Finite Group Databasebeta

← C2×#11748402 #14431643

Subgroups — C2×#11748402 #14431643

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×C5×#926C211yesmaximal, characteristic
2C2×C3×#4070C211yesmaximal, characteristic
3C2×#91114C211yesmaximal, characteristic
4C2×#90989C211yesmaximal, characteristic, complemented
5C2×#90986C211yesmaximal, characteristic, complemented
6#11748402C218yesmaximal, direct product factor
7C2×#90970C211yesmaximal, characteristic, complemented
8C2×#90970C211yesmaximal, characteristic, complemented
9C2×#65285—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C2×C5×#217—21no—
15C5×#926—22no—
16C5×#926C2214yes—
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C4×C5×Dic3—21no—
20C2×C3×C22⋊Dic5—21no—
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C3×#4070—22no—
23C3×#4070C2214yes—
24C2×C3×#683—21no—
25#91114C2214yes—
26#90989C2214yescomplemented
27#90986C2214yescomplemented
28#90970C2214yescomplemented
29#90970C2214yescomplemented
30C2×#5045—51nomaximal, Hall
31C2×C5×#117—31no—
32C2×#4070D311yescharacteristic
33C2×C22⋊#168—31no—
34#65285—38no—
35C2×#3942—31no—
36C2×#3942—31no—
37C2×#3940—31no—
38C2×#3939—31no—
39C24×C3×C5D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D412yes—
44C22×C3×C4×C5C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×C5×Dic3—21no—
47C22×C5×Dic3—21no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5—21no—
50C2×C3×Dic10—22no—
51C2×C3×Dic10—22no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10C2312yes—
54C2×C3⋊#168—22no—
55C2×C3⋊#168—22no—
56C2×C3⋊#168C2312yes—
57C2×C3⋊#168C2312yes—
58C5×#217—24no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3C2312yes—
62C5×C4⋊Dic3C2312yes—
63C4×C5×Dic3—24no—
64C3×C22⋊Dic5—24no—
65C3×C4⋊Dic5—21no—
66C3×C4⋊Dic5C2312yes—
67C3×#683—24no—
68C2×C3×C22⋊Q8—51no—
69C2×#926D511yescharacteristic
70C2×#835—51no—
71C2×#835—51no—
72C2×#830—51no—
73#5045—58no—
74C2×#808—51no—
75C2×#807—51no—
76C23×C4×C5C2×D311yescharacteristic
77C22×Dic10C2×D311yescharacteristic
78C5×#117—34no—
79C5×#117—62no—
80C2×C5×C4⋊C4—31no—
81C2×C5×C4⋊C4—31no—
82C2×C5×C22⋊C4—61no—
83C2×C42×C5—61no—
84C2×C22⋊Dic5—21no—
85C2×C4⋊Dic5C2×D311yescharacteristic
86#4070—22no—
87#4070C2×D314yes—
88C2×#683—21no—
89C22×#168—31no—
90C22×#168—31no—
91C22⋊#168—34no—
92#3942—34no—
93#3942—34no—
94#3940—34no—
95#3939—34no—
96C2×#485—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—22no—
99C23×C3×C5—22no—
100C23×C3×C5C2×D412yes—
101C23×C3×C5C2×D411yescharacteristic
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—24no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5C2×D412yes—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4112yes—
109C2×C3×C4×C5#4112yes—
110C2×C3×C4×C5C2411yescharacteristic
111C2×C5×Dic3—22no—
112C2×C5×Dic3—22no—
113C2×C5×Dic3—42no—
114C2×C5×Dic3—42no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5—42no—
119C3×Dic10—22no—
120C3×Dic10—22no—
121C3×Dic10—42no—
122C3⋊#168—22no—
123C3⋊#168—22no—
124C22×C3×Q8—51no—
125C23×C3×C4C2×D511yescharacteristic
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—21no—
132#926—22no—
133#926C2×D514yes—
134C2×C4⋊Dic3C2×D511yescharacteristic
135C2×C4⋊Dic3C2×D511yescharacteristic
136C2×C4×Dic3—21no—
137C22×C3⋊C8—51no—
138C22×C3⋊C8—51no—
139#835—54no—
