Finite Group Databasebeta

← #14289765

Subgroups — #14289765

Order 1920.

456 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 101 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
1D4×Dic30C211yesmaximal, characteristic
2#11751109C211yesmaximal, characteristic
3#11750951C211yesmaximal, characteristic, complemented
4#11750782C211yesmaximal, characteristic, complemented
5C3×C5×D4⋊C8C211yesmaximal, characteristic
6#11746303C211yesmaximal, characteristic, complemented
7#11746277C211yesmaximal, characteristic, complemented
8#10598982—31nomaximal, Hall
9C22×Dic30—21no—
10C3×C4×C5×D4C2211yescharacteristic
11D4×Dic15—21no—
12#91813—21no—
13#91777—21no—
14#91767—22no—
15#91758C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×Dic30C2211yescharacteristic
18C3×C5×C4⋊C8C2211yescharacteristic
19C3×C4×C5×C8C2211yescharacteristic
20#91116—21no—
21#91102—21no—
22#91100—21no—
23#91100—22no—
24#91092—21no—
25C4⋊(C3⋊#168)C2211yescharacteristic
26#68189—51nomaximal, Hall
27D4×Dic10—31no—
28#65297—31no—
29#65139—31no—
30#64970—31no—
31C5×D4⋊C8D311yescharacteristic
32#64702—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C22×Dic15—22no—
37C2×Dic30—22no—
38C2×Dic30—21no—
39C2×Dic30—21no—
40C2×Dic30—42no—
41C2×Dic30—42no—
42C2×Dic30D411yescharacteristic
43C2×C3×C5×C8—21no—
44C2×C3×C5×C8—21no—
45C3×C5×C4⋊C4D411yescharacteristic
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48#6719—22no—
49C4⋊Dic15—21no—
50C4⋊Dic15—21no—
51C4⋊Dic15—21no—
52C4⋊Dic15D411yescharacteristic
53C4⋊Dic15D412yes—
54#6712—22no—
55#6712—21no—
56C4×Dic15—21no—
57C2×C3⋊#168—21no—
58D4×Dic6—51no—
59#5008—51no—
60#4850—51no—
61#4681—51no—
62C3×D4⋊C8D511yescharacteristic
63#4482—51no—
64#4456—51no—
65C22×Dic10—61no—
66C4×C5×D4C2×D311yescharacteristic
67D4×Dic5—61no—
68#4070—61no—
69#4034—61no—
70#4024—62no—
71#4015—31no—
72#4015—31no—
73C4×Dic10—31no—
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3950—61no—
78#3948—62no—
79#3948—61no—
80#3940—61no—
81C4⋊#168—31no—
82#1637—151noSylow
83C23×C3×C5—21no—
84C3×C5×D4—21no—
85C3×C5×D4Q1612yes—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15—22no—
95C2×Dic15—44no—
96C2×Dic15—41no—
97Dic30—21no—
98Dic30—44no—
99Dic30—41no—
100Dic30—41no—
101Dic30—42no—
102Dic30SD1612yes—
103C3×C5×C8—41no—
104C3×C5×C8—41no—
105C3⋊#168—41no—
106C22×Dic6—101no—
107C3×C4×D4C2×D511yescharacteristic
108D4×Dic3—101no—
109#924—101no—
110#888—101no—
111#878—102no—
112#869—51no—
113#869—51no—
114C4×Dic6—51no—
115C3×C4⋊C8C2×D511yescharacteristic
116C3×C4×C8C2×D511yescharacteristic
117#832—101no—
118#818—101no—
119#816—102no—
120#816—101no—
121#808—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×D4D1211yescharacteristic
124C22×C4×C5—21no—
125C22×Dic5—62no—
126C2×Dic10—31no—
127C2×Dic10—62no—
128C2×Dic10—61no—
129C2×Dic10—61no—
130C2×Dic10—122no—
131C2×Dic10—122no—
132C2×C5×C8—21no—
133C2×C5×C8—21no—
134C5×C4⋊C4D1211yescharacteristic
135C5×C22⋊C4—21no—
136C42×C5C22×D311yescharacteristic
137C22⋊Dic5—62no—
138C4⋊Dic5—32no—
139C4⋊Dic5—31no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5—61no—
143#683—62no—
144#683—61no—
145C4×Dic5—61no—
146C2×#168—61no—
147D4×Q8—151no—
148#487—151no—
149#477—151no—
150#476—151no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8D1511yescharacteristic
154C22×C3×C5—22no—
155C22×C3×C5—41no—
156C22×C3×C5—41no—
157C22×C3×C5#12011yescharacteristic
158C3×C4×C5—21no—
159C3×C4×C5—41no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—22no—
165Dic15—42no—
166Dic15—41no—
167Dic15—81no—
168C2×C3×D4D2011yescharacteristic
169C22×C3×C4—21no—
170C22×Dic3—102no—
171C2×Dic6—51no—
172C2×Dic6—102no—
173C2×Dic6—101no—
174C2×Dic6—101no—
175C2×Dic6—202no—
176C2×Dic6—202no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C3×C4⋊C4D2011yescharacteristic
180C3×C22⋊C4—21no—
181C3×C42C22×D511yescharacteristic
182#217—102no—
183C4⋊Dic3—52no—
184C4⋊Dic3—51no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C4⋊Dic3—101no—
188Dic3⋊C4—102no—
