Finite Group Databasebeta

← #14299675

Subgroups — #14299675

Order 1920.

504 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754120C211yesmaximal, characteristic
2#11751225C211yesmaximal, characteristic, complemented
3C5×#5124C211yesmaximal, characteristic, complemented
4C3×#65418C211yesmaximal, characteristic
5#11748353C211yesmaximal, characteristic
6#11745984C211yesmaximal, characteristic, complemented
7#11745984C211yesmaximal, characteristic, complemented
8#10601527—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C22×C3×#168C2211yescharacteristic
16#91284—22no—
17#91283—22no—
18D5×#208—22no—
19#91106—22no—
20C5×#822—22no—
21C3×#3952—22no—
22#90961C412yes—
23#90958C412yes—
24#70001—51nomaximal, Hall
25#66079—31no—
26C5×#430—31no—
27#65421—31no—
28#65418D311yescharacteristic
29#65413—31no—
30#64778—31no—
31#64778—31no—
32C22×C3×C4×C5C2311yescharacteristic
33C2×C3×C22⋊D5Q812yes—
34C3×#709—21no—
35C3×#709—21no—
36C3×#709—21no—
37C3×#709—21no—
38C2×C3×D20C2×C411yescharacteristic
39C2×C3×C4×D5D412yes—
40C2×C3×Dic10C2×C411yescharacteristic
41C3×C5×M16—21no—
42C3×C5×M16—21no—
43C2×C3×C5×C8—21no—
44#6710—21no—
45#6710—21no—
46#6710C2×C412yes—
47#6710D412yes—
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C5×#208—21no—
51C5×#208—21no—
52C5×#208C2×C412yes—
53C5×#208D412yes—
54C2×C5×C3⋊C8—21no—
55C2×C5×C3⋊C8—21no—
56C2×C3×#168—21no—
57C2×C3×#168—21no—
58C2×C3×#168—21no—
59#6649—24no—
60D5×C3⋊C8—24no—
61#5819—51no—
62C3×#408—51no—
63#5237—51no—
64#5124—51no—
65#5124D511yescharacteristic, complemented
66#4552—51no—
67#4552—51no—
68C2×#709C2×D311yescharacteristic
69C2×C5×M16—31no—
70C2×C5×M16—31no—
71C2×C5×M16C2×D311yescharacteristic
72C2×#681—31no—
73C2×#681—31no—
74C22×#168C2×D311yescharacteristic
75#4053—62no—
76D5×M16—62no—
77#4047—62no—
78C5×#108—62no—
79#3956—32no—
80#3955—32no—
81#3954—62no—
82#3952—22no—
83#1858—151noSylow
84C23×C3×C5C2×Q811yescharacteristic
85C22×C3×D5C4⋊C412yes—
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C3×C22⋊D5—22no—
93C3×C22⋊D5—22no—
94C2×C3×Dic5C4⋊C412yes—
95C3×D20—21no—
96C3×D20—21no—
97C3×C4×D5—22no—
98C3×C4×D5—22no—
99C3×Dic10—21no—
100C3×Dic10—21no—
101C3×C5×C8—41no—
102C3⋊#168—22no—
103C3⋊#168—22no—
104C3×#168—41no—
105C5×C3⋊C8—22no—
106C5×C3⋊C8—22no—
107C2×C3×#41—51no—
108C2×C3×M16C2×D511yescharacteristic
109C22×C3×C8—51no—
110#948—102no—
111#948—102no—
112C2×#208—51no—
113C2×#208—51no—
114C2×#208—102no—
115C2×#208C2×D511yescharacteristic
116C2×#208C2×D511yescharacteristic
117C3×C22⋊C8—102no—
118#836—52no—
119#833—52no—
120#822—22no—
121#822—102no—
122C22×C4×C5C22×D311yescharacteristic
123C2×C22⋊D5Dic612yes—
124#709—21no—
125#709—21no—
126#709—21no—
127#709—21no—
128C2×D20C4×D311yescharacteristic
129C2×C4×D5#6712yes—
130C2×Dic10C4×D311yescharacteristic
131C5×M16—21no—
132C5×M16—21no—
133C5×M16—32no—
134C5×M16—32no—
135C5×M16—61no—
136C5×M16—61no—
137C2×C5×C8—21no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140#681—32no—
141#681—32no—
142#681—61no—
143#681—61no—
144C2×#168—21no—
145C2×#168—21no—
146C2×#168—21no—
147C2×#168—61no—
148C2×#168—61no—
149#676—64no—
150C8×D5—64no—
151#568—151no—
152#430—31no—
153#430—151no—
154#413—151no—
155#408—51no—
156#341—151no—
157#341—151no—
158C22×C3×C5—41no—
159C22×C3×C5C2×C4⋊C411yescharacteristic
160C22×C3×C5C22⋊Q811yescharacteristic
161C22×C3×C5C22⋊Q811yescharacteristic
162C2×C3×D5—22no—
163C2×C3×D5—42no—
164C3×C4×C5C4×D411yescharacteristic
165C3×C4×C5C4×D411yescharacteristic
166C3×C4×C5#12011yescharacteristic
167C3×C4×C5#12311yescharacteristic
168C3×Dic5—22no—
169C3×#41—101no—
170C3×#41—101no—
171C3×#41—101no—
172C3×#41—101no—
173C2×C3×Q8—51no—
174C2×C3×D4—52no—
175C2×C3×D4—51no—
176C22×C3×C4—52no—
177C22×C3×C4C22×D511yescharacteristic
178C3×M16—21no—
179C3×M16—21no—
180C2×C3×C8—21no—
181C2×C3×C8—101no—
182C2×C3×C8—101no—
183C2×C3×C8—101no—
184#208—21no—
185#208—21no—
186#208—52no—
187#208—52no—
188#208—104no—
189#208—101no—
190#208—101no—
191#208C4×D512yes—
192#208C22⋊D512yes—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—104no—
196C2×C3⋊C8—101no—
197C2×C3⋊C8—101no—
198C23×C5C2×Dic611yescharacteristic
