Finite Group Databasebeta

← #14289802

Subgroups — #14289802

Order 1920.

456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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#11752539C211yesmaximal, characteristic
2#11750943C211yesmaximal, characteristic
3#11746930C211yesmaximal, characteristic, complemented
4#11746916C211yesmaximal, characteristic, complemented
5C5×#4486C211yesmaximal, characteristic, complemented
6C3×#64704C211yesmaximal, characteristic, complemented
7#11745839C211yesmaximal, characteristic
8#10599252—31nomaximal, Hall
9C2×D15⋊Q8—21no—
10C4×D60C2211yescharacteristic
11#91758C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91468—21no—
15#91419—22no—
16#91418—21no—
17#91383—21no—
18C3×C5×C4⋊C8C2211yescharacteristic
19#91105—21no—
20#91101—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×#168C2211yescharacteristic
23#90990—21no—
24#90975—22no—
25#90971—21no—
26#68269—51nomaximal, Hall
27#66061—31no—
28#65382—31no—
29#65139—31no—
30#65131—31no—
31C5×#332—31no—
32#64704D311yescharacteristic, complemented
33#64703—31no—
34C2×D60D411yescharacteristic
35C2×C4×D15—21no—
36C2×Dic30—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×#1204—22no—
40C2×#1200—22no—
41D15⋊Q8—42no—
42D15⋊Q8—42no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15D411yescharacteristic
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3D412yes—
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56#6668—22no—
57#6667—22no—
58Q8×D12—51no—
59#5021—51no—
60#4842—51no—
61#4681—51no—
62C3×Q8⋊C8—51no—
63#4486D511yescharacteristic, complemented
64#4459—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8—31no—
67#4092—61no—
68#4042—62no—
69#4039—61no—
70#4034—61no—
71C4×D20—31no—
72#4015—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C5×C4⋊C8C2×D311yescharacteristic
76#3953—61no—
77#3950—61no—
78#3949—61no—
79#3948—61no—
80#3942—62no—
81C4×#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×D15—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—41no—
89D60—21no—
90D60Q1612yes—
91C4×D15—41no—
92C4×D15—41no—
93Dic30—42no—
94C2×C5×Dic3—22no—
95C5×Dic6—41no—
96C5×Dic6—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10SD1612yes—
101#1204—44no—
102#1200—44no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4×Q8—51no—
108#897—101no—
109#897—102no—
110C4×D12—51no—
111C4×D12—101no—
112#869—51no—
113#869—101no—
114#869C2×D511yescharacteristic
115C3×C4⋊C8C2×D511yescharacteristic
116C3×C4×C8—51no—
117#835—101no—
118#821—101no—
119#817—101no—
120#816—102no—
121#807—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—61no—
124Q8×D5—122no—
125Q8×D5—122no—
126C2×D20—31no—
127C2×C4×D5—62no—
128C2×C4×D5—61no—
129C2×Dic10—62no—
130C2×Dic10—61no—
131C2×Dic10D1211yescharacteristic
132C2×C5×C8—21no—
133C2×C5×C8—61no—
134C5×C4⋊C4—32no—
135C5×C4⋊C4—61no—
136C42×C5C22×D311yescharacteristic
137#685—62no—
138#685—61no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5D1211yescharacteristic
143#683—21no—
144#683—62no—
145C4×Dic5—21no—
146C2×#168—21no—
147D4×Q8—151no—
148#487—151no—
149#477—151no—
150#476—151no—
151#332—31no—
152Q8⋊C8—51no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—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—41no—
164Dic15—81no—
165C3×Dic5—22no—
166C3×Dic5—41no—
167C5×Dic3—42no—
168C2×C3×Q8—51no—
169D3×Q8—202no—
170D3×Q8—202no—
171C2×D12—51no—
172C2×C4×D3—102no—
173C2×C4×D3—101no—
174C2×Dic6—21no—
175C2×Dic6—102no—
176C2×Dic6—101no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C42—101no—
182C3×C42C22×D511yescharacteristic
183(C2×D3)⋊C4—102no—
184(C2×D3)⋊C4—101no—
185C4⋊Dic3—21no—
186C4⋊Dic3—51no—
187C4⋊Dic3—102no—
188C4⋊Dic3—101no—
189C4⋊Dic3—101no—
