Finite Group Databasebeta

← #14289789

Subgroups — #14289789

Order 1920.

456 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D12×Dic10C211yesmaximal, characteristic
2#11750782C211yesmaximal, characteristic, complemented
3#11746916C211yesmaximal, characteristic, complemented
4#11746883C211yesmaximal, characteristic
5C5×#4459C211yesmaximal, characteristic
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10598982—31nomaximal, Hall
9C2×D3×Dic10—21no—
10#91758C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91468—21no—
15#91417—22no—
16Dic5×D12—21no—
17#91365—21no—
18C3×C4×C5×C8C2211yescharacteristic
19#91100—22no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90990—21no—
23#90985—21no—
24#90971—21no—
25#90967—21no—
26#68269—51nomaximal, Hall
27D4×Dic10—31no—
28#65297—31no—
29#65139—31no—
30#64970—31no—
31C5×D4⋊C8—31no—
32#64702—31no—
33#64676D311yescharacteristic, complemented
34C2×Dic30—21no—
35C2×Dic30—21no—
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×#1204—22no—
40C2×D3×Dic5—22no—
41D3×Dic10—42no—
42D3×Dic10—42no—
43C2×C3×C5×C8—21no—
44C3×C42×C5C2311yescharacteristic
45C4⋊Dic15—21no—
46C4⋊Dic15—21no—
47C4⋊Dic15—21no—
48C4⋊Dic15D412yes—
49C5×(C2×D3)⋊C4—21no—
50C5×C4⋊Dic3D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—21no—
54C3×C4×Dic5—21no—
55C2×C3×#168—21no—
56#6668—22no—
57(C2×D3)⋊Dic5—22no—
58Q8×D12—51no—
59#5021—51no—
60#4842—51no—
61#4681—51no—
62C3×Q8⋊C8—51no—
63#4486—51no—
64#4459D511yescharacteristic
65C22×Dic10—61no—
66C4×C5×D4—31no—
67D4×Dic5—61no—
68#4070—61no—
69#4034—61no—
70#4024—62no—
71#4015—31no—
72#4015—31no—
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8C2×D311yescharacteristic
76#3964—61no—
77#3950—61no—
78#3948—62no—
79#3948—61no—
80#3940—61no—
81C4⋊#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×C5×D3—21no—
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88C2×Dic15—41no—
89Dic30—41no—
90Dic30—41no—
91Dic30—42no—
92C2×C5×Dic3—21no—
93C5×D12—21no—
94C5×D12Q1612yes—
95C4×C5×D3—41no—
96C4×C5×D3—41no—
97C2×C3×Dic5—21no—
98C2×C3×Dic5—21no—
99C3×Dic10—21no—
100C3×Dic10SD1612yes—
101#1204—44no—
102D3×Dic5—44no—
103C3×C5×C8—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4×Q8—51no—
108#897—102no—
109#897—101no—
110C4×D12—101no—
111C4×D12C2×D511yescharacteristic
112#869—51no—
113#869—51no—
114#869—101no—
115C3×C4⋊C8—51no—
116C3×C4×C8C2×D511yescharacteristic
117#835—101no—
118#821—101no—
119#817—101no—
120#816—102no—
121#807—101no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×D4—31no—
124C22×C4×C5—61no—
125C22×Dic5—62no—
126C2×Dic10—62no—
127C2×Dic10—61no—
128C2×Dic10—61no—
129C2×Dic10—122no—
130C2×Dic10—122no—
131C2×Dic10D1211yescharacteristic
132C2×C5×C8—21no—
133C2×C5×C8—61no—
134C5×C4⋊C4—31no—
135C5×C22⋊C4—61no—
136C42×C5C22×D311yescharacteristic
137C22⋊Dic5—62no—
138C4⋊Dic5—32no—
139C4⋊Dic5—61no—
140C4⋊Dic5—61no—
141C4⋊Dic5—61no—
142C4⋊Dic5D1211yescharacteristic
143#683—21no—
144#683—62no—
145C4×Dic5—21no—
146C2×#168—21no—
147D4×Q8—151no—
148#487—151no—
149#477—151no—
150#476—151no—
151#332—151no—
152Q8⋊C8—51no—
153D4⋊C8—31no—
154C22×C3×C5#12011yescharacteristic
155C2×C5×D3—22no—
156C2×C5×D3—41no—
157C2×C5×D3—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—42no—
164Dic15—81no—
165C3×Dic5—22no—
166C3×Dic5—41no—
167C5×Dic3—41no—
168C2×C3×Q8—51no—
169D3×Q8—202no—
170D3×Q8—202no—
171C2×D12D2011yescharacteristic
172C2×C4×D3—21no—
173C2×C4×D3—102no—
174C2×Dic6—102no—
175C2×Dic6—101no—
176C2×Dic6—101no—
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C42—101no—
182C3×C42C22×D511yescharacteristic
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—102no—
185C4⋊Dic3—52no—
186C4⋊Dic3—102no—
187C4⋊Dic3—101no—
188C4⋊Dic3—101no—
189C4⋊Dic3—101no—
190C4⋊Dic3D2011yescharacteristic
