Finite Group Databasebeta

← #14289782

Subgroups — #14289782

Order 1920.

456 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 98 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
1Q8×D60C211yesmaximal, characteristic
2C3×#65310C211yesmaximal, characteristic, complemented
3#11746942C211yesmaximal, characteristic
4#11746920C211yesmaximal, characteristic, complemented
5C5×#4535C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic
8#10599062—31nomaximal, Hall
9C2×Q8×D15—21no—
10C3×C4×C5×Q8C2211yescharacteristic
11#91786—21no—
12#91786—22no—
13C4×D60—21no—
14C4×D60C2211yescharacteristic
15#91758—21no—
16#91758C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C4×C5×C3⋊C8C2211yescharacteristic
20C3×#3967—21no—
21C3×#3939—21no—
22C3×C4⋊#168C2211yescharacteristic
23#90987—21no—
24#90971—22no—
25#90968—21no—
26#71163—51nomaximal, Hall
27Q8×D20—31no—
28#65310D311yescharacteristic, complemented
29#65131—31no—
30#64970—31no—
31C5×Q8⋊C8—31no—
32#64706—31no—
33#64679—31no—
34C2×C3×C5×Q8D411yescharacteristic
35Q8×D15—42no—
36Q8×D15—42no—
37C2×D60D411yescharacteristic
38C2×C4×D15—22no—
39C2×C4×D15—21no—
40C2×Dic30—22no—
41C2×Dic30—21no—
42C2×C3×Dic10—21no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5—21no—
46C3×C42×C5C2311yescharacteristic
47#6714—22no—
48#6714—21no—
49C4⋊Dic15—22no—
50C4⋊Dic15—21no—
51C4⋊Dic15D412yes—
52C4⋊Dic15D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C3×C4⋊Dic5—21no—
56C3×C4⋊Dic5—21no—
57C2×C3×#168—21no—
58Q8×D12—51no—
59C3×#477—51no—
60#5084—51no—
61#5079—51no—
62#4535D511yescharacteristic, complemented
63#4483—51no—
64#4482—51no—
65C2×Q8×D5—61no—
66C4×C5×Q8C2×D311yescharacteristic
67#4043—62no—
68#4043—61no—
69C4×D20—31no—
70C4×D20—61no—
71#4015—31no—
72#4015—61no—
73#4015C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3967—21no—
77#3953—61no—
78#3949—61no—
79#3948—62no—
80#3939—21no—
81C4⋊#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×D15—21no—
84C3×C5×Q8—21no—
85C3×C5×Q8SD1612yes—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—22no—
93D60—21no—
94D60Q1612yes—
95C4×D15—44no—
96C4×D15—41no—
97C4×D15—41no—
98Dic30—44no—
99Dic30—41no—
100Dic30—41no—
101C2×C3×Dic5—41no—
102C3×Dic10—42no—
103C3×#168—41no—
104C5×C3⋊C8—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4⋊Q8—51no—
108C3×C4×Q8C2×D511yescharacteristic
109#897—102no—
110#897—101no—
111C4×D12—51no—
112C4×D12—101no—
113#869—51no—
114#869—101no—
115C3×#107—101no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#835—102no—
119#809—101no—
120#808—101no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8#6711yescharacteristic
124Q8×D5—122no—
125Q8×D5—122no—
126C2×D20—31no—
127C2×C4×D5—62no—
128C2×C4×D5—61no—
129C2×Dic10—21no—
130C2×Dic10—62no—
131C2×Dic10—61no—
132C2×C5×C8—61no—
133C2×C5×C8—61no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4#6711yescharacteristic
136C42×C5—21no—
137C42×C5C22×D311yescharacteristic
138#685—62no—
139#685—61no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C4⋊Dic5—32no—
143C4⋊Dic5—31no—
144C4⋊Dic5—62no—
145C4⋊Dic5—61no—
146C2×#168—21no—
147D4×Q8—151no—
148#487—151no—
149#477—51no—
150#476—151no—
151#332—151no—
152Q8⋊C8—31no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—22no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5C2×Q1611yescharacteristic
163C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—41no—
166Dic15—42no—
167C3×Dic5—81no—
168C2×C3×Q8—101no—
169C2×C3×Q8D2011yescharacteristic
170D3×Q8—202no—
171D3×Q8—202no—
172C2×D12—51no—
173C2×C4×D3—102no—
174C2×C4×D3—101no—
175C2×Dic6—102no—
176C2×Dic6—101no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—101no—
180C3×C4⋊C4—101no—
181C3×C4⋊C4D2011yescharacteristic
182C3×C42—21no—
183C3×C42C22×D511yescharacteristic
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—51no—
187C4⋊Dic3—52no—
188C4⋊Dic3—102no—
