Finite Group Databasebeta

← #14289540

Subgroups — #14289540

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#11752657C211yesmaximal, characteristic
2C5×#4850C211yesmaximal, characteristic, complemented
3#11747096C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746302C211yesmaximal, characteristic, complemented
6C3×#64703C211yesmaximal, characteristic
7#11745843C211yesmaximal, characteristic, complemented
8#10601949—31nomaximal, Hall
9#91758C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C4×C5×Dic6C2211yescharacteristic
12C3×C4×D20C2211yescharacteristic
13#91431—22no—
14Dic3×D20—21no—
15D5×C4⋊Dic3—21no—
16#91381—21no—
17#91359—21no—
18C2×#6663—22no—
19C3×C5×C4⋊C8C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#818—21no—
22C5×#816—21no—
23C3×C4×#168C2211yescharacteristic
24#90986—21no—
25#90964—21no—
26#68202—51nomaximal, Hall
27#65913—31no—
28C5×#477—31no—
29#65381—31no—
30#65373—31no—
31Q8⋊#168—31no—
32#64703D311yescharacteristic
33#64701—31no—
34C2×Dic30D412yes—
35C2×C5×Dic6—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×D5×Dic3—22no—
40C2×C3×C5×C8—21no—
41C3×C42×C5C2311yescharacteristic
42C4⋊Dic15—21no—
43C4⋊Dic15—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3D411yescharacteristic
48C5×Dic3⋊C4—21no—
49C4×C5×Dic3—21no—
50C3×#685—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C2×C3×#168—21no—
53#6669—22no—
54#6668—22no—
55#6665—22no—
56#6663—44no—
57#5543—51no—
58#5008—51no—
59#4850D511yescharacteristic, complemented
60#4699—51no—
61C3×D4⋊C8—51no—
62#4481—51no—
63#4456—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8—31no—
66#4092—61no—
67C2×#689—62no—
68#4042—62no—
69D5×C4⋊C4—61no—
70C4×D20—61no—
71C4×D20C2×D311yescharacteristic
72#4016—61no—
73#4015—31no—
74C5×#107—61no—
75C5×C4⋊C8C2×D311yescharacteristic
76C5×#103—61no—
77#3941—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168C2×D311yescharacteristic
81#1632—151noSylow
82C22×C3×D5—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—
89C2×C5×Dic3—21no—
90C2×C5×Dic3—41no—
91C5×Dic6—21no—
92C5×Dic6—21no—
93C5×Dic6—42no—
94C2×C3×Dic5—21no—
95C3×D20—21no—
96C3×D20Q1612yescomplemented
97C3×C4×D5—41no—
98C3×C4×D5—41no—
99D5×Dic3—82no—
100C3×C5×C8—41no—
101C3⋊#168—41no—
102C3×#168—22no—
103C3×C4×D4—51no—
104D4×Dic3—101no—
105C2×C4⋊Dic3—101no—
106#924—101no—
107C2×Dic12—102no—
108#890—101no—
109#878—102no—
110#869—51no—
111#869C2×D511yescharacteristic
112C4×Dic6C2×D511yescharacteristic
113C3×C4⋊C8C2×D511yescharacteristic
114C3×C4×C8—51no—
115#832—101no—
116#818—21no—
117#816—21no—
118#808—101no—
119C4⋊(C3⋊C8)—51no—
120C2×C5×Q8—31no—
121C2×C5×Q8—61no—
122C2×D20D1211yescharacteristic
123C2×C4×D5—21no—
124C2×C4×D5—62no—
125C2×Dic10—32no—
126C2×C5×C8—21no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4—61no—
131C42×C5—61no—
132C42×C5C22×D311yescharacteristic
133#689—124no—
134#685—21no—
135#685—62no—
136C4⋊Dic5—61no—
137C4⋊Dic5—61no—
138C4⋊Dic5D1211yescharacteristic
139#683—62no—
140#683—62no—
141C2×#168—21no—
142C2×#168—61no—
143#554—151no—
144#494—151no—
145#477—31no—
146#476—151no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—51no—
150C22×C3×C5#12011yescharacteristic
151C2×C3×D5—22no—
152C2×C3×D5—41no—
153C2×C3×D5—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—
161C5×Dic3—41no—
162C5×Dic3—41no—
163C5×Dic3—81no—
164C2×C3×D4—51no—
165C22×C3×C4—101no—
166C22×Dic3—102no—
167C2×Dic6—21no—
168C2×Dic6—52no—
169C2×Dic6C22⋊D511yescharacteristic
170C2×C3×C8—21no—
171C2×C3×C8—101no—
172C3×C4⋊C4—51no—
173C3×C22⋊C4—101no—
174C3×C42C22×D511yescharacteristic
175#217—102no—
176C4⋊Dic3—21no—
177C4⋊Dic3—21no—
178C4⋊Dic3—102no—
179C4⋊Dic3—101no—
180C4⋊Dic3—101no—
181C4⋊Dic3C22⋊D511yescharacteristic
