Finite Group Databasebeta

← #14289505

Subgroups — #14289505

Order 1920.

428 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 96 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×#66064C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic, complemented
3#11746954C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746367C211yesmaximal, characteristic, complemented
6#11745841C211yesmaximal, characteristic, complemented
7#11745835C211yesmaximal, characteristic
8#10602096—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C2×C5×#216—22no—
11C5×#869C2211yescharacteristic
12C3×#4092—22no—
13C3×#4043—21no—
14C3×#4039—21no—
15C3×D5×C4⋊C4—21no—
16C3×#4036—21no—
17C3×C4×D20C2211yescharacteristic
18C3×C4×Dic10C2211yescharacteristic
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4⋊(C3⋊#168)C2211yescharacteristic
21C4×C5×C3⋊C8C2211yescharacteristic
22#90989—21no—
23#90986—21no—
24#90970—21no—
25#90964—21no—
26#71924—51nomaximal, Hall
27#66064D311yescharacteristic
28C5×#494—31no—
29#65380—31no—
30#65373—31no—
31#64766—31no—
32#64679—31no—
33#64676—31no—
34C2×C3×C5×Q8D412yes—
35C2×C5×Dic6—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—22no—
39C2×C3×Dic10D411yescharacteristic
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×#216—44no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×#685—22no—
50C3×#685—21no—
51C3×C4⋊Dic5—22no—
52C3×C4⋊Dic5D411yescharacteristic
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×#683—21no—
56C3×C4×Dic5—21no—
57C3×#554—51no—
58#5092D511yescharacteristic, complemented
59#5021—51no—
60#5008—51no—
61#4546—51no—
62#4535—51no—
63D4⋊(C3⋊C8)—51no—
64C2×C5×Q16—62no—
65C5×C4⋊Q8—31no—
66C5×C4⋊Q8C2×D311yescharacteristic
67#4092—22no—
68#4043—21no—
69#4039—21no—
70D5×C4⋊C4—21no—
71#4036—21no—
72C4×D20C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C4×C5×C8—31no—
75#3942—61no—
76#3941—61no—
77#3940—61no—
78#3939—61no—
79C4⋊#168—31no—
80C4⋊#168—31no—
81#1632—151noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—42no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C5×Dic3—41no—
89C5×Dic6—42no—
90C2×C3×Dic5—21no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—21no—
93C3×D20—21no—
94C3×D20Q1612yescomplemented
95C3×C4×D5—41no—
96C3×C4×D5—41no—
97C3×C4×D5—82no—
98C3×Dic10—21no—
99C3×Dic10—21no—
100C3⋊#168—41no—
101C3⋊#168—41no—
102C5×C3⋊C8—22no—
103C3×C4⋊Q8C2×D511yescharacteristic
104C3×#125—101no—
105C3×C22⋊Q8—101no—
106C3×C22⋊Q8—102no—
107C3×C4×Q8—51no—
108C3×C4×D4—51no—
109C3×C4×D4—101no—
110C2×C3×C4⋊C4—101no—
111C2×#216—22no—
112#869C2×D511yescharacteristic
113#835—101no—
114#832—101no—
115#808—101no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)—51no—
119C4×C3⋊C8C2×D511yescharacteristic
120C2×C5×Q8—61no—
121C2×C5×Q8#6712yes—
122C2×D20#6711yescharacteristic
123C2×C4×D5—21no—
124C2×C4×D5—22no—
125C2×Dic10#6711yescharacteristic
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—22no—
134#685—21no—
135C4⋊Dic5—22no—
136C4⋊Dic5#6711yescharacteristic
137C4⋊Dic5#6711yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—21no—
141C2×#168—61no—
142C2×#168—61no—
143#554—51no—
144#494—31no—
145#477—151no—
146#476—151no—
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—42no—
156C3×C4×C5C2×Q1611yescharacteristic
157C3×C4×C5#13511yescharacteristic
158C3×C4×C5#13711yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×Dic5—41no—
161C3×Dic5—41no—
162C3×Dic5—41no—
163C5×Dic3—81no—
164C2×C3×Q8—51no—
165C2×C3×Q8C22⋊D512yes—
166C2×C3×D4—51no—
167C22×C3×C4—102no—
168C22×C3×C4—101no—
169C2×Dic6—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—51no—
173C3×C4⋊C4—51no—
174C3×C4⋊C4—102no—