189C4⋊Dic3—101no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192C22×D5—61no—
193C5×Q8—21no—
194C5×Q8#21512yes—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5C2×#6711yescharacteristic
200C2×Dic5—41no—
201C2×Dic5—62no—
202C2×Dic5—61no—
203D20—32no—
204D20—61no—
205C4×D5—124no—
206C4×D5—121no—
207C4×D5—121no—
208Dic10—42no—
209Dic10—124no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—121no—
213C5×C8—121no—
214#168—41no—
215C22×Q8—301no—
216C4⋊Q8—51no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8D3×D511yescharacteristic
222C4×D4—151no—
223C4×D4—301no—
224#107—101no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#103—101no—
229#103—302no—
230#102—301no—
231C4×C8—31no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—42no—
236C22×D3—101no—
237C3×Q8—21no—
238C3×Q8—202no—
239C3×Q8#67712yes—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—201no—
243C2×C3×C4C2×D2011yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×Dic3—101no—
247C2×Dic3—102no—
248D12—52no—
249D12—101no—
250C4×D3—204no—
251C4×D3—201no—
252C4×D3—201no—
253Dic6—204no—
254Dic6—201no—
255Dic6—201no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C22×C5#93711yescharacteristic
260C2×D5—62no—
261C2×D5—121no—
262C2×D5—121no—
263C4×C5—21no—
264C4×C5—22no—
265C4×C5—41no—
266C4×C5D3×Q1611yescharacteristic
267C4×C5#91811yescharacteristic
268C4×C5C2×#21511yescharacteristic
269C4×C5#94911yescharacteristic
270Dic5—81no—
271Dic5—121no—
272Dic5—122no—
273C2×Q8—101no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—602no—
277C2×Q8—602no—
278C2×Q8#120211yescharacteristic
279C2×D4—151no—
280C22×C4—302no—
281C22×C4—301no—
282C2×C8—61no—
283C2×C8—61no—
284C2×C8—101no—
285C4⋊C4—21no—
286C4⋊C4—101no—
287C4⋊C4—101no—
288C4⋊C4—152no—
289C4⋊C4—151no—
290C4⋊C4—302no—
291C4⋊C4—301no—
292C4⋊C4#120211yescharacteristic
293C22⋊C4—302no—
294C22⋊C4—301no—
295C42—21no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#402811yescharacteristic
299C2×D3—102no—
300C2×D3—201no—
301C2×D3—201no—
302C3×C4—21no—
303C3×C4—22no—
304C3×C4—41no—
305C3×C4—401no—
306C3×C4C2×#67711yescharacteristic
307C3×C4#405411yescharacteristic
308C3×C4#406111yescharacteristic
309C3×C4D5×Q1611yescharacteristic
310Dic3—201no—
311Dic3—202no—
312C2×C5#504611yescharacteristic
313C2×C5#518611yescharacteristic
314C2×C5#520111yescharacteristic
315D5—122no—
316C23—301no—
317Q8—21no—
318Q8—202no—
319Q8—604no—
320Q8—601no—
321Q8—601no—
322Q8#665812yes—
323D4—152no—
324D4—301no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—201no—
328C2×C4—302no—
329C2×C4—301no—
330C2×C4—604no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4C2×#120211yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—121no—
338C8—201no—
339C2×C3#6502011yescharacteristic
340C2×C3#6509711yescharacteristic
341C2×C3#6511611yescharacteristic
342D3—202no—
343C5#7116311yescharacteristic, complemented, Sylow
344C22—302no—
345C22—601no—
346C22—601no—
347C22#9157211yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—401no—
352C4—602no—
353C4—601no—
354C4#9130111yescharacteristic
355C4C2×#665811yescharacteristic
356C4#9151111yescharacteristic
357C4#9152411yescharacteristic
358C3#1059906211yescharacteristic, complemented, Sylow
359C2—602no—
360C2#1174855111yescharacteristic
361C2#1174931011yescharacteristic
362C2#1174946011yescharacteristic
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1637
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. C3×#65310C2semidirect
4. #11746920C2semidirect
5. C5×#4535C2semidirect
6. #11745860C2semidirect
28. #65310D3semidirect
62. #4535D5semidirect
297. C3×C5#1637semidirect
343. C5#71163semidirect
358. C3#10599062semidirect

Maximal subgroups

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

subgroupindex
Q8×D602
C3×#653102
#117469422
#117469202
C5×#45352
#117458602
#117458382
#105990623
#711635