Finite Group Databasebeta

← #14289785

Subgroups — #14289785

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#11752552C211yesmaximal, characteristic
2C5×#4681C211yesmaximal, characteristic, complemented
3#11746963C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746277C211yesmaximal, characteristic, complemented
6C3×#64679C211yesmaximal, characteristic
7#11745858C211yesmaximal, characteristic, complemented
8#10602030—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C4×Dic30C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C5×#869C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91470—21no—
15#91434—21no—
16#91430—22no—
17#91359—21no—
18C3×C4×C5×C8C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C5×#816—22no—
21C3×C4⋊#168C2211yescharacteristic
22#90988—21no—
23#90986—21no—
24#90975—21no—
25#90964—21no—
26#68189—51nomaximal, Hall
27#66061—31no—
28C5×#487—31no—
29#65380—31no—
30#65373—31no—
31#64767—31no—
32#64679D311yescharacteristic
33#64676—31no—
34C2×Dic30D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C5×Dic6—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×#1204—22no—
40C2×D5×Dic3—22no—
41D5×Dic6—42no—
42D5×Dic6—42no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47C4×Dic15—21no—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3D412yes—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56#6669—22no—
57#6665—22no—
58D4×Dic6—51no—
59#5008—51no—
60#4850—51no—
61#4681D511yescharacteristic, complemented
62C3×D4⋊C8—51no—
63#4482—51no—
64#4456—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8—31no—
67C5×C4⋊Q8—31no—
68#4092—61no—
69#4042—62no—
70#4039—61no—
71#4034—61no—
72C4×D20C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×#103—62no—
75C4×C5×C8C2×D311yescharacteristic
76#3942—61no—
77#3941—61no—
78#3940—61no—
79#3939—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×C3×D5—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—21no—
88C2×Dic15—21no—
89Dic30—21no—
90Dic30SD1612yes—
91C2×C5×Dic3—22no—
92C2×C5×Dic3—41no—
93C5×Dic6—41no—
94C5×Dic6—41no—
95C5×Dic6—42no—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20Q1612yes—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101#1204—44no—
102D5×Dic3—44no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C22×Dic6—101no—
107C3×C4×D4—51no—
108D4×Dic3—101no—
109#924—101no—
110#888—101no—
111#878—102no—
112#869C2×D511yescharacteristic
113#869C2×D511yescharacteristic
114C4×Dic6—51no—
115C3×C4⋊C8—51no—
116C3×C4×C8C2×D511yescharacteristic
117#832—101no—
118#818—101no—
119#816—22no—
120#816—101no—
121#808—101no—
122C4⋊(C3⋊C8)—51no—
123C2×C5×Q8—61no—
124C2×C5×Q8—61no—
125Q8×D5—122no—
126Q8×D5—122no—
127C2×D20D1211yescharacteristic
128C2×C4×D5—21no—
129C2×C4×D5—62no—
130C2×Dic10—31no—
131C2×Dic10—62no—
132C2×C5×C8—21no—
133C5×C4⋊C4—32no—
134C5×C4⋊C4—61no—
135C5×C4⋊C4—61no—
136C5×C4⋊C4—61no—
137C42×C5C22×D311yescharacteristic
138#685—21no—
139#685—62no—
140C4⋊Dic5—31no—
141C4⋊Dic5D1211yescharacteristic
142#683—62no—
143#683—61no—
144C4×Dic5—61no—
145C2×#168—21no—
146C2×#168—61no—
147D4×Q8—151no—
148#487—31no—
149#477—151no—
150#476—151no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—51no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—22no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—21no—
159C3×C4×C5C2×SD1611yescharacteristic
160C3×C4×C5C2×Q1611yescharacteristic
161C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C3×C4×C5#13711yescharacteristic
163Dic15—22no—
164Dic15—41no—
165C3×Dic5—41no—
166C5×Dic3—42no—
167C5×Dic3—81no—
168C2×C3×D4—51no—
169C22×C3×C4—101no—
170C22×Dic3—102no—
171C2×Dic6—21no—
172C2×Dic6—21no—
173C2×Dic6—51no—
174C2×Dic6—102no—
175C2×Dic6—202no—
176C2×Dic6—202no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C22⋊C4—101no—
181C3×C42C22×D511yescharacteristic
