Finite Group Databasebeta

← #14281963

Subgroups — #14281963

Order 1920.

468 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 90 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#11754854C211yesmaximal, characteristic
2C4×#6740C211yesmaximal, characteristic, complemented
3#11751901C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊#170)C211yesmaximal, characteristic, complemented
5C3×D4⋊#170C211yesmaximal, characteristic, complemented
6#11746493C211yesmaximal, characteristic, complemented
7#11746492C211yesmaximal, characteristic, complemented
8#10604553—31nomaximal, Hall
9C2×#6740—21no—
10C2×#6738—21no—
11#91827C411yescharacteristic
12C5×#936C411yescharacteristic
13C3×D4×Dic5C2211yescharacteristic
14#91562—21no—
15#91552—21no—
16#91530—21no—
17#91528—21no—
18C4×#1200C2211yescharacteristic
19#91383C411yescharacteristic
20#91381C411yescharacteristic
21Dic5×Dic6C2211yescharacteristic
22C4⋊(C3⋊#170)C2211yescharacteristic
23C4×C3⋊#170C2211yescharacteristic
24C3×C4⋊#170C2211yescharacteristic
25C3×C4×#170C2211yescharacteristic
26#91177—21no—
27#91169—21no—
28#68170—51nomaximal, Hall
29#66014—31no—
30D5⋊(C4⋊C8)—31no—
31C4×#700—31no—
32Q8⋊#170—31no—
33Q8⋊#170—31no—
34D4⋊#170—31no—
35D4⋊#170D311yescharacteristic, complemented
36C2×C3×C5×D4C2×C411yescharacteristic
37C2×#1220—21no—
38C2×C4×D15C2×C411yescharacteristic
39C2×C5×Dic6C2×C411yescharacteristic
40C22×C3×Dic5—21no—
41C2×#1200D411yescharacteristic
42C2×#1200D411yescharacteristic
43C2×C3⋊#170—21no—
44C2×C3⋊#170—21no—
45C2×C3×#170—21no—
46C2×C3×#170—21no—
47#6740—24no—
48#6738—42no—
49#6719—21no—
50C4⋊Dic15C2×C411yescharacteristic
51C5×#217—21no—
52C5×#217—21no—
53C4×C5×Dic3C2×C411yescharacteristic
54C3×C22⋊Dic5—21no—
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×C4×Dic5C2311yescharacteristic
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6668—21no—
60#6668—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63Dic3×Dic5D411yescharacteristic
64Dic3×Dic5D411yescharacteristic
65#5557—51no—
66D3×C4⋊C8—51no—
67C4×ΓL(1,𝔽25)—51no—
68C3×D4⋊C8—51no—
69D4⋊(C3⋊C8)—51no—
70#4484—51no—
71#4456—51no—
72C2×#700—61no—
73C2×D5⋊C8—61no—
74C5×#124—31no—
75#4092—31no—
76Q8×Dic5—31no—
77#4084—31no—
78D4×Dic5C2×D311yescharacteristic
79#4029—61no—
80#4027—61no—
81#4025—61no—
82#4023—61no—
83C42×D5—31no—
84#4016—31no—
85#4004—61no—
86#4002—61no—
87C4⋊#170—31no—
88C4⋊#170C2×D311yescharacteristic
89C4×#170—31no—
90C4×#170C2×D311yescharacteristic
91#1483—151noSylow
92C23×C3×C5—21no—
93C22×D15C22⋊C411yescharacteristic
94C3×C5×D4—21no—
95C3×C5×D4—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97#1220—42no—
98C2×Dic15—21no—
99C2×Dic15C22⋊C411yescharacteristic
100C4×D15—21no—
101C4×D15—21no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3C22⋊C411yescharacteristic
104C2×C5×Dic3C22⋊C411yescharacteristic
105C5×Dic6—21no—
106C5×Dic6—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5C2×D411yescharacteristic
111C2×C3×Dic5C2×D411yescharacteristic
112#1200—22no—
113#1200—21no—
114#1200—21no—
115C3⋊#170—22no—
116C3⋊#170—41no—
117C3×#170—22no—
118C3×#170—41no—
119C3×C4×D4—51no—
120#938—51no—
121#936AGL(1,𝔽5)11yescharacteristic
122C4×#67—101no—
123#926—101no—
124C2×ΓL(1,𝔽25)—101no—
