Finite Group Databasebeta

← #14285277

Subgroups — #14285277

Order 1920.

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

normal subgroups only

This group has 456 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#11753425C211yesmaximal, characteristic
2#11751790C211yesmaximal, characteristic
3#11751790C211yesmaximal, characteristic
4#11746744C211yesmaximal, characteristic, complemented
5C3×#64873C211yesmaximal, characteristic, complemented
6#11746510C211yesmaximal, characteristic, complemented
7#11746509C211yesmaximal, characteristic, complemented
8#10604661—31nomaximal, Hall
9C2×D15⋊Q8—21no—
10C4⋊C4×D15C411yescharacteristic
11C5×#888C411yescharacteristic
12C3×#4034C2211yescharacteristic
13#91469C411yescharacteristic
14#91468C2211yescharacteristic
15#91437C411yescharacteristic
16#91404—21no—
17C4×#1200C2211yescharacteristic
18#91329—21no—
19#91327—21no—
20#91233C2211yescharacteristic
21#91233C2211yescharacteristic
22C3×#4004C2211yescharacteristic
23C3×#4004C2211yescharacteristic
24#91171—21no—
25#91171—21no—
26#91169—21no—
27#91169—21no—
28#68428—51nomaximal, Hall
29D5×C4⋊Q8—31no—
30#65684—31no—
31#65684—31no—
32#64873—31no—
33#64873—31no—
34#64873—31no—
35#64873D311yescharacteristic, complemented
36C2×C4×D15—21no—
37C2×C4×D15C2×C411yescharacteristic
38C2×C5×Dic6—21no—
39C2×C3×Dic10—21no—
40C2×#1204—21no—
41C2×#1204—21no—
42C2×#1200—21no—
43C2×#1200D411yescharacteristic
44C2×#1200D411yescharacteristic
45D15⋊Q8—42no—
46D15⋊Q8—42no—
47C2×C3⋊#170—21no—
48C2×C3⋊#170—21no—
49C2×C3×#170—21no—
50C2×C3×#170—21no—
51C3×C5×C4⋊C4C2×C411yescharacteristic
52C4⋊Dic15C2×C411yescharacteristic
53#6712—21no—
54C5×C4⋊Dic3C2×C411yescharacteristic
55C5×Dic3⋊C4—21no—
56C4×C5×Dic3C2×C411yescharacteristic
57C3×C4⋊Dic5C2×C411yescharacteristic
58C3×#683—21no—
59C3×C4×Dic5C2311yescharacteristic
60Dic3⋊Dic5—21no—
61#6669—21no—
62#6668—21no—
63Dic3×Dic5D411yescharacteristic
64Dic3×Dic5D411yescharacteristic
65D3×C4⋊Q8—51no—
66#4835—51no—
67#4835—51no—
68C3×#332—51no—
69#4547—51no—
70#4486—51no—
71#4482—51no—
72C2×Q8×D5—61no—
73C5×C4⋊Q8—31no—
74#4090—61no—
75D5×C4⋊C4—31no—
76D5×C4⋊C4—31no—
77D5×C4⋊C4—61no—
78#4034—31no—
79#4034—61no—
80#4034C2×D311yescharacteristic
81C42×D5—31no—
82#4015—31no—
83#4004—31no—
84#4004—31no—
85#4004C2×D311yescharacteristic
86#4004C2×D311yescharacteristic
87#4003—61no—
88#4003—61no—
89#4002—61no—
90#4002—61no—
91#1556—151noSylow
92C22×D15C22⋊C411yescharacteristic
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5C22×C411yescharacteristic
95C2×Dic15—21no—
96C2×Dic15C22⋊C411yescharacteristic
97C4×D15—22no—
98C4×D15—42no—
99C2×C5×Dic3—21no—
100C2×C5×Dic3C22⋊C411yescharacteristic
101C2×C5×Dic3C22⋊C411yescharacteristic
102C5×Dic6—42no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5C2×D411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×Dic10—41no—
107C3×Dic10—41no—
108#1204—42no—
109#1204—41no—
110#1204—41no—
111#1200—21no—
112#1200—21no—
113#1200—21no—
114#1200—21no—
115#1200—42no—
116C3⋊#170—41no—
117C3⋊#170—41no—
118C3×#170—41no—
119C3×#170—41no—
120C2×D3×Q8—101no—
121C3×C4⋊Q8—51no—
122#944—101no—
123D3×C4⋊C4—51no—
124D3×C4⋊C4—51no—
125D3×C4⋊C4—101no—
