Finite Group Databasebeta

← #14289651

Subgroups — #14289651

Order 1920.

468 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#66060C211yesmaximal, characteristic
2#11751194C211yesmaximal, characteristic, complemented
3#11746881C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic, complemented
5C5×#4547C211yesmaximal, characteristic, complemented
6#11745834C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10599227—31nomaximal, Hall
9C2×C3×#713—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91758C2211yescharacteristic
12C3×#4092—21no—
13C3×#4041—21no—
14C3×#4040—22no—
15C3×D5×C4⋊C4—21no—
16C3×C4×D20C2211yescharacteristic
17C3×C4×D20C2211yescharacteristic
18#91094—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22#90987—21no—
23#90987—21no—
24#90965—21no—
25#90965—21no—
26#71911—51nomaximal, Hall
27#66060D311yescharacteristic
28#65382—31no—
29#65131—31no—
30#65131—31no—
31C5×#332—31no—
32#64703—31no—
33#64703—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C3×#713—42no—
37C3×#713—42no—
38C2×C3×D20—22no—
39C2×C3×D20D411yescharacteristic
40C2×C3×D20D411yescharacteristic
41C2×C3×C4×D5—22no—
42C2×C3×C4×D5—21no—
43C2×C3×C4×D5—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4D412yes—
46C3×C42×C5C2311yescharacteristic
47C4⋊Dic15—21no—
48C4⋊Dic15—21no—
49C2×C3⋊#168—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—22no—
53C3×#685—21no—
54C3×#685—21no—
55C3×C4⋊Dic5D411yescharacteristic
56C3×C4⋊Dic5D411yescharacteristic
57C3×#683—22no—
58C3×#547—51no—
59#5093—51no—
60#5008—51no—
61#5008—51no—
62#4547D511yescharacteristic, complemented
63D4⋊(C3⋊C8)—51no—
64D4⋊(C3⋊C8)—51no—
65C2×#713—21no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4092—21no—
68#4041—21no—
69#4040—22no—
70D5×C4⋊C4—21no—
71C4×D20C2×D311yescharacteristic
72C4×D20C2×D311yescharacteristic
73#4015—31no—
74C5×C4⋊C8—31no—
75C5×C4⋊C8—31no—
76#3953—61no—
77#3953—61no—
78#3949—61no—
79#3949—61no—
80#3942—62no—
81C4×#168—31no—
82#1635—151noSylow
83C22×C3×D5—21no—
84C22×C3×D5—21no—
85C3×C5×Q8—41no—
86C3×C5×Q8—41no—
87C2×C3×C4×C5—22no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—41no—
92Dic30—42no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20—21no—
97C3×D20—21no—
98C3×D20—44no—
99C3×D20SD1612yes—
100C3×C4×D5—44no—
101C3×C4×D5—41no—
102C3×C4×D5—41no—
103C3×C4×D5—41no—
104C3×C4×D5—41no—
105C3⋊#168—41no—
106C5×C3⋊C8—41no—
107C5×C3⋊C8—41no—
108C2×C3×#41—101no—
109C3×C4⋊Q8C2×D511yescharacteristic
110C3×#123—102no—
111C3×C22⋊Q8—101no—
112C3×#121—101no—
113C3×C4×D4—51no—
114C3×C4×D4—51no—
115C2×C3×C4⋊C4—101no—
116#869—51no—
117#832—101no—
118#832—101no—
119#810—102no—
120#808—101no—
121#808—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C4×C3⋊C8—51no—
125C2×C5×Q8—21no—
126#713—42no—
127#713—42no—
128C2×D20—22no—
129C2×D20#6711yescharacteristic
130C2×D20#6711yescharacteristic
131C2×C4×D5—22no—
132C2×C4×D5—21no—
133C2×C4×D5—21no—
134C2×Dic10—61no—
135C2×C5×C8—61no—
136C2×C5×C8—61no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4#6712yes—
139C42×C5C22×D311yescharacteristic
140#685—22no—
141#685—21no—
142#685—21no—
143C4⋊Dic5—61no—
144C4⋊Dic5—61no—
145C4⋊Dic5#6711yescharacteristic
146C4⋊Dic5#6711yescharacteristic
147#683—22no—
148C2×#168—61no—
149#547—51no—
150#487—151no—
151#476—151no—
152#476—151no—
153#332—31no—
154D4⋊C8—151no—
155D4⋊C8—151no—
156C22×C3×C5#12011yescharacteristic
157C2×C3×D5—22no—
158C2×C3×D5—41no—
159C2×C3×D5—41no—
160C2×C3×D5—41no—
161C2×C3×D5—41no—
162C2×C3×D5—41no—
163C3×C4×C5—21no—
164C3×C4×C5—42no—
165C3×C4×C5C2×SD1611yescharacteristic
166C3×C4×C5#13511yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5#13711yescharacteristic
169Dic15—81no—
170C3×Dic5—41no—
171C3×Dic5—41no—
172C3×#41—202no—
173C3×#41—202no—
174C2×C3×Q8—21no—
175C2×C3×D4—51no—
176C2×C3×D4—51no—
177C2×C3×D4—102no—
178C22×C3×C4—102no—
179C22×C3×C4—101no—
180C22×C3×C4—101no—
181C2×Dic6—101no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—51no—
184C3×C4⋊C4—51no—
185C3×C4⋊C4—102no—
186C3×C4⋊C4D2012yes—
187C3×C22⋊C4—102no—
188C3×C22⋊C4—101no—
189C3×C22⋊C4—101no—
190C3×C42C22×D511yescharacteristic
191C4⋊Dic3—101no—
192C4⋊Dic3—101no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—101no—
196C22×D5—21no—
197C22×D5—21no—
