Finite Group Databasebeta

← #14281847

Subgroups — #14281847

Order 1920.

432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 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#11753464C211yesmaximal, characteristic
2#11751901C211yesmaximal, characteristic
3#11751797C211yesmaximal, characteristic
4#11746743C211yesmaximal, characteristic, complemented
5C3×#64872C211yesmaximal, characteristic, complemented
6#11746495C211yesmaximal, characteristic, complemented
7#11746494C211yesmaximal, characteristic, complemented
8#10604646—31nomaximal, Hall
9C2×#6738—21no—
10#91786C411yescharacteristic
11C5×#888C411yescharacteristic
12C3×#4033C2211yescharacteristic
13#91424—21no—
14#91402—21no—
15C4×#1200C2211yescharacteristic
16#91390C411yescharacteristic
17#91389C411yescharacteristic
18#91343—21no—
19#91333C2211yescharacteristic
20Dic5×Dic6—21no—
21C4⋊(C3⋊#170)C2211yescharacteristic
22C4×C3⋊#170C2211yescharacteristic
23C3×C4⋊#170C2211yescharacteristic
24C3×C4×#170C2211yescharacteristic
25#91177—21no—
26Dic3⋊#170—21no—
27#91171—21no—
28#68232—51nomaximal, Hall
29#66062—31no—
30#65680—31no—
31D5⋊(C4⋊C8)—31no—
32#64872—31no—
33#64872—31no—
34#64872—31no—
35#64872D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×Dic30C2×C411yescharacteristic
38C2×C5×Dic6—21no—
39C2×C3×Dic10C2×C411yescharacteristic
40C2×#1200D411yescharacteristic
41C2×#1200D411yescharacteristic
42C2×C3⋊#170—21no—
43C2×C3⋊#170—21no—
44C2×C3×#170—21no—
45C2×C3×#170—21no—
46#6738—42no—
47C3×C5×C4⋊C4C2×C411yescharacteristic
48#6714—21no—
49C4⋊Dic15—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—
57Dic3⋊Dic5—21no—
58Dic3⋊Dic5—21no—
59#6669—21no—
60#6667—21no—
61Dic3×Dic5—21no—
62Dic3×Dic5D411yescharacteristic
63Dic3×Dic5D411yescharacteristic
64#5578—51no—
65D3×C4⋊C8—51no—
66#4685—51no—
67C3×Q8⋊C8—51no—
68#4535—51no—
69#4484—51no—
70#4456—51no—
71C2×D5⋊C8—61no—
72C5×C4⋊Q8—31no—
73#4092—61no—
74Q8×Dic5—61no—
75#4043—31no—
76#4043—31no—
77#4038—61no—
78#4036—61no—
79#4033—31no—
80#4033C2×D311yescharacteristic
81C42×D5—31no—
82#4015—31no—
83#4004—61no—
84#4003—61no—
85C4⋊#170—31no—
86C4⋊#170—61no—
87C4⋊#170C2×D311yescharacteristic
88C4×#170—31no—
89C4×#170C2×D311yescharacteristic
90#1481—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5C22×C411yescharacteristic
94C2×Dic15—21no—
95C2×Dic15C22⋊C411yescharacteristic
96C4×D15—21no—
97C4×D15—21no—
98Dic30—21no—
99Dic30—21no—
100C2×C5×Dic3—21no—
101C2×C5×Dic3C22⋊C411yescharacteristic
102C2×C5×Dic3C22⋊C411yescharacteristic
103C5×Dic6—42no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5C2×D411yescharacteristic
106C2×C3×Dic5C2×D411yescharacteristic
107C3×Dic10—21no—
108C3×Dic10—21no—
109#1200—41no—
110#1200SD1612yes—
111#1200Q1612yes—
112C3⋊#170—41no—
113C3⋊#170—41no—
114C3×#170—41no—
115C3×#170—41no—
116C3×C4×Q8—51no—
117#946—51no—
118#944—51no—
119C2×D3×C8—101no—
120#897—51no—
121#896—101no—
122#889—101no—
123#888AGL(1,𝔽5)11yescharacteristic
