Finite Group Databasebeta

← #14289769

Subgroups — #14289769

Order 1920.

456 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic6×D20C211yesmaximal, characteristic
2#11751180C211yesmaximal, characteristic, complemented
3C5×#5091C211yesmaximal, characteristic, complemented
4C3×#65373C211yesmaximal, characteristic
5#11745859C211yesmaximal, characteristic, complemented
6#11745842C211yesmaximal, characteristic, complemented
7#11745834C211yesmaximal, characteristic
8#10601956—31nomaximal, Hall
9C2×D5×Dic6—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11#91758C2211yescharacteristic
12C4×C5×Dic6C2211yescharacteristic
13C3×C4×D20C2211yescharacteristic
14#91469—21no—
15Dic3×D20—21no—
16#91422—22no—
17#91360—21no—
18#91119—22no—
19C4×C3⋊#168C2211yescharacteristic
20C5×#810—21no—
21C5×#807—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×#3941—21no—
24C3×#3940—21no—
25C3×C4⋊#168C2211yescharacteristic
26#71142—51nomaximal, Hall
27Q8×D20—31no—
28C5×#477—31no—
29#65373D311yescharacteristic
30#65370—31no—
31Q8⋊#168—31no—
32#64703—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30—21no—
36C2×C5×Dic6D411yescharacteristic
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×#1204—22no—
40C2×D5×Dic3—22no—
41D5×Dic6—42no—
42D5×Dic6—42no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15—21no—
47C4⋊Dic15D412yes—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×Dic3⋊C4—21no—
51C4×C5×Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C3×#685—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C2×C3×#168—21no—
56Dic3⋊Dic5—22no—
57#6665—22no—
58D4×Dic6—51no—
59C3×#476—51no—
60#5091D511yescharacteristic, complemented
61#5079—51no—
62D4⋊(C3⋊C8)—51no—
63#4486—51no—
64#4484—51no—
65C2×Q8×D5—61no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C4×C5×Q8—31no—
68#4043—62no—
69#4043—61no—
70C4×D20—61no—
71C4×D20C2×D311yescharacteristic
72#4015—31no—
73#4015—61no—
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3967—62no—
78#3941—21no—
79#3940—21no—
80C4⋊#168C2×D311yescharacteristic
81C4×#168—31no—
82#1637—151noSylow
83C22×C3×D5—21no—
84C3×C5×Q8—42no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—22no—
90Dic30—41no—
91Dic30—41no—
92C2×C5×Dic3—21no—
93C2×C5×Dic3—21no—
94C5×Dic6—21no—
95C5×Dic6SD1612yes—
96C2×C3×Dic5—21no—
97C3×D20—21no—
98C3×D20Q1612yes—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101#1204—44no—
102D5×Dic3—44no—
103C3⋊#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C22×Dic6—101no—
107C3×C4⋊Q8C2×D511yescharacteristic
108C3×C4×D4—51no—
109D4×Dic3—101no—
110#924—101no—
111#888—101no—
112#878—102no—
113#869—51no—
114C4×Dic6C2×D511yescharacteristic
115C3×#106—101no—
116C3×C4⋊C8—51no—
117C3×#102—101no—
118#835—102no—
119#810—21no—
120#807—21no—
121C4⋊(C3⋊C8)C2×D511yescharacteristic
122C4×C3⋊C8—51no—
123C2×C5×Q8—21no—
124C2×C5×Q8—31no—
125Q8×D5—122no—
126Q8×D5—122no—
127C2×D20#6711yescharacteristic
128C2×C4×D5—21no—
129C2×C4×D5—62no—
130C2×Dic10—62no—
131C2×Dic10—61no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—31no—
136C5×C4⋊C4—61no—
137C42×C5—61no—
138C42×C5C22×D311yescharacteristic
139#685—21no—
140#685—62no—
141C4⋊Dic5—32no—
142C4⋊Dic5—62no—
143C4⋊Dic5—61no—
144C4⋊Dic5#6711yescharacteristic
145C2×#168—21no—
146C2×#168—61no—
147D4×Q8—151no—
148#487—151no—
149#477—31no—
150#476—51no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C3×D5—22no—
156C2×C3×D5—41no—
157C2×C3×D5—41no—
158C3×C4×C5—21no—
159C3×C4×C5—81no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—42no—
165C3×Dic5—41no—
166C5×Dic3—22no—
167C5×Dic3—41no—
168C2×C3×Q8—21no—
169C2×C3×D4—51no—
170C22×C3×C4—101no—
171C22×Dic3—102no—
172C2×Dic6—102no—
173C2×Dic6—101no—
174C2×Dic6—202no—
175C2×Dic6—202no—
176C2×Dic6C22⋊D511yescharacteristic
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—51no—
181C3×C22⋊C4—101no—
182C3×C42C22×D511yescharacteristic
183#217—102no—
184C4⋊Dic3—52no—
185C4⋊Dic3—101no—
186C4⋊Dic3C22⋊D511yescharacteristic
