Finite Group Databasebeta

← #14297585

Subgroups — #14297585

Order 1920.

672 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 112 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×#91406C211yesmaximal, characteristic
2#11752012C212yesmaximal, complemented
3C2×#91174C212yesmaximal
4#11746790C211yesmaximal, characteristic, complemented
5C3×#64919C211yesmaximal, characteristic, complemented
6#10604246—31nomaximal, Hall
7C22×C4×D15C411yescharacteristic
8C22×#1203C2211yescharacteristic
9C22×D3×Dic5C411yescharacteristic
10C2×#6762C2212yes—
11C2×C3×#704C2212yes—
12C2×C5×(C2×D3)⋊C4C411yescharacteristic
13C2×C3×#683C2211yescharacteristic
14C2×#6667C411yescharacteristic
15C2×Dic3×Dic5C2211yescharacteristic
16#91406—22no—
17#91406—22no—
18#91177—22no—
19Dic3⋊#170—22no—
20#91174—24no—
21#68994—51nomaximal, Hall
22C2×#4027—31no—
23C2×#4013—32no—
24#65758—32no—
25#64919—31no—
26#64919D311yescharacteristic, complemented
27C23×D15C2×C411yescharacteristic
28C23×C5×D3C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×Dic15C2×C411yescharacteristic
31C2×C4×D15—21no—
32C2×C4×D15—21no—
33C2×C4×D15—42no—
34C22×C5×Dic3C2×C411yescharacteristic
35C22×C3×Dic5C2×C411yescharacteristic
36C22×C3×Dic5C2311yescharacteristic
37C2×#1203—22no—
38C2×#1203—22no—
39C2×#1203D412yes—
40C2×#1203Q812yes—
41C2×D3×Dic5—21no—
42C2×D3×Dic5—21no—
43C2×D3×Dic5—42no—
44#6762—22no—
45#6762—22no—
46C2×C3⋊#170—22no—
47C3×#704—22no—
48C3×#704—22no—
49C2×C3×#170—22no—
50C5×(C2×D3)⋊C4—22no—
51C3×#683—22no—
52#6667—22no—
53Dic3×Dic5D412yes—
54Dic3×Dic5D412yes—
55C2×#893—51no—
56C2×#823—52no—
57#5118—52no—
58C3×#343—51no—
59#4530—51no—
60C22×C22⋊D5—31no—
61C23×Dic5—31no—
62C22×C4×D5—31no—
63C2×#704—32no—
64C2×#704C2×D312yes—
65C2×C5×C22⋊C4—31no—
66C2×#685—31no—
67C2×#683C2×D311yescharacteristic
68C2×C4×Dic5—31no—
69#4027—62no—
70#4027—62no—
71#4013—64no—
72#4004—62no—
73C4⋊#170—62no—
74#1800—151noSylow
75C23×C3×C5C22×C411yescharacteristic
76C22×D15—21no—
77C22×D15—21no—
78C22×D15—41no—
79C22×D15—41no—
80C22×D15C4⋊C412yes—
81C22×C5×D3—21no—
82C22×C5×D3—21no—
83C22×C5×D3—41no—
84C22×C5×D3—41no—
85C22×C5×D3C4⋊C412yes—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×Dic15—22no—
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C4×D15—42no—
92C4×D15—42no—
93C2×C5×Dic3—41no—
94C2×C5×Dic3C22⋊C412yes—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—41no—
97C2×C3×Dic5C2×D411yescharacteristic
98C2×C3×Dic5C2×D412yes—
99C2×C3×Dic5C2×Q811yescharacteristic
100C2×C3×Dic5#4112yes—
101#1203—24no—
102#1203—24no—
103D3×Dic5—42no—
104D3×Dic5—42no—
105C3⋊#170—42no—
106C3×#170—42no—
107C22×D12—51no—
108C22×C4×D3—51no—
109C22×C4×D3—51no—
110C2×C3×M16—52no—
111C2×C3×C4⋊C4—51no—
112C2×(C2×D3)⋊C4—51no—
113C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic
114C2×C4×Dic3—51no—
115C2×#208—52no—
116#893—102no—
117#893—102no—
118#823—104no—
119Dic3⋊C8—102no—
120Dic3⋊C8—102no—
121C24×C5—31no—
122C23×D5—31no—
123C22×C4×C5—31no—
124C22×C4×C5C4×D311yescharacteristic
125C2×C22⋊D5—32no—
126C2×C22⋊D5—32no—
127C2×C22⋊D5—62no—
128C2×C22⋊D5—62no—
129C22×Dic5—31no—
130C22×Dic5—61no—
131C22×Dic5—61no—
132C22×Dic5—122no—
133C22×Dic5C4×D311yescharacteristic
134C22×Dic5C22×D311yescharacteristic
135C2×C4×D5—61no—