124#872—101no—
125C42×D3—51no—
126C4×Dic6—51no—
127C4×Dic6—101no—
128C3×C4⋊C8—51no—
129C3×C4×C8—51no—
130(C2×D3)⋊C8—101no—
131Dic3⋊C8—101no—
132Dic3⋊C8—101no—
133C4⋊(C3⋊C8)—51no—
134C4×C3⋊C8—51no—
135C2×C5×Q8—61no—
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×Dic10—31no—
140C2×Dic10C4×D311yescharacteristic
141C2×#170—21no—
142C2×#170—21no—
143C2×#170—61no—
144C2×#170—61no—
145D5⋊C8—122no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4C4×D311yescharacteristic
149C42×C5—31no—
150#685—61no—
151#685—61no—
152C4⋊Dic5—61no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156#683—21no—
157#683—61no—
158C4×Dic5—21no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—61no—
162C4×Dic5C22×D311yescharacteristic
163#533—151no—
164#431—151no—
165C2×C4⋊C8—151no—
166Q8⋊C8—51no—
167Q8⋊C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15#10312yes—
174C3×C4×C5—41no—
175C3×C4×C5#13111yescharacteristic
176C3×C4×C5#13111yescharacteristic
177Dic15—21no—
178Dic15—41no—
179C3×Dic5—21no—
180C3×Dic5—41no—
181C3×Dic5C2×SD1611yescharacteristic
182C3×Dic5C2×Q1611yescharacteristic
183C5×Dic3—21no—
184C5×Dic3—41no—
185C5×Dic3#10312yes—
186C2×C3×Q8—51no—
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×Dic6—21no—
191C2×Dic6—51no—
192C2×C3×C8—101no—
193C2×C3×C8—101no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
196C3×C42—51no—
197C3×C42—101no—
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—101no—
201C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207C4×Dic3—51no—
208C4×Dic3—51no—
209C4×Dic3—101no—
210C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
211C2×C3⋊C8—101no—
212C2×C3⋊C8—101no—
213D3×C8—202no—
214C22×D5—31no—
215C5×Q8—122no—
216C2×C4×C5—21no—
217C2×C4×C5—31no—
218C2×C4×C5—31no—
219C2×C4×C5—61no—
220C2×C4×C5C2×C4×D311yescharacteristic
221C2×Dic5—21no—
222C2×Dic5—31no—
223C2×Dic5—61no—
224C2×Dic5D3×D411yescharacteristic
225C2×Dic5D3×D411yescharacteristic
226C4×D5—32no—
227C4×D5—32no—
228C4×D5—61no—
229C4×D5—61no—
230C4×D5—121no—
231Dic10—21no—
232Dic10—21no—
233Dic10—61no—
234Dic10—61no—
235#170—41no—
236#170—41no—
237#170—121no—
238#170—121no—
239C22×C8—301no—
240C4⋊Q8—31no—
241C4⋊Q8—151no—
242#125—301no—
243C22⋊Q8—151no—
244C22⋊Q8—151no—
245C22⋊Q8—301no—
246C4×Q8—51no—
247C4×Q8—151no—
248C4×Q8—301no—
249#117—301no—
250C2×C42—151no—
251C4⋊C8—51no—
252C4⋊C8—151no—
253C4⋊C8—301no—
254C4⋊C8—301no—
255C22⋊C8—301no—
256C4×C8—51no—
257C4×C8—151no—
258C2×C3×C5#40811yescharacteristic
259C2×C3×C5C2×#10311yescharacteristic
260C2×C3×C5#42111yescharacteristic
261D15—22no—
262C22×D3—51no—
263C3×Q8—101no—
264C3×Q8—101no—
265C2×C3×C4—21no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×C3×C4—101no—
269C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
270C2×Dic3—21no—
271C2×Dic3—51no—
272C2×Dic3—101no—
273C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
274C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
275C4×D3—52no—
