Finite Group Databasebeta

← #14289499

Subgroups — #14289499

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#11752648C211yesmaximal, characteristic
2#11751192C211yesmaximal, characteristic, complemented
3C5×#5092C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic
5#11745862C211yesmaximal, characteristic, complemented
6#11745844C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic
8#10602096—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C4×Dic30C2211yescharacteristic
11C2×C5×#216—22no—
12C5×#869C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91434—21no—
15#91421—22no—
16D5×C4⋊Dic3—21no—
17#91384—21no—
18#91360—21no—
19#91094—21no—
20#91091—21no—
21C4⋊(C3⋊#168)C2211yescharacteristic
22C4×C5×C3⋊C8C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71144—51nomaximal, Hall
27#66064—31no—
28C5×#494—31no—
29#65380—31no—
30#65373D311yescharacteristic
31#64766—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×Dic6D412yes—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×D5×Dic3—22no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C4⋊Dic15D411yescharacteristic
44#6712—21no—
45C4×Dic15—21no—
46C2×C3⋊#168—21no—
47C5×#216—44no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×C4⋊Dic5D411yescharacteristic
53C2×C3×#168—21no—
54Dic3⋊Dic5—22no—
55#6668—22no—
56#6665—22no—
57#5543—51no—
58C3×#476—51no—
59#5092D511yescharacteristic, complemented
60#5091—51no—
61D4⋊(C3⋊C8)—51no—
62#4484—51no—
63#4481—51no—
64C2×C5×Q16—62no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4092—62no—
68#4043—61no—
69#4039—61no—
70D5×C4⋊C4—61no—
71#4036—61no—
72C4×D20C2×D311yescharacteristic
73C4×Dic10—31no—
74C4×C5×C8—31no—
75#3942—61no—
76#3941—21no—
77#3940—21no—
78#3939—61no—
79C4⋊#168—31no—
80C4⋊#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—21no—
89C2×Dic15—21no—
90Dic30—21no—
91Dic30—21no—
92C2×C5×Dic3—22no—
93C5×Dic6—42no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20Q1612yescomplemented
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99D5×Dic3—82no—
100C3⋊#168—41no—
101C3×#168—41no—
102C5×C3⋊C8—22no—
103C3×C4⋊Q8C2×D511yescharacteristic
104C3×C4×D4—51no—
105C2×#216—22no—
106D4×Dic3—101no—
107C2×C4⋊Dic3—101no—
108#924—101no—
109#890—101no—
110#878—102no—
111#869C2×D511yescharacteristic
112C4×Dic6—51no—
113C3×#106—101no—
114C3×C4⋊C8—51no—
115C3×#102—101no—
116#810—101no—
117#807—101no—
118C4⋊(C3⋊C8)—51no—
119C4×C3⋊C8C2×D511yescharacteristic
120C2×C5×Q8—21no—
121C2×C5×Q8—32no—
122C2×D20#6711yescharacteristic
123C2×C4×D5—21no—
124C2×C4×D5—62no—
125C2×Dic10—31no—
126C5×Q16—124no—
127C2×C5×C8—61no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—21no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C42×C5C22×D311yescharacteristic
133#685—21no—
134#685—62no—
135C4⋊Dic5—31no—
136C4⋊Dic5—62no—
137C4⋊Dic5#6711yescharacteristic
138#683—62no—
139#683—61no—
140C4×Dic5—61no—
141C2×#168—21no—
142C2×#168—61no—
143#554—151no—
144#494—31no—
145#477—151no—
146#476—51no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
150C22×C3×C5#12011yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—41no—
153C2×C3×D5—41no—
154C3×C4×C5—21no—
155C3×C4×C5—81no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160Dic15—41no—
161Dic15—41no—
162C3×Dic5—41no—
163C5×Dic3—42no—
164C2×C3×Q8—21no—
165C2×C3×D4—51no—
166C22×C3×C4—101no—
167C22×Dic3—102no—
168C2×Dic6—51no—
169C2×Dic6C22⋊D512yes—
170C2×C3×C8—101no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—51no—
174C3×C22⋊C4—101no—
175C3×C42C22×D511yescharacteristic
176#217—102no—
177#216—44no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—51no—
181C4⋊Dic3—102no—
182Dic3⋊C4—102no—
183Dic3⋊C4—101no—
184C4×Dic3—101no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—101no—