125C2×D3×C8—101no—
126#897—51no—
127#890—51no—
128#883—101no—
129#879—101no—
130C42×D3—51no—
131C4×Dic6—51no—
132C3×C4⋊C8—51no—
133C3×C4×C8—51no—
134#815—101no—
135Dic3⋊C8—101no—
136C4⋊(C3⋊C8)—51no—
137C4×C3⋊C8—51no—
138C2×C5×Q8—31no—
139C2×C5×D4C4×D311yescharacteristic
140C2×C22⋊D5—61no—
141C22×Dic5—21no—
142C2×C4×D5—31no—
143C2×C4×D5—31no—
144C2×C4×D5—31no—
145C2×#170—21no—
146C2×#170—21no—
147C2×#170—61no—
148C2×#170—61no—
149#700—64no—
150D5⋊C8—122no—
151C5×C22⋊C4—61no—
152C5×C22⋊C4—61no—
153C42×C5—31no—
154C22⋊Dic5—21no—
155C22⋊Dic5—61no—
156#685—61no—
157C4⋊Dic5—31no—
158C4⋊Dic5—61no—
159C4⋊Dic5C4×D311yescharacteristic
160#683—61no—
161#683—61no—
162#683—61no—
163C4×Dic5—31no—
164C4×Dic5—31no—
165C4×Dic5—61no—
166C4×Dic5C22×D311yescharacteristic
167#529—151no—
168C2×C4⋊C8—151no—
169C4×M16—151no—
170Q8⋊C8—151no—
171Q8⋊C8—151no—
172D4⋊C8—51no—
173D4⋊C8—151no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C2×D15—21no—
179C2×D15—21no—
180C2×D15#10412yes—
181C3×C4×C5#13111yescharacteristic
182C3×C4×C5#13111yescharacteristic
183Dic15—21no—
184Dic15—41no—
185C3×Dic5—21no—
186C3×Dic5—41no—
187C3×Dic5AGL(1,ℤ/8)11yescharacteristic
188C3×Dic5#13711yescharacteristic
189C5×Dic3—21no—
190C5×Dic3—21no—
191C5×Dic3—41no—
192C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
193C22×C3×C4—101no—
194C2×#67—101no—
195C2×C4×D3—51no—
196C2×C4×D3—51no—
197C2×C4×D3—51no—
198C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
199C2×C3×C8—101no—
200C2×C3×C8—101no—
201C3×C4⋊C4—51no—
202C3×C22⋊C4—101no—
203C3×C42—51no—
204#217—21no—
205#217—21no—
206#217—101no—
207(C2×D3)⋊C4—101no—
208C4⋊Dic3—51no—
209C4⋊Dic3—101no—
210C4⋊Dic3—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213C4×Dic3—51no—
214C4×Dic3—51no—
215C4×Dic3—101no—
216C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
217C2×C3⋊C8—101no—
218C2×C3⋊C8—101no—
219ΓL(1,𝔽25)—104no—
220D3×C8—202no—
221C23×C5—21no—
222C22×D5—31no—
223C5×Q8—61no—
224C5×Q8—61no—
225C5×D4—21no—
226C5×D4—21no—
227C2×C4×C5—31no—
228C2×C4×C5—31no—
229C2×C4×C5—61no—
230C2×C4×C5C2×C4×D311yescharacteristic
231C22⋊D5—122no—
232C2×Dic5—21no—
233C2×Dic5—31no—
234C2×Dic5—41no—
235C2×Dic5—41no—
236C2×Dic5—61no—
237C2×Dic5D3×D411yescharacteristic
238C2×Dic5D3×D411yescharacteristic
239C4×D5—62no—
240C4×D5—61no—
241C4×D5—61no—
242C4×D5—61no—
243C4×D5—61no—
244#170—22no—
245#170—41no—
246#170—62no—
247#170—121no—
248C2×M16—301no—
249C22×C8—301no—
250#126—301no—
251#125—151no—
252#124—31no—
253#123—301no—
254C22⋊Q8—151no—
255#121—151no—
256C4×Q8—151no—
257C4×D4—51no—
258C4×D4—301no—
259#117—301no—
260C2×C42—151no—
261C4⋊C8—51no—
262C4⋊C8—151no—
263C4⋊C8—301no—
264#97—301no—
265C4×C8—51no—
266C4×C8—151no—
267C2×C3×C5—81no—
268C2×C3×C5#40811yescharacteristic
269C2×C3×C5#41711yescharacteristic
270C2×C3×C5C2×#10411yescharacteristic
271D15—22no—
272C23×C3—21no—
273C22×D3—51no—
274C3×D4—21no—
275C3×D4—21no—
276C2×C3×C4—51no—
277C2×C3×C4—51no—
278C2×C3×C4—101no—
279C2×C3×C4—201no—
280C2×C3×C4—201no—
281C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
282#67—202no—
283C2×Dic3—21no—
284C2×Dic3—51no—
285C2×Dic3—101no—
286C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
287C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
