×C4×D5C22×D312yes—
159C2×C5×C8—32no—
160C2×C5×C8—62no—
161C5×C4⋊C4—32no—
162C5×C4⋊C4—61no—
163#685—24no—
164#685—64no—
165C4⋊Dic5—21no—
166C4⋊Dic5—32no—
167C4⋊Dic5—61no—
168C4⋊Dic5C22×D312yes—
169#683—24no—
170C4×Dic5—64no—
171C2×#168—32no—
172C2×#168—62no—
173C2×C22⋊Q8—51no—
174C2×#117—151no—
175#485—158no—
176C2×#107—151no—
177C2×#106—151no—
178C2×#103—31no—
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—
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8C22×D512yes—
202C22×C3×C4—21no—
203C22×C3×C4—51no—
204C22×C3×C4—52no—
205C22×C3×C4—52no—
206C22×C3×C4—102no—
207C22×C3×C4—102no—
208C22×C3×C4—101no—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—101no—
212C3×C4⋊C4—52no—
213C3×C4⋊C4—104no—
214C3×C4⋊C4—101no—
215C3×C22⋊C4—104no—
216#217—104no—
217C4⋊Dic3—21no—
218C4⋊Dic3—52no—
219C4⋊Dic3—101no—
220C4⋊Dic3C22×D512yes—
221C4×Dic3—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—
231C5×Q8—22no—
232C5×Q8—22no—
233C5×Q8—42no—
234C2×C4×C5—22no—
235C2×C4×C5—42no—
236C2×C4×C5—62no—
237C2×C4×C5—122no—
238C2×C4×C5#23712yes—
239C2×C4×C5#23712yes—
240C2×C4×C5C2×#6711yescharacteristic
241C2×C4×C5C23×D311yescharacteristic
242C2×Dic5—22no—
243C2×Dic5—22no—
244C2×Dic5—42no—
245C2×Dic5—62no—
246C2×Dic5—122no—
247C2×Dic5C2×#6712yes—
248C4×D5—24no—
249C4×D5—22no—
250C4×D5—22no—
251C5×C8—62no—
252#168—62no—
253C22×Q8D3×D511yescharacteristic
254C23×C4—51no—
255C22×C8—31no—
256C22×C8—151no—
257C22⋊Q8—54no—
258C22⋊Q8—102no—
259#117—154no—
260#117—302no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—51no—
263C2×C4⋊C4—101no—
264C2×C4⋊C4—151no—
265C2×C22⋊C4—101no—
266C2×C22⋊C4—301no—
267C2×C42—301no—
268#107—154no—
269#106—154no—
270#103—34no—
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
283C3×Q8—22no—
284C3×Q8—22no—
285C3×Q8—42no—
286C2×C3×C4—22no—
287C2×C3×C4—42no—
288C2×C3×C4—52no—
289C2×C3×C4—102no—
290C2×C3×C4—102no—
291C2×C3×C4—102no—
292C2×C3×C4—104no—
293C2×C3×C4—102no—
294C2×C3×C4—202no—
295C2×C3×C4#70912yes—
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71112yes—
298C2×C3×C4C23×D511yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—42no—
301C2×Dic3—102no—
302C2×Dic3—202no—
303C3⋊C8—22no—
304C3⋊C8—102no—
305C22×C5#93512yes—
306C22×C5#94212yes—
307C22×C5#95012yes—
308C22×C5C22×#6711yescharacteristic
309C2×D5—22no—
310C2×D5—22no—
311C2×D5—22no—
312C2×D5—44no—
313C4×C5—42no—
314C4×C5—122no—
315C4×C5#93512yes—
316C4×C5C2×#23711yescharacteristic
317C4×C5C2×#23711yescharacteristic
318Dic5—22no—
319Dic5—42no—
320Dic5—122no—
321C24—51no—
322C2×Q8—21no—
323C2×Q8—22no—
324C2×Q8—22no—
325C2×Q8C2×D3×D512yes—
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—32no—
341C4⋊C4—52no—
342C4⋊C4—61no—
343C4⋊C4—104no—
344C4⋊C4—101no—
345C4⋊C4—152no—
346C4⋊C4—301no—
347C22⋊C4—104no—
348C22⋊C4—304no—
349C42—304no—
350C3×C5C2×#48511yescharacteristic, complemented, Hall
351C22×C3—102no—
352C22×C3—102no—
353C22×C3—102no—
354C22×C3—204no—
355C22×C3#402912yes—
356C22×C3#406112yes—
357C22×C3#406512yes—
358C22×C3C2×D4×D511yescharacteristic
359C3×C4—42no—
360C3×C4—102no—
361C3×C4—202no—
362C3×C4#402912yes—
363C3×C4C2×#70911yescharacteristic
364C3×C4C2×#71111yescharacteristic
365Dic3—42no—
366Dic3—202no—
367C2×C5#504514yescomplemented
368C2×C5C2×#93511yescharacteristic
369C2×C5C2×#94211yescharacteristic
370C2×C5C2×#95011yescharacteristic
371D5—42no—
372C23—52no—
373C23—102no—
374C23—102no—
375C23—102no—
376C23D5×#6711yescharacteristic
377Q8—22no—
378Q8—22no—
379Q8—42no—
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#677912yes—
394C2×C4#678012yes—
395C2×C4D5×#6711yescharacteristic
396C2×C4C22×D3×D511yescharacteristic
397C8—62no—
398C8—302no—
399C2×C3—202no—
400C2×C3#6510314yescomplemented
401C2×C3C2×#402911yescharacteristic
402C2×C3C2×#406111yescharacteristic
403C2×C3C2×#406511yescharacteristic
404C5C2×#504511yescharacteristic, complemented, Sylow
405C22—102no—
406C22—102no—
407C22—102no—
408C22—204no—
409C22#9151312yes—
410C22#9151612yes—
411C22#9154812yes—
412C22C2×D5×#6711yescharacteristic
413C4—42no—
414C4—102no—
415C4—122no—
416C4—202no—
417C4—602no—
418C4#9154812yes—
419C4C2×#677911yescharacteristic
420C4C2×#678011yescharacteristic
421C3C2×#6510311yescharacteristic, complemented, Sylow
422C2—202no—
423C2#1174920914yesdirect product factor
424C2C2×#9151311yescharacteristic
425C2C2×#9151611yescharacteristic
426C2C2×#9154811yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC23×C3×D5D4
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#91119C2semidirect
4. C2×C5×#835C2semidirect
5. #11749209C2direct (N × H)
6. C2×#90990C2semidirect
7. C2×#90986C2semidirect
25. #91119C22semidirect
26. C5×#835C22semidirect
27. #90990C22semidirect
28. #90986C22semidirect
71. C2×#835D5semidirect
140. #835C2×D5semidirect
273. C2×C3×C5#485semidirect
350. C3×C5C2×#485semidirect
367. C2×C5#5045semidirect
400. C2×C3#65103semidirect
404. C5C2×#5045semidirect
421. C3C2×#65103semidirect
423. C2#11749209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40922
C2×#913582
C2×#911192
C2×C5×#8352
#117492092
C2×#909902
C2×#909862
C2×#909552
C2×#651033
C2×#50455