Finite Group Databasebeta

← #14288858

Subgroups — #14288858

Order 1920.

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

normal subgroups only

This group has 480 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#11752636C211yesmaximal, characteristic, complemented
2#11751176C211yesmaximal, characteristic, complemented
3C5×#5075C211yesmaximal, characteristic, complemented
4C3×#65362C211yesmaximal, characteristic
5#11745852C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745843C211yesmaximal, characteristic, complemented
8#10601824—31nomaximal, Hall
9C3×C5×#127C2211yescharacteristic
10C2×#6716—21no—
11C4×Dic30C2211yescharacteristic
12C2×C5×#214—21no—
13C4×C5×Dic6C2211yescharacteristic
14C2×C3×#686—22no—
15C3×#4020C2211yescharacteristic
16#91434—21no—
17Dic3×D20—21no—
18#91407—22no—
19#91368—21no—
20#91364—21no—
21#91116—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×#832—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26#71284—51nomaximal, Hall
27#65919—31no—
28C5×#460—31no—
29#65364—31no—
30#65362D311yescharacteristic
31Q8⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×Dic30D411yescharacteristic
38C2×C5×Dic6D411yescharacteristic
39C2×C3×D20—21no—
40C2×C3×D20—21no—
41C2×C3×D20D412yes—
42C2×D5×Dic3—22no—
43C3×C42×C5C2311yescharacteristic
44#6716—42no—
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C5×#214—42no—
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C3×#686—44no—
55C2×C3×#168—21no—
56#6665—22no—
57#6665—22no—
58#6665—22no—
59#5713—51no—
60C3×#493—51no—
61#5075—51no—
62#5075D511yescharacteristic, complemented
63#4544—51no—
64#4456—51no—
65#4456—51no—
66C2×C5×SD16—61no—
67C5×#127C2×D311yescharacteristic
68C4×C5×Q8—31no—
69#4093—61no—
70C2×#687—61no—
71C2×#686—22no—
72#4040—62no—
73#4039—61no—
74#4021—61no—
75#4020C2×D311yescharacteristic
76C4×D20—61no—
77C4×Dic10—31no—
78C5×C4⋊C8—31no—
79C5×#102—61no—
80#3964—61no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1620—151noSylow
84C23×C3×C5—41no—
85C22×C3×D5—22no—
86C3×C5×D4—42no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C3×C5×D4—41no—
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93C2×C3×C4×C5C2×D411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15—21no—
96Dic30—21no—
97Dic30—21no—
98C2×C5×Dic3—21no—
99C2×C5×Dic3—21no—
100C5×Dic6—21no—
101C5×Dic6—21no—
102C3×D20—42no—
103C3×D20—41no—
104C3×D20—41no—
105C3×D20—41no—
106C3×D20—41no—
107D5×Dic3—82no—
108C3⋊#168—41no—
109C3×#168—22no—
110C5×C3⋊C8—41no—
111C2×C3×D8—102no—
112C3×#127—51no—
113C3×#127C2×D511yescharacteristic
114#936—101no—
115#936—101no—
116#935—102no—
117D4×Dic3—101no—
118D4×Dic3—101no—
119C2×#214—21no—
120C2×#214—101no—
121C4×Dic6—51no—
122C4×Dic6C2×D511yescharacteristic
123C3×C4×C8—51no—
124#832—21no—
125#832—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C2×C5×Q8—31no—
129C2×C5×D4—21no—
130C2×C5×D4—21no—
131C2×C5×D4—21no—
132C2×D20—21no—
133C2×D20—21no—
134C2×D20#6712yes—
135C2×C4×D5—62no—
136C2×Dic10—31no—
137C5×SD16—122no—
138C2×C5×C8—61no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C42×C5—61no—
142C42×C5C22×D311yescharacteristic
143#687—122no—
144#686—44no—
145#685—62no—
146#685—62no—
147#685—62no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—21no—
152C2×#168—61no—
153#559—151no—
154#493—51no—
155#460—31no—
156#460—151no—
157#331—151no—
158Q8⋊C8—151no—
159Q8⋊C8—151no—
160C22×C3×C5—81no—
161C22×C3×C5—81no—
162C22×C3×C5—81no—
163C22×C3×C5#12011yescharacteristic
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C3×C4×C5—21no—
168C3×C4×C5#13511yescharacteristic
169C3×C4×C5#13511yescharacteristic
170C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172Dic15—41no—
173Dic15—41no—
174C5×Dic3—41no—
175C5×Dic3—41no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—52no—
180C2×C3×D4—101no—
181C2×C3×D4—101no—
182C22×Dic3—102no—
183C2×Dic6—51no—
184C2×Dic6C22⋊D511yescharacteristic
185C3×D8—204no—
186C2×C3×C8—101no—
187C3×C42C22×D511yescharacteristic
188#217—102no—
189#217—102no—
190#217—102no—
191#214—42no—
192#214—202no—
193C4⋊Dic3—51no—
194C4⋊Dic3C22⋊D511yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—101no—
197C4×Dic3—21no—
198C4×Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C23×C5—41no—