199C22×D5Dic3⋊C412yes—
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5D3×D411yescharacteristic
203C2×C4×C5#23711yescharacteristic
204C2×C4×C5#23711yescharacteristic
205C2×C4×C5C2×#6711yescharacteristic
206C22⋊D5—22no—
207C22⋊D5—22no—
208C2×Dic5Dic3⋊C412yes—
209D20—21no—
210D20—21no—
211C4×D5—22no—
212C4×D5—22no—
213Dic10—21no—
214Dic10—21no—
215C5×C8—41no—
216C5×C8—62no—
217C5×C8—62no—
218#168—41no—
219#168—62no—
220#168—62no—
221C2×#41—51no—
222#131—302no—
223#131—302no—
224C2×M16—31no—
225C2×M16—31no—
226C2×M16—151no—
227C2×M16—151no—
228C2×M16—302no—
229C2×M16D3×D511yescharacteristic
230C22×C8—51no—
231#108—62no—
232#108—302no—
233#101—152no—
234#100—152no—
235C22⋊C8—102no—
236C2×C3×C5—21no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5#38511yescharacteristic
240C3×D5—42no—
241C23×C3—52no—
242C23×C3Q8×D511yescharacteristic
243C3×Q8—101no—
244C3×Q8—101no—
245C3×D4—102no—
246C3×D4—102no—
247C3×D4—101no—
248C3×D4—101no—
249C2×C3×C4—52no—
250C2×C3×C4—102no—
251C2×C3×C4—102no—
252C2×C3×C4C2×C4×D511yescharacteristic
253C2×C3×C4#70911yescharacteristic
254C2×C3×C4D4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4#71311yescharacteristic
257C2×C3×C4C2×C22⋊D511yescharacteristic
258C3×C8—41no—
259C3×C8—201no—
260C3⋊C8—22no—
261C3⋊C8—22no—
262C3⋊C8—102no—
263C3⋊C8—102no—
264C22×C5—41no—
265C22×C5#87811yescharacteristic
266C22×C5#87811yescharacteristic
267C22×C5C2×Dic3⋊C411yescharacteristic
268C2×D5—22no—
269C2×D5—42no—
270C4×C5#67⋊C411yescharacteristic
271C4×C5#67⋊C411yescharacteristic
272C4×C5#93511yescharacteristic
273C4×C5#93711yescharacteristic
274Dic5—22no—
275#41—101no—
276#41—101no—
277#41—101no—
278#41—101no—
279C2×Q8—51no—
280C2×D4—52no—
281C2×D4—51no—
282C22×C4—52no—
283C22×C4C2×D3×D511yescharacteristic
284M16—21no—
285M16—21no—
286M16—32no—
287M16—32no—
288M16—61no—
289M16—61no—
290M16—152no—
291M16—152no—
292M16—304no—
293M16—301no—
294M16—301no—
295C2×C8—21no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—101no—
299C2×C8—101no—
300C2×C8—101no—
301C2×C8—304no—
302C2×C8—301no—
303C2×C8—301no—
304C3×C5#185811yescharacteristic, complemented, Hall
305C22×C3—41no—
306C22×C3—102no—
307C22×C3—202no—
308C22×C3D5×C4⋊C411yescharacteristic
309C22×C3#404211yescharacteristic
310C22×C3#409211yescharacteristic
311C3×C4—102no—
312C3×C4#403911yescharacteristic
313C3×C4#404011yescharacteristic
314C3×C4C4×C22⋊D511yescharacteristic
315C3×C4#408311yescharacteristic
316C2×C5—21no—
317C2×C5—21no—
318C2×C5—21no—
319C2×C5#494611yescharacteristic
320D5—42no—
321C23—52no—
322C23D5×Dic611yescharacteristic
323Q8—101no—
324Q8—101no—
325D4—102no—
326D4—102no—
327D4—101no—
328D4—101no—
329C2×C4—52no—
330C2×C4—102no—
331C2×C4—102no—
332C2×C4#676511yescharacteristic
333C2×C4#676611yescharacteristic
334C2×C4C4×D3×D511yescharacteristic
335C2×C4D5×#6711yescharacteristic
336C2×C4D3×C22⋊D511yescharacteristic
337C2×C4#679011yescharacteristic
338C8—41no—
339C8—62no—
340C8—62no—
341C8—201no—
342C8—302no—
343C8—302no—
344C2×C3—21no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—202no—
348C2×C3#6527811yescharacteristic
349C5#7000111yescharacteristic, complemented, Sylow
350C22—41no—
351C22—102no—
352C22—202no—
353C22D5×Dic3⋊C411yescharacteristic
354C22#9142111yescharacteristic
355C22#9143111yescharacteristic
356C4—102no—
357C4#9139611yescharacteristic
358C4#9140711yescharacteristic
359C4#9144111yescharacteristic
360C4#9157711yescharacteristic
361C3#1060152711yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—21no—
365C2—202no—
366C2#1174889111yescharacteristic
subgroupG/H
centerC4#91577
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#385
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1858
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11751225C2semidirect
3. C5×#5124C2semidirect
6. #11745984C2semidirect
7. #11745984C2semidirect
65. #5124D5semidirect
304. C3×C5#1858semidirect
349. C5#70001semidirect
361. C3#10601527semidirect

Maximal subgroups

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

subgroupindex
#117541202
#117512252
C5×#51242
C3×#654182
#117483532
#117459842
#106015273
#700015