Finite Group Databasebeta

← #14289805

Subgroups — #14289805

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
2C3×#65131C211yesmaximal, characteristic
3#11746959C211yesmaximal, characteristic, complemented
4#11746920C211yesmaximal, characteristic, complemented
5#11746307C211yesmaximal, characteristic, complemented
6C5×#4484C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic
8#10599062—31nomaximal, Hall
9C2×D5×Dic6—21no—
10#91758C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91469—21no—
15Dic3×D20—21no—
16#91422—22no—
17#91360—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C5×C3⋊C8C2211yescharacteristic
21C3×#3953—21no—
22C3×#3949—21no—
23#90989—21no—
24#90972—21no—
25#90971—22no—
26#71142—51nomaximal, Hall
27Q8×D20—31no—
28#65310—31no—
29#65131D311yescharacteristic
30#64970—31no—
31C5×Q8⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×Dic30—21no—
35C2×C5×Dic6D411yescharacteristic
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×Dic10—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⋊Dic15D412yes—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3D411yescharacteristic
49C5×Dic3⋊C4—21no—
50C4×C5×Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5—21no—
55C3×C4⋊Dic5D411yescharacteristic
56Dic3⋊Dic5—22no—
57#6665—22no—
58D4×Dic6—51no—
59C3×#476—51no—
60#5091—51no—
61#5079—51no—
62D4⋊(C3⋊C8)—51no—
63#4486—51no—
64#4484D511yescharacteristic, 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—61no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3967—61no—
77#3953—21no—
78#3949—21no—
79#3948—62no—
80#3939—61no—
81C4⋊#168—31no—
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—
88Dic30—41no—
89Dic30—41no—
90C2×C5×Dic3—21no—
91C2×C5×Dic3—21no—
92C5×Dic6—21no—
93C5×Dic6SD1612yes—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—41no—
96C3×D20—21no—
97C3×D20Q1612yes—
98C3×C4×D5—41no—
99C3×C4×D5—41no—
100C3×Dic10—42no—
101#1204—44no—
102D5×Dic3—44no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C5×C3⋊C8—41no—
106C22×Dic6—101no—
107C3×C4⋊Q8—51no—
108C3×C4×D4—51no—
109D4×Dic3—101no—
110#924—101no—
111#888—101no—
112#878—102no—
113#869—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×#106—101no—
116C3×C4⋊C8C2×D511yescharacteristic
117C3×#102—101no—
118#835—102no—
119#810—101no—
120#807—101no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8—31no—
124Q8×D5—122no—
125Q8×D5—122no—
126C2×D20#6711yescharacteristic
127C2×C4×D5—21no—
128C2×C4×D5—62no—
129C2×Dic10—21no—
130C2×Dic10—62no—
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—21no—
141C4⋊Dic5—21no—
142C4⋊Dic5—32no—
143C4⋊Dic5—62no—
144C4⋊Dic5—61no—
145C4⋊Dic5#6711yescharacteristic
146C2×#168—61no—
147D4×Q8—151no—
148#487—151no—
149#477—151no—
150#476—51no—
151#332—151no—
152Q8⋊C8—31no—
153D4⋊C8—151no—
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—
164C3×Dic5—41no—
165C3×Dic5—81no—
166C5×Dic3—22no—
167C5×Dic3—41no—
168C2×C3×Q8—101no—
169C2×C3×D4—51no—
170C22×C3×C4—101no—
171C22×Dic3—102no—
172C2×Dic6—102no—
173C2×Dic6—101no—
174C2×Dic6—202no—
175C2×Dic6—202no—
176C2×Dic6D2011yescharacteristic
177C2×C3×C8—21no—
178C3×C4⋊C4—51no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C22⋊C4—101no—
182C3×C42C22×D511yescharacteristic
183#217—102no—
184C4⋊Dic3—52no—
185C4⋊Dic3—101no—
186C4⋊Dic3D2011yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—102no—
189C4×Dic3—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—21no—
193C5×Q8—32no—
194C5×Q8—61no—
195C2×C4×C5—61no—
196C2×C4×C5—61no—
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—21no—
201C2×Dic5—41no—
202C2×Dic5—62no—
203D20—21no—
204D20#21612yes—
205C4×D5—41no—
206C4×D5—41no—
207C4×D5—124no—
208Dic10—42no—
209Dic10—124no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—41no—
213C5×C8—121no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—51no—
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—101no—
226C4⋊C8—151no—
227C4⋊C8D3×D511yescharacteristic
228#103—301no—
229#103—302no—
230#102—101no—
231C4×C8—31no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—42no—
236C23×C3—101no—
237C3×Q8—202no—
238C3×D4—52no—
239C3×D4—101no—
240C2×C3×C4—101no—
241C2×C3×C4—201no—
242C2×C3×C4—201no—
243C2×C3×C4—201no—
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—102no—
250C2×Dic3—204no—
251Dic6—21no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255Dic6#67712yes—
256C3×C8—41no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—22no—
261C2×D5—41no—
262C2×D5—41no—
263C4×C5—21no—
264C4×C5—62no—
265C4×C5—121no—
266C4×C5D3×SD1611yescharacteristic
267C4×C5#91411yescharacteristic
268C4×C5C2×#21611yescharacteristic
269C4×C5#95111yescharacteristic
270Dic5—41no—
271Dic5—81no—
272Dic5—122no—
273C2×Q8—31no—
274C2×Q8—101no—
275C2×Q8—302no—
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—301no—
285C4⋊C4—31no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—101no—
289C4⋊C4—101no—
290C4⋊C4—152no—
291C4⋊C4—302no—
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×C4—401no—
305C3×C4C2×#67711yescharacteristic
306C3×C4#405411yescharacteristic
307C3×C4#406111yescharacteristic
308C3×C4D5×Q1611yescharacteristic
309Dic3—22no—
310Dic3—41no—
311Dic3—202no—
312C2×C5#505011yescharacteristic
313C2×C5#516911yescharacteristic
314C2×C5#520111yescharacteristic
315D5—42no—
316C23—101no—
317Q8—32no—
318Q8—61no—
319Q8—202no—
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—201no—
331C2×C4—302no—
332C2×C4—604no—
333C2×C4D3×D2011yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C8—41no—
337C8—121no—
338C8—601no—
339C2×C3—202no—
340C2×C3#6502011yescharacteristic
341C2×C3#6509711yescharacteristic
342C2×C3#6511611yescharacteristic
343C5#7114211yescharacteristic, complemented, Sylow
344C22—102no—
345C22—201no—
346C22—201no—
347C22#9147411yescharacteristic
348C4—21no—
349C4—62no—
350C4—121no—
351C4—201no—
352C4—401no—
353C4—602no—
354C4D3×#67711yescharacteristic
355C4#9125311yescharacteristic
356C4#9148411yescharacteristic
357C4D5×#21611yescharacteristic
358C3#1059906211yescharacteristic, complemented, Sylow
359C2—202no—
360C2#1174749211yescharacteristic
361C2#1174811011yescharacteristic
362C2#1174825411yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊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
3. #11746959C2semidirect
4. #11746920C2semidirect
5. #11746307C2semidirect
6. C5×#4484C2semidirect
64. #4484D5semidirect
297. C3×C5#1637semidirect
343. C5#71142semidirect
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
C3×#651312
#117469592
#117469202
#117463072
C5×#44842
#117458352
#105990623
#711425