198C5×Q8—41no—
199C5×Q8—41no—
200C2×C4×C5—22no—
201C2×C4×C5C2×#6711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×C4×C5C2×#6711yescharacteristic
204C2×Dic5—21no—
205C2×Dic5—21no—
206C2×Dic5—121no—
207D20—21no—
208D20—21no—
209D20—21no—
210D20—44no—
211D20#21412yes—
212C4×D5—44no—
213C4×D5—41no—
214C4×D5—41no—
215C4×D5—41no—
216C4×D5—41no—
217Dic10—122no—
218C5×C8—121no—
219C5×C8—121no—
220#168—121no—
221C2×#41—101no—
222C4⋊Q8—151no—
223C4⋊Q8D3×D511yescharacteristic
224#123—102no—
225C22⋊Q8—101no—
226#121—101no—
227C4×D4—51no—
228C4×D4—51no—
229C2×C4⋊C4—101no—
230#106—301no—
231#106—301no—
232C4⋊C8—31no—
233C4⋊C8—31no—
234#103—302no—
235#102—301no—
236#102—301no—
237C4×C8—151no—
238C2×C3×C5#45011yescharacteristic
239C2×C3×C5#45211yescharacteristic
240C2×C3×C5#45411yescharacteristic
241C3×D5—42no—
242C3×D5—81no—
243C23×C3—101no—
244C23×C3—101no—
245C3×Q8—41no—
246C3×Q8—41no—
247C3×D4—52no—
248C3×D4—101no—
249C3×D4—101no—
250C3×D4—101no—
251C3×D4—204no—
252C2×C3×C4—22no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—204no—
256C2×C3×C4—201no—
257C2×C3×C4—201no—
258C2×C3×C4—201no—
259C2×C3×C4—201no—
260C2×C3×C4C2×D2011yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×Dic3—201no—
264Dic6—202no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C3⋊C8—201no—
268C22×C5#95311yescharacteristic
269C2×D5—22no—
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—41no—
273C2×D5—41no—
274C2×D5—41no—
275C4×C5—21no—
276C4×C5—42no—
277C4×C5#93211yescharacteristic
278C4×C5C2×#21411yescharacteristic
279C4×C5#95011yescharacteristic
280C4×C5#95111yescharacteristic
281Dic5—41no—
282Dic5—41no—
283Dic5—241no—
284#41—202no—
285#41—202no—
286C2×Q8—21no—
287C2×Q8—301no—
288C2×D4—51no—
289C2×D4—51no—
290C2×D4—102no—
291C22×C4—102no—
292C22×C4—101no—
293C22×C4—101no—
294C2×C8—61no—
295C2×C8—61no—
296C2×C8—301no—
297C4⋊C4—21no—
298C4⋊C4—51no—
299C4⋊C4—51no—
300C4⋊C4—102no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4#120212yes—
304C22⋊C4—102no—
305C22⋊C4—101no—
306C22⋊C4—101no—
307C42C2×D3×D511yescharacteristic
308C3×C5#163511yescharacteristic, complemented, Hall
309C22×C3—102no—
310C22×C3—201no—
311C22×C3—201no—
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#402811yescharacteristic
316C3×C4—21no—
317C3×C4—42no—
318C3×C4—201no—
319C3×C4—201no—
320C3×C4#405711yescharacteristic
321C3×C4D5×SD1611yescharacteristic
322C3×C4#406211yescharacteristic
323C3×C4#406411yescharacteristic
324Dic3—401no—
325C2×C5#521811yescharacteristic
326C2×C5#523911yescharacteristic
327C2×C5#524511yescharacteristic
328D5—42no—
329D5—81no—
330C23—101no—
331C23—101no—
332Q8—41no—
333Q8—41no—
334Q8—602no—
335D4—52no—
336D4—101no—
337D4—101no—
338D4—101no—
339D4—204no—
340C2×C4—22no—
341C2×C4—101no—
342C2×C4—101no—
343C2×C4—204no—
344C2×C4—201no—
345C2×C4—201no—
346C2×C4—201no—
347C2×C4—201no—
348C2×C4—601no—
349C2×C4C2×#120211yescharacteristic
350C2×C4D5×#6711yescharacteristic
351C2×C4D5×#6711yescharacteristic
352C8—121no—
353C8—121no—
354C8—601no—
355C2×C3—202no—
356C2×C3—401no—
357C2×C3#6504211yescharacteristic
358C2×C3#6506511yescharacteristic
359C2×C3#6509911yescharacteristic
360C5#7191111yescharacteristic, complemented, Sylow
361C22—102no—
362C22—201no—
363C22—201no—
364C22—201no—
365C22—201no—
366C22—201no—
367C22#9156411yescharacteristic
368C4—21no—
369C4—42no—
370C4—201no—
371C4—201no—
372C4—1201no—
373C4D5×#21411yescharacteristic
374C4#9148911yescharacteristic
375C4#9150811yescharacteristic
376C4#9151411yescharacteristic
377C3#1059922711yescharacteristic, complemented, Sylow
378C2—202no—
379C2—401no—
380C2#1174904511yescharacteristic
381C2#1174929511yescharacteristic
382C2#1174938411yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC3×#66060C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1635
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751194C2semidirect
3. #11746881C2semidirect
4. #11746881C2semidirect
5. C5×#4547C2semidirect
6. #11745834C2semidirect
7. #11745834C2semidirect
62. #4547D5semidirect
308. C3×C5#1635semidirect
360. C5#71911semidirect
377. C3#10599227semidirect

Maximal subgroups

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

subgroupindex
C3×#660602
#117511942
#117468812
C5×#45472
#117458342
#105992273
#719115