Finite Group Databasebeta

← #14297583

Subgroups — #14297583

Order 1920.

672 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 122 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×#91559C211yesmaximal, characteristic
2C2×#91242C211yesmaximal, characteristic
3C2×C3×#4013C211yesmaximal, characteristic
4#11752012C212yesmaximal, complemented
5#11746574C212yesmaximal, complemented
6#10604246—31nomaximal, Hall
7C23×Dic15C411yescharacteristic
8C22×C3×C22⋊D5C2211yescharacteristic
9C22×D5×Dic3C411yescharacteristic
10C2×#6762C2212yes—
11C2×C3×#704C2212yes—
12C2×C5×#217C411yescharacteristic
13#91559—22no—
14#91559—22no—
15C2×#6668C2211yescharacteristic
16C2×#6665C411yescharacteristic
17C2×Dic3×Dic5C2211yescharacteristic
18#91242—22no—
19C3×#4013—22no—
20#91177—22no—
21Dic3⋊#170—22no—
22#70063—51nomaximal, Hall
23C2×#4027—31no—
24C2×#4013—31no—
25C2×#4013D311yescharacteristic
26#65758—32no—
27#64919—32no—
28C24×C3×C5C2×C411yescharacteristic
29C23×C3×D5C2×C411yescharacteristic
30C22×Dic15—21no—
31C22×Dic15—21no—
32C22×Dic15—42no—
33C22×Dic15C2×C411yescharacteristic
34C22×Dic15C2×C411yescharacteristic
35C22×C5×Dic3C2×C411yescharacteristic
36C22×C5×Dic3C2×C411yescharacteristic
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—22no—
39C2×C3×C22⋊D5D412yes—
40C2×C3×C22⋊D5Q812yes—
41C22×C3×Dic5C2311yescharacteristic
42C2×D5×Dic3—21no—
43C2×D5×Dic3—21no—
44C2×D5×Dic3—42no—
45#6762—22no—
46#6762—22no—
47C2×C3⋊#170—22no—
48C3×#704—22no—
49C3×#704—22no—
50C2×C3×#170—22no—
51C5×#217—22no—
52#6668—22no—
53#6665—22no—
54Dic3×Dic5D412yes—
55Dic3×Dic5D412yes—
56C2×D4×Dic3—51no—
57C2×C3×#100—51no—
58C2×#833—51no—
59#5118—52no—
60#4554—52no—
61C22×C22⋊D5C2×D311yescharacteristic
62C23×Dic5—31no—
63C22×C4×D5—31no—
64C2×#704—32no—
65C2×#704C2×D312yes—
66C2×C5×C22⋊C4—31no—
67C2×#685—31no—
68C2×#683—31no—
69C2×C4×Dic5—31no—
70#4027—62no—
71#4027—62no—
72#4013—22no—
73#4013—62no—
74#4004—62no—
75C4⋊#170—62no—
76#1800—151noSylow
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—41no—
80C23×C3×C5—41no—
81C23×C3×C5C4⋊C412yes—
82C23×C3×C5C22×C411yescharacteristic
83C22×C3×D5—21no—
84C22×C3×D5—21no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5C4⋊C412yes—
88C2×Dic15—22no—
89C2×Dic15—21no—
90C2×Dic15—42no—
91C2×Dic15—42no—
92C2×Dic15—41no—
93C2×Dic15C22⋊C411yescharacteristic
94C2×Dic15C22⋊C411yescharacteristic
95C2×C5×Dic3—21no—
96C2×C5×Dic3—41no—
97C2×C5×Dic3—41no—
98C2×C5×Dic3C22⋊C412yes—
99C3×C22⋊D5—24no—
100C3×C22⋊D5—24no—
101C2×C3×Dic5C2×D411yescharacteristic
102C2×C3×Dic5C2×D412yes—
103C2×C3×Dic5C2×Q811yescharacteristic
104C2×C3×Dic5#4112yes—
105D5×Dic3—42no—
106D5×Dic3—42no—
107C3⋊#170—42no—
108C3×#170—42no—
109C22×C3×D4—51no—
110C23×Dic3—51no—
111C23×Dic3—51no—
112C2×C3×M16—52no—
113C2×#217—51no—
114C2×#217AGL(1,𝔽5)11yescharacteristic
115D4×Dic3—102no—
116D4×Dic3—102no—
117C2×C4⋊Dic3—51no—
118C2×C4×Dic3—51no—
119C2×#208—52no—
120C3×#100—102no—
121#833—102no—
122Dic3⋊C8—102no—
123Dic3⋊C8—102no—
124C24×C5C4×D311yescharacteristic
125C23×D5C4×D311yescharacteristic
126C22×C4×C5—31no—
127C22×C4×C5—31no—
128C2×C22⋊D5—22no—
129C2×C22⋊D5—22no—
130C2×C22⋊D5Dic612yes—
131C2×C22⋊D5#6712yes—
132C22×Dic5—31no—
133C22×Dic5—31no—
134C22×Dic5—61no—
135C22×Dic5—61no—
136C22×Dic5—122no—
137C22×Dic5C22×D311yescharacteristic
