Finite Group Databasebeta

← #14289538

Subgroups — #14289538

Order 1920.

428 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 90 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#11752660C211yesmaximal, characteristic
2C3×#65139C211yesmaximal, characteristic, complemented
3#11747100C211yesmaximal, characteristic, complemented
4#11746882C211yesmaximal, characteristic
5#11746302C211yesmaximal, characteristic, complemented
6C5×#4483C211yesmaximal, characteristic
7#11745841C211yesmaximal, characteristic, complemented
8#10598995—31nomaximal, Hall
9#91758C2211yescharacteristic
10C4×C5×D12C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×C4×Dic10C2211yescharacteristic
13#91432—22no—
14D3×C4⋊Dic5—21no—
15Dic5×D12—21no—
16#91388—21no—
17#91369—21no—
18C2×#6662—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22C3×#3950—21no—
23C3×#3948—21no—
24#90986—21no—
25#90966—21no—
26#71156—51nomaximal, Hall
27#65877—31no—
28#65297—31no—
29#65139D311yescharacteristic, complemented
30#64988—31no—
31C5×D4⋊C8—31no—
32#64701—31no—
33#64676—31no—
34C2×Dic30D412yes—
35C2×C5×D12D411yescharacteristic
36C2×C4×C5×D3—21no—
37C2×C3×Dic10—21no—
38C2×C3×Dic10D411yescharacteristic
39C2×D3×Dic5—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C5×(C2×D3)⋊C4—21no—
46C5×C4⋊Dic3D411yescharacteristic
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—21no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5D411yescharacteristic
51C3×#683—21no—
52C3×C4×Dic5—21no—
53Dic3⋊Dic5—22no—
54#6669—22no—
55(C2×D3)⋊Dic5—22no—
56#6662—44no—
57#5579—51no—
58C3×#477—51no—
59#5092—51no—
60#5084—51no—
61#4535—51no—
62#4483D511yescharacteristic
63#4481—51no—
64C4×C5×D4—31no—
65D4×Dic5—61no—
66C2×C4⋊Dic5—61no—
67#4070—61no—
68C2×Dic20—62no—
69#4036—61no—
70#4024—62no—
71#4015—31no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×C4⋊C8C2×D311yescharacteristic
75C4×C5×C8—31no—
76#3964—61no—
77#3950—21no—
78#3948—21no—
79#3940—61no—
80C4⋊#168—31no—
81#1632—151noSylow
82C22×C5×D3—21no—
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5C2×D411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×Dic15—22no—
87Dic30—42no—
88C2×C5×Dic3—21no—
89C5×D12—21no—
90C5×D12Q1612yescomplemented
91C4×C5×D3—41no—
92C4×C5×D3—41no—
93C2×C3×Dic5—21no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—41no—
96C3×Dic10—21no—
97C3×Dic10—21no—
98C3×Dic10—42no—
99D3×Dic5—82no—
100C3×C5×C8—41no—
101C3⋊#168—41no—
102C5×C3⋊C8—22no—
103C3×C4⋊Q8—51no—
104C3×C4×Q8—51no—
105#946—101no—
106C2×#216—102no—
107#896—102no—
108D3×C4⋊C4—101no—
109C4×D12—101no—
110C4×D12C2×D511yescharacteristic
111#870—101no—
112#869—51no—
113C3×#107—101no—
114C3×C4⋊C8C2×D511yescharacteristic
115C3×#103—101no—
116#809—101no—
117#808—101no—
118C4⋊(C3⋊C8)—51no—
119C4×C3⋊C8C2×D511yescharacteristic
120C2×C5×D4—31no—
121C22×C4×C5—61no—
122C22×Dic5—62no—
123C2×Dic10—21no—
124C2×Dic10—32no—
125C2×Dic10#6711yescharacteristic
126C2×C5×C8—21no—
127C2×C5×C8—61no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—61no—
130C42×C5C22×D311yescharacteristic
131C22⋊Dic5—62no—
132C4⋊Dic5—21no—
133C4⋊Dic5—21no—
134C4⋊Dic5—62no—
135C4⋊Dic5—61no—
136C4⋊Dic5—61no—
137C4⋊Dic5#6711yescharacteristic
138#683—21no—
139#683—62no—
140C4×Dic5—21no—
141C2×#168—61no—
142Dic20—124no—
143#554—151no—
144#494—151no—
145#477—51no—
146#476—151no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—31no—
150C22×C3×C5#12011yescharacteristic
151C2×C5×D3—22no—
152C2×C5×D3—41no—
153C2×C5×D3—41no—
154C3×C4×C5—21no—
155C3×C4×C5C2×Q1611yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5#13711yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—42no—
160C3×Dic5—41no—
161C3×Dic5—41no—
162C3×Dic5—81no—
163C5×Dic3—41no—
164C2×C3×Q8—51no—
165C2×C3×Q8—101no—
166C2×D12D2011yescharacteristic
167C2×C4×D3—21no—
168C2×C4×D3—102no—
169C2×Dic6—52no—
170C2×C3×C8—21no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—101no—
173C3×C4⋊C4—101no—
174C3×C4⋊C4—101no—
175C3×C42—101no—
176C3×C42C22×D511yescharacteristic
