Finite Group Databasebeta

← #14289512

Subgroups — #14289512

Order 1920.

428 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 96 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#11756302C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic
3#11747096C211yesmaximal, characteristic, complemented
4#11746963C211yesmaximal, characteristic, complemented
5C3×D4⋊#168C211yesmaximal, characteristic
6#11745863C211yesmaximal, characteristic, complemented
7#11745845C211yesmaximal, characteristic, complemented
8#10601937—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10D4×Dic15—21no—
11C2×C4⋊Dic15—21no—
12#91813—21no—
13#91779—21no—
14#91767—22no—
15#91758C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×#6663—22no—
19C5×#832—21no—
20C5×#808—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90988—21no—
25#90975—21no—
26#68202—51nomaximal, Hall
27#65877—31no—
28C5×#476—31no—
29#65381—31no—
30#65380—31no—
31D4⋊#168D311yescharacteristic
32#64704—31no—
33#64701—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×Dic15—22no—
37C2×Dic30D411yescharacteristic
38C2×Dic30D412yes—
39C2×C5×Dic6—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43#6719—22no—
44C4⋊Dic15—22no—
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15D411yescharacteristic
48#6712—22no—
49#6712—21no—
50C4×Dic15—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—44no—
57#5543—51no—
58#5008D511yescharacteristic
59#4850—51no—
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4456—51no—
64C5×C4⋊Q8—31no—
65C4×C5×D4C2×D311yescharacteristic
66C2×#689—62no—
67D4×Dic5—61no—
68C2×C4⋊Dic5—61no—
69#4070—61no—
70#4036—61no—
71#4024—62no—
72#4015—31no—
73C4×Dic10—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3942—61no—
78#3939—61no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168C2×D311yescharacteristic
81#1632—151noSylow
82C23×C3×C5—21no—
83C3×C5×D4—21no—
84C3×C5×D4Q1612yescomplemented
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×Dic15—21no—
92C2×Dic15—21no—
93C2×Dic15—22no—
94C2×Dic15—82no—
95Dic30—21no—
96Dic30—21no—
97Dic30—42no—
98C2×C5×Dic3—41no—
99C5×Dic6—42no—
100C3×#168—22no—
101C3×#168—41no—
102C5×C3⋊C8—41no—
103C3×C4×D4C2×D511yescharacteristic
104D4×Dic3—101no—
105C2×C4⋊Dic3—101no—
106#924—101no—
107C2×Dic12—102no—
108#890—101no—
109#878—102no—
110#869—51no—
111#869C2×D511yescharacteristic
112C4×Dic6—51no—
113C3×C4⋊C8—51no—
114C3×C4×C8—51no—
115#832—21no—
116#818—101no—
117#816—101no—
118#808—21no—
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—61no—
121C2×C5×D4D1211yescharacteristic
122C22×C4×C5—21no—
123C22×Dic5—62no—
124C2×Dic10—31no—
125C2×Dic10—32no—
126C2×C5×C8—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4D1211yescharacteristic
130C5×C22⋊C4—21no—
131C42×C5C22×D311yescharacteristic
132C22⋊Dic5—62no—
133#689—124no—
134C4⋊Dic5—31no—
135C4⋊Dic5—62no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138#683—62no—
139#683—61no—
140C4×Dic5—61no—
141C2×#168—21no—
142C2×#168—21no—
143#554—151no—
144#494—151no—
145#477—151no—
146#476—31no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—51no—
150C22×C3×C5—22no—
151C22×C3×C5—41no—
152C22×C3×C5—41no—
153C22×C3×C5#12011yescharacteristic
154C3×C4×C5—21no—
155C3×C4×C5—41no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161Dic15—42no—
162Dic15—41no—
163C5×Dic3—81no—
164C2×C3×D4C22⋊D511yescharacteristic
165C22×C3×C4—21no—
166C22×Dic3—102no—
167C2×Dic6—21no—
168C2×Dic6—51no—
169C2×Dic6—52no—
170C2×C3×C8—101no—
171C2×C3×C8—101no—
172C3×C4⋊C4C22⋊D511yescharacteristic
173C3×C22⋊C4—21no—
174C3×C42C22×D511yescharacteristic
175#217—102no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—51no—