138C2×C4×D5—61no—
139C2×C4×D5—61no—
140C2×C4×D5—122no—
141#704—22no—
142#704—22no—
143#704—62no—
144#704—62no—
145C2×#170—22no—
146C2×#170—62no—
147C5×C22⋊C4—62no—
148#685—62no—
149#683—62no—
150C4×Dic5—32no—
151C4×Dic5—32no—
152C2×C4×D4—151no—
153#423—152no—
154C2×#100—51no—
155C2×#100—151no—
156#343—152no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5—22no—
160C22×C3×C5—42no—
161C22×C3×C5—42no—
162C22×C3×C5—41no—
163C22×C3×C5—41no—
164C22×C3×C5C2×C22⋊C411yescharacteristic
165C22×C3×C5C2×C4⋊C411yescharacteristic
166C22×C3×C5#11711yescharacteristic
167C2×C3×D5—22no—
168C2×C3×D5—42no—
169C2×C3×D5—41no—
170C2×C3×D5—41no—
171C2×C3×D5—42no—
172Dic15—21no—
173Dic15—41no—
174Dic15#10012yescomplemented
175C3×Dic5#12112yes—
176C3×Dic5C22⋊Q812yes—
177C5×Dic3—22no—
178C5×Dic3—41no—
179C24×C3—51no—
180C24×C3C2×AGL(1,𝔽5)11yescharacteristic
181C2×C3×D4—52no—
182C2×C3×D4—52no—
183C2×C3×D4—102no—
184C2×C3×D4—102no—
185C22×C3×C4—51no—
186C22×Dic3—51no—
187C22×Dic3—51no—
188C22×Dic3—101no—
189C22×Dic3—101no—
190C22×Dic3—101no—
191C22×Dic3—101no—
192C22×Dic3—202no—
193C22×Dic3—202no—
194C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
195C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
196C3×M16—102no—
197C3×M16—102no—
198C2×C3×C8—102no—
199#217—22no—
200#217—102no—
201C4⋊Dic3—102no—
202C4×Dic3—52no—
203C4×Dic3—52no—
204#208—102no—
205#208—102no—
206C2×C3⋊C8—102no—
207C23×C5—21no—
208C23×C5—21no—
209C23×C5—41no—
210C23×C5—41no—
211C23×C5Dic3⋊C412yes—
212C23×C5C2×C4×D311yescharacteristic
213C22×D5—21no—
214C22×D5—21no—
215C22×D5—41no—
216C22×D5—41no—
217C22×D5Dic3⋊C412yes—
218C2×C4×C5—32no—
219C2×C4×C5—61no—
220C2×C4×C5—121no—
221C2×C4×C5—121no—
222C22⋊D5—24no—
223C22⋊D5—24no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—62no—
227C2×Dic5—61no—
228C2×Dic5—122no—
229C2×Dic5—122no—
230C2×Dic5—121no—
231C2×Dic5C2×Dic611yescharacteristic
232C2×Dic5D3×D412yes—
233C2×Dic5#23712yes—
234C2×Dic5C2×#6711yescharacteristic
235C4×D5—122no—
236C4×D5—122no—
237#170—42no—
238#170—122no—
239C22×D4—51no—
240C23×C4—151no—
241C23×C4—151no—
242C2×M16—52no—
243C2×M16—152no—
244C4×D4—302no—
245C4×D4—302no—
246C2×C4⋊C4—151no—
247C2×C22⋊C4—31no—
248C2×C22⋊C4—151no—
249C2×C42—151no—
250C4⋊C8—302no—
251C4⋊C8—302no—
252#100—102no—
253#100—302no—
254C2×C3×C5—21no—
255C2×C3×C5—21no—
256C2×C3×C5—42no—
257C2×C3×C5#38011yescharacteristic
258C2×C3×C5C2×#10011yescharacteristic
259C2×C3×C5#41311yescharacteristic
260C3×D5—42no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—52no—
266C23×C3—101no—
267C23×C3—101no—
268C23×C3—201no—
269C23×C3—201no—
270C23×C3C4⋊AGL(1,𝔽5)12yes—
271C23×C3C22×AGL(1,𝔽5)11yescharacteristic
272C3×D4—104no—
273C3×D4—104no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—52no—
277C2×C3×C4—52no—
278C2×Dic3—21no—
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—51no—
282C2×Dic3—51no—
283C2×Dic3—102no—
284C2×Dic3—101no—
285C2×Dic3—202no—
286C2×Dic3—202no—
287C2×Dic3—202no—
288C2×Dic3—202no—
289C2×Dic3—201no—
290C2×Dic3C22⋊AGL(1,𝔽5)12yes—
291C3×C8—202no—
292C3⋊C8—202no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—22no—
296C22×C5—42no—
297C22×C5—42no—
298C22×C5—41no—
299C22×C5—41no—
300C22×C5#87711yescharacteristic
301C22×C5D3×C22⋊C411yescharacteristic
