Finite Group Databasebeta

← #14289039

Subgroups — #14289039

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
1Dic6×Dic10C211yesmaximal, characteristic, complemented
2#11750794C211yesmaximal, characteristic
3#11747078C211yesmaximal, characteristic
4#11747064C211yesmaximal, characteristic
5C5×#4456C211yesmaximal, characteristic, complemented
6C3×#64676C211yesmaximal, characteristic, complemented
7#11745863C211yesmaximal, characteristic, complemented
8#10599057—31nomaximal, Hall
9C2×#6706—22no—
10#91763C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×C4×Dic10C2211yescharacteristic
14#91469—21no—
15#91468—21no—
16Dic5×Dic6—21no—
17Dic3×Dic10—21no—
18#91328—22no—
19C2×#6660—21no—
20C2×#6658—21no—
21C3×C4×C5×C8C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊#168C2211yescharacteristic
24#90969—21no—
25#90968—21no—
26#68264—51nomaximal, Hall
27Q8×Dic10—31no—
28#65316—31no—
29#65137—31no—
30#64982—31no—
31C5×Q8⋊C8—31no—
32#64701—31no—
33#64676D311yescharacteristic, complemented
34C2×D60—21no—
35C2×D60—21no—
36C2×D60—21no—
37C2×Dic30D412yes—
38C2×C5×Dic6D411yescharacteristic
39C2×C3×Dic10D411yescharacteristic
40C2×#1204—22no—
41C2×C3×C5×C8—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45#6706—44no—
46C5×C4⋊Dic3D411yescharacteristic
47C5×Dic3⋊C4—21no—
48C4×C5×Dic3—21no—
49C2×C5×C3⋊C8—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6668—22no—
56Dic3×Dic5—22no—
57#6660—42no—
58#6658—42no—
59Q8×Dic6—51no—
60#5027—51no—
61#4848—51no—
62#4693—51no—
63C3×Q8⋊C8—51no—
64#4481—51no—
65#4456D511yescharacteristic, complemented
66C4×C5×Q8—31no—
67Q8×Dic5—61no—
68C2×#688—61no—
69C2×#677—62no—
70C2×#677—61no—
71#4034—61no—
72#4034—62no—
73#4020—31no—
74#4015—31no—
75#4015—61no—
76C4×Dic10—61no—
77C4×Dic10C2×D311yescharacteristic
78C5×C4⋊C8—31no—
79C4×C5×C8C2×D311yescharacteristic
80#3953—61no—
81#3941—61no—
82C4⋊#168C2×D311yescharacteristic
83#1623—151noSylow
84C22×D15—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—22no—
89D60—42no—
90D60—41no—
91D60—41no—
92D60—41no—
93D60—41no—
94Dic30—42no—
95C2×C5×Dic3—21no—
96C2×C5×Dic3—21no—
97C5×Dic6—21no—
98C5×Dic6SD1612yescomplemented
99C2×C3×Dic5—21no—
100C2×C3×Dic5—21no—
101C3×Dic10—21no—
102C3×Dic10SD1612yescomplemented
103#1204—82no—
104C3×C5×C8—22no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C3×C4×Q8—51no—
108Q8×Dic3—101no—
109C2×#215—101no—
110C2×#204—102no—
111C2×#204—101no—
112#888—101no—
113#888—102no—
114#874—51no—
115#869—51no—
116#869—101no—
117C4×Dic6—101no—
118C4×Dic6C2×D511yescharacteristic
119C3×C4⋊C8—51no—
120C3×C4×C8C2×D511yescharacteristic
121#821—101no—
122#809—101no—
123C4⋊(C3⋊C8)C2×D511yescharacteristic
124C2×C5×Q8—31no—
125C2×D20—61no—