187Dic3⋊C4—21no—
188Dic3⋊C4—102no—
189C4×Dic3—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C22×D5—21no—
193C5×Q8—32no—
194C5×Q8—42no—
195C5×Q8—61no—
196C2×C4×C5—41no—
197C2×C4×C5—61no—
198C2×C4×C5—61no—
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5C2×#6711yescharacteristic
202C2×Dic5—21no—
203C2×Dic5—62no—
204D20—21no—
205D20#21612yes—
206C4×D5—41no—
207C4×D5—41no—
208C4×D5—124no—
209Dic10—124no—
210Dic10—121no—
211Dic10—121no—
212C5×C8—121no—
213#168—41no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—151no—
217C4⋊Q8—301no—
218C4⋊Q8D3×D511yescharacteristic
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—31no—
222C4×D4—51no—
223C4×D4—301no—
224#107—61no—
225#106—101no—
226C4⋊C8—31no—
227C4⋊C8—51no—
228#103—61no—
229#103—302no—
230#102—101no—
231C4×C8—151no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C3×D5—42no—
236C23×C3—101no—
237C3×Q8—42no—
238C3×D4—52no—
239C3×D4—101no—
240C2×C3×C4—41no—
241C2×C3×C4—101no—
242C2×C3×C4—201no—
243C2×C3×C4—201no—
244C2×C3×C4D4×D511yescharacteristic
245C2×C3×C4D4×D511yescharacteristic
246C2×C3×C4C2×C22⋊D511yescharacteristic
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—102no—
250C2×Dic3—204no—
251Dic6—21no—
252Dic6—204no—
253Dic6—201no—
254Dic6—201no—
255Dic6#68812yes—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5#93711yescharacteristic
260C2×D5—22no—
261C2×D5—41no—
262C2×D5—41no—
263C4×C5—21no—
264C4×C5—62no—
265C4×C5—81no—
266C4×C5—121no—
267C4×C5D3×SD1611yescharacteristic
268C4×C5#91411yescharacteristic
269C4×C5C2×#21611yescharacteristic
270C4×C5#95111yescharacteristic
271Dic5—41no—
272Dic5—122no—
273C2×Q8—21no—
274C2×Q8—31no—
275C2×Q8—302no—
276C2×Q8—301no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—51no—
280C22×C4—101no—
281C22×C4—302no—
282C2×C8—61no—
283C2×C8—101no—
284C2×C8—301no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—31no—
288C4⋊C4—51no—
289C4⋊C4—61no—
290C4⋊C4—152no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C22⋊C4—101no—
294C22⋊C4—302no—
295C42—61no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3—102no—
299C22×C3—201no—
300C22×C3—201no—
301C22×C3#408311yescharacteristic
302C3×C4—21no—
303C3×C4—81no—
304C3×C4—201no—
305C3×C4D5×Q1611yescharacteristic
306C3×C4#406411yescharacteristic
307C3×C4C2×#68811yescharacteristic
308C3×C4#409511yescharacteristic
309Dic3—22no—
310Dic3—41no—
311Dic3—202no—
312C2×C5#505011yescharacteristic
313C2×C5#516911yescharacteristic
314C2×C5#520111yescharacteristic
315D5—42no—
316C23—101no—
317Q8—32no—
318Q8—42no—
319Q8—61no—
320Q8—604no—
321Q8—601no—
322Q8—601no—
323D4—52no—
324D4—101no—
325C2×C4—41no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—101no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4—302no—
332C2×C4—604no—
333C2×C4D5×#6711yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—601no—
339C2×C3—202no—
340C2×C3#6533511yescharacteristic
341C2×C3#6547511yescharacteristic
342C2×C3#6549011yescharacteristic
343C5#7114211yescharacteristic, complemented, Sylow
344C22—102no—
345C22—201no—
346C22—201no—
347C22#9157711yescharacteristic
348C4—21no—
349C4—62no—
350C4—81no—
351C4—121no—
352C4—201no—
353C4—602no—
354C4D3×#68811yescharacteristic
355C4#9150411yescharacteristic
356C4D5×#21611yescharacteristic
357C4#9150811yescharacteristic
358C3#1060195611yescharacteristic, complemented, Sylow
359C2—202no—
360C2#1174916611yescharacteristic
361C2#1174939811yescharacteristic
362C2#1174940011yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1637
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. #11751180C2semidirect
3. C5×#5091C2semidirect
5. #11745859C2semidirect
6. #11745842C2semidirect
60. #5091D5semidirect
297. C3×C5#1637semidirect
343. C5#71142semidirect
358. C3#10601956semidirect

Maximal subgroups

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

subgroupindex
Dic6×D202
#117511802
C5×#50912
C3×#653732
#117458592
#117458422
#117458342
#106019563
#711425