Finite Group Databasebeta

← #14281906

Subgroups — #14281906

Order 1920.

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

normal subgroups only

This group has 424 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#11753549C211yesmaximal, characteristic
2#11751797C211yesmaximal, characteristic, complemented
3#11751777C211yesmaximal, characteristic, complemented
4#11746743C211yesmaximal, characteristic, complemented
5C3×#64872C211yesmaximal, characteristic, complemented
6#11746491C211yesmaximal, characteristic, complemented
7#11746490C211yesmaximal, characteristic, complemented
8#10604580—31nomaximal, Hall
9#91784C411yescharacteristic
10C5×#890C411yescharacteristic
11C3×#4033C2211yescharacteristic
12#91433—21no—
13#91418—21no—
14#91418C2211yescharacteristic
15#91402—21no—
16C4×#1200C2211yescharacteristic
17#91390C411yescharacteristic
18#91374C411yescharacteristic
19#91337—21no—
20C4⋊(C3⋊#170)C2211yescharacteristic
21C4×C3⋊#170C2211yescharacteristic
22C3×C4⋊#170C2211yescharacteristic
23C3×C4×#170C2211yescharacteristic
24Dic3⋊#170—21no—
25#91171—21no—
26#91171—21no—
27Dic3×#170—21no—
28#68233—51nomaximal, Hall
29#66025—31no—
30#65680—31no—
31#65680—31no—
32#64872—31no—
33#64872D311yescharacteristic, complemented
34#64871—31no—
35#64871—31no—
36C2×D60—21no—
37C2×D60C2×C411yescharacteristic
38C2×C4×D15C2×C411yescharacteristic
39C2×C3×Dic10C2×C411yescharacteristic
40C2×#1200—21no—
41C2×#1200D411yescharacteristic
42C2×#1200D411yescharacteristic
43C2×C3⋊#170—21no—
44C2×C3⋊#170—21no—
45C2×C3×#170—21no—
46C2×C3×#170—21no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48#6714—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3C2×C411yescharacteristic
51C5×Dic3⋊C4—21no—
52C4×C5×Dic3C2×C411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5C2311yescharacteristic
56Dic3⋊Dic5—21no—
57#6667—21no—
58#6667—21no—
59#6667—21no—
60#6667—21no—
61Dic3×Dic5D411yescharacteristic
62Dic3×Dic5D411yescharacteristic
63#5580—51no—
64#4833—51no—
65#4685—51no—
66C3×Q8⋊C8—51no—
67#4535—51no—
68#4483—51no—
69#4459—51no—
70C5×#125—31no—
71#4044—61no—
72#4043—31no—
73#4041—31no—
74#4040—61no—
75#4039—31no—
76#4039—61no—
77#4038—61no—
78#4033C2×D311yescharacteristic
79#4021—31no—
80C42×D5—31no—
81#4003—61no—
82#4003—61no—
83C4⋊#170—31no—
84C4⋊#170—61no—
85C4⋊#170C2×D311yescharacteristic
86C4×#170—31no—
87C4×#170—61no—
88C4×#170C2×D311yescharacteristic
89#1482—151noSylow
90C22×D15—21no—
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×Dic15C22⋊C411yescharacteristic
95D60—21no—
96D60—21no—
97D60—42no—
98C4×D15—21no—
99C4×D15—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C2×C3×Dic5—21no—
104C2×C3×Dic5C2×D411yescharacteristic
105C2×C3×Dic5C2×D411yescharacteristic
106C3×Dic10—21no—
107C3×Dic10—21no—
108#1200—21no—
109#1200—21no—
110#1200—41no—
111#1200—41no—
112#1200—41no—
113C3⋊#170—41no—
114C3⋊#170—41no—
115C3×#170—41no—
116C3×#170—41no—
117C3×C4×Q8—51no—
118#947—51no—
119#946—51no—
120#898—101no—
121#895—51no—
122#894—101no—
123#890AGL(1,𝔽5)11yescharacteristic
124C4×D12—51no—
125C4×D12—101no—
126#872—101no—
127C42×D3—51no—
