Finite Group Databasebeta

← #14415325

Subgroups — #14415325

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91916C211yesmaximal, characteristic, complemented
2C2×#91913C211yesmaximal, characteristic, complemented
3#11752673C211yesmaximal, characteristic
4C4×D5⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C3×#65682C211yesmaximal, characteristic, complemented
6#11751926C214yesmaximal, complemented
7#11751880C214yesmaximal, complemented
8#11751814C211yesmaximal, characteristic, complemented
9#11751811C211yesmaximal, characteristic, complemented
10#10617309—31nomaximal, Hall
11C2×#6773C2211yescharacteristic
12C2×#6772C2211yescharacteristic
13C2×D5⋊(C3⋊C8)C2211yescharacteristic
14C2×D5⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×#700C2211yescharacteristic
16C2×C3×#700C2211yescharacteristic
17C2×#6740C2212yes—
18C2×#6739C2212yes—
19C2×#6738C2212yes—
20C2×D3×#170C2212yes—
21#91916—24no—
22#91913—24no—
23#91764C411yescharacteristic
24C5×#875C411yescharacteristic
25C3×C42×D5C2211yescharacteristic
26#91451C411yescharacteristic
27#91448C414yes—
28#91405C2214yes—
29#91376C411yescharacteristic
30C4×C3⋊#170C2212yes—
31C4×C3⋊#170C2212yes—
32C3×#4004C2214yes—
33#91171C2214yes—
34(C2×D3)⋊#170C2214yes—
35#79041—51nomaximal, Hall
36C2×#4133—31no—
37C2×#4131—31no—
38#66002—31no—
39#65787—31no—
40#65776—31no—
41#65695—34no—
42#65692—34no—
43#65682D311yescharacteristic, complemented
44C4×D5⋊C8—31no—
45C2×D60C2×C411yescharacteristic
46C2×Dic30C2×C411yescharacteristic
47C2×C5×D12C2×C411yescharacteristic
48C2×C5×Dic6C2×C411yescharacteristic
49C2×C3×C4×D5C2×C412yes—
50C2×C3×C4×D5C2311yescharacteristic
51C2×#1203C2×C414yes—
52C2×#1202C2×C412yes—
53C2×#1201C2×C412yes—
54C2×#1200C2312yes—
55C2×D3×Dic5C2312yes—
56#6773—22no—
57#6773—22no—
58#6772—22no—
59#6772—22no—
60C2×C3⋊#170C2312yes—
61C2×C3⋊#170C2311yescharacteristic
62C2×C3⋊#170C2311yescharacteristic
63D5⋊(C3⋊C8)—22no—
64D5⋊(C3⋊C8)D414yescomplemented
65C2×C3×#170C2312yes—
66C2×C3×#170C2312yes—
67C3×#700—22no—
68C3×#700—22no—
69#6740—24no—
70#6739—24no—
71#6738—24no—
72D3×#170—24no—
73C3×C42×C5C2×C411yescharacteristic
74#6714C2×C414yes—
75C5×(C2×D3)⋊C4C2×C414yes—
76C3×C4×Dic5C2×C411yescharacteristic
77C3×C4×Dic5C2312yes—
78#6668C2×C414yes—
79C2×#907—51no—
80C2×#907—51no—
81#5477—51no—
82C3×#423—51no—
83#5129—51no—
84#5129—51no—
85C2×C4×C3⋊C8—51no—
86#4838—54no—
87#4834—54no—
88C2×#713—31no—
89C2×#711—31no—
90C2×#704—32no—
91C22×#170—32no—
92#4133—64no—
93#4131—64no—
94C2×#700—32no—
95C2×#700C2×D311yescharacteristic
96C2×#700C2×D311yescharacteristic
