Finite Group Databasebeta

← #14289766

Subgroups — #14289766

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#11751185C211yesmaximal, characteristic
3C5×#5079C211yesmaximal, characteristic, complemented
4C3×#65380C211yesmaximal, characteristic, complemented
5#11745858C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745838C211yesmaximal, characteristic
8#10602030—31nomaximal, Hall
9C2×D15⋊Q8—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C4×D60C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91468—21no—
15#91419—22no—
16#91418—21no—
17#91383—21no—
18#91093—21no—
19#91092—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#835—22no—
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3942—21no—
24C3×#3939—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71163—51nomaximal, Hall
27#66061—31no—
28C5×#487—31no—
29#65380D311yescharacteristic, complemented
30#65373—31no—
31#64767—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×D60D411yescharacteristic
36C2×C4×D15—21no—
37C2×C5×Dic6—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×#1204—22no—
40C2×#1200—22no—
41D15⋊Q8—42no—
42D15⋊Q8—42no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46#6714—21no—
47C4⋊Dic15D411yescharacteristic
48C2×C3⋊#168—21no—
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—
59C3×#477—51no—
60#5084—51no—
61#5079D511yescharacteristic, complemented
62#4535—51no—
63#4483—51no—
64#4482—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8—31no—
67C5×C4⋊Q8C2×D311yescharacteristic
68#4092—61no—
69#4042—62no—
70#4039—61no—
71#4034—61no—
72C4×D20—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×#103—62no—
75C4×C5×C8—31no—
76#3942—21no—
77#3941—61no—
78#3940—61no—
79#3939—21no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×D15—21no—
84C3×C5×Q8—42no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90D60—21no—
91D60Q1612yes—
92C4×D15—41no—
93C4×D15—41no—
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⋊#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4⋊Q8C2×D511yescharacteristic
108C3×C4×Q8—51no—
109#897—101no—
110#897—102no—
111C4×D12—51no—
112C4×D12—101no—
113#869—101no—
114#869C2×D511yescharacteristic
115C3×#107—101no—
116C3×C4⋊C8—51no—
117C3×#103—101no—
118#835—22no—
119#809—101no—
120#808—101no—
121C4⋊(C3⋊C8)—51no—
122C4×C3⋊C8C2×D511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×Q8—61no—
125Q8×D5—122no—
126Q8×D5—122no—
127C2×D20—31no—
128C2×C4×D5—62no—
129C2×C4×D5—61no—
130C2×Dic10—62no—
131C2×Dic10#6711yescharacteristic
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—32no—
136C5×C4⋊C4—61no—
137C42×C5C22×D311yescharacteristic
138#685—62no—
139#685—61no—
140C4⋊Dic5—31no—
141C4⋊Dic5#6711yescharacteristic
142#683—21no—
143#683—62no—
144C4×Dic5—21no—
145C2×#168—21no—
146C2×#168—61no—
147D4×Q8—151no—
148#487—31no—
149#477—51no—
150#476—151no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×D15—22no—
156C2×D15—41no—
157C2×D15—41no—
158C3×C4×C5—21no—
159C3×C4×C5—81no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—41no—
165C3×Dic5—22no—
166C3×Dic5—41no—
167C5×Dic3—42no—
168C2×C3×Q8—21no—
169C2×C3×Q8—51no—
170D3×Q8—202no—
171D3×Q8—202no—
172C2×D12—51no—
173C2×C4×D3—102no—
174C2×C4×D3—101no—
175C2×Dic6—21no—
176C2×Dic6—102no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—51no—
181C3×C4⋊C4—101no—
182C3×C42—101no—
183C3×C42C22×D511yescharacteristic
184(C2×D3)⋊C4—102no—
185(C2×D3)⋊C4—101no—
186C4⋊Dic3—21no—
187C4⋊Dic3—51no—
188C4⋊Dic3—102no—
189C4⋊Dic3C22⋊D512yes—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—61no—
193C5×Q8—42no—
194C5×Q8—121no—
195C5×Q8—121no—
196C2×C4×C5—41no—
