Finite Group Databasebeta

← #14284162

Subgroups — #14284162

Order 1920.

432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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
1#11756450C211yesmaximal, characteristic
2#11746940C211yesmaximal, characteristic, complemented
3#11746844C211yesmaximal, characteristic, complemented
4C5×#4543C211yesmaximal, characteristic, complemented
5C3×#64763C211yesmaximal, characteristic, complemented
6#11745848C211yesmaximal, characteristic, complemented
7#11745848C211yesmaximal, characteristic, complemented
8#10599157—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10#91787—21no—
11#91786C411yescharacteristic
12#91784C411yescharacteristic
13#91783—21no—
14#91782—21no—
15#91782C411yescharacteristic
16#91781—21no—
17#91776C411yescharacteristic
18#91764C2211yescharacteristic
19C42×D15C2211yescharacteristic
20C2×#6651—21no—
21C5×#803C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C3×#3935C2211yescharacteristic
24C3×#3935C2211yescharacteristic
25#90983—21no—
26#90957—21no—
27#90951—21no—
28#68364—51nomaximal, Hall
29#66025—31no—
30#64996—31no—
31#64994—31no—
32C5×#330—31no—
33#64763D311yescharacteristic, complemented
34#64684—31no—
35#64684—31no—
36C2×D60—21no—
37C2×D60C2×C411yescharacteristic
38C2×C4×D15—21no—
39C2×C4×D15C2×C411yescharacteristic
40C2×C4×D15D411yescharacteristic
41C2×C4×D15D411yescharacteristic
42C2×Dic30C2×C411yescharacteristic
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C5×C4⋊C4C2×C411yescharacteristic
46C3×C5×C4⋊C4C2×C411yescharacteristic
47C3×C42×C5C2311yescharacteristic
48#6714—21no—
49#6714—21no—
50#6714—21no—
51#6714—21no—
52#6714—21no—
53C4⋊Dic15—21no—
54#6712—21no—
55C4×Dic15—21no—
56C4×Dic15C2×C411yescharacteristic
57C4×Dic15D411yescharacteristic
58C4×Dic15D411yescharacteristic
59C2×C5×C3⋊C8—21no—
60C2×C5×C3⋊C8—21no—
61C2×C3×#168—21no—
62C2×C3×#168—21no—
63#6651—24no—
64#5691—51no—
65#4707—51no—
66#4705—51no—
67C3×#330—51no—
68#4543D511yescharacteristic, complemented
69#4464—51no—
70#4464—51no—
71C5×#125C2×D311yescharacteristic
72C2×#676—61no—
73#4044—61no—
74#4043—31no—
75#4041—31no—
76#4040—61no—
77#4039—31no—
78#4039—61no—
79#4038—61no—
80#4033—31no—
81#4021—31no—
82C42×D5—31no—
83C5×#97—31no—
84C5×#97—31no—
85#3952—61no—
86#3946—61no—
87C8×Dic5—61no—
88#3935C2×D311yescharacteristic
89#3935C2×D311yescharacteristic
90#1529—151noSylow
91C22×D15—21no—
92C22×D15C22⋊C411yescharacteristic
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C22×C411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15C22⋊C411yescharacteristic
100C2×Dic15C22⋊C411yescharacteristic
101C2×Dic15C22⋊C411yescharacteristic
102D60—41no—
103D60—42no—
104C4×D15—22no—
105C4×D15—41no—
106C4×D15—41no—
107C4×D15—42no—
108Dic30—41no—
109C3×#168—22no—
110C3×#168—41no—
111C5×C3⋊C8—22no—
112C5×C3⋊C8—41no—
113C3×#125C2×D511yescharacteristic
114C2×ΓL(1,𝔽25)—101no—
115#898—101no—
116#897—51no—
117#895—51no—
118#894—101no—
119#893—51no—
120#893—101no—
121#892—101no—
122#887—51no—
123#875—51no—
124C42×D3—51no—
125C3×#97—51no—
126C3×#97—51no—
127(C2×D3)⋊C8—101no—
128Dic3⋊C8—101no—
129C8×Dic3—101no—
130#803C2×D511yescharacteristic
131#803C2×D511yescharacteristic
132C2×D20—31no—
133C2×D20—61no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—61no—
138C2×Dic10—31no—
139C2×C5×C8—61no—
140C2×C5×C8—61no—
141C5×C4⋊C4—21no—
142C5×C4⋊C4—21no—
143C5×C4⋊C4C4×D311yescharacteristic
144C5×C4⋊C4C4×D311yescharacteristic
145C42×C5C22×D311yescharacteristic
146#685—61no—
147#685—61no—
148#685—61no—
149#685—61no—
150#685—61no—
151C4⋊Dic5—61no—
152#683—61no—
153C4×Dic5—31no—
154C4×Dic5—31no—
155C4×Dic5—31no—
156C4×Dic5—61no—
157C2×#168—21no—
158C2×#168—21no—
159#676—64no—
160#529—151no—
161#432—151no—
162C4×M16—151no—
163#330—31no—
164#330—51no—
165#329—151no—
166#329—151no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C2×D15—21no—
169C2×D15—21no—
170C2×D15—21no—
171C2×D15—41no—
172C2×D15—41no—
173C2×D15—41no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—41no—
178C3×C4×C5—41no—
179Dic15—21no—
180Dic15—21no—
181Dic15—41no—
182Dic15#10412yes—
183C2×D12—51no—
184C2×D12—101no—
185C2×C4×D3—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×C4×D3—101no—
189C2×Dic6—51no—
190C2×C3×C8—101no—
191C2×C3×C8—101no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4C4×D511yescharacteristic
195C3×C4⋊C4C4×D511yescharacteristic
196C3×C42C22×D511yescharacteristic
