Finite Group Databasebeta

← #14313329

Subgroups — #14313329

Order 1920.

468 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 86 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
1#11755008C211yesmaximal, characteristic
2C5×#4745C211yesmaximal, characteristic
3#11749173C211yesmaximal, characteristic
4#11746297C211yesmaximal, characteristic, complemented
5C3×#64696C211yesmaximal, characteristic, complemented
6#11746004C211yesmaximal, characteristic, complemented
7#11746001C211yesmaximal, characteristic, complemented
8#10600940—31nomaximal, Hall
9C2×C5×#237C2211yescharacteristic
10C22×#1204C411yescharacteristic, complemented
11#91824C2211yescharacteristic
12C5×D3×M16—21no—
13C3×#4081C2211yescharacteristic
14#91575—21no—
15#91543C411yescharacteristic, complemented
16#91539C411yescharacteristic, complemented
17#91529—21no—
18#91529C411yescharacteristic, complemented
19#91525—21no—
20#91352—21no—
21#91329—21no—
22C3×C5×#100C2211yescharacteristic
23#91118C2211yescharacteristic
24C5×#833C2211yescharacteristic
25C5×#824—21no—
26C3×#3966C2211yescharacteristic
27#90996—21no—
28#69145—51nomaximal, Hall
29#66159—31no—
30C5×#413—31no—
31#65529—31no—
32#64696—31no—
33#64696—31no—
34#64696—31no—
35#64696D311yescharacteristic, complemented
36C2×C3×C5×D4C2311yescharacteristic
37C22×Dic15C2×C411yescharacteristic
38C2×C5×#67C2×C411yescharacteristic
39C2×C5×#67D411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C5×#237—41no—
43C5×#237—41no—
44C2×C4×C5×D3D411yescharacteristic
45C2×C5×Dic6D411yescharacteristic
46C22×C3×Dic5C2×C411yescharacteristic
47C2×#1204—21no—
48C2×#1204—21no—
49C2×#1204—41no—
50C2×#1204—41no—
51C3×C5×M16—21no—
52#6719—21no—
53#6719—21no—
54#6719C2×C411yescharacteristic
55#6712—21no—
56C5×#208—21no—
57C5×ΓL(1,𝔽25)—41no—
58C5×D3×C8—41no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×C22⋊Dic5C2×C411yescharacteristic
62C3×#683—21no—
63Dic3⋊Dic5—21no—
64Dic3⋊Dic5—41no—
65#6669—21no—
66#6668—21no—
67(C2×D3)⋊Dic5—21no—
68(C2×D3)⋊Dic5—21no—
69Dic3×Dic5—21no—
70Dic3×Dic5—41no—
71#5648—51no—
72#4745D511yescharacteristic
73#4740—51no—
74C3×#352—51no—
75#4539—51no—
76#4476—51no—
77#4472—51no—
78C2×C5×#41—31no—
79C22×Dic10—31no—
80C2×C5×M16—61no—
81#4090—61no—
82#4082—61no—
83#4081—31no—
84#4081—31no—
85#4081—31no—
86#4081C2×D311yescharacteristic
87#4072—31no—
88#4072—61no—
89#4070—61no—
90#4070—61no—
91C5×#101—61no—
92C5×#100—31no—
93C5×#100C2×D311yescharacteristic
94#3966—31no—
95#3966—61no—
96#3966C2×D311yescharacteristic
97#2123—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3C22⋊C411yescharacteristic
101C3×C5×D4—41no—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C5×#67—41no—
108C5×#67—41no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3C22⋊C411yescharacteristic
114C2×C5×Dic3C22⋊C411yescharacteristic
115C2×C5×Dic3C22⋊C411yescharacteristic
116C4×C5×D3—21no—
117C4×C5×D3—21no—
118C5×Dic6—41no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123#1204—42no—
124#1204—41no—
125#1204—41no—
126C3×C5×C8—41no—
127C5×C3⋊C8—41no—
128C2×#237C2×D511yescharacteristic
129C22×Dic6—51no—
130C3×#123—51no—
131#935—51no—
132#929—51no—
133D3×M16—21no—
134#896—101no—
135#888—101no—
136#886—51no—
137#885—101no—
138#878—101no—
139#877—51no—
140#877—101no—