189Dic3⋊C4—101no—
190C4×Dic3—101no—
191C2×C3⋊C8—101no—
192C23×C5—21no—
193C5×D4—21no—
194C5×D4Dic1212yes—
195C2×C4×C5—21no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×Dic5—61no—
202C2×Dic5—61no—
203C2×Dic5—62no—
204C2×Dic5—124no—
205C2×Dic5—121no—
206Dic10—32no—
207Dic10—61no—
208Dic10—124no—
209Dic10—121no—
210Dic10—121no—
211Dic10—122no—
212C5×C8—41no—
213C5×C8—41no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—151no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—151no—
222C4×D4—301no—
223C4×D4C2×D1511yescharacteristic
224#107—301no—
225#106—301no—
226C4⋊C8—151no—
227C4⋊C8C2×D1511yescharacteristic
228#103—302no—
229#103—301no—
230#102—301no—
231C4×C8C2×D1511yescharacteristic
232C2×C3×C5—42no—
233C2×C3×C5#45011yescharacteristic
234C2×C3×C5#45111yescharacteristic
235C2×C3×C5#45411yescharacteristic
236C23×C3—21no—
237C3×D4—21no—
238C3×D4Dic2012yes—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—101no—
246C2×Dic3—101no—
247C2×Dic3—102no—
248C2×Dic3—204no—
249C2×Dic3—201no—
250Dic6—52no—
251Dic6—101no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255Dic6—202no—
256C3×C8—41no—
257C3×C8—41no—
258C3⋊C8—201no—
259C22×C5—22no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#88211yescharacteristic
263C4×C5—21no—
264C4×C5—41no—
265C4×C5C2×Dic1211yescharacteristic
266C4×C5#90911yescharacteristic
267C4×C5#91111yescharacteristic
268C4×C5D3×SD1611yescharacteristic
269Dic5—62no—
270Dic5—122no—
271Dic5—121no—
272Dic5—241no—
273C2×Q8—151no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—301no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4D6011yescharacteristic
280C22×C4—21no—
281C22×C4—302no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—301no—
285C4⋊C4—152no—
286C4⋊C4—151no—
287C4⋊C4—302no—
288C4⋊C4—301no—
289C4⋊C4—301no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4D6011yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—302no—
295C42—301no—
296C42C22×D1511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—22no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3#402811yescharacteristic
302C3×C4—21no—
303C3×C4—41no—
304C3×C4C2×Dic2011yescharacteristic
305C3×C4#405511yescharacteristic
306C3×C4#405711yescharacteristic
307C3×C4D5×SD1611yescharacteristic
308Dic3—102no—
309Dic3—202no—
310Dic3—201no—
311Dic3—401no—
312C2×C5—42no—
313C2×C5#473911yescharacteristic
314C2×C5#477611yescharacteristic
315C2×C5#482711yescharacteristic
316C23—21no—
317Q8—152no—
318Q8—301no—
319Q8—602no—
320Q8—604no—
321Q8—601no—
322Q8—601no—
323D4—21no—
324D4Dic6012yes—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—302no—
331C2×C4—604no—
332C2×C4—601no—
333C2×C4C2×D6011yescharacteristic
334C2×C4D4×D1511yescharacteristic
335C2×C4D4×D1511yescharacteristic
336C8—41no—
337C8—41no—
338C8—601no—
339C2×C3—42no—
340C2×C3#6502811yescharacteristic
341C2×C3#6506511yescharacteristic
342C2×C3#6511611yescharacteristic
343C5#6818911yescharacteristic, complemented, Sylow
344C22—22no—
345C22—41no—
346C22—41no—
347C22#9177111yescharacteristic
348C4—21no—
349C4—41no—
350C4—302no—
351C4—601no—
352C4—602no—
353C4—1201no—
354C4C2×Dic6011yescharacteristic
355C4#9179811yescharacteristic
356C4#9180011yescharacteristic
357C4SD16×D1511yescharacteristic
358C3#1059898211yescharacteristic, complemented, Sylow
359C2—42no—
360C2#1175084011yescharacteristic
361C2#1175087711yescharacteristic
362C2#1175092811yescharacteristic
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×D4⋊C8C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenterD4⋊C8D15
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11750951C2semidirect
4. #11750782C2semidirect
6. #11746303C2semidirect
7. #11746277C2semidirect
297. C3×C5#1637semidirect
343. C5#68189semidirect
358. C3#10598982semidirect

Maximal subgroups

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

subgroupindex
D4×Dic302
#117511092
#117509512
#117507822
C3×C5×D4⋊C82
#117463032
#117462772
#105989823
#681895