197(C2×D3)⋊C4—101no—
198(C2×D3)⋊C4—101no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202C4⋊Dic3—101no—
203Dic3⋊C4—101no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C4×Dic3—51no—
207C4×Dic3—101no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210ΓL(1,𝔽25)—104no—
211C22×D5—31no—
212C22×D5—61no—
213C2×C4×C5—21no—
214C2×C4×C5—21no—
215C2×C4×C5C2×C4×D311yescharacteristic
216C2×C4×C5D3×D411yescharacteristic
217C2×C4×C5D3×D411yescharacteristic
218C2×Dic5—31no—
219C2×Dic5—31no—
220C2×Dic5—31no—
221C2×Dic5—61no—
222D20—121no—
223D20—122no—
224C4×D5—62no—
225C4×D5—122no—
226C4×D5—121no—
227C4×D5—121no—
228Dic10—121no—
229C5×C8—62no—
230C5×C8—121no—
231#168—22no—
232#168—41no—
233C2×M16—301no—
234#126—301no—
235#125D3×D511yescharacteristic
236#124—151no—
237#123—301no—
238C22⋊Q8—151no—
239#121—151no—
240C4×Q8—151no—
241C4×D4—151no—
242C4×D4—301no—
243#117—301no—
244C2×C42—151no—
245C4⋊C8—301no—
246C22⋊C8—301no—
247#97—31no—
248#97—31no—
249#97—51no—
250#97—51no—
251C4×C8—301no—
252C2×C3×C5#41311yescharacteristic
253C2×C3×C5C2×#10411yescharacteristic
254C2×C3×C5#42111yescharacteristic
255D15—41no—
256D15—81no—
257C22×D3—51no—
258C22×D3—101no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4C2×C4×D511yescharacteristic
262C2×C3×C4D4×D511yescharacteristic
263C2×C3×C4D4×D511yescharacteristic
264C2×Dic3—51no—
265C2×Dic3—51no—
266C2×Dic3—51no—
267C2×Dic3—101no—
268D12—201no—
269D12—202no—
270C4×D3—102no—
271C4×D3—202no—
272C4×D3—201no—
273C4×D3—201no—
274Dic6—201no—
275C3×C8—102no—
276C3×C8—201no—
277C3⋊C8—22no—
278C3⋊C8—41no—
279C22×C5D3×C22⋊C411yescharacteristic
280C2×D5—61no—
281C2×D5—61no—
282C2×D5—61no—
283C2×D5—121no—
284C2×D5—121no—
285C2×D5—121no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—41no—
290C4×C5—41no—
291Dic5—32no—
292Dic5—61no—
293Dic5—61no—
294Dic5—121no—
295C2×Q8—151no—
296C2×D4—151no—
297C2×D4—301no—
298C22×C4—151no—
299C22×C4—151no—
300C22×C4—151no—
301C22×C4—301no—
302M16—304no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—101no—
306C2×C8—101no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—301no—
310C4⋊C4—301no—
311C4⋊C4#120011yescharacteristic
312C4⋊C4#120011yescharacteristic
313C22⋊C4—301no—
314C22⋊C4—301no—
315C22⋊C4—301no—
316C22⋊C4—301no—
317C22⋊C4—301no—
318C42—151no—
319C42—151no—
320C42—151no—
321C42—301no—
322C42C2×D3×D511yescharacteristic
323C3×C5#152911yescharacteristic, complemented, Hall
324C22×C3D5×C22⋊C411yescharacteristic
325C2×D3—101no—
326C2×D3—101no—
327C2×D3—101no—
328C2×D3—201no—
329C2×D3—201no—
330C2×D3—201no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—41no—
336Dic3—52no—
337Dic3—101no—
338Dic3—101no—
339Dic3—201no—
340C2×C5#475111yescharacteristic
341C2×C5D3×#10411yescharacteristic
342C2×C5#482111yescharacteristic
343D5—121no—
344D5—241no—
345C23—151no—
346C23—301no—
347Q8—601no—
348D4—601no—
349D4—602no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—151no—
353C2×C4—151no—
354C2×C4—151no—
355C2×C4—302no—
356C2×C4—301no—
357C2×C4—601no—
358C2×C4—601no—
359C2×C4—602no—
360C2×C4C2×#120011yescharacteristic
361C2×C4#679011yescharacteristic
362C2×C4#679011yescharacteristic
363C8—62no—
364C8—102no—
365C8—121no—
366C8—201no—
367C2×C3#6504011yescharacteristic
368C2×C3D5×#10411yescharacteristic
369C2×C3#6511011yescharacteristic
370D3—201no—
371D3—401no—
372C5#6836411yescharacteristic, complemented, Sylow
373C22—301no—
374C22—301no—
375C22—301no—
376C22—601no—
377C22—601no—
378C22—601no—
379C22#9156111yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—41no—
385C4—152no—
386C4—301no—
387C4—301no—
388C4—601no—
389C3#1059915711yescharacteristic, complemented, Sylow
390C2—601no—
391C2—1201no—
392C2#1174937411yescharacteristic
393C2#1174943011yescharacteristic
394C2#1174943111yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5C2×C22⋊C4
prime radical#91784C4
cosocleC3×C42×C5C23
hypercenter#125D3×D5
hypocenterC3×C5#1529
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #11746940C2semidirect
3. #11746844C2semidirect
4. C5×#4543C2semidirect
5. C3×#64763C2semidirect
6. #11745848C2semidirect
7. #11745848C2semidirect
33. #64763D3semidirect
68. #4543D5semidirect
323. C3×C5#1529semidirect
372. C5#68364semidirect
389. C3#10599157semidirect

Maximal subgroups

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

subgroupindex
#117564502
#117469402
#117468442
C5×#45432
C3×#647632
#117458482
#105991573
#683645