Finite Group Databasebeta

← #14289529

Subgroups — #14289529

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×#65913C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic, complemented
3#11747103C211yesmaximal, characteristic, complemented
4#11746880C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic, complemented
6#11745861C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10601949—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4092—21no—
12C3×#4042—22no—
13C3×D5×C4⋊C4—21no—
14C3×C4×D20—21no—
15C3×C4×D20C2211yescharacteristic
16C3×#4016—21no—
17C3×#4015C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#835—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90986—21no—
25#90964—21no—
26#71924—51nomaximal, Hall
27#65913D311yescharacteristic
28C5×#477—31no—
29#65381—31no—
30#65373—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64701—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C3×D20D411yescharacteristic
37C2×C3×C4×D5—21no—
38C2×C3×C4×D5—22no—
39C2×C3×Dic10D412yes—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C42×C5—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×#685—22no—
50C3×#685—21no—
51C3×C4⋊Dic5—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5D411yescharacteristic
54C3×#683—22no—
55C3×#683—22no—
56#6661—44no—
57C3×#554—51no—
58#5092—51no—
59#5021D511yescharacteristic, complemented
60#5008—51no—
61#4546—51no—
62#4535—51no—
63D4⋊(C3⋊C8)—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8C2×D311yescharacteristic
66#4092—21no—
67C2×#689—62no—
68#4042—22no—
69D5×C4⋊C4—21no—
70C4×D20—21no—
71C4×D20C2×D311yescharacteristic
72#4016—21no—
73#4015C2×D311yescharacteristic
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3941—61no—
78#3940—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1632—151noSylow
82C22×C3×D5—21no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C5×Dic3—41no—
91C5×Dic6—42no—
92C2×C3×Dic5—21no—
93C2×C3×Dic5—22no—
94C3×D20—21no—
95C3×D20Q1612yescomplemented
96C3×C4×D5—41no—
97C3×C4×D5—41no—
98C3×C4×D5—82no—
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×Q8C2×D511yescharacteristic
108C3×C4×D4—51no—
109C3×C4×D4—101no—
110C2×C3×C4⋊C4—101no—
111C2×#216—102no—
112#869C2×D511yescharacteristic
113#835—21no—
114#832—101no—
115#808—101no—
116#807—21no—
117C4⋊(C3⋊C8)—51no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4×C3⋊C8—51no—
120C2×C5×Q8—61no—
121C2×C5×Q8#6711yescharacteristic
122C2×D20#6711yescharacteristic
123C2×C4×D5—21no—
124C2×C4×D5—22no—
125C2×Dic10#6712yes—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—61no—
129C5×C4⋊C4—61no—
130C5×C4⋊C4#6711yescharacteristic
131C42×C5—21no—
132C42×C5C22×D311yescharacteristic
133#689—124no—
134#685—22no—
135#685—21no—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5#6711yescharacteristic
139#683—22no—
140#683—22no—
141C2×#168—61no—
142C2×#168—61no—
143#554—51no—
144#494—151no—
145#477—31no—
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—41no—
156C3×C4×C5—41no—
157C3×C4×C5C2×Q1611yescharacteristic
158C3×C4×C5#13511yescharacteristic
159C3×C4×C5#13711yescharacteristic
160C3×C4×C5#13711yescharacteristic
161C3×Dic5—41no—
162C3×Dic5—42no—
163C5×Dic3—81no—
164C2×C3×Q8—52no—
165C2×C3×Q8C22⋊D511yescharacteristic
166C2×C3×D4—51no—
167C22×C3×C4—102no—
168C22×C3×C4—101no—
169C2×Dic6—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—51no—
172C3×C4⋊C4—102no—
173C3×C4⋊C4—102no—
174C3×C4⋊C4—101no—
175C3×C4⋊C4—101no—
176C3×C4⋊C4C22⋊D511yescharacteristic
177C3×C22⋊C4—102no—
178C3×C22⋊C4—101no—
179C3×C42—21no—
180C3×C42C22×D511yescharacteristic
181#216—204no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—101no—