126C2×D20—61no—
127C2×D20—61no—
128C2×Dic10—32no—
129C2×Dic10—62no—
130C2×Dic10D1211yescharacteristic
131C2×C5×C8—21no—
132C2×C5×C8—61no—
133C5×C4⋊C4—31no—
134C5×C4⋊C4—61no—
135C42×C5—61no—
136C42×C5C22×D311yescharacteristic
137#688—122no—
138C4⋊Dic5—62no—
139C4⋊Dic5—61no—
140C4⋊Dic5—61no—
141C4⋊Dic5D1211yescharacteristic
142#683—21no—
143#683—62no—
144C4×Dic5—21no—
145C4×Dic5—62no—
146C2×#168—21no—
147#677—124no—
148#677—122no—
149Q82—151no—
150#492—151no—
151#460—151no—
152#460—151no—
153#333—151no—
154Q8⋊C8—31no—
155Q8⋊C8—51no—
156C22×C3×C5#12011yescharacteristic
157C2×D15—81no—
158C2×D15—81no—
159C2×D15—81no—
160C3×C4×C5—21no—
161C3×C4×C5C2×SD1611yescharacteristic
162C3×C4×C5C2×SD1611yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165Dic15—42no—
166C3×Dic5—22no—
167C3×Dic5—41no—
168C5×Dic3—22no—
169C5×Dic3—41no—
170C2×C3×Q8—51no—
171C2×D12—101no—
172C2×D12—101no—
173C2×D12—101no—
174C2×Dic6—52no—
175C2×Dic6—102no—
176C2×Dic6D2011yescharacteristic
177C2×C3×C8—21no—
178C2×C3×C8—101no—
179C3×C4⋊C4—51no—
180C3×C4⋊C4—101no—
181C3×C42—101no—
182C3×C42C22×D511yescharacteristic
183#215—202no—
184C4⋊Dic3—102no—
185C4⋊Dic3—101no—
186C4⋊Dic3—101no—
187C4⋊Dic3D2011yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—102no—
190C4×Dic3—21no—
191C4×Dic3—102no—
192C2×C3⋊C8—21no—
193#204—204no—
194#204—202no—
195C22×D5—121no—
196C5×Q8—32no—
197C5×Q8—61no—
198C2×C4×C5—61no—
199C2×C4×C5—61no—
200C2×C4×C5C2×D1211yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×Dic5—21no—
204C2×Dic5—21no—
205C2×Dic5—62no—
206D20—122no—
207D20—121no—
208D20—121no—
209D20—121no—
210D20—121no—
211Dic10—21no—
212Dic10—122no—
213Dic10—242no—
214Dic10#20412yescomplemented
215C5×C8—22no—
216C5×C8—121no—
217#168—41no—
218C2×SD16—302no—
219C2×SD16—301no—
220C2×SD16—301no—
221C4⋊Q8—151no—
222C4⋊Q8—301no—
223C4⋊Q8—301no—
224C4⋊Q8—302no—
225#127—151no—
226C4×Q8—31no—
227C4×Q8—51no—
228C4×Q8—301no—
229C4×Q8—301no—
230C4⋊C8—31no—
231C4⋊C8—51no—
232#102—301no—
233#102—301no—
234C4×C8D3×D511yescharacteristic
235C2×C3×C5#44811yescharacteristic
236C2×C3×C5#44811yescharacteristic
237C2×C3×C5#45311yescharacteristic
238D15—161no—
239C22×D3—201no—
240C3×Q8—52no—
241C3×Q8—101no—
242C2×C3×C4—101no—
243C2×C3×C4—101no—
244C2×C3×C4C2×D2011yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4D4×D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—102no—
250D12—202no—
251D12—201no—
252D12—201no—
253D12—201no—
254D12—201no—
255Dic6—21no—
256Dic6—202no—
257Dic6—402no—
258Dic6#67712yescomplemented
259C3×C8—22no—
260C3×C8—201no—
261C3⋊C8—41no—
262C22×C5#88211yescharacteristic
263C2×D5—241no—
264C2×D5—241no—
265C2×D5—241no—
266C4×C5—21no—
267C4×C5—62no—
268C4×C5—121no—