179C4⋊Dic3—102no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182Dic3⋊C4—102no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—21no—
186Dic12—204no—
187C23×C5—21no—
188C5×Q8—122no—
189C5×D4—21no—
190C5×D4Dic1212yescomplemented
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—121no—
195C2×C4×C5C2×D1211yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×C4×C5D3×D411yescharacteristic
198C2×Dic5—61no—
199C2×Dic5—61no—
200C2×Dic5—62no—
201C2×Dic5—242no—
202Dic10—61no—
203Dic10—61no—
204Dic10—122no—
205C5×C8—121no—
206#168—22no—
207#168—41no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—151no—
215C4×D4—301no—
216C4×D4D3×D511yescharacteristic
217C2×C4⋊C4—301no—
218#107—301no—
219#106—61no—
220C4⋊C8—31no—
221C4⋊C8—51no—
222#103—301no—
223#102—61no—
224C4×C8—51no—
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×D4—21no—
231C3×D4#68912yescomplemented
232C2×C3×C4—21no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—41no—
239C2×Dic3—101no—
240C2×Dic3—101no—
241C2×Dic3—102no—
242C2×Dic3—402no—
243Dic6—42no—
244Dic6—101no—
245Dic6—101no—
246Dic6—202no—
247C3×C8—102no—
248C3×C8—201no—
249C3⋊C8—41no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5#88211yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—241no—
257C4×C5C2×Dic1211yescharacteristic
258C4×C5#90911yescharacteristic
259C4×C5#91211yescharacteristic
260C4×C5#91511yescharacteristic
261Dic5—121no—
262Dic5—122no—
263Dic5—121no—
264C2×Q8—61no—
265C2×Q8—151no—
266C2×Q8—152no—
267C2×D4#120311yescharacteristic
268C22×C4—21no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—61no—
272C2×C8—101no—
273C2×C8—101no—
274C4⋊C4—61no—
275C4⋊C4—61no—
276C4⋊C4—151no—
277C4⋊C4—302no—
278C4⋊C4—302no—
279C4⋊C4—301no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4#120311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—302no—
285C42—301no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3#408311yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4C2×#68911yescharacteristic
297C3×C4#409711yescharacteristic
298Dic3—81no—
299Dic3—201no—
300Dic3—202no—
301Dic3—201no—
302C2×C5—42no—
303C2×C5#473911yescharacteristic
304C2×C5#478311yescharacteristic
305C2×C5#482211yescharacteristic
306C23—21no—
307Q8—122no—
308Q8—301no—
309Q8—301no—
310Q8—602no—
311D4—21no—
312D4#666312yescomplemented
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—121no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4—302no—
320C2×C4—1202no—
321C2×C4C2×#120311yescharacteristic
322C2×C4#679011yescharacteristic
323C2×C4#679011yescharacteristic
324C8—102no—
325C8—121no—
326C8—201no—
327C2×C3—42no—
328C2×C3#6533911yescharacteristic
329C2×C3#6546211yescharacteristic
330C2×C3#6548711yescharacteristic
331C5#6820211yescharacteristic, complemented, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22#9157311yescharacteristic
336C4—21no—
337C4—41no—
338C4—241no—
339C4—601no—
340C4—602no—
341C4—601no—
342C4C2×#666311yescharacteristic
343C4#9132211yescharacteristic
344C4#9148811yescharacteristic
345C4#9149711yescharacteristic
346C3#1060193711yescharacteristic, complemented, Sylow
347C2—42no—
348C2#1174856511yescharacteristic
349C2#1174906111yescharacteristic
350C2#1174942211yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterC4×D4D3×D5
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #11747096C2semidirect
4. #11746963C2semidirect
6. #11745863C2semidirect
7. #11745845C2semidirect
84. C3×C5×D4Q16semidirect
190. C5×D4Dic12semidirect
231. C3×D4#689semidirect
287. C3×C5#1632semidirect
312. D4#6663semidirect
331. C5#68202semidirect
346. C3#10601937semidirect

Maximal subgroups

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

subgroupindex
#117563022
C5×#50082
#117470962
#117469632
C3×D4⋊#1682
#117458632
#117458452
#106019373
#682025