197C2×C4×C5—62no—
198C2×C4×C5D3×D411yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5C2×#6711yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—61no—
204D20—32no—
205D20—61no—
206C4×D5—124no—
207C4×D5—121no—
208C4×D5—121no—
209Dic10—21no—
210Dic10—124no—
211Dic10#21512yes—
212C5×C8—121no—
213#168—41no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—31no—
217C4⋊Q8—301no—
218C4⋊Q8D3×D511yescharacteristic
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—51no—
222C4×D4—151no—
223C4×D4—301no—
224#107—101no—
225#106—301no—
226C4⋊C8—51no—
227C4⋊C8—151no—
228#103—62no—
229#103—101no—
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—42no—
238C3×Q8—52no—
239C3×Q8—101no—
240C2×C3×C4—41no—
241C2×C3×C4—101no—
242C2×C3×C4—101no—
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4C2×C22⋊D511yescharacteristic
246C2×Dic3—22no—
247C2×Dic3—101no—
248D12—52no—
249D12—101no—
250C4×D3—204no—
251C4×D3—201no—
252C4×D3—201no—
253Dic6—41no—
254Dic6—41no—
255Dic6—204no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—62no—
261C2×D5—121no—
262C2×D5—121no—
263C4×C5—21no—
264C4×C5—81no—
265C4×C5—122no—
266C4×C5D3×Q1611yescharacteristic
267C4×C5#91811yescharacteristic
268C4×C5C2×#21511yescharacteristic
269C4×C5#94911yescharacteristic
270Dic5—22no—
271Dic5—41no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—51no—
275C2×Q8—61no—
276C2×Q8—302no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—151no—
280C22×C4—302no—
281C22×C4—301no—
282C2×C8—61no—
283C2×C8—101no—
284C2×C8—301no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—32no—
288C4⋊C4—51no—
289C4⋊C4—61no—
290C4⋊C4—101no—
291C4⋊C4—151no—
292C4⋊C4—302no—
293C22⋊C4—302no—
294C22⋊C4—301no—
295C42—101no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#408311yescharacteristic
299C2×D3—102no—
300C2×D3—201no—
301C2×D3—201no—
302C3×C4—21no—
303C3×C4—81no—
304C3×C4—102no—
305C3×C4—201no—
306C3×C4D5×SD1611yescharacteristic
307C3×C4#406011yescharacteristic
308C3×C4D5×Q1611yescharacteristic
309C3×C4#406411yescharacteristic
310Dic3—42no—
311Dic3—201no—
312C2×C5#504611yescharacteristic
313C2×C5#518611yescharacteristic
314C2×C5#520111yescharacteristic
315D5—122no—
316C23—301no—
317Q8—42no—
318Q8—52no—
319Q8—101no—
320Q8—121no—
321Q8—121no—
322Q8—604no—
323D4—152no—
324D4—301no—
325C2×C4—41no—
326C2×C4—62no—
327C2×C4—101no—
328C2×C4—101no—
329C2×C4—301no—
330C2×C4—604no—
331C2×C4—601no—
332C2×C4—601no—
333C2×C4D5×#6711yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—601no—
339C2×C3#6535111yescharacteristic
340C2×C3#6545811yescharacteristic
341C2×C3#6547511yescharacteristic
342D3—202no—
343C5#7116311yescharacteristic, complemented, Sylow
344C22—302no—
345C22—601no—
346C22—601no—
347C22#9157711yescharacteristic
348C4—21no—
349C4—81no—
350C4—102no—
351C4—122no—
352C4—201no—
353C4—601no—
354C4D5×#21511yescharacteristic
355C4#9150211yescharacteristic
356C4#9151111yescharacteristic
357C4#9151211yescharacteristic
358C3#1060203011yescharacteristic, complemented, Sylow
359C2—602no—
360C2#1174916711yescharacteristic
361C2#1174939711yescharacteristic
362C2#1174940211yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊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
3. C5×#5079C2semidirect
4. C3×#65380C2semidirect
5. #11745858C2semidirect
6. #11745841C2semidirect
29. #65380D3semidirect
61. #5079D5semidirect
297. C3×C5#1637semidirect
343. C5#71163semidirect
358. C3#10602030semidirect

Maximal subgroups

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

subgroupindex
#117525392
#117511852
C5×#50792
C3×#653802
#117458582
#117458412
#117458382
#106020303
#711635