128C3×C4⋊C8—51no—
129C3×C4×C8—51no—
130(C2×D3)⋊C8—101no—
131(C2×D3)⋊C8—101no—
132Dic3⋊C8—101no—
133C8×Dic3—101no—
134C4⋊(C3⋊C8)—51no—
135C4×C3⋊C8—51no—
136C2×D20—31no—
137C2×D20—61no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5—61no—
142C2×Dic10C4×D311yescharacteristic
143C2×#170—21no—
144C2×#170—21no—
145C2×#170—61no—
146C2×#170—61no—
147C5×C4⋊C4—31no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—61no—
150C5×C4⋊C4C4×D311yescharacteristic
151C42×C5—31no—
152#685—61no—
153#685—61no—
154#685—61no—
155#685—61no—
156#685—61no—
157C4⋊Dic5—61no—
158#683—21no—
159C4×Dic5—21no—
160C4×Dic5—31no—
161C4×Dic5—31no—
162C4×Dic5C22×D311yescharacteristic
163#529—151no—
164#431—151no—
165#431—151no—
166Q8⋊C8—51no—
167Q8⋊C8—151no—
168D4⋊C8—151no—
169D4⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C2×D15—41no—
175C2×D15—41no—
176C2×D15—41no—
177C3×C4×C5—41no—
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5#13111yescharacteristic
180Dic15—21no—
181C3×Dic5—21no—
182C3×Dic5—41no—
183C3×Dic5#13511yescharacteristic
184C3×Dic5#13511yescharacteristic
185C5×Dic3—21no—
186C5×Dic3—21no—
187C5×Dic3—41no—
188C2×C3×Q8—51no—
189C2×D12—51no—
190C2×D12—101no—
191C2×C4×D3—51no—
192C2×C4×D3—51no—
193C2×C4×D3—51no—
194C2×C4×D3—101no—
195C2×C3×C8—101no—
196C2×C3×C8—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
199C3×C42—51no—
200C3×C42—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206C4⋊Dic3—21no—
207C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
208Dic3⋊C4—21no—
209Dic3⋊C4—101no—
210C4×Dic3—51no—
211C4×Dic3—51no—
212C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C22×D5—31no—
216C22×D5—61no—
217C2×C4×C5—21no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—61no—
221C2×C4×C5C2×C4×D311yescharacteristic
222C2×Dic5—21no—
223C2×Dic5—31no—
224C2×Dic5D3×D411yescharacteristic
225C2×Dic5D3×D411yescharacteristic
226D20—61no—
227D20—61no—
228D20—122no—
229C4×D5—61no—
230C4×D5—61no—
231C4×D5—61no—
232C4×D5—61no—
233C4×D5—121no—
234C4×D5—121no—
235C4×D5—121no—
236Dic10—21no—
237Dic10—21no—
238#170—41no—
239#170—41no—
240#170—121no—
241#170—121no—
242#126—301no—
243#125—31no—
244#124—151no—
245#123—301no—
246C22⋊Q8—151no—
247#121—151no—
248C4×Q8—51no—
249C4×D4—151no—
250C4×D4—301no—
251#117—301no—
252C2×C42—151no—
253C4⋊C8—51no—
254C4⋊C8—151no—
255C4⋊C8—301no—
256C22⋊C8—301no—
257C22⋊C8—301no—
258C4×C8—51no—
259C4×C8—151no—
260C4×C8—301no—
261C2×C3×C5#40811yescharacteristic
262C2×C3×C5#41611yescharacteristic
263C2×C3×C5#42111yescharacteristic
264D15—41no—
265D15—81no—
266C22×D3—51no—
267C22×D3—101no—
268C3×Q8—101no—
269C3×Q8—101no—
270C2×C3×C4—21no—
271C2×C3×C4—51no—
272C2×C3×C4—51no—
273C2×C3×C4—101no—
274C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
275C2×Dic3—21no—
276C2×Dic3—51no—
277C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
278C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
279D12—101no—
280D12—101no—
281D12—202no—
282C4×D3—101no—
283C4×D3—101no—
284C4×D3—101no—
285C4×D3—101no—
286C4×D3—201no—
287C4×D3—201no—
288C4×D3—201no—
289C3×C8—201no—
290C3×C8—201no—
