Finite Group Databasebeta

← #14281908

Subgroups — #14281908

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#11753521C211yesmaximal, characteristic
2#11751797C211yesmaximal, characteristic, complemented
3#11751777C211yesmaximal, characteristic, complemented
4#11746742C211yesmaximal, characteristic, complemented
5C3×#64871C211yesmaximal, characteristic, complemented
6#11746495C211yesmaximal, characteristic, complemented
7#11746494C211yesmaximal, characteristic, complemented
8#10604580—31nomaximal, Hall
9#91786C411yescharacteristic
10C5×#890C411yescharacteristic
11C3×#4039C2211yescharacteristic
12#91465C411yescharacteristic
13#91444—21no—
14C4×#1200C2211yescharacteristic
15#91364C411yescharacteristic
16#91362—21no—
17#91358—21no—
18#91356—21no—
19#91333C2211yescharacteristic
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#68169—51nomaximal, Hall
29#66025—31no—
30#65680—31no—
31#65680—31no—
32#64872—31no—
33#64872—31no—
34#64871—31no—
35#64871D311yescharacteristic, complemented
36C2×C4×D15C2×C411yescharacteristic
37C2×Dic30C2×C411yescharacteristic
38C2×C3×D20C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×#1202—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—
49C4⋊Dic15—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3C2×C411yescharacteristic
52C5×Dic3⋊C4—21no—
53C4×C5×Dic3C2×C411yescharacteristic
54C3×#685—21no—
55C3×C4×Dic5C2311yescharacteristic
56#6669—21no—
57#6665—21no—
58#6665—21no—
59#6665—21no—
60Dic3×Dic5—21no—
61Dic3×Dic5D411yescharacteristic
62Dic3×Dic5D411yescharacteristic
63#5557—51no—
64#4833—51no—
65#4685—51no—
66C3×D4⋊C8—51no—
67D4⋊(C3⋊C8)—51no—
68#4484—51no—
69#4456—51no—
70C5×#125—31no—
71#4044—61no—
72#4043—31no—
73#4041—31no—
74#4040—61no—
75#4039—61no—
76#4039C2×D311yescharacteristic
77#4038—61no—
78#4033—31no—
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×D15C22⋊C411yescharacteristic
91C22×C3×D5—21no—
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
103C2×C3×Dic5C2×D411yescharacteristic
104C2×C3×Dic5C2×D411yescharacteristic
105C3×D20—21no—
106C3×D20—21no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109#1202—42no—
110#1200—21no—
111#1200—21no—
112#1200—41no—
113C3⋊#170—41no—
114C3⋊#170—41no—
115C3×#170—41no—
116C3×#170—41no—
117C3×C4×D4—51no—
118#938—51no—
119#936—51no—
120C4×#67—101no—
121#926—101no—
122#897—51no—
123#890AGL(1,𝔽5)11yescharacteristic
124#883—101no—
125#879—101no—
126C42×D3—51no—
127C4×Dic6—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—61no—
137C2×D20C4×D311yescharacteristic
138C2×C4×D5—21no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×C4×D5—31no—
142C2×Dic10—31no—
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—21no—
153#685—61no—
154#685—61no—
155#685—61no—
156#685—61no—
157C4⋊Dic5—61no—
158#683—61no—
159C4×Dic5—31no—
160C4×Dic5—31no—
161C4×Dic5—61no—
162C4×Dic5C22×D311yescharacteristic
163#529—151no—
164#431—151no—
165#431—151no—
166Q8⋊C8—151no—
167Q8⋊C8—151no—
168D4⋊C8—51no—
169D4⋊C8—151no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15—21no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C3×C4×C5—41no—
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5#13111yescharacteristic
180Dic15—21no—
181Dic15—41no—
182C3×Dic5—21no—
183C3×Dic5#13511yescharacteristic
184C3×Dic5#13511yescharacteristic
185C5×Dic3—21no—
186C5×Dic3—21no—
187C5×Dic3—41no—
188C2×C3×D4—51no—
189C22×C3×C4—101no—
190C2×#67—101no—
191C2×C4×D3—51no—
192C2×C4×D3—51no—
193C2×C4×D3—51no—
194C2×Dic6—51no—
195C2×C3×C8—101no—
196C2×C3×C8—101no—
197C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
198C3×C22⋊C4—101no—
199C3×C42—51no—
200#217—101no—
201#217—101no—
202#217—101no—
203(C2×D3)⋊C4—101no—
204C4⋊Dic3—21no—
205C4⋊Dic3—101no—
206C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
207Dic3⋊C4—21no—
208Dic3⋊C4—101no—
209C4×Dic3—51no—
210C4×Dic3—51no—
211C4×Dic3—101no—
212C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
213C2×C3⋊C8—101no—
214C2×C3⋊C8—101no—
215C22×D5—21no—
216C22×D5—31no—
217C2×C4×C5—21no—
218C2×C4×C5—31no—
