Finite Group Databasebeta

← #14283273

Subgroups — #14283273

Order 1920.

652 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 652 conjugacy classes of subgroups — too many to draw. Only its 105 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
1C3×D5×#121C211yesmaximal, characteristic
2#11752423C211yesmaximal, characteristic, complemented
3#11752415C211yesmaximal, characteristic, complemented
4#11746791C212yesmaximal, complemented
5#11746739C212yesmaximal, complemented
6#10604469—31nomaximal, Hall
7C2×C3×D4×D5—21no—
8C2×C3×D4×D5C411yescharacteristic, complemented
9C22×C3×C4×D5C2211yescharacteristic
10C2×#6763—21no—
11C2×#6758—21no—
12C3×C5×#121C411yescharacteristic, complemented
13C3×#4085—21no—
14C3×#4084C2211yescharacteristic
15C3×#4076C411yescharacteristic, complemented
16C3×#4041C2211yescharacteristic
17C3×D5×C4⋊C4C411yescharacteristic, complemented
18C3×#4030—21no—
19C3×D5×C22⋊C4—21no—
20#91241—21no—
21#91235—21no—
22#91235C2212yescomplemented
23#91232C2212yescomplemented
24#71674—51nomaximal, Hall
25D5×#121D311yescharacteristic
26#65764—31no—
27#65756—31no—
28#64920—32no—
29#64868—32no—
30C23×C3×D5—21no—
31C23×C3×D5D411yescharacteristic
32C22×ΓL(1,𝔽16)—22no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C2×C3×C22⋊D5—21no—
37C2×C3×C22⋊D5—21no—
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5D411yescharacteristic
40C3×D4×D5—42no—
41C3×D4×D5—44no—
42C2×C3×D20—21no—
43C2×C3×D20C2×C411yescharacteristic
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—42no—
46C2×C3×C4×D5C2×C411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×C3×C4×D5D411yescharacteristic
49C2×C3×C4×D5C2311yescharacteristic
50#6763—42no—
51C2×C3⋊#170—22no—
52#6758—42no—
53C3×C5×C4⋊C4C2×C411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×C4⋊Dic5C2×C411yescharacteristic
59C3×#683—21no—
60C2×C3×#121—51no—
61#5211—51no—
62#5207—51no—
63#4537—52no—
64#4537—52no—
65C2×D4×D5—21no—
66C2×D4×D5Dic311yescharacteristic, complemented
67C22×C4×D5C2×D311yescharacteristic
68C2×C22⋊AGL(1,𝔽5)—61no—
69C2×#700—61no—
70C5×#121Dic311yescharacteristic, complemented
71#4085—21no—
72#4084C2×D311yescharacteristic
73#4076Dic311yescharacteristic, complemented
74#4041C2×D311yescharacteristic
75D5×C4⋊C4Dic311yescharacteristic, complemented
76#4030—21no—
77D5×C22⋊C4—21no—
78C22⋊#170—61no—
79(C2×AGL(1,𝔽5))⋊C4—32no—
80(C2×AGL(1,𝔽5))⋊C4—61no—
81#4003—32no—
82#1510—151noSylow
83C23×C3×C5—21no—
84C23×C3×C5C22⋊C411yescharacteristic
85C22×C3×D5—22no—
86C22×C3×D5—22no—
87C22×C3×D5—21no—
88C22×C3×D5—41no—
89C22×C3×D5—42no—
90C22×C3×D5—42no—
91C22×C3×D5—42no—
92C22×C3×D5C22⋊C411yescharacteristic
93C22×C3×D5C2×D411yescharacteristic
94C2×ΓL(1,𝔽16)—42no—
95C2×ΓL(1,𝔽16)—42no—
96C2×ΓL(1,𝔽16)—42no—
97C3×C5×D4—41no—
98C3×C5×D4—42no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—41no—
101C2×C3×C4×C5C22⋊C411yescharacteristic
102C2×C3×C4×C5C22×C411yescharacteristic
103C3×C22⋊D5—42no—
104C3×C22⋊D5—42no—
105C3×C22⋊D5—42no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—41no—
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C2×D411yescharacteristic
110C3×D20—41no—
111C3×D20—42no—
112C3×C4×D5—22no—
113C3×C4×D5—22no—
114C3×C4×D5—41no—
115C3×C4×D5—41no—
116C3×C4×D5—42no—
117C3⋊#170—42no—
118C22×C3×D4—51no—
119C22×C3×D4—101no—
120C23×C3×C4—51no—
121C3×#121—51no—
122C3×#121—51no—
123C3×#121—51no—
124C3×#121—101no—
125C3×#121—101no—
126C3×#121AGL(1,𝔽5)11yescharacteristic, complemented
127C2×C3×C4⋊C4—51no—
128C2×C3×C22⋊C4—101no—
129C2×#217—101no—
130C2×#208—101no—
131C3⋊#95—52no—
132C3⋊#95—101no—
133#830—52no—
134#830—101no—
135C23×D5—21no—
136C23×D5#6711yescharacteristic
137C22×AGL(1,𝔽5)—62no—
138C2×C5×D4—21no—
139C2×C5×D4C2×Dic311yescharacteristic
140C22×C4×C5C2×Dic311yescharacteristic
141C2×C22⋊D5—21no—
