Finite Group Databasebeta

← #14289787

Subgroups — #14289787

Order 1920.

456 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D20C211yesmaximal, characteristic
2#11750782C211yesmaximal, characteristic, complemented
3#11746961C211yesmaximal, characteristic, complemented
4#11746881C211yesmaximal, characteristic
5C5×#4456C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7#11745860C211yesmaximal, characteristic, complemented
8#10599062—31nomaximal, Hall
9C2×D5×Dic6—21no—
10#91758C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91469—21no—
15Dic3×D20—21no—
16#91422—22no—
17#91360—21no—
18C3×C4×C5×C8C2211yescharacteristic
19#91100—22no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90987—21no—
24#90973—21no—
25#90965—21no—
26#68189—51nomaximal, Hall
27Q8×D20—31no—
28#65310—31no—
29#65131—31no—
30#64970—31no—
31C5×Q8⋊C8—31no—
32#64706—31no—
33#64679D311yescharacteristic
34C2×Dic30—21no—
35C2×Dic30—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×#1204—22no—
40C2×D5×Dic3—22no—
41D5×Dic6—42no—
42D5×Dic6—42no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15D412yes—
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—22no—
57#6665—22no—
58D4×Dic6—51no—
59#5008—51no—
60#4850—51no—
61#4681—51no—
62C3×D4⋊C8—51no—
63#4482—51no—
64#4456D511yescharacteristic, complemented
65C2×Q8×D5—61no—
66C4×C5×Q8—31no—
67#4043—62no—
68#4043—61no—
69C4×D20—61no—
70C4×D20C2×D311yescharacteristic
71#4015—31no—
72#4015—31no—
73#4015—61no—
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3967—61no—
77#3953—61no—
78#3949—61no—
79#3948—62no—
80#3939—61no—
81C4⋊#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×C3×D5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88C2×Dic15—41no—
89Dic30—41no—
90Dic30—41no—
91Dic30—42no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6SD1612yes—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20Q1612yes—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101#1204—44no—
102D5×Dic3—44no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C22×Dic6—101no—
107C3×C4×D4—51no—
108D4×Dic3—101no—
109#924—101no—
110#888—101no—
111#878—102no—
112#869—51no—
113#869—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×C4⋊C8—51no—
116C3×C4×C8C2×D511yescharacteristic
117#832—101no—
118#818—101no—
119#816—102no—
120#816—101no—
121#808—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—31no—
124Q8×D5—122no—
125Q8×D5—122no—
126C2×D20D1211yescharacteristic
127C2×C4×D5—21no—
128C2×C4×D5—62no—
129C2×Dic10—62no—
130C2×Dic10—61no—
131C2×Dic10—61no—
132C2×C5×C8—21no—
133C2×C5×C8—61no—
134C5×C4⋊C4—31no—
135C5×C4⋊C4—61no—
136C42×C5—61no—
137C42×C5C22×D311yescharacteristic
138#685—21no—
139#685—62no—
140C4⋊Dic5—32no—
141C4⋊Dic5—62no—
142C4⋊Dic5—61no—
143C4⋊Dic5—61no—
144C4⋊Dic5—61no—
145C4⋊Dic5D1211yescharacteristic
146C2×#168—21no—
147D4×Q8—151no—
148#487—151no—
149#477—151no—
150#476—151no—
151#332—151no—
152Q8⋊C8—31no—
153D4⋊C8—51no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—22no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—21no—
159C3×C4×C5C2×SD1611yescharacteristic
160C3×C4×C5C2×Q1611yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—42no—
164Dic15—81no—
165C3×Dic5—41no—
166C5×Dic3—22no—
167C5×Dic3—41no—
168C2×C3×D4—51no—
169C22×C3×C4—101no—
170C22×Dic3—102no—
171C2×Dic6—102no—
172C2×Dic6—101no—
173C2×Dic6—101no—
174C2×Dic6—202no—
175C2×Dic6—202no—
176C2×Dic6D2011yescharacteristic
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C22⋊C4—101no—
181C3×C42C22×D511yescharacteristic
182#217—102no—
183C4⋊Dic3—52no—
184C4⋊Dic3—101no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C4⋊Dic3D2011yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—102no—
