Finite Group Databasebeta

← #14289516

Subgroups — #14289516

Order 1920.

428 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#65877C211yesmaximal, characteristic
2#11751109C211yesmaximal, characteristic
3#11747100C211yesmaximal, characteristic, complemented
4#11746916C211yesmaximal, characteristic, complemented
5C5×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#11745861C211yesmaximal, characteristic, complemented
7#11745841C211yesmaximal, characteristic, complemented
8#10598995—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×D4×Dic5—21no—
12C2×C3×C4⋊Dic5—21no—
13C3×#4070—21no—
14C3×#4036—21no—
15C3×#4024—22no—
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C2×#6662—22no—
19#91116—21no—
20#91092—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#90990—21no—
25#90971—21no—
26#71924—51nomaximal, Hall
27#65877D311yescharacteristic
28#65297—31no—
29#65139—31no—
30#64988—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64676—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×Dic30—21no—
37C22×C3×Dic5—22no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×Dic10D412yes—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15—21no—
44C4⋊Dic15—21no—
45C2×C3⋊#168—21no—
46C2×C5×C3⋊C8—21no—
47C2×C5×C3⋊C8—21no—
48C3×C22⋊Dic5—22no—
49C3×C4⋊Dic5—22no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×#683—22no—
54C3×#683—21no—
55C3×C4×Dic5—21no—
56#6662—44no—
57C3×#554—51no—
58#5092—51no—
59#5021—51no—
60#5008—51no—
61#4546—51no—
62#4535—51no—
63D4⋊(C3⋊C8)D511yescharacteristic
64C4×C5×D4C2×D311yescharacteristic
65D4×Dic5—21no—
66C2×C4⋊Dic5—21no—
67#4070—21no—
68C2×Dic20—62no—
69#4036—21no—
70#4024—22no—
71#4015—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8—31no—
75C4×C5×C8—31no—
76#3964—61no—
77#3950—61no—
78#3948—61no—
79#3940—61no—
80C4⋊#168—31no—
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—41no—
92Dic30—42no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—82no—
97C3×Dic10—21no—
98C3×Dic10—21no—
99C3×Dic10—42no—
100C3⋊#168—41no—
101C5×C3⋊C8—22no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8—51no—
104C3×#125—101no—
105C3×C22⋊Q8—102no—
106C3×C22⋊Q8—101no—
107C3×C4×Q8—51no—
108C3×C4×D4—101no—
109C3×C4×D4C2×D511yescharacteristic
110C2×C3×C4⋊C4—101no—
111C2×#216—102no—
112#869—51no—
113#835—101no—
114#832—101no—
115#808—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4×C3⋊C8C2×D511yescharacteristic
120C2×C5×D4#6711yescharacteristic
121C22×C4×C5—21no—
122C22×Dic5—22no—
123C2×Dic10—61no—
124C2×Dic10#6711yescharacteristic
125C2×Dic10#6712yes—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C5×C4⋊C4#6711yescharacteristic
129C5×C22⋊C4—21no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—22no—
132C4⋊Dic5—22no—
133C4⋊Dic5—21no—
134C4⋊Dic5—21no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5#6711yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—21no—
141C2×#168—61no—
142Dic20—124no—
143#554—51no—
144#494—151no—
145#477—151no—
146#476—151no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—31no—
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—81no—
161C3×Dic5—41no—
162C3×Dic5—42no—
163C3×Dic5—41no—
164C2×C3×Q8—51no—
165C2×C3×Q8—52no—
166C2×C3×D4D2011yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—102no—
169C2×Dic6—101no—
170C3×C4⋊C4—51no—
171C3×C4⋊C4—102no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4D2011yescharacteristic
177C3×C22⋊C4—21no—
178C3×C22⋊C4—102no—
179C3×C42—101no—
180C3×C42C22×D511yescharacteristic
181#216—204no—
182C4⋊Dic3—101no—
183C4⋊Dic3—101no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C23×C5—21no—
188C5×D4—21no—
189C5×D4#21612yescomplemented
