Finite Group Databasebeta

← #14281811

Subgroups — #14281811

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756337C211yesmaximal, characteristic
2D15×C4⋊C8C211yesmaximal, characteristic
3#11750786C211yesmaximal, characteristic
4C3×C5×Q8⋊C8C211yesmaximal, characteristic, complemented
5#11746356C211yesmaximal, characteristic, complemented
6#11746305C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10599025—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91835C411yescharacteristic
11#91833C411yescharacteristic
12C2×C8×D15—21no—
13#91786C411yescharacteristic
14#91785—21no—
15#91778—21no—
16#91777C411yescharacteristic
17#91761—21no—
18C42×D15C2211yescharacteristic
19C4×Dic30—21no—
20C4×Dic30C2211yescharacteristic
21C3×C5×C4⋊C8C2211yescharacteristic
22C3×C4×C5×C8C2211yescharacteristic
23#91104—21no—
24#91098—21no—
25#91098—21no—
26C4⋊(C3⋊#168)C2211yescharacteristic
27C4×C3⋊#168C2211yescharacteristic
28#68232—51nomaximal, Hall
29#65912—31no—
30D5×C4⋊C8—31no—
31#64974—31no—
32C5×Q8⋊C8D311yescharacteristic, complemented
33Q8⋊#168—31no—
34#64704—31no—
35#64676—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C4×D15C2×C411yescharacteristic
38C2×C4×D15D411yescharacteristic
39C2×C4×D15D411yescharacteristic
40C2×Dic30—21no—
41C2×Dic30C2×C411yescharacteristic
42C2×C3×C5×C8—21no—
43C2×C3×C5×C8—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C42×C5—21no—
47C3×C42×C5C2311yescharacteristic
48#6714—21no—
49#6714—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15C2×C411yescharacteristic
52#6712—21no—
53#6712—21no—
54#6712—21no—
55#6712—21no—
56#6712—21no—
57C4×Dic15—21no—
58C4×Dic15C2×C411yescharacteristic
59C4×Dic15D411yescharacteristic
60C4×Dic15D411yescharacteristic
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C8×D15—42no—
64#5578—51no—
65D3×C4⋊C8—51no—
66#4685—51no—
67C3×Q8⋊C8D511yescharacteristic, complemented
68#4535—51no—
69#4484—51no—
70#4456—51no—
71C4×C5×Q8C2×D311yescharacteristic
72#4092—31no—
73#4090—31no—
74C2×C8×D5—61no—
75#4043—31no—
76#4042—61no—
77#4035—61no—
78#4034—31no—
79#4018—61no—
80C42×D5—31no—
81C4×Dic10—31no—
82C4×Dic10—61no—
83C5×C4⋊C8C2×D311yescharacteristic
84C4×C5×C8C2×D311yescharacteristic
85#3952—61no—
86#3946—61no—
87#3946—61no—
88C4⋊#168—31no—
89C4×#168—31no—
90#1481—151noSylow
91C22×D15C22⋊C411yescharacteristic
92C3×C5×Q8—21no—
93C3×C5×Q8—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×Dic15C22⋊C411yescharacteristic
102C2×Dic15C22⋊C411yescharacteristic
103C2×Dic15C22⋊C411yescharacteristic
104C4×D15—21no—
105C4×D15—21no—
106C4×D15—41no—
107C4×D15SD1612yes—
108C4×D15Q1612yes—
109Dic30—21no—
110Dic30—21no—
111Dic30—42no—
112C3×C5×C8—41no—
113C3×C5×C8—41no—
114C3⋊#168—41no—
115C3⋊#168—41no—
116C3×C4×Q8C2×D511yescharacteristic
117#946—51no—
118#944—51no—
119C2×D3×C8—101no—
120#897—51no—
121#896—101no—
122#889—101no—
123#888—51no—
124#872—101no—
125C42×D3—51no—
126C4×Dic6—51no—
127C4×Dic6—101no—
128C3×C4⋊C8C2×D511yescharacteristic
129C3×C4×C8C2×D511yescharacteristic
