Finite Group Databasebeta

← #14289440

Subgroups — #14289440

Order 1920.

512 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 88 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#11752554C211yesmaximal, characteristic
2#11751192C211yesmaximal, characteristic, complemented
3C5×#5084C211yesmaximal, characteristic, complemented
4C3×#65374C211yesmaximal, characteristic, complemented
5#11745852C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic, complemented
8#10601934—31nomaximal, Hall
9C2×#6765—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C4×Dic30C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C2×C3×#688—22no—
14C3×#4020C2211yescharacteristic
15#91463—21no—
16#91456—21no—
17#91434—21no—
18#91408—22no—
19#91094—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×#809—21no—
23C5×#808—21no—
24C5×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×#168C2211yescharacteristic
26#71271—51nomaximal, Hall
27#65887—31no—
28C5×#476—31no—
29#65380—31no—
30#65374D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20D412yes—
41C2×#1201—22no—
42C2×#1201—22no—
43C2×D5×Dic3—22no—
44#6765—42no—
45#6765—42no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C42×C5C2311yescharacteristic
49C4⋊Dic15D411yescharacteristic
50#6712—21no—
51C4×Dic15—21no—
52C2×C3⋊#168—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×C4⋊Dic3D411yescharacteristic
55C2×C5×C3⋊C8—21no—
56C3×#688—44no—
57C2×C3×#168—21no—
58#6665—22no—
59#5718—51no—
60C3×#492—51no—
61#5091—51no—
62#5084D511yescharacteristic, complemented
63#4544—51no—
64#4459—51no—
65#4456—51no—
66C2×#709—61no—
67C5×C4⋊Q8C2×D311yescharacteristic
68C4×C5×D4—31no—
69C2×#688—22no—
70#4086—61no—
71#4076—61no—
72#4039—61no—
73#4030—62no—
74#4020C2×D311yescharacteristic
75C4×Dic10—31no—
76C5×#106—61no—
77C5×C4⋊C8—31no—
78C5×#102—61no—
79#3942—61no—
80#3939—61no—
81C4⋊#168—31no—
82C4×#168C2×D311yescharacteristic
83#1631—151noSylow
84C22×C5×D3—21no—
85C22×C3×D5—22no—
86C3×C5×Q8—42no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93Dic30—21no—
94Dic30SD1612yescomplemented
95C2×C5×Dic3—21no—
96C5×D12—21no—
97C5×D12—21no—
98C4×C5×D3—41no—
99C4×C5×D3—41no—
100C3×D20—42no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104C3×D20—41no—
105#1201—44no—
106#1201—82no—
107D5×Dic3—44no—
108C3⋊#168—41no—
109C3×#168—22no—
110C5×C3⋊C8—41no—
111C2×#237—101no—
112C2×C3×SD16—102no—
113C3×C4⋊Q8C2×D511yescharacteristic
114C3×#127—51no—
115#940—101no—
116#939—102no—
117#938—101no—
118D4×Dic3—101no—
119C4×D12C2×D511yescharacteristic
120C4×Dic6—51no—
121C3×C4×C8—51no—
122#810—101no—
123#809—21no—
124#808—21no—
125#807—101no—
126C4⋊(C3⋊C8)—51no—
127C4⋊(C3⋊C8)C2×D511yescharacteristic
128C2×C5×Q8—21no—
129C2×C5×D4—31no—
130C22×C4×C5—61no—
131C2×C22⋊D5—62no—
132C2×C22⋊D5—62no—
133#709—122no—
134#709—122no—
135C2×D20—21no—
136C2×D20—21no—
137C2×D20#6712yes—
138C2×C4×D5—62no—
139C2×Dic10—31no—
140C2×C5×C8—61no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—61no—
145C42×C5C22×D311yescharacteristic
146#688—44no—
147#685—62no—
148C4⋊Dic5—31no—
149#683—61no—
150C4×Dic5—61no—
151C2×#168—21no—
152C2×#168—61no—
153#550—151no—
154#492—51no—
155#477—151no—
156#476—31no—
157#331—151no—
158Q8⋊C8—151no—
159D4⋊C8—151no—
160C22×C3×C5#12011yescharacteristic
161C2×C5×D3—41no—
162C2×C5×D3—41no—
163C2×C5×D3—41no—
164C2×C3×D5—42no—
165C2×C3×D5—42no—
166C2×C3×D5—42no—
167C3×C4×C5—21no—
168C3×C4×C5—81no—
169C3×C4×C5C2×SD1611yescharacteristic
170C3×C4×C5#13511yescharacteristic
171C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C3×C4×C5#13711yescharacteristic
173Dic15—22no—
174Dic15—41no—
175C5×Dic3—41no—
176C2×C3×Q8—21no—
177C2×C3×D4—52no—
178C2×C3×D4—101no—
179C2×C3×D4—101no—
180C2×#67—102no—
181C2×#67—102no—
182C22×Dic3—102no—
183#237—202no—
184#237—202no—
185C2×D12C22⋊D511yescharacteristic
186C2×C4×D3—21no—
187C2×Dic6—51no—
188C3×SD16—204no—
189C2×C3×C8—101no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C42C22×D511yescharacteristic
193#217—102no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3—51no—
196C4⋊Dic3C22⋊D511yescharacteristic
197Dic3⋊C4—101no—
198C4×Dic3—101no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—101no—
201C23×C5—61no—
202C22×D5—22no—
203C5×Q8—42no—
204C5×D4—61no—
205C5×D4—61no—
206C2×C4×C5—41no—
