Finite Group Databasebeta

← #14281192

Subgroups — #14281192

Order 1920.

560 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4040C211yesmaximal, characteristic
2#11752415C211yesmaximal, characteristic, complemented
3D5⋊#830C211yesmaximal, characteristic, complemented
4#11746786C212yesmaximal, complemented
5#11746785C212yesmaximal, complemented
6#10604296—31nomaximal, Hall
7C22×C3×D20C411yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9C2×#6758—21no—
10C2×D5⋊(C3⋊C8)—21no—
11C2×C3×C5×C4⋊C4C411yescharacteristic
12C2×C3×#685C411yescharacteristic
13C2×C3×#685C411yescharacteristic
14C2×C3×#685C2211yescharacteristic
15C2×C3×#683C2211yescharacteristic
16C3×#4040—21no—
17C3×#4040—21no—
18C3×#4040—21no—
19C3×#4040—21no—
20#91241C2212yes—
21#91241C2212yes—
22#91232—21no—
23#91232—21no—
24#71702—51nomaximal, Hall
25C2×#4040D311yescharacteristic
26#65756—31no—
27D5⋊(C22⋊C8)—31no—
28#64915—32no—
29#64914—32no—
30C23×C3×D5C2×C411yescharacteristic
31C23×C3×D5C2×C411yescharacteristic
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2311yescharacteristic
37C2×C3×D20—21no—
38C2×C3×D20—21no—
39C2×C3×D20—42no—
40C2×C3×C4×D5—42no—
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5D411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3⋊#170—22no—
46C2×C3⋊#170—22no—
47#6758—42no—
48D5⋊(C3⋊C8)—42no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×#683—21no—
58C3×#683—21no—
59C2×C3×#123—51no—
60#5207—51no—
61C2×#830—51no—
62#4528—52no—
63#4525—52no—
64C22×D20Dic311yescharacteristic
65C22×C4×D5C2×D311yescharacteristic
66C2×#700—61no—
67C2×D5⋊C8—61no—
68C2×C5×C4⋊C4Dic311yescharacteristic
69C2×#685Dic311yescharacteristic
70C2×#685Dic311yescharacteristic
71C2×#685C2×D311yescharacteristic
72C2×#683C2×D311yescharacteristic
73#4040—21no—
74#4040—21no—
75#4040—21no—
76#4040—21no—
77C22⋊#170—32no—
78C22⋊#170—32no—
79#4003—61no—
80#4003—61no—
81#1468—151noSylow
82C23×C3×C5C22×C411yescharacteristic
83C22×C3×D5—22no—
84C22×C3×D5—22no—
85C22×C3×D5—21no—
86C22×C3×D5—22no—
87C22×C3×D5—41no—
88C22×C3×D5—41no—
89C22×C3×D5—41no—
90C22×C3×D5C22⋊C411yescharacteristic
91C22×C3×D5C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×Dic5—21no—
100C2×C3×Dic5—22no—
101C2×C3×Dic5—41no—
102C2×C3×Dic5C2×D411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104C3×D20—42no—
105C3×D20—42no—
106C3×C4×D5—22no—
107C3×C4×D5—22no—
108C3×C4×D5—41no—
109C3×C4×D5—41no—
110C3⋊#170—42no—
111C3⋊#170—42no—
112C22×C3×D4—51no—
113C23×C3×C4—51no—
114C3×#123—101no—
115C3×#123—101no—
116C3×#123—101no—
117C3×#123—101no—
118C2×C3×C4⋊C4—51no—
119C2×C3×C4⋊C4AGL(1,𝔽5)11yescharacteristic
120C2×C3×C22⋊C4—51no—
121C2×C3×C22⋊C4—51no—
122C2×C3×C22⋊C4—51no—
123C2×#208—101no—
124C22×C3⋊C8—101no—
125#830—52no—
126#830—52no—
127#830—101no—
128#830—101no—
129C23×D5C2×Dic311yescharacteristic
130C23×D5C2×Dic311yescharacteristic
131C22×C4×C5C2×Dic311yescharacteristic
132C22×C4×C5C2×Dic311yescharacteristic
133C22×C4×C5C2×Dic311yescharacteristic
134C22×Dic5C2×Dic311yescharacteristic
135C22×Dic5C22×D311yescharacteristic
136C2×D20—21no—
137C2×D20—21no—
138C2×D20—42no—
139C2×C4×D5—42no—
140C2×C4×D5#6711yescharacteristic
141C2×C4×D5#6711yescharacteristic
142C2×C4×D5#6711yescharacteristic
143C2×C4×D5#6711yescharacteristic
144C2×#170—62no—
145C2×#170—62no—
146#700—122no—
147D5⋊C8—122no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150#685—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155#685—21no—
156#683—21no—
157#683—21no—
158C2×#123—51no—
159#407—151no—
160C2×C22⋊C8—151no—
161#324—152no—
162#323—152no—
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5C2×C22⋊C411yescharacteristic
166C22×C3×C5#13112yes—
167C2×C3×D5—21no—
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5—44no—
173C2×C3×D5—41no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—82no—
177C2×C3×D5#9912yes—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×Dic5—21no—
183C3×Dic5—21no—
184C3×Dic5—41no—
185C24×C3—51no—
186C24×C3—51no—
187C2×C3×D4—101no—
188C2×C3×D4—101no—
189C2×C3×D4—202no—
190C22×C3×C4—51no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—202no—
197C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
198C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
199C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210#208—202no—
211C2×C3⋊C8—102no—
212C2×C3⋊C8—102no—
213C2×C3⋊C8—202no—
214C23×C5C22×Dic311yescharacteristic
215C22×D5—22no—
216C22×D5—22no—
217C22×D5—21no—
218C22×D5—22no—
219C22×D5—41no—
220C22×D5—41no—
221C22×D5—41no—
222C22×D5#21711yescharacteristic
223C22×D5#21711yescharacteristic
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—41no—