182Dic3⋊C4—21no—
183Dic3⋊C4—102no—
184C4×Dic3—21no—
185C2×C3⋊C8—101no—
186Dic12—204no—
187C22×D5—21no—
188C5×Q8—61no—
189C5×Q8—61no—
190C5×Q8—122no—
191C2×C4×C5—61no—
192C2×C4×C5—61no—
193C2×C4×C5—121no—
194C2×C4×C5C2×D1211yescharacteristic
195C2×C4×C5D3×D411yescharacteristic
196C2×C4×C5D3×D411yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—62no—
199D20—21no—
200D20Dic1212yescomplemented
201C4×D5—41no—
202C4×D5—41no—
203C4×D5—242no—
204Dic10—122no—
205C5×C8—41no—
206#168—22no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—151no—
211#125—301no—
212C22⋊Q8—302no—
213C22⋊Q8—301no—
214C4×Q8—31no—
215C4×D4—51no—
216C4×D4—301no—
217C2×C4⋊C4—301no—
218#107—61no—
219#106—301no—
220C4⋊C8—151no—
221C4⋊C8D3×D511yescharacteristic
222#103—61no—
223#102—301no—
224C4×C8—51no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×D4—52no—
231C3×D4—101no—
232C2×C3×C4—101no—
233C2×C3×C4—201no—
234C2×C3×C4—201no—
235C2×C3×C4D4×D511yescharacteristic
236C2×C3×C4D4×D511yescharacteristic
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—41no—
241C2×Dic3—102no—
242C2×Dic3—402no—
243Dic6—21no—
244Dic6—21no—
245Dic6—42no—
246Dic6—202no—
247C3×C8—41no—
248C3×C8—102no—
249C3⋊C8—201no—
250C22×C5#88211yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—121no—
256C4×C5—121no—
257C4×C5—241no—
258C4×C5C2×Dic1211yescharacteristic
259C4×C5#90911yescharacteristic
260C4×C5#91211yescharacteristic
261C4×C5#91511yescharacteristic
262Dic5—41no—
263Dic5—122no—
264C2×Q8—31no—
265C2×Q8—61no—
266C2×Q8—152no—
267C2×D4—51no—
268C22×C4—101no—
269C22×C4—302no—
270Q16—604no—
271C2×C8—21no—
272C2×C8—101no—
273C2×C8—301no—
274C4⋊C4—31no—
275C4⋊C4—51no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—302no—
280C4⋊C4—302no—
281C4⋊C4—301no—
282C4⋊C4—301no—
283C22⋊C4—101no—
284C22⋊C4—302no—
285C42—61no—
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—201no—
294C3×C4D5×Q1611yescharacteristic
295C3×C4#406411yescharacteristic
296C3×C4#408811yescharacteristic
297C3×C4#409611yescharacteristic
298Dic3—41no—
299Dic3—41no—
300Dic3—81no—
301Dic3—202no—
302C2×C5#473911yescharacteristic
303C2×C5#478311yescharacteristic
304C2×C5#482211yescharacteristic
305D5—42no—
306C23—101no—
307Q8—61no—
308Q8—61no—
309Q8—122no—
310Q8—602no—
311D4—52no—
312D4—101no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—101no—
316C2×C4—121no—
317C2×C4—201no—
318C2×C4—201no—
319C2×C4—302no—
320C2×C4—1202no—
321C2×C4D5×D1211yescharacteristic
322C2×C4#677711yescharacteristic
323C2×C4D3×C22⋊D511yescharacteristic
324C8—41no—
325C8—102no—
326C8—601no—
327C2×C3—202no—
328C2×C3#6533611yescharacteristic
329C2×C3#6547511yescharacteristic
330C2×C3#6548711yescharacteristic
331C5#6820211yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22#9147511yescharacteristic
336C4—21no—
337C4—121no—
338C4—121no—
339C4—201no—
340C4—241no—
341C4—602no—
342C4D5×Dic1211yescharacteristic
343C4#9126111yescharacteristic
344C4#9149311yescharacteristic
345C4#9151811yescharacteristic
346C3#1060194911yescharacteristic, complemented, Sylow
347C2—202no—
348C2#1174751411yescharacteristic
349C2#1174812911yescharacteristic
350C2#1174824711yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
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. C5×#4850C2semidirect
3. #11747096C2semidirect
5. #11746302C2semidirect
7. #11745843C2semidirect
59. #4850D5semidirect
96. C3×D20Q16semidirect
200. D20Dic12semidirect
287. C3×C5#1632semidirect
331. C5#68202semidirect
346. C3#10601949semidirect

Maximal subgroups

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

subgroupindex
#117526572
C5×#48502
#117470962
#117468802
#117463022
C3×#647032
#117458432
#106019493
#682025