186C2×C3⋊C8—101no—
187C22×D5—21no—
188C5×Q8—21no—
189C5×Q8—21no—
190C5×Q8—122no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—121no—
194C2×C4×C5C2×#6711yescharacteristic
195C2×C4×C5C2×#6711yescharacteristic
196C2×C4×C5C2×#6711yescharacteristic
197C2×Dic5—21no—
198C2×Dic5—22no—
199D20—21no—
200D20#21612yescomplemented
201C4×D5—41no—
202C4×D5—41no—
203C4×D5—82no—
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×Q8D3×D511yescharacteristic
215C4×D4—51no—
216C4×D4—101no—
217C2×C4⋊C4—101no—
218#107—61no—
219#106—301no—
220C4⋊C8—31no—
221C4⋊C8—151no—
222#103—61no—
223#102—301no—
224C4×C8—151no—
225C2×C3×C5#45111yescharacteristic
226C2×C3×C5#45211yescharacteristic
227C2×C3×C5#45311yescharacteristic
228C3×D5—42no—
229C23×C3—101no—
230C3×Q8—21no—
231C3×Q8—21no—
232C3×Q8—202no—
233C3×D4—52no—
234C3×D4—101no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—101no—
238C2×C3×C4—102no—
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—41no—
248C3⋊C8—102no—
249C3⋊C8—201no—
250C22×C5#95311yescharacteristic
251C2×D5—22no—
252C2×D5—41no—
253C2×D5—41no—
254C4×C5—21no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—241no—
258C4×C5#94211yescharacteristic
259C4×C5C2×#21611yescharacteristic
260C4×C5#95011yescharacteristic
261C4×C5#95111yescharacteristic
262Dic5—41no—
263Dic5—42no—
264C2×Q8—52no—
265C2×Q8—61no—
266C2×Q8#120111yescharacteristic
267C2×D4—51no—
268C22×C4—102no—
269C22×C4—101no—
270Q16—604no—
271C2×C8—61no—
272C2×C8—301no—
273C2×C8—301no—
274C4⋊C4—21no—
275C4⋊C4—51no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—102no—
279C4⋊C4—102no—
280C4⋊C4—101no—
281C4⋊C4—101no—
282C4⋊C4#120111yescharacteristic
283C22⋊C4—102no—
284C22⋊C4—101no—
285C42—21no—
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—41no—
294C3×C4—41no—
295C3×C4—201no—
296C3×C4—202no—
297C3×C4D5×Q1611yescharacteristic
298C3×C4#406411yescharacteristic
299C3×C4#408811yescharacteristic
300C3×C4#409611yescharacteristic
301Dic3—81no—
302C2×C5#522811yescharacteristic
303C2×C5#523911yescharacteristic
304C2×C5#524111yescharacteristic
305D5—42no—
306C23—101no—
307Q8—21no—
308Q8—21no—
309Q8—122no—
310Q8—202no—
311D4—52no—
312D4—101no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—101no—
316C2×C4—102no—
317C2×C4—121no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—402no—
321C2×C4C2×#120111yescharacteristic
322C2×C4D5×#6711yescharacteristic
323C2×C4D5×#6711yescharacteristic
324C8—121no—
325C8—302no—
326C8—601no—
327C2×C3—202no—
328C2×C3#6533611yescharacteristic
329C2×C3#6547511yescharacteristic
330C2×C3#6548711yescharacteristic
331C5#7192411yescharacteristic, complemented, Sylow
332C22—102no—
333C22—201no—
334C22—201no—
335C22#9156311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—202no—
340C4—201no—
341C4—241no—
342C4#9129711yescharacteristic
343C4#9130711yescharacteristic
344C4D5×#21611yescharacteristic
345C4#9151511yescharacteristic
346C3#1060194911yescharacteristic, complemented, Sylow
347C2—202no—
348C2#1174852811yescharacteristic
349C2#1174929011yescharacteristic
350C2#1174941711yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×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×#5021C2semidirect
3. #11747103C2semidirect
5. #11746356C2semidirect
6. #11745861C2semidirect
59. #5021D5semidirect
95. C3×D20Q16semidirect
200. D20#216semidirect
287. C3×C5#1632semidirect
331. C5#71924semidirect
346. C3#10601949semidirect

Maximal subgroups

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

subgroupindex
C3×#659132
C5×#50212
#117471032
#117468802
#117463562
#117458612
#117458342
#106019493
#719245