141C3×#100C2×D511yescharacteristic
142C3×#99—51no—
143#834—51no—
144#833C2×D511yescharacteristic
145#824—21no—
146#806—101no—
147C5×#41—121no—
148C5×#41—121no—
149C2×C5×Q8—31no—
150C2×C5×D4—31no—
151C2×C5×D4—31no—
152C2×C5×D4C22×D311yescharacteristic
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×Dic5—31no—
157C22×Dic5C4×D311yescharacteristic
158C2×Dic10—61no—
159C2×Dic10—61no—
160C2×Dic10—121no—
161C2×Dic10—121no—
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—121no—
165C2×C5×C8—121no—
166C22⋊Dic5—21no—
167C22⋊Dic5—21no—
168C22⋊Dic5—31no—
169C22⋊Dic5—61no—
170C22⋊Dic5—61no—
171C22⋊Dic5—61no—
172C22⋊Dic5—61no—
173C22⋊Dic5C4×D311yescharacteristic
174C4⋊Dic5—61no—
175C4⋊Dic5—121no—
176#683—21no—
177#683—61no—
178#683—61no—
179#683—61no—
180C4×Dic5—61no—
181C4×Dic5—121no—
182#536—151no—
183#413—31no—
184#410—151no—
185#352—51no—
186#352—151no—
187#352—151no—
188#352—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C2×C5×D3—21no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197Dic15—41no—
198Dic15—41no—
199Dic15—81no—
200C3×Dic5—41no—
201C3×Dic5—41no—
202C3×Dic5—81no—
203C5×Dic3—21no—
204C5×Dic3—21no—
205C5×Dic3#9911yescharacteristic
206C5×Dic3#9911yescharacteristic
207C2×C3×D4C22×D511yescharacteristic
208C22×C3×C4—51no—
209C2×#67C4×D511yescharacteristic
210C2×#67D2011yescharacteristic
211C22×Dic3—51no—
212C22×Dic3C4×D511yescharacteristic
213C22×Dic3D2011yescharacteristic
214#237—41no—
215#237—41no—
216C2×C4×D3C22⋊D511yescharacteristic
217C2×Dic6—101no—
218C2×Dic6—101no—
219C2×Dic6—201no—
220C2×Dic6—201no—
221C2×Dic6C22⋊D511yescharacteristic
222C3×M16—21no—
223C3×C4⋊C4—101no—
224C3×C22⋊C4—51no—
225C3×C22⋊C4—101no—
226C3×C22⋊C4—101no—
227#217—51no—
228#217—101no—
229#217—101no—
230(C2×D3)⋊C4—101no—
231(C2×D3)⋊C4—101no—
232C4⋊Dic3—101no—
233Dic3⋊C4—101no—
234Dic3⋊C4—101no—
235Dic3⋊C4—101no—
236Dic3⋊C4—201no—
237C4×Dic3—101no—
238C4×Dic3—201no—
239#208—21no—
240ΓL(1,𝔽25)—41no—
241D3×C8—41no—
242C23×C5—31no—
243C23×C5C2×C4×D311yescharacteristic
244C23×C5D3×D411yescharacteristic
245C5×Q8—121no—
246C5×D4—41no—
247C5×D4—121no—
248C5×D4—121no—
249C2×C4×C5—31no—
250C2×C4×C5—31no—
251C2×C4×C5—31no—
252C2×C4×C5—61no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×C4×C5—61no—
257C2×C4×C5—61no—
258C2×C4×C5D3×D411yescharacteristic
259C2×Dic5—21no—
260C2×Dic5—21no—
261C2×Dic5—41no—
262C2×Dic5—41no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5—121no—
266C2×Dic5—121no—
267Dic10—121no—
268Dic10—121no—
269Dic10—122no—
270C5×C8—41no—
271C5×C8—121no—
272C2×#41—31no—
273C22×Q8—151no—
274C2×M16—61no—
275C4⋊Q8—301no—
276#124—301no—
277#123—51no—
278#123—151no—
279#123—151no—
280#123—151no—
281C22⋊Q8—301no—
282C22⋊Q8—301no—
283#117—151no—
284#117—301no—
285#101—61no—
286#100—31no—
287#100D3×D511yescharacteristic
288#99—51no—
289#99—151no—
290#99—301no—
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C5×D3—41no—
296C23×C3C2×C4×D511yescharacteristic
297C23×C3C2×D2011yescharacteristic
298C22×D3#68511yescharacteristic
299C3×D4—41no—
300C2×C3×C4—101no—
301C2×C3×C4—101no—
302C2×C3×C4—201no—
303C2×C3×C4—201no—
304C2×C3×C4C2×C22⋊D511yescharacteristic
305#67—41no—
306#67—41no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—101no—
312C2×Dic3—101no—