142C2×C22⋊D5—21no—
143C2×C22⋊D5—21no—
144C22×Dic5#6711yescharacteristic
145D4×D5—42no—
146D4×D5—44no—
147C2×D20—21no—
148C2×D20C2×Dic311yescharacteristic
149C2×C4×D5—21no—
150C2×C4×D5—42no—
151C2×C4×D5C2×Dic311yescharacteristic
152C2×C4×D5#6711yescharacteristic
153C2×C4×D5#6711yescharacteristic
154C2×C4×D5C22×D311yescharacteristic
155C22⋊AGL(1,𝔽5)—122no—
156C2×#170—62no—
157#700—122no—
158C5×C4⋊C4C2×Dic311yescharacteristic
159C5×C22⋊C4—21no—
160C22⋊Dic5—21no—
161#685—21no—
162#685—21no—
163C4⋊Dic5C2×Dic311yescharacteristic
164#683—21no—
165C2×#121—51no—
166#407—151no—
167#381—151no—
168#327—152no—
169#327—152no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—41no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5C2×C22⋊C411yescharacteristic
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C2×C3×D5—21no—
180C2×C3×D5—21no—
181C2×C3×D5—44no—
182C2×C3×D5—41no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—84no—
186C2×C3×D5#9912yes—
187C2×C3×D5AGL(1,ℤ/8)12yes—
188ΓL(1,𝔽16)—82no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×Dic5—21no—
193C3×Dic5—21no—
194C3×Dic5—41no—
195C24×C3—51no—
196C24×C3—101no—
197C2×C3×D4—21no—
198C2×C3×D4—51no—
199C2×C3×D4—101no—
200C2×C3×D4—101no—
201C2×C3×D4—101no—
202C2×C3×D4—101no—
203C2×C3×D4—202no—
204C2×C3×D4—204no—
205C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4—51no—
209C22×C3×C4—51no—
210C22×C3×C4—51no—
211C22×C3×C4—101no—
212C22×C3×C4—202no—
213C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
214C22×Dic3—102no—
215C3×C4⋊C4—51no—
216C3×C4⋊C4—101no—
217C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
218C3×C22⋊C4—21no—
219C3×C22⋊C4—101no—
220C3×C22⋊C4—101no—
221C3×C22⋊C4—101no—
222#217—202no—
223#208—202no—
224C2×C3⋊C8—102no—
225C23×C5—21no—
226C23×C5#21711yescharacteristic
227C22×D5—22no—
228C22×D5—22no—
229C22×D5—21no—
230C22×D5—41no—
231C22×D5—42no—
232C22×D5—42no—
233C22×D5—42no—
234C22×D5#21711yescharacteristic
235C22×D5C2×#6711yescharacteristic
236C2×AGL(1,𝔽5)—122no—
237C2×AGL(1,𝔽5)—122no—
238C2×AGL(1,𝔽5)—122no—
239C5×D4—41no—
240C5×D4—42no—
241C2×C4×C5—21no—
242C2×C4×C5—41no—
243C2×C4×C5#21711yescharacteristic
244C2×C4×C5C22×Dic311yescharacteristic
245C22⋊D5—42no—
246C22⋊D5—42no—
247C22⋊D5—42no—
248C2×Dic5—21no—
249C2×Dic5—41no—
250C2×Dic5#21711yescharacteristic
251C2×Dic5C2×#6711yescharacteristic
252D20—41no—
253D20—42no—
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—41no—
257C4×D5—41no—
258C4×D5—42no—
259#170—122no—
260C22×D4—51no—
261C22×D4—101no—
262C23×C4—51no—
263C2×M16—301no—
264#121—51no—
265#121—51no—
266#121—51no—
267#121—101no—
268#121—101no—
269#121ΓL(1,𝔽16)11yescharacteristic, complemented
270C2×C4⋊C4—51no—
271C2×C22⋊C4—101no—
272C2×C22⋊C4—301no—
273C22⋊C8—152no—
274C22⋊C8—301no—
275#95—152no—
276#95—301no—
277C2×C3×C5—41no—
278C2×C3×C5—81no—
279C2×C3×C5C2×#9911yescharacteristic
280C2×C3×C5#41811yescharacteristic
281C2×C3×C5#42111yescharacteristic
282C3×D5—22no—
283C3×D5—22no—
284C3×D5—81no—
285C23×C3—21no—
286C23×C3—51no—
287C23×C3—51no—
288C23×C3—102no—
289C23×C3—102no—
290C23×C3—101no—
291C23×C3—201no—
292C23×C3—202no—
293C23×C3—202no—
294C23×C3—202no—
295C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
296C3×D4—41no—
297C3×D4—42no—
298C3×D4—201no—
299C3×D4—202no—
300C3×D4—202no—
301C3×D4—202no—
302C3×D4—202no—
303C2×C3×C4—21no—
304C2×C3×C4—41no—
305C2×C3×C4—51no—
306C2×C3×C4—51no—
307C2×C3×C4—102no—
308C2×C3×C4—102no—
309C2×C3×C4—101no—
310C2×C3×C4—201no—
311C2×C3×C4—201no—
312C2×C3×C4—202no—
313C2×C3×C4—201no—
314C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
315C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
316C2×Dic3—202no—
317C2×Dic3—202no—
318C2×Dic3—202no—