190C4⋊Dic3D2012yes—
191C2×C3⋊C8—21no—
192C22×D5—61no—
193C5×Q8—121no—
194C5×Q8—121no—
195C2×C4×C5—62no—
196C2×C4×C5C2×D1211yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×C4×C5D3×D411yescharacteristic
199C2×Dic5—21no—
200C2×Dic5—21no—
201C2×Dic5—61no—
202C2×Dic5—121no—
203D20—32no—
204D20—61no—
205C4×D5—124no—
206C4×D5—121no—
207C4×D5—121no—
208Dic10—21no—
209Dic10—124no—
210Dic10—122no—
211Dic10#20412yes—
212C5×C8—41no—
213C5×C8—121no—
214#168—41no—
215C22×Q8—301no—
216C4⋊Q8—31no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—51no—
222C4×D4—151no—
223C4×D4—301no—
224#107—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8D3×D511yescharacteristic
228#103—302no—
229#103—301no—
230#102—301no—
231C4×C8—51no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235D15—42no—
236C22×D3—101no—
237C3×Q8—52no—
238C3×Q8—101no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×Dic3—22no—
245C2×Dic3—101no—
246C2×Dic3—201no—
247D12—52no—
248D12—101no—
249C4×D3—204no—
250C4×D3—201no—
251C4×D3—201no—
252Dic6—41no—
253Dic6—41no—
254Dic6—204no—
255Dic6—202no—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—62no—
261C2×D5—121no—
262C2×D5—121no—
263C4×C5—21no—
264C4×C5—122no—
265C4×C5C2×#20411yescharacteristic
266C4×C5#90811yescharacteristic
267C4×C5#91511yescharacteristic
268C4×C5D3×Q1611yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—121no—
272Dic5—241no—
273C2×Q8—51no—
274C2×Q8—61no—
275C2×Q8—302no—
276C2×Q8—301no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—151no—
280C22×C4—302no—
281C22×C4—301no—
282C2×C8—21no—
283C2×C8—61no—
284C2×C8—101no—
285C4⋊C4—32no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—101no—
289C4⋊C4—151no—
290C4⋊C4—302no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C22⋊C4—302no—
294C22⋊C4—301no—
295C42—101no—
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—102no—
304C3×C4—201no—
305C3×C4#405711yescharacteristic
306C3×C4D5×SD1611yescharacteristic
307C3×C4#406111yescharacteristic
308C3×C4D5×Q1611yescharacteristic
309Dic3—42no—
310Dic3—201no—
311Dic3—401no—
312C2×C5#473111yescharacteristic
313C2×C5#480911yescharacteristic
314C2×C5#482711yescharacteristic
315D5—122no—
316C23—301no—
317Q8—52no—
318Q8—101no—
319Q8—121no—
320Q8—121no—
321Q8—602no—
322Q8—604no—
323D4—152no—
324D4—301no—
325C2×C4—62no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—301no—
329C2×C4—604no—
330C2×C4—601no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4D5×D1211yescharacteristic
334C2×C4D3×D2011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—41no—
337C8—121no—
338C8—201no—
339C2×C3#6504211yescharacteristic
340C2×C3#6506511yescharacteristic
341C2×C3#6509711yescharacteristic
342D3—202no—
343C5#6826911yescharacteristic, complemented, Sylow
344C22—302no—
345C22—601no—
346C22—601no—
347C22#9147611yescharacteristic
348C4—21no—
349C4—102no—
350C4—122no—
351C4—201no—
352C4—601no—
353C4—1201no—
354C4D5×#20411yescharacteristic
355C4#9125011yescharacteristic
356C4#9148811yescharacteristic
357C4#9151111yescharacteristic
358C3#1059925211yescharacteristic, complemented, Sylow
359C2—602no—
360C2#1174749611yescharacteristic
361C2#1174811511yescharacteristic
362C2#1174826111yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×D60D4
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. #11746930C2semidirect
4. #11746916C2semidirect
5. C5×#4486C2semidirect
6. C3×#64704C2semidirect
32. #64704D3semidirect
63. #4486D5semidirect
297. C3×C5#1637semidirect
343. C5#68269semidirect
358. C3#10599252semidirect

Maximal subgroups

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

subgroupindex
#117525392
#117509432
#117469302
#117469162
C5×#44862
C3×#647042
#117458392
#105992523
#682695