187C22×D5—21no—
188C5×Q8—42no—
189C5×Q8—122no—
190C2×C4×C5—41no—
191C2×C4×C5—62no—
192C2×C4×C5D3×D411yescharacteristic
193C2×C4×C5D3×D411yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×Dic5—21no—
196C2×Dic5—61no—
197C2×Dic5—61no—
198D20—21no—
199D20#21612yescomplemented
200C4×D5—41no—
201C4×D5—41no—
202C4×D5—242no—
203Dic10—61no—
204Dic10—61no—
205C5×C8—62no—
206#168—41no—
207#168—121no—
208C2×Q16—62no—
209C4⋊Q8—31no—
210C4⋊Q8D3×D511yescharacteristic
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—151no—
215C4×D4—51no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—301no—
219#106—101no—
220C4⋊C8—51no—
221C4⋊C8—151no—
222#103—301no—
223#102—101no—
224C4×C8—31no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×Q8—42no—
231C3×D4—52no—
232C3×D4—101no—
233C2×C3×C4—41no—
234C2×C3×C4—101no—
235C2×C3×C4—201no—
236C2×C3×C4—201no—
237C2×C3×C4D4×D511yescharacteristic
238C2×C3×C4D4×D511yescharacteristic
239C2×C3×C4C2×C22⋊D511yescharacteristic
240C2×Dic3—22no—
241C2×Dic3—101no—
242C2×Dic3—101no—
243C2×Dic3—402no—
244Dic6—42no—
245Dic6—101no—
246Dic6—101no—
247C3×C8—201no—
248C3⋊C8—22no—
249C3⋊C8—201no—
250C22×C5#93711yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—81no—
256C4×C5—122no—
257C4×C5#91511yescharacteristic
258C4×C5#91611yescharacteristic
259C4×C5C2×#21611yescharacteristic
260C4×C5#95111yescharacteristic
261Dic5—41no—
262Dic5—121no—
263Dic5—121no—
264C2×Q8—21no—
265C2×Q8—32no—
266C2×Q8—151no—
267C2×D4—51no—
268C22×C4—101no—
269C22×C4—302no—
270Q16—124no—
271C2×C8—61no—
272C2×C8—101no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—51no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—151no—
280C4⋊C4—302no—
281C4⋊C4—302no—
282C4⋊C4—301no—
283C22⋊C4—101no—
284C22⋊C4—302no—
285C42—301no—
286C42C2×D3×D511yescharacteristic
287C3×C5#163211yescharacteristic, complemented, Hall
288C22×C3—102no—
289C22×C3—201no—
290C22×C3—201no—
291C22×C3#408311yescharacteristic
292C3×C4—21no—
293C3×C4—81no—
294C3×C4—201no—
295C3×C4D5×Q1611yescharacteristic
296C3×C4#406411yescharacteristic
297C3×C4#406411yescharacteristic
298C3×C4#406511yescharacteristic
299Dic3—42no—
300Dic3—201no—
301Dic3—201no—
302C2×C5#505011yescharacteristic
303C2×C5#517311yescharacteristic
304C2×C5#519811yescharacteristic
305D5—42no—
306C23—101no—
307Q8—42no—
308Q8—122no—
309Q8—301no—
310Q8—301no—
311D4—52no—
312D4—101no—
313C2×C4—41no—
314C2×C4—62no—
315C2×C4—101no—
316C2×C4—201no—
317C2×C4—201no—
318C2×C4—301no—
319C2×C4—301no—
320C2×C4—1202no—
321C2×C4D5×#6711yescharacteristic
322C2×C4D3×C22⋊D511yescharacteristic
323C2×C4#679011yescharacteristic
324C8—62no—
325C8—201no—
326C8—601no—
327C2×C3—202no—
328C2×C3#6536611yescharacteristic
329C2×C3#6547511yescharacteristic
330C2×C3#6547611yescharacteristic
331C5#7114411yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22#9157711yescharacteristic
336C4—21no—
337C4—81no—
338C4—122no—
339C4—201no—
340C4—601no—
341C4—601no—
342C4D5×#21611yescharacteristic
343C4#9150811yescharacteristic
344C4#9152111yescharacteristic
345C4#9152211yescharacteristic
346C3#1060209611yescharacteristic, complemented, Sylow
347C2—202no—
348C2#1174916511yescharacteristic
349C2#1174940011yescharacteristic
350C2#1174940411yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1632
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751192C2semidirect
3. C5×#5092C2semidirect
5. #11745862C2semidirect
6. #11745844C2semidirect
59. #5092D5semidirect
96. C3×D20Q16semidirect
199. D20#216semidirect
287. C3×C5#1632semidirect
331. C5#71144semidirect
346. C3#10602096semidirect

Maximal subgroups

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

subgroupindex
#117526482
#117511922
C5×#50922
C3×#653732
#117458622
#117458442
#117458352
#106020963
#711445