219C2×C4×C5—31no—
220C2×C4×C5—61no—
221C2×C4×C5C2×C4×D311yescharacteristic
222C2×Dic5—31no—
223C2×Dic5—61no—
224C2×Dic5D3×D411yescharacteristic
225C2×Dic5D3×D411yescharacteristic
226D20—21no—
227D20—21no—
228D20—122no—
229C4×D5—41no—
230C4×D5—41no—
231C4×D5—61no—
232C4×D5—61no—
233C4×D5—61no—
234C4×D5—61no—
235C4×D5—121no—
236Dic10—61no—
237Dic10—61no—
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—151no—
249C4×D4—51no—
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—
265C3×D5—81no—
266C23×C3—101no—
267C22×D3—51no—
268C3×D4—101no—
269C3×D4—101no—
270C2×C3×C4—21no—
271C2×C3×C4—51no—
272C2×C3×C4—51no—
273C2×C3×C4—201no—
274C2×C3×C4—201no—
275C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
276#67—202no—
277C2×Dic3—21no—
278C2×Dic3—51no—
279C2×Dic3—101no—
280C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
281C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
282C4×D3—101no—
283C4×D3—101no—
284C4×D3—101no—
285C4×D3—101no—
286C4×D3—201no—
287Dic6—101no—
288Dic6—101no—
289C3×C8—201no—
290C3×C8—201no—
291C3⋊C8—201no—
292C3⋊C8—201no—
293C22×C5D3×C22⋊C411yescharacteristic
294C2×D5—41no—
295C2×D5—41no—
296C2×D5—41no—
297C2×D5—61no—
298C2×D5—61no—
299C2×D5—61no—
300C4×C5—41no—
301C4×C5—61no—
302C4×C5—61no—
303C4×C5—121no—
304C4×C5#90111yescharacteristic
305C4×C5#90711yescharacteristic
306Dic5—21no—
307Dic5—61no—
308Dic5—121no—
309Dic5#91211yescharacteristic
310Dic5#91611yescharacteristic
311C2×Q8—151no—
312C2×D4—51no—
313C2×D4—301no—
314C22×C4—101no—
315C22×C4—151no—
316C22×C4—151no—
317C22×C4—151no—
318C2×C8—101no—
319C2×C8—101no—
320C2×C8—301no—
321C2×C8—301no—
322C4⋊C4—31no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
328C22⋊C4—101no—
329C22⋊C4—301no—
330C22⋊C4—301no—
331C22⋊C4—301no—
332C22⋊C4—301no—
333C42—31no—
334C42—51no—
335C42—151no—
336C42—151no—
337C42—301no—
338C3×C5#148211yescharacteristic, complemented, Hall
339C22×C3—201no—
340C22×C3—201no—
341C22×C3—201no—
342C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
343C2×D3—101no—
344C2×D3—101no—
345C2×D3—101no—
346C3×C4—41no—
347C3×C4—51no—
348C3×C4—51no—
349C3×C4—101no—
350C3×C4#413311yescharacteristic
351C3×C4#413311yescharacteristic
352Dic3—21no—
353Dic3—21no—
354Dic3—41no—
355Dic3—101no—
356Dic3—201no—
357C2×C5#472711yescharacteristic
358C2×C5#477211yescharacteristic
359C2×C5#482111yescharacteristic
360D5—81no—
361D5—121no—
362C23—101no—
363C23—151no—
364Q8—301no—
365Q8—301no—
366D4—101no—
367D4—101no—
368D4—602no—
369C2×C4—21no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—51no—
373C2×C4—51no—
374C2×C4—61no—
375C2×C4—151no—
376C2×C4—201no—
377C2×C4—201no—
378C2×C4—301no—
379C2×C4—301no—
380C2×C4—301no—
381C2×C4—301no—
382C2×C4—301no—
383C2×C4—601no—
384C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
385C8—201no—
386C8—201no—
387C8—601no—
388C8—601no—
389C2×C3—401no—
390C2×C3#6578711yescharacteristic
391C2×C3#6579411yescharacteristic
392C2×C3#6579511yescharacteristic
393D3—201no—
394C5#6816911yescharacteristic, complemented, Sylow
395C22—201no—
396C22—201no—
397C22—201no—
398C22—301no—
399C22—301no—
400C22—301no—
401C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
402C4—41no—
403C4—51no—
404C4—51no—
405C4—61no—
406C4—61no—
407C4—101no—
408C4—121no—
409C4—301no—
410C4—601no—
411C4#9191411yescharacteristic
412C4#9191611yescharacteristic
413C3#1060458011yescharacteristic, complemented, Sylow
414C2—401no—
415C2—601no—
416C2#1175190011yescharacteristic
417C2#1175194711yescharacteristic
418C2#1175197311yescharacteristic
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#91465C4
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. #11746742C2semidirect
5. C3×#64871C2semidirect
6. #11746495C2semidirect
7. #11746494C2semidirect
35. #64871D3semidirect
338. C3×C5#1482semidirect
394. C5#68169semidirect
413. C3#10604580semidirect

Maximal subgroups

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

subgroupindex
#117535212
#117517972
#117517772
#117467422
C3×#648712
#117464952
#117464942
#106045803
#681695