269C4×C5C2×#20411yescharacteristic
270C4×C5#90911yescharacteristic
271C4×C5D3×SD1611yescharacteristic
272C4×C5#91811yescharacteristic
273Dic5—22no—
274Dic5—41no—
275Dic5—122no—
276C2×Q8—31no—
277C2×Q8—51no—
278C2×Q8—152no—
279C2×Q8—302no—
280C2×D4—301no—
281C2×D4—301no—
282C2×D4—301no—
283SD16—604no—
284SD16—602no—
285SD16—602no—
286C2×C8—21no—
287C2×C8—61no—
288C2×C8—101no—
289C4⋊C4—31no—
290C4⋊C4—51no—
291C4⋊C4—61no—
292C4⋊C4—101no—
293C4⋊C4—302no—
294C4⋊C4—302no—
295C4⋊C4—301no—
296C4⋊C4—301no—
297C42—61no—
298C42—101no—
299C42—302no—
300C42C2×D3×D511yescharacteristic
301C3×C5#162311yescharacteristic, complemented, Hall
302C22×C3#402811yescharacteristic
303C2×D3—401no—
304C2×D3—401no—
305C2×D3—401no—
306C3×C4—21no—
307C3×C4—102no—
308C3×C4—201no—
309C3×C4C2×#67711yescharacteristic
310C3×C4#405511yescharacteristic
311C3×C4D5×SD1611yescharacteristic
312C3×C4#406411yescharacteristic
313Dic3—22no—
314Dic3—41no—
315Dic3—202no—
316C2×C5#473811yescharacteristic
317C2×C5#480611yescharacteristic
318C2×C5#482211yescharacteristic
319D5—481no—
320C23—601no—
321Q8—32no—
322Q8—52no—
323Q8—61no—
324Q8—101no—
325Q8—602no—
326Q8—1202no—
327D4—602no—
328D4—601no—
329D4—601no—
330D4—601no—
331D4—601no—
332C2×C4—61no—
333C2×C4—61no—
334C2×C4—101no—
335C2×C4—101no—
336C2×C4—302no—
337C2×C4D5×D1211yescharacteristic
338C2×C4D3×D2011yescharacteristic
339C2×C4#679011yescharacteristic
340C8—22no—
341C8—121no—
342C8—201no—
343C2×C3#6502711yescharacteristic
344C2×C3#6509511yescharacteristic
345C2×C3#6511111yescharacteristic
346D3—801no—
347C5#6826411yescharacteristic, complemented, Sylow
348C22—1201no—
349C22—1201no—
350C22—1201no—
351C22#9147611yescharacteristic
352C4—21no—
353C4—62no—
354C4—102no—
355C4—121no—
356C4—201no—
357C4—602no—
358C4D5×#20411yescharacteristic
359C4D3×#67711yescharacteristic
360C4#9126111yescharacteristic
361C4#9126311yescharacteristic
362C3#1059905711yescharacteristic, complemented, Sylow
363C2—2401no—
364C2#1174711811yescharacteristic
365C2#1174812811yescharacteristic
366C2#1174813211yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4×C8D3×D5
hypocenterC3×C5#1623
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
1. Dic6×Dic10C2semidirect
5. C5×#4456C2semidirect
6. C3×#64676C2semidirect
7. #11745863C2semidirect
33. #64676D3semidirect
65. #4456D5semidirect
98. C5×Dic6SD16semidirect
102. C3×Dic10SD16semidirect
214. Dic10#204semidirect
258. Dic6#677semidirect
301. C3×C5#1623semidirect
347. C5#68264semidirect
362. C3#10599057semidirect

Maximal subgroups

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

subgroupindex
Dic6×Dic102
#117507942
#117470782
#117470642
C5×#44562
C3×#646762
#117458632
#105990573
#682645