97C2×D5⋊C8—31no—
98C2×D5⋊C8—31no—
99C2×D5⋊C8—32no—
100C5×#124—31no—
101#4090—31no—
102#4086—31no—
103#4030—34no—
104#4027—34no—
105#4021—31no—
106C42×D5C2×D311yescharacteristic
107C22⋊#170—34no—
108#4004C2×D314yes—
109#4003—34no—
110C4×#170—32no—
111C4×#170—32no—
112#2931—151noSylow
113C22×D15C22×C412yes—
114C22×C5×D3C22×C412yes—
115C22×C3×D5C22×C411yescharacteristic
116C2×C3×C4×C5C22×C412yes—
117C2×C3×C4×C5C22×C411yescharacteristic
118C2×Dic15C22×C412yes—
119D60—22no—
120Dic30—22no—
121C2×C5×Dic3C22×C412yes—
122C5×D12—22no—
123C5×Dic6—22no—
124C2×C3×Dic5C22×C412yes—
125C2×C3×Dic5C2411yescharacteristic
126C3×C4×D5—24no—
127C3×C4×D5C2×D412yes—
128C3×C4×D5#4112yes—
129#1203—28no—
130#1202—24no—
131#1201—24no—
132#1200—22no—
133#1200—22no—
134D3×Dic5—22no—
135D3×Dic5—22no—
136C3⋊#170—22no—
137C3⋊#170C2×D412yes—
138C3⋊#170C2×D412yes—
139C3×#170—22no—
140C3×#170—22no—
141C2×#235—51no—
142C2×#235—51no—
143C2×C3×M16—51no—
144C2×C3×M16—51no—
145C2×C3×C42—51no—
146#930—54no—
147C22×C3⋊C8—51no—
148C22×C3⋊C8—51no—
149#907—104no—
150#907—104no—
151C2×ΓL(1,𝔽25)—52no—
152C2×ΓL(1,𝔽25)—52no—
153C2×D3×C8—52no—
154C2×D3×C8—52no—
155#875—51no—
156#875AGL(1,𝔽5)11yescharacteristic
157#874—51no—
158C4×D12—54no—
159#869—51no—
160C3×C4⋊C8—54no—
161(C2×D3)⋊C8—54no—
162(C2×D3)⋊C8—54no—
163C4×C3⋊C8—52no—
164C4×C3⋊C8—52no—
165C2×C5×Q8—31no—
166C2×C5×D4—31no—
167C2×C22⋊D5—32no—
168C2×C22⋊D5—34no—
169C22×Dic5—32no—
170#713—62no—
171#713—62no—
172#711—62no—
173#711—62no—
174C2×D20—32no—
175C2×D20—31no—
176C2×C4×D5—32no—
177C2×C4×D5C4×D312yes—
178C2×C4×D5C22×D311yescharacteristic
179C2×Dic10—31no—
180#704—64no—
181C2×#170—31no—
182C2×#170—31no—
183C2×#170—32no—
184C2×#170—64no—
185C2×#170C22×D312yes—
186C2×#170C22×D312yes—
187#700—22no—
188#700—22no—
189#700—64no—
190D5⋊C8—34no—
191D5⋊C8—64no—
192D5⋊C8—62no—
193C5×C22⋊C4—34no—
194C42×C5C4×D311yescharacteristic
195#685—34no—
196#683—34no—
197C4×Dic5C4×D311yescharacteristic
198C4×Dic5C22×D312yes—
199C2×#131—151no—
200C2×#131—151no—
201#532—151no—
202#436—154no—
203C8×D4—154no—
204#423—51no—
205#408—151no—
206#408—151no—
207C2×C4×C8—151no—
208C22×C3×C5C23×C411yescharacteristic
209C2×D15—22no—
210C2×D15—24no—
211C2×C5×D3—22no—
212C2×C5×D3—24no—
213C2×C3×D5—22no—
214C2×C3×D5C4×D412yes—
215C3×C4×C5—22no—
216C3×C4×C5C4×D412yes—
217Dic15—22no—
218C3×Dic5#13114yescomplemented
219C3×Dic5C22×D411yescharacteristic
220C3×Dic5C2×#4111yescharacteristic
221C5×Dic3—22no—
222C22×C3×C4—51no—
223C22×C3×C4—52no—
224C2×#67—52no—
225C2×#67—52no—
226#235—102no—
227#235—102no—
228#235—102no—
229#235—102no—
230C2×D12—54no—