227C2×C4×C5—41no—
228C2×C4×C5—41no—
229C2×C4×C5#21711yescharacteristic
230C2×C4×C5#21711yescharacteristic
231C2×Dic5—22no—
232C2×Dic5—21no—
233C2×Dic5—41no—
234C2×Dic5C2×#6711yescharacteristic
235C2×Dic5C2×#6711yescharacteristic
236D20—42no—
237D20—42no—
238C4×D5—22no—
239C4×D5—22no—
240C4×D5—41no—
241C4×D5—41no—
242#170—122no—
243#170—122no—
244C22×D4—51no—
245C23×C4—51no—
246C2×M16—301no—
247C22×C8—301no—
248#123—101no—
249#123—101no—
250#123—101no—
251#123—101no—
252C2×C4⋊C4—51no—
253C2×C4⋊C4ΓL(1,𝔽16)11yescharacteristic
254C2×C22⋊C4—51no—
255C2×C22⋊C4—51no—
256C2×C22⋊C4—51no—
257C22⋊C8—152no—
258C22⋊C8—152no—
259C22⋊C8—301no—
260C22⋊C8—301no—
261C2×C3×C5—22no—
262C2×C3×C5#40811yescharacteristic
263C2×C3×C5C2×#9911yescharacteristic
264C2×C3×C5#41311yescharacteristic
265C3×D5—22no—
266C3×D5—41no—
267C3×D5—81no—
268C23×C3—51no—
269C23×C3—51no—
270C23×C3—102no—
271C23×C3—102no—
272C23×C3—101no—
273C23×C3—102no—
274C23×C3—201no—
275C23×C3—201no—
276C23×C3—201no—
277C23×C3C22×AGL(1,𝔽5)11yescharacteristic
278C3×D4—202no—
279C3×D4—202no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4—102no—
288C2×C3×C4—102no—
289C2×C3×C4—102no—
290C2×C3×C4—101no—
291C2×C3×C4—201no—
292C2×C3×C4—201no—
293C2×C3×C4—201no—
294C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
295C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
296C3⋊C8—202no—
297C3⋊C8—202no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5#94812yes—
301C22×C5C2×#21711yescharacteristic
302C2×D5—21no—
303C2×D5—21no—
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—44no—
308C2×D5—41no—
309C2×D5—41no—
310C2×D5—41no—
311C2×D5—82no—
312C2×D5#83412yes—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—41no—
316C4×C5—41no—
317Dic5—21no—
318Dic5—21no—
319Dic5—41no—
320C24—51no—
321C24—51no—
322C2×D4—101no—
323C2×D4—101no—
324C2×D4—202no—
325C22×C4—51no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—51no—
329C22×C4—51no—
330C22×C4—51no—
331C22×C4—202no—
332C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
333C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
334C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
335M16—602no—
336C2×C8—302no—
337C2×C8—302no—
338C2×C8—602no—
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—101no—
342C4⋊C4—101no—
343C22⋊C4—101no—
344C22⋊C4—101no—
345C22⋊C4—101no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C3×C5#146811yescharacteristic, complemented, Hall
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—52no—
353C22×C3—101no—
354C22×C3—101no—
355C22×C3—101no—
356C22×C3—101no—
357C22×C3—101no—
358C22×C3—204no—
359C22×C3—201no—
360C22×C3—201no—
361C22×C3—201no—
362C22×C3—402no—
363C22×C3#413312yes—
364C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—101no—
370C3×C4—101no—
371C3×C4—201no—
372C2×C5—22no—
373C2×C5C2×#83411yescharacteristic
374C2×C5#523411yescharacteristic
375C2×C5#523711yescharacteristic
376D5—22no—
377D5—41no—
378D5—81no—
379C23—51no—
380C23—51no—
381C23—102no—
382C23—102no—
383C23—101no—
384C23—102no—
385C23—201no—
386C23—201no—
387C23—201no—
388C23C22×ΓL(1,𝔽16)11yescharacteristic
389D4—202no—
390D4—202no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—102no—
401C2×C4—101no—
402C2×C4—201no—
403C2×C4—201no—
404C2×C4—201no—
405C2×C4#676311yescharacteristic
406C2×C4#676311yescharacteristic
407C8—602no—
408C8—602no—
409C2×C3—22no—
410C2×C3—102no—
411C2×C3—201no—
412C2×C3—401no—
413C2×C3#6576111yescharacteristic
414C2×C3D5⋊#9911yescharacteristic
415C2×C3#6578711yescharacteristic
416C5#7170211yescharacteristic, complemented, Sylow
417C22—21no—
418C22—21no—
419C22—52no—
420C22—101no—
421C22—101no—
422C22—101no—
423C22—101no—
424C22—101no—
425C22—204no—
426C22—201no—
427C22—201no—
428C22—201no—
429C22—402no—
430C22#9199212yes—
431C22C2×#676311yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—101no—
437C4—101no—
438C4—201no—
439C3#1060429611yescharacteristic, complemented, Sylow
440C2—22no—
441C2—102no—
442C2—201no—
443C2—401no—
444C2#1175242011yescharacteristic
445C2D5⋊#83411yescharacteristic
446C2#1175244611yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC2×C3×C5×C4⋊C4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C4
cosocleC22×C3×Dic5C23
hypercenterC2×C4⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1468
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11752415C2semidirect
3. D5⋊#830C2semidirect
4. #11746786C2semidirect
5. #11746785C2semidirect
349. C3×C5#1468semidirect
416. C5#71702semidirect
439. C3#10604296semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40402
#117524152
D5⋊#8302
#117467862
#117467852
#106042963
#717025