190C2×C4×C5—21no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5C2×#6711yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5—22no—
199C2×Dic5—82no—
200C2×Dic5—121no—
201Dic10—21no—
202Dic10—21no—
203Dic10—42no—
204Dic10—122no—
205C5×C8—62no—
206C5×C8—121no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—51no—
210C4⋊Q8—151no—
211#125—101no—
212C22⋊Q8—102no—
213C22⋊Q8—101no—
214C4×Q8—51no—
215C4×D4—101no—
216C4×D4D3×D511yescharacteristic
217C2×C4⋊C4—101no—
218#107—301no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—151no—
222#103—301no—
223#102—301no—
224C4×C8—31no—
225C2×C3×C5—42no—
226C2×C3×C5#45111yescharacteristic
227C2×C3×C5#45211yescharacteristic
228C2×C3×C5#45311yescharacteristic
229C23×C3—21no—
230C3×Q8—101no—
231C3×Q8—101no—
232C3×Q8—202no—
233C3×D4—21no—
234C3×D4Dic2012yescomplemented
235C2×C3×C4—21no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—101no—
239C2×C3×C4—101no—
240C2×C3×C4—102no—
241C2×C3×C4—402no—
242C2×C3×C4C2×D2011yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4D4×D511yescharacteristic
245C2×Dic3—201no—
246Dic6—202no—
247C3⋊C8—22no—
248C3⋊C8—41no—
249C3⋊C8—201no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5#95311yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5#94211yescharacteristic
257C4×C5C2×#21611yescharacteristic
258C4×C5#95011yescharacteristic
259C4×C5#95111yescharacteristic
260Dic5—41no—
261Dic5—42no—
262Dic5—41no—
263Dic5—241no—
264C2×Q8—51no—
265C2×Q8—52no—
266C2×Q8—301no—
267C2×D4#120211yescharacteristic
268C22×C4—21no—
269C22×C4—102no—
270Q16—604no—
271C2×C8—61no—
272C2×C8—61no—
273C2×C8—301no—
274C4⋊C4—51no—
275C4⋊C4—102no—
276C4⋊C4—102no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C4⋊C4—301no—
281C4⋊C4—301no—
282C4⋊C4#120211yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—102no—
285C42—101no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—22no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3#402811yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—201no—
295C3×C4—201no—
296C3×C4—202no—
297C3×C4C2×Dic2011yescharacteristic
298C3×C4#405511yescharacteristic
299C3×C4#405811yescharacteristic
300C3×C4#406111yescharacteristic
301Dic3—401no—
302C2×C5—42no—
303C2×C5#522811yescharacteristic
304C2×C5#523911yescharacteristic
305C2×C5#524111yescharacteristic
306C23—21no—
307Q8—101no—
308Q8—101no—
309Q8—202no—
310Q8—602no—
311D4—21no—
312D4#666212yescomplemented
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—102no—
319C2×C4—402no—
320C2×C4—601no—
321C2×C4C2×#120211yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—62no—
325C8—121no—
326C8—601no—
327C2×C3—42no—
328C2×C3#6502811yescharacteristic
329C2×C3#6507211yescharacteristic
330C2×C3#6511111yescharacteristic
331C5#7192411yescharacteristic, complemented, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22#9156411yescharacteristic
336C4—21no—
337C4—41no—
338C4—201no—
339C4—202no—
340C4—201no—
341C4—1201no—
342C4#9131511yescharacteristic
343C4C2×#666211yescharacteristic
344C4#9148411yescharacteristic
345C4#9149011yescharacteristic
346C3#1059899511yescharacteristic, complemented, Sylow
347C2—42no—
348C2#1174855611yescharacteristic
349C2#1174904911yescharacteristic
350C2#1174941811yescharacteristic
subgroupG/H
centerC22#91564
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. #11747100C2semidirect
4. #11746916C2semidirect
6. #11745861C2semidirect
7. #11745841C2semidirect
84. C3×C5×D4Q16semidirect
189. C5×D4#216semidirect
234. C3×D4Dic20semidirect
287. C3×C5#1632semidirect
312. D4#6662semidirect
331. C5#71924semidirect
346. C3#10598995semidirect

Maximal subgroups

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

subgroupindex
C3×#658772
#117511092
#117471002
#117469162
C5×D4⋊(C3⋊C8)2
#117458612
#117458412
#105989953
#719245