313C2×Dic3—201no—
314C2×Dic3—201no—
315C2×Dic3#68511yescharacteristic
316C2×Dic3#68511yescharacteristic
317C2×Dic3#68511yescharacteristic
318C4×D3—21no—
319C4×D3—21no—
320Dic6—41no—
321Dic6—202no—
322Dic6—201no—
323Dic6—201no—
324C3×C8—41no—
325C3⋊C8—41no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—41no—
329C22×C5—41no—
330C22×C5—61no—
331C22×C5—121no—
332C22×C5D3×C22⋊C411yescharacteristic
333C4×C5—21no—
334C4×C5—31no—
335C4×C5—31no—
336C4×C5—61no—
337C4×C5—61no—
338Dic5—41no—
339Dic5—41no—
340Dic5—81no—
341Dic5—121no—
342Dic5—121no—
343Dic5—241no—
344#41—121no—
345#41—121no—
346C2×Q8—31no—
347C2×Q8—301no—
348C2×Q8—301no—
349C2×Q8—601no—
350C2×Q8—601no—
351C2×D4—31no—
352C2×D4—31no—
353C2×D4C2×D3×D511yescharacteristic
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—51no—
358C22×C4—151no—
359M16—21no—
360M16—61no—
361M16—121no—
362C2×C8—121no—
363C4⋊C4—101no—
364C4⋊C4—301no—
365C4⋊C4—301no—
366C4⋊C4—301no—
367C4⋊C4—301no—
368C4⋊C4—601no—
369C22⋊C4—51no—
370C22⋊C4—101no—
371C22⋊C4—101no—
372C22⋊C4—151no—
373C22⋊C4—301no—
374C22⋊C4—301no—
375C22⋊C4—301no—
376C22⋊C4—301no—
377C42—301no—
378C42—601no—
379C3×C5#212311yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3C2×#68511yescharacteristic
385C2×D3—21no—
386C2×D3—41no—
387C3×C4—21no—
388C3×C4—201no—
389C3×C4—201no—
390C3×C4—401no—
391Dic3—21no—
392Dic3—21no—
393Dic3—201no—
394Dic3—201no—
395Dic3—401no—
396Dic3#393811yescharacteristic
397Dic3#393811yescharacteristic
398C2×C5—21no—
399C2×C5—41no—
400C2×C5—41no—
401C2×C5—121no—
402C2×C5D3×#9911yescharacteristic
403C23—31no—
404C23C4×D3×D511yescharacteristic
405C23D3×D2011yescharacteristic
406Q8—121no—
407Q8—601no—
408Q8—601no—
409Q8—602no—
410D4—41no—
411D4—121no—
412D4—121no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—101no—
423C2×C4—101no—
424C2×C4—201no—
425C2×C4—201no—
426C2×C4—301no—
427C2×C4—301no—
428C2×C4—601no—
429C2×C4—601no—
430C2×C4D3×C22⋊D511yescharacteristic
431C8—41no—
432C8—121no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3C2×#393811yescharacteristic
437D3—41no—
438C5#6914511yescharacteristic, complemented, Sylow
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—61no—
444C22—121no—
445C22D3×#68511yescharacteristic
446C4—21no—
447C4—31no—
448C4—31no—
449C4—61no—
450C4—61no—
451C4—201no—
452C4—201no—
453C4—401no—
454C4—601no—
455C4—601no—
456C4—1201no—
457C3#1060094011yescharacteristic, complemented, Sylow
458C2—21no—
459C2—41no—
460C2—41no—
461C2—121no—
462C2D3×#393811yescharacteristic
subgroupG/H
centerC2D3×#3938
commutatorC23×C3×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#100C22
socleC2×C3×C5C2×#99
prime radicalC2×C5×#237C22
cosocleC2×C3×C5×D4C23
hypercenter#100D3×D5
hypocenterC3×C5#2123
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
4. #11746297C2semidirect
5. C3×#64696C2semidirect
6. #11746004C2semidirect
7. #11746001C2semidirect
10. C22×#1204C4semidirect
15. #91543C4semidirect
16. #91539C4semidirect
18. #91529C4semidirect
35. #64696D3semidirect
379. C3×C5#2123semidirect
438. C5#69145semidirect
457. C3#10600940semidirect

Maximal subgroups

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

subgroupindex
#117550082
C5×#47452
#117491732
#117462972
C3×#646962
#117460042
#117460012
#106009403
#691455