182#217—102no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—51no—
187C4⋊Dic3C22⋊D512yes—
188Dic3⋊C4—102no—
189Dic3⋊C4—101no—
190C4×Dic3—101no—
191C2×C3⋊C8—101no—
192C22×D5—21no—
193C5×Q8—122no—
194C5×Q8—121no—
195C5×Q8—121no—
196C2×C4×C5—62no—
197C2×C4×C5—121no—
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—61no—
203C2×Dic5—61no—
204D20—21no—
205D20Dic1212yes—
206C4×D5—41no—
207C4×D5—41no—
208C4×D5—124no—
209Dic10—32no—
210Dic10—61no—
211Dic10—124no—
212C5×C8—41no—
213#168—41no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—31no—
217C4⋊Q8—31no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—151no—
222C4×D4—51no—
223C4×D4—301no—
224#107—301no—
225#106—301no—
226C4⋊C8—51no—
227C4⋊C8—151no—
228#103—62no—
229#103—301no—
230#102—301no—
231C4×C8D3×D511yescharacteristic
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—42no—
236C23×C3—101no—
237C3×D4—52no—
238C3×D4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—201no—
241C2×C3×C4—201no—
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×Dic3—22no—
246C2×Dic3—41no—
247C2×Dic3—101no—
248C2×Dic3—101no—
249C2×Dic3—204no—
250Dic6—41no—
251Dic6—41no—
252Dic6—42no—
253Dic6—52no—
254Dic6—101no—
255Dic6—204no—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—201no—
259C22×C5#88211yescharacteristic
260C2×D5—22no—
261C2×D5—41no—
262C2×D5—41no—
263C4×C5—21no—
264C4×C5—122no—
265C4×C5—241no—
266C4×C5C2×Dic1211yescharacteristic
267C4×C5#90911yescharacteristic
268C4×C5#91111yescharacteristic
269C4×C5D3×SD1611yescharacteristic
270Dic5—41no—
271Dic5—62no—
272Dic5—121no—
273C2×Q8—61no—
274C2×Q8—61no—
275C2×Q8—151no—
276C2×Q8—302no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—51no—
280C22×C4—101no—
281C22×C4—302no—
282C2×C8—21no—
283C2×C8—101no—
284C2×C8—301no—
285C4⋊C4—32no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—151no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C22⋊C4—101no—
294C22⋊C4—302no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—102no—
299C22×C3—201no—
300C22×C3—201no—
301C22×C3#408311yescharacteristic
302C3×C4—21no—
303C3×C4—201no—
304C3×C4D5×SD1611yescharacteristic
305C3×C4#406011yescharacteristic
306C3×C4D5×Q1611yescharacteristic
307C3×C4#406411yescharacteristic
308Dic3—42no—
309Dic3—81no—
310Dic3—102no—
311Dic3—201no—
312C2×C5#473911yescharacteristic
313C2×C5#477611yescharacteristic
314C2×C5#482711yescharacteristic
315D5—42no—
316C23—101no—
317Q8—122no—
318Q8—121no—
319Q8—121no—
320Q8—152no—
321Q8—301no—
322Q8—604no—
323D4—52no—
324D4—101no—
325C2×C4—62no—
326C2×C4—101no—
327C2×C4—121no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—604no—
333C2×C4D5×D1211yescharacteristic
334C2×C4#677711yescharacteristic
335C2×C4D3×C22⋊D511yescharacteristic
336C8—41no—
337C8—201no—
338C8—601no—
339C2×C3—202no—
340C2×C3#6535111yescharacteristic
341C2×C3#6545811yescharacteristic
342C2×C3#6547511yescharacteristic
343C5#6818911yescharacteristic, complemented, Sylow
344C22—102no—
345C22—201no—
346C22—201no—
347C22#9147511yescharacteristic
348C4—21no—
349C4—122no—
350C4—201no—
351C4—241no—
352C4—302no—
353C4—601no—
354C4#9125511yescharacteristic
355C4#9125811yescharacteristic
356C4D5×Dic1211yescharacteristic
357C4#9126111yescharacteristic
358C3#1060203011yescharacteristic, complemented, Sylow
359C2—202no—
360C2#1174712311yescharacteristic
361C2#1174811811yescharacteristic
362C2#1174812911yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4×C8D3×D5
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C5×#4681C2semidirect
3. #11746963C2semidirect
5. #11746277C2semidirect
7. #11745858C2semidirect
61. #4681D5semidirect
297. C3×C5#1637semidirect
343. C5#68189semidirect
358. C3#10602030semidirect

Maximal subgroups

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

subgroupindex
#117525522
C5×#46812
#117469632
#117468802
#117462772
C3×#646792
#117458582
#106020303
#681895