126#888—51no—
127#888—101no—
128#888AGL(1,𝔽5)11yescharacteristic
129C42×D3—51no—
130#869—51no—
131C3×C4⋊C8—51no—
132C3×C4⋊C8—51no—
133(C2×D3)⋊C8—101no—
134(C2×D3)⋊C8—101no—
135#815—101no—
136#815—101no—
137C4⋊(C3⋊C8)—51no—
138C4⋊(C3⋊C8)—51no—
139C2×C5×Q8—61no—
140Q8×D5—122no—
141Q8×D5—122no—
142C2×C4×D5—31no—
143C2×C4×D5—31no—
144C2×C4×D5—31no—
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C2×Dic10—21no—
148C2×Dic10—61no—
149C2×Dic10—61no—
150C2×#170—21no—
151C2×#170—21no—
152C2×#170—61no—
153C2×#170—61no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—61no—
156C5×C4⋊C4C4×D311yescharacteristic
157C42×C5—31no—
158C4⋊Dic5—31no—
159C4⋊Dic5—61no—
160C4⋊Dic5C4×D311yescharacteristic
161#683—21no—
162#683—61no—
163#683—61no—
164#683—61no—
165C4×Dic5—31no—
166C4×Dic5—31no—
167C4×Dic5C22×D311yescharacteristic
168C2×C4⋊Q8—151no—
169#432—151no—
170#432—151no—
171#332—51no—
172#332—151no—
173#332—151no—
174#332—151no—
175C22×C3×C5C2×C22⋊C411yescharacteristic
176C2×D15—21no—
177C2×D15—21no—
178C2×D15#10112yes—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181Dic15—21no—
182Dic15—41no—
183C3×Dic5—41no—
184C3×Dic5AGL(1,ℤ/8)11yescharacteristic
185C3×Dic5AGL(1,ℤ/8)11yescharacteristic
186C3×Dic5#13711yescharacteristic
187C3×Dic5#13711yescharacteristic
188C5×Dic3—21no—
189C5×Dic3—21no—
190C5×Dic3—41no—
191C2×C3×Q8—101no—
192D3×Q8—202no—
193D3×Q8—202no—
194C2×C4×D3—51no—
195C2×C4×D3—51no—
196C2×C4×D3—51no—
197C2×C4×D3—101no—
198C2×C4×D3—101no—
199C2×Dic6—21no—
200C2×Dic6—101no—
201C2×Dic6—101no—
202C2×C3×C8—101no—
203C2×C3×C8—101no—
204C3×C4⋊C4—51no—
205C3×C4⋊C4—101no—
206C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
207C3×C42—51no—
208C4⋊Dic3—51no—
209C4⋊Dic3—101no—
210C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
211Dic3⋊C4—21no—
212Dic3⋊C4—101no—
213Dic3⋊C4—101no—
214Dic3⋊C4—101no—
215C4×Dic3—51no—
216C4×Dic3—51no—
217C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
218C2×C3⋊C8—101no—
219C2×C3⋊C8—101no—
220C22×D5—31no—
221C5×Q8—122no—
222C2×C4×C5—21no—
223C2×C4×C5—31no—
224C2×C4×C5—31no—
225C2×C4×C5—61no—
226C2×C4×C5C2×C4×D311yescharacteristic
227C2×Dic5—21no—
228C2×Dic5—31no—
229C2×Dic5—61no—
230C2×Dic5D3×D411yescharacteristic
231C2×Dic5D3×D411yescharacteristic
232C4×D5—62no—
233C4×D5—61no—
234C4×D5—61no—
235C4×D5—61no—
236C4×D5—61no—
237C4×D5—122no—
238C4×D5—122no—
239Dic10—41no—
240Dic10—41no—
241Dic10—122no—
242Dic10—121no—
243Dic10—121no—
244#170—41no—
245#170—41no—
246#170—121no—
247#170—121no—
248C22×Q8—301no—
249C4⋊Q8—31no—
250C4⋊Q8—51no—
251C4⋊Q8—151no—
252C4⋊Q8—151no—
253C4⋊Q8—301no—
254C4⋊Q8—301no—
255C2×C4⋊C4—151no—
256C2×C4⋊C4—151no—
257C2×C4⋊C4—301no—
258C2×C42—151no—
259C4⋊C8—51no—
260C4⋊C8—51no—
261C4⋊C8—151no—
262C4⋊C8—151no—
263C22⋊C8—301no—
264C22⋊C8—301no—
265#97—301no—
266#97—301no—
267C2×C3×C5C2×#10111yescharacteristic
268C2×C3×C5#41811yescharacteristic
269C2×C3×C5#41911yescharacteristic
270D15—22no—
271C22×D3—51no—
272C3×Q8—201no—
273C3×Q8—201no—
274C2×C3×C4—21no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—101no—
278C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
279C2×Dic3—21no—
280C2×Dic3—51no—
281C2×Dic3—101no—