175C3×C4⋊C4—102no—
176C3×C4⋊C4—101no—
177C3×C22⋊C4—102no—
178C3×C22⋊C4—101no—
179C3×C42—101no—
180C3×C42C22×D511yescharacteristic
181#216—44no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C22×D5—21no—
188C5×Q8—42no—
189C5×Q8—122no—
190C2×C4×C5—22no—
191C2×C4×C5—121no—
192C2×C4×C5C2×#6711yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×Dic5—21no—
196C2×Dic5—21no—
197C2×Dic5—21no—
198D20—21no—
199D20#21612yescomplemented
200C4×D5—41no—
201C4×D5—41no—
202C4×D5—82no—
203Dic10—21no—
204Dic10—21no—
205C5×C8—62no—
206#168—121no—
207#168—121no—
208C2×Q16—62no—
209C4⋊Q8—31no—
210C4⋊Q8D3×D511yescharacteristic
211#125—101no—
212C22⋊Q8—101no—
213C22⋊Q8—102no—
214C4×Q8—51no—
215C4×D4—51no—
216C4×D4—101no—
217C2×C4⋊C4—101no—
218#107—301no—
219#106—301no—
220C4⋊C8—151no—
221C4⋊C8—151no—
222#103—301no—
223#102—301no—
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×Q8—101no—
232C3×Q8—101no—
233C3×D4—52no—
234C3×D4—101no—
235C2×C3×C4—22no—
236C2×C3×C4—101no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—201no—
240C2×C3×C4—201no—
241C2×C3×C4—402no—
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×Dic3—41no—
246Dic6—42no—
247C3⋊C8—22no—
248C3⋊C8—201no—
249C3⋊C8—201no—
250C22×C5#95311yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5—241no—
257C4×C5#94211yescharacteristic
258C4×C5C2×#21611yescharacteristic
259C4×C5#95011yescharacteristic
260C4×C5#95111yescharacteristic
261Dic5—41no—
262Dic5—41no—
263Dic5—41no—
264C2×Q8—51no—
265C2×Q8—61no—
266C2×Q8#120112yes—
267C2×D4—51no—
268C22×C4—102no—
269C22×C4—101no—
270Q16—124no—
271C2×C8—61no—
272C2×C8—301no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—51no—
277C4⋊C4—51no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—102no—
281C4⋊C4—102no—
282C4⋊C4—101no—
283C22⋊C4—102no—
284C22⋊C4—101no—
285C42—101no—
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—42no—
294C3×C4—201no—
295C3×C4—201no—
296C3×C4—201no—
297C3×C4D5×Q1611yescharacteristic
298C3×C4#406411yescharacteristic
299C3×C4#406411yescharacteristic
300C3×C4#406511yescharacteristic
301Dic3—81no—
302C2×C5#522811yescharacteristic
303C2×C5#523911yescharacteristic
304C2×C5#524111yescharacteristic
305D5—42no—
306C23—101no—
307Q8—42no—
308Q8—101no—
309Q8—101no—
310Q8—122no—
311D4—52no—
312D4—101no—
313C2×C4—22no—
314C2×C4—101no—
315C2×C4—101no—
316C2×C4—101no—
317C2×C4—121no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—402no—
321C2×C4C2×#120111yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—62no—
325C8—601no—
326C8—601no—
327C2×C3—202no—
328C2×C3#6536611yescharacteristic
329C2×C3#6547511yescharacteristic
330C2×C3#6547611yescharacteristic
331C5#7192411yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22#9156311yescharacteristic
336C4—21no—
337C4—42no—
338C4—201no—
339C4—201no—
340C4—201no—
341C4—241no—
342C4D5×#21611yescharacteristic
343C4#9150811yescharacteristic
344C4#9151511yescharacteristic
345C4#9151611yescharacteristic
346C3#1060209611yescharacteristic, complemented, Sylow
347C2—202no—
348C2#1174913711yescharacteristic
349C2#1174929011yescharacteristic
350C2#1174929411yescharacteristic
subgroupG/H
centerC22#91563
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. C5×#5092C2semidirect
3. #11746954C2semidirect
5. #11746367C2semidirect
6. #11745841C2semidirect
58. #5092D5semidirect
94. C3×D20Q16semidirect
199. D20#216semidirect
287. C3×C5#1632semidirect
331. C5#71924semidirect
346. C3#10602096semidirect

Maximal subgroups

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

subgroupindex
C3×#660642
C5×#50922
#117469542
#117468802
#117463672
#117458412
#117458352
#106020963
#719245