291C3⋊C8—201no—
292C3⋊C8—201no—
293C22×C5D3×C22⋊C411yescharacteristic
294C2×D5—61no—
295C2×D5—61no—
296C2×D5—61no—
297C2×D5—121no—
298C2×D5—121no—
299C2×D5—121no—
300C4×C5—41no—
301C4×C5—61no—
302C4×C5—61no—
303C4×C5—121no—
304C4×C5#90111yescharacteristic
305C4×C5#90711yescharacteristic
306Dic5—21no—
307Dic5—41no—
308Dic5—61no—
309Dic5#91611yescharacteristic
310Dic5#91911yescharacteristic
311C2×Q8—51no—
312C2×D4—151no—
313C2×D4—301no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C22×C4—301no—
318C2×C8—101no—
319C2×C8—101no—
320C2×C8—301no—
321C2×C8—301no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—101no—
326C4⋊C4—301no—
327C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
328C22⋊C4—301no—
329C22⋊C4—301no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C22⋊C4—301no—
333C42—31no—
334C42—51no—
335C42—101no—
336C42—151no—
337C42—151no—
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
340C2×D3—101no—
341C2×D3—101no—
342C2×D3—101no—
343C2×D3—201no—
344C2×D3—201no—
345C2×D3—201no—
346C3×C4—41no—
347C3×C4—51no—
348C3×C4—51no—
349C3×C4—101no—
350C3×C4—201no—
351C3×C4#413311yescharacteristic
352C3×C4#413311yescharacteristic
353Dic3—21no—
354Dic3—21no—
355Dic3—41no—
356Dic3—101no—
357C2×C5#472711yescharacteristic
358C2×C5#480411yescharacteristic
359C2×C5#482111yescharacteristic
360D5—121no—
361D5—241no—
362C23—151no—
363C23—301no—
364Q8—101no—
365Q8—101no—
366D4—301no—
367D4—301no—
368D4—602no—
369C2×C4—21no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—61no—
375C2×C4—101no—
376C2×C4—151no—
377C2×C4—301no—
378C2×C4—301no—
379C2×C4—301no—
380C2×C4—301no—
381C2×C4—601no—
382C2×C4—601no—
383C2×C4—601no—
384C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
385C8—201no—
386C8—201no—
387C8—601no—
388C8—601no—
389C2×C3#6578711yescharacteristic
390C2×C3#6579411yescharacteristic
391C2×C3#6579511yescharacteristic
392D3—201no—
393D3—401no—
394C5#6823311yescharacteristic, complemented, Sylow
395C22—301no—
396C22—301no—
397C22—301no—
398C22—601no—
399C22—601no—
400C22—601no—
401C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
402C4—41no—
403C4—51no—
404C4—51no—
405C4—61no—
406C4—61no—
407C4—101no—
408C4—121no—
409C4—201no—
410C4—301no—
411C4#9191411yescharacteristic
412C4#9191611yescharacteristic
413C3#1060458011yescharacteristic, complemented, Sylow
414C2—601no—
415C2—1201no—
416C2#1175190011yescharacteristic
417C2#1175194911yescharacteristic
418C2#1175197111yescharacteristic
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 radical#91784C4
cosocleC3×C4×Dic5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1482
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751797C2semidirect
3. #11751777C2semidirect
4. #11746743C2semidirect
5. C3×#64872C2semidirect
6. #11746491C2semidirect
7. #11746490C2semidirect
33. #64872D3semidirect
338. C3×C5#1482semidirect
394. C5#68233semidirect
413. C3#10604580semidirect

Maximal subgroups

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

subgroupindex
#117535492
#117517972
#117517772
#117467432
C3×#648722
#117464912
#117464902
#106045803
#682335