282C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
283C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
284C4×D3—101no—
285C4×D3—101no—
286C4×D3—101no—
287C4×D3—101no—
288C4×D3—102no—
289C4×D3—202no—
290C4×D3—202no—
291Dic6—42no—
292Dic6—202no—
293Dic6—201no—
294Dic6—201no—
295C3×C8—201no—
296C3×C8—201no—
297C3⋊C8—201no—
298C3⋊C8—201no—
299C22×C5D3×C22⋊C411yescharacteristic
300C2×D5—32no—
301C2×D5—61no—
302C2×D5—61no—
303C4×C5—21no—
304C4×C5—41no—
305C4×C5—61no—
306C4×C5—61no—
307C4×C5—121no—
308Dic5—41no—
309Dic5—61no—
310Dic5—121no—
311Dic5#91111yescharacteristic
312Dic5#91411yescharacteristic
313Dic5#91511yescharacteristic
314Dic5#91811yescharacteristic
315C2×Q8—61no—
316C2×Q8—101no—
317C2×Q8—301no—
318C2×Q8—301no—
319C2×Q8—602no—
320C2×Q8—602no—
321C22×C4—151no—
322C22×C4—151no—
323C22×C4—151no—
324C22×C4—301no—
325C22×C4—301no—
326C2×C8—101no—
327C2×C8—101no—
328C2×C8—301no—
329C2×C8—301no—
330C4⋊C4—31no—
331C4⋊C4—51no—
332C4⋊C4—61no—
333C4⋊C4—101no—
334C4⋊C4—151no—
335C4⋊C4—301no—
336C4⋊C4—301no—
337C4⋊C4—301no—
338C4⋊C4—301no—
339C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
340C42—31no—
341C42—51no—
342C42—151no—
343C42—151no—
344C3×C5#155611yescharacteristic, complemented, Hall
345C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
346C2×D3—52no—
347C2×D3—101no—
348C2×D3—101no—
349C3×C4—21no—
350C3×C4—41no—
351C3×C4—51no—
352C3×C4—51no—
353C3×C4—51no—
354C3×C4—51no—
355C3×C4—201no—
356Dic3—21no—
357Dic3—21no—
358Dic3—41no—
359Dic3—101no—
360Dic3—201no—
361C2×C5D3×#10111yescharacteristic
362C2×C5#477011yescharacteristic
363C2×C5#480211yescharacteristic
364D5—62no—
365C23—151no—
366Q8—122no—
367Q8—201no—
368Q8—201no—
369Q8—601no—
370Q8—601no—
371Q8—602no—
372C2×C4—21no—
373C2×C4—31no—
374C2×C4—31no—
375C2×C4—51no—
376C2×C4—51no—
377C2×C4—61no—
378C2×C4—101no—
379C2×C4—151no—
380C2×C4—302no—
381C2×C4—301no—
382C2×C4—301no—
383C2×C4—301no—
384C2×C4—301no—
385C2×C4—301no—
386C2×C4—602no—
387C2×C4—602no—
388C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
389C8—201no—
390C8—201no—
391C8—601no—
392C8—601no—
393C2×C3#6576711yescharacteristic
394C2×C3#6578211yescharacteristic
395C2×C3D5⋊#10111yescharacteristic
396D3—102no—
397C5#6842811yescharacteristic, complemented, Sylow
398C22—152no—
399C22—301no—
400C22—301no—
401C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
402C4—21no—
403C4—41no—
404C4—51no—
405C4—51no—
406C4—51no—
407C4—51no—
408C4—61no—
409C4—61no—
410C4—121no—
411C4—201no—
412C4—301no—
413C4—601no—
414C3#1060466111yescharacteristic, complemented, Sylow
415C2—302no—
416C2#1175191811yescharacteristic
417C2#1175193811yescharacteristic
418C2#1175196211yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1556
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746744C2semidirect
5. C3×#64873C2semidirect
6. #11746510C2semidirect
7. #11746509C2semidirect
35. #64873D3semidirect
344. C3×C5#1556semidirect
397. C5#68428semidirect
414. C3#10604661semidirect

Maximal subgroups

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

subgroupindex
#117534252
#117517902
#117467442
C3×#648732
#117465102
#117465092
#106046613
#684285