Finite Group Databasebeta

← #14289511

Subgroups — #14289511

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
2C5×#5008C211yesmaximal, characteristic
3#11747103C211yesmaximal, characteristic, complemented
4#11746954C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic
6#11745861C211yesmaximal, characteristic, complemented
7#11745840C211yesmaximal, characteristic, complemented
8#10601937—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×D4×Dic5—21no—
12C2×C3×C4⋊Dic5—21no—
13C3×#4070—21no—
14C3×#4036—21no—
15C3×#4024—22no—
16C3×#4015C2211yescharacteristic
17C3×C4×Dic10C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#832—21no—
22C5×#808—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90989—21no—
25#90970—21no—
26#71924—51nomaximal, Hall
27#65877D311yescharacteristic
28C5×#476—31no—
29#65381—31no—
30#65380—31no—
31D4⋊#168—31no—
32#64704—31no—
33#64701—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C22×C3×Dic5—22no—
38C2×C3×Dic10D411yescharacteristic
39C2×C3×Dic10D412yes—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C5×C22⋊C4—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—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#6661—44no—
57C3×#554—51no—
58#5092—51no—
59#5021—51no—
60#5008D511yescharacteristic
61#4546—51no—
62#4535—51no—
63D4⋊(C3⋊C8)—51no—
64C5×C4⋊Q8—31no—
65C4×C5×D4C2×D311yescharacteristic
66C2×#689—62no—
67D4×Dic5—21no—
68C2×C4⋊Dic5—21no—
69#4070—21no—
70#4036—21no—
71#4024—22no—
72#4015C2×D311yescharacteristic
73C4×Dic10C2×D311yescharacteristic
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3942—61no—
78#3939—61no—
79C4⋊#168—31no—
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×C5×Dic3—41no—
92C5×Dic6—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—22no—
101C3⋊#168—41no—
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#869C2×D511yescharacteristic
113#835—101no—
114#832—21no—
115#808—21no—
116#807—101no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4×C3⋊C8—51no—
120C2×C5×Q8—61no—
121C2×C5×D4#6711yescharacteristic
122C22×C4×C5—21no—
123C22×Dic5—22no—
124C2×Dic10#6711yescharacteristic
125C2×Dic10#6712yes—
126C2×C5×C8—61no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4#6711yescharacteristic
130C5×C22⋊C4—21no—
131C42×C5C22×D311yescharacteristic
132C22⋊Dic5—22no—
133#689—124no—
134C4⋊Dic5—22no—
135C4⋊Dic5—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5#6711yescharacteristic
138#683—22no—
139#683—21no—
140C4×Dic5—21no—
141C2×#168—61no—
142C2×#168—61no—
143#554—51no—
144#494—151no—
145#477—151no—
146#476—31no—
147#333—151no—
148Q8⋊C8—151no—
149D4⋊C8—151no—
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
160C3×Dic5—41no—
161C3×Dic5—42no—
162C3×Dic5—41no—
163C5×Dic3—81no—
164C2×C3×Q8—51no—
165C2×C3×Q8—52no—
166C2×C3×D4C22⋊D511yescharacteristic
167C22×C3×C4—21no—
168C22×C3×C4—102no—
169C2×Dic6—21no—
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⋊C4C22⋊D511yescharacteristic
177C3×C22⋊C4—21no—
178C3×C22⋊C4—102no—
179C3×C42—101no—
180C3×C42C22×D511yescharacteristic
181#216—204no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C23×C5—21no—
188C5×Q8—122no—
189C5×D4—21no—
190C5×D4#21612yescomplemented
191C2×C4×C5—21no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—121no—
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×C4×C5C2×#6711yescharacteristic
198C2×Dic5—21no—
199C2×Dic5—21no—
200C2×Dic5—22no—
201C2×Dic5—82no—
202Dic10—21no—
203Dic10—21no—
204Dic10—42no—
205C5×C8—121no—
206#168—62no—
207#168—121no—
208C2×Q16—302no—
209C4⋊Q8—31no—
210C4⋊Q8—51no—
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—61no—
220C4⋊C8—31no—
221C4⋊C8—151no—
222#103—301no—
223#102—61no—
224C4×C8—151no—
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×D4#68912yescomplemented
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×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×Dic3—41no—
246Dic6—42no—
247C3⋊C8—41no—
248C3⋊C8—102no—
249C3⋊C8—201no—
250C22×C5—22no—
251C22×C5—41no—
252C22×C5—41no—
253C22×C5#95311yescharacteristic
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—241no—
257C4×C5#94211yescharacteristic
258C4×C5C2×#21611yescharacteristic
259C4×C5#95011yescharacteristic
260C4×C5#95111yescharacteristic
261Dic5—41no—
262Dic5—42no—
263Dic5—41no—
264C2×Q8—51no—
265C2×Q8—52no—
266C2×Q8—61no—
267C2×D4#120111yescharacteristic
268C22×C4—21no—
269C22×C4—102no—
270Q16—604no—
271C2×C8—61no—
272C2×C8—301no—
273C2×C8—301no—
274C4⋊C4—51no—
275C4⋊C4—61no—
276C4⋊C4—61no—
277C4⋊C4—102no—
278C4⋊C4—102no—
279C4⋊C4—101no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4#120111yescharacteristic
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#408311yescharacteristic
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—201no—
295C3×C4—201no—
296C3×C4—202no—
297C3×C4#406111yescharacteristic
298C3×C4#406211yescharacteristic
299C3×C4C2×#68911yescharacteristic
300C3×C4#409711yescharacteristic
301Dic3—81no—
302C2×C5—42no—
303C2×C5#522811yescharacteristic
304C2×C5#523911yescharacteristic
305C2×C5#524111yescharacteristic
306C23—21no—
307Q8—101no—
308Q8—101no—
309Q8—122no—
310Q8—202no—
311D4—21no—
312D4#666112yescomplemented
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—102no—
319C2×C4—121no—
320C2×C4—402no—
321C2×C4C2×#120111yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—121no—
325C8—302no—
326C8—601no—
327C2×C3—42no—
328C2×C3#6533911yescharacteristic
329C2×C3#6546211yescharacteristic
330C2×C3#6548711yescharacteristic
331C5#7192411yescharacteristic, complemented, Sylow
332C22—22no—
333C22—41no—
334C22—41no—
335C22#9156311yescharacteristic
336C4—21no—
337C4—41no—
338C4—201no—
339C4—202no—
340C4—201no—
341C4—241no—
342C4#9130911yescharacteristic
343C4C2×#666111yescharacteristic
344C4#9148411yescharacteristic
345C4#9149211yescharacteristic
346C3#1060193711yescharacteristic, complemented, Sylow
347C2—42no—
348C2#1174855511yescharacteristic
349C2#1174904711yescharacteristic
350C2#1174941711yescharacteristic
subgroupG/H
centerC22#91563
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. #11747103C2semidirect
4. #11746954C2semidirect
6. #11745861C2semidirect
7. #11745840C2semidirect
84. C3×C5×D4Q16semidirect
190. C5×D4#216semidirect
234. C3×D4#689semidirect
287. C3×C5#1632semidirect
312. D4#6661semidirect
331. C5#71924semidirect
346. C3#10601937semidirect

Maximal subgroups

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

subgroupindex
C3×#658772
C5×#50082
#117471032
#117469542
D4⋊(C3⋊#168)2
#117458612
#117458402
#106019373
#719245