Finite Group Databasebeta

← #14285017

Subgroups — #14285017

Order 1920.

504 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 105 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#11756475C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3D15×C4⋊C8C211yesmaximal, characteristic, complemented
4C3×C5×#331C211yesmaximal, characteristic, complemented
5#11746365C211yesmaximal, characteristic, complemented
6#11746302C211yesmaximal, characteristic, complemented
7#11746302C211yesmaximal, characteristic, complemented
8#10599178—31nomaximal, Hall
9C2×#6819C412yes—
10C3×C5×#127C2211yescharacteristic
11#91827—21no—
12#91827—21no—
13#91825C412yes—
14D4×Dic15—21no—
15D4×Dic15—21no—
16C2×C8×D15—21no—
17C42×D15C2211yescharacteristic
18#91758C2211yescharacteristic
19C3×C5×C4⋊C8C2211yescharacteristic
20C3×C5×C4⋊C8C2211yescharacteristic
21#91104—21no—
22#91099—21no—
23#91098—21no—
24C4⋊(C3⋊#168)C2211yescharacteristic
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68385—51nomaximal, Hall
27#66050—31no—
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#331D311yescharacteristic, complemented
31#64764—31no—
32#64701—31no—
33#64701—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C412yes—
37C2×#1220—22no—
38C22×Dic15—22no—
39#6819—44no—
40C2×C4×D15C2×C411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×C4×D15D411yescharacteristic
43C2×Dic30C2×C412yes—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47#6719—22no—
48#6719—22no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4×Dic15C2×C411yescharacteristic
52C4×Dic15D411yescharacteristic
53C4×Dic15D411yescharacteristic
54C2×C3⋊#168—21no—
55C2×C3⋊#168—21no—
56C8×D15—42no—
57#5716—51no—
58#4835—51no—
59D3×C4⋊C8—51no—
60C3×#331D511yescharacteristic, complemented
61#4544—51no—
62#4481—51no—
63#4481—51no—
64C2×#711—32no—
65C5×#127C2×D311yescharacteristic
66#4084—61no—
67#4084—61no—
68#4082—32no—
69D4×Dic5—61no—
70D4×Dic5—61no—
71C2×C8×D5—61no—
72C42×D5—31no—
73#4015—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C5×C4⋊C8C2×D311yescharacteristic
76#3952—61no—
77#3947—61no—
78#3946—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1551—151noSylow
82C23×C3×C5—22no—
83C22×D15C22⋊C411yescharacteristic
84C3×C5×D4—42no—
85C3×C5×D4—41no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92#1220—44no—
93C2×Dic15—22no—
94C2×Dic15—44no—
95C2×Dic15C22⋊C411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—22no—
99C4×D15—21no—
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—21no—
103Dic30—42no—
104C3×C5×C8—41no—
105C3×C5×C8—41no—
106C3⋊#168—41no—
107C3⋊#168—41no—
108C2×#237—52no—
109C3×#127C2×D511yescharacteristic
110#938—101no—
111#938—101no—
112#936—52no—
113D4×Dic3—101no—
114D4×Dic3—101no—
115C2×D3×C8—101no—
116C42×D3—51no—
117#869—51no—
118C3×C4⋊C8C2×D511yescharacteristic
119C3×C4⋊C8C2×D511yescharacteristic
120(C2×D3)⋊C8—101no—
121#815—101no—
122Dic3⋊C8—101no—
123C4⋊(C3⋊C8)—51no—
124C4⋊(C3⋊C8)—51no—
125C2×C5×D4—21no—
126C2×C5×D4—21no—
127C2×C5×D4C4×D312yes—
128C2×C22⋊D5—62no—
129C22×Dic5—62no—
130#711—124no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×Dic10—32no—
135C2×C5×C8—21no—
136C2×C5×C8—21no—
137C42×C5C22×D311yescharacteristic
138C22⋊Dic5—62no—
139C22⋊Dic5—62no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145C2×#168—61no—
146C2×#168—61no—
147C8×D5—122no—
148#532—151no—
149#432—151no—
150C2×C4⋊C8—151no—
151#333—151no—
152#333—151no—
153#331—151no—
154#331D1511yescharacteristic, complemented
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5—42no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×D15—21no—
160C2×D15—21no—
161C2×D15#10012yes—
162C3×C4×C5—21no—
163C3×C4×C5#13511yescharacteristic
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C3×C4×C5#13711yescharacteristic
167Dic15—21no—
168Dic15—21no—
169Dic15—21no—
170Dic15—42no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4C4×D512yes—
174C2×#67—102no—
175C22×Dic3—102no—
176#237—204no—
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×Dic6—52no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C3×C42C22×D511yescharacteristic
184#217—102no—
185#217—102no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188C4×Dic3—51no—
189C4×Dic3—51no—
190C4×Dic3—51no—
191C2×C3⋊C8—101no—
192C2×C3⋊C8—101no—
193D3×C8—202no—
194C23×C5—22no—