190C4×Dic3—21no—
191C2×C3⋊C8—21no—
192C22×D5—21no—
193C5×Q8—32no—
194C5×Q8—61no—
195C2×C4×C5—61no—
196C2×C4×C5—61no—
197C2×C4×C5C2×D1211yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—62no—
202C2×Dic5—121no—
203D20—21no—
204D20Dic1212yes—
205C4×D5—41no—
206C4×D5—41no—
207C4×D5—124no—
208Dic10—124no—
209Dic10—121no—
210Dic10—121no—
211Dic10—122no—
212C5×C8—41no—
213C5×C8—121no—
214#168—41no—
215C22×Q8—301no—
216C4⋊Q8—151no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—31no—
222C4×D4—51no—
223C4×D4—301no—
224#107—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#103—302no—
229#103—301no—
230#102—301no—
231C4×C8D3×D511yescharacteristic
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—42no—
236C23×C3—101no—
237C3×D4—52no—
238C3×D4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—102no—
248C2×Dic3—204no—
249C2×Dic3—201no—
250Dic6—21no—
251Dic6—204no—
252Dic6—201no—
253Dic6—201no—
254Dic6—202no—
255Dic6#67712yes—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—22no—
261C2×D5—41no—
262C2×D5—41no—
263C4×C5—21no—
264C4×C5—62no—
265C4×C5—121no—
266C4×C5C2×Dic1211yescharacteristic
267C4×C5#90911yescharacteristic
268C4×C5#91111yescharacteristic
269C4×C5D3×SD1611yescharacteristic
270Dic5—41no—
271Dic5—122no—
272Dic5—241no—
273C2×Q8—31no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—301no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—51no—
280C22×C4—101no—
281C22×C4—302no—
282C2×C8—21no—
283C2×C8—61no—
284C2×C8—101no—
285C4⋊C4—31no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—152no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C22⋊C4—101no—
294C22⋊C4—302no—
295C42—61no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—102no—
299C22×C3—201no—
300C22×C3—201no—
301C22×C3#402811yescharacteristic
302C3×C4—21no—
303C3×C4—201no—
304C3×C4C2×#67711yescharacteristic
305C3×C4#405411yescharacteristic
306C3×C4#406111yescharacteristic
307C3×C4D5×Q1611yescharacteristic
308Dic3—22no—
309Dic3—41no—
310Dic3—202no—
311Dic3—401no—
312C2×C5#473911yescharacteristic
313C2×C5#477611yescharacteristic
314C2×C5#482711yescharacteristic
315D5—42no—
316C23—101no—
317Q8—32no—
318Q8—61no—
319Q8—602no—
320Q8—604no—
321Q8—601no—
322Q8—601no—
323D4—52no—
324D4—101no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—101no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—302no—
331C2×C4—604no—
332C2×C4—601no—
333C2×C4D5×D1211yescharacteristic
334C2×C4D3×D2011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—41no—
337C8—121no—
338C8—201no—
339C2×C3—202no—
340C2×C3#6502011yescharacteristic
341C2×C3#6509711yescharacteristic
342C2×C3#6511611yescharacteristic
343C5#6818911yescharacteristic, complemented, Sylow
344C22—102no—
345C22—201no—
346C22—201no—
347C22#9147611yescharacteristic
348C4—21no—
349C4—62no—
350C4—121no—
351C4—201no—
352C4—602no—
353C4—1201no—
354C4D3×#67711yescharacteristic
355C4#9125411yescharacteristic
356C4D5×Dic1211yescharacteristic
357C4#9126011yescharacteristic
358C3#1059906211yescharacteristic, complemented, Sylow
359C2—202no—
360C2#1174712511yescharacteristic
361C2#1174812011yescharacteristic
362C2#1174813011yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11750782C2semidirect
3. #11746961C2semidirect
5. C5×#4456C2semidirect
7. #11745860C2semidirect
64. #4456D5semidirect
297. C3×C5#1637semidirect
343. C5#68189semidirect
358. C3#10599062semidirect

Maximal subgroups

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

subgroupindex
Dic6×D202
#117507822
#117469612
#117468812
C5×#44562
C3×#646792
#117458602
#105990623
#681895