177#216—204no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—102no—
180C4⋊Dic3—101no—
181C4⋊Dic3—101no—
182C4⋊Dic3D2011yescharacteristic
183Dic3⋊C4—102no—
184Dic3⋊C4—102no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C23×C5—61no—
188C5×D4—32no—
189C5×D4—61no—
190C2×C4×C5—61no—
191C2×C4×C5—121no—
192C2×C4×C5—121no—
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5D3×D411yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5—41no—
199C2×Dic5—62no—
200C2×Dic5—242no—
201Dic10—21no—
202Dic10—21no—
203Dic10—42no—
204Dic10—122no—
205C5×C8—41no—
206C5×C8—62no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—51no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—51no—
215C4×D4—31no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—101no—
219#106—301no—
220C4⋊C8—151no—
221C4⋊C8D3×D511yescharacteristic
222#103—101no—
223#102—301no—
224C4×C8—31no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C5×D3—42no—
229C22×D3—21no—
230C3×Q8—101no—
231C3×Q8—101no—
232C3×Q8—202no—
233C2×C3×C4—101no—
234C2×C3×C4—101no—
235C2×C3×C4—201no—
236C2×C3×C4C2×D2011yescharacteristic
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×Dic3—21no—
240C2×Dic3—102no—
241D12—21no—
242D12Dic2012yescomplemented
243C4×D3—41no—
244C4×D3—41no—
245C4×D3—402no—
246Dic6—202no—
247C3×C8—41no—
248C3⋊C8—22no—
249C3⋊C8—201no—
250C22×C5—62no—
251C22×C5—121no—
252C22×C5—121no—
253C22×C5#93711yescharacteristic
254C4×C5—21no—
255C4×C5—121no—
256C4×C5D3×Q1611yescharacteristic
257C4×C5#91811yescharacteristic
258C4×C5#94211yescharacteristic
259C4×C5#95011yescharacteristic
260Dic5—41no—
261Dic5—41no—
262Dic5—81no—
263Dic5—122no—
264C2×Q8—51no—
265C2×Q8—101no—
266C2×Q8—152no—
267C2×D4—31no—
268C22×C4—61no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—61no—
273C2×C8—301no—
274C4⋊C4—31no—
275C4⋊C4—51no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—101no—
279C4⋊C4—302no—
280C4⋊C4—302no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—61no—
284C22⋊C4—302no—
285C42—101no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3#402811yescharacteristic
289C2×D3—22no—
290C2×D3—41no—
291C2×D3—41no—
292C3×C4—21no—
293C3×C4—201no—
294C3×C4—201no—
295C3×C4—401no—
296C3×C4C2×Dic2011yescharacteristic
297C3×C4#405511yescharacteristic
298C3×C4#405811yescharacteristic
299C3×C4#406111yescharacteristic
300Dic3—41no—
301Dic3—202no—
302C2×C5—122no—
303C2×C5#504711yescharacteristic
304C2×C5#518611yescharacteristic
305C2×C5#519811yescharacteristic
306C23—61no—
307Q8—101no—
308Q8—101no—
309Q8—202no—
310Q8—602no—
311D4—32no—
312D4—61no—
313C2×C4—61no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—121no—
317C2×C4—121no—
318C2×C4—201no—
319C2×C4—302no—
320C2×C4—1202no—
321C2×C4D3×D2011yescharacteristic
322C2×C4#677711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—41no—
325C8—62no—
326C8—601no—
327C2×C3#6502811yescharacteristic
328C2×C3#6507211yescharacteristic
329C2×C3#6511111yescharacteristic
330D3—42no—
331C5#7115611yescharacteristic, complemented, Sylow
332C22—62no—
333C22—121no—
334C22—121no—
335C22#9147411yescharacteristic
336C4—21no—
337C4—121no—
338C4—201no—
339C4—201no—
340C4—401no—
341C4—602no—
342C4D3×Dic2011yescharacteristic
343C4#9126311yescharacteristic
344C4#9149011yescharacteristic
345C4#9151311yescharacteristic
346C3#1059899511yescharacteristic, complemented, Sylow
347C2—122no—
348C2#1174751111yescharacteristic
349C2#1174812511yescharacteristic
350C2#1174824211yescharacteristic
subgroupG/H
centerC22#91474
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1632
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. C3×#65139C2semidirect
3. #11747100C2semidirect
5. #11746302C2semidirect
7. #11745841C2semidirect
29. #65139D3semidirect
90. C5×D12Q16semidirect
242. D12Dic20semidirect
287. C3×C5#1632semidirect
331. C5#71156semidirect
346. C3#10598995semidirect

Maximal subgroups

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

subgroupindex
#117526602
C3×#651392
#117471002
#117468822
#117463022
C5×#44832
#117458412
#105989953
#711565