Finite Group Databasebeta

← #14289604

Subgroups — #14289604

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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×#65897C211yesmaximal, characteristic
2C5×#5008C211yesmaximal, characteristic, complemented
3#11747103C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic, complemented
8#10601938—31nomaximal, Hall
9C3×C4×C5×D4C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4084—21no—
12C3×#4076—21no—
13C3×#4072—21no—
14C3×#4038—21no—
15C3×#4031—22no—
16C3×C4×D20C2211yescharacteristic
17C3×#4015C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#832—21no—
22C5×#808—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90986—21no—
25#90964—21no—
26#71928—51nomaximal, Hall
27#65897D311yescharacteristic
28C5×#476—31no—
29#65381—31no—
30#65373—31no—
31D4⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×D4D411yescharacteristic
35C22×C3×C4×C5—21no—
36C2×C5×Dic6—21no—
37C2×C3×C22⋊D5—22no—
38C2×C3×D20D411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×Dic10D412yes—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C2×C3⋊#168—21no—
45C2×C3⋊#168—21no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C3×C22⋊Dic5—22no—
50C3×#685—22no—
51C3×#685—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×C4×Dic5—22no—
56#6661—44no—
57C3×#555—51no—
58#5092—51no—
59#5008—51no—
60#5008D511yescharacteristic, complemented
61#4546—51no—
62D4⋊(C3⋊C8)—51no—
63D4⋊(C3⋊C8)—51no—
64C5×C4⋊Q8—31no—
65C4×C5×D4C2×D311yescharacteristic
66C2×#689—62no—
67#4084—21no—
68#4076—21no—
69#4072—21no—
70#4038—21no—
71#4031—22no—
72C4×D20C2×D311yescharacteristic
73#4015C2×D311yescharacteristic
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3941—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1634—151noSylow
82C23×C3×C5—21no—
83C22×C3×D5—21no—
84C3×C5×D4—21no—
85C3×C5×D4—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C5×Dic3—41no—
93C5×Dic6—42no—
94C3×C22⋊D5—82no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—22no—
97C3×D20—21no—
98C3×D20—21no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101C3×Dic10—42no—
102C3⋊#168—22no—
103C3⋊#168—41no—
104C5×C3⋊C8—41no—
105C3×C4⋊Q8—51no—
106C3×#124—102no—
107C3×#121—101no—
108C3×#121—101no—
109C3×C4×D4—51no—
110C3×C4×D4C2×D511yescharacteristic
111C3×#117—101no—
112C3×#117—101no—
113C2×#216—102no—
114#869C2×D511yescharacteristic
115#832—21no—
116#832—101no—
117#808—21no—
118#808—101no—
119C4⋊(C3⋊C8)—51no—
120C4⋊(C3⋊C8)C2×D511yescharacteristic
121C4×C3⋊C8—51no—
122C2×C5×Q8—61no—
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—21no—
125C2×C22⋊D5—22no—
126C2×D20#6711yescharacteristic
127C2×C4×D5—21no—
128C2×Dic10#6712yes—
129C2×C5×C8—61no—
130C5×C4⋊C4—61no—
131C5×C4⋊C4—61no—
132C5×C4⋊C4#6711yescharacteristic
133C5×C22⋊C4—21no—
134C42×C5C22×D311yescharacteristic
135C22⋊Dic5—22no—
136#689—124no—
137#685—22no—
138#685—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—21no—
141C4⋊Dic5#6711yescharacteristic
142C4×Dic5—22no—
143C2×#168—61no—
144C2×#168—61no—
145#555—51no—
146#494—151no—
147#476—31no—
148#476—151no—
149#333—151no—
150D4⋊C8—151no—
151D4⋊C8—151no—
152C22×C3×C5—41no—
153C22×C3×C5—41no—
154C22×C3×C5—41no—
155C22×C3×C5#12011yescharacteristic
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C2×C3×D5—41no—
159C3×C4×C5—21no—
160C3×C4×C5—41no—
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5#13511yescharacteristic
163C3×C4×C5#13711yescharacteristic
164C3×C4×C5#13711yescharacteristic
165C3×Dic5—41no—
166C3×Dic5—42no—
167C5×Dic3—81no—
168C2×C3×Q8—52no—
169C2×C3×D4—51no—
170C2×C3×D4—102no—
171C2×C3×D4C22⋊D511yescharacteristic
172C22×C3×C4—21no—
173C22×C3×C4—101no—
174C2×Dic6—21no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—101no—
177C3×C4⋊C4—101no—
178C3×C4⋊C4C22⋊D511yescharacteristic
179C3×C22⋊C4—21no—
180C3×C22⋊C4—102no—
181C3×C22⋊C4—102no—
182C3×C22⋊C4—101no—
183C3×C42—102no—
184C3×C42C22×D511yescharacteristic
185#216—204no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—101no—
190C2×C3⋊C8—101no—
191C23×C5—21no—
192C22×D5—21no—
193C5×Q8—122no—
194C5×D4—21no—