319C3⋊C8—202no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—21no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—41no—
326C22×C5C2×#21711yescharacteristic
327C2×D5—21no—
328C2×D5—21no—
329C2×D5—21no—
330C2×D5—21no—
331C2×D5—44no—
332C2×D5—41no—
333C2×D5—41no—
334C2×D5—41no—
335C2×D5—84no—
336C2×D5#83412yes—
337C2×D5#93212yes—
338AGL(1,𝔽5)—242no—
339C4×C5—21no—
340C4×C5—21no—
341C4×C5—41no—
342Dic5—21no—
343Dic5—21no—
344Dic5—41no—
345C24—51no—
346C24—101no—
347C2×D4—21no—
348C2×D4—51no—
349C2×D4—101no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—202no—
354C2×D4—204no—
355C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
356C22×C4—51no—
357C22×C4—51no—
358C22×C4—51no—
359C22×C4—51no—
360C22×C4—51no—
361C22×C4—101no—
362C22×C4—202no—
363C22×C4—302no—
364C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
365M16—602no—
366C2×C8—302no—
367C4⋊C4—51no—
368C4⋊C4—101no—
369C4⋊C4C2×ΓL(1,𝔽16)11yescharacteristic
370C22⋊C4—21no—
371C22⋊C4—101no—
372C22⋊C4—101no—
373C22⋊C4—101no—
374C22⋊C4—602no—
375C3×C5#151011yescharacteristic, complemented, Hall
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—52no—
383C22×C3—52no—
384C22×C3—101no—
385C22×C3—101no—
386C22×C3—101no—
387C22×C3—101no—
388C22×C3—204no—
389C22×C3—201no—
390C22×C3—201no—
391C22×C3—201no—
392C22×C3—404no—
393C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—41no—
397C3×C4—101no—
398C3×C4—101no—
399C3×C4—201no—
400Dic3—402no—
401C2×C5—41no—
402C2×C5—81no—
403C2×C5#521511yescharacteristic
404C2×C5C2×#83411yescharacteristic
405C2×C5#523611yescharacteristic
406D5—22no—
407D5—22no—
408D5—81no—
409C23—21no—
410C23—51no—
411C23—51no—
412C23—102no—
413C23—102no—
414C23—101no—
415C23—201no—
416C23—202no—
417C23—202no—
418C23—202no—
419C23#676311yescharacteristic
420D4—41no—
421D4—42no—
422D4—201no—
423D4—202no—
424D4—202no—
425D4—202no—
426D4—202no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—51no—
430C2×C4—51no—
431C2×C4—102no—
432C2×C4—102no—
433C2×C4—101no—
434C2×C4—201no—
435C2×C4—201no—
436C2×C4—202no—
437C2×C4—201no—
438C2×C4—602no—
439C2×C4—602no—
440C2×C4—602no—
441C2×C4#676311yescharacteristic
442C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
443C8—602no—
444C2×C3—41no—
445C2×C3—81no—
446C2×C3—102no—
447C2×C3—102no—
448C2×C3—401no—
449C2×C3#6576711yescharacteristic
450C2×C3D5⋊#9911yescharacteristic
451C2×C3#6579511yescharacteristic
452C5#7167411yescharacteristic, complemented, Sylow
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—52no—
460C22—52no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—101no—
465C22—204no—
466C22—201no—
467C22—201no—
468C22—201no—
469C22—404no—
470C22C2×#676311yescharacteristic
471C4—21no—
472C4—21no—
473C4—41no—
474C4—101no—
475C4—101no—
476C4—201no—
477C4—1202no—
478C3#1060446911yescharacteristic, complemented, Sylow
479C2—41no—
480C2—81no—
481C2—102no—
482C2—102no—
483C2—401no—
484C2#1175242611yescharacteristic
485C2D5⋊#83411yescharacteristic
486C2#1175245411yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#121C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×D5×#121C2
cosocleC2×C3×C4×D5C23
hypercenter#121ΓL(1,𝔽16)
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11752423C2semidirect
3. #11752415C2semidirect
4. #11746791C2semidirect
5. #11746739C2semidirect
8. C2×C3×D4×D5C4semidirect
12. C3×C5×#121C4semidirect
15. C3×#4076C4semidirect
17. C3×D5×C4⋊C4C4semidirect
22. #91235C22semidirect
23. #91232C22semidirect
66. C2×D4×D5Dic3semidirect
70. C5×#121Dic3semidirect
73. #4076Dic3semidirect
75. D5×C4⋊C4Dic3semidirect
126. C3×#121AGL(1,𝔽5)semidirect
269. #121ΓL(1,𝔽16)semidirect
375. C3×C5#1510semidirect
452. C5#71674semidirect
478. C3#10604469semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1212
#117524232
#117524152
#117467912
#117467392
#106044693
#716745