202C22×D5—22no—
203C5×Q8—61no—
204C5×Q8—61no—
205C5×D4—42no—
206C5×D4—41no—
207C5×D4—41no—
208C5×D4—41no—
209C5×D4—41no—
210C2×C4×C5—61no—
211C2×C4×C5—61no—
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C2×Dic5—61no—
216C2×Dic5—61no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—242no—
223Dic10—61no—
224Dic10—61no—
225C5×C8—121no—
226#168—22no—
227#168—121no—
228C2×SD16—61no—
229C2×SD16—301no—
230C2×D8—102no—
231#127—51no—
232#127D3×D511yescharacteristic
233#124—301no—
234#124—301no—
235#123—302no—
236C4×Q8—31no—
237C4×Q8—151no—
238C4×D4—301no—
239C4×D4—301no—
240C4⋊C8—31no—
241C4⋊C8—151no—
242#102—61no—
243#102—301no—
244C4×C8—51no—
245C2×C3×C5—161no—
246C2×C3×C5#44911yescharacteristic
247C2×C3×C5#44911yescharacteristic
248C2×C3×C5#45311yescharacteristic
249C3×D5—82no—
250C23×C3—41no—
251C23×C3—102no—
252C3×D4—42no—
253C3×D4—41no—
254C3×D4—41no—
255C3×D4—41no—
256C3×D4—41no—
257C3×D4—202no—
258C3×D4—201no—
259C3×D4—201no—
260C3×D4—201no—
261C3×D4—201no—
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×C3×C4C2×C22⋊D511yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—101no—
268C2×Dic3—101no—
269C2×Dic3—402no—
270Dic6—21no—
271Dic6—21no—
272Dic6—101no—
273Dic6—101no—
274C3×C8—102no—
275C3⋊C8—41no—
276C3⋊C8—201no—
277C22×C5—81no—
278C22×C5—81no—
279C22×C5—81no—
280C22×C5#93711yescharacteristic
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—42no—
284C4×C5—21no—
285C4×C5—121no—
286C4×C5—121no—
287C4×C5#91111yescharacteristic
288C4×C5#91111yescharacteristic
289C4×C5#91211yescharacteristic
290C4×C5#91211yescharacteristic
291Dic5—121no—
292Dic5—121no—
293C2×Q8—31no—
294C2×Q8—151no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—52no—
299C2×D4—101no—
300C2×D4—101no—
301C22×C4—302no—
302SD16—122no—
303SD16—602no—
304D8—204no—
305C2×C8—61no—
306C2×C8—101no—
307C2×C8—301no—
308C4⋊C4—31no—
309C4⋊C4—61no—
310C4⋊C4—151no—
311C4⋊C4—301no—
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C42—61no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#162011yescharacteristic, complemented, Hall
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3—202no—
323C22×C3—202no—
324C22×C3—202no—
325C22×C3#408311yescharacteristic
326C3×C4—21no—
327C3×C4#406011yescharacteristic
328C3×C4#406211yescharacteristic
329C3×C4#407811yescharacteristic
330C3×C4#409611yescharacteristic
331Dic3—41no—
332Dic3—41no—
333Dic3—201no—
334Dic3—201no—
335C2×C5—161no—
336C2×C5#507711yescharacteristic
337C2×C5#515811yescharacteristic
338C2×C5#515811yescharacteristic
339D5—82no—
340C23—41no—
341C23—102no—
342Q8—61no—
343Q8—61no—
344Q8—301no—
345Q8—301no—
346D4—42no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—41no—
351D4—202no—
352D4—201no—
353D4—201no—
354D4—201no—
355D4—201no—
356C2×C4—61no—
357C2×C4—61no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—1202no—
361C2×C4D5×#6711yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4#679011yescharacteristic
364C8—102no—
365C8—121no—
366C8—601no—
367C2×C3—161no—
368C2×C3—402no—
369C2×C3#6532611yescharacteristic
370C2×C3#6546111yescharacteristic
371C2×C3#6548711yescharacteristic
372C5#7128411yescharacteristic, complemented, Sylow
373C22—81no—
374C22—81no—
375C22—81no—
376C22—202no—
377C22—202no—
378C22—202no—
379C22#9157711yescharacteristic
380C4—21no—
381C4—121no—
382C4—121no—
383C4—601no—
384C4—601no—
385C4#9149311yescharacteristic
386C4#9149411yescharacteristic
387C4#9149711yescharacteristic
388C4#9149811yescharacteristic
389C3#1060182411yescharacteristic, complemented, Sylow
390C2—161no—
391C2—402no—
392C2#1174915711yescharacteristic
393C2#1174915811yescharacteristic
394C2#1174916311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC3×#65362C2
hypercenter#127D3×D5
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #11752636C2semidirect
2. #11751176C2semidirect
3. C5×#5075C2semidirect
5. #11745852C2semidirect
6. #11745845C2semidirect
7. #11745843C2semidirect
62. #5075D5semidirect
318. C3×C5#1620semidirect
372. C5#71284semidirect
389. C3#10601824semidirect

Maximal subgroups

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

subgroupindex
#117526362
#117511762
C5×#50752
C3×#653622
#117458522
#117458452
#117458432
#106018243
#712845