231C2×D12—51no—
232C2×D12C2×AGL(1,𝔽5)11yescharacteristic
233C2×C4×D3—52no—
234C2×C4×D3—52no—
235C2×Dic6—51no—
236C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
237C3×M16—102no—
238C3×M16—102no—
239C2×C3×C8—52no—
240C2×C3×C8—52no—
241C3×C42—51no—
242C3×C42—52no—
243C3×C42C2×AGL(1,𝔽5)11yescharacteristic
244(C2×D3)⋊C4—54no—
245(C2×D3)⋊C4C2×AGL(1,𝔽5)14yes—
246C4⋊Dic3—54no—
247C2×C3⋊C8—51no—
248C2×C3⋊C8—51no—
249C2×C3⋊C8—54no—
250C2×C3⋊C8—52no—
251C2×C3⋊C8—102no—
252ΓL(1,𝔽25)—104no—
253ΓL(1,𝔽25)—104no—
254D3×C8—104no—
255D3×C8—104no—
256C23×C5—32no—
257C22×D5—32no—
258C22×D5C2×C4×D311yescharacteristic
259C5×Q8—62no—
260C5×D4—62no—
261C2×C4×C5—32no—
262C2×C4×C5C2×C4×D312yes—
263C2×C4×C5C2×C4×D311yescharacteristic
264C22⋊D5—64no—
265C22⋊D5—68no—
266C2×Dic5—32no—
267C2×Dic5—62no—
268C2×Dic5—62no—
269C2×Dic5C2×C4×D312yes—
270C2×Dic5C23×D311yescharacteristic
271D20—64no—
272D20—62no—
273C4×D5—24no—
274C4×D5—62no—
275C4×D5—62no—
276C4×D5D3×D412yes—
277C4×D5#23912yes—
278Dic10—62no—
279#170—22no—
280#170—22no—
281#170—32no—
282#170—32no—
283#170—62no—
284C2×#41—151no—
285C2×#41—151no—
286#131—304no—
287#131—304no—
288C2×M16—51no—
289C2×M16—51no—
290C2×M16—152no—
291C2×M16—152no—
292C22×C8—152no—
293C22×C8—152no—
294C22×C8—151no—
295C22×C8—151no—
296C4⋊Q8—151no—
297#127—151no—
298#124—31no—
299#124—151no—
300#121—154no—
301C4×D4—154no—
302C2×C42—51no—
303C4⋊C8—54no—
304C22⋊C8—154no—
305C22⋊C8—154no—
306C4×C8—152no—
307C4×C8—152no—
308C2×C3×C5C2×C4×D411yescharacteristic
309C2×C3×C5C2×#13112yes—
310D15—42no—
311C3×D5—22no—
312C5×D3—42no—
313C23×C3—51no—
314C22×D3—52no—
315C22×D3C22×AGL(1,𝔽5)12yes—
316C2×C3×C4—52no—
317C2×C3×C4—51no—
318C2×C3×C4—52no—
319C2×C3×C4—52no—
320C2×C3×C4—104no—
321C2×C3×C4C22×AGL(1,𝔽5)12yes—
322C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
323#67—104no—
324#67—104no—
325C2×Dic3—52no—
326C2×Dic3C22×AGL(1,𝔽5)12yes—
327D12—22no—
328D12—108no—
329D12—102no—
330C4×D3—102no—
331C4×D3—102no—
332C4×D3—102no—
333C4×D3—102no—
334Dic6—22no—
335Dic6—102no—
336C3×C8—102no—
337C3×C8—102no—
338C3⋊C8—52no—
339C3⋊C8—52no—
340C3⋊C8—102no—
341C22×C5—64no—
342C22×C5—62no—
343C22×C5C22×C4×D311yescharacteristic
344C2×D5—22no—
345C2×D5—64no—
346C2×D5—62no—
347C2×D5#89312yes—
348C4×C5—22no—
349C4×C5—62no—
350C4×C5#89312yes—
351Dic5—62no—
352Dic5#90714yescomplemented
353Dic5C2×D3×D411yescharacteristic
354Dic5C2×#23911yescharacteristic
355#41—302no—
356#41—302no—
357#41—302no—
358#41—302no—
359C2×Q8—31no—
360C2×Q8—151no—
361C2×D4—31no—
362C2×D4—152no—
363C2×D4—154no—
364C2×D4—152no—
365C2×D4—151no—