130(C2×D3)⋊C8—101no—
131Dic3⋊C8—101no—
132Dic3⋊C8—101no—
133C4⋊(C3⋊C8)—51no—
134C4×C3⋊C8—51no—
135C2×C5×Q8C4×D311yescharacteristic
136C2×C4×D5—31no—
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×Dic10—31no—
140C2×Dic10—61no—
141C2×C5×C8—21no—
142C2×C5×C8—21no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4C4×D311yescharacteristic
145C42×C5—21no—
146C42×C5C22×D311yescharacteristic
147#685—61no—
148#685—61no—
149C4⋊Dic5—31no—
150C4⋊Dic5—61no—
151#683—61no—
152#683—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C4×Dic5—31no—
157C4×Dic5—31no—
158C4×Dic5—31no—
159C4×Dic5—61no—
160C2×#168—61no—
161C2×#168—61no—
162C8×D5—122no—
163#533—151no—
164#431—151no—
165C2×C4⋊C8—151no—
166Q8⋊C8—151no—
167Q8⋊C8—151no—
168Q8⋊C8—151no—
169Q8⋊C8D1511yescharacteristic, complemented
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×D15—21no—
172C2×D15—21no—
173C2×D15#10312yes—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176C3×C4×C5—41no—
177C3×C4×C5#13111yescharacteristic
178C3×C4×C5#13111yescharacteristic
179C3×C4×C5C2×SD1611yescharacteristic
180C3×C4×C5C2×Q1611yescharacteristic
181Dic15—21no—
182Dic15—21no—
183Dic15—41no—
184Dic15—41no—
185Dic15#10312yes—
186C2×C3×Q8C4×D511yescharacteristic
187C2×C4×D3—51no—
188C2×C4×D3—51no—
189C2×C4×D3—51no—
190C2×Dic6—51no—
191C2×Dic6—101no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4C4×D511yescharacteristic
196C3×C42—21no—
197C3×C42C22×D511yescharacteristic
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200C4⋊Dic3—51no—
201C4⋊Dic3—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205Dic3⋊C4—101no—
206Dic3⋊C4—101no—
207C4×Dic3—51no—
208C4×Dic3—51no—
209C4×Dic3—51no—
210C4×Dic3—101no—
211C2×C3⋊C8—101no—
212C2×C3⋊C8—101no—
213D3×C8—202no—
214C22×D5—31no—
215C5×Q8—21no—
216C5×Q8—21no—
217C2×C4×C5—21no—
218C2×C4×C5—21no—
219C2×C4×C5C2×C4×D311yescharacteristic
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—61no—
226C2×Dic5—61no—
227C4×D5—32no—
228C4×D5—32no—
229C4×D5—61no—
230C4×D5—61no—
231C4×D5—121no—
232Dic10—61no—
233Dic10—61no—
234Dic10—122no—
235C5×C8—41no—
236C5×C8—41no—
237#168—121no—
238#168—121no—
239C22×C8—301no—
240C4⋊Q8—151no—
241C4⋊Q8—151no—
242#125—301no—
243C22⋊Q8—151no—
244C22⋊Q8—151no—
245C22⋊Q8—301no—
246C4×Q8—151no—
247C4×Q8—301no—
248C4×Q8C2×D1511yescharacteristic
249#117—301no—
250C2×C42—151no—
251C4⋊C8—151no—
252C4⋊C8—301no—
253C4⋊C8—301no—
254C4⋊C8C2×D1511yescharacteristic
255C22⋊C8—301no—
256C4×C8—151no—
257C4×C8C2×D1511yescharacteristic
258C2×C3×C5#40811yescharacteristic
259C2×C3×C5C2×#10311yescharacteristic
260C2×C3×C5#42111yescharacteristic
261D15—22no—
262C22×D3—51no—
263C3×Q8—21no—
264C3×Q8—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4D4×D511yescharacteristic
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—101no—
274C2×Dic3—101no—
275C4×D3—52no—
276C4×D3—52no—
277C4×D3—101no—
278C4×D3—101no—
279C4×D3—201no—
280Dic6—101no—
281Dic6—101no—
282Dic6—202no—
283C3×C8—41no—
284C3×C8—41no—
285C3⋊C8—201no—
286C3⋊C8—201no—