140#835—54no—
141#830—54no—
142#808—54no—
143#807—54no—
144C24×C5#6711yescharacteristic
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—61no—
148C22×C4×C5—61no—
149C22×C4×C5#6711yescharacteristic
150C22×C4×C5#6712yes—
151C22×C4×C5C22×D312yes—
152C22×C4×C5C22×D311yescharacteristic
153C22×Dic5—21no—
154C22×Dic5—21no—
155C2×Dic10—22no—
156C2×Dic10—22no—
157C2×Dic10—21no—
158C2×Dic10C22×D312yes—
159C5×C4⋊C4—32no—
160C5×C4⋊C4—32no—
161C5×C4⋊C4—61no—
162C5×C4⋊C4—61no—
163C5×C22⋊C4—64no—
164C42×C5—64no—
165C22⋊Dic5—24no—
166C4⋊Dic5—21no—
167C4⋊Dic5C22×D312yes—
168#683—24no—
169C2×#168—32no—
170C2×#168—32no—
171C2×#168—62no—
172C2×#168—62no—
173C2×C22⋊Q8—51no—
174C2×#117—31no—
175#485—158no—
176C2×#107—151no—
177C2×#106—151no—
178C2×#103—151no—
179C2×#103—151no—
180C2×C22⋊C8—151no—
181C22×C3×C5—22no—
182C22×C3×C5—22no—
183C22×C3×C5—22no—
184C22×C3×C5—44no—
185C22×C3×C5#12312yes—
186C22×C3×C5#13512yes—
187C22×C3×C5#13712yes—
188C22×C3×C5C22×D411yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5#12312yes—
191C3×C4×C5C2×#4111yescharacteristic
192C3×C4×C5C2×#4111yescharacteristic
193C3×Dic5—42no—
194C3×Dic5—42no—
195C5×Dic3—42no—
196C5×Dic3—42no—
197C24×C3C22⋊D511yescharacteristic
198C2×C3×Q8—52no—
199C2×C3×Q8—101no—
200C2×C3×Q8—102no—
201C2×C3×Q8—102no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4C22⋊D511yescharacteristic
207C22×C3×C4C22⋊D512yes—
208C22×C3×C4C22×D512yes—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—21no—
211C22×Dic3—21no—
212C3×C4⋊C4—52no—
213C3×C4⋊C4—104no—
214C3×C4⋊C4—101no—
215C3×C22⋊C4—104no—
216#217—24no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3C22×D512yes—
220C4⋊Dic3C22×D512yes—
221C4×Dic3—24no—
222C2×C3⋊C8—52no—
223C2×C3⋊C8—52no—
224C2×C3⋊C8—102no—
225C2×C3⋊C8—102no—
226C23×C5—22no—
227C23×C5—22no—
228C23×C5—22no—
229C23×C5C2×#6712yes—
230C23×C5C2×#6711yescharacteristic
231C2×C4×C5—22no—
232C2×C4×C5—24no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5—62no—
236C2×C4×C5—62no—
237C2×C4×C5—122no—
238C2×C4×C5—122no—
239C2×C4×C5#23712yes—
240C2×C4×C5#23712yes—
241C2×C4×C5C2×#6712yes—
242C2×C4×C5C2×#6711yescharacteristic
243C2×C4×C5C23×D311yescharacteristic
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—42no—
247C2×Dic5—42no—
248Dic10—22no—
249Dic10—22no—
250Dic10—42no—
251#168—62no—
252#168—62no—
253C22×Q8—51no—
254C23×C4D3×D511yescharacteristic
255C22×C8—151no—
256C22×C8—151no—
257C22⋊Q8—54no—
258C22⋊Q8—102no—
259#117—34no—
260#117—62no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—51no—
264C2×C4⋊C4—101no—
265C2×C22⋊C4—61no—
266C2×C22⋊C4—101no—
267C2×C42—61no—
268#107—154no—
269#106—154no—
270#103—154no—
271#103—154no—
272C22⋊C8—154no—
273C2×C3×C5—42no—
274C2×C3×C5#48514yescomplemented
275C2×C3×C5C2×#12311yescharacteristic
276C2×C3×C5C2×#13511yescharacteristic
277C2×C3×C5C2×#13711yescharacteristic
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3C2×C22⋊D512yes—
282C23×C3C2×C22⋊D511yescharacteristic
283C3×Q8—102no—
284C3×Q8—102no—
285C3×Q8—202no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—24no—
290C2×C3×C4—102no—
291C2×C3×C4—102no—
292C2×C3×C4—202no—
293C2×C3×C4—202no—
294C2×C3×C4#70912yes—
295C2×C3×C4#70912yes—
296C2×C3×C4C2×C22⋊D512yes—
297C2×C3×C4C2×C22⋊D511yescharacteristic