195C22×D5—31no—
196C5×D4—42no—
197C5×D4—41no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C22⋊D5—124no—
205C2×Dic5—31no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—62no—
209C2×Dic5—124no—
210C4×D5—62no—
211C4×D5—61no—
212C4×D5—61no—
213C4×D5—61no—
214C4×D5—61no—
215Dic10—122no—
216C5×C8—41no—
217C5×C8—41no—
218#168—121no—
219#168—121no—
220C2×#41—152no—
221C22×C8—301no—
222C4⋊Q8—151no—
223#127C2×D1511yescharacteristic
224#124—152no—
225#121—301no—
226#121—301no—
227C4×D4—301no—
228C4×D4—301no—
229C2×C42—151no—
230C4⋊C8—151no—
231C4⋊C8—151no—
232C4⋊C8—301no—
233C4⋊C8C2×D1511yescharacteristic
234C4⋊C8C2×D1511yescharacteristic
235C22⋊C8—301no—
236#97—301no—
237C2×C3×C5—82no—
238C2×C3×C5C2×#10011yescharacteristic
239C2×C3×C5#41611yescharacteristic
240C2×C3×C5#41711yescharacteristic
241D15—22no—
242C23×C3—22no—
243C22×D3—51no—
244C3×D4—42no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—41no—
248C3×D4—41no—
249C2×C3×C4C2×C4×D511yescharacteristic
250C2×C3×C4D4×D511yescharacteristic
251C2×C3×C4D4×D511yescharacteristic
252#67—204no—
253C2×Dic3—51no—
254C2×Dic3—51no—
255C2×Dic3—51no—
256C2×Dic3—102no—
257C2×Dic3—204no—
258C4×D3—102no—
259C4×D3—101no—
260C4×D3—101no—
261C4×D3—101no—
262C4×D3—101no—
263Dic6—202no—
264C3×C8—41no—
265C3×C8—41no—
266C3⋊C8—201no—
267C3⋊C8—201no—
268C22×C5—42no—
269C22×C5—42no—
270C22×C5—42no—
271C22×C5D3×C22⋊C411yescharacteristic
272C2×D5—32no—
273C2×D5—61no—
274C2×D5—61no—
275C4×C5—21no—
276C4×C5#91111yescharacteristic
277C4×C5#91211yescharacteristic
278C4×C5#91511yescharacteristic
279C4×C5#91611yescharacteristic
280Dic5—61no—
281Dic5—61no—
282Dic5—61no—
283Dic5—122no—
284#41—604no—
285C2×Q8—152no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—302no—
289C2×D4C4×D1512yes—
290C22×C4—151no—
291C22×C4—151no—
292C22×C4—151no—
293C22×C4—302no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—301no—
297C2×C8—301no—
298C2×C8—602no—
299C4⋊C4—301no—
300C4⋊C4—301no—
301C22⋊C4—302no—
302C22⋊C4—302no—
303C42—151no—
304C42—151no—
305C42—151no—
306C42C22×D1511yescharacteristic
307C3×C5#155111yescharacteristic, complemented, Hall
308C22×C3—42no—
309C22×C3—42no—
310C22×C3—42no—
311C22×C3D5×C22⋊C411yescharacteristic
312C2×D3—52no—
313C2×D3—101no—
314C2×D3—101no—
315C3×C4—21no—
316C3×C4#405711yescharacteristic
317C3×C4#405811yescharacteristic
318C3×C4#406111yescharacteristic
319C3×C4#406211yescharacteristic
320Dic3—101no—
321Dic3—101no—
322Dic3—101no—
323Dic3—202no—
324C2×C5—82no—
325C2×C5D3×#10011yescharacteristic
326C2×C5#477111yescharacteristic
327C2×C5#477211yescharacteristic
328D5—62no—
329C23—22no—
330C23—151no—
331Q8—602no—
332D4—42no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—604no—
338C2×C4—151no—
339C2×C4—151no—
340C2×C4—151no—
341C2×C4—302no—
342C2×C4—301no—
343C2×C4—301no—
344C2×C4—301no—
345C2×C4—301no—
346C2×C4—302no—
347C2×C4—604no—
348C2×C4C2×C4×D1511yescharacteristic
349C2×C4D4×D1511yescharacteristic
350C2×C4D4×D1511yescharacteristic
351C8—41no—
352C8—41no—
353C8—601no—
354C8—601no—
355C2×C3—82no—
356C2×C3D5×#10011yescharacteristic
357C2×C3#6506011yescharacteristic
358C2×C3#6506111yescharacteristic
359D3—102no—
360C5#6838511yescharacteristic, complemented, Sylow
361C22—42no—
362C22—42no—
363C22—42no—
364C22—152no—
365C22—301no—
366C22—301no—
367C22C22⋊C4×D1511yescharacteristic
368C4—21no—
369C4—301no—
370C4—301no—
371C4—301no—
372C4—602no—
373C4#9180011yescharacteristic
374C4#9180111yescharacteristic
375C4#9180411yescharacteristic
376C4#9180511yescharacteristic
377C3#1059917811yescharacteristic, complemented, Sylow
378C2—82no—
379C2—302no—
380C2D15×#10011yescharacteristic
381C2#1175087211yescharacteristic
382C2#1175087311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756475C2
cosocleC3×C42×C5C23
hypercenter#331D15
hypocenterC3×C5#1551
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. D15×C4⋊C8C2semidirect
4. C3×C5×#331C2semidirect
5. #11746365C2semidirect
6. #11746302C2semidirect
7. #11746302C2semidirect
30. C5×#331D3semidirect
60. C3×#331D5semidirect
154. #331D15semidirect
307. C3×C5#1551semidirect
360. C5#68385semidirect
377. C3#10599178semidirect

Maximal subgroups

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

subgroupindex
#117564752
#117509362
D15×C4⋊C82
C3×C5×#3312
#117463652
#117463022
#105991783
#683855