195C5×D4—21no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—121no—
200C2×C4×C5C2×#6711yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C22⋊D5—82no—
204C2×Dic5—21no—
205C2×Dic5—22no—
206D20—21no—
207D20—21no—
208C4×D5—41no—
209C4×D5—41no—
210Dic10—42no—
211C5×C8—121no—
212#168—62no—
213#168—121no—
214C2×Q16—302no—
215C4⋊Q8—31no—
216C4⋊Q8—51no—
217#124—102no—
218#121—101no—
219#121—101no—
220C4×D4—51no—
221C4×D4D3×D511yescharacteristic
222#117—101no—
223#117—101no—
224#106—61no—
225#106—301no—
226C4⋊C8—31no—
227C4⋊C8—151no—
228#102—61no—
229#102—301no—
230C4×C8—151no—
231C2×C3×C5—81no—
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45211yescharacteristic
234C2×C3×C5#45311yescharacteristic
235C3×D5—81no—
236C23×C3—21no—
237C23×C3—101no—
238C3×Q8—202no—
239C3×D4—21no—
240C3×D4—21no—
241C3×D4—101no—
242C3×D4—101no—
243C3×D4—402no—
244C2×C3×C4—21no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—101no—
248C2×C3×C4—102no—
249C2×C3×C4—201no—
250C2×C3×C4—201no—
251C2×C3×C4D4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4C2×C22⋊D511yescharacteristic
254C2×Dic3—41no—
255Dic6—42no—
256C3⋊C8—41no—
257C3⋊C8—102no—
258C3⋊C8—201no—
259C22×C5—41no—
260C22×C5—41no—
261C22×C5—41no—
262C22×C5#95311yescharacteristic
263C2×D5—41no—
264C2×D5—41no—
265C2×D5—41no—
266C4×C5—21no—
267C4×C5—41no—
268C4×C5—241no—
269C4×C5#95011yescharacteristic
270C4×C5#95011yescharacteristic
271C4×C5#95111yescharacteristic
272C4×C5#95111yescharacteristic
273Dic5—41no—
274Dic5—42no—
275C2×Q8—52no—
276C2×Q8—61no—
277C2×D4—51no—
278C2×D4—102no—
279C2×D4#120111yescharacteristic
280C22×C4—21no—
281C22×C4—101no—
282Q16—604no—
283C2×C8—61no—
284C2×C8—301no—
285C2×C8—301no—
286C4⋊C4—51no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—101no—
290C4⋊C4—101no—
291C4⋊C4#120111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—102no—
294C22⋊C4—102no—
295C22⋊C4—101no—
296C42—102no—
297C42C2×D3×D511yescharacteristic
298C3×C5#163411yescharacteristic, complemented, Hall
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—201no—
303C22×C3—201no—
304C22×C3—201no—
305C22×C3#408311yescharacteristic
306C3×C4—21no—
307C3×C4—41no—
308C3×C4—201no—
309C3×C4—202no—
310C3×C4#406111yescharacteristic
311C3×C4#406211yescharacteristic
312C3×C4#408811yescharacteristic
313C3×C4#409611yescharacteristic
314Dic3—81no—
315C2×C5—81no—
316C2×C5#523911yescharacteristic
317C2×C5#523911yescharacteristic
318C2×C5#524111yescharacteristic
319D5—81no—
320C23—21no—
321C23—101no—
322Q8—122no—
323Q8—202no—
324D4—21no—
325D4—21no—
326D4—101no—
327D4—101no—
328D4—402no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—101no—
333C2×C4—102no—
334C2×C4—121no—
335C2×C4—201no—
336C2×C4—201no—
337C2×C4C2×#120111yescharacteristic
338C2×C4D5×#6711yescharacteristic
339C2×C4D5×#6711yescharacteristic
340C8—121no—
341C8—302no—
342C8—601no—
343C2×C3—81no—
344C2×C3—401no—
345C2×C3#6533611yescharacteristic
346C2×C3#6546211yescharacteristic
347C2×C3#6548711yescharacteristic
348C5#7192811yescharacteristic, complemented, Sylow
349C22—41no—
350C22—41no—
351C22—41no—
352C22—201no—
353C22—201no—
354C22—201no—
355C22#9156311yescharacteristic
356C4—21no—
357C4—41no—
358C4—202no—
359C4—201no—
360C4—241no—
361C4#9129711yescharacteristic
362C4#9130711yescharacteristic
363C4#9148411yescharacteristic
364C4#9149211yescharacteristic
365C3#1060193811yescharacteristic, complemented, Sylow
366C2—81no—
367C2—401no—
368C2#1174852811yescharacteristic
369C2#1174904711yescharacteristic
370C2#1174941711yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5#120
prime radicalC3×#65897C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#1634
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
2. C5×#5008C2semidirect
3. #11747103C2semidirect
4. #11746880C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
6. #11745861C2semidirect
7. #11745834C2semidirect
60. #5008D5semidirect
298. C3×C5#1634semidirect
348. C5#71928semidirect
365. C3#10601938semidirect

Maximal subgroups

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

subgroupindex
C3×#658972
C5×#50082
#117471032
#117468802
D4⋊(C3⋊#168)2
#117458612
#117458342
#106019383
#719285