298C2×C3×C4C23×D511yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—42no—
302C2×Dic3—42no—
303C3⋊C8—102no—
304C3⋊C8—102no—
305C22×C5—22no—
306C22×C5—22no—
307C22×C5—22no—
308C22×C5—44no—
309C22×C5#93512yes—
310C22×C5#94212yes—
311C22×C5#95012yes—
312C22×C5C22×#6711yescharacteristic
313C4×C5—22no—
314C4×C5—122no—
315C4×C5—122no—
316C4×C5#93512yes—
317C4×C5C2×#23711yescharacteristic
318C4×C5C2×#23711yescharacteristic
319Dic5—42no—
320Dic5—42no—
321C24#120111yescharacteristic
322C2×Q8—52no—
323C2×Q8—101no—
324C2×Q8—102no—
325C2×Q8—102no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—101no—
331C22×C4—101no—
332C22×C4#120112yes—
333C22×C4#120111yescharacteristic
334C22×C4C2×D3×D512yes—
335C22×C4C2×D3×D511yescharacteristic
336C2×C8—152no—
337C2×C8—152no—
338C2×C8—302no—
339C2×C8—302no—
340C4⋊C4—32no—
341C4⋊C4—32no—
342C4⋊C4—52no—
343C4⋊C4—61no—
344C4⋊C4—61no—
345C4⋊C4—101no—
346C4⋊C4—104no—
347C22⋊C4—64no—
348C22⋊C4—104no—
349C42—64no—
350C3×C5C2×#48511yescharacteristic, complemented, Hall
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—44no—
355C22×C3#407512yes—
356C22×C3#409612yes—
357C22×C3#409712yes—
358C22×C3C22×C22⋊D511yescharacteristic
359C3×C4—22no—
360C3×C4—202no—
361C3×C4—202no—
362C3×C4#407512yes—
363C3×C4C2×#70911yescharacteristic
364C3×C4C2×#70911yescharacteristic
365Dic3—42no—
366Dic3—42no—
367C2×C5—42no—
368C2×C5#504514yescomplemented
369C2×C5C2×#93511yescharacteristic
370C2×C5C2×#94211yescharacteristic
371C2×C5C2×#95011yescharacteristic
372C23—22no—
373C23—22no—
374C23—22no—
375C23C2×#120112yes—
376C23C2×#120111yescharacteristic
377Q8—102no—
378Q8—102no—
379Q8—202no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—102no—
387C2×C4—102no—
388C2×C4—122no—
389C2×C4—122no—
390C2×C4—202no—
391C2×C4—202no—
392C2×C4#677912yes—
393C2×C4#677912yes—
394C2×C4C2×#120112yes—
395C2×C4C2×#120111yescharacteristic
396C2×C4C22×D3×D511yescharacteristic
397C8—302no—
398C8—302no—
399C2×C3—42no—
400C2×C3#6528514yescomplemented
401C2×C3C2×#407511yescharacteristic
402C2×C3C2×#409611yescharacteristic
403C2×C3C2×#409711yescharacteristic
404C5C2×#504511yescharacteristic, complemented, Sylow
405C22—22no—
406C22—22no—
407C22—22no—
408C22—44no—
409C22#9129712yes—
410C22#9130912yes—
411C22#9153612yes—
412C22C22×#120111yescharacteristic
413C4—22no—
414C4—122no—
415C4—122no—
416C4—202no—
417C4—202no—
418C4#9153612yes—
419C4C2×#677911yescharacteristic
420C4C2×#677911yescharacteristic
421C3C2×#6528511yescharacteristic, complemented, Sylow
422C2—42no—
423C2#1174840214yesdirect product factor
424C2C2×#9129711yescharacteristic
425C2C2×#9130911yescharacteristic
426C2C2×#9153611yescharacteristic
subgroupG/H
centerC23C2×#1201
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#90989C2semidirect
5. C2×#90986C2semidirect
6. #11748402C2direct (N × H)
7. C2×#90970C2semidirect
8. C2×#90970C2semidirect
26. #90989C22semidirect
27. #90986C22semidirect
28. #90970C22semidirect
29. #90970C22semidirect
274. C2×C3×C5#485semidirect
350. C3×C5C2×#485semidirect
368. C2×C5#5045semidirect
400. C2×C3#65285semidirect
404. C5C2×#5045semidirect
421. C3C2×#65285semidirect
423. C2#11748402direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#9262
C2×C3×#40702
C2×#911142
C2×#909892
C2×#909862
#117484022
C2×#909702
C2×#652853
C2×#50455