276C4×D3—52no—
277C4×D3—101no—
278C4×D3—101no—
279C4×D3—201no—
280Dic6—42no—
281Dic6—101no—
282Dic6—101no—
283C3×C8—201no—
284C3×C8—201no—
285C3⋊C8—201no—
286C3⋊C8—201no—
287C22×C5D3×C22⋊C411yescharacteristic
288C2×D5—32no—
289C2×D5—61no—
290C2×D5—61no—
291C4×C5—32no—
292C4×C5—41no—
293C4×C5—61no—
294C4×C5—121no—
295C4×C5#90111yescharacteristic
296C4×C5#90711yescharacteristic
297Dic5—21no—
298Dic5—41no—
299Dic5—61no—
300Dic5—121no—
301Dic5D3×SD1611yescharacteristic
302Dic5D3×Q1611yescharacteristic
303C2×Q8—51no—
304C2×Q8—61no—
305C2×Q8—151no—
306C22×C4—151no—
307C22×C4—151no—
308C22×C4—151no—
309C2×C8—101no—
310C2×C8—101no—
311C2×C8—301no—
312C2×C8—301no—
313C2×C8—602no—
314C4⋊C4—31no—
315C4⋊C4—61no—
316C4⋊C4—101no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
323C22⋊C4—301no—
324C22⋊C4—301no—
325C42—31no—
326C42—51no—
327C42—101no—
328C42—151no—
329C42—151no—
330C42—301no—
331C3×C5#148111yescharacteristic, complemented, Hall
332C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
333C2×D3—52no—
334C2×D3—101no—
335C2×D3—101no—
336C3×C4—41no—
337C3×C4—51no—
338C3×C4—51no—
339C3×C4—101no—
340C3×C4—201no—
341C3×C4#413311yescharacteristic
342C3×C4#413311yescharacteristic
343Dic3—21no—
344Dic3—41no—
345Dic3—101no—
346Dic3—201no—
347Dic3#400912yes—
348C2×C5#472711yescharacteristic
349C2×C5D3×#10311yescharacteristic
350C2×C5#482111yescharacteristic
351D5—62no—
352C23—151no—
353Q8—101no—
354Q8—101no—
355Q8—122no—
356Q8—301no—
357Q8—301no—
358C2×C4—21no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—61no—
364C2×C4—101no—
365C2×C4—152no—
366C2×C4—152no—
367C2×C4—151no—
368C2×C4—301no—
369C2×C4—301no—
370C2×C4—301no—
371C2×C4—601no—
372C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
373C8—201no—
374C8—201no—
375C8—601no—
376C8—601no—
377C2×C3#6576911yescharacteristic
378C2×C3C2×#400911yescharacteristic
379C2×C3#6578711yescharacteristic
380D3—102no—
381C5#6823211yescharacteristic, complemented, Sylow
382C22—152no—
383C22—301no—
384C22—301no—
385C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
386C4—32no—
387C4—41no—
388C4—51no—
389C4—51no—
390C4—61no—
391C4—101no—
392C4—121no—
393C4—201no—
394C4—301no—
395C4—601no—
396C4#9191411yescharacteristic
397C4#9191611yescharacteristic
398C3#1060464611yescharacteristic, complemented, Sylow
399C2—302no—
400C2#1175190011yescharacteristic
401C2#1175195011yescharacteristic
402C2D3×#400911yescharacteristic
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#1481
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
4. #11746743C2semidirect
5. C3×#64872C2semidirect
6. #11746495C2semidirect
7. #11746494C2semidirect
35. #64872D3semidirect
331. C3×C5#1481semidirect
381. C5#68232semidirect
398. C3#10604646semidirect

Maximal subgroups

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

subgroupindex
#117534642
#117519012
#117517972
#117467432
C3×#648722
#117464952
#117464942
#106046463
#682325