287C22×C5D3×C22⋊C411yescharacteristic
288C2×D5—32no—
289C2×D5—61no—
290C2×D5—61no—
291C4×C5—21no—
292C4×C5—41no—
293C4×C5—41no—
294C4×C5#90111yescharacteristic
295C4×C5#90711yescharacteristic
296C4×C5D3×SD1611yescharacteristic
297C4×C5D3×Q1611yescharacteristic
298Dic5—32no—
299Dic5—61no—
300Dic5—61no—
301Dic5—121no—
302Dic5—121no—
303C2×Q8—151no—
304C2×Q8—301no—
305C2×Q8C4×D1511yescharacteristic
306C22×C4—151no—
307C22×C4—151no—
308C22×C4—151no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—301no—
312C2×C8—301no—
313C2×C8—602no—
314C4⋊C4—21no—
315C4⋊C4—151no—
316C4⋊C4—301no—
317C4⋊C4—301no—
318C4⋊C4—301no—
319C4⋊C4—301no—
320C4⋊C4—301no—
321C4⋊C4—301no—
322C4⋊C4C4×D1511yescharacteristic
323C22⋊C4—301no—
324C22⋊C4—301no—
325C42—21no—
326C42—151no—
327C42—151no—
328C42—151no—
329C42—301no—
330C42C22×D1511yescharacteristic
331C3×C5#148111yescharacteristic, complemented, Hall
332C22×C3D5×C22⋊C411yescharacteristic
333C2×D3—52no—
334C2×D3—101no—
335C2×D3—101no—
336C3×C4—21no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4#404711yescharacteristic
340C3×C4#405311yescharacteristic
341C3×C4D5×SD1611yescharacteristic
342C3×C4D5×Q1611yescharacteristic
343Dic3—52no—
344Dic3—101no—
345Dic3—101no—
346Dic3—201no—
347Dic3—201no—
348C2×C5#472711yescharacteristic
349C2×C5D3×#10311yescharacteristic
350C2×C5#482111yescharacteristic
351D5—62no—
352C23—151no—
353Q8—21no—
354Q8—21no—
355Q8—301no—
356Q8—301no—
357Q8—602no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—151no—
361C2×C4—152no—
362C2×C4—152no—
363C2×C4—151no—
364C2×C4—151no—
365C2×C4—301no—
366C2×C4—301no—
367C2×C4—301no—
368C2×C4—301no—
369C2×C4—601no—
370C2×C4C2×C4×D1511yescharacteristic
371C2×C4D4×D1511yescharacteristic
372C2×C4D4×D1511yescharacteristic
373C8—41no—
374C8—41no—
375C8—601no—
376C8—601no—
377C2×C3#6501611yescharacteristic
378C2×C3D5×#10311yescharacteristic
379C2×C3#6511011yescharacteristic
380D3—102no—
381C5#6823211yescharacteristic, complemented, Sylow
382C22—152no—
383C22—301no—
384C22—301no—
385C22C22⋊C4×D1511yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—152no—
390C4—301no—
391C4—301no—
392C4—601no—
393C4—601no—
394C4#9179011yescharacteristic
395C4#9179611yescharacteristic
396C4SD16×D1511yescharacteristic
397C4Q16×D1511yescharacteristic
398C3#1059902511yescharacteristic, complemented, Sylow
399C2—302no—
400C2#1175082811yescharacteristic
401C2D15×#10311yescharacteristic
402C2#1175092211yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterQ8⋊C8D15
hypocenterC3×C5#1481
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×C5×Q8⋊C8C2semidirect
5. #11746356C2semidirect
6. #11746305C2semidirect
7. #11746277C2semidirect
32. C5×Q8⋊C8D3semidirect
67. C3×Q8⋊C8D5semidirect
169. Q8⋊C8D15semidirect
331. C3×C5#1481semidirect
381. C5#68232semidirect
398. C3#10599025semidirect

Maximal subgroups

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

subgroupindex
#117563372
D15×C4⋊C82
#117507862
C3×C5×Q8⋊C82
#117463562
#117463052
#117462772
#105990253
#682325