207C2×C4×C5—61no—
208C2×C4×C5—121no—
209C2×C4×C5—121no—
210C2×C4×C5D3×D411yescharacteristic
211C2×C4×C5D3×D411yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—242no—
215C2×Dic5—61no—
216C2×Dic5—61no—
217D20—42no—
218D20—41no—
219D20—41no—
220D20—41no—
221D20—41no—
222C4×D5—124no—
223Dic10—32no—
224Dic10—61no—
225C5×C8—121no—
226#168—22no—
227#168—121no—
228C2×#41—301no—
229C2×SD16—102no—
230C4⋊Q8D3×D511yescharacteristic
231#127—51no—
232#127—301no—
233#121—302no—
234#121—301no—
235C4×Q8—151no—
236C4×D4—31no—
237C4×D4—301no—
238#107—301no—
239#106—61no—
240C4⋊C8—31no—
241C4⋊C8—151no—
242#103—301no—
243#102—61no—
244C4×C8—51no—
245C2×C3×C5#45011yescharacteristic
246C2×C3×C5#45211yescharacteristic
247C2×C3×C5#45311yescharacteristic
248C3×D5—82no—
249C5×D3—81no—
250C23×C3—102no—
251C22×D3—21no—
252C3×Q8—42no—
253C3×D4—202no—
254C3×D4—201no—
255C3×D4—201no—
256C3×D4—201no—
257C3×D4—201no—
258C2×C3×C4—41no—
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4C2×C22⋊D511yescharacteristic
262#67—204no—
263#67—402no—
264C2×Dic3—21no—
265C2×Dic3—101no—
266C2×Dic3—101no—
267C2×Dic3—204no—
268D12—21no—
269D12—21no—
270C4×D3—41no—
271C4×D3—41no—
272Dic6—52no—
273Dic6—101no—
274C3×C8—102no—
275C3⋊C8—41no—
276C3⋊C8—201no—
277C22×C5—121no—
278C22×C5—121no—
279C22×C5—121no—
280C22×C5#93711yescharacteristic
281C2×D5—42no—
282C2×D5—42no—
283C2×D5—42no—
284C4×C5—21no—
285C4×C5—81no—
286C4×C5—121no—
287C4×C5D3×SD1611yescharacteristic
288C4×C5#91411yescharacteristic
289C4×C5#91511yescharacteristic
290C4×C5#91611yescharacteristic
291Dic5—62no—
292Dic5—121no—
293#41—602no—
294#41—602no—
295C2×Q8—21no—
296C2×Q8—151no—
297C2×D4—31no—
298C2×D4—52no—
299C2×D4—101no—
300C2×D4—101no—
301C2×D4—302no—
302C2×D4—302no—
303C22×C4—61no—
304C22×C4—302no—
305SD16—204no—
306C2×C8—61no—
307C2×C8—101no—
308C2×C8—301no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—31no—
312C4⋊C4—151no—
313C4⋊C4—301no—
314C22⋊C4—61no—
315C22⋊C4—302no—
316C42—301no—
317C42C2×D3×D511yescharacteristic
318C3×C5#163111yescharacteristic, complemented, Hall
319C22×C3—202no—
320C22×C3—202no—
321C22×C3—202no—
322C22×C3#408311yescharacteristic
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C3×C4—21no—
327C3×C4—81no—
328C3×C4D5×SD1611yescharacteristic
329C3×C4#406011yescharacteristic
330C3×C4#408811yescharacteristic
331C3×C4#409611yescharacteristic
332Dic3—41no—
333Dic3—102no—
334Dic3—201no—
335C2×C5—241no—
336C2×C5#507711yescharacteristic
337C2×C5#516911yescharacteristic
338C2×C5#517311yescharacteristic
339D5—82no—
340C23—61no—
341C23—102no—
342Q8—42no—
343Q8—152no—
344Q8—301no—
345D4—61no—
346D4—61no—
347D4—202no—
348D4—201no—
349D4—201no—
350D4—201no—
351D4—201no—
352D4—604no—
353D4—1202no—
354C2×C4—41no—
355C2×C4—61no—
356C2×C4—121no—
357C2×C4—121no—
358C2×C4—301no—
359C2×C4—301no—
360C2×C4—604no—
361C2×C4D5×#6711yescharacteristic
362C2×C4D3×C22⋊D511yescharacteristic
363C2×C4#679011yescharacteristic
364C8—102no—
365C8—121no—
366C8—601no—
367C2×C3—402no—
368C2×C3#6533611yescharacteristic
369C2×C3#6545811yescharacteristic
370C2×C3#6548711yescharacteristic
371D3—81no—
372C5#7127111yescharacteristic, complemented, Sylow
373C22—121no—
374C22—121no—
375C22—121no—
376C22—202no—
377C22—202no—
378C22—202no—
379C22#9157711yescharacteristic
380C4—21no—
381C4—81no—
382C4—121no—
383C4—302no—
384C4—601no—
385C4#9150511yescharacteristic
386C4#9150611yescharacteristic
387C4#9151711yescharacteristic
388C4#9151811yescharacteristic
389C3#1060193411yescharacteristic, complemented, Sylow
390C2—241no—
391C2—402no—
392C2#1174916311yescharacteristic
393C2#1174939911yescharacteristic
394C2#1174940311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radical#11752554C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1631
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751192C2semidirect
3. C5×#5084C2semidirect
4. C3×#65374C2semidirect
5. #11745852C2semidirect
6. #11745845C2semidirect
7. #11745837C2semidirect
30. #65374D3semidirect
62. #5084D5semidirect
94. Dic30SD16semidirect
318. C3×C5#1631semidirect
372. C5#71271semidirect
389. C3#10601934semidirect

Maximal subgroups

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

subgroupindex
#117525542
#117511922
C5×#50842
C3×#653742
#117458522
#117458452
#117458372
#106019343
#712715