136C2×C4×D5—61no—
137C2×C4×D5—122no—
138#704—22no—
139#704—22no—
140#704—62no—
141#704—62no—
142C2×#170—22no—
143C2×#170—62no—
144C5×C22⋊C4—62no—
145#685—62no—
146#683—22no—
147C4×Dic5—32no—
148C4×Dic5—32no—
149C2×C4×D4—151no—
150#423—152no—
151C2×#100—152no—
152#343—51no—
153#343—151no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C2×C4⋊C411yescharacteristic
158C22×C3×C5#11711yescharacteristic
159C2×D15—22no—
160C2×D15—42no—
161C2×D15—41no—
162C2×D15—41no—
163C2×D15—42no—
164C2×C5×D3—22no—
165C2×C5×D3—42no—
166C2×C5×D3—41no—
167C2×C5×D3—41no—
168C2×C5×D3—42no—
169C3×C4×C5—41no—
170Dic15—21no—
171Dic15#10012yescomplemented
172C3×Dic5—41no—
173C3×Dic5#12112yes—
174C3×Dic5C22⋊Q812yes—
175C5×Dic3—22no—
176C23×D3—51no—
177C23×D3C2×AGL(1,𝔽5)11yescharacteristic
178C22×C3×C4—51no—
179C22×C3×C4—51no—
180C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
181C22×Dic3—51no—
182C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
183C2×D12—52no—
184C2×D12—52no—
185C2×D12—102no—
186C2×D12—102no—
187C2×C4×D3—101no—
188C2×C4×D3—101no—
189C2×C4×D3—101no—
190C2×C4×D3—101no—
191C2×C4×D3—202no—
192C2×C4×D3—202no—
193C3×M16—102no—
194C3×M16—102no—
195C2×C3×C8—102no—
196C3×C4⋊C4—102no—
197(C2×D3)⋊C4—22no—
198(C2×D3)⋊C4—102no—
199C4×Dic3—52no—
200C4×Dic3—52no—
201#208—102no—
202#208—102no—
203C2×C3⋊C8—102no—
204C23×C5—32no—
205C23×C5—61no—
206C23×C5—61no—
207C23×C5—121no—
208C23×C5—121no—
209C23×C5C2×C4×D311yescharacteristic
210C22×D5—32no—
211C22×D5—61no—
212C22×D5—61no—
213C22×D5—121no—
214C22×D5—121no—
215C2×C4×C5—21no—
216C2×C4×C5—32no—
217C2×C4×C5—41no—
218C2×C4×C5—121no—
219C22⋊D5—64no—
220C22⋊D5—64no—
221C2×Dic5—21no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—41no—
225C2×Dic5—62no—
226C2×Dic5—122no—
227C2×Dic5—122no—
228C2×Dic5#23512yes—
229C2×Dic5D3×D411yescharacteristic
230C2×Dic5D3×D412yes—
231C2×Dic5D3×Q811yescharacteristic
232C4×D5—122no—
233C4×D5—122no—
234#170—42no—
235#170—122no—
236C22×D4—151no—
237C23×C4—151no—
238C23×C4—151no—
239C2×M16—52no—
240C2×M16—152no—
241C4×D4—302no—
242C4×D4—302no—
243C2×C4⋊C4—51no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—151no—
246C2×C42—151no—
247C4⋊C8—302no—
248C4⋊C8—302no—
249#100—304no—
250C2×C3×C5—21no—
251C2×C3×C5—21no—
252C2×C3×C5#38011yescharacteristic
253C2×C3×C5C2×#10011yescharacteristic
254C2×C3×C5#41311yescharacteristic
255D15—42no—
256C5×D3—42no—
257C23×C3C22×AGL(1,𝔽5)11yescharacteristic
258C22×D3—21no—
259C22×D3—21no—
260C22×D3—41no—
261C22×D3—41no—
262C22×D3—52no—
263C22×D3—101no—
264C22×D3—101no—
265C22×D3—201no—
266C22×D3—201no—
267C22×D3C4⋊AGL(1,𝔽5)12yes—
268C2×C3×C4—21no—
269C2×C3×C4—41no—
270C2×C3×C4—51no—
271C2×C3×C4—51no—
272C2×C3×C4—52no—
273C2×C3×C4—52no—
274C2×C3×C4—101no—
275C2×C3×C4—201no—
276C2×Dic3—41no—
277C2×Dic3—51no—
278C2×Dic3—51no—
279C2×Dic3—102no—
280C2×Dic3C22⋊AGL(1,𝔽5)12yes—
281D12—104no—
282D12—104no—
283C4×D3—202no—
284C4×D3—202no—
285C4×D3—202no—
286C4×D3—202no—
287C3×C8—202no—
288C3⋊C8—202no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—62no—
292C22×C5—122no—
293C22×C5—122no—
294C22×C5—121no—
295C22×C5—121no—
296C22×C5#87211yescharacteristic
297C22×C5D3×C22⋊C411yescharacteristic
298C22×C5D3×C4⋊C411yescharacteristic
299C2×D5—62no—