288C4×D3—101no—
289C4×D3—101no—
290C4×D3—102no—
291C4×D3—101no—
292C4×D3—101no—
293Dic6—21no—
294Dic6—21no—
295C3×C8—102no—
296C3×C8—201no—
297C3⋊C8—102no—
298C3⋊C8—201no—
299C22×C5—41no—
300C22×C5—41no—
301C22×C5—41no—
302C22×C5D3×C22⋊C411yescharacteristic
303C2×D5—32no—
304C2×D5—61no—
305C2×D5—61no—
306C4×C5—61no—
307C4×C5—61no—
308C4×C5—121no—
309C4×C5#90111yescharacteristic
310C4×C5#90711yescharacteristic
311Dic5—21no—
312Dic5—41no—
313Dic5—61no—
314Dic5—121no—
315Dic5#91111yescharacteristic
316Dic5#91511yescharacteristic
317C2×Q8—31no—
318C2×D4—301no—
319C2×D4D3×AGL(1,𝔽5)11yescharacteristic
320C22×C4—101no—
321C22×C4—151no—
322C22×C4—151no—
323C22×C4—151no—
324M16—304no—
325C2×C8—101no—
326C2×C8—101no—
327C2×C8—301no—
328C2×C8—301no—
329C2×C8—602no—
330C4⋊C4—51no—
331C4⋊C4—151no—
332C4⋊C4—301no—
333C4⋊C4—301no—
334C4⋊C4—301no—
335C4⋊C4—301no—
336C22⋊C4—61no—
337C22⋊C4—61no—
338C22⋊C4—101no—
339C22⋊C4—301no—
340C22⋊C4—301no—
341C42—31no—
342C42—51no—
343C42—151no—
344C42—151no—
345C42—301no—
346C3×C5#148311yescharacteristic, complemented, Hall
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
351C2×D3—52no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—51no—
355C3×C4—51no—
356C3×C4—101no—
357C3×C4—201no—
358C3×C4#413111yescharacteristic
359C3×C4#413111yescharacteristic
360Dic3—21no—
361Dic3—21no—
362Dic3—41no—
363Dic3—101no—
364Dic3—201no—
365C2×C5—81no—
366C2×C5#472711yescharacteristic
367C2×C5#477111yescharacteristic
368C2×C5D3×#10411yescharacteristic
369D5—62no—
370C23—21no—
371C23—151no—
372Q8—61no—
373Q8—61no—
374D4—21no—
375D4—21no—
376D4—602no—
377C2×C4—31no—
378C2×C4—31no—
379C2×C4—51no—
380C2×C4—51no—
381C2×C4—61no—
382C2×C4—101no—
383C2×C4—151no—
384C2×C4—201no—
385C2×C4—201no—
386C2×C4—301no—
387C2×C4—301no—
388C2×C4—302no—
389C2×C4—301no—
390C2×C4—301no—
391C2×C4—301no—
392C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
393C8—102no—
394C8—201no—
395C8—302no—
396C8—601no—
397C2×C3—81no—
398C2×C3#6577611yescharacteristic
399C2×C3D5⋊#10411yescharacteristic
400C2×C3#6579311yescharacteristic
401D3—102no—
402C5#6817011yescharacteristic, complemented, Sylow
403C22—41no—
404C22—41no—
405C22—41no—
406C22—152no—
407C22—301no—
408C22—301no—
409C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
410C4—51no—
411C4—51no—
412C4—61no—
413C4—61no—
414C4—101no—
415C4—121no—
416C4—201no—
417C4—301no—
418C4—601no—
419C4#9192711yescharacteristic
420C4#9192911yescharacteristic
421C3#1060455311yescharacteristic, complemented, Sylow
422C2—81no—
423C2—302no—
424C2#1175193511yescharacteristic
425C2#1175193711yescharacteristic
426C2#1175204011yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radical#91827C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. C4×#6740C2semidirect
3. #11751901C2semidirect
4. D4⋊(C3⋊#170)C2semidirect
5. C3×D4⋊#170C2semidirect
6. #11746493C2semidirect
7. #11746492C2semidirect
35. D4⋊#170D3semidirect
346. C3×C5#1483semidirect
402. C5#68170semidirect
421. C3#10604553semidirect

Maximal subgroups

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

subgroupindex
#117548542
C4×#67402
#117519012
D4⋊(C3⋊#170)2
C3×D4⋊#1702
#117464932
#117464922
#106045533
#681705