302C22×C5C2×Dic3⋊C411yescharacteristic
303C2×D5—22no—
304C2×D5—42no—
305C2×D5—41no—
306C2×D5—41no—
307C2×D5—42no—
308C4×C5—62no—
309C4×C5—121no—
310Dic5—32no—
311Dic5—61no—
312Dic5—121no—
313Dic5#87812yes—
314Dic5#93912yes—
315C24—51no—
316C24D3×AGL(1,𝔽5)11yescharacteristic
317C2×D4—52no—
318C2×D4—52no—
319C2×D4—102no—
320C2×D4—102no—
321C22×C4—31no—
322C22×C4—31no—
323C22×C4—51no—
324C22×C4—151no—
325C22×C4—151no—
326C22×C4—301no—
327C22×C4—301no—
328C22×C4—301no—
329C22×C4—301no—
330C22×C4—602no—
331C22×C4—602no—
332M16—102no—
333M16—102no—
334M16—302no—
335M16—302no—
336C2×C8—102no—
337C2×C8—302no—
338C4⋊C4—302no—
339C22⋊C4—62no—
340C22⋊C4—302no—
341C42—152no—
342C42—152no—
343C3×C5#180011yescharacteristic, complemented, Hall
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—22no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—102no—
352C22×C3—202no—
353C22×C3—202no—
354C22×C3—201no—
355C22×C3—201no—
356C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
357C22×C3#413011yescharacteristic
358C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
359C3×C4—52no—
360C3×C4—52no—
361Dic3—22no—
362Dic3—41no—
363Dic3—52no—
364Dic3—101no—
365Dic3—201no—
366C2×C5—21no—
367C2×C5—21no—
368C2×C5—42no—
369C2×C5D3×#10011yescharacteristic
370C2×C5#474511yescharacteristic
371C2×C5#494211yescharacteristic
372D5—42no—
373C23—21no—
374C23—21no—
375C23—41no—
376C23—41no—
377C23—52no—
378C23—101no—
379C23—101no—
380C23—201no—
381C23—201no—
382C23Dic3⋊AGL(1,𝔽5)12yes—
383C23C2×D3×AGL(1,𝔽5)11yescharacteristic
384D4—104no—
385D4—104no—
386C2×C4—32no—
387C2×C4—52no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—52no—
391C2×C4—61no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—151no—
395C2×C4—151no—
396C2×C4—302no—
397C2×C4—301no—
398C2×C4—602no—
399C2×C4—602no—
400C2×C4—602no—
401C2×C4—602no—
402C2×C4—601no—
403C8—202no—
404C8—602no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—42no—
408C2×C3—202no—
409C2×C3#6576511yescharacteristic
410C2×C3#6577711yescharacteristic
411C2×C3D5⋊#10011yescharacteristic
412C5#7006311yescharacteristic, complemented, Sylow
413C22—21no—
414C22—21no—
415C22—22no—
416C22—42no—
417C22—42no—
418C22—41no—
419C22—41no—
420C22—102no—
421C22—202no—
422C22—202no—
423C22—201no—
424C22—201no—
425C22#9192311yescharacteristic
426C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
427C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
428C4—52no—
429C4—52no—
430C4—62no—
431C4—121no—
432C4—152no—
433C4—301no—
434C4—601no—
435C3#1060424611yescharacteristic, complemented, Sylow
436C2—21no—
437C2—21no—
438C2—42no—
439C2—202no—
440C2#1175202811yescharacteristic
441C2#1175204811yescharacteristic
442C2#1175205011yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
FittingC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C22
cosocleC22×C3×Dic5C23
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#1800
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #11752012C2semidirect
5. #11746574C2semidirect
174. Dic15#100semidirect
343. C3×C5#1800semidirect
412. C5#70063semidirect
435. C3#10604246semidirect

Maximal subgroups

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

subgroupindex
C2×#915592
C2×#912422
C2×C3×#40132
#117520122
#117465742
#106042463
#700635