300C2×D5—122no—
301C2×D5—121no—
302C2×D5—121no—
303C2×D5—122no—
304C4×C5—41no—
305C4×C5—62no—
306Dic5—32no—
307Dic5—41no—
308Dic5—61no—
309Dic5#88412yes—
310Dic5#89612yes—
311C24—31no—
312C24—151no—
313C2×D4—152no—
314C2×D4—152no—
315C2×D4—302no—
316C2×D4—302no—
317C22×C4—31no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—151no—
321C22×C4—301no—
322C22×C4—301no—
323C22×C4—301no—
324C22×C4—301no—
325C22×C4—602no—
326C22×C4—602no—
327C22×C4D3×AGL(1,𝔽5)11yescharacteristic
328M16—102no—
329M16—102no—
330M16—302no—
331M16—302no—
332C2×C8—102no—
333C2×C8—302no—
334C4⋊C4—102no—
335C22⋊C4—62no—
336C22⋊C4—302no—
337C42—152no—
338C42—152no—
339C3×C5#180011yescharacteristic, complemented, Hall
340C22×C3—21no—
341C22×C3—21no—
342C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
343C22×C3#413011yescharacteristic
344C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
345C2×D3—22no—
346C2×D3—42no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—42no—
350C2×D3—102no—
351C2×D3—202no—
352C2×D3—201no—
353C2×D3—201no—
354C2×D3—202no—
355C3×C4—41no—
356C3×C4—52no—
357C3×C4—52no—
358C3×C4—201no—
359Dic3—22no—
360Dic3—52no—
361Dic3—101no—
362C2×C5—21no—
363C2×C5—21no—
364C2×C5—122no—
365C2×C5#466711yescharacteristic
366C2×C5D3×#10011yescharacteristic
367C2×C5#475111yescharacteristic
368D5—122no—
369C23—32no—
370C23—61no—
371C23—61no—
372C23—121no—
373C23—121no—
374C23—152no—
375C23—301no—
376C23—301no—
377C23—601no—
378C23—601no—
379C23C2×D3×AGL(1,𝔽5)11yescharacteristic
380D4—304no—
381D4—304no—
382C2×C4—21no—
383C2×C4—32no—
384C2×C4—41no—
385C2×C4—52no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—52no—
389C2×C4—101no—
390C2×C4—121no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—201no—
394C2×C4—302no—
395C2×C4—602no—
396C2×C4—602no—
397C2×C4—602no—
398C2×C4—602no—
399C8—202no—
400C8—602no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3#6576511yescharacteristic
404C2×C3#6577711yescharacteristic
405C2×C3D5⋊#10011yescharacteristic
406D3—42no—
407D3—202no—
408C5#6899411yescharacteristic, complemented, Sylow
409C22—21no—
410C22—21no—
411C22—62no—
412C22—122no—
413C22—122no—
414C22—121no—
415C22—121no—
416C22—302no—
417C22—602no—
418C22—602no—
419C22—601no—
420C22—601no—
421C22#9190911yescharacteristic
422C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
423C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
424C4—41no—
425C4—52no—
426C4—52no—
427C4—62no—
428C4—152no—
429C4—201no—
430C4—301no—
431C3#1060424611yescharacteristic, complemented, Sylow
432C2—21no—
433C2—21no—
434C2—122no—
435C2—602no—
436C2#1175185411yescharacteristic
437C2#1175191611yescharacteristic
438C2#1175205011yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1203C22
cosocleC22×C3×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1800
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #11752012C2semidirect
4. #11746790C2semidirect
5. C3×#64919C2semidirect
26. #64919D3semidirect
171. Dic15#100semidirect
339. C3×C5#1800semidirect
408. C5#68994semidirect
431. C3#10604246semidirect

Maximal subgroups

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

subgroupindex
C2×#914062
#117520122
C2×#911742
#117467902
C3×#649192
#106042463
#689945