191C2×C3⋊C8—21no—
192C23×C5—61no—
193C5×D4—32no—
194C5×D4—61no—
195C2×C4×C5—61no—
196C2×C4×C5—121no—
197C2×C4×C5—121no—
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—62no—
204C2×Dic5—124no—
205C2×Dic5—121no—
206Dic10—21no—
207Dic10—124no—
208Dic10—121no—
209Dic10—121no—
210Dic10—122no—
211Dic10#20412yes—
212C5×C8—41no—
213C5×C8—121no—
214#168—41no—
215C22×Q8—301no—
216C4⋊Q8—151no—
217C4⋊Q8—151no—
218C4⋊Q8—301no—
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—51no—
222C4×D4—31no—
223C4×D4—301no—
224#107—301no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#103—302no—
229#103—301no—
230#102—301no—
231C4×C8D3×D511yescharacteristic
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—42no—
236C22×D3—21no—
237C3×Q8—52no—
238C3×Q8—101no—
239C2×C3×C4—101no—
240C2×C3×C4—101no—
241C2×C3×C4C2×D2011yescharacteristic
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×Dic3—21no—
245C2×Dic3—102no—
246C2×Dic3—201no—
247D12—21no—
248D12Dic2012yes—
249C4×D3—41no—
250C4×D3—41no—
251C4×D3—204no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255Dic6—202no—
256C3×C8—41no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5—62no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5#88211yescharacteristic
263C4×C5—21no—
264C4×C5—121no—
265C4×C5C2×#20411yescharacteristic
266C4×C5#90811yescharacteristic
267C4×C5#91511yescharacteristic
268C4×C5D3×Q1611yescharacteristic
269Dic5—22no—
270Dic5—41no—
271Dic5—122no—
272Dic5—241no—
273C2×Q8—51no—
274C2×Q8—302no—
275C2×Q8—301no—
276C2×Q8—301no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—31no—
280C22×C4—61no—
281C22×C4—302no—
282C2×C8—21no—
283C2×C8—61no—
284C2×C8—101no—
285C4⋊C4—31no—
286C4⋊C4—51no—
287C4⋊C4—101no—
288C4⋊C4—152no—
289C4⋊C4—302no—
290C4⋊C4—301no—
291C4⋊C4—301no—
292C4⋊C4—301no—
293C22⋊C4—61no—
294C22⋊C4—302no—
295C42—101no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#402811yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—21no—
303C3×C4—102no—
304C3×C4—201no—
305C3×C4C2×Dic2011yescharacteristic
306C3×C4#405511yescharacteristic
307C3×C4#405711yescharacteristic
308C3×C4D5×SD1611yescharacteristic
309Dic3—41no—
310Dic3—202no—
311Dic3—401no—
312C2×C5—122no—
313C2×C5#473111yescharacteristic
314C2×C5#480911yescharacteristic
315C2×C5#482711yescharacteristic
316C23—61no—
317Q8—52no—
318Q8—101no—
319Q8—602no—
320Q8—604no—
321Q8—601no—
322Q8—601no—
323D4—32no—
324D4—61no—
325C2×C4—61no—
326C2×C4—101no—
327C2×C4—101no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4—302no—
331C2×C4—604no—
332C2×C4—601no—
333C2×C4D5×D1211yescharacteristic
334C2×C4D3×D2011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—41no—
337C8—121no—
338C8—201no—
339C2×C3#6502811yescharacteristic
340C2×C3#6506511yescharacteristic
341C2×C3#6511611yescharacteristic
342D3—42no—
343C5#6826911yescharacteristic, complemented, Sylow
344C22—62no—
345C22—121no—
346C22—121no—
347C22#9147611yescharacteristic
348C4—21no—
349C4—102no—
350C4—121no—
351C4—201no—
352C4—602no—
353C4—1201no—
354C4D5×#20411yescharacteristic
355C4#9125011yescharacteristic
356C4D3×Dic2011yescharacteristic
357C4#9127411yescharacteristic
358C3#1059898211yescharacteristic, complemented, Sylow
359C2—122no—
360C2#1174712511yescharacteristic
361C2#1174811511yescharacteristic
362C2#1174813311yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
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. #11750782C2semidirect
3. #11746916C2semidirect
6. C3×#64676C2semidirect
7. #11745859C2semidirect
33. #64676D3semidirect
297. C3×C5#1637semidirect
343. C5#68269semidirect
358. C3#10598982semidirect

Maximal subgroups

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

subgroupindex
D12×Dic102
#117507822
#117469162
#117468832
C5×#44592
C3×#646762
#117458592
#105989823
#682695