366C22×C4—51no—
367C22×C4—52no—
368C22×C4—152no—
369C22×C4—152no—
370M16—102no—
371M16—102no—
372M16—304no—
373M16—304no—
374C2×C8—52no—
375C2×C8—52no—
376C2×C8—151no—
377C2×C8—151no—
378C2×C8—154no—
379C2×C8—152no—
380C2×C8—304no—
381C2×C8—304no—
382C2×C8—302no—
383C4⋊C4—154no—
384C22⋊C4—34no—
385C22⋊C4—154no—
386C42—52no—
387C42—51no—
388C42D3×AGL(1,𝔽5)11yescharacteristic
389C3×C5#293111yescharacteristic, complemented, Hall
390C22×C3—52no—
391C22×C3—102no—
392C22×C3C23×AGL(1,𝔽5)11yescharacteristic
393C2×D3—22no—
394C2×D3—24no—
395C2×D3—102no—
396C2×D3—104no—
397C3×C4—22no—
398C3×C4—51no—
399C3×C4—51no—
400C3×C4—54no—
401C3×C4D4×AGL(1,𝔽5)12yes—
402Dic3—22no—
403Dic3—102no—
404C2×C5—122no—
405C2×C5C2×#89311yescharacteristic
406C2×C5C2×#90712yes—
407D5—22no—
408D5—122no—
409C23—32no—
410C23—51no—
411C23—152no—
412Q8—62no—
413Q8—302no—
414D4—62no—
415D4—308no—
416D4—304no—
417D4—304no—
418D4—302no—
419C2×C4—32no—
420C2×C4—52no—
421C2×C4—51no—
422C2×C4—52no—
423C2×C4—52no—
424C2×C4—104no—
425C2×C4—152no—
426C2×C4—302no—
427C2×C4—302no—
428C2×C4—302no—
429C2×C4—302no—
430C2×C4C2×D3×AGL(1,𝔽5)12yes—
431C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
432C8—102no—
433C8—102no—
434C8—152no—
435C8—152no—
436C8—302no—
437C2×C3—102no—
438C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
439C2×C3D5⋊#13112yes—
440D3—42no—
441D3—202no—
442C5#7904111yescharacteristic, complemented, Sylow
443C22—52no—
444C22—64no—
445C22—62no—
446C22—102no—
447C22—304no—
448C22—302no—
449C22C22×D3×AGL(1,𝔽5)11yescharacteristic
450C4—22no—
451C4—54no—
452C4—51no—
453C4—51no—
454C4—62no—
455C4—302no—
456C4#9192112yes—
457C3#1061730911yescharacteristic, complemented, Sylow
458C2—102no—
459C2—122no—
460C2—602no—
461C2D5⋊#90712yes—
462C2C2×#9192111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C42×C5C2×C4
prime radical#11752673C2
cosocleC2×C3×Dic5C24
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#2931
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×#91916C2semidirect
2. C2×#91913C2semidirect
4. C4×D5⋊(C3⋊C8)C2semidirect
5. C3×#65682C2semidirect
6. #11751926C2semidirect
7. #11751880C2semidirect
8. #11751814C2semidirect
9. #11751811C2semidirect
43. #65682D3semidirect
64. D5⋊(C3⋊C8)D4semidirect
218. C3×Dic5#131semidirect
352. Dic5#907semidirect
389. C3×C5#2931semidirect
442. C5#79041semidirect
457. C3#10617309semidirect

Maximal subgroups

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

subgroupindex
C2×#919162
C2×#919132
#117526732
C4×D5⋊(C3⋊C8)2
C3×#656822
#117519262
#117518802
#117518142
#117518112
#106173093
#790415